Finite Group Databasebeta

← #28293348

Subgroups — #28293348

Order 13568.

6666 conjugacy classes of subgroups.

The subgroup lattice has 1872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289331C214yesmaximal, complemented
2#20289327C214yesmaximal, complemented
3#20289274C214yesmaximal, complemented
4#20289273C214yesmaximal, complemented
5#20289008C214yesmaximal, complemented
6#20289003C214yesmaximal, complemented
7#20289000C214yesmaximal, complemented
8#20288995C214yesmaximal, complemented
9#20288935C214yesmaximal, complemented
10#20288930C214yesmaximal, complemented
11#20288912C214yesmaximal, complemented
12#20288911C214yesmaximal, complemented
13#20288552C212yesmaximal, complemented
14#20288545C212yesmaximal, complemented
15#20288515C212yesmaximal, complemented
16#20288513C212yesmaximal, complemented
17#20288404C211yesmaximal, characteristic, complemented
18#20288402C212yesmaximal, complemented
19C2×#16811249C211yesmaximal, characteristic, complemented
20C2×#16811208C212yesmaximal, complemented
21C53×#3490C211yesmaximal, characteristic, complemented
22#16811376C2214yescomplemented
23#16811376C2214yescomplemented
24#16811376C2214yescomplemented
25#16811375C2214yescomplemented
26#16811375C2214yescomplemented
27#16811374C2214yescomplemented
28#16811374C2214yescomplemented
29#16811373C2214yescomplemented
30#16811370C2214yescomplemented
31#16811370C2214yescomplemented
32#16811370C2214yescomplemented
33#16811368C2214yescomplemented
34#16811368C2214yescomplemented
35#16811368C2214yescomplemented
36#16811368C2214yescomplemented
37#16811367C2214yescomplemented
38#16811343C2214yescomplemented
39#16811342C2214yescomplemented
40#16811341C2214yescomplemented
41#16811340C2214yescomplemented
42#16811332C2214yescomplemented
43#16811332C2214yescomplemented
44#16811332C2214yescomplemented
45#16811332C2214yescomplemented
46#16811331C2214yescomplemented
47#16811331C2214yescomplemented
48#16811330C2214yescomplemented
49#16811330C2214yescomplemented
50#16811327C2214yescomplemented
51#16811327C2214yescomplemented
52#16811327C2214yescomplemented
53#16811327C2214yescomplemented
54#16811325C2214yescomplemented
55#16811322C2214yescomplemented
56#16811322C2214yescomplemented
57#16811319C2214yescomplemented
58#16811316C2214yescomplemented
59#16811316C2214yescomplemented
60#16811313C2214yescomplemented
61#16811312C2214yescomplemented
62#16811310C2214yescomplemented
63#16811310C2214yescomplemented
64#16811309C2214yescomplemented
65#16811306C2214yescomplemented
66#16811304C2214yescomplemented
67#16811304C2214yescomplemented
68#16811304C2214yescomplemented
69#16811299C2214yescomplemented
70#16811299C2214yescomplemented
71#16811299C2214yescomplemented
72#16811299C2214yescomplemented
73#16811299C2214yescomplemented
74#16811297C2214yescomplemented
75#16811296C2214yescomplemented
76D4×Dic106C2214yescomplemented
77D4×Dic106C2214yescomplemented
78#16811286C2214yescomplemented
79#16811286C2214yescomplemented
80#16811282C2214yescomplemented
81#16811282C2214yescomplemented
82#16811281C2214yescomplemented
83#16811280C2214yescomplemented
84#16811279C2214yescomplemented
85#16811279C2214yescomplemented
86#16811278C2214yescomplemented
87#16811273C2214yescomplemented
88#16811272C2214yescomplemented
89#16811271C2214yescomplemented
90#16811267C2214yescomplemented
91#16811267C2214yescomplemented
92#16811263C2214yescomplemented
93#16811263C2214yescomplemented
94#16811263C2214yescomplemented
95#16811260C2214yescomplemented
96#16811260C2214yescomplemented
97#16811260C2214yescomplemented
98#16811252C2214yescomplemented
99#16811251C2214yescomplemented
100#16811249C2211yescharacteristic
101#16811249C2212yes—
102#16811249C2214yescomplemented
103#16811249C2214yescomplemented
104#16811249C2214yescomplemented
105#16811249C2214yescomplemented
106#16811249C2214yescomplemented
107#16811248C2214yescomplemented
108#16811244C2214yescomplemented
109#16811242C2214yescomplemented
110#16811241C2214yescomplemented
111#16811241C2214yescomplemented
112#16811241C2214yescomplemented
113#16811240C2214yescomplemented
114#16811240C2214yescomplemented
115#16811239C2214yescomplemented
116#16811238C2214yescomplemented
117#16811238C2214yescomplemented
118#16811237C2214yescomplemented
119#16811237C2214yescomplemented
120#16811235C2214yescomplemented
121#16811233C2214yescomplemented
122#16811230C2214yescomplemented
123#16811230C2214yescomplemented
124#16811218C2214yescomplemented
125#16811217C2214yescomplemented
126#16811217C2214yescomplemented
127#16811216C2214yescomplemented
128#16811216C2214yescomplemented
129#16811216C2214yescomplemented
130#16811215C2214yescomplemented
131#16811215C2214yescomplemented
132#16811215C2214yescomplemented
133#16811214C2214yescomplemented
134#16811211C2214yescomplemented
135#16811208C2214yes—
136#16811208C2214yes—
137#16811208C2214yes—
138#16811208C2214yes—
139#16811208C2214yescomplemented
140#16811208C2214yescomplemented
141#16811208C2214yescomplemented
142#16811208C2214yescomplemented
143#16811208C2214yescomplemented
144#16811208C2214yescomplemented
145#16811208C2214yescomplemented
146#16811206C2214yescomplemented
147#16811202C2214yescomplemented
148#16811202C2214yescomplemented
149#16811201C2214yescomplemented
150#16811200C2214yescomplemented
151#16811196C2214yescomplemented
152#16811195C2214yescomplemented
153#16811194C2214yescomplemented
154#16811193C2214yescomplemented
155#16811185C2211yescharacteristic
156#16811182C2212yes—
157#16811176C2214yescomplemented
158#16811175C2214yescomplemented
159#16811153C2214yescomplemented
160#16811150C2214yescomplemented
161C2×#13133210C2212yescomplemented
162C2×#13133210C2212yescomplemented
163C2×#13133204C2212yescomplemented
164C2×#13133203C2212yescomplemented
165#16811134C2214yescomplemented
166#16811132C2214yescomplemented
167#16811129C2214yescomplemented
168#16811129C2214yescomplemented
169#16811129C2214yescomplemented
170C2×#13133199C2212yescomplemented
171C2×#13133198C2212yescomplemented
172C2×#13133196C2212yescomplemented
173C2×#13133196C2212yescomplemented
174C2×#13133194C2212yes—
175C2×#13133194C2212yes—
176C2×#13133194C2212yes—
177C2×#13133194C2212yescomplemented
178C2×#13133194C2212yescomplemented
179C2×#13133194C2214yescomplemented
180C22⋊Q8×D53C2214yescomplemented
181C2×#13133189C2212yes—
182C2×#13133189C2212yescomplemented
183C2×#13133188C2212yescomplemented
184C2×#13133186C2212yes—
185#16811098C2212yes—
186#16811096C2212yes—
187#16811096C2212yes—
188C2×D4×Dic53C2212yes—
189C2×#13133177C2212yes—
190C22×C22⋊Dic53C2211yescharacteristic
191C22×C22⋊Dic53C2211yescharacteristic
192C53×#551C2214yescomplemented
193C53×#551C2214yescomplemented
194C53×#546C2214yescomplemented
195C53×#546C2214yescomplemented
196C53×#543C2211yescharacteristic
197C53×#538C2214yescomplemented
198C53×#534C2211yescharacteristic
199C53×#525C2214yescomplemented
200C2×#120×C53C2212yes—
201C53×#518C2212yes—
202C22×C22⋊C4×C53C2211yescharacteristic
203C2×#11719945C2314yes—
204C2×#11719945C2314yescomplemented
205C2×#11719947C2314yes—
206C2×#11719947C2314yes—
207C2×#11719947C2314yescomplemented
208C22×Dic106C2312yes—
209C22×Dic106C2312yes—
210C22×Dic106C2312yes—
211C22×Dic106C2314yescomplemented
212C2×Q8×D53C2314yescomplemented
213C22×C22⋊D53C2312yes—
214C22×C22⋊D53C2312yes—
215C22×C22⋊D53C2312yes—
216C22×C22⋊D53C2312yes—
217C23×Dic53C2312yes—
218C23×Dic53C2312yes—
219C23×Dic53C2312yes—
220C22×C4×D53C2312yes—
221#13133217C2314yescomplemented
222#13133217C2314yescomplemented
223#13133216C2314yescomplemented
224#13133216C2314yescomplemented
225#13133216C2314yescomplemented
226#13133216C2314yescomplemented
227#13133216C2314yescomplemented
228#13133216C2314yescomplemented
229#13133216C2314yescomplemented
230#13133215C2314yescomplemented
231#13133215C2314yescomplemented
232#13133215C2314yescomplemented
233#13133212C2314yescomplemented
234#13133212C2314yescomplemented
235#13133212C2314yescomplemented
236#13133212C2314yescomplemented
237#13133211C2314yescomplemented
238#13133211C2314yescomplemented
239#13133210C2314yes—
240#13133210C2314yes—
241#13133210C2314yes—
242#13133210C2314yes—
243#13133210C2314yes—
244#13133210C2314yes—
245#13133210C2314yes—
246#13133210C2314yes—
247#13133210C2314yes—
248#13133210C2314yes—
249#13133210C2314yes—
250#13133210C2314yes—
251#13133210C2314yes—
252#13133210C2314yes—
253#13133210C2314yescomplemented
254#13133210C2314yescomplemented
255#13133210C2314yescomplemented
256#13133210C2314yescomplemented
257#13133210C2314yescomplemented
258#13133210C2314yescomplemented
259#13133209C2314yescomplemented
260#13133209C2314yescomplemented
261#13133209C2314yescomplemented
262#13133208C2314yescomplemented
263#13133208C2314yescomplemented
264#13133208C2314yescomplemented
265#13133208C2314yescomplemented
266#13133208C2314yescomplemented
267#13133207C2314yescomplemented
268#13133207C2314yescomplemented
269#13133207C2314yescomplemented
270#13133207C2314yescomplemented
271#13133207C2314yescomplemented
272#13133207C2314yescomplemented
273#13133207C2314yescomplemented
274#13133207C2314yescomplemented
275#13133207C2314yescomplemented
276#13133207C2314yescomplemented
277#13133205C2314yescomplemented
278#13133204C2314yes—
279#13133204C2314yes—
280#13133204C2314yes—
281#13133204C2314yes—
282#13133204C2314yes—
283#13133204C2314yes—
284#13133204C2314yescomplemented
285#13133203C2314yes—
286#13133203C2314yes—
287#13133203C2314yes—
288#13133203C2314yes—
289#13133203C2314yes—
290#13133203C2314yes—
291#13133203C2314yes—
292#13133203C2314yes—
293#13133203C2314yescomplemented
294#13133203C2314yescomplemented
295#13133203C2314yescomplemented
296#13133203C2314yescomplemented
297#13133202C2314yescomplemented
298#13133202C2314yescomplemented
299#13133201C2314yes—
300#13133201C2314yes—
301#13133201C2314yes—
302#13133201C2314yescomplemented
303#13133201C2314yescomplemented
304#13133200C2314yes—
305#13133200C2314yes—
306#13133200C2314yes—
307#13133200C2314yescomplemented
308#13133200C2314yescomplemented
309#13133199C2314yes—
310#13133199C2314yes—
311#13133199C2314yes—
312#13133199C2314yes—
313#13133199C2314yes—
314#13133199C2314yes—
315#13133199C2314yes—
316#13133199C2314yes—
317#13133199C2314yescomplemented
318#13133199C2314yescomplemented
319#13133199C2314yescomplemented
320#13133199C2314yescomplemented
321#13133198C2314yes—
322#13133198C2314yes—
323#13133198C2314yes—
324#13133198C2314yes—
325#13133198C2314yes—
326#13133198C2314yes—
327#13133198C2314yes—
328#13133198C2314yes—
329#13133198C2314yes—
330#13133198C2314yescomplemented
331#13133198C2314yescomplemented
332#13133197C2314yescomplemented
333#13133197C2314yescomplemented
334#13133197C2314yescomplemented
335#13133197C2314yescomplemented
336#13133196C2314yes—
337#13133196C2314yes—
338#13133196C2314yes—
339#13133196C2314yes—
340#13133196C2314yes—
341#13133196C2314yes—
342#13133196C2314yes—
343#13133196C2314yes—
344#13133196C2314yes—
345#13133196C2314yes—
346#13133196C2314yes—
347#13133196C2314yes—
348#13133196C2314yescomplemented
349#13133196C2314yescomplemented
350#13133196C2314yescomplemented
351#13133196C2314yescomplemented
352#13133196C2314yescomplemented
353#13133195C2314yescomplemented
354#13133195C2314yescomplemented
355#13133195C2314yescomplemented
356#13133195C2314yescomplemented
357#13133195C2314yescomplemented
358#13133195C2314yescomplemented
359#13133195C2314yescomplemented
360#13133195C2314yescomplemented
361#13133194C2314yes—
362#13133194C2314yes—
363#13133194C2314yes—
364#13133194C2314yes—
365#13133194C2314yes—
366#13133194C2314yes—
367#13133194C2314yes—
368#13133194C2314yes—
369#13133194C2314yes—
370#13133194C2314yes—
371#13133194C2314yes—
372#13133194C2314yes—
373#13133194C2314yes—
374#13133194C2314yes—
375#13133194C2314yes—
376#13133194C2314yes—
377#13133194C2314yes—
378#13133194C2314yes—
379#13133194C2314yes—
380#13133194C2314yes—
381#13133194C2314yes—
382#13133194C2314yes—
383#13133194C2314yes—
384#13133194C2314yes—
385#13133194C2314yes—
386#13133194C2314yes—
387#13133194C2314yes—
388#13133194C2314yes—
389#13133194C2314yescomplemented
390#13133194C2314yescomplemented
391#13133194C2314yescomplemented
392#13133194C2314yescomplemented
393#13133194C2314yescomplemented
394#13133194C2314yescomplemented
395#13133194C2314yescomplemented
396#13133194C2314yescomplemented
397#13133194C2314yescomplemented
398#13133194C2314yescomplemented
399#13133193C2314yescomplemented
400#13133193C2314yescomplemented
401#13133193C2314yescomplemented
402#13133191C2314yes—
403#13133191C2314yes—
404#13133191C2314yescomplemented
405#13133190C2314yes—
406#13133190C2314yes—
407#13133190C2314yescomplemented
408#13133190C2314yescomplemented
409#13133189C2314yes—
410#13133189C2314yes—
411#13133189C2314yes—
412#13133189C2314yes—
413#13133189C2314yes—
414#13133189C2314yes—
415#13133189C2314yes—
416#13133189C2314yes—
417#13133189C2314yes—
418#13133189C2314yes—
419#13133189C2314yes—
420#13133189C2314yes—
421#13133189C2314yes—
422#13133189C2314yes—
423#13133189C2314yescomplemented
424#13133189C2314yescomplemented
425#13133188C2314yes—
426#13133188C2314yes—
427#13133188C2314yes—
428#13133188C2314yes—
429#13133188C2314yes—
430#13133188C2314yes—
431#13133188C2314yescomplemented
432#13133187C2314yes—
433#13133186C2314yes—
434#13133186C2314yes—
435#13133186C2314yes—
436#13133186C2314yes—
437#13133186C2314yes—
438#13133185C2314yes—
439Q8×Dic53C2314yescomplemented
440C4×Dic106C2314yescomplemented
441C4×Dic106C2314yescomplemented
442C4×Dic106C2314yescomplemented
443C4×Dic106C2314yescomplemented
444C4×Dic106C2314yescomplemented
445#13133182C2314yescomplemented
446#13133182C2314yescomplemented
447#13133182C2314yescomplemented
448#13133182C2314yescomplemented
449C4×D212C2314yescomplemented
450D4×Dic53C2314yes—
451D4×Dic53C2314yes—
452D4×Dic53C2314yes—
453D4×Dic53C2314yes—
454D4×Dic53C2314yes—
455D4×Dic53C2314yes—
456D4×Dic53C2314yes—
457D4×Dic53C2314yes—
458D4×Dic53C2314yes—
459D4×Dic53C2314yes—
460D4×Dic53C2314yescomplemented
461C4×C22⋊D53C2314yes—
462C4×C22⋊D53C2314yes—
463C4×C22⋊D53C2314yes—
464C4×C22⋊D53C2314yes—
465C4×C22⋊D53C2314yes—
466C4×C22⋊D53C2314yes—
467C4×C22⋊D53C2314yescomplemented
468C4×C22⋊D53C2314yescomplemented
469#13133177C2314yes—
470#13133177C2314yes—
471#13133177C2314yes—
472#13133177C2314yes—
473#13133177C2314yes—
474#13133177C2314yes—
475#13133177C2314yes—
476#13133177C2314yes—
477#13133177C2314yes—
478#13133177C2314yes—
479#13133177C2314yescomplemented
480#13133177C2314yescomplemented
481#13133176C2314yes—
482#13133176C2314yes—
483#13133176C2314yescomplemented
484#13133175C2314yescomplemented
485#13133174C2314yescomplemented
486#13133174C2314yescomplemented
487#13133173C2314yes—
488#13133173C2314yes—
489#13133173C2314yes—
490#13133173C2314yes—
491#13133173C2314yescomplemented
492#13133173C2314yescomplemented
493C2×C4⋊Dic53C2312yes—
494C2×C4⋊Dic53C2312yes—
495C2×C4⋊Dic53C2312yes—
496C2×C4⋊Dic53C2312yes—
497C2×C4⋊Dic53C2314yescomplemented
498C2×#11719919C2312yes—
499C2×#11719919C2312yes—
500C2×#11719919C2312yes—
501C2×#11719919C2312yes—
502C2×#11719919C2312yes—
503C2×#11719919C2312yes—
504C2×#11719919C2312yes—
505C2×#11719919C2312yes—
506C2×#11719919C2314yescomplemented
507C2×#11719919C2314yescomplemented
508C4⋊C4×D53C2314yescomplemented
509C4⋊C4×D53C2314yescomplemented
510C4⋊C4×D53C2314yescomplemented
511C2×C22⋊Dic53C2314yes—
512C2×C22⋊Dic53C2314yes—
513C2×C22⋊Dic53C2314yes—
514C2×C22⋊Dic53C2312yes—
515C2×C22⋊Dic53C2312yes—
516C2×C22⋊Dic53C2312yes—
517C2×C22⋊Dic53C2312yes—
518C2×C22⋊Dic53C2312yes—
519C2×C22⋊Dic53C2312yes—
520C2×C22⋊Dic53C2311yescharacteristic
521C2×C22⋊Dic53C2311yescharacteristic
522C2×C22⋊Dic53C2312yes—
523C2×C22⋊Dic53C2311yescharacteristic
524C2×C22⋊Dic53C2311yescharacteristic
525C2×C22⋊Dic53C2312yes—
526C2×C22⋊Dic53C2312yes—
527C2×C22⋊Dic53C2312yes—
528C2×C22⋊Dic53C2312yes—
529C2×#11719921C2312yes—
530C2×#11719921C2312yes—
531C22⋊C4×D53C2314yes—
532C22⋊C4×D53C2314yes—
533C2×C4×Dic53C2312yes—
534C2×C4×Dic53C2312yes—
535C25×C53C2311yescharacteristic
536C2×#41×C53C2314yes—
537C22×D4×C53C2312yes—
538C22×D4×C53C2312yes—
539C22×D4×C53C2312yes—
540C23×C4×C53C2312yes—
541#126×C53C2314yes—
542#126×C53C2314yes—
543#124×C53C2314yes—
544#124×C53C2314yes—
545#123×C53C2314yes—
546#123×C53C2314yes—
547#123×C53C2314yes—
548#123×C53C2314yes—
549#123×C53C2314yes—
550C22⋊Q8×C53C2314yes—
551C22⋊Q8×C53C2314yes—
552C22⋊Q8×C53C2314yes—
553C22⋊Q8×C53C2314yes—
554#121×C53C2314yes—
555#121×C53C2314yes—
556#121×C53C2314yes—
557#121×C53C2314yes—
558#120×C53C2314yes—
559#120×C53C2314yes—
560#120×C53C2314yes—
561#120×C53C2314yes—
562#120×C53C2314yes—
563C4×D4×C53C2314yes—
564C4×D4×C53C2314yes—
565C4×D4×C53C2314yes—
566C4×D4×C53C2314yes—
567C4×D4×C53C2314yes—
568C4×D4×C53C2314yes—
569#117×C53C2314yes—
570#117×C53C2314yes—
571C2×C22⋊C4×C53C2311yescharacteristic
572C2×C22⋊C4×C53C2314yes—
573C2×C22⋊C4×C53C2314yes—
574C2×C22⋊C4×C53C2311yescharacteristic
575C2×C22⋊C4×C53C2312yes—
576C2×C22⋊C4×C53C2314yes—
577C2×C22⋊C4×C53C2312yes—
578C2×C22⋊C4×C53C2312yes—
579C2×C22⋊C4×C53C2312yes—
580C24×C53—24no—
581C24×C53—82no—
582C24×C53C2412yes—
583C24×C53C2412yes—
584C24×C53C2411yescharacteristic
585C24×C53C2412yes—
586C24×C53C2411yescharacteristic
587C24×C53C2411yescharacteristic
588C23×D53C2412yes—
589#41×C53—84no—
590C2×Q8×C53C2414yes—
591C2×D4×C53—28no—
592C2×D4×C53—82no—
593C2×D4×C53—82no—
594C2×D4×C53C2414yes—
595C2×D4×C53C2414yes—
596C2×D4×C53C2414yes—
597C2×D4×C53C2414yes—
598C2×D4×C53C2414yes—
599C2×D4×C53C2414yes—
600C2×D4×C53C2414yes—
601C22×C4×C53—82no—
602C22×C4×C53C2412yes—
603C22×C4×C53C2414yes—
604C22×C4×C53C2412yes—
605C22×C4×C53C2414yes—
606C22×C4×C53C2412yes—
607C22×C4×C53C2412yes—
608C22×C4×C53C2412yes—
609C22×C4×C53C2414yes—
610C22×C4×C53C2414yes—
611C2×C22⋊D53—28no—
612C2×C22⋊D53—82no—
613C2×C22⋊D53—82no—
614C2×C22⋊D53—82no—
615C2×C22⋊D53C2414yes—
616C2×C22⋊D53C2414yes—
617C2×C22⋊D53C2414yes—
618C2×C22⋊D53C2414yes—
619C2×C22⋊D53C2414yes—
620C2×C22⋊D53C2414yes—
621C2×C22⋊D53C2414yes—
622C2×C22⋊D53C2414yes—
623C2×C22⋊D53C2414yes—
624C2×C22⋊D53C2414yes—
625C22×Dic53—82no—
626C22×Dic53—82no—
627C22×Dic53—82no—
628C22×Dic53C2412yes—
629C22×Dic53C2412yes—
630C22×Dic53C2412yes—
631C22×Dic53C2412yes—
632C22×Dic53C2412yes—
633C22×Dic53C2412yes—
634C22×Dic53C2412yes—
635C22×Dic53C2412yes—
636C22×Dic53C2412yes—
637C22×Dic53C2412yes—
638C22×Dic53C2412yes—
639C22×Dic53C2414yes—
640C22×Dic53C2414yes—
641C22×Dic53C2414yes—
642C22×Dic53C2414yes—
643C22×Dic53C2414yes—
644C22×Dic53C2414yes—
645Q8×D53—84no—
646#11719947—84no—
647#11719947—84no—
648#11719947—84no—
649#11719945—84no—
650#11719945—84no—
651C2×D212C2414yes—
652C2×C4×D53—82no—
653C2×C4×D53C2414yes—
654C2×C4×D53C2414yes—
655C2×C4×D53C2414yes—
656C2×C4×D53C2414yes—
657C2×C4×D53C2414yes—
658C2×C4×D53C2414yes—
659C2×Dic106—82no—
660C2×Dic106—82no—
661C2×Dic106—82no—
662C2×Dic106—84no—
663C2×Dic106C2414yes—
664C2×Dic106C2414yes—
665C2×Dic106C2414yes—
666C2×Dic106C2414yes—
667C2×Dic106C2414yes—
668C2×Dic106C2414yes—
669C2×Dic106C2414yes—
670C2×Dic106C2414yes—
671C2×Dic106C2414yes—
672C4⋊C4×C53C2414yes—
673C4⋊C4×C53C2414yes—
674C4⋊C4×C53C2414yes—
675C4⋊C4×C53C2414yes—
676C4⋊C4×C53C2414yes—
677C4⋊C4×C53C2414yes—
678C22⋊C4×C53C2414yes—
679C22⋊C4×C53C2414yes—
680C22⋊C4×C53C2414yes—
681C22⋊C4×C53C2414yes—
682C22⋊C4×C53C2414yes—
683C22⋊C4×C53C2414yes—
684C22⋊C4×C53C2414yes—
685C22⋊C4×C53C2414yes—
686C22⋊C4×C53C2414yes—
687C22⋊C4×C53C2414yes—
688C22⋊C4×C53C2414yes—
689C22⋊C4×C53C2414yes—
690C22⋊C4×C53C2414yes—
691C22⋊C4×C53C2414yes—
692C42×C53C2414yes—
693C42×C53C2414yes—
694C22⋊Dic53C2414yes—
695C22⋊Dic53C2414yes—
696C22⋊Dic53C2414yes—
697C22⋊Dic53C2411yescharacteristic
698C22⋊Dic53C2412yes—
699C22⋊Dic53C2412yes—
700C22⋊Dic53C2412yes—
701C22⋊Dic53C2414yes—
702C22⋊Dic53C2414yes—
703C22⋊Dic53C2411yescharacteristic
704C22⋊Dic53C2412yes—
705C22⋊Dic53C2412yes—
706C22⋊Dic53C2411yescharacteristic
707C22⋊Dic53C2411yescharacteristic
708C22⋊Dic53C2412yes—
709C22⋊Dic53C2414yes—
710C22⋊Dic53C2414yes—
711C22⋊Dic53C2414yes—
712C22⋊Dic53C2414yes—
713C22⋊Dic53C2414yes—
714C22⋊Dic53C2414yes—
715C22⋊Dic53C2414yes—
716C22⋊Dic53C2414yes—
717C22⋊Dic53C2414yes—
718C22⋊Dic53C2414yes—
719C22⋊Dic53C2414yes—
720C22⋊Dic53C2414yes—
721C22⋊Dic53C2414yes—
722#11719921C2414yes—
723#11719921C2414yes—
724#11719921C2414yes—
725#11719921C2414yes—
726#11719921C2414yes—
727#11719921C2414yes—
728#11719921C2414yes—
729#11719921C2414yes—
730#11719921C2414yes—
731#11719921C2414yes—
732#11719921C2414yes—
733#11719921C2414yes—
734C4⋊Dic53C2414yes—
735C4⋊Dic53C2414yes—
736C4⋊Dic53C2414yes—
737C4⋊Dic53C2414yes—
738C4⋊Dic53C2414yes—
739C4⋊Dic53C2414yes—
740C4⋊Dic53C2414yes—
741C4⋊Dic53C2414yes—
742C4⋊Dic53C2414yes—
743C4⋊Dic53C2414yes—
744C4⋊Dic53C2414yes—
745C4⋊Dic53C2414yes—
746C4⋊Dic53C2414yes—
747C4⋊Dic53C2414yes—
748#11719919C2414yes—
749#11719919C2414yes—
750#11719919C2414yes—
751#11719919C2414yes—
752#11719919C2414yes—
753#11719919C2414yes—
754#11719919C2414yes—
755#11719919C2414yes—
756#11719919C2414yes—
757#11719919C2414yes—
758#11719919C2414yes—
759#11719919C2414yes—
760#11719919C2414yes—
761#11719919C2414yes—
762#11719919C2414yes—
763#11719919C2414yes—
764#11719919C2414yes—
765#11719919C2414yes—
766#11719919C2414yes—
767#11719919C2414yes—
768#11719919C2414yes—
769#11719919C2414yes—
770#11719919C2414yes—
771#11719919C2414yes—
772#11719919C2414yes—
773#11719919C2414yes—
774#11719919C2414yes—
775#11719919C2414yes—
776C4×Dic53C2414yes—
777C4×Dic53C2414yes—
778C4×Dic53C2414yes—
779C4×Dic53C2414yes—
780C4×Dic53C2414yes—
781C4×Dic53C2414yes—
782C4×Dic53C2414yes—
783C4×Dic53C2414yes—
784C4×Dic53C2414yes—
785C4×Dic53C2414yes—
786C23×C53—22no—
787C23×C53—22no—
788C23×C53—24no—
789C23×C53—24no—
790C23×C53—24no—
791C23×C53—42no—
792C23×C53—42no—
793C23×C53—42no—
794C23×C53—42no—
795C23×C53—42no—
796C23×C53—42no—
797C23×C53—42no—
798C23×C53—42no—
799C23×C53—42no—
800C23×C53—88no—
801C23×C532−1+414yes—
802C23×C53C2514yes—
803C23×C53C2511yescharacteristic
804C23×C53C2511yescharacteristic
805C23×C53C2512yes—
806C23×C53C2511yescharacteristic
807C23×C53C2512yes—
808C22×D53—24no—
809C22×D53—42no—
810C22×D53—42no—
811C22×D53C2514yes—
812Q8×C53—44no—
813D4×C53—28no—
814D4×C53—28no—
815D4×C53—44no—
816D4×C53—44no—
817D4×C53—44no—
818D4×C53—44no—
819D4×C53—44no—
820C2×C4×C53—24no—
821C2×C4×C53—42no—
822C2×C4×C53—42no—
823C2×C4×C53—42no—
824C2×C4×C53—44no—
825C2×C4×C53—42no—
826C2×C4×C53—44no—
827C2×C4×C53—44no—
828C2×C4×C53—44no—
829C2×C4×C53C2514yes—
830C2×C4×C53C2514yes—
831C2×C4×C53C2514yes—
832C2×C4×C53C2514yes—
833C2×C4×C53C2514yes—
834C22⋊D53—28no—
835C22⋊D53—28no—
836C22⋊D53—44no—
837C22⋊D53—44no—
838C22⋊D53—44no—
839C22⋊D53—44no—
840C22⋊D53—44no—
841C22⋊D53—44no—
842C22⋊D53—44no—
843C22⋊D53—44no—
844C2×Dic53—24no—
845C2×Dic53—44no—
846C2×Dic53—42no—
847C2×Dic53—42no—
848C2×Dic53—42no—
849C2×Dic53—44no—
850C2×Dic53—42no—
851C2×Dic53—42no—
852C2×Dic53—42no—
853C2×Dic53—42no—
854C2×Dic53—44no—
855C2×Dic53—44no—
856C2×Dic53—44no—
857C2×Dic53—44no—
858C2×Dic53—42no—
859C2×Dic53—42no—
860C2×Dic53—42no—
861C2×Dic53C2512yes—
862C2×Dic53C2514yes—
863C2×Dic53C2512yes—
864C2×Dic53C2514yes—
865C2×Dic53C2514yes—
866C2×Dic53C2512yes—
867C2×Dic53C2514yes—
868C2×Dic53C2512yes—
869C2×Dic53C2514yes—
870D212—44no—
871C4×D53—44no—
872C4×D53—44no—
873C4×D53—44no—
874C4×D53—44no—
875C4×D53—44no—
876C4×D53—44no—
877Dic106—44no—
878Dic106—44no—
879Dic106—44no—
880Dic106—44no—
881Dic106—44no—
882Dic106—44no—
883Dic106—44no—
884Dic106—44no—
885Dic106—44no—
886#62864—531nomaximal, Sylow
887C22×C53—22no—
888C22×C53—22no—
889C22×C53—22no—
890C22×C53—24no—
891C22×C53—21no—
892C22×C53—21no—
893C22×C53—22no—
894C22×C53—24no—
895C22×C53—22no—
896C22×C53—22no—
897C22×C53—24no—
898C22×C53—22no—
899C22×C53—22no—
900C22×C53—44no—
901C22×C53—44no—
902C22×C53—44no—
903C22×C53—84no—
904C22×C53—84no—
905C22×C53—84no—
906C22×C53C2×2−1+414yes—
907C22×C53C2×2−1+412yes—
908C22×C53C2611yescharacteristic
909C2×D53—24no—
910C2×D53—24no—
911C2×D53—24no—
912C2×D53—84no—
913C4×C53—24no—
914C4×C53—24no—
915C4×C53—24no—
916C4×C53—24no—
917C4×C53—24no—
918Dic53—24no—
919Dic53—22no—
920Dic53—24no—
921Dic53—22no—
922Dic53—24no—
923Dic53—24no—
924Dic53—22no—
925Dic53—24no—
926Dic53—22no—
927#3564—534no—
928#3564—534no—
929#3561—534no—
930#3561—534no—
931#3541—534no—
932#3541—534no—
933#3541—534no—
934#3541—534no—
935#3536—534no—
936#3536—534no—
937#3535—534no—
938#3535—534no—
939#3505—532no—
940#3505—532no—
941#3501—532no—
942#3501—532no—
943#3490—532no—
944#3490—531no—
945#3490D5311yescharacteristic, complemented
946C2×#543—531no—
947C2×#538—532no—
948C2×C53—24no—
949C2×C53—22no—
950C2×C53—41no—
951C2×C53—41no—
952C2×C53—42no—
953C2×C53—44no—
954C2×C53C22×2−1+411yescharacteristic
955C2×C53H(7,𝔽2)12yes—
956D53—44no—
957#563—534no—
958#563—534no—
959#563—534no—
960#563—534no—
961#563—534no—
962#563—534no—
963#563—534no—
964#563—534no—
965#562—534no—
966#562—534no—
967#562—534no—
968#562—534no—
969#562—534no—
970#562—534no—
971#562—534no—
972#562—534no—
973#556—534no—
974#556—534no—
975#556—534no—
976#556—534no—
977#554—534no—
978#554—534no—
979#554—534no—
980#554—534no—
981#554—534no—
982#554—534no—
983#554—534no—
984#554—534no—
985#554—534no—
986#554—534no—
987#554—534no—
988#554—534no—
989#553—534no—
990#553—534no—
991#553—534no—
992#553—534no—
993#553—534no—
994#553—534no—
995#552—534no—
996#552—534no—
997#552—534no—
998#552—534no—
999#552—534no—
1000#552—534no—
1001#551—534no—
1002#551—534no—
1003#551—534no—
1004#551—534no—
1005#551—534no—
1006#551—534no—
1007#551—534no—
1008#551—534no—
1009#551—534no—
1010#551—534no—
1011#551C2×D5314yescomplemented
1012#551C2×D5314yescomplemented
1013D4×Q8—534no—
1014D4×Q8—534no—
1015D4×Q8—534no—
1016D4×Q8—534no—
1017#548—534no—
1018#548—534no—
1019#548—534no—
1020#548—534no—
1021#548—534no—
1022#548—534no—
1023#547—534no—
1024#547—534no—
1025#547—534no—
1026#547—534no—
1027#546—534no—
1028#546—534no—
1029#546—534no—
1030#546—534no—
1031#546—534no—
1032#546—534no—
1033#546—534no—
1034#546—534no—
1035#546C2×D5314yescomplemented
1036#546C2×D5314yescomplemented
1037#544—534no—
1038#544—534no—
1039#543—534no—
1040#543—534no—
1041#543—534no—
1042#543—534no—
1043#543—534no—
1044#543—532no—
1045#543—531no—
1046#543—534no—
1047#543C2×D5311yescharacteristic
1048#542—534no—
1049#542—534no—
1050#542—534no—
1051#542—534no—
1052#542—534no—
1053#542—534no—
1054#542—534no—
1055#542—534no—
1056#542—534no—
1057#542—534no—
1058#542—534no—
1059#542—534no—
1060#541—534no—
1061#541—534no—
1062#541—534no—
1063#541—534no—
1064#539—534no—
1065#539—534no—
1066#539—534no—
1067#539—534no—
1068#539—534no—
1069#539—534no—
1070#539—534no—
1071#539—534no—
1072#539—534no—
1073#539—534no—
1074#538—534no—
1075#538—534no—
1076#538—534no—
1077#538—534no—
1078#538—534no—
1079#538—534no—
1080#538—534no—
1081#538—534no—
1082#538—534no—
1083#538—534no—
1084#538—534no—
1085#538—534no—
1086#538—534no—
1087#538C2×D5314yescomplemented
1088#537—534no—
1089#537—534no—
1090#537—534no—
1091#537—534no—
1092#536—534no—
1093#536—534no—
1094#536—534no—
1095#536—534no—
1096#534—532no—
1097#534—531no—
1098#534C2×D5311yescharacteristic
1099#533—534no—
1100#533—534no—
1101#529—534no—
1102#529—534no—
1103C2×#126—532no—
1104C2×#126—532no—
1105C2×#124—532no—
1106C2×#124—532no—
1107#525—534no—
1108#525—534no—
1109#525—534no—
1110#525—534no—
1111#525—534no—
1112#525C2×D5314yescomplemented
1113C2×#123—532no—
1114C2×#123—532no—
1115C2×C22⋊Q8—532no—
1116C2×C22⋊Q8—532no—
1117C2×C22⋊Q8—534no—
1118C2×C22⋊Q8—532no—
1119C2×C22⋊Q8—532no—
1120C2×C22⋊Q8—532no—
1121C2×C22⋊Q8—532no—
1122C2×C22⋊Q8—532no—
1123C2×C22⋊Q8—534no—
1124C2×#121—532no—
1125C2×#121—532no—
1126C2×#121—532no—
1127C2×#120—532no—
1128C2×#120C2×D5312yes—
1129#518—532no—
1130#518—532no—
1131#518—532no—
1132#518C2×D5312yes—
1133C2×C4×D4—532no—
1134C2×C4×D4—532no—
1135C22×C22⋊C4—531no—
1136C22×C22⋊C4—531no—
1137C22×C22⋊C4C2×D5311yescharacteristic
1138C53#6286411yescharacteristic, complemented, Sylow
1139C25C22×D5311yescharacteristic
1140C2×#41—534no—
1141C2×#41—534no—
1142C2×#41—534no—
1143C2×#41—534no—
1144C2×#41—534no—
1145C2×#41C22×D5314yes—
1146C22×Q8—534no—
1147C22×Q8—532no—
1148C22×Q8—532no—
1149C22×Q8—532no—
1150C22×Q8—534no—
1151C22×D4—532no—
1152C22×D4—532no—
1153C22×D4—532no—
1154C22×D4—532no—
1155C22×D4C22×D5312yes—
1156C22×D4C22×D5312yes—
1157C22×D4C22×D5312yes—
1158C23×C4—532no—
1159C23×C4—532no—
1160C23×C4—532no—
1161C23×C4—532no—
1162C23×C4C22×D5312yes—
1163C4⋊Q8—534no—
1164C4⋊Q8—534no—
1165C4⋊Q8—534no—
1166C4⋊Q8—534no—
1167C4⋊Q8—534no—
1168C4⋊Q8—534no—
1169C4⋊Q8—534no—
1170C4⋊Q8—534no—
1171C4⋊Q8—534no—
1172C4⋊Q8—534no—
1173C4⋊Q8—534no—
1174C4⋊Q8—534no—
1175#126—534no—
1176#126—534no—
1177#126—534no—
1178#126—534no—
1179#126—534no—
1180#126—534no—
1181#126—534no—
1182#126—534no—
1183#126—534no—
1184#126—534no—
1185#126—534no—
1186#126—534no—
1187#126—534no—
1188#126—534no—
1189#126—534no—
1190#126—534no—
1191#126—534no—
1192#126—534no—
1193#126—534no—
1194#126—534no—
1195#126—534no—
1196#126—534no—
1197#126—534no—
1198#126—534no—
1199#126—534no—
1200#126—534no—
1201#126C22×D5314yes—
1202#126C22×D5314yes—
1203#125—534no—
1204#125—534no—
1205#125—534no—
1206#125—534no—
1207#125—534no—
1208#125—534no—
1209#125—534no—
1210#125—534no—
1211#125—534no—
1212#125—534no—
1213#125—534no—
1214#125—534no—
1215#125—534no—
1216#125—534no—
1217#125—534no—
1218#125—534no—
1219#125—534no—
1220#125—534no—
1221#124—534no—
1222#124—534no—
1223#124—534no—
1224#124—534no—
1225#124—534no—
1226#124—534no—
1227#124—534no—
1228#124—534no—
1229#124—534no—
1230#124—534no—
1231#124—534no—
1232#124—534no—
1233#124—534no—
1234#124—534no—
1235#124—534no—
1236#124—534no—
1237#124—534no—
1238#124—534no—
1239#124—534no—
1240#124—534no—
1241#124C22×D5314yes—
1242#124C22×D5314yes—
1243#123—534no—
1244#123—534no—
1245#123—534no—
1246#123—534no—
1247#123—534no—
1248#123—534no—
1249#123—534no—
1250#123—534no—
1251#123—534no—
1252#123—534no—
1253#123—534no—
1254#123—534no—
1255#123—534no—
1256#123—534no—
1257#123—534no—
1258#123—534no—
1259#123—534no—
1260#123—534no—
1261#123—534no—
1262#123—534no—
1263#123—534no—
1264#123—534no—
1265#123—534no—
1266#123—534no—
1267#123—534no—
1268#123—534no—
1269#123—534no—
1270#123—534no—
1271#123—534no—
1272#123—534no—
1273#123—534no—
1274#123—534no—
1275#123—534no—
1276#123—534no—
1277#123—534no—
1278#123C22×D5314yes—
1279#123C22×D5314yes—
1280#123C22×D5314yes—
1281#123C22×D5314yes—
1282#123C22×D5314yes—
1283C22⋊Q8—534no—
1284C22⋊Q8—534no—
1285C22⋊Q8—534no—
1286C22⋊Q8—534no—
1287C22⋊Q8—534no—
1288C22⋊Q8—534no—
1289C22⋊Q8—534no—
1290C22⋊Q8—534no—
1291C22⋊Q8—534no—
1292C22⋊Q8—534no—
1293C22⋊Q8—534no—
1294C22⋊Q8—534no—
1295C22⋊Q8—534no—
1296C22⋊Q8—534no—
1297C22⋊Q8—534no—
1298C22⋊Q8—534no—
1299C22⋊Q8—534no—
1300C22⋊Q8—534no—
1301C22⋊Q8—534no—
1302C22⋊Q8—534no—
1303C22⋊Q8—534no—
1304C22⋊Q8—534no—
1305C22⋊Q8—534no—
1306C22⋊Q8—534no—
1307C22⋊Q8—534no—
1308C22⋊Q8—534no—
1309C22⋊Q8—534no—
1310C22⋊Q8—534no—
1311C22⋊Q8—534no—
1312C22⋊Q8—534no—
1313C22⋊Q8—534no—
1314C22⋊Q8—534no—
1315C22⋊Q8—534no—
1316C22⋊Q8—534no—
1317C22⋊Q8—534no—
1318C22⋊Q8—534no—
1319C22⋊Q8—534no—
1320C22⋊Q8—534no—
1321C22⋊Q8—534no—
1322C22⋊Q8—534no—
1323C22⋊Q8—534no—
1324C22⋊Q8—534no—
1325C22⋊Q8—534no—
1326C22⋊Q8—534no—
1327C22⋊Q8—534no—
1328C22⋊Q8—534no—
1329C22⋊Q8—534no—
1330C22⋊Q8—534no—
1331C22⋊Q8—534no—
1332C22⋊Q8—534no—
1333C22⋊Q8—534no—
1334C22⋊Q8—534no—
1335C22⋊Q8—534no—
1336C22⋊Q8—534no—
1337C22⋊Q8—534no—
1338C22⋊Q8—534no—
1339C22⋊Q8—534no—
1340C22⋊Q8—534no—
1341C22⋊Q8—534no—
1342C22⋊Q8—534no—
1343C22⋊Q8—534no—
1344C22⋊Q8—534no—
1345C22⋊Q8—534no—
1346C22⋊Q8—534no—
1347C22⋊Q8—534no—
1348C22⋊Q8—534no—
1349C22⋊Q8—534no—
1350C22⋊Q8—534no—
1351C22⋊Q8—534no—
1352C22⋊Q8—534no—
1353C22⋊Q8C22×D5314yes—
1354C22⋊Q8C22×D5314yes—
1355C22⋊Q8C22×D5314yes—
1356C22⋊Q8C22×D5314yes—
1357#121—534no—
1358#121—534no—
1359#121—534no—
1360#121—534no—
1361#121—534no—
1362#121—534no—
1363#121—534no—
1364#121—534no—
1365#121—534no—
1366#121—534no—
1367#121—534no—
1368#121—534no—
1369#121—534no—
1370#121—534no—
1371#121—534no—
1372#121—534no—
1373#121—534no—
1374#121—534no—
1375#121—534no—
1376#121—534no—
1377#121—534no—
1378#121—534no—
1379#121—534no—
1380#121—534no—
1381#121—534no—
1382#121—534no—
1383#121—534no—
1384#121—534no—
1385#121—534no—
1386#121—534no—
1387#121C22×D5314yes—
1388#121C22×D5314yes—
1389#121C22×D5314yes—
1390#121C22×D5314yes—
1391#120—534no—
1392#120—534no—
1393#120—534no—
1394#120—534no—
1395#120—534no—
1396#120—534no—
1397#120—534no—
1398#120C22×D5314yes—
1399#120C22×D5314yes—
1400#120C22×D5314yes—
1401#120C22×D5314yes—
1402#120C22×D5314yes—
1403C4×Q8—534no—
1404C4×Q8—534no—
1405C4×Q8—534no—
1406C4×Q8—534no—
1407C4×Q8—534no—
1408C4×Q8—534no—
1409C4×Q8—534no—
1410C4×Q8—534no—
1411C4×Q8—534no—
1412C4×Q8—534no—
1413C4×D4—534no—
1414C4×D4—534no—
1415C4×D4—534no—
1416C4×D4—534no—
1417C4×D4—534no—
1418C4×D4—534no—
1419C4×D4—534no—
1420C4×D4—534no—
1421C4×D4—534no—
1422C4×D4—534no—
1423C4×D4—534no—
1424C4×D4—534no—
1425C4×D4—534no—
1426C4×D4—534no—
1427C4×D4—534no—
1428C4×D4—534no—
1429C4×D4—534no—
1430C4×D4—534no—
1431C4×D4—534no—
1432C4×D4—534no—
1433C4×D4—534no—
1434C4×D4—534no—
1435C4×D4—534no—
1436C4×D4—534no—
1437C4×D4—534no—
1438C4×D4—534no—
1439C4×D4—534no—
1440C4×D4—534no—
1441C4×D4—534no—
1442C4×D4—534no—
1443C4×D4—534no—
1444C4×D4—534no—
1445C4×D4C22×D5314yes—
1446C4×D4C22×D5314yes—
1447C4×D4C22×D5314yes—
1448C4×D4C22×D5314yes—
1449C4×D4C22×D5314yes—
1450C4×D4C22×D5314yes—
1451#117—534no—
1452#117—534no—
1453#117—534no—
1454#117—534no—
1455#117—534no—
1456#117—534no—
1457#117—534no—
1458#117—534no—
1459#117—534no—
1460#117—534no—
1461#117—534no—
1462#117—534no—
1463#117C22×D5314yes—
1464#117C22×D5314yes—
1465C2×C4⋊C4—532no—
1466C2×C4⋊C4—532no—
1467C2×C4⋊C4—532no—
1468C2×C4⋊C4—532no—
1469C2×C4⋊C4—532no—
1470C2×C4⋊C4—532no—
1471C2×C4⋊C4—532no—
1472C2×C4⋊C4—532no—
1473C2×C4⋊C4—532no—
1474C2×C4⋊C4—532no—
1475C2×C4⋊C4—532no—
1476C2×C4⋊C4—532no—
1477C2×C4⋊C4—534no—
1478C2×C4⋊C4—534no—
1479C2×C4⋊C4—534no—
1480C2×C4⋊C4—534no—
1481C2×C4⋊C4—534no—
1482C2×C4⋊C4—534no—
1483C2×C22⋊C4—532no—
1484C2×C22⋊C4—532no—
1485C2×C22⋊C4—532no—
1486C2×C22⋊C4—532no—
1487C2×C22⋊C4—531no—
1488C2×C22⋊C4—531no—
1489C2×C22⋊C4—531no—
1490C2×C22⋊C4—531no—
1491C2×C22⋊C4—532no—
1492C2×C22⋊C4—532no—
1493C2×C22⋊C4—534no—
1494C2×C22⋊C4—534no—
1495C2×C22⋊C4—532no—
1496C2×C22⋊C4—532no—
1497C2×C22⋊C4—534no—
1498C2×C22⋊C4—532no—
1499C2×C22⋊C4—532no—
1500C2×C22⋊C4—532no—
1501C2×C22⋊C4—532no—
1502C2×C22⋊C4—532no—
1503C2×C22⋊C4—534no—
1504C2×C22⋊C4—534no—
1505C2×C22⋊C4C22×D5311yescharacteristic
1506C2×C22⋊C4C22×D5311yescharacteristic
1507C2×C22⋊C4C22×D5312yes—
1508C2×C22⋊C4C22×D5314yes—
1509C2×C22⋊C4C22×D5314yes—
1510C2×C22⋊C4C22×D5312yes—
1511C2×C22⋊C4C22×D5314yes—
1512C2×C22⋊C4C22×D5312yes—
1513C2×C22⋊C4C22×D5312yes—
1514C2×C42—532no—
1515C2×C42—532no—
1516C24—24no—
1517C24—82no—
1518C24—532no—
1519C24C23×D5312yes—
1520C24C23×D5312yes—
1521C24C23×D5312yes—
1522C24C23×D5311yescharacteristic
1523C24C23×D5311yescharacteristic
1524C24C23×D5311yescharacteristic
1525#41—84no—
1526#41—4244no—
1527#41—4244no—
1528#41—4244no—
1529#41—4244no—
1530#41—4244no—
1531C2×Q8—534no—
1532C2×Q8—534no—
1533C2×Q8—534no—
1534C2×Q8—534no—
1535C2×Q8—534no—
1536C2×Q8—534no—
1537C2×Q8—534no—
1538C2×Q8—534no—
1539C2×Q8—534no—
1540C2×Q8—4242no—
1541C2×Q8—4242no—
1542C2×Q8—4242no—
1543C2×Q8—4244no—
1544C2×Q8—4244no—
1545C2×Q8C23×D5314yes—
1546C2×D4—28no—
1547C2×D4—82no—
1548C2×D4—82no—
1549C2×D4—534no—
1550C2×D4—534no—
1551C2×D4—534no—
1552C2×D4—534no—
1553C2×D4—534no—
1554C2×D4—534no—
1555C2×D4—534no—
1556C2×D4—534no—
1557C2×D4—534no—
1558C2×D4—534no—
1559C2×D4—534no—
1560C2×D4—1068no—
1561C2×D4—4242no—
1562C2×D4—4242no—
1563C2×D4—4242no—
1564C2×D4C23×D5314yes—
1565C2×D4C23×D5314yes—
1566C2×D4C23×D5314yes—
1567C2×D4C23×D5314yes—
1568C2×D4C23×D5314yes—
1569C2×D4C23×D5314yes—
1570C2×D4C23×D5314yes—
1571C22×C4—82no—
1572C22×C4—532no—
1573C22×C4—532no—
1574C22×C4—532no—
1575C22×C4—532no—
1576C22×C4—532no—
1577C22×C4—532no—
1578C22×C4—532no—
1579C22×C4—532no—
1580C22×C4—532no—
1581C22×C4—532no—
1582C22×C4—532no—
1583C22×C4—534no—
1584C22×C4—534no—
1585C22×C4—534no—
1586C22×C4—534no—
1587C22×C4—534no—
1588C22×C4—534no—
1589C22×C4—534no—
1590C22×C4—534no—
1591C22×C4—534no—
1592C22×C4—534no—
1593C22×C4—534no—
1594C22×C4—534no—
1595C22×C4—4242no—
1596C22×C4—4242no—
1597C22×C4—4242no—
1598C22×C4—4242no—
1599C22×C4C23×D5312yes—
1600C22×C4C23×D5312yes—
1601C22×C4C23×D5312yes—
1602C22×C4C23×D5312yes—
1603C22×C4C23×D5312yes—
1604C22×C4C23×D5314yes—
1605C22×C4C23×D5314yes—
1606C22×C4C23×D5314yes—
1607C22×C4C23×D5314yes—
1608C4⋊C4—534no—
1609C4⋊C4—534no—
1610C4⋊C4—534no—
1611C4⋊C4—534no—
1612C4⋊C4—534no—
1613C4⋊C4—534no—
1614C4⋊C4—534no—
1615C4⋊C4—534no—
1616C4⋊C4—534no—
1617C4⋊C4—534no—
1618C4⋊C4—534no—
1619C4⋊C4—534no—
1620C4⋊C4—534no—
1621C4⋊C4—534no—
1622C4⋊C4—534no—
1623C4⋊C4—534no—
1624C4⋊C4—534no—
1625C4⋊C4—534no—
1626C4⋊C4—534no—
1627C4⋊C4—534no—
1628C4⋊C4—534no—
1629C4⋊C4—534no—
1630C4⋊C4—534no—
1631C4⋊C4—534no—
1632C4⋊C4—534no—
1633C4⋊C4—534no—
1634C4⋊C4—534no—
1635C4⋊C4—534no—
1636C4⋊C4—534no—
1637C4⋊C4—534no—
1638C4⋊C4—534no—
1639C4⋊C4—534no—
1640C4⋊C4—534no—
1641C4⋊C4—534no—
1642C4⋊C4—534no—
1643C4⋊C4—534no—
1644C4⋊C4—534no—
1645C4⋊C4—534no—
1646C4⋊C4—534no—
1647C4⋊C4—534no—
1648C4⋊C4—534no—
1649C4⋊C4—534no—
1650C4⋊C4C23×D5314yes—
1651C4⋊C4C23×D5314yes—
1652C4⋊C4C23×D5314yes—
1653C4⋊C4C23×D5314yes—
1654C4⋊C4C23×D5314yes—
1655C4⋊C4C23×D5314yes—
1656C22⋊C4—534no—
1657C22⋊C4—534no—
1658C22⋊C4—534no—
1659C22⋊C4—532no—
1660C22⋊C4—531no—
1661C22⋊C4—531no—
1662C22⋊C4—532no—
1663C22⋊C4—532no—
1664C22⋊C4—532no—
1665C22⋊C4—532no—
1666C22⋊C4—534no—
1667C22⋊C4—534no—
1668C22⋊C4—532no—
1669C22⋊C4—531no—
1670C22⋊C4—531no—
1671C22⋊C4—534no—
1672C22⋊C4—534no—
1673C22⋊C4—534no—
1674C22⋊C4—534no—
1675C22⋊C4—534no—
1676C22⋊C4—534no—
1677C22⋊C4—534no—
1678C22⋊C4—534no—
1679C22⋊C4—534no—
1680C22⋊C4—534no—
1681C22⋊C4—534no—
1682C22⋊C4—534no—
1683C22⋊C4—534no—
1684C22⋊C4—534no—
1685C22⋊C4—534no—
1686C22⋊C4—534no—
1687C22⋊C4—534no—
1688C22⋊C4—534no—
1689C22⋊C4—534no—
1690C22⋊C4—534no—
1691C22⋊C4—534no—
1692C22⋊C4—534no—
1693C22⋊C4—534no—
1694C22⋊C4—534no—
1695C22⋊C4—534no—
1696C22⋊C4C23×D5314yes—
1697C22⋊C4C23×D5314yes—
1698C22⋊C4C23×D5314yes—
1699C22⋊C4C23×D5314yes—
1700C22⋊C4C23×D5314yes—
1701C22⋊C4C23×D5314yes—
1702C22⋊C4C23×D5314yes—
1703C22⋊C4C23×D5314yes—
1704C22⋊C4C23×D5314yes—
1705C22⋊C4C23×D5314yes—
1706C22⋊C4C23×D5314yes—
1707C22⋊C4C23×D5314yes—
1708C22⋊C4C23×D5314yes—
1709C22⋊C4C23×D5314yes—
1710C42—534no—
1711C42—534no—
1712C42—534no—
1713C42—534no—
1714C42—534no—
1715C42—534no—
1716C42—534no—
1717C42—534no—
1718C42—534no—
1719C42—534no—
1720C42C23×D5314yes—
1721C42C23×D5314yes—
1722C23—22no—
1723C23—22no—
1724C23—24no—
1725C23—24no—
1726C23—24no—
1727C23—42no—
1728C23—42no—
1729C23—42no—
1730C23—42no—
1731C23—42no—
1732C23—42no—
1733C23—42no—
1734C23—42no—
1735C23—42no—
1736C23—88no—
1737C23—534no—
1738C23—1064no—
1739C23—2122no—
1740C23—2122no—
1741C23#1313326414yes—
1742C23C24×D5312yes—
1743C23C24×D5311yescharacteristic
1744C23C24×D5311yescharacteristic
1745C23C24×D5314yes—
1746C23C24×D5312yes—
1747C23C24×D5311yescharacteristic
1748Q8—44no—
1749Q8—2124no—
1750Q8—2124no—
1751Q8—2124no—
1752Q8—2124no—
1753Q8—2124no—
1754Q8—2124no—
1755Q8—2124no—
1756Q8—2124no—
1757Q8—2124no—
1758D4—28no—
1759D4—28no—
1760D4—44no—
1761D4—44no—
1762D4—44no—
1763D4—44no—
1764D4—44no—
1765D4—1068no—
1766D4—1068no—
1767D4—2124no—
1768D4—2124no—
1769D4—2124no—
1770D4—2124no—
1771D4—2124no—
1772D4—2124no—
1773D4—2124no—
1774D4—2124no—
1775D4—2124no—
1776C2×C4—24no—
1777C2×C4—42no—
1778C2×C4—42no—
1779C2×C4—44no—
1780C2×C4—44no—
1781C2×C4—42no—
1782C2×C4—42no—
1783C2×C4—44no—
1784C2×C4—44no—
1785C2×C4—534no—
1786C2×C4—534no—
1787C2×C4—532no—
1788C2×C4—532no—
1789C2×C4—534no—
1790C2×C4—534no—
1791C2×C4—532no—
1792C2×C4—534no—
1793C2×C4—532no—
1794C2×C4—1064no—
1795C2×C4—2124no—
1796C2×C4—2124no—
1797C2×C4—2124no—
1798C2×C4—2124no—
1799C2×C4—2124no—
1800C2×C4—2124no—
1801C2×C4—2122no—
1802C2×C4—2122no—
1803C2×C4—2122no—
1804C2×C4—2122no—
1805C2×C4—2122no—
1806C2×C4—2122no—
1807C2×C4—2124no—
1808C2×C4—2122no—
1809C2×C4—2122no—
1810C2×C4—2122no—
1811C2×C4—2124no—
1812C2×C4—2124no—
1813C2×C4—2124no—
1814C2×C4—2122no—
1815C2×C4—2124no—
1816C2×C4—2124no—
1817C2×C4C24×D5314yes—
1818C2×C4C24×D5314yes—
1819C2×C4C24×D5314yes—
1820C2×C4C24×D5314yes—
1821C2×C4C24×D5314yes—
1822C22—22no—
1823C22—22no—
1824C22—22no—
1825C22—24no—
1826C22—22no—
1827C22—21no—
1828C22—21no—
1829C22—22no—
1830C22—22no—
1831C22—24no—
1832C22—24no—
1833C22—22no—
1834C22—22no—
1835C22—44no—
1836C22—44no—
1837C22—44no—
1838C22—84no—
1839C22—84no—
1840C22—84no—
1841C22—1064no—
1842C22—1064no—
1843C22—1064no—
1844C22—4244no—
1845C22C2×#1313326414yes—
1846C22C2×#1313326412yes—
1847C22C25×D5311yescharacteristic
1848C4—24no—
1849C4—24no—
1850C4—24no—
1851C4—24no—
1852C4—24no—
1853C4—1064no—
1854C4—1062no—
1855C4—1064no—
1856C4—1062no—
1857C4—1064no—
1858C4—1064no—
1859C4—1062no—
1860C4—1062no—
1861C4—1064no—
1862C2—22no—
1863C2—24no—
1864C2—42no—
1865C2—41no—
1866C2—41no—
1867C2—44no—
1868C2—2124no—
1869C2C22×#1313326411yescharacteristic
1870C2#2028952512yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3490C2
hypercenter#3490D53
hypocenterC53#62864
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289331C2semidirect
2. #20289327C2semidirect
3. #20289274C2semidirect
4. #20289273C2semidirect
5. #20289008C2semidirect
6. #20289003C2semidirect
7. #20289000C2semidirect
8. #20288995C2semidirect
9. #20288935C2semidirect
10. #20288930C2semidirect
11. #20288912C2semidirect
12. #20288911C2semidirect
13. #20288552C2semidirect
14. #20288545C2semidirect
15. #20288515C2semidirect
16. #20288513C2semidirect
17. #20288404C2semidirect
18. #20288402C2semidirect
19. C2×#16811249C2semidirect
20. C2×#16811208C2semidirect
21. C53×#3490C2semidirect
22. #16811376C22semidirect
23. #16811376C22semidirect
24. #16811376C22semidirect
25. #16811375C22semidirect
26. #16811375C22semidirect
27. #16811374C22semidirect
28. #16811374C22semidirect
29. #16811373C22semidirect
30. #16811370C22semidirect
31. #16811370C22semidirect
32. #16811370C22semidirect
33. #16811368C22semidirect
34. #16811368C22semidirect
35. #16811368C22semidirect
36. #16811368C22semidirect
37. #16811367C22semidirect
38. #16811343C22semidirect
39. #16811342C22semidirect
40. #16811341C22semidirect
41. #16811340C22semidirect
42. #16811332C22semidirect
43. #16811332C22semidirect
44. #16811332C22semidirect
45. #16811332C22semidirect
46. #16811331C22semidirect
47. #16811331C22semidirect
48. #16811330C22semidirect
49. #16811330C22semidirect
50. #16811327C22semidirect
51. #16811327C22semidirect
52. #16811327C22semidirect
53. #16811327C22semidirect
54. #16811325C22semidirect
55. #16811322C22semidirect
56. #16811322C22semidirect
57. #16811319C22semidirect
58. #16811316C22semidirect
59. #16811316C22semidirect
60. #16811313C22semidirect
61. #16811312C22semidirect
62. #16811310C22semidirect
63. #16811310C22semidirect
64. #16811309C22semidirect
65. #16811306C22semidirect
66. #16811304C22semidirect
67. #16811304C22semidirect
68. #16811304C22semidirect
69. #16811299C22semidirect
70. #16811299C22semidirect
71. #16811299C22semidirect
72. #16811299C22semidirect
73. #16811299C22semidirect
74. #16811297C22semidirect
75. #16811296C22semidirect
76. D4×Dic106C22semidirect
77. D4×Dic106C22semidirect
78. #16811286C22semidirect
79. #16811286C22semidirect
80. #16811282C22semidirect
81. #16811282C22semidirect
82. #16811281C22semidirect
83. #16811280C22semidirect
84. #16811279C22semidirect
85. #16811279C22semidirect
86. #16811278C22semidirect
87. #16811273C22semidirect
88. #16811272C22semidirect
89. #16811271C22semidirect
90. #16811267C22semidirect
91. #16811267C22semidirect
92. #16811263C22semidirect
93. #16811263C22semidirect
94. #16811263C22semidirect
95. #16811260C22semidirect
96. #16811260C22semidirect
97. #16811260C22semidirect
98. #16811252C22semidirect
99. #16811251C22semidirect
102. #16811249C22semidirect
103. #16811249C22semidirect
104. #16811249C22semidirect
105. #16811249C22semidirect
106. #16811249C22semidirect
107. #16811248C22semidirect
108. #16811244C22semidirect
109. #16811242C22semidirect
110. #16811241C22semidirect
111. #16811241C22semidirect
112. #16811241C22semidirect
113. #16811240C22semidirect
114. #16811240C22semidirect
115. #16811239C22semidirect
116. #16811238C22semidirect
117. #16811238C22semidirect
118. #16811237C22semidirect
119. #16811237C22semidirect
120. #16811235C22semidirect
121. #16811233C22semidirect
122. #16811230C22semidirect
123. #16811230C22semidirect
124. #16811218C22semidirect
125. #16811217C22semidirect
126. #16811217C22semidirect
127. #16811216C22semidirect
128. #16811216C22semidirect
129. #16811216C22semidirect
130. #16811215C22semidirect
131. #16811215C22semidirect
132. #16811215C22semidirect
133. #16811214C22semidirect
134. #16811211C22semidirect
139. #16811208C22semidirect
140. #16811208C22semidirect
141. #16811208C22semidirect
142. #16811208C22semidirect
143. #16811208C22semidirect
144. #16811208C22semidirect
145. #16811208C22semidirect
146. #16811206C22semidirect
147. #16811202C22semidirect
148. #16811202C22semidirect
149. #16811201C22semidirect
150. #16811200C22semidirect
151. #16811196C22semidirect
152. #16811195C22semidirect
153. #16811194C22semidirect
154. #16811193C22semidirect
157. #16811176C22semidirect
158. #16811175C22semidirect
159. #16811153C22semidirect
160. #16811150C22semidirect
161. C2×#13133210C22semidirect
162. C2×#13133210C22semidirect
163. C2×#13133204C22semidirect
164. C2×#13133203C22semidirect
165. #16811134C22semidirect
166. #16811132C22semidirect
167. #16811129C22semidirect
168. #16811129C22semidirect
169. #16811129C22semidirect
170. C2×#13133199C22semidirect
171. C2×#13133198C22semidirect
172. C2×#13133196C22semidirect
173. C2×#13133196C22semidirect
177. C2×#13133194C22semidirect
178. C2×#13133194C22semidirect
179. C2×#13133194C22semidirect
180. C22⋊Q8×D53C22semidirect
182. C2×#13133189C22semidirect
183. C2×#13133188C22semidirect
192. C53×#551C22semidirect
193. C53×#551C22semidirect
194. C53×#546C22semidirect
195. C53×#546C22semidirect
197. C53×#538C22semidirect
199. C53×#525C22semidirect
204. C2×#11719945C23semidirect
207. C2×#11719947C23semidirect
211. C22×Dic106C23semidirect
212. C2×Q8×D53C23semidirect
221. #13133217C23semidirect
222. #13133217C23semidirect
223. #13133216C23semidirect
224. #13133216C23semidirect
225. #13133216C23semidirect
226. #13133216C23semidirect
227. #13133216C23semidirect
228. #13133216C23semidirect
229. #13133216C23semidirect
230. #13133215C23semidirect
231. #13133215C23semidirect
232. #13133215C23semidirect
233. #13133212C23semidirect
234. #13133212C23semidirect
235. #13133212C23semidirect
236. #13133212C23semidirect
237. #13133211C23semidirect
238. #13133211C23semidirect
253. #13133210C23semidirect
254. #13133210C23semidirect
255. #13133210C23semidirect
256. #13133210C23semidirect
257. #13133210C23semidirect
258. #13133210C23semidirect
259. #13133209C23semidirect
260. #13133209C23semidirect
261. #13133209C23semidirect
262. #13133208C23semidirect
263. #13133208C23semidirect
264. #13133208C23semidirect
265. #13133208C23semidirect
266. #13133208C23semidirect
267. #13133207C23semidirect
268. #13133207C23semidirect
269. #13133207C23semidirect
270. #13133207C23semidirect
271. #13133207C23semidirect
272. #13133207C23semidirect
273. #13133207C23semidirect
274. #13133207C23semidirect
275. #13133207C23semidirect
276. #13133207C23semidirect
277. #13133205C23semidirect
284. #13133204C23semidirect
293. #13133203C23semidirect
294. #13133203C23semidirect
295. #13133203C23semidirect
296. #13133203C23semidirect
297. #13133202C23semidirect
298. #13133202C23semidirect
302. #13133201C23semidirect
303. #13133201C23semidirect
307. #13133200C23semidirect
308. #13133200C23semidirect
317. #13133199C23semidirect
318. #13133199C23semidirect
319. #13133199C23semidirect
320. #13133199C23semidirect
330. #13133198C23semidirect
331. #13133198C23semidirect
332. #13133197C23semidirect
333. #13133197C23semidirect
334. #13133197C23semidirect
335. #13133197C23semidirect
348. #13133196C23semidirect
349. #13133196C23semidirect
350. #13133196C23semidirect
351. #13133196C23semidirect
352. #13133196C23semidirect
353. #13133195C23semidirect
354. #13133195C23semidirect
355. #13133195C23semidirect
356. #13133195C23semidirect
357. #13133195C23semidirect
358. #13133195C23semidirect
359. #13133195C23semidirect
360. #13133195C23semidirect
389. #13133194C23semidirect
390. #13133194C23semidirect
391. #13133194C23semidirect
392. #13133194C23semidirect
393. #13133194C23semidirect
394. #13133194C23semidirect
395. #13133194C23semidirect
396. #13133194C23semidirect
397. #13133194C23semidirect
398. #13133194C23semidirect
399. #13133193C23semidirect
400. #13133193C23semidirect
401. #13133193C23semidirect
404. #13133191C23semidirect
407. #13133190C23semidirect
408. #13133190C23semidirect
423. #13133189C23semidirect
424. #13133189C23semidirect
431. #13133188C23semidirect
439. Q8×Dic53C23semidirect
440. C4×Dic106C23semidirect
441. C4×Dic106C23semidirect
442. C4×Dic106C23semidirect
443. C4×Dic106C23semidirect
444. C4×Dic106C23semidirect
445. #13133182C23semidirect
446. #13133182C23semidirect
447. #13133182C23semidirect
448. #13133182C23semidirect
449. C4×D212C23semidirect
460. D4×Dic53C23semidirect
467. C4×C22⋊D53C23semidirect
468. C4×C22⋊D53C23semidirect
479. #13133177C23semidirect
480. #13133177C23semidirect
483. #13133176C23semidirect
484. #13133175C23semidirect
485. #13133174C23semidirect
486. #13133174C23semidirect
491. #13133173C23semidirect
492. #13133173C23semidirect
497. C2×C4⋊Dic53C23semidirect
506. C2×#11719919C23semidirect
507. C2×#11719919C23semidirect
508. C4⋊C4×D53C23semidirect
509. C4⋊C4×D53C23semidirect
510. C4⋊C4×D53C23semidirect
945. #3490D53semidirect
1011. #551C2×D53semidirect
1012. #551C2×D53semidirect
1035. #546C2×D53semidirect
1036. #546C2×D53semidirect
1087. #538C2×D53semidirect
1112. #525C2×D53semidirect
1138. C53#62864semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202893312
#202893272
#202892742
#202892732
#202890082
#202890032
#202890002
#202889952
#202889352
#202889302
#202889122
#202889112
#202885522
#202885452
#202885152
#202885132
#202884042
#202884022
C2×#168112492
C2×#168112082
C53×#34902
#6286453