Finite Group Databasebeta

← #28293068

Subgroups — #28293068

Order 13568.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289366C214yesmaximal, complemented
2#20289362C214yesmaximal, complemented
3#20289206C212yesmaximal, complemented
4#20289191C212yesmaximal, complemented
5#20289107C212yesmaximal, complemented
6#20289092C212yesmaximal, complemented
7#20289002C214yesmaximal, complemented
8#20288994C214yesmaximal, complemented
9#20288731C212yesmaximal, complemented
10#20288729C212yesmaximal, complemented
11#20288699C214yesmaximal, complemented
12#20288697C214yesmaximal, complemented
13#20288694C212yesmaximal, complemented
14#20288684C212yesmaximal, complemented
15#20288636C212yesmaximal, complemented
16#20288622C212yesmaximal, complemented
17#20288622C211yesmaximal, characteristic, complemented
18#20288616C212yesmaximal, complemented
19#20288602C212yesmaximal, complemented
20#20288594C212yesmaximal, complemented
21#20288537C212yesmaximal, complemented
22#20288534C211yesmaximal, characteristic, complemented
23#20288531C211yesmaximal, characteristic, complemented
24#20288434C212yesmaximal, complemented
25#20288428C212yesmaximal, complemented
26#20288010C211yesmaximal, characteristic, complemented
27#20288008C211yesmaximal, characteristic, complemented
28C2×#16811178C211yesmaximal, characteristic, complemented
29C53×#3511C211yesmaximal, characteristic, complemented
30#16811375C2218yes—
31#16811374C2218yes—
32#16811370C2218yes—
33#16811367C2218yes—
34Q8×Dic106C2212yescomplemented
35#16811353C2212yescomplemented
36#16811352C2212yescomplemented
37#16811352C2214yescomplemented
38#16811352C2214yescomplemented
39#16811350C2214yescomplemented
40#16811349C2214yescomplemented
41#16811348C2212yescomplemented
42#16811346C2214yes—
43#16811346C2214yes—
44#16811344C2214yes—
45#16811344C2214yes—
46#16811343C2214yescomplemented
47#16811343C2212yescomplemented
48#16811342C2218yescomplemented
49#16811342C2214yescomplemented
50#16811341C2214yes—
51#16811341C2214yes—
52#16811340C2218yescomplemented
53#16811338C2214yes—
54#16811338C2212yescomplemented
55#16811337C2214yes—
56#16811337C2214yes—
57#16811336C2214yes—
58#16811334C2212yescomplemented
59#16811332C2218yes—
60#16811332C2214yescomplemented
61#16811330C2214yes—
62#16811330C2218yes—
63#16811330C2212yescomplemented
64#16811330C2214yescomplemented
65#16811330C2212yescomplemented
66#16811328C2214yes—
67#16811325C2214yes—
68#16811325C2214yes—
69#16811325C2214yes—
70#16811325C2218yes—
71#16811325C2214yescomplemented
72#16811323C2214yes—
73#16811321C2214yes—
74#16811320C2214yescomplemented
75#16811316C2218yes—
76#16811315C2214yes—
77#16811315C2214yes—
78#16811315C2214yes—
79#16811315C2214yescomplemented
80#16811315C2214yescomplemented
81#16811315C2218yescomplemented
82#16811314C2214yes—
83#16811312C2214yescomplemented
84#16811311C2214yes—
85#16811310C2218yescomplemented
86#16811308C2214yes—
87#16811307C2214yescomplemented
88D4×Dic106C2214yes—
89D4×Dic106C2212yescomplemented
90#16811288C2212yescomplemented
91Q8×C22⋊D53C2214yes—
92#16811281C2214yes—
93#16811280C2214yescomplemented
94#16811279C2214yes—
95#16811279C2214yes—
96#16811279C2214yescomplemented
97#16811277C2214yes—
98#16811277C2212yescomplemented
99#16811272C2214yes—
100#16811254C2212yes—
101#16811254C2214yescomplemented
102#16811251C2212yes—
103#16811251C2214yescomplemented
104#16811251C2214yescomplemented
105#16811250C2214yescomplemented
106#16811242C2214yes—
107#16811242C2218yescomplemented
108#16811242C2214yescomplemented
109#16811242C2214yescomplemented
110#16811241C2218yescomplemented
111#16811240C2214yescomplemented
112#16811239C2218yes—
113#16811238C2214yes—
114#16811237C2218yes—
115#16811236C2214yes—
116#16811236C2214yescomplemented
117#16811233C2214yescomplemented
118#16811233C2218yescomplemented
119#16811233C2214yescomplemented
120#16811231C2214yes—
121#16811230C2218yescomplemented
122#16811226C2214yescomplemented
123#16811222C2218yes—
124#16811217C2218yes—
125#16811210C2218yes—
126#16811206C2218yes—
127#16811202C2214yes—
128#16811201C2214yes—
129#16811201C2212yes—
130#16811199C2214yes—
131#16811196C2214yes—
132#16811180C2211yescharacteristic
133#16811180C2212yescomplemented
134#16811178C2212yes—
135#16811178C2212yes—
136#16811178C2212yes—
137#16811178C2212yes—
138#16811178C2212yes—
139#16811178C2212yes—
140#16811178C2212yes—
141#16811178C2212yes—
142#16811178C2211yescharacteristic
143#16811178C2211yescharacteristic
144#16811178C2212yescomplemented
145#16811178C2212yescomplemented
146#16811177C2211yescharacteristic
147#16811177C2211yescharacteristic
148#16811176C2211yescharacteristic
149#16811176C2214yescomplemented
150#16811171C2211yescharacteristic
151#16811171C2211yescharacteristic
152#16811171C2212yescomplemented
153#16811170C2211yescharacteristic
154#16811170C2211yescharacteristic
155#16811169C2211yescharacteristic
156C2×#13133217C2211yescharacteristic
157C2×#13133217C2212yescomplemented
158C4⋊Q8×D53C2212yescomplemented
159#16811160C2211yescharacteristic
160#16811160C2211yescharacteristic
161#16811159C2214yescomplemented
162#16811155C2211yescharacteristic
163#16811155C2211yescharacteristic
164#16811155C2212yes—
165#16811155C2212yes—
166#16811154C2212yes—
167#16811154C2212yes—
168#16811154C2218yes—
169#16811154C2214yescomplemented
170#16811153C2212yes—
171#16811153C2212yes—
172#16811153C2218yes—
173#16811152C2212yes—
174#16811152C2212yes—
175#16811151C2212yes—
176#16811151C2212yes—
177C2×#13133208C2212yes—
178C2×#13133208C2214yescomplemented
179#16811135C2211yescharacteristic
180#16811133C2212yes—
181#16811133C2212yes—
182#16811132C2212yes—
183#16811132C2212yes—
184#16811130C2211yescharacteristic
185#16811130C2212yes—
186C2×#13133197C2212yes—
187C2×#13133193C2212yes—
188#16811106C2212yes—
189#16811106C2212yes—
190#16811106C2214yescomplemented
191#16811104C2212yes—
192#16811102C2214yescomplemented
193#16811100C2214yescomplemented
194#16811099C2214yescomplemented
195#41×Dic53C2212yes—
196C4×#11719945C2211yescharacteristic
197C4×#11719945C2212yes—
198C4×#11719945C2212yes—
199C4×#11719947C2212yes—
200C4×#11719947C2212yes—
201C2×Q8×Dic53C2212yes—
202C2×#13133182C2212yes—
203C2×#13133175C2212yes—
204C2×C42×D53C2211yescharacteristic
205C53×#556C2212yescomplemented
206C53×#555C2212yescomplemented
207C53×#554C2212yescomplemented
208C53×#553C2214yes—
209C53×#548C2214yes—
210C53×#547C2212yescomplemented
211C53×#542C2214yescomplemented
212C53×#537C2212yes—
213C53×#533C2212yescomplemented
214C53×#532C2211yescharacteristic
215C53×#532C2212yescomplemented
216C2×C4⋊Q8×C53C2211yescharacteristic
217C53×#520C2212yes—
218C4×#41×C53C2211yescharacteristic
219C2×#11719945C2311yescharacteristic
220C2×#11719945C2312yes—
221C2×#11719945C2312yes—
222C2×#11719947C2312yes—
223C2×#11719947C2312yes—
224C2×#11719947C2314yes—
225C22×Dic106C2312yes—
226C22×Dic106C2314yes—
227C2×Q8×D53C2314yes—
228C22×C4×D53C2311yescharacteristic
229C22×C4×D53C2311yescharacteristic
230C22×C4×D53C2311yescharacteristic
231#13133217C2314yes—
232#13133217C2312yes—
233#13133217C2314yes—
234#13133217C2318yes—
235#13133217C2312yes—
236#13133217C2314yes—
237#13133217C2311yescharacteristic
238#13133217C2312yes—
239#13133217C2312yes—
240#13133217C2311yescharacteristic
241#13133216C2314yes—
242#13133216C2318yes—
243#13133216C2314yes—
244#13133216C2314yes—
245#13133216C2318yes—
246#13133216C2314yes—
247#13133216C2311yescharacteristic
248#13133216C2311yescharacteristic
249#13133215C2314yes—
250#13133215C2318yes—
251#13133215C2311yescharacteristic
252#13133213C2311yescharacteristic
253#13133212C2318yes—
254#13133212C2318yes—
255#13133212C2318yes—
256#13133212C2312yes—
257#13133212C2318yes—
258#13133212C2318yes—
259#13133212C2312yes—
260#13133211C2318yes—
261#13133210C2318yes—
262#13133210C2312yes—
263#13133210C2318yes—
264#13133210C2318yes—
265#13133210C2318yes—
266#13133210C2318yes—
267#13133210C2318yes—
268#13133210C2318yes—
269#13133210C2312yes—
270#13133210C2314yes—
271#13133210C2314yes—
272#13133209C2318yes—
273#13133209C2314yes—
274#13133209C2312yes—
275#13133208C2314yes—
276#13133208C2314yes—
277#13133208C2318yes—
278#13133208C2318yes—
279#13133208C2312yes—
280#13133208C2318yes—
281#13133208C2314yes—
282#13133208C2314yes—
283#13133208C2314yes—
284#13133208C2312yes—
285#13133208C2314yes—
286#13133208C2318yes—
287#13133208C2318yes—
288#13133208C2318yes—
289#13133208C2314yes—
290#13133208C2314yes—
291#13133208C2311yescharacteristic
292#13133208C2311yescharacteristic
293#13133207C2318yes—
294#13133207C2318yes—
295#13133207C2318yes—
296#13133207C2312yes—
297#13133207C2312yes—
298#13133206C2311yescharacteristic
299#13133205C2318yes—
300#13133204C2314yes—
301#13133204C2312yes—
302#13133204C2312yes—
303#13133204C2318yes—
304#13133204C2311yescharacteristic
305#13133203C2318yes—
306#13133203C2318yes—
307#13133203C2318yes—
308#13133203C2318yes—
309#13133203C2318yes—
310#13133203C2312yes—
311#13133203C2312yes—
312#13133202C2318yes—
313#13133202C2312yes—
314#13133202C2312yes—
315#13133201C2318yes—
316#13133201C2318yes—
317#13133201C2318yes—
318#13133201C2318yes—
319#13133201C2318yes—
320#13133201C2312yes—
321#13133200C2318yes—
322#13133199C2318yes—
323#13133199C2314yes—
324#13133199C2314yes—
325#13133199C2312yes—
326#13133199C2312yes—
327#13133198C2318yes—
328#13133198C2312yes—
329#13133198C2314yes—
330#13133197C2314yes—
331#13133197C2314yes—
332#13133197C2314yes—
333#13133197C2311yescharacteristic
334#13133197C2311yescharacteristic
335#13133197C2314yes—
336#13133197C2314yes—
337#13133197C2314yes—
338#13133197C2312yes—
339#13133197C2312yes—
340#13133196C2314yes—
341#13133196C2318yes—
342#13133196C2312yes—
343#13133196C2318yes—
344#13133196C2312yes—
345#13133196C2314yes—
346#13133196C2314yes—
347#13133196C2318yes—
348#13133195C2318yes—
349#13133195C2312yes—
350#13133195C2312yes—
351#13133194C2318yes—
352#13133194C2318yes—
353#13133194C2318yes—
354#13133194C2318yes—
355#13133194C2318yes—
356#13133194C2318yes—
357#13133194C2318yes—
358#13133194C2312yes—
359#13133194C2318yes—
360#13133194C2312yes—
361#13133193C2314yes—
362#13133193C2314yes—
363#13133193C2318yes—
364#13133193C2314yes—
365#13133193C2312yes—
366#13133193C2311yescharacteristic
367#13133193C2312yes—
368#13133193C2311yescharacteristic
369#13133193C2314yes—
370#13133193C2314yes—
371#13133193C2314yes—
372#13133192C2311yescharacteristic
373#13133192C2311yescharacteristic
374#13133191C2318yes—
375#13133191C2314yes—
376#13133190C2318yes—
377#13133190C2312yes—
378#13133190C2312yes—
379#13133189C2318yes—
380#13133189C2318yes—
381#13133189C2318yes—
382#13133189C2318yes—
383#13133189C2312yes—
384#13133189C2312yes—
385#13133188C2314yes—
386#13133188C2318yes—
387#13133188C2314yes—
388#13133188C2312yes—
389#13133188C2311yescharacteristic
390#13133188C2312yes—
391#13133188C2311yescharacteristic
392#13133188C2312yes—
393#13133188C2312yes—
394#13133187C2312yes—
395#13133185C2312yes—
396#13133185C2314yes—
397Q8×Dic53C2314yes—
398Q8×Dic53C2314yes—
399Q8×Dic53C2312yes—
400Q8×Dic53C2314yes—
401Q8×Dic53C2314yes—
402Q8×Dic53C2314yes—
403Q8×Dic53C2312yes—
404Q8×Dic53C2314yes—
405Q8×Dic53C2314yes—
406C4×Dic106C2314yes—
407C4×Dic106C2312yes—
408C4×Dic106C2314yes—
409C4×Dic106C2312yes—
410C4×Dic106C2318yes—
411C4×Dic106C2311yescharacteristic
412C4×Dic106C2312yes—
413C4×Dic106C2318yes—
414C4×Dic106C2312yes—
415C4×Dic106C2318yes—
416C4×Dic106C2312yes—
417C4×Dic106C2312yes—
418C4×Dic106C2311yescharacteristic
419#13133182C2314yes—
420#13133182C2314yes—
421#13133182C2314yes—
422#13133182C2314yes—
423#13133182C2314yes—
424#13133182C2318yes—
425#13133182C2314yes—
426#13133182C2314yes—
427#13133182C2312yes—
428#13133182C2312yes—
429C4×D212C2312yes—
430C4×D212C2311yescharacteristic
431C4×D212C2312yes—
432C4×D212C2311yescharacteristic
433C4×D212C2312yes—
434C4×D212C2312yes—
435D4×Dic53C2314yes—
436D4×Dic53C2318yes—
437D4×Dic53C2318yes—
438D4×Dic53C2318yes—
439D4×Dic53C2318yes—
440D4×Dic53C2314yes—
441D4×Dic53C2314yes—
442D4×Dic53C2312yes—
443D4×Dic53C2314yes—
444D4×Dic53C2314yes—
445D4×Dic53C2312yes—
446D4×Dic53C2312yes—
447D4×Dic53C2312yes—
448#13133179C2314yes—
449C4×C22⋊D53C2312yes—
450C4×C22⋊D53C2312yes—
451C4×C22⋊D53C2312yes—
452C4×C22⋊D53C2312yes—
453C4×C22⋊D53C2312yes—
454C4×C22⋊D53C2318yes—
455C4×C22⋊D53C2312yes—
456C4×C22⋊D53C2318yes—
457C4×C22⋊D53C2312yes—
458C4×C22⋊D53C2314yes—
459C4×C22⋊D53C2312yes—
460C4×C22⋊D53C2314yes—
461C4×C22⋊D53C2312yes—
462C4×C22⋊D53C2312yes—
463#13133177C2318yes—
464#13133177C2314yes—
465#13133177C2314yes—
466#13133176C2314yes—
467#13133176C2318yes—
468#13133176C2314yes—
469#13133176C2312yes—
470#13133176C2311yescharacteristic
471#13133176C2312yes—
472#13133176C2312yes—
473#13133176C2314yes—
474#13133175C2318yes—
475#13133175C2314yes—
476#13133175C2312yes—
477#13133175C2314yes—
478#13133175C2312yes—
479#13133175C2314yes—
480#13133175C2314yes—
481#13133175C2314yes—
482#13133175C2314yes—
483#13133174C2318yes—
484#13133174C2312yes—
485#13133174C2312yes—
486#13133174C2312yes—
487#13133174C2312yes—
488#13133174C2312yes—
489#13133173C2314yes—
490#13133173C2318yes—
491#13133173C2318yes—
492#13133173C2318yes—
493#13133173C2314yes—
494C2×C4⋊Dic53C2318yes—
495C2×C4⋊Dic53C2314yes—
496C2×C4⋊Dic53C2314yes—
497C2×C4⋊Dic53C2314yes—
498C2×C4⋊Dic53C2312yes—
499C2×C4⋊Dic53C2314yes—
500C2×C4⋊Dic53C2312yes—
501C2×#11719919C2318yes—
502C2×#11719919C2314yes—
503C4⋊C4×D53C2314yes—
504C4⋊C4×D53C2314yes—
505C2×#11719921C2314yes—
506C2×C4×Dic53C2311yescharacteristic
507C2×C4×Dic53C2311yescharacteristic
508C2×C4×Dic53C2311yescharacteristic
509C2×C4×Dic53C2314yes—
510C2×C4×Dic53C2314yes—
511C42×D53C2311yescharacteristic
512C42×D53C2311yescharacteristic
513C42×D53C2311yescharacteristic
514C42×D53C2311yescharacteristic
515C42×D53C2311yescharacteristic
516C42×D53C2311yescharacteristic
517C42×D53C2311yescharacteristic
518C42×D53C2311yescharacteristic
519C42×D53C2312yes—
520C2×#41×C53C2311yescharacteristic
521C2×#41×C53C2312yes—
522C2×#41×C53C2314yes—
523C22×Q8×C53C2312yes—
524C4⋊Q8×C53C2312yes—
525C4⋊Q8×C53C2312yes—
526C4⋊Q8×C53C2312yes—
527C4⋊Q8×C53C2312yes—
528C4⋊Q8×C53C2311yescharacteristic
529#127×C53C2311yescharacteristic
530#126×C53C2318yes—
531#125×C53C2314yes—
532#124×C53C2314yes—
533#124×C53C2312yes—
534#124×C53C2318yes—
535#123×C53C2318yes—
536C22⋊Q8×C53C2314yes—
537C22⋊Q8×C53C2314yes—
538C22⋊Q8×C53C2314yes—
539C22⋊Q8×C53C2318yes—
540#121×C53C2312yes—
541#121×C53C2314yes—
542#121×C53C2312yes—
543#121×C53C2314yes—
544#121×C53C2318yes—
545#121×C53C2314yes—
546C4×Q8×C53C2311yescharacteristic
547C4×Q8×C53C2311yescharacteristic
548C4×Q8×C53C2314yes—
549C4×Q8×C53C2314yes—
550C4×D4×C53C2314yes—
551C4×D4×C53C2312yes—
552C4×D4×C53C2312yes—
553C4×D4×C53C2311yescharacteristic
554C4×D4×C53C2311yescharacteristic
555C4×D4×C53C2312yes—
556C4×D4×C53C2314yes—
557C4×D4×C53C2318yes—
558C4×D4×C53C2312yes—
559#117×C53C2311yescharacteristic
560#117×C53C2312yes—
561#117×C53C2314yes—
562#117×C53C2314yes—
563C2×C4⋊C4×C53C2314yes—
564C2×C4⋊C4×C53C2312yes—
565C2×C4⋊C4×C53C2312yes—
566C2×C42×C53C2311yescharacteristic
567C2×C42×C53C2312yes—
568C23×D53C2411yescharacteristic
569#41×C53—24no—
570#41×C53—28no—
571#41×C53—48no—
572C2×Q8×C53—44no—
573C2×Q8×C53C2411yescharacteristic
574C2×Q8×C53C2412yes—
575C2×Q8×C53C2414yes—
576C2×Q8×C53C2414yes—
577C2×D4×C53C2412yes—
578C2×D4×C53C2412yes—
579C2×D4×C53C2414yes—
580C2×D4×C53C2411yescharacteristic
581C2×D4×C53C2412yes—
582C2×D4×C53C2412yes—
583C2×D4×C53C2418yes—
584C22×C4×C53C2411yescharacteristic
585C22×C4×C53C2412yes—
586C22×C4×C53C2412yes—
587C22×C4×C53C2411yescharacteristic
588C22×C4×C53C2412yes—
589C22×C4×C53C2414yes—
590C22×C4×C53C2414yes—
591C22×C4×C53C2418yes—
592C22×C4×C53C2411yescharacteristic
593C2×C22⋊D53C2412yes—
594C2×C22⋊D53C2414yes—
595C2×C22⋊D53C2414yes—
596C2×C22⋊D53C2418yes—
597C2×C22⋊D53C2412yes—
598C2×C22⋊D53C2412yes—
599C2×C22⋊D53C2412yes—
600C2×C22⋊D53C2412yes—
601C22×Dic53C2411yescharacteristic
602C22×Dic53C2411yescharacteristic
603C22×Dic53C2411yescharacteristic
604C22×Dic53C2414yes—
605C22×Dic53C2414yes—
606C22×Dic53C2414yes—
607C22×Dic53C2418yes—
608C22×Dic53C2418yes—
609Q8×D53—48no—
610#11719947—44no—
611#11719947—48no—
612#11719947—44no—
613#11719945—24no—
614#11719945—44no—
615#11719945—44no—
616C2×D212C2411yescharacteristic
617C2×D212C2412yes—
618C2×D212C2412yes—
619C2×C4×D53—24no—
620C2×C4×D53—42no—
621C2×C4×D53—42no—
622C2×C4×D53C2411yescharacteristic
623C2×C4×D53C2411yescharacteristic
624C2×C4×D53C2411yescharacteristic
625C2×C4×D53C2411yescharacteristic
626C2×C4×D53C2411yescharacteristic
627C2×C4×D53C2411yescharacteristic
628C2×C4×D53C2411yescharacteristic
629C2×C4×D53C2411yescharacteristic
630C2×C4×D53C2412yes—
631C2×C4×D53C2412yes—
632C2×C4×D53C2412yes—
633C2×C4×D53C2411yescharacteristic
634C2×C4×D53C2411yescharacteristic
635C2×C4×D53C2411yescharacteristic
636C2×C4×D53C2411yescharacteristic
637C2×C4×D53C2418yes—
638C2×Dic106—44no—
639C2×Dic106—48no—
640C2×Dic106C2411yescharacteristic
641C2×Dic106C2412yes—
642C2×Dic106C2414yes—
643C2×Dic106C2412yes—
644C2×Dic106C2414yes—
645C2×Dic106C2418yes—
646C2×Dic106C2412yes—
647C2×Dic106C2418yes—
648C2×Dic106C2412yes—
649C4⋊C4×C53C2411yescharacteristic
650C4⋊C4×C53C2414yes—
651C4⋊C4×C53C2414yes—
652C4⋊C4×C53C2414yes—
653C4⋊C4×C53C2418yes—
654C4⋊C4×C53C2414yes—
655C4⋊C4×C53C2411yescharacteristic
656C4⋊C4×C53C2412yes—
657C4⋊C4×C53C2412yes—
658C4⋊C4×C53C2412yes—
659C4⋊C4×C53C2412yes—
660C4⋊C4×C53C2418yes—
661C22⋊C4×C53C2412yes—
662C22⋊C4×C53C2418yes—
663C22⋊C4×C53C2412yes—
664C22⋊C4×C53C2412yes—
665C22⋊C4×C53C2418yes—
666C22⋊C4×C53C2418yes—
667C22⋊C4×C53C2414yes—
668C22⋊C4×C53C2414yes—
669C42×C53C2411yescharacteristic
670C42×C53C2412yes—
671C42×C53C2411yescharacteristic
672C42×C53C2412yes—
673C42×C53C2411yescharacteristic
674C42×C53C2411yescharacteristic
675C42×C53C2412yes—
676C42×C53C2418yes—
677C22⋊Dic53C2412yes—
678C22⋊Dic53C2412yes—
679C22⋊Dic53C2414yes—
680C22⋊Dic53C2414yes—
681C22⋊Dic53C2412yes—
682C22⋊Dic53C2414yes—
683C22⋊Dic53C2412yes—
684C22⋊Dic53C2412yes—
685C22⋊Dic53C2414yes—
686C22⋊Dic53C2414yes—
687C22⋊Dic53C2418yes—
688C22⋊Dic53C2418yes—
689C22⋊Dic53C2418yes—
690#11719921C2418yes—
691#11719921C2418yes—
692#11719921C2412yes—
693#11719921C2412yes—
694#11719921C2418yes—
695#11719921C2412yes—
696#11719921C2412yes—
697#11719921C2412yes—
698#11719921C2412yes—
699#11719921C2412yes—
700#11719921C2412yes—
701#11719921C2412yes—
702#11719921C2412yes—
703#11719921C2414yes—
704#11719921C2414yes—
705#11719921C2418yes—
706C4⋊Dic53C2412yes—
707C4⋊Dic53C2412yes—
708C4⋊Dic53C2411yescharacteristic
709C4⋊Dic53C2412yes—
710C4⋊Dic53C2412yes—
711C4⋊Dic53C2414yes—
712C4⋊Dic53C2414yes—
713C4⋊Dic53C2412yes—
714C4⋊Dic53C2414yes—
715C4⋊Dic53C2418yes—
716C4⋊Dic53C2418yes—
717C4⋊Dic53C2418yes—
718C4⋊Dic53C2418yes—
719C4⋊Dic53C2418yes—
720C4⋊Dic53C2418yes—
721C4⋊Dic53C2414yes—
722C4⋊Dic53C2411yescharacteristic
723C4⋊Dic53C2412yes—
724C4⋊Dic53C2414yes—
725C4⋊Dic53C2414yes—
726C4⋊Dic53C2412yes—
727C4⋊Dic53C2412yes—
728#11719919C2418yes—
729#11719919C2418yes—
730#11719919C2412yes—
731#11719919C2418yes—
732#11719919C2418yes—
733#11719919C2418yes—
734#11719919C2412yes—
735#11719919C2414yes—
736#11719919C2414yes—
737#11719919C2414yes—
738#11719919C2414yes—
739#11719919C2418yes—
740#11719919C2418yes—
741#11719919C2412yes—
742#11719919C2412yes—
743#11719919C2412yes—
744#11719919C2412yes—
745#11719919C2412yes—
746#11719919C2412yes—
747#11719919C2412yes—
748#11719919C2412yes—
749#11719919C2418yes—
750C4×Dic53C2411yescharacteristic
751C4×Dic53C2411yescharacteristic
752C4×Dic53C2411yescharacteristic
753C4×Dic53C2411yescharacteristic
754C4×Dic53C2411yescharacteristic
755C4×Dic53C2411yescharacteristic
756C4×Dic53C2411yescharacteristic
757C4×Dic53C2411yescharacteristic
758C4×Dic53C2411yescharacteristic
759C4×Dic53C2411yescharacteristic
760C4×Dic53C2411yescharacteristic
761C4×Dic53C2411yescharacteristic
762C4×Dic53C2412yes—
763C4×Dic53C2412yes—
764C4×Dic53C2412yes—
765C4×Dic53C2414yes—
766C4×Dic53C2418yes—
767C4×Dic53C2414yes—
768C4×Dic53C2418yes—
769C4×Dic53C2414yes—
770C4×Dic53C2418yes—
771C4×Dic53C2418yes—
772C4×Dic53C2418yes—
773C23×C53C2512yes—
774C23×C53C2514yes—
775C23×C53C2511yescharacteristic
776C22×D53—22no—
777C22×D53—41no—
778C22×D53—41no—
779C22×D53C2512yes—
780C22×D53C2511yescharacteristic
781C22×D53C2511yescharacteristic
782Q8×C53—22no—
783Q8×C53—24no—
784Q8×C53—28no—
785Q8×C53—44no—
786D4×C53—24no—
787D4×C53—28no—
788D4×C53—22no—
789D4×C53—24no—
790D4×C53—24no—
791D4×C53—24no—
792D4×C53—48no—
793C2×C4×C53—28no—
794C2×C4×C53—24no—
795C2×C4×C53—22no—
796C2×C4×C53—24no—
797C2×C4×C53—22no—
798C2×C4×C53—24no—
799C2×C4×C53—44no—
800C2×C4×C53—48no—
801C2×C4×C532−1+414yes—
802C2×C4×C53C2512yes—
803C2×C4×C53C2511yescharacteristic
804C2×C4×C53C2518yes—
805C2×C4×C53C2512yes—
806C2×C4×C53C2511yescharacteristic
807C2×C4×C53C2512yes—
808C2×C4×C53C2514yes—
809C2×C4×C53C2511yescharacteristic
810C2×C4×C53C2511yescharacteristic
811C2×C4×C53C2511yescharacteristic
812C2×C4×C53C2511yescharacteristic
813C22⋊D53—24no—
814C22⋊D53—42no—
815C22⋊D53—42no—
816C22⋊D53—42no—
817C22⋊D53—42no—
818C22⋊D53—44no—
819C22⋊D53—44no—
820C22⋊D53—48no—
821C2×Dic53—22no—
822C2×Dic53—44no—
823C2×Dic53—48no—
824C2×Dic53—41no—
825C2×Dic53—41no—
826C2×Dic53—44no—
827C2×Dic53—48no—
828C2×Dic53—44no—
829C2×Dic53C2512yes—
830C2×Dic53C2514yes—
831C2×Dic53C2518yes—
832C2×Dic53C2514yes—
833C2×Dic53C2511yescharacteristic
834C2×Dic53C2511yescharacteristic
835C2×Dic53C2512yes—
836C2×Dic53C2512yes—
837C2×Dic53C2511yescharacteristic
838C2×Dic53C2511yescharacteristic
839C2×Dic53C2511yescharacteristic
840C2×Dic53C2511yescharacteristic
841D212—22no—
842D212—42no—
843D212—42no—
844C4×D53—22no—
845C4×D53—22no—
846C4×D53—22no—
847C4×D53—22no—
848C4×D53—24no—
849C4×D53—22no—
850C4×D53—22no—
851C4×D53—22no—
852C4×D53—22no—
853C4×D53—24no—
854C4×D53—24no—
855C4×D53—41no—
856C4×D53—41no—
857C4×D53—41no—
858C4×D53—41no—
859C4×D53—48no—
860Dic106—22no—
861Dic106—28no—
862Dic106—24no—
863Dic106—24no—
864Dic106—48no—
865Dic106—44no—
866Dic106—42no—
867Dic106—42no—
868Dic106—48no—
869#62838—531nomaximal, Sylow
870C22×C53—21no—
871C22×C53—21no—
872C22×C53—22no—
873C22×C53—24no—
874C22×C53—22no—
875C22×C53—24no—
876C22×C53—24no—
877C22×C53—22no—
878C22×C53C2×2−1+412yes—
879C22×C53C2611yescharacteristic
880C2×D53—21no—
881C2×D53—21no—
882C2×D53—22no—
883C2×D53—22no—
884C2×D53—21no—
885C2×D53—21no—
886C2×D53—21no—
887C2×D53—21no—
888C2×D53—22no—
889C2×D53—44no—
890C4×C53—24no—
891C4×C53—22no—
892C4×C53—22no—
893C4×C53—21no—
894C4×C53—28no—
895C4×C53—22no—
896C4×C53—21no—
897C4×C53C2×2−1+412yes—
898C4×C53C2×2−1+412yes—
899C4×C53#58512yes—
900C4×C53#58512yes—
901Dic53—22no—
902Dic53—21no—
903Dic53—21no—
904Dic53—24no—
905Dic53—24no—
906Dic53—28no—
907Dic53—22no—
908Dic53—21no—
909Dic53—21no—
910Dic53—22no—
911Dic53—21no—
912Dic53—21no—
913#3565—534no—
914#3565—534no—
915#3555—532no—
916#3555—532no—
917#3547—532no—
918#3547—532no—
919#3541—534no—
920#3541—534no—
921#3518—532no—
922#3518—532no—
923#3516—534no—
924#3516—534no—
925#3515—532no—
926#3515—532no—
927#3512—532no—
928#3511—531no—
929#3511—532no—
930#3511—532no—
931#3511D5311yescharacteristic, complemented
932#3509—532no—
933#3509—532no—
934#3504—532no—
935#3503—531no—
936#3503—531no—
937#3493—532no—
938#3493—532no—
939#3444—531no—
940#3444—531no—
941C2×#533—531no—
942C2×C53—22no—
943C2×C53—42no—
944C2×C53—44no—
945C2×C53C22×2−1+411yescharacteristic
946C2×C53C2×#58511yescharacteristic
947C2×C53C2×#58511yescharacteristic
948D53—42no—
949D53—41no—
950D53—41no—
951#563—538no—
952#563—538no—
953#562—538no—
954#562—538no—
955Q82—532no—
956Q82—532no—
957#557—532no—
958#557—534no—
959#557—534no—
960#557—532no—
961#557—534no—
962#557—534no—
963#556—538no—
964#556—534no—
965#556—538no—
966#556—534no—
967#556—534no—
968#556—534no—
969#556—534no—
970#556—534no—
971#556—532no—
972#556—534no—
973#556—534no—
974#556C2×D5312yescomplemented
975#555—534no—
976#555—534no—
977#555—534no—
978#555—532no—
979#555—534no—
980#555C2×D5312yescomplemented
981#554—532no—
982#554—534no—
983#554—538no—
984#554—532no—
985#554—534no—
986#554—532no—
987#554—538no—
988#554—534no—
989#554—534no—
990#554C2×D5312yescomplemented
991#553—538no—
992#553—534no—
993#553—534no—
994#553—534no—
995#553—534no—
996#553—538no—
997#553—534no—
998#553—534no—
999#553—534no—
1000#553C2×D5314yes—
1001#552—534no—
1002#552—538no—
1003#552—534no—
1004#552—534no—
1005#552—534no—
1006#552—534no—
1007#552—534no—
1008#552—534no—
1009#552—538no—
1010#552—534no—
1011#552—534no—
1012#552—534no—
1013D4×Q8—534no—
1014D4×Q8—532no—
1015D4×Q8—534no—
1016D4×Q8—532no—
1017#548—534no—
1018#548—534no—
1019#548—534no—
1020#548—534no—
1021#548—534no—
1022#548C2×D5314yes—
1023#547—534no—
1024#547—534no—
1025#547—532no—
1026#547C2×D5312yescomplemented
1027#544—534no—
1028#544—532no—
1029#544—534no—
1030#544—534no—
1031#544—532no—
1032#544—534no—
1033#542—538no—
1034#542—534no—
1035#542—534no—
1036#542—534no—
1037#542—538no—
1038#542—538no—
1039#542—538no—
1040#542—534no—
1041#542—534no—
1042#542C2×D5314yescomplemented
1043#541—538no—
1044#541—534no—
1045#541—534no—
1046#541—534no—
1047#541—534no—
1048#541—538no—
1049#541—534no—
1050#540—534no—
1051#539—538no—
1052#539—538no—
1053#538—538no—
1054#538—538no—
1055#537—532no—
1056#537—534no—
1057#537—534no—
1058#537C2×D5312yes—
1059#536—534no—
1060#536—534no—
1061#533—532no—
1062#533—532no—
1063#533—532no—
1064#533—532no—
1065#533—532no—
1066#533—532no—
1067#533—532no—
1068#533—532no—
1069#533—531no—
1070#533—531no—
1071#533—532no—
1072#533—532no—
1073#533—531no—
1074#533—531no—
1075#533—531no—
1076#533—534no—
1077#533—531no—
1078#533—532no—
1079#533C2×D5312yescomplemented
1080#532—531no—
1081#532—531no—
1082#532—531no—
1083#532—532no—
1084#532—531no—
1085#532—531no—
1086#532C2×D5311yescharacteristic
1087#532C2×D5312yescomplemented
1088C2×C4⋊Q8—532no—
1089C2×C4⋊Q8—531no—
1090C2×C4⋊Q8—532no—
1091C2×C4⋊Q8C2×D5311yescharacteristic
1092#529—532no—
1093#529—532no—
1094#529—534no—
1095#529—532no—
1096#529—532no—
1097#529—538no—
1098#529—534no—
1099#529—531no—
1100#529—531no—
1101#529—532no—
1102#529—532no—
1103#529—531no—
1104#529—531no—
1105#529—532no—
1106#529—532no—
1107#529—538no—
1108#529—532no—
1109#529—532no—
1110C2×#125—532no—
1111C2×#125—534no—
1112#525—531no—
1113#525—532no—
1114#525—532no—
1115#525—532no—
1116#525—532no—
1117#525—532no—
1118#525—531no—
1119C2×C22⋊Q8—532no—
1120C2×C22⋊Q8—532no—
1121#520—532no—
1122#520—532no—
1123#520—534no—
1124#520—534no—
1125#520—532no—
1126#520C2×D5312yes—
1127#519—534no—
1128#519—534no—
1129C4×#41—532no—
1130C4×#41—532no—
1131C4×#41—532no—
1132C4×#41—531no—
1133C4×#41—532no—
1134C4×#41—532no—
1135C4×#41C2×D5311yescharacteristic
1136C2×C4×Q8—532no—
1137C2×C4×Q8—532no—
1138C2×#117—532no—
1139C22×C42—531no—
1140C53#6283811yescharacteristic, complemented, Sylow
1141C2×#41—532no—
1142C2×#41—532no—
1143C2×#41—534no—
1144C2×#41—531no—
1145C2×#41—532no—
1146C2×#41—532no—
1147C2×#41C22×D5312yes—
1148C2×#41C22×D5311yescharacteristic
1149C2×#41C22×D5314yes—
1150C22×Q8—534no—
1151C22×Q8—532no—
1152C22×Q8—534no—
1153C22×Q8C22×D5312yes—
1154C23×C4—531no—
1155C23×C4—531no—
1156C23×C4—531no—
1157C4⋊Q8—534no—
1158C4⋊Q8—531no—
1159C4⋊Q8—538no—
1160C4⋊Q8—534no—
1161C4⋊Q8—534no—
1162C4⋊Q8—531no—
1163C4⋊Q8—531no—
1164C4⋊Q8—534no—
1165C4⋊Q8—534no—
1166C4⋊Q8—538no—
1167C4⋊Q8—538no—
1168C4⋊Q8—531no—
1169C4⋊Q8—532no—
1170C4⋊Q8—531no—
1171C4⋊Q8—532no—
1172C4⋊Q8—532no—
1173C4⋊Q8—532no—
1174C4⋊Q8—534no—
1175C4⋊Q8—534no—
1176C4⋊Q8—534no—
1177C4⋊Q8—538no—
1178C4⋊Q8C22×D5312yes—
1179C4⋊Q8C22×D5312yes—
1180C4⋊Q8C22×D5312yes—
1181C4⋊Q8C22×D5312yes—
1182C4⋊Q8C22×D5311yescharacteristic
1183#127—531no—
1184#127C22×D5311yescharacteristic
1185#126—532no—
1186#126—532no—
1187#126—538no—
1188#126—538no—
1189#126—538no—
1190#126—538no—
1191#126—538no—
1192#126—534no—
1193#126—534no—
1194#126—532no—
1195#126—532no—
1196#126—538no—
1197#126—538no—
1198#126—538no—
1199#126—538no—
1200#126—538no—
1201#126—538no—
1202#126—538no—
1203#126—538no—
1204#126C22×D5318yes—
1205#125—531no—
1206#125—534no—
1207#125—534no—
1208#125—534no—
1209#125—534no—
1210#125—538no—
1211#125—538no—
1212#125—534no—
1213#125—534no—
1214#125—531no—
1215#125—532no—
1216#125—532no—
1217#125—532no—
1218#125—532no—
1219#125—538no—
1220#125—538no—
1221#125—534no—
1222#125—534no—
1223#125—538no—
1224#125—538no—
1225#125—538no—
1226#125—538no—
1227#125—538no—
1228#125—532no—
1229#125—534no—
1230#125—538no—
1231#125C22×D5314yes—
1232#124—531no—
1233#124—531no—
1234#124—532no—
1235#124—532no—
1236#124—538no—
1237#124—534no—
1238#124—532no—
1239#124—532no—
1240#124—538no—
1241#124—538no—
1242#124—538no—
1243#124—538no—
1244#124—538no—
1245#124—538no—
1246#124C22×D5312yes—
1247#124C22×D5314yes—
1248#124C22×D5318yes—
1249#123—532no—
1250#123—534no—
1251#123—538no—
1252#123—538no—
1253#123—532no—
1254#123—532no—
1255#123—538no—
1256#123—532no—
1257#123—532no—
1258#123—532no—
1259#123—534no—
1260#123—534no—
1261#123—538no—
1262#123—538no—
1263#123—538no—
1264#123—538no—
1265#123—538no—
1266#123—538no—
1267#123C22×D5318yes—
1268C22⋊Q8—534no—
1269C22⋊Q8—534no—
1270C22⋊Q8—534no—
1271C22⋊Q8—534no—
1272C22⋊Q8—531no—
1273C22⋊Q8—532no—
1274C22⋊Q8—532no—
1275C22⋊Q8—531no—
1276C22⋊Q8—534no—
1277C22⋊Q8—534no—
1278C22⋊Q8—538no—
1279C22⋊Q8—532no—
1280C22⋊Q8—532no—
1281C22⋊Q8—534no—
1282C22⋊Q8—538no—
1283C22⋊Q8—534no—
1284C22⋊Q8—534no—
1285C22⋊Q8—538no—
1286C22⋊Q8—538no—
1287C22⋊Q8—534no—
1288C22⋊Q8—534no—
1289C22⋊Q8—534no—
1290C22⋊Q8—534no—
1291C22⋊Q8—532no—
1292C22⋊Q8—532no—
1293C22⋊Q8—531no—
1294C22⋊Q8—531no—
1295C22⋊Q8—532no—
1296C22⋊Q8—532no—
1297C22⋊Q8—534no—
1298C22⋊Q8—534no—
1299C22⋊Q8—538no—
1300C22⋊Q8—532no—
1301C22⋊Q8—532no—
1302C22⋊Q8—538no—
1303C22⋊Q8—538no—
1304C22⋊Q8—538no—
1305C22⋊Q8—538no—
1306C22⋊Q8—538no—
1307C22⋊Q8—538no—
1308C22⋊Q8—538no—
1309C22⋊Q8—538no—
1310C22⋊Q8C22×D5314yes—
1311C22⋊Q8C22×D5314yes—
1312C22⋊Q8C22×D5314yes—
1313C22⋊Q8C22×D5318yes—
1314#121—532no—
1315#121—532no—
1316#121—531no—
1317#121—532no—
1318#121—532no—
1319#121—532no—
1320#121—532no—
1321#121—531no—
1322#121—538no—
1323#121—534no—
1324#121—534no—
1325#121—538no—
1326#121—538no—
1327#121—538no—
1328#121—538no—
1329#121—534no—
1330#121—538no—
1331#121—531no—
1332#121—531no—
1333#121—532no—
1334#121—532no—
1335#121—538no—
1336#121C22×D5312yes—
1337#121C22×D5312yes—
1338#121C22×D5318yes—
1339#121C22×D5314yes—
1340#121C22×D5314yes—
1341#121C22×D5314yes—
1342#120—532no—
1343#120—534no—
1344#120—532no—
1345C4×Q8—534no—
1346C4×Q8—534no—
1347C4×Q8—534no—
1348C4×Q8—534no—
1349C4×Q8—532no—
1350C4×Q8—532no—
1351C4×Q8—534no—
1352C4×Q8—534no—
1353C4×Q8—534no—
1354C4×Q8—534no—
1355C4×Q8—534no—
1356C4×Q8—534no—
1357C4×Q8—534no—
1358C4×Q8—532no—
1359C4×Q8—532no—
1360C4×Q8—538no—
1361C4×Q8—534no—
1362C4×Q8—534no—
1363C4×Q8—534no—
1364C4×Q8—532no—
1365C4×Q8—532no—
1366C4×Q8—532no—
1367C4×Q8—532no—
1368C4×Q8—531no—
1369C4×Q8—532no—
1370C4×Q8—532no—
1371C4×Q8—531no—
1372C4×Q8—538no—
1373C4×Q8—534no—
1374C4×Q8—538no—
1375C4×Q8—538no—
1376C4×Q8—534no—
1377C4×Q8C22×D5311yescharacteristic
1378C4×Q8C22×D5311yescharacteristic
1379C4×Q8C22×D5314yes—
1380C4×Q8C22×D5314yes—
1381C4×D4—532no—
1382C4×D4—532no—
1383C4×D4—534no—
1384C4×D4—534no—
1385C4×D4—532no—
1386C4×D4—532no—
1387C4×D4—538no—
1388C4×D4—538no—
1389C4×D4—538no—
1390C4×D4—534no—
1391C4×D4—538no—
1392C4×D4—534no—
1393C4×D4—534no—
1394C4×D4—532no—
1395C4×D4—532no—
1396C4×D4—532no—
1397C4×D4—532no—
1398C4×D4—532no—
1399C4×D4—534no—
1400C4×D4—534no—
1401C4×D4—532no—
1402C4×D4—532no—
1403C4×D4—532no—
1404C4×D4—532no—
1405C4×D4—532no—
1406C4×D4—538no—
1407C4×D4—538no—
1408C4×D4—534no—
1409C4×D4—534no—
1410C4×D4—534no—
1411C4×D4—538no—
1412C4×D4—532no—
1413C4×D4—532no—
1414C4×D4—532no—
1415C4×D4—532no—
1416C4×D4—531no—
1417C4×D4—531no—
1418C4×D4C22×D5312yes—
1419C4×D4C22×D5312yes—
1420C4×D4C22×D5312yes—
1421C4×D4C22×D5312yes—
1422C4×D4C22×D5311yescharacteristic
1423C4×D4C22×D5311yescharacteristic
1424C4×D4C22×D5314yes—
1425C4×D4C22×D5318yes—
1426C4×D4C22×D5314yes—
1427#117—532no—
1428#117—531no—
1429#117—532no—
1430#117—532no—
1431#117—534no—
1432#117—538no—
1433#117—534no—
1434#117—534no—
1435#117—534no—
1436#117—534no—
1437#117—534no—
1438#117—534no—
1439#117—532no—
1440#117—532no—
1441#117—538no—
1442#117—534no—
1443#117—534no—
1444#117—534no—
1445#117—534no—
1446#117—538no—
1447#117—538no—
1448#117—538no—
1449#117—532no—
1450#117—532no—
1451#117—532no—
1452#117—532no—
1453#117—532no—
1454#117—538no—
1455#117C22×D5311yescharacteristic
1456#117C22×D5312yes—
1457#117C22×D5314yes—
1458#117C22×D5314yes—
1459C2×C4⋊C4—532no—
1460C2×C4⋊C4—534no—
1461C2×C4⋊C4—534no—
1462C2×C4⋊C4—532no—
1463C2×C4⋊C4—538no—
1464C2×C4⋊C4—538no—
1465C2×C4⋊C4—534no—
1466C2×C4⋊C4—534no—
1467C2×C4⋊C4—534no—
1468C2×C4⋊C4—534no—
1469C2×C4⋊C4—534no—
1470C2×C4⋊C4C22×D5312yes—
1471C2×C4⋊C4C22×D5312yes—
1472C2×C4⋊C4C22×D5314yes—
1473C2×C22⋊C4—534no—
1474C2×C42—534no—
1475C2×C42—531no—
1476C2×C42—531no—
1477C2×C42—534no—
1478C2×C42—531no—
1479C2×C42—532no—
1480C2×C42—531no—
1481C2×C42—531no—
1482C2×C42—531no—
1483C2×C42—531no—
1484C2×C42—531no—
1485C2×C42—531no—
1486C2×C42—531no—
1487C2×C42—531no—
1488C2×C42C22×D5312yes—
1489C2×C42C22×D5311yescharacteristic
1490C24—531no—
1491#41—28no—
1492#41—24no—
1493#41—48no—
1494#41—1064no—
1495#41—2124no—
1496#41—2124no—
1497#41—2124no—
1498#41—2124no—
1499#41—2128no—
1500C2×Q8—44no—
1501C2×Q8—531no—
1502C2×Q8—532no—
1503C2×Q8—534no—
1504C2×Q8—532no—
1505C2×Q8—534no—
1506C2×Q8—532no—
1507C2×Q8—532no—
1508C2×Q8—538no—
1509C2×Q8—538no—
1510C2×Q8—2124no—
1511C2×Q8—2128no—
1512C2×Q8—2128no—
1513C2×Q8C23×D5312yes—
1514C2×Q8C23×D5311yescharacteristic
1515C2×Q8C23×D5314yes—
1516C2×Q8C23×D5314yes—
1517C2×D4—532no—
1518C2×D4—532no—
1519C2×D4—534no—
1520C2×D4—534no—
1521C2×D4—532no—
1522C2×D4—538no—
1523C2×D4—532no—
1524C2×D4—532no—
1525C2×D4—531no—
1526C2×D4—532no—
1527C2×D4—532no—
1528C2×D4C23×D5314yes—
1529C2×D4C23×D5312yes—
1530C2×D4C23×D5312yes—
1531C2×D4C23×D5311yescharacteristic
1532C2×D4C23×D5312yes—
1533C2×D4C23×D5312yes—
1534C2×D4C23×D5318yes—
1535C22×C4—531no—
1536C22×C4—531no—
1537C22×C4—531no—
1538C22×C4—534no—
1539C22×C4—534no—
1540C22×C4—534no—
1541C22×C4—538no—
1542C22×C4—538no—
1543C22×C4—531no—
1544C22×C4—531no—
1545C22×C4—531no—
1546C22×C4—531no—
1547C22×C4—531no—
1548C22×C4—531no—
1549C22×C4—531no—
1550C22×C4—531no—
1551C22×C4—532no—
1552C22×C4—532no—
1553C22×C4—532no—
1554C22×C4—531no—
1555C22×C4—531no—
1556C22×C4—531no—
1557C22×C4—531no—
1558C22×C4—538no—
1559C22×C4—1064no—
1560C22×C4—2122no—
1561C22×C4—2122no—
1562C22×C4C23×D5311yescharacteristic
1563C22×C4C23×D5311yescharacteristic
1564C22×C4C23×D5314yes—
1565C22×C4C23×D5312yes—
1566C22×C4C23×D5312yes—
1567C22×C4C23×D5312yes—
1568C22×C4C23×D5314yes—
1569C22×C4C23×D5318yes—
1570C22×C4C23×D5311yescharacteristic
1571C4⋊C4—531no—
1572C4⋊C4—532no—
1573C4⋊C4—532no—
1574C4⋊C4—534no—
1575C4⋊C4—534no—
1576C4⋊C4—532no—
1577C4⋊C4—532no—
1578C4⋊C4—534no—
1579C4⋊C4—532no—
1580C4⋊C4—532no—
1581C4⋊C4—538no—
1582C4⋊C4—538no—
1583C4⋊C4—538no—
1584C4⋊C4—538no—
1585C4⋊C4—538no—
1586C4⋊C4—538no—
1587C4⋊C4—538no—
1588C4⋊C4—538no—
1589C4⋊C4—538no—
1590C4⋊C4—538no—
1591C4⋊C4—538no—
1592C4⋊C4—534no—
1593C4⋊C4—531no—
1594C4⋊C4—532no—
1595C4⋊C4—532no—
1596C4⋊C4—534no—
1597C4⋊C4—534no—
1598C4⋊C4—532no—
1599C4⋊C4—532no—
1600C4⋊C4—532no—
1601C4⋊C4—532no—
1602C4⋊C4—532no—
1603C4⋊C4—532no—
1604C4⋊C4—532no—
1605C4⋊C4—532no—
1606C4⋊C4—532no—
1607C4⋊C4—534no—
1608C4⋊C4—534no—
1609C4⋊C4—534no—
1610C4⋊C4—534no—
1611C4⋊C4—532no—
1612C4⋊C4—538no—
1613C4⋊C4—538no—
1614C4⋊C4—538no—
1615C4⋊C4C23×D5314yes—
1616C4⋊C4C23×D5314yes—
1617C4⋊C4C23×D5311yescharacteristic
1618C4⋊C4C23×D5314yes—
1619C4⋊C4C23×D5318yes—
1620C4⋊C4C23×D5314yes—
1621C4⋊C4C23×D5312yes—
1622C4⋊C4C23×D5312yes—
1623C4⋊C4C23×D5318yes—
1624C4⋊C4C23×D5311yescharacteristic
1625C4⋊C4C23×D5312yes—
1626C4⋊C4C23×D5312yes—
1627C22⋊C4—532no—
1628C22⋊C4—532no—
1629C22⋊C4—534no—
1630C22⋊C4—534no—
1631C22⋊C4—532no—
1632C22⋊C4—534no—
1633C22⋊C4—532no—
1634C22⋊C4—532no—
1635C22⋊C4—534no—
1636C22⋊C4—534no—
1637C22⋊C4—538no—
1638C22⋊C4—538no—
1639C22⋊C4—538no—
1640C22⋊C4—538no—
1641C22⋊C4—538no—
1642C22⋊C4—532no—
1643C22⋊C4—532no—
1644C22⋊C4—538no—
1645C22⋊C4—532no—
1646C22⋊C4—532no—
1647C22⋊C4—532no—
1648C22⋊C4—532no—
1649C22⋊C4—534no—
1650C22⋊C4—534no—
1651C22⋊C4—532no—
1652C22⋊C4—532no—
1653C22⋊C4—538no—
1654C22⋊C4—532no—
1655C22⋊C4—532no—
1656C22⋊C4C23×D5318yes—
1657C22⋊C4C23×D5318yes—
1658C22⋊C4C23×D5314yes—
1659C22⋊C4C23×D5314yes—
1660C22⋊C4C23×D5312yes—
1661C22⋊C4C23×D5318yes—
1662C22⋊C4C23×D5312yes—
1663C22⋊C4C23×D5312yes—
1664C42—531no—
1665C42—531no—
1666C42—531no—
1667C42—531no—
1668C42—531no—
1669C42—531no—
1670C42—531no—
1671C42—531no—
1672C42—531no—
1673C42—531no—
1674C42—531no—
1675C42—531no—
1676C42—534no—
1677C42—534no—
1678C42—538no—
1679C42—538no—
1680C42—532no—
1681C42—532no—
1682C42—534no—
1683C42—532no—
1684C42—538no—
1685C42—538no—
1686C42—538no—
1687C42C23×D5311yescharacteristic
1688C42C23×D5311yescharacteristic
1689C42C23×D5311yescharacteristic
1690C42C23×D5311yescharacteristic
1691C42C23×D5312yes—
1692C42C23×D5312yes—
1693C42C23×D5312yes—
1694C42C23×D5318yes—
1695C23—531no—
1696C23—531no—
1697C23—532no—
1698C23—1062no—
1699C23—2121no—
1700C23—2121no—
1701C23C24×D5312yes—
1702C23C24×D5314yes—
1703C23C24×D5311yescharacteristic
1704Q8—22no—
1705Q8—24no—
1706Q8—28no—
1707Q8—44no—
1708Q8—1062no—
1709Q8—1064no—
1710Q8—1068no—
1711Q8—1064no—
1712Q8—2128no—
1713Q8—2124no—
1714Q8—2128no—
1715Q8—2122no—
1716Q8—2122no—
1717D4—28no—
1718D4—24no—
1719D4—22no—
1720D4—24no—
1721D4—24no—
1722D4—24no—
1723D4—48no—
1724D4—1064no—
1725D4—1062no—
1726D4—2122no—
1727D4—2122no—
1728D4—2122no—
1729D4—2122no—
1730D4—2124no—
1731D4—2122no—
1732D4—2122no—
1733D4—2124no—
1734D4—2128no—
1735C2×C4—28no—
1736C2×C4—24no—
1737C2×C4—22no—
1738C2×C4—24no—
1739C2×C4—22no—
1740C2×C4—24no—
1741C2×C4—44no—
1742C2×C4—48no—
1743C2×C4—531no—
1744C2×C4—531no—
1745C2×C4—531no—
1746C2×C4—531no—
1747C2×C4—532no—
1748C2×C4—532no—
1749C2×C4—534no—
1750C2×C4—534no—
1751C2×C4—538no—
1752C2×C4—531no—
1753C2×C4—531no—
1754C2×C4—532no—
1755C2×C4—1062no—
1756C2×C4—1062no—
1757C2×C4—1062no—
1758C2×C4—1062no—
1759C2×C4—1062no—
1760C2×C4—1064no—
1761C2×C4—1062no—
1762C2×C4—1062no—
1763C2×C4—1064no—
1764C2×C4—1062no—
1765C2×C4—1062no—
1766C2×C4—1064no—
1767C2×C4—2121no—
1768C2×C4—2121no—
1769C2×C4—2121no—
1770C2×C4—2121no—
1771C2×C4—2128no—
1772C2×C4—2121no—
1773C2×C4—2121no—
1774C2×C4—2124no—
1775C2×C4—2128no—
1776C2×C4—2124no—
1777C2×C4—2124no—
1778C2×C4—2128no—
1779C2×C4#1313326414yes—
1780C2×C4C24×D5314yes—
1781C2×C4C24×D5312yes—
1782C2×C4C24×D5318yes—
1783C2×C4C24×D5311yescharacteristic
1784C2×C4C24×D5311yescharacteristic
1785C2×C4C24×D5312yes—
1786C2×C4C24×D5312yes—
1787C2×C4C24×D5311yescharacteristic
1788C2×C4C24×D5311yescharacteristic
1789C2×C4C24×D5311yescharacteristic
1790C2×C4C24×D5311yescharacteristic
1791C22—21no—
1792C22—21no—
1793C22—22no—
1794C22—24no—
1795C22—22no—
1796C22—24no—
1797C22—22no—
1798C22—24no—
1799C22—1061no—
1800C22—1061no—
1801C22—1062no—
1802C22—1062no—
1803C22—1061no—
1804C22—1061no—
1805C22—1061no—
1806C22—1061no—
1807C22—1062no—
1808C22—2124no—
1809C22C2×#1313326412yes—
1810C22C25×D5311yescharacteristic
1811C4—24no—
1812C4—22no—
1813C4—22no—
1814C4—21no—
1815C4—28no—
1816C4—21no—
1817C4—22no—
1818C4—1061no—
1819C4—1061no—
1820C4—1062no—
1821C4—1061no—
1822C4—1061no—
1823C4—1062no—
1824C4—1064no—
1825C4—1061no—
1826C4—1062no—
1827C4—1061no—
1828C4—1064no—
1829C4—1068no—
1830C4C2×#1313326412yes—
1831C4C2×#1313326412yes—
1832C4#1681145812yes—
1833C4#1681146012yes—
1834C2—22no—
1835C2—42no—
1836C2—44no—
1837C2—2121no—
1838C2—2121no—
1839C2—2122no—
1840C2C22×#1313326411yescharacteristic
1841C2C2×#1681145811yescharacteristic
1842C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3511C2
hypercenter#3511D53
hypocenterC53#62838
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #20289366C2semidirect
2. #20289362C2semidirect
3. #20289206C2semidirect
4. #20289191C2semidirect
5. #20289107C2semidirect
6. #20289092C2semidirect
7. #20289002C2semidirect
8. #20288994C2semidirect
9. #20288731C2semidirect
10. #20288729C2semidirect
11. #20288699C2semidirect
12. #20288697C2semidirect
13. #20288694C2semidirect
14. #20288684C2semidirect
15. #20288636C2semidirect
16. #20288622C2semidirect
17. #20288622C2semidirect
18. #20288616C2semidirect
19. #20288602C2semidirect
20. #20288594C2semidirect
21. #20288537C2semidirect
22. #20288534C2semidirect
23. #20288531C2semidirect
24. #20288434C2semidirect
25. #20288428C2semidirect
26. #20288010C2semidirect
27. #20288008C2semidirect
28. C2×#16811178C2semidirect
29. C53×#3511C2semidirect
34. Q8×Dic106C22semidirect
35. #16811353C22semidirect
36. #16811352C22semidirect
37. #16811352C22semidirect
38. #16811352C22semidirect
39. #16811350C22semidirect
40. #16811349C22semidirect
41. #16811348C22semidirect
46. #16811343C22semidirect
47. #16811343C22semidirect
48. #16811342C22semidirect
49. #16811342C22semidirect
52. #16811340C22semidirect
54. #16811338C22semidirect
58. #16811334C22semidirect
60. #16811332C22semidirect
63. #16811330C22semidirect
64. #16811330C22semidirect
65. #16811330C22semidirect
71. #16811325C22semidirect
74. #16811320C22semidirect
79. #16811315C22semidirect
80. #16811315C22semidirect
81. #16811315C22semidirect
83. #16811312C22semidirect
85. #16811310C22semidirect
87. #16811307C22semidirect
89. D4×Dic106C22semidirect
90. #16811288C22semidirect
93. #16811280C22semidirect
96. #16811279C22semidirect
98. #16811277C22semidirect
101. #16811254C22semidirect
103. #16811251C22semidirect
104. #16811251C22semidirect
105. #16811250C22semidirect
107. #16811242C22semidirect
108. #16811242C22semidirect
109. #16811242C22semidirect
110. #16811241C22semidirect
111. #16811240C22semidirect
116. #16811236C22semidirect
117. #16811233C22semidirect
118. #16811233C22semidirect
119. #16811233C22semidirect
121. #16811230C22semidirect
122. #16811226C22semidirect
133. #16811180C22semidirect
144. #16811178C22semidirect
145. #16811178C22semidirect
149. #16811176C22semidirect
152. #16811171C22semidirect
157. C2×#13133217C22semidirect
158. C4⋊Q8×D53C22semidirect
161. #16811159C22semidirect
169. #16811154C22semidirect
178. C2×#13133208C22semidirect
190. #16811106C22semidirect
192. #16811102C22semidirect
193. #16811100C22semidirect
194. #16811099C22semidirect
205. C53×#556C22semidirect
206. C53×#555C22semidirect
207. C53×#554C22semidirect
210. C53×#547C22semidirect
211. C53×#542C22semidirect
213. C53×#533C22semidirect
215. C53×#532C22semidirect
931. #3511D53semidirect
974. #556C2×D53semidirect
980. #555C2×D53semidirect
990. #554C2×D53semidirect
1026. #547C2×D53semidirect
1042. #542C2×D53semidirect
1079. #533C2×D53semidirect
1087. #532C2×D53semidirect
1140. C53#62838semidirect

Maximal subgroups

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

subgroupindex
#202893662
#202893622
#202892062
#202891912
#202891072
#202890922
#202890022
#202889942
#202887312
#202887292
#202886992
#202886972
#202886942
#202886842
#202886362
#202886222
#202886162
#202886022
#202885942
#202885372
#202885342
#202885312
#202884342
#202884282
#202880102
#202880082
C2×#168111782
C53×#35112
#6283853