Finite Group Databasebeta

← #28292727

Subgroups — #28292727

Order 13568.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289013C214yesmaximal, complemented
2#20288994C214yesmaximal, complemented
3#20288956C214yesmaximal, complemented
4#20288931C214yesmaximal, complemented
5#20288914C218yesmaximal, complemented
6#20288765C214yesmaximal, complemented
7#20288757C214yesmaximal, complemented
8#20288551C214yesmaximal, complemented
9#20288510C214yesmaximal, complemented
10#20288464C212yesmaximal, complemented
11#20288457C212yesmaximal, complemented
12#20288421C212yesmaximal, complemented
13#20288416C214yesmaximal, complemented
14#20288398C214yesmaximal, complemented
15#20288393C212yesmaximal, complemented
16#20288388C212yesmaximal, complemented
17#20288366C211yesmaximal, characteristic, complemented
18#525×D53C212yesmaximal, complemented
19C22×#13133193C211yesmaximal, characteristic, complemented
20C53×#3486C211yesmaximal, characteristic, complemented
21C2×#13133265C2211yescharacteristic, complemented
22C2×#41×D53C2212yescomplemented
23C23×C4×D53C2211yescharacteristic
24#16811374C2218yescomplemented
25#16811372C2218yescomplemented
26#16811369C2218yescomplemented
27#16811367C2218yescomplemented
28#16811346C2214yescomplemented
29#16811344C2214yescomplemented
30#16811334C2218yescomplemented
31#16811333C2214yescomplemented
32#16811332C2218yescomplemented
33#16811331C2214yescomplemented
34#16811331C2214yescomplemented
35#16811330C2214yescomplemented
36#16811327C2218yescomplemented
37#16811327C2218yescomplemented
38#16811325C2214yescomplemented
39#16811322C2218yescomplemented
40#16811319C2214yescomplemented
41#16811316C2218yescomplemented
42#16811315C2214yescomplemented
43#16811315C2214yescomplemented
44#16811314C2214yescomplemented
45#16811314C2214yescomplemented
46#16811313C2214yescomplemented
47#16811310C2218yescomplemented
48#16811307C2214yescomplemented
49#16811306C2218yescomplemented
50#16811303C2218yescomplemented
51#16811302C2218yescomplemented
52#16811300C2218yescomplemented
53#16811300C2218yescomplemented
54#16811297C2218yescomplemented
55#16811296C2218yescomplemented
56#16811288C2214yescomplemented
57Q8×C22⋊D53C2214yescomplemented
58Q8×C22⋊D53C2214yescomplemented
59Q8×C22⋊D53C2214yescomplemented
60#16811284C2214yescomplemented
61#16811284C2214yescomplemented
62#16811284C2214yescomplemented
63#16811281C2214yescomplemented
64#16811277C2214yescomplemented
65#16811276C2214yescomplemented
66#16811273C2214yescomplemented
67#16811272C2218yescomplemented
68#16811272C2214yescomplemented
69#16811271C2218yescomplemented
70#16811268C2218yescomplemented
71#16811266C2214yescomplemented
72#16811265C2218yescomplemented
73#16811262C2218yescomplemented
74#16811261C2218yescomplemented
75#16811261C2214yescomplemented
76#16811252C2214yescomplemented
77#16811251C2212yescomplemented
78#16811250C2218yescomplemented
79#16811248C2214yes—
80#16811248C2218yescomplemented
81#16811247C2218yescomplemented
82#16811245C2214yescomplemented
83#16811242C2214yescomplemented
84#16811237C2218yescomplemented
85#16811234C2214yescomplemented
86#16811231C2214yescomplemented
87#16811222C2214yescomplemented
88#16811222C2218yescomplemented
89#16811219C2218yescomplemented
90#16811219C2218yescomplemented
91#16811218C2214yescomplemented
92#16811217C2218yescomplemented
93#16811215C2218yescomplemented
94#16811213C2214yescomplemented
95#16811210C2214yescomplemented
96#16811207C2218yescomplemented
97#16811206C2218yescomplemented
98#16811203C2214yescomplemented
99#16811201C2212yescomplemented
100#16811201C2214yescomplemented
101#16811200C2214yescomplemented
102#16811197C2212yescomplemented
103#16811197C2214yescomplemented
104#16811197C2214yescomplemented
105#16811196C2214yescomplemented
106#16811181C2214yes—
107#16811178C2214yescomplemented
108#16811177C2214yescomplemented
109#16811160C2214yescomplemented
110#16811152C2214yescomplemented
111#16811136C2212yes—
112#16811136C2212yescomplemented
113#16811136C2214yescomplemented
114#16811135C2212yes—
115#16811134C2214yescomplemented
116#16811134C2212yescomplemented
117#16811133C2212yes—
118#16811133C2212yescomplemented
119#16811132C2214yes—
120#16811132C2214yescomplemented
121#16811131C2214yes—
122#16811130C2212yes—
123#16811130C2214yescomplemented
124#16811129C2218yescomplemented
125#16811129C2214yescomplemented
126#123×D53C2214yescomplemented
127C2×#13133193C2214yes—
128C2×#13133193C2212yescomplemented
129C2×#13133193C2212yescomplemented
130C2×#13133193C2214yescomplemented
131C2×#13133193C2214yescomplemented
132C2×#13133193C2214yescomplemented
133C2×#13133193C2214yescomplemented
134C2×#13133193C2214yescomplemented
135C22⋊Q8×D53C2212yes—
136C22⋊Q8×D53C2212yescomplemented
137C22⋊Q8×D53C2214yescomplemented
138#121×D53C2212yes—
139#121×D53C2212yescomplemented
140#120×D53C2214yes—
141#16811106C2212yescomplemented
142#16811103C2212yescomplemented
143#16811102C2218yescomplemented
144#16811101C2211yescharacteristic, complemented
145#16811095C2218yes—
146C4×D4×D53C2214yes—
147C4×D4×D53C2214yescomplemented
148#117×D53C2212yescomplemented
149C22×C4⋊Dic53C2211yescharacteristic, complemented
150C22×#11719919C2212yescomplemented
151C22×#11719921C2212yes—
152C2×2−1+4×C53C2211yescharacteristic, complemented
153C23×Q8×C53C2211yescharacteristic, complemented
154D4×Q8×C53C2214yescomplemented
155D4×Q8×C53C2214yescomplemented
156C53×#548C2214yescomplemented
157C53×#548C2214yescomplemented
158C53×#536C2212yescomplemented
159C53×#536C2214yescomplemented
160C53×#525C2214yescomplemented
161C53×#525C2212yescomplemented
162C53×#519C2211yescharacteristic, complemented
163C24×D53C2311yescharacteristic
164#13133265—44no—
165C2×#11719949C2312yes—
166C2×#11719949C2314yescomplemented
167C2×#11719945C2312yes—
168C2×#11719945C2314yes—
169C2×#11719945C2314yes—
170C2×#11719947C2318yes—
171C2×#11719947C2314yes—
172C2×#11719947C2312yes—
173#41×D53—48no—
174C2×Q8×D53C2312yes—
175C2×Q8×D53C2314yescomplemented
176C2×D4×D53C2314yes—
177C2×D4×D53C2314yes—
178C2×D4×D53C2312yes—
179C2×D4×D53C2314yes—
180C23×Dic53C2312yes—
181C23×Dic53C2311yescharacteristic
182C22×C4×D53—44no—
183C22×C4×D53C2312yes—
184C22×C4×D53C2312yes—
185C22×C4×D53C2314yes—
186C22×C4×D53C2312yes—
187C22×C4×D53C2312yes—
188C22×C4×D53C2312yes—
189C22×C4×D53C2312yes—
190#13133217C2314yescomplemented
191#13133216C2318yescomplemented
192#13133216C2314yescomplemented
193#13133215C2314yescomplemented
194#13133215C2318yescomplemented
195#13133215C2318yescomplemented
196#13133212C2318yes—
197#13133212C2318yes—
198#13133212C2318yes—
199#13133212C2318yescomplemented
200#13133212C2318yescomplemented
201#13133211C2318yes—
202#13133211C2318yescomplemented
203#13133210C2318yescomplemented
204#13133210C2318yescomplemented
205#13133210C2318yescomplemented
206#13133209C2318yescomplemented
207#13133209C2314yescomplemented
208#13133208C2314yescomplemented
209#13133208C2318yescomplemented
210#13133208C2318yescomplemented
211#13133207C2318yescomplemented
212#13133207C2318yescomplemented
213#13133207C2318yescomplemented
214#13133207C2318yescomplemented
215#13133207C2318yescomplemented
216#13133206C2318yes—
217#13133206C2314yescomplemented
218#13133206C2318yescomplemented
219#13133205C2318yes—
220#13133203C2318yes—
221#13133203C2318yes—
222#13133202C2318yes—
223#13133202C2318yes—
224#13133202C2318yes—
225#13133202C2314yes—
226#13133202C2314yes—
227#13133202C2318yescomplemented
228#13133201C2318yes—
229#13133201C2318yes—
230#13133201C2314yes—
231#13133201C2318yescomplemented
232#13133200C2318yes—
233#13133200C2318yes—
234#13133200C2314yes—
235#13133200C2318yescomplemented
236#13133199C2318yes—
237#13133199C2314yes—
238#13133199C2314yes—
239#13133199C2318yescomplemented
240#13133199C2318yescomplemented
241#13133198C2314yes—
242#13133198C2318yes—
243#13133198C2318yescomplemented
244#13133197C2318yes—
245#13133197C2312yes—
246#13133197C2312yes—
247#13133197C2318yescomplemented
248#13133196C2314yes—
249#13133196C2312yes—
250#13133196C2312yes—
251#13133196C2314yes—
252#13133196C2314yescomplemented
253#13133196C2318yescomplemented
254#13133195C2318yes—
255#13133195C2318yes—
256#13133195C2314yes—
257#13133195C2314yes—
258#13133195C2318yescomplemented
259#13133195C2318yescomplemented
260#13133194C2318yes—
261#13133194C2314yes—
262#13133194C2318yes—
263#13133194C2314yes—
264#13133194C2318yescomplemented
265#13133194C2318yescomplemented
266#13133194C2318yescomplemented
267#13133193C2314yes—
268#13133193C2314yes—
269#13133193C2314yes—
270#13133193C2318yes—
271#13133193C2314yes—
272#13133193C2318yes—
273#13133193C2318yes—
274#13133193C2312yes—
275#13133193C2314yes—
276#13133193C2312yes—
277#13133193C2314yes—
278#13133193C2318yes—
279#13133193C2314yes—
280#13133193C2314yes—
281#13133193C2318yes—
282#13133193C2318yescomplemented
283#13133193C2314yescomplemented
284#13133193C2318yescomplemented
285#13133193C2314yescomplemented
286#13133193C2314yescomplemented
287#13133193C2318yescomplemented
288#13133192C2318yes—
289#13133192C2312yes—
290#13133192C2312yes—
291#13133191C2314yes—
292#13133191C2318yes—
293#13133191C2312yes—
294#13133191C2312yes—
295#13133191C2314yes—
296#13133191C2314yescomplemented
297#13133190C2318yes—
298#13133190C2314yes—
299#13133190C2314yes—
300#13133190C2318yescomplemented
301#13133189C2318yes—
302#13133189C2318yes—
303#13133189C2314yes—
304#13133189C2318yes—
305#13133189C2314yes—
306#13133189C2318yescomplemented
307#13133188C2312yes—
308#13133188C2312yes—
309#13133188C2314yescomplemented
310#13133187C2314yes—
311#13133187C2318yes—
312#13133187C2314yes—
313#13133187C2314yes—
314#13133186C2314yes—
315#13133185C2314yes—
316#13133185C2314yes—
317#13133185C2318yes—
318#13133185C2314yes—
319Q8×Dic53C2314yescomplemented
320Q8×Dic53C2314yescomplemented
321Q8×Dic53C2314yescomplemented
322C4×Dic106C2314yescomplemented
323C4×Dic106C2318yescomplemented
324#13133182C2318yescomplemented
325C4×D212C2314yes—
326C4×D212C2318yes—
327C4×D212C2314yes—
328C4×D212C2314yescomplemented
329D4×Dic53C2318yes—
330D4×Dic53C2314yes—
331D4×Dic53C2318yes—
332D4×Dic53C2314yes—
333D4×Dic53C2314yescomplemented
334#13133179C2318yes—
335#13133179C2314yes—
336#13133179C2314yes—
337C4×C22⋊D53C2314yes—
338C4×C22⋊D53C2314yes—
339C4×C22⋊D53C2318yes—
340C4×C22⋊D53C2318yes—
341C4×C22⋊D53C2314yes—
342C4×C22⋊D53C2318yes—
343C4×C22⋊D53C2314yes—
344C4×C22⋊D53C2318yescomplemented
345#13133177C2318yes—
346#13133177C2318yes—
347#13133177C2314yes—
348#13133177C2318yes—
349#13133177C2314yes—
350#13133177C2314yes—
351#13133177C2314yes—
352#13133177C2318yescomplemented
353#13133176C2314yes—
354#13133176C2312yes—
355#13133176C2314yescomplemented
356#13133175C2318yes—
357#13133175C2312yes—
358#13133175C2312yes—
359#13133175C2314yescomplemented
360#13133174C2318yes—
361#13133174C2314yes—
362#13133174C2318yescomplemented
363#13133173C2318yes—
364#13133173C2314yes—
365#13133173C2318yescomplemented
366C2×C4⋊Dic53C2314yes—
367C2×C4⋊Dic53C2314yes—
368C2×C4⋊Dic53C2312yes—
369C2×C4⋊Dic53C2312yes—
370C2×C4⋊Dic53C2314yescomplemented
371C2×#11719919C2314yes—
372C2×#11719919C2314yes—
373C2×#11719919C2318yes—
374C2×#11719919C2314yes—
375C2×#11719919C2314yes—
376C2×#11719919C2318yescomplemented
377C4⋊C4×D53C2312yes—
378C4⋊C4×D53C2314yes—
379C4⋊C4×D53C2312yes—
380C4⋊C4×D53C2314yes—
381C4⋊C4×D53C2318yescomplemented
382C4⋊C4×D53C2314yescomplemented
383C2×#11719921C2314yes—
384C2×#11719921C2318yes—
385C2×#11719921C2318yes—
386C2×#11719921C2314yes—
387C2×#11719921C2314yes—
388C2×#11719921C2314yes—
389C22⋊C4×D53C2318yes—
390C22⋊C4×D53C2314yes—
391C22⋊C4×D53C2314yes—
392C22⋊C4×D53C2314yes—
393C22⋊C4×D53C2314yes—
394C22⋊C4×D53C2314yes—
395C42×D53C2314yes—
3962−1+4×C53—44no—
397C2×#41×C53C2312yes—
398C2×#41×C53C2314yes—
399C2×#41×C53C2314yescomplemented
400C22×Q8×C53—44no—
401C22×Q8×C53C2311yescharacteristic
402C22×Q8×C53C2311yescharacteristic
403C22×Q8×C53C2314yes—
404C22×Q8×C53C2314yes—
405C22×Q8×C53C2312yes—
406C22×Q8×C53C2314yescomplemented
407C23×C4×C53C2311yescharacteristic
408C23×C4×C53C2312yes—
409C4⋊Q8×C53C2314yescomplemented
410C4⋊Q8×C53C2318yescomplemented
411#124×C53C2314yescomplemented
412#124×C53C2318yescomplemented
413#123×C53C2318yes—
414#123×C53C2314yes—
415C22⋊Q8×C53C2314yes—
416C22⋊Q8×C53C2312yes—
417C22⋊Q8×C53C2314yes—
418C22⋊Q8×C53C2312yes—
419C22⋊Q8×C53C2318yescomplemented
420C22⋊Q8×C53C2314yescomplemented
421C22⋊Q8×C53C2318yescomplemented
422C22⋊Q8×C53C2314yescomplemented
423#121×C53C2312yes—
424#121×C53C2314yes—
425#121×C53C2312yes—
426#121×C53C2314yes—
427#120×C53C2314yes—
428C4×Q8×C53C2314yescomplemented
429C4×Q8×C53C2314yescomplemented
430C4×D4×C53C2318yes—
431C4×D4×C53C2314yes—
432C4×D4×C53C2314yes—
433C4×D4×C53C2318yes—
434#117×C53C2314yes—
435#117×C53C2312yes—
436C24×C53C2411yescharacteristic
437C23×D53—24no—
438C23×D53—42no—
439C23×D53—42no—
440C23×D53C2412yes—
441C23×D53C2412yes—
442C23×D53C2414yes—
443C23×D53C2411yescharacteristic
444C23×D53C2411yescharacteristic
445#41×C53—28no—
446#41×C53—48no—
447#41×C53—48no—
448C2×Q8×C53—24no—
449C2×Q8×C53—24no—
450C2×Q8×C53—44no—
451C2×Q8×C53—48no—
452C2×Q8×C53—48no—
453C2×Q8×C53—48no—
454C2×Q8×C53C2414yes—
455C2×Q8×C53C2412yes—
456C2×Q8×C53C2414yes—
457C2×Q8×C53C2414yes—
458C2×Q8×C53C2418yes—
459C2×D4×C53C2414yes—
460C2×D4×C53C2414yes—
461C2×D4×C53C2414yes—
462C2×D4×C53C2412yes—
463C2×D4×C53C2414yes—
464C22×C4×C53—24no—
465C22×C4×C53—44no—
466C22×C4×C53C2412yes—
467C22×C4×C53C2412yes—
468C22×C4×C53C2412yes—
469C22×C4×C53C2414yes—
470C22×C4×C53C2412yes—
471C22×C4×C53C2411yescharacteristic
472C22×C4×C53C2414yes—
473C22×C4×C53C2414yes—
474C22×C4×C53C2418yes—
475C22×C4×C53C2411yescharacteristic
476C2×C22⋊D53C2414yes—
477C2×C22⋊D53C2414yes—
478C2×C22⋊D53C2414yes—
479C2×C22⋊D53C2414yes—
480C2×C22⋊D53C2414yes—
481C2×C22⋊D53C2418yes—
482C2×C22⋊D53C2414yes—
483C2×C22⋊D53C2414yes—
484C22×Dic53—42no—
485C22×Dic53—44no—
486C22×Dic53C2414yes—
487C22×Dic53C2412yes—
488C22×Dic53C2414yes—
489C22×Dic53C2414yes—
490C22×Dic53C2418yes—
491C22×Dic53C2411yescharacteristic
492C22×Dic53C2412yes—
493C22×Dic53C2411yescharacteristic
494C22×Dic53C2414yes—
495#11719949—44no—
496#11719949—48no—
497Q8×D53—44no—
498Q8×D53—48no—
499#11719947—44no—
500#11719947—48no—
501#11719947—416no—
502D4×D53—216no—
503D4×D53—44no—
504D4×D53—48no—
505D4×D53—48no—
506#11719945—28no—
507#11719945—48no—
508#11719945—48no—
509C2×D212C2414yes—
510C2×D212C2412yes—
511C2×D212C2414yes—
512C2×D212C2414yes—
513C2×D212C2414yes—
514C2×C4×D53—28no—
515C2×C4×D53—44no—
516C2×C4×D53—44no—
517C2×C4×D53—44no—
518C2×C4×D53—44no—
519C2×C4×D53—48no—
520C2×C4×D53—44no—
521C2×C4×D53C2412yes—
522C2×C4×D53C2414yes—
523C2×C4×D53C2412yes—
524C2×C4×D53C2414yes—
525C2×C4×D53C2412yes—
526C2×C4×D53C2412yes—
527C2×C4×D53C2414yes—
528C2×C4×D53C2412yes—
529C2×C4×D53C2414yes—
530C2×C4×D53C2412yes—
531C2×C4×D53C2418yes—
532C2×C4×D53C2418yes—
533C2×C4×D53C2414yes—
534C2×C4×D53C2412yes—
535C2×C4×D53C2412yes—
536C2×Dic106C2412yes—
537C2×Dic106C2418yes—
538C2×Dic106C2414yes—
539C2×Dic106C2414yes—
540C4⋊C4×C53C2412yes—
541C4⋊C4×C53C2412yes—
542C4⋊C4×C53C2414yes—
543C4⋊C4×C53C2414yes—
544C4⋊C4×C53C2414yes—
545C4⋊C4×C53C2414yes—
546C4⋊C4×C53C2418yes—
547C4⋊C4×C53C2418yes—
548C22⋊C4×C53C2414yes—
549C22⋊C4×C53C2414yes—
550C22⋊C4×C53C2414yes—
551C22⋊C4×C53C2418yes—
552C22⋊C4×C53C2414yes—
553C22⋊C4×C53C2414yes—
554C22⋊C4×C53C2418yes—
555C42×C53C2414yes—
556C42×C53C2418yes—
557C22⋊Dic53C2414yes—
558C22⋊Dic53C2414yes—
559C22⋊Dic53C2414yes—
560C22⋊Dic53C2414yes—
561C22⋊Dic53C2414yes—
562C22⋊Dic53C2418yes—
563C22⋊Dic53C2418yes—
564#11719921C2414yes—
565#11719921C2418yes—
566#11719921C2414yes—
567#11719921C2414yes—
568#11719921C2414yes—
569#11719921C2414yes—
570#11719921C2414yes—
571#11719921C2414yes—
572#11719921C2414yes—
573#11719921C2414yes—
574#11719921C2414yes—
575#11719921C2418yes—
576#11719921C2418yes—
577#11719921C2418yes—
578#11719921C2418yes—
579#11719921C2418yes—
580#11719921C2418yes—
581#11719921C2418yes—
582C4⋊Dic53C2414yes—
583C4⋊Dic53C2412yes—
584C4⋊Dic53C2412yes—
585C4⋊Dic53C2414yes—
586C4⋊Dic53C2414yes—
587C4⋊Dic53C2414yes—
588C4⋊Dic53C2418yes—
589C4⋊Dic53C2418yes—
590C4⋊Dic53C2418yes—
591C4⋊Dic53C2414yes—
592C4⋊Dic53C2414yes—
593#11719919C2414yes—
594#11719919C2414yes—
595#11719919C2414yes—
596#11719919C2414yes—
597#11719919C2414yes—
598#11719919C2414yes—
599#11719919C2418yes—
600#11719919C2418yes—
601#11719919C2418yes—
602#11719919C2418yes—
603#11719919C2418yes—
604#11719919C2418yes—
605#11719919C2418yes—
606#11719919C2418yes—
607#11719919C2418yes—
608#11719919C2418yes—
609C4×Dic53C2414yes—
610C4×Dic53C2414yes—
611C4×Dic53C2414yes—
612C4×Dic53C2418yes—
613C4×Dic53C2418yes—
614C4×Dic53C2418yes—
615C23×C53—22no—
616C23×C53—22no—
617C23×C53—22no—
618C23×C53C2514yes—
619C23×C53C2511yescharacteristic
620C23×C53C2511yescharacteristic
621C23×C53C2511yescharacteristic
622C22×D53—24no—
623C22×D53—22no—
624C22×D53—24no—
625C22×D53—24no—
626C22×D53—24no—
627C22×D53—28no—
628C22×D53—41no—
629C22×D53—42no—
630C22×D53—41no—
631C22×D53—41no—
632C22×D53—42no—
633C22×D53—41no—
634C22×D53—44no—
635C22×D53—44no—
636C22×D53—416no—
637C22×D532−1+414yescomplemented
638C22×D53C2514yes—
639C22×D53C2512yes—
640C22×D53C2512yes—
641Q8×C53—28no—
642Q8×C53—24no—
643Q8×C53—28no—
644Q8×C53—48no—
645Q8×C53—44no—
646D4×C53—28no—
647D4×C53—28no—
648D4×C53—28no—
649D4×C53—24no—
650D4×C53—44no—
651C2×C4×C53—22no—
652C2×C4×C53—24no—
653C2×C4×C53—24no—
654C2×C4×C53—24no—
655C2×C4×C53—24no—
656C2×C4×C53—28no—
657C2×C4×C53—44no—
658C2×C4×C53—44no—
659C2×C4×C53—48no—
660C2×C4×C53H(5,𝔽2)14yes—
661C2×C4×C53C2514yes—
662C2×C4×C53C2514yes—
663C2×C4×C53C2514yes—
664C2×C4×C53C2512yes—
665C2×C4×C53C2514yes—
666C2×C4×C53C2514yes—
667C2×C4×C53C2512yes—
668C22⋊D53—28no—
669C22⋊D53—28no—
670C22⋊D53—28no—
671C22⋊D53—28no—
672C22⋊D53—44no—
673C22⋊D53—44no—
674C22⋊D53—44no—
675C22⋊D53—48no—
676C2×Dic53—24no—
677C2×Dic53—28no—
678C2×Dic53—41no—
679C2×Dic53—42no—
680C2×Dic53—41no—
681C2×Dic53—44no—
682C2×Dic53—48no—
683C2×Dic53—44no—
684C2×Dic53—44no—
685C2×Dic53C2514yes—
686C2×Dic53C2512yes—
687C2×Dic53C2514yes—
688C2×Dic53C2518yes—
689C2×Dic53C2512yes—
690C2×Dic53C2514yes—
691D212—28no—
692D212—24no—
693D212—44no—
694D212—44no—
695D212—44no—
696C4×D53—28no—
697C4×D53—24no—
698C4×D53—24no—
699C4×D53—24no—
700C4×D53—24no—
701C4×D53—28no—
702C4×D53—42no—
703C4×D53—42no—
704C4×D53—42no—
705C4×D53—42no—
706C4×D53—44no—
707C4×D53—44no—
708C4×D53—48no—
709C4×D53—44no—
710C4×D53—48no—
711Dic106—24no—
712Dic106—44no—
713Dic106—44no—
714Dic106—48no—
715#62819—531nomaximal, Sylow
716C22×C53—28no—
717C22×C53—21no—
718C22×C53—21no—
719C22×C53—21no—
720C22×C53—21no—
721C22×C53—21no—
722C22×C53—21no—
723C22×C53—24no—
724C22×C53—24no—
725C22×C53—24no—
726C22×C53C2×H(5,𝔽2)12yes—
727C22×C53C2×2−1+412yes—
728C22×C53#58512yes—
729C22×C53C2611yescharacteristic
730C2×D53—22no—
731C2×D53—22no—
732C2×D53—22no—
733C2×D53—24no—
734C2×D53—24no—
735C2×D53—22no—
736C2×D53—24no—
737C2×D53—22no—
738C2×D53—44no—
739C2×D53—48no—
740C2×D53—48no—
741C2×D53—44no—
742C2×D53—88no—
743C2×D53C2×2−1+414yes—
744C4×C53—24no—
745C4×C53—24no—
746C4×C53—22no—
747C4×C53—24no—
748C4×C53—24no—
749C4×C53—24no—
750C4×C53C2×H(5,𝔽2)14yes—
751Dic53—24no—
752Dic53—22no—
753Dic53—22no—
754Dic53—24no—
755Dic53—24no—
756Dic53—28no—
757#3541—534no—
758#3541—534no—
759#3538—534no—
760#3536—534no—
761#3535—538no—
762#3520—534no—
763#3520—534no—
764#3505—534no—
765#3501—534no—
766#3495—532no—
767#3495—532no—
768#3492—534no—
769#3492—532no—
770#3490—534no—
771#3489—532no—
772#3489—532no—
773#3486—531no—
774#3486D5311yescharacteristic, complemented
775C2×#525—532no—
776C22×C22⋊Q8—531no—
777C2×C53—22no—
778C2×C53—22no—
779C2×C53—22no—
780C2×C53—44no—
781C2×C53C22×H(5,𝔽2)11yescharacteristic
782C2×C53C22×2−1+411yescharacteristic
783C2×C53C2×#58511yescharacteristic
784D53—24no—
785D53—42no—
786D53—44no—
787C2×2−1+4—531no—
788C2×2−1+4C2×D5311yescharacteristic, complemented
789C22×#41—532no—
790C23×Q8C2×D5311yescharacteristic, complemented
791C24×C4—531no—
792#563—538no—
793#563—538no—
794#562—538no—
795#562—538no—
796#556—534no—
797#556—534no—
798#554—538no—
799#554—538no—
800#554—534no—
801#554—538no—
802#554—534no—
803#554—534no—
804#554—534no—
805#554—538no—
806#553—538no—
807#553—534no—
808#553—534no—
809#553—538no—
810#552—538no—
811#552—534no—
812#552—534no—
813#552—534no—
814#552—534no—
815#552—534no—
816#552—534no—
817#552—538no—
818#551—538no—
819#551—538no—
820#551—538no—
821#551—538no—
822#551—538no—
823#551—538no—
824D4×Q8—534no—
825D4×Q8—534no—
826D4×Q8—534no—
827D4×Q8—534no—
828D4×Q8C2×D5314yescomplemented
829D4×Q8C2×D5314yescomplemented
830#548—534no—
831#548—534no—
832#548—534no—
833#548—534no—
834#548C2×D5314yescomplemented
835#548C2×D5314yescomplemented
836#547—538no—
837#547—534no—
838#547—534no—
839#547—538no—
840#547—534no—
841#547—534no—
842#546—538no—
843#546—534no—
844#546—534no—
845#546—538no—
846#546—538no—
847#546—538no—
848#544—538no—
849#544—534no—
850#544—532no—
851#543—534no—
852#543—538no—
853#542—538no—
854#542—534no—
855#542—538no—
856#542—534no—
857#541—534no—
858#541—534no—
859#539—538no—
860#539—534no—
861#539—538no—
862#539—538no—
863#539—538no—
864#539—534no—
865#539—538no—
866#538—538no—
867#538—534no—
868#538—534no—
869#538—538no—
870#537—532no—
871#537—534no—
872#537—534no—
873#537—534no—
874#536—532no—
875#536—534no—
876#536—534no—
877#536—534no—
878#536C2×D5312yescomplemented
879#536C2×D5314yescomplemented
880#534—534no—
881#533—534no—
882#533—534no—
883#529—534no—
884#529—534no—
885#525—532no—
886#525—534no—
887#525—532no—
888#525—534no—
889#525—534no—
890#525—532no—
891#525—532no—
892#525—534no—
893#525—532no—
894#525—532no—
895#525—534no—
896#525—538no—
897#525—534no—
898#525—534no—
899#525—532no—
900#525C2×D5312yescomplemented
901#525C2×D5314yescomplemented
902C2×#123—534no—
903C2×C22⋊Q8—534no—
904C2×C22⋊Q8—532no—
905C2×C22⋊Q8—532no—
906C2×C22⋊Q8—534no—
907C2×C22⋊Q8—534no—
908C2×C22⋊Q8—534no—
909C2×C22⋊Q8—534no—
910C2×C22⋊Q8—534no—
911C2×C22⋊Q8—532no—
912C2×C22⋊Q8—532no—
913C2×C22⋊Q8—534no—
914C2×#121—532no—
915C2×#121—532no—
916C2×#120—534no—
917#520—532no—
918#520—538no—
919#520—532no—
920#519—531no—
921#519C2×D5311yescharacteristic, complemented
922#518—538no—
923C2×C4×D4—534no—
924C2×C4×D4—534no—
925C2×#117—532no—
926C22×C4⋊C4—532no—
927C22×C4⋊C4—531no—
928C22×C22⋊C4—532no—
929C53#6281911yescharacteristic, complemented, Sylow
930C25—531no—
9312−1+4—44no—
9322−1+4—2124no—
933C2×#41—532no—
934C2×#41—534no—
935C2×#41—538no—
936C2×#41—534no—
937C2×#41—532no—
938C2×#41—532no—
939C2×#41—534no—
940C2×#41—534no—
941C2×#41—2128no—
942C2×#41C22×D5312yes—
943C2×#41C22×D5314yes—
944C2×#41C22×D5314yescomplemented
945C22×Q8—44no—
946C22×Q8—532no—
947C22×Q8—534no—
948C22×Q8C22×D5311yescharacteristic
949C22×Q8C22×D5311yescharacteristic
950C22×Q8C22×D5312yes—
951C22×Q8C22×D5314yes—
952C22×Q8C22×D5314yes—
953C22×Q8C22×D5314yescomplemented
954C22×D4—534no—
955C22×D4—534no—
956C22×D4—534no—
957C22×D4—532no—
958C23×C4—532no—
959C23×C4—531no—
960C23×C4—532no—
961C23×C4—532no—
962C23×C4—532no—
963C23×C4—534no—
964C23×C4—532no—
965C23×C4—532no—
966C23×C4—532no—
967C23×C4—2124no—
968C23×C4C22×D5311yescharacteristic
969C23×C4C22×D5312yes—
970C4⋊Q8—534no—
971C4⋊Q8—538no—
972C4⋊Q8—538no—
973C4⋊Q8—534no—
974C4⋊Q8—538no—
975C4⋊Q8—534no—
976C4⋊Q8C22×D5314yescomplemented
977C4⋊Q8C22×D5318yescomplemented
978#126—538no—
979#126—538no—
980#126—538no—
981#126—538no—
982#126—538no—
983#126—538no—
984#126—538no—
985#126—538no—
986#126—538no—
987#126—538no—
988#125—534no—
989#125—538no—
990#125—538no—
991#125—538no—
992#125—538no—
993#125—538no—
994#125—538no—
995#125—538no—
996#125—534no—
997#125—538no—
998#124—534no—
999#124—538no—
1000#124—538no—
1001#124—538no—
1002#124—538no—
1003#124—538no—
1004#124C22×D5314yescomplemented
1005#124C22×D5318yescomplemented
1006#123—534no—
1007#123—538no—
1008#123—538no—
1009#123—534no—
1010#123—538no—
1011#123—538no—
1012#123—538no—
1013#123—534no—
1014#123—534no—
1015#123—538no—
1016#123—538no—
1017#123—538no—
1018#123—538no—
1019#123—534no—
1020#123—534no—
1021#123—534no—
1022#123—538no—
1023#123—538no—
1024#123—538no—
1025#123—538no—
1026#123—538no—
1027#123—538no—
1028#123C22×D5314yes—
1029#123C22×D5318yes—
1030C22⋊Q8—534no—
1031C22⋊Q8—534no—
1032C22⋊Q8—532no—
1033C22⋊Q8—534no—
1034C22⋊Q8—534no—
1035C22⋊Q8—538no—
1036C22⋊Q8—538no—
1037C22⋊Q8—534no—
1038C22⋊Q8—534no—
1039C22⋊Q8—534no—
1040C22⋊Q8—534no—
1041C22⋊Q8—538no—
1042C22⋊Q8—538no—
1043C22⋊Q8—532no—
1044C22⋊Q8—534no—
1045C22⋊Q8—534no—
1046C22⋊Q8—538no—
1047C22⋊Q8—538no—
1048C22⋊Q8—534no—
1049C22⋊Q8—538no—
1050C22⋊Q8—538no—
1051C22⋊Q8—532no—
1052C22⋊Q8—532no—
1053C22⋊Q8—534no—
1054C22⋊Q8—534no—
1055C22⋊Q8—534no—
1056C22⋊Q8—538no—
1057C22⋊Q8—532no—
1058C22⋊Q8—532no—
1059C22⋊Q8—534no—
1060C22⋊Q8—534no—
1061C22⋊Q8—538no—
1062C22⋊Q8—538no—
1063C22⋊Q8—538no—
1064C22⋊Q8—538no—
1065C22⋊Q8—538no—
1066C22⋊Q8—538no—
1067C22⋊Q8—534no—
1068C22⋊Q8—534no—
1069C22⋊Q8—538no—
1070C22⋊Q8—538no—
1071C22⋊Q8—538no—
1072C22⋊Q8—538no—
1073C22⋊Q8—538no—
1074C22⋊Q8C22×D5312yes—
1075C22⋊Q8C22×D5312yes—
1076C22⋊Q8C22×D5314yes—
1077C22⋊Q8C22×D5314yes—
1078C22⋊Q8C22×D5314yescomplemented
1079C22⋊Q8C22×D5314yescomplemented
1080C22⋊Q8C22×D5318yescomplemented
1081C22⋊Q8C22×D5318yescomplemented
1082#121—532no—
1083#121—534no—
1084#121—532no—
1085#121—534no—
1086#121—538no—
1087#121—534no—
1088#121—538no—
1089#121—538no—
1090#121—538no—
1091#121—532no—
1092#121—532no—
1093#121—534no—
1094#121—534no—
1095#121—534no—
1096#121—538no—
1097#121—532no—
1098#121—532no—
1099#121—538no—
1100#121—534no—
1101#121—534no—
1102#121—538no—
1103#121—538no—
1104#121C22×D5312yes—
1105#121C22×D5312yes—
1106#121C22×D5314yes—
1107#121C22×D5314yes—
1108#120—534no—
1109#120—534no—
1110#120—534no—
1111#120—534no—
1112#120—538no—
1113#120—534no—
1114#120—534no—
1115#120—534no—
1116#120—538no—
1117#120C22×D5314yes—
1118C4×Q8—534no—
1119C4×Q8—534no—
1120C4×Q8—534no—
1121C4×Q8—538no—
1122C4×Q8—534no—
1123C4×Q8—538no—
1124C4×Q8C22×D5314yescomplemented
1125C4×Q8C22×D5314yescomplemented
1126C4×D4—534no—
1127C4×D4—534no—
1128C4×D4—538no—
1129C4×D4—538no—
1130C4×D4—534no—
1131C4×D4—534no—
1132C4×D4—534no—
1133C4×D4—534no—
1134C4×D4—534no—
1135C4×D4—538no—
1136C4×D4—538no—
1137C4×D4—538no—
1138C4×D4—538no—
1139C4×D4—534no—
1140C4×D4—534no—
1141C4×D4—538no—
1142C4×D4—534no—
1143C4×D4—534no—
1144C4×D4—534no—
1145C4×D4—534no—
1146C4×D4—538no—
1147C4×D4—538no—
1148C4×D4—538no—
1149C4×D4—538no—
1150C4×D4—534no—
1151C4×D4—534no—
1152C4×D4—538no—
1153C4×D4—534no—
1154C4×D4C22×D5314yes—
1155C4×D4C22×D5314yes—
1156C4×D4C22×D5318yes—
1157C4×D4C22×D5318yes—
1158#117—532no—
1159#117—534no—
1160#117—534no—
1161#117—532no—
1162#117—532no—
1163#117—538no—
1164#117—534no—
1165#117—534no—
1166#117—538no—
1167#117—538no—
1168#117—534no—
1169#117—538no—
1170#117—538no—
1171#117C22×D5312yes—
1172#117C22×D5314yes—
1173C2×C4⋊C4—532no—
1174C2×C4⋊C4—534no—
1175C2×C4⋊C4—534no—
1176C2×C4⋊C4—532no—
1177C2×C4⋊C4—534no—
1178C2×C4⋊C4—534no—
1179C2×C4⋊C4—534no—
1180C2×C4⋊C4—538no—
1181C2×C4⋊C4—534no—
1182C2×C4⋊C4—534no—
1183C2×C4⋊C4—538no—
1184C2×C4⋊C4—532no—
1185C2×C4⋊C4—532no—
1186C2×C4⋊C4—534no—
1187C2×C4⋊C4—534no—
1188C2×C4⋊C4—534no—
1189C2×C4⋊C4—538no—
1190C2×C22⋊C4—534no—
1191C2×C22⋊C4—534no—
1192C2×C22⋊C4—538no—
1193C2×C22⋊C4—534no—
1194C2×C22⋊C4—534no—
1195C2×C22⋊C4—538no—
1196C2×C22⋊C4—534no—
1197C2×C22⋊C4—534no—
1198C2×C22⋊C4—534no—
1199C2×C22⋊C4—534no—
1200C2×C22⋊C4—534no—
1201C2×C22⋊C4—538no—
1202C2×C42—534no—
1203C24—531no—
1204C24—532no—
1205C24—532no—
1206C24—534no—
1207C24—531no—
1208C24—1064no—
1209C24—2122no—
1210C24—2122no—
1211C24C23×D5311yescharacteristic
1212#41—28no—
1213#41—48no—
1214#41—48no—
1215#41—1068no—
1216#41—2128no—
1217#41—2128no—
1218#41—21216no—
1219#41—2128no—
1220#41—2124no—
1221#41—2124no—
1222#41—2128no—
1223C2×Q8—24no—
1224C2×Q8—24no—
1225C2×Q8—44no—
1226C2×Q8—48no—
1227C2×Q8—48no—
1228C2×Q8—48no—
1229C2×Q8—532no—
1230C2×Q8—538no—
1231C2×Q8—534no—
1232C2×Q8—534no—
1233C2×Q8—2124no—
1234C2×Q8—2128no—
1235C2×Q8C23×D5312yes—
1236C2×Q8C23×D5314yes—
1237C2×Q8C23×D5314yes—
1238C2×Q8C23×D5318yes—
1239C2×Q8C23×D5314yes—
1240C2×D4—534no—
1241C2×D4—534no—
1242C2×D4—534no—
1243C2×D4—534no—
1244C2×D4—538no—
1245C2×D4—534no—
1246C2×D4—534no—
1247C2×D4—534no—
1248C2×D4—534no—
1249C2×D4—532no—
1250C2×D4—534no—
1251C2×D4—534no—
1252C2×D4—534no—
1253C2×D4—10616no—
1254C2×D4—2124no—
1255C2×D4—2128no—
1256C2×D4—2128no—
1257C2×D4C23×D5314yes—
1258C2×D4C23×D5314yes—
1259C2×D4C23×D5312yes—
1260C2×D4C23×D5314yes—
1261C2×D4C23×D5314yes—
1262C22×C4—24no—
1263C22×C4—44no—
1264C22×C4—534no—
1265C22×C4—532no—
1266C22×C4—534no—
1267C22×C4—534no—
1268C22×C4—538no—
1269C22×C4—531no—
1270C22×C4—532no—
1271C22×C4—531no—
1272C22×C4—534no—
1273C22×C4—532no—
1274C22×C4—534no—
1275C22×C4—532no—
1276C22×C4—534no—
1277C22×C4—532no—
1278C22×C4—532no—
1279C22×C4—534no—
1280C22×C4—532no—
1281C22×C4—534no—
1282C22×C4—532no—
1283C22×C4—538no—
1284C22×C4—538no—
1285C22×C4—534no—
1286C22×C4—532no—
1287C22×C4—532no—
1288C22×C4—1068no—
1289C22×C4—2124no—
1290C22×C4—2124no—
1291C22×C4—2124no—
1292C22×C4—2124no—
1293C22×C4—2128no—
1294C22×C4—2124no—
1295C22×C4—2124no—
1296C22×C4—2122no—
1297C22×C4C23×D5312yes—
1298C22×C4C23×D5312yes—
1299C22×C4C23×D5312yes—
1300C22×C4C23×D5312yes—
1301C22×C4C23×D5311yescharacteristic
1302C22×C4C23×D5314yes—
1303C22×C4C23×D5314yes—
1304C22×C4C23×D5314yes—
1305C22×C4C23×D5318yes—
1306C22×C4C23×D5311yescharacteristic
1307C4⋊C4—534no—
1308C4⋊C4—534no—
1309C4⋊C4—538no—
1310C4⋊C4—538no—
1311C4⋊C4—532no—
1312C4⋊C4—534no—
1313C4⋊C4—534no—
1314C4⋊C4—538no—
1315C4⋊C4—538no—
1316C4⋊C4—538no—
1317C4⋊C4—538no—
1318C4⋊C4—532no—
1319C4⋊C4—534no—
1320C4⋊C4—534no—
1321C4⋊C4—534no—
1322C4⋊C4—534no—
1323C4⋊C4—534no—
1324C4⋊C4—534no—
1325C4⋊C4—538no—
1326C4⋊C4—538no—
1327C4⋊C4—538no—
1328C4⋊C4—538no—
1329C4⋊C4—538no—
1330C4⋊C4—538no—
1331C4⋊C4—538no—
1332C4⋊C4—534no—
1333C4⋊C4—534no—
1334C4⋊C4C23×D5312yes—
1335C4⋊C4C23×D5312yes—
1336C4⋊C4C23×D5314yes—
1337C4⋊C4C23×D5314yes—
1338C4⋊C4C23×D5318yes—
1339C4⋊C4C23×D5318yes—
1340C4⋊C4C23×D5314yes—
1341C4⋊C4C23×D5314yes—
1342C22⋊C4—534no—
1343C22⋊C4—534no—
1344C22⋊C4—534no—
1345C22⋊C4—534no—
1346C22⋊C4—534no—
1347C22⋊C4—538no—
1348C22⋊C4—538no—
1349C22⋊C4—538no—
1350C22⋊C4—538no—
1351C22⋊C4—534no—
1352C22⋊C4—534no—
1353C22⋊C4—538no—
1354C22⋊C4—538no—
1355C22⋊C4—534no—
1356C22⋊C4—534no—
1357C22⋊C4—534no—
1358C22⋊C4—534no—
1359C22⋊C4—534no—
1360C22⋊C4—534no—
1361C22⋊C4—538no—
1362C22⋊C4—538no—
1363C22⋊C4—534no—
1364C22⋊C4—534no—
1365C22⋊C4—538no—
1366C22⋊C4—538no—
1367C22⋊C4C23×D5314yes—
1368C22⋊C4C23×D5314yes—
1369C22⋊C4C23×D5314yes—
1370C22⋊C4C23×D5318yes—
1371C22⋊C4C23×D5314yes—
1372C22⋊C4C23×D5314yes—
1373C22⋊C4C23×D5318yes—
1374C42—534no—
1375C42—534no—
1376C42—534no—
1377C42—538no—
1378C42—538no—
1379C42—538no—
1380C42C23×D5314yes—
1381C42C23×D5318yes—
1382C23—22no—
1383C23—22no—
1384C23—22no—
1385C23—532no—
1386C23—534no—
1387C23—532no—
1388C23—534no—
1389C23—1068no—
1390C23—1064no—
1391C23—1064no—
1392C23—1064no—
1393C23—1062no—
1394C23—1064no—
1395C23—2124no—
1396C23—2124no—
1397C23—2121no—
1398C23—2122no—
1399C23—2121no—
1400C23—2121no—
1401C23—2122no—
1402C23—2121no—
1403C23—21216no—
1404C23C24×D5314yes—
1405C23C24×D5311yescharacteristic
1406C23C24×D5311yescharacteristic
1407C23C24×D5311yescharacteristic
1408Q8—28no—
1409Q8—28no—
1410Q8—24no—
1411Q8—48no—
1412Q8—44no—
1413Q8—1064no—
1414Q8—2124no—
1415Q8—2124no—
1416Q8—2128no—
1417D4—28no—
1418D4—28no—
1419D4—28no—
1420D4—24no—
1421D4—44no—
1422D4—1068no—
1423D4—1068no—
1424D4—1068no—
1425D4—1068no—
1426D4—1068no—
1427D4—1064no—
1428D4—2124no—
1429D4—2124no—
1430D4—2124no—
1431D4—2124no—
1432D4—2124no—
1433D4—2124no—
1434D4—2128no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—28no—
1441C2×C4—44no—
1442C2×C4—44no—
1443C2×C4—48no—
1444C2×C4—534no—
1445C2×C4—534no—
1446C2×C4—532no—
1447C2×C4—538no—
1448C2×C4—534no—
1449C2×C4—532no—
1450C2×C4—1068no—
1451C2×C4—1064no—
1452C2×C4—1068no—
1453C2×C4—1064no—
1454C2×C4—1064no—
1455C2×C4—1064no—
1456C2×C4—1064no—
1457C2×C4—1068no—
1458C2×C4—2122no—
1459C2×C4—2122no—
1460C2×C4—2122no—
1461C2×C4—2122no—
1462C2×C4—2124no—
1463C2×C4—2124no—
1464C2×C4—2124no—
1465C2×C4—2128no—
1466C2×C4—2128no—
1467C2×C4—2124no—
1468C2×C4—2124no—
1469C2×C4—2121no—
1470C2×C4—2122no—
1471C2×C4—2121no—
1472C2×C4—2124no—
1473C2×C4—2128no—
1474C2×C4#1313326214yes—
1475C2×C4C24×D5314yes—
1476C2×C4C24×D5314yes—
1477C2×C4C24×D5314yes—
1478C2×C4C24×D5314yes—
1479C2×C4C24×D5314yes—
1480C2×C4C24×D5312yes—
1481C2×C4C24×D5312yes—
1482C22—28no—
1483C22—21no—
1484C22—21no—
1485C22—21no—
1486C22—21no—
1487C22—21no—
1488C22—21no—
1489C22—24no—
1490C22—24no—
1491C22—24no—
1492C22—534no—
1493C22—1062no—
1494C22—1062no—
1495C22—1062no—
1496C22—1064no—
1497C22—1064no—
1498C22—1062no—
1499C22—1064no—
1500C22—1062no—
1501C22—4248no—
1502C22—2124no—
1503C22—2128no—
1504C22—2128no—
1505C22—2124no—
1506C22C2×#1313326212yes—
1507C222−1+4×D5312yes—
1508C22#1681146012yes—
1509C22C25×D5311yescharacteristic
1510C4—22no—
1511C4—24no—
1512C4—24no—
1513C4—24no—
1514C4—24no—
1515C4—24no—
1516C4—1062no—
1517C4—1062no—
1518C4—1064no—
1519C4—1064no—
1520C4—1068no—
1521C4—1064no—
1522C4C2×#1313326214yes—
1523C2—22no—
1524C2—22no—
1525C2—22no—
1526C2—44no—
1527C2—1064no—
1528C2—2124no—
1529C2—2122no—
1530C2C22×#1313326211yescharacteristic
1531C2C2×2−1+4×D5311yescharacteristic
1532C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3486C2
hypercenter#3486D53
hypocenterC53#62819
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #20289013C2semidirect
2. #20288994C2semidirect
3. #20288956C2semidirect
4. #20288931C2semidirect
5. #20288914C2semidirect
6. #20288765C2semidirect
7. #20288757C2semidirect
8. #20288551C2semidirect
9. #20288510C2semidirect
10. #20288464C2semidirect
11. #20288457C2semidirect
12. #20288421C2semidirect
13. #20288416C2semidirect
14. #20288398C2semidirect
15. #20288393C2semidirect
16. #20288388C2semidirect
17. #20288366C2semidirect
18. #525×D53C2semidirect
19. C22×#13133193C2semidirect
20. C53×#3486C2semidirect
21. C2×#13133265C22semidirect
22. C2×#41×D53C22semidirect
24. #16811374C22semidirect
25. #16811372C22semidirect
26. #16811369C22semidirect
27. #16811367C22semidirect
28. #16811346C22semidirect
29. #16811344C22semidirect
30. #16811334C22semidirect
31. #16811333C22semidirect
32. #16811332C22semidirect
33. #16811331C22semidirect
34. #16811331C22semidirect
35. #16811330C22semidirect
36. #16811327C22semidirect
37. #16811327C22semidirect
38. #16811325C22semidirect
39. #16811322C22semidirect
40. #16811319C22semidirect
41. #16811316C22semidirect
42. #16811315C22semidirect
43. #16811315C22semidirect
44. #16811314C22semidirect
45. #16811314C22semidirect
46. #16811313C22semidirect
47. #16811310C22semidirect
48. #16811307C22semidirect
49. #16811306C22semidirect
50. #16811303C22semidirect
51. #16811302C22semidirect
52. #16811300C22semidirect
53. #16811300C22semidirect
54. #16811297C22semidirect
55. #16811296C22semidirect
56. #16811288C22semidirect
57. Q8×C22⋊D53C22semidirect
58. Q8×C22⋊D53C22semidirect
59. Q8×C22⋊D53C22semidirect
60. #16811284C22semidirect
61. #16811284C22semidirect
62. #16811284C22semidirect
63. #16811281C22semidirect
64. #16811277C22semidirect
65. #16811276C22semidirect
66. #16811273C22semidirect
67. #16811272C22semidirect
68. #16811272C22semidirect
69. #16811271C22semidirect
70. #16811268C22semidirect
71. #16811266C22semidirect
72. #16811265C22semidirect
73. #16811262C22semidirect
74. #16811261C22semidirect
75. #16811261C22semidirect
76. #16811252C22semidirect
77. #16811251C22semidirect
78. #16811250C22semidirect
80. #16811248C22semidirect
81. #16811247C22semidirect
82. #16811245C22semidirect
83. #16811242C22semidirect
84. #16811237C22semidirect
85. #16811234C22semidirect
86. #16811231C22semidirect
87. #16811222C22semidirect
88. #16811222C22semidirect
89. #16811219C22semidirect
90. #16811219C22semidirect
91. #16811218C22semidirect
92. #16811217C22semidirect
93. #16811215C22semidirect
94. #16811213C22semidirect
95. #16811210C22semidirect
96. #16811207C22semidirect
97. #16811206C22semidirect
98. #16811203C22semidirect
99. #16811201C22semidirect
100. #16811201C22semidirect
101. #16811200C22semidirect
102. #16811197C22semidirect
103. #16811197C22semidirect
104. #16811197C22semidirect
105. #16811196C22semidirect
107. #16811178C22semidirect
108. #16811177C22semidirect
109. #16811160C22semidirect
110. #16811152C22semidirect
112. #16811136C22semidirect
113. #16811136C22semidirect
115. #16811134C22semidirect
116. #16811134C22semidirect
118. #16811133C22semidirect
120. #16811132C22semidirect
123. #16811130C22semidirect
124. #16811129C22semidirect
125. #16811129C22semidirect
126. #123×D53C22semidirect
128. C2×#13133193C22semidirect
129. C2×#13133193C22semidirect
130. C2×#13133193C22semidirect
131. C2×#13133193C22semidirect
132. C2×#13133193C22semidirect
133. C2×#13133193C22semidirect
134. C2×#13133193C22semidirect
136. C22⋊Q8×D53C22semidirect
137. C22⋊Q8×D53C22semidirect
139. #121×D53C22semidirect
141. #16811106C22semidirect
142. #16811103C22semidirect
143. #16811102C22semidirect
144. #16811101C22semidirect
147. C4×D4×D53C22semidirect
148. #117×D53C22semidirect
149. C22×C4⋊Dic53C22semidirect
150. C22×#11719919C22semidirect
152. C2×2−1+4×C53C22semidirect
153. C23×Q8×C53C22semidirect
154. D4×Q8×C53C22semidirect
155. D4×Q8×C53C22semidirect
156. C53×#548C22semidirect
157. C53×#548C22semidirect
158. C53×#536C22semidirect
159. C53×#536C22semidirect
160. C53×#525C22semidirect
161. C53×#525C22semidirect
162. C53×#519C22semidirect
166. C2×#11719949C23semidirect
175. C2×Q8×D53C23semidirect
190. #13133217C23semidirect
191. #13133216C23semidirect
192. #13133216C23semidirect
193. #13133215C23semidirect
194. #13133215C23semidirect
195. #13133215C23semidirect
199. #13133212C23semidirect
200. #13133212C23semidirect
202. #13133211C23semidirect
203. #13133210C23semidirect
204. #13133210C23semidirect
205. #13133210C23semidirect
206. #13133209C23semidirect
207. #13133209C23semidirect
208. #13133208C23semidirect
209. #13133208C23semidirect
210. #13133208C23semidirect
211. #13133207C23semidirect
212. #13133207C23semidirect
213. #13133207C23semidirect
214. #13133207C23semidirect
215. #13133207C23semidirect
217. #13133206C23semidirect
218. #13133206C23semidirect
227. #13133202C23semidirect
231. #13133201C23semidirect
235. #13133200C23semidirect
239. #13133199C23semidirect
240. #13133199C23semidirect
243. #13133198C23semidirect
247. #13133197C23semidirect
252. #13133196C23semidirect
253. #13133196C23semidirect
258. #13133195C23semidirect
259. #13133195C23semidirect
264. #13133194C23semidirect
265. #13133194C23semidirect
266. #13133194C23semidirect
282. #13133193C23semidirect
283. #13133193C23semidirect
284. #13133193C23semidirect
285. #13133193C23semidirect
286. #13133193C23semidirect
287. #13133193C23semidirect
296. #13133191C23semidirect
300. #13133190C23semidirect
306. #13133189C23semidirect
309. #13133188C23semidirect
319. Q8×Dic53C23semidirect
320. Q8×Dic53C23semidirect
321. Q8×Dic53C23semidirect
322. C4×Dic106C23semidirect
323. C4×Dic106C23semidirect
324. #13133182C23semidirect
328. C4×D212C23semidirect
333. D4×Dic53C23semidirect
344. C4×C22⋊D53C23semidirect
352. #13133177C23semidirect
355. #13133176C23semidirect
359. #13133175C23semidirect
362. #13133174C23semidirect
365. #13133173C23semidirect
370. C2×C4⋊Dic53C23semidirect
376. C2×#11719919C23semidirect
381. C4⋊C4×D53C23semidirect
382. C4⋊C4×D53C23semidirect
399. C2×#41×C53C23semidirect
406. C22×Q8×C53C23semidirect
409. C4⋊Q8×C53C23semidirect
410. C4⋊Q8×C53C23semidirect
411. #124×C53C23semidirect
412. #124×C53C23semidirect
419. C22⋊Q8×C53C23semidirect
420. C22⋊Q8×C53C23semidirect
421. C22⋊Q8×C53C23semidirect
422. C22⋊Q8×C53C23semidirect
428. C4×Q8×C53C23semidirect
429. C4×Q8×C53C23semidirect
637. C22×D532−1+4semidirect
774. #3486D53semidirect
788. C2×2−1+4C2×D53semidirect
790. C23×Q8C2×D53semidirect
828. D4×Q8C2×D53semidirect
829. D4×Q8C2×D53semidirect
834. #548C2×D53semidirect
835. #548C2×D53semidirect
878. #536C2×D53semidirect
879. #536C2×D53semidirect
900. #525C2×D53semidirect
901. #525C2×D53semidirect
921. #519C2×D53semidirect
929. C53#62819semidirect
944. C2×#41C22×D53semidirect
953. C22×Q8C22×D53semidirect
976. C4⋊Q8C22×D53semidirect
977. C4⋊Q8C22×D53semidirect
1004. #124C22×D53semidirect
1005. #124C22×D53semidirect
1078. C22⋊Q8C22×D53semidirect
1079. C22⋊Q8C22×D53semidirect
1080. C22⋊Q8C22×D53semidirect
1081. C22⋊Q8C22×D53semidirect
1124. C4×Q8C22×D53semidirect
1125. C4×Q8C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202890132
#202889942
#202889562
#202889312
#202889142
#202887652
#202887572
#202885512
#202885102
#202884642
#202884572
#202884212
#202884162
#202883982
#202883932
#202883882
#202883662
#525×D532
C22×#131331932
C53×#34862
#6281953