Finite Group Databasebeta

← #11910373

Subgroups — #11910373

Order 1152.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596137C211yesmaximal, characteristic, complemented
2C3×#5656C211yesmaximal, characteristic, complemented
3C3×#5651C211yesmaximal, characteristic, complemented
4#10595262C211yesmaximal, characteristic, complemented
5#10595261C211yesmaximal, characteristic, complemented
6#10595159C211yesmaximal, characteristic, complemented
7#10595153C211yesmaximal, characteristic, complemented
8#10595005C212yesmaximal, complemented
9#10594978C212yesmaximal, complemented
10#10594593C212yesmaximal, complemented
11#10594518C212yesmaximal, complemented
12#10594403C212yesmaximal, complemented
13#10594340C212yesmaximal, complemented
14#10594242C212yesmaximal, complemented
15#10594240C212yesmaximal, complemented
16#10594236C212yesmaximal, complemented
17#10594107C212yesmaximal, complemented
18#10594106C212yesmaximal, complemented
19#10594066C212yesmaximal, complemented
20#87115—31nomaximal
21#86048—31nomaximal
22C2×C3×#237C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×#624C2211yescharacteristic, complemented
25C2×#3799C2212yes—
26C2×#3799C2211yescharacteristic, complemented
27C32×#123C2211yescharacteristic
28#64149C2211yescharacteristic
29#64146C2211yescharacteristic
30#64139C2212yes—
31#64107C2212yescomplemented
32#64104C2212yescomplemented
33#64093C2212yes—
34#64092C2212yescomplemented
35#64091C2212yescomplemented
36C3×#937C2211yescharacteristic
37C3×#936C2211yescharacteristic
38C3×#935C2211yescharacteristic
39C3×#929C2211yescharacteristic, complemented
40C3×#924C2212yescomplemented
41C3×#896C2212yescomplemented
42C3×#893C2212yescomplemented
43C3×#889C2212yescomplemented
44C3×#888C2212yescomplemented
45C3×#884C2212yes—
46C3×#882C2211yescharacteristic, complemented
47C3×#67⋊C4C2212yes—
48C3×#879C2212yescomplemented
49C3×#879C2212yescomplemented
50C3×#878C2212yescomplemented
51C3×#877C2211yescharacteristic, complemented
52#63981C2212yes—
53#63981C2211yescharacteristic, complemented
54#63978C2212yes—
55#63977C2212yes—
56#63977C2212yescomplemented
57#63975C2212yescomplemented
58#63971C2212yescomplemented
59#63971C2212yescomplemented
60#63961C2211yescharacteristic, complemented
61#63959C2212yes—
62#63958C2212yes—
63#63958C2212yes—
64#63955C2211yescharacteristic, complemented
65#63953C2212yes—
66#63952C2212yes—
67#63952C2212yescomplemented
68#63952C2212yescomplemented
69#63916C2212yescomplemented
70#63911C2212yes—
71#63910C2212yes—
72#63910C2212yescomplemented
73#63910C2212yescomplemented
74#63909C2212yes—
75#63907C2212yes—
76#63907C2212yescomplemented
77#63904C2212yes—
78#63904C2212yescomplemented
79#63904C2212yescomplemented
80#63897C2212yescomplemented
81#63897C2212yescomplemented
82#63895C2212yescomplemented
83#63894C2212yescomplemented
84#63893C2212yescomplemented
85#63890C2212yescomplemented
86#63888C2212yescomplemented
87#63888C2212yescomplemented
88#63886C2212yes—
89#63884C2212yescomplemented
90C4×#624C2212yescomplemented
91C4×D3×Dic3C2211yescharacteristic, complemented
92#63873C2211yescharacteristic, complemented
93#63868C2212yescomplemented
94#63865C2212yescomplemented
95#63864C2211yescharacteristic, complemented
96#63862C2212yescomplemented
97#63859C2212yescomplemented
98#63856C2212yescomplemented
99#63854C2212yes—
100#63853C2212yescomplemented
101#63852C2212yes—
102#63850C2212yes—
103#63850C2212yescomplemented
104#63847C2212yescomplemented
105#63845C2212yescomplemented
106#63841C2212yescomplemented
107#63837C2212yescomplemented
108#63836C2212yescomplemented
109C3×#563—31no—
110C3×#525—31no—
111#5832—31no—
112#5828—31no—
113#5791—32no—
114#5735—32no—
115#5725—32no—
116#5711—32no—
117#5711—32no—
118#5706—32no—
119#5706—32no—
120#5700—32no—
121#5691—32no—
122#5683—31no—
123#5668—31no—
124#5667—32no—
125#5666—31no—
126#5666—31no—
127#5666—31no—
128#5666—61no—
129#5656—31no—
130#5656D311yescharacteristic, complemented
131#5651D311yescharacteristic, complemented
132#5647—32no—
133#5647—32no—
134#5647—32no—
135#5646—32no—
136#5627—32no—
137#5627—32no—
138#5621—32no—
139#5620—32no—
140#5595—31no—
141#5595—32no—
142#5594—31no—
143#5557—32no—
144#5548—32no—
145#5547—32no—
146#5538—32no—
147#5528—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C2×C32×D4C2311yescharacteristic
151C22×C32×C4C2311yescharacteristic
152C2×#638C2312yes—
153C2×#638C2312yes—
154C2×#638C2312yes—
155C2×C4⋊(C3⋊D3)C2312yes—
156C2×C4⋊(C3⋊D3)C2311yescharacteristic
157C2×C4⋊(C3⋊D3)C2312yes—
158C2×C4×C3⋊D3C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2311yescharacteristic
161C2×C3×#67C2311yescharacteristic
162C22×C3×Dic3C2311yescharacteristic
163C22×C3×Dic3C2311yescharacteristic
164C22×C3×Dic3C2311yescharacteristic
165C3×#237—42no—
166C2×C3×D12C2312yes—
167C2×C3×C4×D3—42no—
168C2×C3×C4×D3C2312yes—
169C2×C3×C4×D3C2311yescharacteristic
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2311yescharacteristic
173C2×C3×Dic6C2311yescharacteristic
174C2×#627C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#624—42no—
182C2×#624C2312yes—
183C2×#624C2312yes—
184C2×#624C2312yes—
185C2×#624C2312yes—
186C2×D3×Dic3C2312yes—
187#3799—44no—
188#3799—42no—
189C32×C4⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191C32×C22⋊C4C2312yes—
192#3757C2311yescharacteristic
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3752C2312yes—
197C4⋊(C3⋊Dic3)C2312yes—
198#3750C2312yes—
199C4×C3⋊Dic3C2311yescharacteristic
200C3×#217C2311yescharacteristic
201C3×#217C2312yes—
202C3×#217C2311yescharacteristic
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×C4⋊Dic3C2312yes—
209C3×C4⋊Dic3C2312yes—
210C3×Dic3⋊C4C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×C4×Dic3C2312yes—
218C3×C4×Dic3C2312yes—
219C3×C4×Dic3C2311yescharacteristic
220#3724C2312yes—
221#3724C2312yes—
222#3724C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3529—91noSylow
241C2×C3×#41—31no—
242C23×C3×C4—31no—
243C2×#239—31no—
244C2×#239—32no—
245C2×#237C2×D311yescharacteristic
246C2×#235—32no—
247C2×#235—31no—
248C22×C4×D3—31no—
249C22×C4×D3—31no—
250C22×C4×D3C2×D311yescharacteristic, complemented
251C3×C4⋊Q8—32no—
252C3×#126—32no—
253C3×#126—32no—
254C3×#125—32no—
255C3×#124—31no—
256C3×#123—21no—
257C3×#123—31no—
258C3×#123—31no—
259C3×#123C2×D311yescharacteristic
260C3×#123C2×D311yescharacteristic
261C3×C22⋊Q8—32no—
262C3×C22⋊Q8—32no—
263C3×C22⋊Q8—32no—
264C3×#121—32no—
265C3×#120—31no—
266C3×#120—31no—
267C3×C4×D4—32no—
268C3×C4×D4—32no—
269C3×#117—31no—
270#953—32no—
271#953—32no—
272#947—32no—
273#947—32no—
274#947—31no—
275#946—32no—
276#946—32no—
277#946—32no—
278#944—31no—
279#944—31no—
280#940—31no—
281#940—31no—
282#940—32no—
283#940—61no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#938—32no—
289#938—32no—
290#938—32no—
291#937—31no—
292#937—31no—
293#937—32no—
294#937—31no—
295#937—61no—
296#937C2×D311yescharacteristic
297#936—32no—
298#936C2×D311yescharacteristic
299#935—31no—
300#935—32no—
301#935C2×D311yescharacteristic
302#930—32no—
303#930—32no—
304#930—32no—
305#930—32no—
306#930—62no—
307#929—31no—
308#929—32no—
309#929—32no—
310#929C2×D311yescharacteristic, complemented
311C4×#67—32no—
312C4×#67—32no—
313C4×#67—32no—
314C4×#67—32no—
315C4×#67—32no—
316C4×#67—32no—
317#926—31no—
318#926—32no—
319#924—32no—
320#924C2×D312yescomplemented
321C2×C4×Dic3—31no—
322#898—32no—
323#898—32no—
324#898—32no—
325#898—32no—
326#898—62no—
327#897—32no—
328#897—32no—
329#896—32no—
330#896—32no—
331#896—32no—
332#896—32no—
333#896—32no—
334#896C2×D312yescomplemented
335#895—32no—
336#895—32no—
337#895—32no—
338#895—32no—
339#895—32no—
340#895—32no—
341#895—32no—
342#895—32no—
343#895—62no—
344#894—32no—
345#894—32no—
346#894—32no—
347#894—32no—
348#894—32no—
349#894—32no—
350#894—32no—
351#894—32no—
352#894—32no—
353#894—32no—
354#893—32no—
355#893—32no—
356#893—32no—
357#893—32no—
358#893C2×D312yescomplemented
359#892—32no—
360#892—32no—
361#890—32no—
362#889—32no—
363#889—32no—
364#889—32no—
365#889C2×D312yescomplemented
366#888C2×D312yescomplemented
367#887—32no—
368#886—32no—
369#885—32no—
370#885—32no—
371#885—32no—
372#885—32no—
373#885—32no—
374#885—32no—
375#884—32no—
376#884—32no—
377#884—32no—
378#884—32no—
379#884—32no—
380#884—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#884—62no—
385#884C2×D312yes—
386#883—32no—
387#883—32no—
388#883—32no—
389#883—32no—
390#883—32no—
391#883—32no—
392#883—62no—
393#882—32no—
394#882—32no—
395#882—31no—
396#882—32no—
397#882—32no—
398#882—32no—
399#882—62no—
400#882C2×D311yescharacteristic, complemented
401#67⋊C4—32no—
402#67⋊C4—32no—
403#67⋊C4—32no—
404#67⋊C4C2×D312yes—
405#879—32no—
406#879—32no—
407#879C2×D312yescomplemented
408#879C2×D312yescomplemented
409#878—32no—
410#878C2×D312yescomplemented
411#877—31no—
412#877C2×D311yescharacteristic, complemented
413#876—32no—
414#876—32no—
415#875—31no—
416#875—32no—
417#874—32no—
418C4×D12—32no—
419#872—32no—
420C42×D3—31no—
421C42×D3—32no—
422C42×D3—32no—
423C4×Dic6—32no—
424C23×C32C2411yescharacteristic
425C23×C32C2411yescharacteristic
426C22×C3⋊D3—42no—
427C22×C3⋊D3—41no—
428C22×C3⋊D3C2412yes—
429C22×C3⋊D3C2412yes—
430C22×C3×D3—42no—
431C22×C3×D3—41no—
432C22×C3×D3C2412yes—
433C22×C3×D3C2411yescharacteristic
434C32×D4—41no—
435C2×C32×C4—41no—
436C2×C32×C4C2412yes—
437C2×C32×C4C2411yescharacteristic
438C2×C32×C4C2412yes—
439#638—42no—
440#638—42no—
441#638—42no—
442C2×C3⋊Dic3C2412yes—
443C2×C3⋊Dic3C2412yes—
444C4⋊(C3⋊D3)—41no—
445C4⋊(C3⋊D3)—42no—
446C4⋊(C3⋊D3)—42no—
447C4×C3⋊D3—42no—
448C3×#67—41no—
449C3×#67—41no—
450C3×#67—42no—
451C2×C3×Dic3—22no—
452C2×C3×Dic3—22no—
453C2×C3×Dic3—41no—
454C2×C3×Dic3C2412yes—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C2×C3×Dic3C2412yes—
458C2×C3×Dic3C2412yes—
459C2×C3×Dic3C2411yescharacteristic
460C2×C3×Dic3C2411yescharacteristic
461C2×C3×Dic3C2411yescharacteristic
462C3×D12—42no—
463C3×C4×D3—24no—
464C3×C4×D3—22no—
465C3×C4×D3—42no—
466C3×Dic6—42no—
467C3×Dic6—41no—
468C3×Dic6—41no—
469#627—42no—
470#626—42no—
471#626—42no—
472#626—42no—
473#626—42no—
474#626—42no—
475#626—42no—
476#624—24no—
477#624—24no—
478#624—42no—
479#624—42no—
480D3×Dic3—42no—
481#563—31no—
482#563—92no—
483#562—92no—
484#562—92no—
485#562—92no—
486H(3,𝔽4)—91no—
487#560—91no—
488#560—92no—
489#560—92no—
490#560—91no—
491#532—92no—
492#532—91no—
493#529—92no—
494#529—92no—
495#529—92no—
496#525—31no—
497#525—92no—
498#525—92no—
499#525—91no—
500C24×C3—31no—
501C23×D3—31no—
502C23×D3—31no—
503C23×D3—61no—
504C23×D3C22×D311yescharacteristic
505C3×#41—122no—
506C2×C3×Q8—31no—
507C2×C3×Q8—31no—
508C2×C3×Q8—32no—
509C2×C3×D4—21no—
510C2×C3×D4—31no—
511C2×C3×D4—32no—
512C2×C3×D4—31no—
513C2×C3×D4—32no—
514C2×C3×D4C22×D311yescharacteristic
515C2×C3×D4C22×D311yescharacteristic
516C22×C3×C4—21no—
517C22×C3×C4—31no—
518C22×C3×C4—31no—
519C22×C3×C4—31no—
520C22×C3×C4—31no—
521C22×C3×C4—32no—
522C22×C3×C4—32no—
523C22×C3×C4—122no—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D311yescharacteristic
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—62no—
539C2×#67—62no—
540C2×#67—62no—
541C2×#67C22×D312yes—
542C2×#67C22×D311yescharacteristic
543C2×#67C22×D311yescharacteristic
544C22×Dic3—32no—
545C22×Dic3C22×D311yescharacteristic
546C22×Dic3C22×D311yescharacteristic
547C22×Dic3C22×D311yescharacteristic
548#239—124no—
549#239—122no—
550#237—42no—
551#235—124no—
552#235—122no—
553C2×D12—32no—
554C2×D12—32no—
555C2×D12—32no—
556C2×D12—32no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—32no—
560C2×D12—32no—
561C2×D12—31no—
562C2×D12—32no—
563C2×D12—32no—
564C2×D12—31no—
565C2×D12—62no—
566C2×D12—62no—
567C2×D12—61no—
568C2×D12C22×D312yes—
569C2×C4×D3—32no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—42no—
581C2×C4×D3—62no—
582C2×C4×D3—122no—
583C2×C4×D3—122no—
584C2×C4×D3C22×D311yescharacteristic
585C2×C4×D3C22×D312yes—
586C2×C4×D3C22×D312yes—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6C22×D311yescharacteristic
590C2×Dic6C22×D312yes—
591C2×Dic6C22×D311yescharacteristic
592C3×C4⋊C4—22no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4C22×D312yes—
603C3×C4⋊C4C22×D312yes—
604C3×C22⋊C4—22no—
605C3×C22⋊C4—21no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4C22×D311yescharacteristic
615C3×C22⋊C4C22×D312yes—
616C3×C22⋊C4C22×D311yescharacteristic
617C3×C22⋊C4C22×D312yes—
618C3×C42—32no—
619C3×C42—32no—
620C3×C42—31no—
621#217—31no—
622#217—31no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—61no—
629#217C22×D311yescharacteristic
630#217C22×D312yes—
631#217C22×D311yescharacteristic
632#217C22×D312yes—
633#217C22×D312yes—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4—32no—
653(C2×D3)⋊C4—32no—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—32no—
657(C2×D3)⋊C4—32no—
658(C2×D3)⋊C4—32no—
659(C2×D3)⋊C4—62no—
660(C2×D3)⋊C4—62no—
661(C2×D3)⋊C4—62no—
662(C2×D3)⋊C4—62no—
663(C2×D3)⋊C4C22×D312yes—
664(C2×D3)⋊C4C22×D312yes—
665(C2×D3)⋊C4C22×D312yes—
666C4⋊Dic3—32no—
667C4⋊Dic3—32no—
668C4⋊Dic3—32no—
669C4⋊Dic3—32no—
670C4⋊Dic3—32no—
671C4⋊Dic3—62no—
672C4⋊Dic3C22×D312yes—
673C4⋊Dic3C22×D312yes—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—62no—
686Dic3⋊C4C22×D312yes—
687Dic3⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692Dic3⋊C4C22×D312yes—
693C4×Dic3—31no—
694C4×Dic3—31no—
695C4×Dic3—32no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—61no—
702C4×Dic3C22×D312yes—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—21no—
706C22×C32—21no—
707C22×C32—22no—
708C22×C32—22no—
709C22×C32C2511yescharacteristic
710C2×C3⋊D3—22no—
711C2×C3⋊D3—22no—
712C2×C3⋊D3—22no—
713C2×C3⋊D3—22no—
714C2×C3⋊D3—22no—
715C2×C3⋊D3—22no—
716C2×C3⋊D3—44no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—22no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—44no—
723C32×C4—21no—
724C32×C4—22no—
725C32×C4—22no—
726C3⋊Dic3—22no—
727C3⋊Dic3—22no—
728C3×Dic3—22no—
729C3×Dic3—22no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—22no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3H(5,𝔽2)12yes—
736C2×#41—31no—
737C2×#41—92no—
738C2×#41—91no—
739C23×C4—31no—
740C23×C4—91no—
741C4⋊Q8—32no—
742C4⋊Q8—91no—
743#127—92no—
744#127—91no—
745#126—32no—
746#126—32no—
747#126—92no—
748#126—92no—
749#126—92no—
750#126—92no—
751#125—32no—
752#125—92no—
753#125—92no—
754#124—31no—
755#124—92no—
756#124—91no—
757#124—92no—
758#124—92no—
759#124—92no—
760#124—92no—
761#123—31no—
762#123—31no—
763#123—92no—
764#123—92no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—91no—
773#123—92no—
774#123D3211yescharacteristic
775C22⋊Q8—32no—
776C22⋊Q8—32no—
777C22⋊Q8—32no—
778C22⋊Q8—92no—
779C22⋊Q8—92no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784#121—32no—
785#121—92no—
786#121—92no—
787#121—92no—
788#121—92no—
789#121—92no—
790#121—92no—
791#121—92no—
792#121—92no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—92no—
797#121—92no—
798#121—92no—
799#120—31no—
800#120—31no—
801#120—91no—
802#120—92no—
803#120—92no—
804#120—92no—
805#120—91no—
806#120—92no—
807C4×Q8—92no—
808C4×D4—32no—
809C4×D4—32no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817#117—31no—
818#117—92no—
819#117—91no—
820#117—92no—
821C2×C42—92no—
822C2×C42—91no—
823C23×C3—21no—
824C23×C3—21no—
825C23×C3—32no—
826C23×C3—31no—
827C23×C3—121no—
828C23×C3—122no—
829C23×C3C23×D311yescharacteristic
830C23×C3C23×D311yescharacteristic
831C23×C3C23×D311yescharacteristic
832C23×C3C23×D311yescharacteristic
833C22×D3—32no—
834C22×D3—32no—
835C22×D3—32no—
836C22×D3—32no—
837C22×D3—41no—
838C22×D3—42no—
839C22×D3—62no—
840C22×D3—62no—
841C22×D3—121no—
842C22×D3—121no—
843C22×D3—122no—
844C22×D3—122no—
845C22×D3—241no—
846C22×D3—242no—
847C22×D3C23×D312yes—
848C22×D3C23×D311yescharacteristic
849C3×Q8—121no—
850C3×Q8—122no—
851C3×Q8—121no—
852C3×D4—41no—
853C3×D4—41no—
854C3×D4—81no—
855C3×D4—122no—
856C3×D4—122no—
857C3×D4—121no—
858C3×D4—121no—
859C2×C3×C4—21no—
860C2×C3×C4—22no—
861C2×C3×C4—22no—
862C2×C3×C4—31no—
863C2×C3×C4—32no—
864C2×C3×C4—32no—
865C2×C3×C4—32no—
866C2×C3×C4—32no—
867C2×C3×C4—31no—
868C2×C3×C4—31no—
869C2×C3×C4—32no—
870C2×C3×C4—41no—
871C2×C3×C4—41no—
872C2×C3×C4—64no—
873C2×C3×C4—62no—
874C2×C3×C4—62no—
875C2×C3×C4—62no—
876C2×C3×C4—81no—
877C2×C3×C4—122no—
878C2×C3×C4—121no—
879C2×C3×C4C23×D311yescharacteristic
880C2×C3×C4C23×D311yescharacteristic
881C2×C3×C4C23×D312yes—
882C2×C3×C4C23×D312yes—
883C2×C3×C4C23×D312yes—
884C2×C3×C4C23×D312yes—
885#67—41no—
886#67—41no—
887#67—42no—
888#67—122no—
889#67—122no—
890#67—122no—
891#67—122no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—122no—
900#67—242no—
901#67—242no—
902#67—242no—
903C2×Dic3—22no—
904C2×Dic3—22no—
905C2×Dic3—32no—
906C2×Dic3—32no—
907C2×Dic3—32no—
908C2×Dic3—32no—
909C2×Dic3—41no—
910C2×Dic3—62no—
911C2×Dic3—62no—
912C2×Dic3—122no—
913C2×Dic3C23×D312yes—
914C2×Dic3C23×D312yes—
915C2×Dic3C23×D312yes—
916C2×Dic3C23×D312yes—
917C2×Dic3C23×D311yescharacteristic
918C2×Dic3C23×D311yescharacteristic
919C2×Dic3C23×D312yes—
920C2×Dic3C23×D311yescharacteristic
921D12—42no—
922D12—122no—
923D12—122no—
924D12—122no—
925D12—121no—
926D12—121no—
927D12—122no—
928D12—122no—
929D12—122no—
930D12—122no—
931D12—122no—
932D12—122no—
933D12—122no—
934D12—242no—
935D12—241no—
936D12—242no—
937C4×D3—24no—
938C4×D3—22no—
939C4×D3—42no—
940C4×D3—64no—
941C4×D3—64no—
942C4×D3—64no—
943C4×D3—64no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—122no—
950C4×D3—122no—
951C4×D3—242no—
952Dic6—41no—
953Dic6—42no—
954Dic6—41no—
955Dic6—122no—
956Dic6—122no—
957C2×C32—41no—
958C2×C32—41no—
959C2×C32C2×H(5,𝔽2)11yescharacteristic
960C2×C32#58512yes—
961C3⋊D3—42no—
962C3⋊D3—42no—
963C3×D3—41no—
964C3×D3—42no—
965C24—31no—
966C24—91no—
967#41—122no—
968#41—364no—
969#41—362no—
970C2×Q8—32no—
971C2×Q8—31no—
972C2×Q8—31no—
973C2×Q8—92no—
974C2×D4—32no—
975C2×D4—31no—
976C2×D4—31no—
977C2×D4—32no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—92no—
988C2×D4—92no—
989C2×D4—91no—
990C2×D4C2×D3211yescharacteristic
991C22×C4—31no—
992C22×C4—31no—
993C22×C4—31no—
994C22×C4—31no—
995C22×C4—32no—
996C22×C4—32no—
997C22×C4—92no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—122no—
1004C22×C4—362no—
1005C22×C4C2×D3211yescharacteristic
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—32no—
1014C4⋊C4—32no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4C2×D3212yes—
1024C22⋊C4—31no—
1025C22⋊C4—31no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—92no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—91no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4C2×D3211yescharacteristic
1049C22⋊C4C2×D3212yes—
1050C42—32no—
1051C42—31no—
1052C42—32no—
1053C42—92no—
1054C42—92no—
1055C42—92no—
1056C42—91no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—22no—
1060C22×C3—22no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—21no—
1066C22×C3—42no—
1067C22×C3—42no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—62no—
1071C22×C3—61no—
1072C22×C3—62no—
1073C22×C3—62no—
1074C22×C3—62no—
1075C22×C3—124no—
1076C22×C3C24×D311yescharacteristic
1077C22×C3C24×D311yescharacteristic
1078C2×D3—22no—
1079C2×D3—21no—
1080C2×D3—22no—
1081C2×D3—22no—
1082C2×D3—22no—
1083C2×D3—44no—
1084C2×D3—62no—
1085C2×D3—62no—
1086C2×D3—62no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—122no—
1097C2×D3—122no—
1098C2×D3—122no—
1099C2×D3—122no—
1100C2×D3—122no—
1101C2×D3—122no—
1102C2×D3—124no—
1103C2×D3—124no—
1104C2×D3—244no—
1105C3×C4—21no—
1106C3×C4—22no—
1107C3×C4—22no—
1108C3×C4—22no—
1109C3×C4—21no—
1110C3×C4—22no—
1111C3×C4—32no—
1112C3×C4—42no—
1113C3×C4—42no—
1114C3×C4—41no—
1115C3×C4—62no—
1116C3×C4—62no—
1117C3×C4—62no—
1118C3×C4—62no—
1119C3×C4—61no—
1120C3×C4—61no—
1121C3×C4—62no—
1122Dic3—21no—
1123Dic3—21no—
1124Dic3—22no—
1125Dic3—22no—
1126Dic3—22no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—122no—
1134Dic3—122no—
1135Dic3#100412yes—
1136C32#352911yescharacteristic, complemented, Sylow
1137C23—32no—
1138C23—31no—
1139C23—92no—
1140C23—92no—
1141C23—121no—
1142C23—122no—
1143C23—361no—
1144C23—362no—
1145C23C22×D3211yescharacteristic
1146C23C22×D3211yescharacteristic
1147Q8—121no—
1148Q8—122no—
1149Q8—121no—
1150Q8—362no—
1151D4—41no—
1152D4—122no—
1153D4—121no—
1154D4—121no—
1155D4—122no—
1156D4—362no—
1157D4—361no—
1158D4—362no—
1159D4—362no—
1160D4—362no—
1161D4—362no—
1162D4—362no—
1163D4—362no—
1164D4—362no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168C2×C4—31no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—32no—
1172C2×C4—32no—
1173C2×C4—31no—
1174C2×C4—32no—
1175C2×C4—31no—
1176C2×C4—41no—
1177C2×C4—64no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—92no—
1182C2×C4—92no—
1183C2×C4—122no—
1184C2×C4—121no—
1185C2×C4—184no—
1186C2×C4—184no—
1187C2×C4—362no—
1188C2×C4—362no—
1189C2×C4—362no—
1190C2×C4—362no—
1191C2×C4C22×D3212yes—
1192C2×C4C22×D3211yescharacteristic
1193C2×C4C22×D3212yes—
1194C2×C3—21no—
1195C2×C3—22no—
1196C2×C3—41no—
1197C2×C3—41no—
1198C2×C3—41no—
1199C2×C3—41no—
1200C2×C3—81no—
1201C2×C3—81no—
1202C2×C3—122no—
1203C2×C3—121no—
1204C2×C3C2×#100411yescharacteristic
1205C2×C3#596412yes—
1206C2×C3D3×H(5,𝔽2)11yescharacteristic
1207C2×C3#596812yes—
1208D3—42no—
1209D3—41no—
1210D3—122no—
1211D3—122no—
1212D3—122no—
1213D3—122no—
1214D3—242no—
1215D3—242no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—22no—
1220C22—62no—
1221C22—61no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—124no—
1226C22—182no—
1227C22—182no—
1228C22—182no—
1229C22—182no—
1230C22—182no—
1231C22—182no—
1232C22—364no—
1233C22C23×D3211yescharacteristic
1234C4—22no—
1235C4—21no—
1236C4—22no—
1237C4—32no—
1238C4—61no—
1239C4—61no—
1240C4—62no—
1241C4—62no—
1242C4—62no—
1243C4—62no—
1244C4—62no—
1245C4—182no—
1246C4—182no—
1247C3—21no—
1248C3#8604811yescharacteristic, complemented
1249C3#8711511yescharacteristic, complemented
1250C2—41no—
1251C2—41no—
1252C2—122no—
1253C2—121no—
1254C2—362no—
1255C2—362no—
1256C2D3×#100411yescharacteristic
1257C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #10596137C2semidirect
2. C3×#5656C2semidirect
3. C3×#5651C2semidirect
4. #10595262C2semidirect
5. #10595261C2semidirect
6. #10595159C2semidirect
7. #10595153C2semidirect
8. #10595005C2semidirect
9. #10594978C2semidirect
10. #10594593C2semidirect
11. #10594518C2semidirect
12. #10594403C2semidirect
13. #10594340C2semidirect
14. #10594242C2semidirect
15. #10594240C2semidirect
16. #10594236C2semidirect
17. #10594107C2semidirect
18. #10594106C2semidirect
19. #10594066C2semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×#624C22semidirect
26. C2×#3799C22semidirect
31. #64107C22semidirect
32. #64104C22semidirect
34. #64092C22semidirect
35. #64091C22semidirect
39. C3×#929C22semidirect
40. C3×#924C22semidirect
41. C3×#896C22semidirect
42. C3×#893C22semidirect
43. C3×#889C22semidirect
44. C3×#888C22semidirect
46. C3×#882C22semidirect
48. C3×#879C22semidirect
49. C3×#879C22semidirect
50. C3×#878C22semidirect
51. C3×#877C22semidirect
53. #63981C22semidirect
56. #63977C22semidirect
57. #63975C22semidirect
58. #63971C22semidirect
59. #63971C22semidirect
60. #63961C22semidirect
64. #63955C22semidirect
67. #63952C22semidirect
68. #63952C22semidirect
69. #63916C22semidirect
72. #63910C22semidirect
73. #63910C22semidirect
76. #63907C22semidirect
78. #63904C22semidirect
79. #63904C22semidirect
80. #63897C22semidirect
81. #63897C22semidirect
82. #63895C22semidirect
83. #63894C22semidirect
84. #63893C22semidirect
85. #63890C22semidirect
86. #63888C22semidirect
87. #63888C22semidirect
89. #63884C22semidirect
90. C4×#624C22semidirect
91. C4×D3×Dic3C22semidirect
92. #63873C22semidirect
93. #63868C22semidirect
94. #63865C22semidirect
95. #63864C22semidirect
96. #63862C22semidirect
97. #63859C22semidirect
98. #63856C22semidirect
100. #63853C22semidirect
103. #63850C22semidirect
104. #63847C22semidirect
105. #63845C22semidirect
106. #63841C22semidirect
107. #63837C22semidirect
108. #63836C22semidirect
130. #5656D3semidirect
131. #5651D3semidirect
250. C22×C4×D3C2×D3semidirect
310. #929C2×D3semidirect
320. #924C2×D3semidirect
334. #896C2×D3semidirect
358. #893C2×D3semidirect
365. #889C2×D3semidirect
366. #888C2×D3semidirect
400. #882C2×D3semidirect
407. #879C2×D3semidirect
408. #879C2×D3semidirect
410. #878C2×D3semidirect
412. #877C2×D3semidirect
1136. C32#3529semidirect
1248. C3#86048semidirect
1249. C3#87115semidirect

Maximal subgroups

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

subgroupindex
#105961372
C3×#56562
C3×#56512
#105952622
#105952612
#105951592
#105951532
#105950052
#105949782
#105945932
#105945182
#105944032
#105943402
#105942422
#105942402
#105942362
#105941072
#105941062
#105940662
#871153
#860483