Finite Group Databasebeta

← #11910045

Subgroups — #11910045

Order 1152.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596003C211yesmaximal, characteristic, complemented
2C3×#5529C211yesmaximal, characteristic, complemented
3C3×#5522C211yesmaximal, characteristic, complemented
4#10595007C211yesmaximal, characteristic, complemented
5#10594955C211yesmaximal, characteristic, complemented
6#10594839C211yesmaximal, characteristic, complemented
7#10594830C211yesmaximal, characteristic, complemented
8#10594594C211yesmaximal, characteristic, complemented
9#10594592C211yesmaximal, characteristic, complemented
10#10594566C211yesmaximal, characteristic, complemented
11#10594561C211yesmaximal, characteristic, complemented
12#10594347C211yesmaximal, characteristic, complemented
13#10594329C211yesmaximal, characteristic, complemented
14#10594327C211yesmaximal, characteristic, complemented
15#10594322C211yesmaximal, characteristic, complemented
16#10594208C212yesmaximal, complemented
17#10594203C212yesmaximal, complemented
18#10594202C212yesmaximal, complemented
19#10594108C212yesmaximal, complemented
20#10593977C212yesmaximal, complemented
21#10593976C212yesmaximal, complemented
22#10593973C212yesmaximal, complemented
23#10593872C212yesmaximal, complemented
24#86843—31nomaximal
25#85855—31nomaximal
26C2×C3×#235C2211yescharacteristic
27C2×#3799C2211yescharacteristic
28C2×#3797C2211yescharacteristic
29C32×#117C2211yescharacteristic
30#64139C2211yescharacteristic
31C4×#638C2211yescharacteristic
32#64104C2211yescharacteristic
33#64102C2211yescharacteristic
34#64101C2211yescharacteristic
35#64097C2211yescharacteristic
36#64094C2212yes—
37#64093C2212yes—
38#64084C2212yes—
39#64081C2212yes—
40C3×C4×#67C2211yescharacteristic
41C3×#924C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#897C2211yescharacteristic
44C3×#893C2211yescharacteristic
45C3×#893C2211yescharacteristic
46C3×D3×C4⋊C4C2211yescharacteristic
47C3×#890C2211yescharacteristic
48C3×#887C2211yescharacteristic
49C3×#887C2211yescharacteristic
50C3×#887C2211yescharacteristic
51C3×#883C2212yes—
52C3×#67⋊C4C2212yes—
53C3×#67⋊C4C2212yes—
54C3×#879C2212yes—
55C3×#872C2212yes—
56C3×#872C2212yes—
57C3×C42×D3C2212yes—
58C3×#870C2212yes—
59#63979C2212yes—
60#63978C2211yescharacteristic
61#63966C2211yescharacteristic
62#63966C2212yes—
63#63964C2211yescharacteristic
64#63961C2211yescharacteristic
65#63959C2212yes—
66#63958C2212yes—
67#63958C2212yes—
68#63952C2212yes—
69C4×#627C2211yescharacteristic
70C4×#627C2212yes—
71#63916C2211yescharacteristic
72#63913C2212yes—
73#63911C2211yescharacteristic
74#63910C2212yes—
75#63910C2212yes—
76#63909C2212yes—
77#63908C2211yescharacteristic
78#63906C2212yes—
79#63906C2212yes—
80#63905C2212yes—
81#63904C2212yes—
82#63904C2212yes—
83#63904C2212yes—
84C4×#626C2211yescharacteristic
85C4×#626C2212yes—
86C4×#626C2212yes—
87C4×#625C2212yes—
88#63895C2212yes—
89#63894C2211yescharacteristic
90#63894C2212yes—
91#63883C2212yes—
92#63874C2211yescharacteristic
93#63869C2211yescharacteristic
94#63868C2211yescharacteristic
95#63868C2212yes—
96#63867C2212yes—
97#63867C2211yescharacteristic
98#63864C2211yescharacteristic
99#63863C2211yescharacteristic
100#63862C2212yes—
101#63859C2211yescharacteristic
102#63858C2212yes—
103#63857C2212yes—
104#63855C2211yescharacteristic
105#63854C2212yes—
106#63853C2212yes—
107#63852C2212yes—
108#63852C2211yescharacteristic
109#63852C2212yes—
110#63851C2212yes—
111#63850C2212yes—
112#63850C2212yes—
113#63850C2212yes—
114#63846C2212yes—
115#63844C2212yes—
116#63843C2211yescharacteristic
117Dic3×Dic6C2211yescharacteristic
118Dic3×Dic6C2211yescharacteristic
119#63840C2212yes—
120#63838C2212yes—
121#63836C2212yes—
122#63836C2212yes—
123#63836C2212yes—
124#63836C2212yes—
125C3×#552—31no—
126C3×C4×#41—31no—
127#5834—31no—
128#5831—31no—
129#5710—32no—
130#5709—32no—
131#5697—31no—
132#5693—32no—
133#5691—32no—
134#5685—31no—
135#5664—32no—
136#5663—32no—
137#5643—31no—
138#5633—31no—
139#5633—31no—
140#5624—31no—
141#5585—31no—
142#5576—31no—
143#5574—31no—
144#5572—31no—
145#5572—31no—
146#5569—31no—
147#5562—31no—
148#5562—32no—
149#5561—31no—
150#5561—32no—
151#5559—31no—
152#5559—32no—
153#5558—31no—
154#5558—32no—
155#5553—31no—
156#5538—31no—
157#5532—31no—
158#5532—31no—
159#5532—32no—
160#5532—32no—
161#5532—61no—
162#5529—32no—
163#5529D311yescharacteristic, complemented
164#5528—32no—
165#5522D311yescharacteristic, complemented
166#5514—31no—
167#5504—31no—
168#5479—31no—
169#5479—31no—
170#5479—32no—
171#5479—32no—
172C22×C32×C4C2311yescharacteristic
173C2×#638C2311yescharacteristic
174C2×#638C2312yes—
175C2×C4⋊(C3⋊D3)C2311yescharacteristic
176C2×C4⋊(C3⋊D3)C2312yes—
177C2×C4×C3⋊D3C2311yescharacteristic
178C2×C4×C3⋊D3C2312yes—
179C2×#634C2312yes—
180C2×C3×#67C2312yes—
181C2×C3×#67C2311yescharacteristic
182C22×C3×Dic3C2311yescharacteristic
183C22×C3×Dic3C2311yescharacteristic
184C3×#235—24no—
185C2×C3×D12C2311yescharacteristic
186C2×C3×C4×D3C2311yescharacteristic
187C2×C3×C4×D3C2312yes—
188C2×C3×C4×D3C2312yes—
189C2×C3×C4×D3C2312yes—
190C2×C3×C4×D3C2312yes—
191C2×C3×Dic6C2311yescharacteristic
192C2×C3×Dic6C2311yescharacteristic
193C2×#627C2312yes—
194C2×#627C2311yescharacteristic
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#626C2312yes—
198C2×#626C2312yes—
199C2×#626C2311yescharacteristic
200C2×#625C2312yes—
201C2×#624C2312yes—
202C2×#624C2312yes—
203C2×#624C2312yes—
204#3799—24no—
205#3797—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C4⋊C4C2311yescharacteristic
208C32×C22⋊C4C2312yes—
209C32×C42C2312yes—
210#3757C2311yescharacteristic
211#3752C2312yes—
212#3752C2312yes—
213#3752C2311yescharacteristic
214#3752C2312yes—
215#3752C2312yes—
216C4⋊(C3⋊Dic3)C2311yescharacteristic
217#3750C2311yescharacteristic
218#3750C2312yes—
219C4×C3⋊Dic3C2312yes—
220C4×C3⋊Dic3C2311yescharacteristic
221C3×#217C2311yescharacteristic
222C3×#217C2312yes—
223C3×(C2×D3)⋊C4C2312yes—
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2311yescharacteristic
227C3×C4⋊Dic3C2312yes—
228C3×C4⋊Dic3C2312yes—
229C3×C4⋊Dic3C2311yescharacteristic
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2312yes—
233C3×Dic3⋊C4C2312yes—
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×Dic3⋊C4C2311yescharacteristic
237C3×C4×Dic3C2312yes—
238C3×C4×Dic3C2312yes—
239C3×C4×Dic3C2312yes—
240C3×C4×Dic3C2311yescharacteristic
241C3×C4×Dic3C2311yescharacteristic
242C3×C4×Dic3C2311yescharacteristic
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245#3724C2311yescharacteristic
246#3724C2311yescharacteristic
247#3724C2312yes—
248#3724C2311yescharacteristic
249Dic3⋊Dic3C2311yescharacteristic
250Dic3⋊Dic3C2312yes—
251Dic3⋊Dic3C2312yes—
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2311yescharacteristic
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2311yescharacteristic
258#3722C2311yescharacteristic
259#3722C2311yescharacteristic
260#3722C2312yes—
261#3722C2312yes—
262#3722C2311yescharacteristic
263#3722C2312yes—
264(C2×D3)⋊Dic3C2312yes—
265(C2×D3)⋊Dic3C2312yes—
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2312yes—
268(C2×D3)⋊Dic3C2311yescharacteristic
269(C2×D3)⋊Dic3C2311yescharacteristic
270(C2×D3)⋊Dic3C2311yescharacteristic
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3524—91noSylow
275C2×C3×#41—31no—
276C2×#239—31no—
277C2×D3×Q8—31no—
278C2×D3×Q8—31no—
279C2×#235—31no—
280C2×#235C2×D311yescharacteristic
281C3×#126—32no—
282C3×#125—31no—
283C3×#125—32no—
284C3×#123—32no—
285C3×C22⋊Q8—31no—
286C3×C22⋊Q8—31no—
287C3×C4×Q8—31no—
288C3×C4×Q8—31no—
289C3×C4×Q8—31no—
290C3×C4×D4—31no—
291C3×C4×D4—31no—
292C3×C4×D4—31no—
293C3×C4×D4—32no—
294C3×C4×D4—32no—
295C3×#117—21no—
296C3×#117—32no—
297C3×#117—32no—
298C3×#117C2×D311yescharacteristic
299C3×#117C2×D311yescharacteristic
300C2×C3×C4⋊C4—31no—
301C2×C3×C42—31no—
302C2×C3×C42—32no—
303#947—31no—
304#947—31no—
305Q8×Dic3—31no—
306Q8×Dic3—31no—
307Q8×Dic3—31no—
308#940—32no—
309#940—32no—
310#940—31no—
311#939—31no—
312#938—31no—
313#938—32no—
314#938—32no—
315#938—31no—
316#936—31no—
317#936—32no—
318#935—31no—
319#930—31no—
320#930—31no—
321#930—31no—
322#930—31no—
323#930—32no—
324#930—32no—
325#930—32no—
326#930—61no—
327#929—31no—
328#929—31no—
329#929—32no—
330#929—32no—
331#929—32no—
332#929—32no—
333#929—32no—
334C4×#67—31no—
335C4×#67—31no—
336C4×#67—32no—
337C4×#67—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341C4×#67—32no—
342C4×#67—31no—
343C4×#67—32no—
344C4×#67—32no—
345C4×#67—61no—
346C4×#67C2×D311yescharacteristic
347#926—31no—
348#924—31no—
349#924—32no—
350#924—32no—
351#924C2×D311yescharacteristic
352C2×C4×Dic3C2×D311yescharacteristic
353#898—32no—
354#898—32no—
355#898—31no—
356#898—32no—
357#897—32no—
358#897—32no—
359#897C2×D311yescharacteristic
360#896—32no—
361#896—32no—
362#895—31no—
363#895—32no—
364#895—31no—
365#895—31no—
366#895—32no—
367#895—32no—
368#895—61no—
369#894—32no—
370#894—32no—
371#894—32no—
372#894—32no—
373#894—32no—
374#893—32no—
375#893—32no—
376#893—32no—
377#893—31no—
378#893—31no—
379#893—32no—
380#893—31no—
381#893—61no—
382#893C2×D311yescharacteristic
383#893C2×D311yescharacteristic
384#892—31no—
385#892—31no—
386#892—32no—
387#892—32no—
388#892—32no—
389#892—32no—
390#892—61no—
391D3×C4⋊C4—32no—
392D3×C4⋊C4—32no—
393D3×C4⋊C4C2×D311yescharacteristic
394#890—32no—
395#890—31no—
396#890C2×D311yescharacteristic
397#889—32no—
398#889—32no—
399#889—31no—
400#888—31no—
401#888—31no—
402#888—32no—
403#888—32no—
404#888—61no—
405#887—31no—
406#887—32no—
407#887—32no—
408#887—32no—
409#887C2×D311yescharacteristic
410#887C2×D311yescharacteristic
411#887C2×D311yescharacteristic
412#886—32no—
413#886—31no—
414#885—32no—
415#885—32no—
416#885—32no—
417#885—32no—
418#885—32no—
419#885—32no—
420#885—31no—
421#885—32no—
422#885—62no—
423#884—32no—
424#884—32no—
425#884—32no—
426#884—32no—
427#884—32no—
428#884—32no—
429#884—32no—
430#884—32no—
431#884—62no—
432#883—32no—
433#883—32no—
434#883—32no—
435#883C2×D312yes—
436#67⋊C4—32no—
437#67⋊C4C2×D312yes—
438#67⋊C4C2×D312yes—
439#879—32no—
440#879—32no—
441#879—31no—
442#879C2×D312yes—
443#878—31no—
444#876—31no—
445#876—31no—
446#876—32no—
447#875—31no—
448#875—32no—
449#875—32no—
450#875—32no—
451#875—31no—
452#875—32no—
453#875—62no—
454#874—31no—
455C4×D12—32no—
456C4×D12—31no—
457C4×D12—32no—
458C4×D12—32no—
459C4×D12—31no—
460#872—31no—
461#872—32no—
462#872—32no—
463#872—32no—
464#872—32no—
465#872—32no—
466#872—32no—
467#872—31no—
468#872—31no—
469#872—62no—
470#872C2×D312yes—
471#872C2×D312yes—
472C42×D3C2×D312yes—
473#870—31no—
474#870—31no—
475#870—32no—
476#870C2×D312yes—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—32no—
480C4×Dic6—31no—
481C4×Dic6—32no—
482C4×Dic6—31no—
483C4×Dic6—32no—
484C23×C32C2411yescharacteristic
485C22×C3⋊D3C2411yescharacteristic
486C22×C3⋊D3C2412yes—
487C22×C3×D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C2×C32×C4—22no—
490C2×C32×C4C2412yes—
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2412yes—
493C2×C32×C4C2411yescharacteristic
494#638—41no—
495#638—42no—
496C2×C3⋊Dic3C2411yescharacteristic
497C2×C3⋊Dic3C2412yes—
498C2×C3⋊Dic3C2411yescharacteristic
499C2×C3⋊Dic3C2411yescharacteristic
500C4⋊(C3⋊D3)—22no—
501C4⋊(C3⋊D3)—42no—
502C4×C3⋊D3—22no—
503C4×C3⋊D3—42no—
504#634—42no—
505C3×#67—24no—
506C3×#67—41no—
507C2×C3×Dic3—41no—
508C2×C3×Dic3—41no—
509C2×C3×Dic3C2411yescharacteristic
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2412yes—
512C2×C3×Dic3C2412yes—
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2411yescharacteristic
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2412yes—
519C3×D12—22no—
520C3×C4×D3—22no—
521C3×C4×D3—24no—
522C3×C4×D3—42no—
523C3×C4×D3—42no—
524C3×C4×D3—42no—
525C3×Dic6—22no—
526C3×Dic6#4114yes—
527#627—24no—
528#627—41no—
529#626—24no—
530#626—42no—
531#626—42no—
532#626—42no—
533#626—41no—
534#625—42no—
535#624—24no—
536#624—24no—
537#624—42no—
538#559—91no—
539#559—92no—
540#557—91no—
541#555—92no—
542#555—91no—
543#553—91no—
544#553—92no—
545#552—31no—
546#552—92no—
547#550—91no—
548#548—91no—
549#548—91no—
550#542—91no—
551#542—92no—
552#540—92no—
553#540—91no—
554#529—92no—
555#529—91no—
556#529—91no—
557#529—92no—
558#520—91no—
559#519—91no—
560C4×#41—31no—
561C3×#41—64no—
562C2×C3×Q8—31no—
563C2×C3×Q8—31no—
564C2×C3×D4—32no—
565C2×C3×D4—31no—
566C2×C3×D4—31no—
567C22×C3×C4—21no—
568C22×C3×C4—31no—
569C22×C3×C4—31no—
570C22×C3×C4—32no—
571C22×C3×C4—31no—
572C22×C3×C4—32no—
573C22×C3×C4—32no—
574C22×C3×C4—32no—
575C22×C3×C4C22×D311yescharacteristic
576C22×C3×C4C22×D311yescharacteristic
577C2×#67—32no—
578C2×#67—31no—
579C2×#67—31no—
580C2×#67—32no—
581C2×#67—32no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—31no—
586C2×#67—32no—
587C2×#67—32no—
588C2×#67—61no—
589C2×#67—62no—
590C2×#67C22×D312yes—
591C2×#67C22×D311yescharacteristic
592C22×Dic3C22×D311yescharacteristic
593C22×Dic3C22×D311yescharacteristic
594#239—64no—
595D3×Q8—64no—
596D3×Q8—64no—
597#235—24no—
598#235—64no—
599C2×D12—32no—
600C2×D12—31no—
601C2×D12—31no—
602C2×D12—32no—
603C2×D12—31no—
604C2×D12—32no—
605C2×D12—32no—
606C2×D12—32no—
607C2×D12—32no—
608C2×D12—61no—
609C2×D12—62no—
610C2×D12C22×D311yescharacteristic
611C2×C4×D3—31no—
612C2×C4×D3—31no—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—62no—
622C2×C4×D3—61no—
623C2×C4×D3C22×D312yes—
624C2×C4×D3C22×D311yescharacteristic
625C2×C4×D3C22×D312yes—
626C2×C4×D3C22×D312yes—
627C2×C4×D3C22×D312yes—
628C2×Dic6—32no—
629C2×Dic6—32no—
630C2×Dic6—32no—
631C2×Dic6—32no—
632C2×Dic6—31no—
633C2×Dic6—31no—
634C2×Dic6—62no—
635C2×Dic6C22×D311yescharacteristic
636C2×Dic6C22×D311yescharacteristic
637C3×C4⋊C4—21no—
638C3×C4⋊C4—21no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—31no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—32no—
644C3×C4⋊C4—32no—
645C3×C4⋊C4—31no—
646C3×C4⋊C4—32no—
647C3×C4⋊C4—32no—
648C3×C4⋊C4—32no—
649C3×C4⋊C4C22×D311yescharacteristic
650C3×C4⋊C4C22×D311yescharacteristic
651C3×C4⋊C4C22×D311yescharacteristic
652C3×C4⋊C4C22×D311yescharacteristic
653C3×C22⋊C4—22no—
654C3×C22⋊C4—31no—
655C3×C22⋊C4—32no—
656C3×C22⋊C4—32no—
657C3×C22⋊C4—32no—
658C3×C22⋊C4—31no—
659C3×C22⋊C4—32no—
660C3×C22⋊C4C22×D312yes—
661C3×C22⋊C4C22×D312yes—
662C3×C42—22no—
663C3×C42—31no—
664C3×C42—32no—
665C3×C42—31no—
666C3×C42—32no—
667C3×C42—31no—
668C3×C42—32no—
669C3×C42—31no—
670C3×C42—31no—
671C3×C42C22×D312yes—
672C3×C42C22×D312yes—
673#217—31no—
674#217—31no—
675#217—32no—
676#217—31no—
677#217—32no—
678#217—32no—
679#217—31no—
680#217—31no—
681#217—32no—
682#217—61no—
683#217C22×D311yescharacteristic
684#217C22×D312yes—
685(C2×D3)⋊C4—31no—
686(C2×D3)⋊C4—31no—
687(C2×D3)⋊C4—31no—
688(C2×D3)⋊C4—32no—
689(C2×D3)⋊C4—32no—
690(C2×D3)⋊C4—32no—
691(C2×D3)⋊C4—32no—
692(C2×D3)⋊C4—32no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—32no—
695(C2×D3)⋊C4—32no—
696(C2×D3)⋊C4—32no—
697(C2×D3)⋊C4—32no—
698(C2×D3)⋊C4—32no—
699(C2×D3)⋊C4—31no—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—31no—
702(C2×D3)⋊C4—31no—
703(C2×D3)⋊C4—31no—
704(C2×D3)⋊C4—32no—
705(C2×D3)⋊C4—32no—
706(C2×D3)⋊C4—31no—
707(C2×D3)⋊C4—31no—
708(C2×D3)⋊C4—31no—
709(C2×D3)⋊C4—32no—
710(C2×D3)⋊C4—32no—
711(C2×D3)⋊C4—32no—
712(C2×D3)⋊C4—32no—
713(C2×D3)⋊C4—31no—
714(C2×D3)⋊C4—62no—
715(C2×D3)⋊C4—62no—
716(C2×D3)⋊C4—61no—
717(C2×D3)⋊C4—62no—
718(C2×D3)⋊C4—62no—
719(C2×D3)⋊C4C22×D311yescharacteristic
720(C2×D3)⋊C4C22×D312yes—
721(C2×D3)⋊C4C22×D312yes—
722(C2×D3)⋊C4C22×D312yes—
723C4⋊Dic3—31no—
724C4⋊Dic3—31no—
725C4⋊Dic3—31no—
726C4⋊Dic3—32no—
727C4⋊Dic3—31no—
728C4⋊Dic3—32no—
729C4⋊Dic3—31no—
730C4⋊Dic3—32no—
731C4⋊Dic3—31no—
732C4⋊Dic3—32no—
733C4⋊Dic3—31no—
734C4⋊Dic3—61no—
735C4⋊Dic3C22×D312yes—
736C4⋊Dic3C22×D311yescharacteristic
737C4⋊Dic3C22×D312yes—
738Dic3⋊C4—31no—
739Dic3⋊C4—32no—
740Dic3⋊C4—31no—
741Dic3⋊C4—32no—
742Dic3⋊C4—31no—
743Dic3⋊C4—32no—
744Dic3⋊C4—31no—
745Dic3⋊C4—31no—
746Dic3⋊C4—32no—
747Dic3⋊C4—31no—
748Dic3⋊C4—32no—
749Dic3⋊C4—31no—
750Dic3⋊C4—31no—
751Dic3⋊C4—31no—
752Dic3⋊C4—32no—
753Dic3⋊C4—31no—
754Dic3⋊C4—31no—
755Dic3⋊C4—31no—
756Dic3⋊C4—31no—
757Dic3⋊C4—32no—
758Dic3⋊C4—32no—
759Dic3⋊C4—61no—
760Dic3⋊C4—62no—
761Dic3⋊C4C22×D311yescharacteristic
762Dic3⋊C4C22×D312yes—
763Dic3⋊C4C22×D312yes—
764Dic3⋊C4C22×D312yes—
765Dic3⋊C4C22×D312yes—
766Dic3⋊C4C22×D312yes—
767Dic3⋊C4C22×D312yes—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—31no—
771C4×Dic3—31no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—32no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—62no—
779C4×Dic3—61no—
780C4×Dic3C22×D312yes—
781C4×Dic3C22×D311yescharacteristic
782C4×Dic3C22×D312yes—
783C4×Dic3C22×D311yescharacteristic
784C4×Dic3C22×D311yescharacteristic
785C4×Dic3C22×D312yes—
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D311yescharacteristic
788C22×C32—21no—
789C22×C32—21no—
790C22×C32—21no—
791C22×C32C2511yescharacteristic
792C2×C3⋊D3—21no—
793C2×C3⋊D3—22no—
794C2×C3⋊D3—22no—
795C2×C3⋊D3—21no—
796C2×C3⋊D3—21no—
797C2×C3⋊D3—22no—
798C2×C3×D3—21no—
799C2×C3×D3—22no—
800C2×C3×D3—21no—
801C2×C3×D3—22no—
802C2×C3×D3—22no—
803C2×C3×D3—21no—
804C32×C4—21no—
805C32×C4—22no—
806C32×C4—22no—
807C32×C4C2×#4112yes—
808C3⋊Dic3—21no—
809C3⋊Dic3—21no—
810C3⋊Dic3—22no—
811C3⋊Dic3—21no—
812C3×Dic3—21no—
813C3×Dic3—22no—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—21no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3C2×#4114yes—
822C2×#41—31no—
823C2×#41—91no—
824C22×Q8—91no—
825C4⋊Q8—92no—
826C4⋊Q8—91no—
827#127—91no—
828#127—92no—
829#126—32no—
830#126—91no—
831#126—91no—
832#126—92no—
833#126—92no—
834#126—92no—
835#125—31no—
836#125—32no—
837#125—91no—
838#125—92no—
839#125—91no—
840#125—92no—
841#124—92no—
842#124—91no—
843#124—92no—
844#124—91no—
845#124—92no—
846#124—92no—
847#124—91no—
848#124—92no—
849#124—92no—
850#123—32no—
851#123—92no—
852#123—92no—
853#123—92no—
854#123—92no—
855#123—91no—
856#123—92no—
857#123—92no—
858#123—92no—
859#123—91no—
860C22⋊Q8—31no—
861C22⋊Q8—31no—
862C22⋊Q8—91no—
863C22⋊Q8—92no—
864C22⋊Q8—92no—
865C22⋊Q8—92no—
866#121—92no—
867#121—92no—
868#121—92no—
869#121—92no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—91no—
874#121—91no—
875#121—91no—
876#121—91no—
877#121—91no—
878#121—92no—
879C4×Q8—31no—
880C4×Q8—31no—
881C4×Q8—31no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—92no—
885C4×Q8—91no—
886C4×Q8—91no—
887C4×Q8—92no—
888C4×Q8—91no—
889C4×D4—31no—
890C4×D4—31no—
891C4×D4—31no—
892C4×D4—32no—
893C4×D4—32no—
894C4×D4—91no—
895C4×D4—92no—
896C4×D4—92no—
897C4×D4—91no—
898C4×D4—92no—
899C4×D4—92no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—92no—
903C4×D4—92no—
904C4×D4—91no—
905C4×D4—91no—
906#117—32no—
907#117—32no—
908#117—91no—
909#117—92no—
910#117—92no—
911#117—92no—
912#117—92no—
913#117—91no—
914#117—91no—
915#117—92no—
916#117D3211yescharacteristic
917C2×C4⋊C4—31no—
918C2×C4⋊C4—92no—
919C2×C42—31no—
920C2×C42—32no—
921C23×C3—21no—
922C23×C3—32no—
923C23×C3—31no—
924C23×C3C23×D311yescharacteristic
925C23×C3C23×D311yescharacteristic
926C22×D3—31no—
927C22×D3—32no—
928C22×D3—31no—
929C22×D3—32no—
930C22×D3—62no—
931C22×D3—61no—
932C22×D3C23×D312yes—
933C22×D3C23×D311yescharacteristic
934C3×Q8—34no—
935C3×Q8—62no—
936C3×D4—64no—
937C3×D4—62no—
938C3×D4—121no—
939C2×C3×C4—22no—
940C2×C3×C4—22no—
941C2×C3×C4—21no—
942C2×C3×C4—22no—
943C2×C3×C4—21no—
944C2×C3×C4—22no—
945C2×C3×C4—32no—
946C2×C3×C4—31no—
947C2×C3×C4—31no—
948C2×C3×C4—32no—
949C2×C3×C4—32no—
950C2×C3×C4—31no—
951C2×C3×C4—31no—
952C2×C3×C4—31no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—42no—
956C2×C3×C4—64no—
957C2×C3×C4—62no—
958C2×C3×C4—122no—
959C2×C3×C4—122no—
960C2×C3×C4—122no—
961C2×C3×C4—121no—
962C2×C3×C4—121no—
963C2×C3×C4C23×D312yes—
964C2×C3×C4C23×D312yes—
965C2×C3×C4C23×D311yescharacteristic
966C2×C3×C4C23×D312yes—
967C2×C3×C4C23×D311yescharacteristic
968C2×C3×C4C23×D312yes—
969C2×C3×C4C23×D311yescharacteristic
970C2×C3×C4C23×D311yescharacteristic
971#67—24no—
972#67—41no—
973#67—64no—
974#67—121no—
975#67—122no—
976#67—122no—
977#67—122no—
978#67—122no—
979#67—122no—
980#67—121no—
981#67—121no—
982#67—122no—
983#67—122no—
984#67—122no—
985#67—242no—
986C2×Dic3—32no—
987C2×Dic3—32no—
988C2×Dic3—31no—
989C2×Dic3—31no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—31no—
994C2×Dic3—41no—
995C2×Dic3—41no—
996C2×Dic3—61no—
997C2×Dic3—61no—
998C2×Dic3—62no—
999C2×Dic3—61no—
1000C2×Dic3C23×D311yescharacteristic
1001C2×Dic3C23×D311yescharacteristic
1002C2×Dic3C23×D312yes—
1003C2×Dic3C23×D312yes—
1004C2×Dic3C23×D311yescharacteristic
1005C2×Dic3C23×D311yescharacteristic
1006C2×Dic3C23×D311yescharacteristic
1007C2×Dic3C23×D311yescharacteristic
1008C2×Dic3C23×D311yescharacteristic
1009C2×Dic3C23×D312yes—
1010D12—22no—
1011D12—64no—
1012D12—62no—
1013D12—62no—
1014D12—122no—
1015D12—122no—
1016D12—122no—
1017D12—122no—
1018D12—122no—
1019D12—122no—
1020D12—121no—
1021D12—242no—
1022C4×D3—22no—
1023C4×D3—24no—
1024C4×D3—42no—
1025C4×D3—42no—
1026C4×D3—42no—
1027C4×D3—64no—
1028C4×D3—64no—
1029C4×D3—62no—
1030C4×D3—62no—
1031C4×D3—64no—
1032C4×D3—64no—
1033C4×D3—122no—
1034C4×D3—122no—
1035C4×D3—122no—
1036C4×D3—122no—
1037C4×D3—122no—
1038C4×D3—124no—
1039Dic6—22no—
1040Dic6—64no—
1041Dic6—64no—
1042Dic6—121no—
1043Dic6—121no—
1044Dic6—122no—
1045Dic6—122no—
1046Dic6—242no—
1047Dic6#23514yes—
1048C2×C32—41no—
1049C2×C32C22×#4111yescharacteristic
1050C2×C32#58511yescharacteristic
1051C2×C32#58511yescharacteristic
1052C3⋊D3—41no—
1053C3⋊D3—42no—
1054C3×D3—41no—
1055C3×D3—42no—
1056#41—64no—
1057#41—184no—
1058C2×Q8—31no—
1059C2×Q8—31no—
1060C2×Q8—92no—
1061C2×Q8—91no—
1062C2×Q8—92no—
1063C2×Q8—184no—
1064C2×D4—32no—
1065C2×D4—31no—
1066C2×D4—31no—
1067C2×D4—92no—
1068C2×D4—92no—
1069C2×D4—91no—
1070C2×D4—92no—
1071C2×D4—92no—
1072C2×D4—92no—
1073C2×D4—91no—
1074C2×D4—92no—
1075C2×D4—91no—
1076C2×D4—92no—
1077C22×C4—31no—
1078C22×C4—31no—
1079C22×C4—32no—
1080C22×C4—31no—
1081C22×C4—32no—
1082C22×C4—32no—
1083C22×C4—32no—
1084C22×C4—92no—
1085C22×C4—92no—
1086C22×C4—92no—
1087C22×C4—91no—
1088C22×C4—92no—
1089C22×C4C2×D3211yescharacteristic
1090C4⋊C4—32no—
1091C4⋊C4—31no—
1092C4⋊C4—32no—
1093C4⋊C4—32no—
1094C4⋊C4—32no—
1095C4⋊C4—32no—
1096C4⋊C4—32no—
1097C4⋊C4—31no—
1098C4⋊C4—32no—
1099C4⋊C4—32no—
1100C4⋊C4—91no—
1101C4⋊C4—92no—
1102C4⋊C4—91no—
1103C4⋊C4—92no—
1104C4⋊C4—91no—
1105C4⋊C4—92no—
1106C4⋊C4—91no—
1107C4⋊C4—92no—
1108C4⋊C4—92no—
1109C4⋊C4—91no—
1110C4⋊C4—91no—
1111C4⋊C4—91no—
1112C4⋊C4—91no—
1113C4⋊C4—91no—
1114C4⋊C4—91no—
1115C4⋊C4—92no—
1116C4⋊C4C2×D3211yescharacteristic
1117C4⋊C4C2×D3211yescharacteristic
1118C22⋊C4—31no—
1119C22⋊C4—32no—
1120C22⋊C4—31no—
1121C22⋊C4—32no—
1122C22⋊C4—32no—
1123C22⋊C4—32no—
1124C22⋊C4—91no—
1125C22⋊C4—91no—
1126C22⋊C4—92no—
1127C22⋊C4—92no—
1128C22⋊C4—91no—
1129C22⋊C4—92no—
1130C22⋊C4—91no—
1131C22⋊C4—91no—
1132C22⋊C4—91no—
1133C22⋊C4—92no—
1134C22⋊C4—92no—
1135C22⋊C4—92no—
1136C22⋊C4—92no—
1137C22⋊C4—91no—
1138C22⋊C4—92no—
1139C22⋊C4—92no—
1140C22⋊C4—92no—
1141C22⋊C4—92no—
1142C22⋊C4—91no—
1143C22⋊C4C2×D3212yes—
1144C42—31no—
1145C42—31no—
1146C42—32no—
1147C42—31no—
1148C42—32no—
1149C42—31no—
1150C42—32no—
1151C42—31no—
1152C42—92no—
1153C42—92no—
1154C42—92no—
1155C42—92no—
1156C42—91no—
1157C42C2×D3212yes—
1158C22×C3—21no—
1159C22×C3—21no—
1160C22×C3—21no—
1161C22×C3—21no—
1162C22×C3—21no—
1163C22×C3—21no—
1164C22×C3—21no—
1165C22×C3—41no—
1166C22×C3—41no—
1167C22×C3—41no—
1168C22×C3—61no—
1169C22×C3—62no—
1170C22×C3—61no—
1171C22×C3—62no—
1172C22×C3—61no—
1173C22×C3—62no—
1174C22×C3C24×D311yescharacteristic
1175C22×C3C24×D311yescharacteristic
1176C2×D3—22no—
1177C2×D3—21no—
1178C2×D3—21no—
1179C2×D3—22no—
1180C2×D3—22no—
1181C2×D3—21no—
1182C2×D3—61no—
1183C2×D3—62no—
1184C2×D3—61no—
1185C2×D3—62no—
1186C2×D3—62no—
1187C2×D3—62no—
1188C2×D3—61no—
1189C2×D3—61no—
1190C2×D3—62no—
1191C2×D3—61no—
1192C2×D3—61no—
1193C2×D3—62no—
1194C2×D3—121no—
1195C2×D3—122no—
1196C2×D3—122no—
1197C2×D3—121no—
1198C2×D3—122no—
1199C2×D3—121no—
1200C3×C4—21no—
1201C3×C4—21no—
1202C3×C4—22no—
1203C3×C4—22no—
1204C3×C4—22no—
1205C3×C4—22no—
1206C3×C4—22no—
1207C3×C4—34no—
1208C3×C4—42no—
1209C3×C4—42no—
1210C3×C4—41no—
1211C3×C4—62no—
1212C3×C4—61no—
1213C3×C4—61no—
1214C3×C4—61no—
1215C3×C4—62no—
1216C3×C4—61no—
1217C3×C4—61no—
1218C3×C4—61no—
1219C3×C4—61no—
1220C3×C4C2×#23512yes—
1221C3×C4D3×#4112yes—
1222Dic3—22no—
1223Dic3—21no—
1224Dic3—21no—
1225Dic3—21no—
1226Dic3—21no—
1227Dic3—22no—
1228Dic3—21no—
1229Dic3—21no—
1230Dic3—21no—
1231Dic3—62no—
1232Dic3—61no—
1233Dic3—61no—
1234Dic3—61no—
1235Dic3—62no—
1236Dic3—61no—
1237Dic3—61no—
1238Dic3—61no—
1239Dic3—62no—
1240Dic3—121no—
1241Dic3—122no—
1242Dic3—121no—
1243Dic3C2×#23514yes—
1244C32#352411yescharacteristic, complemented, Sylow
1245C23—31no—
1246C23—32no—
1247C23—91no—
1248C23—92no—
1249C23C22×D3211yescharacteristic
1250Q8—34no—
1251Q8—62no—
1252Q8—184no—
1253Q8—362no—
1254Q8—361no—
1255D4—64no—
1256D4—62no—
1257D4—121no—
1258D4—184no—
1259D4—182no—
1260D4—362no—
1261D4—362no—
1262D4—362no—
1263D4—361no—
1264D4—362no—
1265D4—361no—
1266D4—362no—
1267D4—362no—
1268C2×C4—22no—
1269C2×C4—32no—
1270C2×C4—31no—
1271C2×C4—31no—
1272C2×C4—31no—
1273C2×C4—31no—
1274C2×C4—31no—
1275C2×C4—31no—
1276C2×C4—32no—
1277C2×C4—32no—
1278C2×C4—31no—
1279C2×C4—64no—
1280C2×C4—62no—
1281C2×C4—91no—
1282C2×C4—92no—
1283C2×C4—91no—
1284C2×C4—91no—
1285C2×C4—122no—
1286C2×C4—122no—
1287C2×C4—122no—
1288C2×C4—121no—
1289C2×C4—121no—
1290C2×C4—184no—
1291C2×C4—184no—
1292C2×C4—182no—
1293C2×C4—362no—
1294C2×C4—362no—
1295C2×C4C22×D3212yes—
1296C2×C4C22×D3211yescharacteristic
1297C2×C4C22×D3212yes—
1298C2×C4C22×D3211yescharacteristic
1299C2×C3—21no—
1300C2×C3—21no—
1301C2×C3—21no—
1302C2×C3—41no—
1303C2×C3—41no—
1304C2×C3—81no—
1305C2×C3—122no—
1306C2×C3—121no—
1307C2×C3C22×#23511yescharacteristic
1308C2×C3C2×D3×#4111yescharacteristic
1309C2×C3#596411yescharacteristic
1310C2×C3#596411yescharacteristic
1311C2×C3#596411yescharacteristic
1312C2×C3#596811yescharacteristic
1313D3—41no—
1314D3—42no—
1315D3—121no—
1316D3—122no—
1317D3—121no—
1318D3—122no—
1319D3—242no—
1320D3—241no—
1321C22—21no—
1322C22—21no—
1323C22—21no—
1324C22—62no—
1325C22—61no—
1326C22—61no—
1327C22—62no—
1328C22—62no—
1329C22—61no—
1330C22—181no—
1331C22—182no—
1332C22—182no—
1333C22—181no—
1334C22—181no—
1335C22—182no—
1336C22C23×D3211yescharacteristic
1337C4—21no—
1338C4—22no—
1339C4—22no—
1340C4—34no—
1341C4—61no—
1342C4—62no—
1343C4—61no—
1344C4—61no—
1345C4—62no—
1346C4—61no—
1347C4—61no—
1348C4—61no—
1349C4—61no—
1350C4—181no—
1351C4—181no—
1352C4—182no—
1353C4—181no—
1354C4D3×#23512yes—
1355C3—21no—
1356C3#8585511yescharacteristic, complemented
1357C3#8684311yescharacteristic, complemented
1358C2—41no—
1359C2—122no—
1360C2—121no—
1361C2—361no—
1362C2—362no—
1363C2C2×D3×#23511yescharacteristic
1364C2#1059669511yescharacteristic
1365C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596003C2semidirect
2. C3×#5529C2semidirect
3. C3×#5522C2semidirect
4. #10595007C2semidirect
5. #10594955C2semidirect
6. #10594839C2semidirect
7. #10594830C2semidirect
8. #10594594C2semidirect
9. #10594592C2semidirect
10. #10594566C2semidirect
11. #10594561C2semidirect
12. #10594347C2semidirect
13. #10594329C2semidirect
14. #10594327C2semidirect
15. #10594322C2semidirect
16. #10594208C2semidirect
17. #10594203C2semidirect
18. #10594202C2semidirect
19. #10594108C2semidirect
20. #10593977C2semidirect
21. #10593976C2semidirect
22. #10593973C2semidirect
23. #10593872C2semidirect
163. #5529D3semidirect
165. #5522D3semidirect
1244. C32#3524semidirect
1356. C3#85855semidirect
1357. C3#86843semidirect

Maximal subgroups

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

subgroupindex
#105960032
C3×#55292
C3×#55222
#105950072
#105949552
#105948392
#105948302
#105945942
#105945922
#105945662
#105945612
#105943472
#105943292
#105943272
#105943222
#105942082
#105942032
#105942022
#105941082
#105939772
#105939762
#105939732
#105938722
#868433
#858553