Finite Group Databasebeta

← #11909935

Subgroups — #11909935

Order 1152.

2117 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic, complemented
2C3×#5528C211yesmaximal, characteristic
3C3×#5518C211yesmaximal, characteristic, complemented
4#10594942C211yesmaximal, characteristic, complemented
5#10594915C211yesmaximal, characteristic, complemented
6#10594915C211yesmaximal, characteristic, complemented
7#10594841C211yesmaximal, characteristic, complemented
8#10594597C212yesmaximal, complemented
9#10594474C212yesmaximal, complemented
10#10594430C212yesmaximal, complemented
11#10594388C212yesmaximal, complemented
12#10594249C212yesmaximal, complemented
13#10594145C212yesmaximal, complemented
14#10594120C212yesmaximal, complemented
15#10594112C212yesmaximal
16#10593920C211yesmaximal, characteristic, complemented
17#10593904C211yesmaximal, characteristic, complemented
18#10593885C211yesmaximal, characteristic, complemented
19C4×D3×Dic6C211yesmaximal, characteristic, complemented
20#10593880C211yesmaximal, characteristic, complemented
21#10593873C211yesmaximal, characteristic, complemented
22#10593861C211yesmaximal, characteristic, complemented
23#10593852C211yesmaximal, characteristic, complemented
24#86514—31nomaximal
25#86129—31nomaximal
26C22×#634C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×#117C2211yescharacteristic
30#64135C2211yescharacteristic
31#64096C2212yes—
32#64096C2212yes—
33#64086C2212yes—
34#64086C2212yes—
35C4×#634C2211yescharacteristic
36C4×#634C2211yescharacteristic
37C4×#634C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×C4×#67C2211yescharacteristic
40C3×C4×#67C2211yescharacteristic
41C3×#924C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C3×#898C2211yescharacteristic
44C3×#896C2211yescharacteristic
45C3×#894C2211yescharacteristic
46C3×#889C2212yes—
47C3×#889C2212yes—
48C3×#889C2211yescharacteristic
49C3×#885C2211yescharacteristic
50C3×#884C2211yescharacteristic
51C3×#883C2211yescharacteristic
52C3×#879C2212yes—
53C3×#879C2212yes—
54C3×#879C2211yescharacteristic
55C3×C4×D12C2211yescharacteristic
56C3×#872C2211yescharacteristic
57C3×C42×D3C2211yescharacteristic
58C3×#870C2211yescharacteristic
59C3×#869C2211yescharacteristic
60C3×C4×Dic6C2211yescharacteristic
61C3×C4×Dic6C2211yescharacteristic
62C3×C4×Dic6C2211yescharacteristic
63#63982C2212yes—
64#63982C2212yes—
65#67⋊Dic3C2212yes—
66#67⋊Dic3C2212yes—
67#63969C2212yes—
68#63959C2212yes—
69#63956C2212yes—
70#63956C2212yes—
71#63919C2212yes—
72#63918C2211yescharacteristic
73C4×#627C2212yes—
74C4×#627C2212yes—
75#63899C2212yes—
76#63899C2212yes—
77#63898C2212yes—
78#63896C2212yes—
79#63896C2212yes—
80D3×C4⋊Dic3C2211yescharacteristic
81#63884C2212yes—
82#63878C2212yes—
83#63878C2212yes—
84#63878C2212yes—
85#63877C2212yes—
86D3×Dic3⋊C4C2212yes—
87C4×D3×Dic3C2212yes—
88#63872C2212yes—
89#63870C2212yes—
90#63870C2212yes—
91#63870C2212yes—
92#63869C2211yescharacteristic
93#63867C2212yes—
94#63867C2212yes—
95#63866C2211yescharacteristic
96#63866C2211yescharacteristic
97#63862C2212yes—
98#63862C2212yes—
99#63862C2212yes—
100#63859C2212yes—
101#63857C2211yescharacteristic
102#63857C2211yescharacteristic
103#63856C2211yescharacteristic
104#63856C2211yescharacteristic
105#63855C2212yes—
106#63851C2212yes—
107#63847C2212yes—
108#63846C2212yes—
109#63846C2212yes—
110#63846C2212yes—
111#63844C2211yescharacteristic
112#63844C2211yescharacteristic
113#63843C2212yes—
114Dic3×Dic6C2211yescharacteristic
115Dic3×Dic6C2211yescharacteristic
116#63841C2211yescharacteristic
117#63840C2212yes—
118#63840C2212yes—
119#63839C2212yes—
120#63838C2212yes—
121#63838C2212yes—
122#63838C2212yes—
123#63837C2212yes—
124#63837C2212yes—
125C3×#541—31no—
126C3×#529—31no—
127#5727—31no—
128#5721—31no—
129#5708—32no—
130#5706—32no—
131#5702—32no—
132#5701—32no—
133#5701—32no—
134#5701—32no—
135#5696—32no—
136#5694—31no—
137#5693—32no—
138#5688—32no—
139#5685—32no—
140#5685—32no—
141#5685—31no—
142#5671—32no—
143#5650—32no—
144#5650—32no—
145#5641—31no—
146#5639—31no—
147#5632—31no—
148#5632—31no—
149#5622—32no—
150#5600—32no—
151#5583—31no—
152#5578—31no—
153#5572—31no—
154C4×D3×Q8—31no—
155#5570—31no—
156#5567—31no—
157#5542—31no—
158#5541—31no—
159#5541—31no—
160D4×Dic6—31no—
161D4×Dic6—31no—
162D4×Dic6—31no—
163#5528D311yescharacteristic
164#5518—31no—
165#5518D311yescharacteristic, complemented
166#5516—31no—
167#5516—31no—
168#5516—31no—
169#5516—61no—
170#5470—31no—
171C2×C4×Dic6—31no—
172C22×C32×C4C2311yescharacteristic
173C22×C3⋊Dic3C2312yes—
174C2×#634—24no—
175C2×#634C2311yescharacteristic
176C2×#634C2312yes—
177C2×#634C2311yescharacteristic
178C2×C3×#67C2311yescharacteristic
179C2×C3×#67C2311yescharacteristic
180C2×C3×D12C2311yescharacteristic
181C2×C3×C4×D3C2311yescharacteristic
182C2×C3×C4×D3C2311yescharacteristic
183C2×C3×C4×D3C2311yescharacteristic
184C2×C3×C4×D3C2311yescharacteristic
185C2×C3×Dic6C2311yescharacteristic
186C2×C3×Dic6C2311yescharacteristic
187C2×C3×Dic6C2311yescharacteristic
188C2×#627C2312yes—
189C2×#627C2312yes—
190C2×#627C2312yes—
191C2×D3×Dic3C2312yes—
192C2×D3×Dic3C2312yes—
193C2×D3×Dic3C2312yes—
194D3×Dic6—24no—
195D3×Dic6—24no—
196C32×C4⋊C4C2311yescharacteristic
197C32×C4⋊C4C2311yescharacteristic
198C32×C22⋊C4C2311yescharacteristic
199C32×C22⋊C4C2311yescharacteristic
200C32×C42C2311yescharacteristic
201C32×C42C2311yescharacteristic
202#3757C2312yes—
203C4⋊(C3⋊Dic3)C2311yescharacteristic
204C4⋊(C3⋊Dic3)C2311yescharacteristic
205#3750C2312yes—
206#3750C2312yes—
207#3750C2312yes—
208#3750C2312yes—
209C4×C3⋊Dic3C2312yes—
210C4×C3⋊Dic3C2312yes—
211C4×C3⋊Dic3C2312yes—
212C4×C3⋊Dic3C2312yes—
213C4×C3⋊Dic3C2312yes—
214C3×#217C2312yes—
215C3×#217C2312yes—
216C3×#217C2311yescharacteristic
217C3×#217C2311yescharacteristic
218C3×(C2×D3)⋊C4C2311yescharacteristic
219C3×(C2×D3)⋊C4C2311yescharacteristic
220C3×(C2×D3)⋊C4C2311yescharacteristic
221C3×(C2×D3)⋊C4C2311yescharacteristic
222C3×(C2×D3)⋊C4C2311yescharacteristic
223C3×(C2×D3)⋊C4C2311yescharacteristic
224C3×C4⋊Dic3C2312yes—
225C3×C4⋊Dic3C2312yes—
226C3×C4⋊Dic3C2311yescharacteristic
227C3×C4⋊Dic3C2311yescharacteristic
228C3×C4⋊Dic3C2311yescharacteristic
229C3×C4⋊Dic3C2311yescharacteristic
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2312yes—
233C3×Dic3⋊C4C2312yes—
234C3×Dic3⋊C4C2311yescharacteristic
235C3×Dic3⋊C4C2311yescharacteristic
236C3×Dic3⋊C4C2311yescharacteristic
237C3×Dic3⋊C4C2311yescharacteristic
238C3×Dic3⋊C4C2312yes—
239C3×Dic3⋊C4C2312yes—
240C3×Dic3⋊C4C2311yescharacteristic
241C3×Dic3⋊C4C2311yescharacteristic
242C3×C4×Dic3C2312yes—
243C3×C4×Dic3C2312yes—
244C3×C4×Dic3C2311yescharacteristic
245C3×C4×Dic3C2311yescharacteristic
246C3×C4×Dic3C2311yescharacteristic
247C3×C4×Dic3C2311yescharacteristic
248#3724C2312yes—
249#3724C2312yes—
250#3724C2312yes—
251#3724C2312yes—
252#3724C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2312yes—
256Dic3⋊Dic3C2312yes—
257Dic3⋊Dic3C2312yes—
258Dic3⋊Dic3C2312yes—
259Dic3⋊Dic3C2312yes—
260Dic3⋊Dic3C2312yes—
261Dic3⋊Dic3C2312yes—
262Dic3⋊Dic3C2312yes—
263Dic3⋊Dic3C2312yes—
264(C2×D3)⋊Dic3C2312yes—
265(C2×D3)⋊Dic3C2312yes—
266(C2×D3)⋊Dic3C2312yes—
267(C2×D3)⋊Dic3C2312yes—
268(C2×D3)⋊Dic3C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3523—91noSylow
275C2×D3×Q8—31no—
276C2×D3×Q8—31no—
277C22×Dic6—31no—
278C22×Dic6—31no—
279C22×Dic6—31no—
280C22×Dic6—31no—
281C22×Dic6—61no—
282C3×C4⋊Q8—31no—
283C3×#126—31no—
284C3×#126—31no—
285C3×#126—32no—
286C3×#126—32no—
287C3×#125—31no—
288C3×#125—32no—
289C3×#125—32no—
290C3×#125—31no—
291C3×#124—31no—
292C3×#123—31no—
293C3×#123—31no—
294C3×C22⋊Q8—31no—
295C3×C22⋊Q8—31no—
296C3×C22⋊Q8—31no—
297C3×#121—31no—
298C3×C4×Q8—31no—
299C3×C4×Q8—31no—
300C3×C4×Q8—31no—
301C3×C4×D4—31no—
302C3×C4×D4—31no—
303C3×C4×D4—31no—
304C3×#117—21no—
305C3×#117—31no—
306C3×#117C2×D311yescharacteristic
307C3×#117C2×D311yescharacteristic
308C2×C3×C42—31no—
309#946—31no—
310#946—31no—
311Q8×Dic3—32no—
312Q8×Dic3—31no—
313Q8×Dic3—31no—
314#944—32no—
315#944—31no—
316#944—31no—
317#936—32no—
318#935—32no—
319#935—32no—
320D4×Dic3—32no—
321D4×Dic3—32no—
322D4×Dic3—32no—
323C4×#67C2×D311yescharacteristic
324C4×#67C2×D311yescharacteristic
325#926—31no—
326#926—31no—
327#926—31no—
328#926—32no—
329#926—61no—
330C2×C4⋊Dic3—31no—
331#924—31no—
332#924—31no—
333#924—31no—
334#924—31no—
335#924—32no—
336#924C2×D311yescharacteristic
337#924C2×D311yescharacteristic
338C2×Dic3⋊C4—32no—
339C2×C4×Dic3—32no—
340#898—32no—
341#898—32no—
342#898—32no—
343#898C2×D311yescharacteristic
344#897—31no—
345#897—31no—
346#896—32no—
347#896—32no—
348#896—32no—
349#896—32no—
350#896—32no—
351#896C2×D311yescharacteristic
352#894—32no—
353#894C2×D311yescharacteristic
354#893—32no—
355#892—31no—
356#892—32no—
357#892—32no—
358#892—32no—
359D3×C4⋊C4—31no—
360D3×C4⋊C4—32no—
361#890—32no—
362#890—32no—
363#890—32no—
364#890—32no—
365#890—32no—
366#890—31no—
367#889—32no—
368#889—32no—
369#889—32no—
370#889—32no—
371#889—32no—
372#889—32no—
373#889—32no—
374#889—32no—
375#889—32no—
376#889—32no—
377#889—32no—
378#889—32no—
379#889—32no—
380#889C2×D312yes—
381#889C2×D311yescharacteristic
382#889C2×D312yes—
383#888—32no—
384#888—32no—
385#888—32no—
386#888—32no—
387#888—32no—
388#888—32no—
389#888—32no—
390#888—31no—
391#887—32no—
392#887—32no—
393#887—32no—
394#887—32no—
395#887—32no—
396#887—32no—
397#887—32no—
398#887—32no—
399#887—32no—
400#887—32no—
401#887—32no—
402#887—31no—
403#887—31no—
404#887—32no—
405#887—32no—
406#887—62no—
407#887—62no—
408#885—32no—
409#885C2×D311yescharacteristic
410#884C2×D311yescharacteristic
411#883—32no—
412#883C2×D311yescharacteristic
413#67⋊C4—32no—
414#67⋊C4—32no—
415#879—32no—
416#879—32no—
417#879—32no—
418#879—32no—
419#879—32no—
420#879—32no—
421#879—32no—
422#879—32no—
423#879C2×D312yes—
424#879C2×D311yescharacteristic
425#879C2×D312yes—
426#878—32no—
427#878—32no—
428#878—32no—
429#878—32no—
430#878—32no—
431#878—32no—
432#878—32no—
433#878—32no—
434#877—32no—
435#877—32no—
436#877—32no—
437#877—32no—
438#877—32no—
439#877—32no—
440#877—32no—
441#877—32no—
442#877—62no—
443#877—62no—
444#876—32no—
445C4×D12C2×D311yescharacteristic
446#872—32no—
447#872—32no—
448#872C2×D311yescharacteristic
449C42×D3—32no—
450C42×D3C2×D311yescharacteristic
451#870—31no—
452#870—32no—
453#870—32no—
454#870C2×D311yescharacteristic
455#869—31no—
456#869—31no—
457#869—31no—
458#869C2×D311yescharacteristic
459C4×Dic6—31no—
460C4×Dic6—31no—
461C4×Dic6—31no—
462C4×Dic6—31no—
463C4×Dic6—31no—
464C4×Dic6—31no—
465C4×Dic6—31no—
466C4×Dic6—31no—
467C4×Dic6—31no—
468C4×Dic6—31no—
469C4×Dic6—31no—
470C4×Dic6—31no—
471C4×Dic6—32no—
472C4×Dic6—32no—
473C4×Dic6—32no—
474C4×Dic6—32no—
475C4×Dic6—32no—
476C4×Dic6—32no—
477C4×Dic6—61no—
478C4×Dic6—61no—
479C4×Dic6—61no—
480C4×Dic6—61no—
481C4×Dic6C2×D311yescharacteristic
482C4×Dic6C2×D311yescharacteristic
483C4×Dic6C2×D311yescharacteristic
484C23×C32C2411yescharacteristic
485C22×C3×D3C2411yescharacteristic
486C22×C3×D3C2411yescharacteristic
487C2×C32×C4—22no—
488C2×C32×C4C2411yescharacteristic
489C2×C32×C4C2411yescharacteristic
490C2×C32×C4C2411yescharacteristic
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2411yescharacteristic
494C2×C3⋊Dic3—24no—
495C2×C3⋊Dic3C2412yes—
496C2×C3⋊Dic3C2412yes—
497C2×C3⋊Dic3C2412yes—
498C2×C3⋊Dic3C2412yes—
499#634—22no—
500#634—24no—
501#634#4114yes—
502C3×#67—22no—
503C3×#67—22no—
504C2×C3×Dic3C2412yes—
505C2×C3×Dic3C2411yescharacteristic
506C2×C3×Dic3C2411yescharacteristic
507C2×C3×Dic3C2411yescharacteristic
508C2×C3×Dic3C2412yes—
509C2×C3×Dic3C2412yes—
510C2×C3×Dic3C2412yes—
511C2×C3×Dic3C2411yescharacteristic
512C2×C3×Dic3C2411yescharacteristic
513C2×C3×Dic3C2411yescharacteristic
514C3×D12—22no—
515C3×C4×D3—22no—
516C3×C4×D3—22no—
517C3×C4×D3—22no—
518C3×C4×D3—22no—
519C3×Dic6—22no—
520C3×Dic6—22no—
521C3×Dic6—22no—
522#627—24no—
523#627—24no—
524#627—24no—
525D3×Dic3—24no—
526D3×Dic3—24no—
527D3×Dic3—24no—
528#557—91no—
529#557—91no—
530#557—92no—
531#556—91no—
532#556—92no—
533#552—91no—
534#552—91no—
535#552—92no—
536#552—92no—
537D4×Q8—91no—
538D4×Q8—91no—
539D4×Q8—91no—
540#541—31no—
541#541—91no—
542#541—92no—
543#541—92no—
544#533—91no—
545#533—92no—
546#529—31no—
547#529—92no—
548#519—91no—
549#519—91no—
550C2×C4×Q8—91no—
551C2×C3×Q8—31no—
552C2×C3×Q8—31no—
553C2×C3×Q8—31no—
554C2×C3×D4—31no—
555C2×C3×D4—31no—
556C2×C3×D4—31no—
557C22×C3×C4—21no—
558C22×C3×C4—31no—
559C22×C3×C4—31no—
560C22×C3×C4—31no—
561C22×C3×C4—31no—
562C22×C3×C4C22×D311yescharacteristic
563C22×C3×C4C22×D311yescharacteristic
564C2×#67C22×D311yescharacteristic
565C2×#67C22×D311yescharacteristic
566C22×Dic3—32no—
567C22×Dic3—32no—
568C22×Dic3—32no—
569C22×Dic3—32no—
570C22×Dic3—32no—
571C22×Dic3—62no—
572D3×Q8—64no—
573D3×Q8—64no—
574C2×D12C22×D311yescharacteristic
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3C22×D311yescharacteristic
579C2×C4×D3C22×D311yescharacteristic
580C2×C4×D3C22×D311yescharacteristic
581C2×C4×D3C22×D311yescharacteristic
582C2×Dic6—31no—
583C2×Dic6—31no—
584C2×Dic6—31no—
585C2×Dic6—31no—
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6—32no—
590C2×Dic6—32no—
591C2×Dic6—32no—
592C2×Dic6—32no—
593C2×Dic6—32no—
594C2×Dic6—61no—
595C2×Dic6—61no—
596C2×Dic6—62no—
597C2×Dic6—64no—
598C2×Dic6—64no—
599C2×Dic6—64no—
600C2×Dic6—64no—
601C2×Dic6—68no—
602C2×Dic6C22×D311yescharacteristic
603C2×Dic6C22×D311yescharacteristic
604C2×Dic6C22×D311yescharacteristic
605C3×C4⋊C4—21no—
606C3×C4⋊C4—21no—
607C3×C4⋊C4—31no—
608C3×C4⋊C4—31no—
609C3×C4⋊C4—31no—
610C3×C4⋊C4—31no—
611C3×C4⋊C4—31no—
612C3×C4⋊C4—32no—
613C3×C4⋊C4—32no—
614C3×C4⋊C4—32no—
615C3×C4⋊C4—32no—
616C3×C4⋊C4—31no—
617C3×C4⋊C4—32no—
618C3×C4⋊C4—31no—
619C3×C4⋊C4—31no—
620C3×C4⋊C4—32no—
621C3×C4⋊C4—32no—
622C3×C4⋊C4—32no—
623C3×C4⋊C4—31no—
624C3×C4⋊C4—31no—
625C3×C4⋊C4C22×D311yescharacteristic
626C3×C4⋊C4C22×D311yescharacteristic
627C3×C4⋊C4C22×D311yescharacteristic
628C3×C4⋊C4C22×D311yescharacteristic
629C3×C22⋊C4—21no—
630C3×C22⋊C4—21no—
631C3×C22⋊C4—31no—
632C3×C22⋊C4—31no—
633C3×C22⋊C4—32no—
634C3×C22⋊C4—32no—
635C3×C22⋊C4—31no—
636C3×C22⋊C4—31no—
637C3×C22⋊C4—31no—
638C3×C22⋊C4—31no—
639C3×C22⋊C4—31no—
640C3×C22⋊C4—31no—
641C3×C22⋊C4C22×D311yescharacteristic
642C3×C22⋊C4C22×D311yescharacteristic
643C3×C22⋊C4C22×D311yescharacteristic
644C3×C22⋊C4C22×D311yescharacteristic
645C3×C42—21no—
646C3×C42—21no—
647C3×C42—31no—
648C3×C42—31no—
649C3×C42—31no—
650C3×C42—31no—
651C3×C42—32no—
652C3×C42—32no—
653C3×C42C22×D311yescharacteristic
654C3×C42C22×D311yescharacteristic
655C3×C42C22×D311yescharacteristic
656C3×C42C22×D311yescharacteristic
657#217—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—62no—
665#217C22×D311yescharacteristic
666#217C22×D311yescharacteristic
667#217C22×D312yes—
668#217C22×D312yes—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
674(C2×D3)⋊C4C22×D311yescharacteristic
675(C2×D3)⋊C4C22×D311yescharacteristic
676(C2×D3)⋊C4C22×D311yescharacteristic
677(C2×D3)⋊C4C22×D311yescharacteristic
678(C2×D3)⋊C4C22×D311yescharacteristic
679(C2×D3)⋊C4C22×D311yescharacteristic
680C4⋊Dic3—31no—
681C4⋊Dic3—31no—
682C4⋊Dic3—31no—
683C4⋊Dic3—31no—
684C4⋊Dic3—32no—
685C4⋊Dic3—32no—
686C4⋊Dic3—32no—
687C4⋊Dic3—32no—
688C4⋊Dic3—32no—
689C4⋊Dic3—32no—
690C4⋊Dic3—32no—
691C4⋊Dic3—32no—
692C4⋊Dic3—32no—
693C4⋊Dic3—32no—
694C4⋊Dic3—32no—
695C4⋊Dic3—61no—
696C4⋊Dic3—61no—
697C4⋊Dic3C22×D311yescharacteristic
698C4⋊Dic3C22×D311yescharacteristic
699C4⋊Dic3C22×D311yescharacteristic
700C4⋊Dic3C22×D312yes—
701C4⋊Dic3C22×D312yes—
702C4⋊Dic3C22×D311yescharacteristic
703Dic3⋊C4—32no—
704Dic3⋊C4—32no—
705Dic3⋊C4—32no—
706Dic3⋊C4—32no—
707Dic3⋊C4—32no—
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—32no—
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—32no—
718Dic3⋊C4—32no—
719Dic3⋊C4—32no—
720Dic3⋊C4—32no—
721Dic3⋊C4—32no—
722Dic3⋊C4—32no—
723Dic3⋊C4—32no—
724Dic3⋊C4—32no—
725Dic3⋊C4—32no—
726Dic3⋊C4—32no—
727Dic3⋊C4—32no—
728Dic3⋊C4—32no—
729Dic3⋊C4—32no—
730Dic3⋊C4—32no—
731Dic3⋊C4—32no—
732Dic3⋊C4—62no—
733Dic3⋊C4—62no—
734Dic3⋊C4—62no—
735Dic3⋊C4—62no—
736Dic3⋊C4C22×D311yescharacteristic
737Dic3⋊C4C22×D312yes—
738Dic3⋊C4C22×D312yes—
739Dic3⋊C4C22×D311yescharacteristic
740Dic3⋊C4C22×D311yescharacteristic
741Dic3⋊C4C22×D311yescharacteristic
742Dic3⋊C4C22×D312yes—
743Dic3⋊C4C22×D312yes—
744Dic3⋊C4C22×D312yes—
745Dic3⋊C4C22×D312yes—
746Dic3⋊C4C22×D311yescharacteristic
747Dic3⋊C4C22×D311yescharacteristic
748C4×Dic3—32no—
749C4×Dic3—32no—
750C4×Dic3—32no—
751C4×Dic3—32no—
752C4×Dic3—32no—
753C4×Dic3—32no—
754C4×Dic3—32no—
755C4×Dic3—32no—
756C4×Dic3—32no—
757C4×Dic3—32no—
758C4×Dic3—32no—
759C4×Dic3—32no—
760C4×Dic3—32no—
761C4×Dic3—32no—
762C4×Dic3—32no—
763C4×Dic3—32no—
764C4×Dic3—32no—
765C4×Dic3—32no—
766C4×Dic3—32no—
767C4×Dic3—32no—
768C4×Dic3—62no—
769C4×Dic3—62no—
770C4×Dic3—62no—
771C4×Dic3—62no—
772C4×Dic3—62no—
773C4×Dic3C22×D311yescharacteristic
774C4×Dic3C22×D311yescharacteristic
775C4×Dic3C22×D312yes—
776C4×Dic3C22×D312yes—
777C4×Dic3C22×D311yescharacteristic
778C4×Dic3C22×D311yescharacteristic
779C22×C32—21no—
780C22×C32—21no—
781C22×C32—21no—
782C22×C32C2511yescharacteristic
783C2×C3×D3—21no—
784C2×C3×D3—21no—
785C2×C3×D3—21no—
786C2×C3×D3—21no—
787C2×C3×D3—21no—
788C2×C3×D32−1+412yes—
789C32×C4—21no—
790C32×C4—21no—
791C32×C4—21no—
792C32×C4—21no—
793C32×C4—21no—
794C32×C4C2×#4112yes—
795C3⋊Dic3—22no—
796C3⋊Dic3—22no—
797C3⋊Dic3—22no—
798C3⋊Dic3C2×#4114yes—
799C3×Dic3—22no—
800C3×Dic3—22no—
801C3×Dic3—21no—
802C3×Dic3—21no—
803C3×Dic3—22no—
804C3×Dic3—22no—
805C3×Dic3—21no—
806C3×Dic3—21no—
807C3×Dic3—21no—
808C3×Dic32−1+412yes—
809C22×Q8—91no—
810C22×Q8—91no—
811C22×Q8—91no—
812C4⋊Q8—31no—
813C4⋊Q8—91no—
814C4⋊Q8—91no—
815C4⋊Q8—91no—
816C4⋊Q8—92no—
817C4⋊Q8—92no—
818C4⋊Q8—92no—
819C4⋊Q8—92no—
820#126—31no—
821#126—31no—
822#126—32no—
823#126—32no—
824#126—92no—
825#126—92no—
826#126—92no—
827#126—92no—
828#126—92no—
829#126—92no—
830#125—31no—
831#125—32no—
832#125—32no—
833#125—31no—
834#125—92no—
835#125—92no—
836#125—91no—
837#125—92no—
838#125—92no—
839#125—92no—
840#125—92no—
841#125—92no—
842#125—92no—
843#125—92no—
844#125—92no—
845#124—31no—
846#124—92no—
847#123—31no—
848#123—31no—
849#123—92no—
850#123—92no—
851C22⋊Q8—31no—
852C22⋊Q8—31no—
853C22⋊Q8—31no—
854C22⋊Q8—92no—
855C22⋊Q8—92no—
856C22⋊Q8—92no—
857C22⋊Q8—92no—
858C22⋊Q8—92no—
859C22⋊Q8—92no—
860C22⋊Q8—92no—
861C22⋊Q8—91no—
862C22⋊Q8—91no—
863C22⋊Q8—91no—
864C22⋊Q8—91no—
865#121—31no—
866C4×Q8—31no—
867C4×Q8—31no—
868C4×Q8—31no—
869C4×Q8—92no—
870C4×Q8—92no—
871C4×Q8—91no—
872C4×Q8—92no—
873C4×Q8—91no—
874C4×Q8—92no—
875C4×Q8—91no—
876C4×Q8—91no—
877C4×Q8—92no—
878C4×Q8—92no—
879C4×Q8—92no—
880C4×Q8—92no—
881C4×Q8—92no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—91no—
885C4×Q8—91no—
886C4×Q8—91no—
887C4×D4—31no—
888C4×D4—31no—
889C4×D4—31no—
890C4×D4—92no—
891C4×D4—92no—
892C4×D4—92no—
893#117—31no—
894#117—92no—
895#117—92no—
896#117—92no—
897#117—92no—
898#117—92no—
899#117—91no—
900#117—91no—
901#117—92no—
902#117—92no—
903#117D3211yescharacteristic
904C2×C4⋊C4—92no—
905C2×C4⋊C4—91no—
906C2×C42—31no—
907C2×C42—92no—
908C23×C3—21no—
909C23×C3—31no—
910C23×C3—31no—
911C23×C3C23×D311yescharacteristic
912C23×C3C23×D311yescharacteristic
913C22×D3C23×D311yescharacteristic
914C22×D3C23×D311yescharacteristic
915C3×Q8—62no—
916C3×Q8—62no—
917C3×Q8—62no—
918C3×D4—62no—
919C3×D4—62no—
920C3×D4—62no—
921C2×C3×C4—24no—
922C2×C3×C4—22no—
923C2×C3×C4—22no—
924C2×C3×C4—21no—
925C2×C3×C4—21no—
926C2×C3×C4—21no—
927C2×C3×C4—21no—
928C2×C3×C4—21no—
929C2×C3×C4—21no—
930C2×C3×C4—31no—
931C2×C3×C4—31no—
932C2×C3×C4—31no—
933C2×C3×C4—31no—
934C2×C3×C4—32no—
935C2×C3×C4—32no—
936C2×C3×C4—32no—
937C2×C3×C4—32no—
938C2×C3×C4—31no—
939C2×C3×C4—31no—
940C2×C3×C4—62no—
941C2×C3×C4—62no—
942C2×C3×C4—62no—
943C2×C3×C4—62no—
944C2×C3×C4C23×D311yescharacteristic
945C2×C3×C4C23×D311yescharacteristic
946C2×C3×C4C23×D311yescharacteristic
947C2×C3×C4C23×D311yescharacteristic
948C2×C3×C4C23×D311yescharacteristic
949C2×C3×C4C23×D311yescharacteristic
950C2×C3×C4C23×D311yescharacteristic
951C2×C3×C4C23×D311yescharacteristic
952C2×C3×C4C23×D311yescharacteristic
953C2×C3×C4C23×D311yescharacteristic
954C2×C3×C4C23×D311yescharacteristic
955C2×C3×C4C23×D311yescharacteristic
956#67—22no—
957#67—22no—
958C2×Dic3—32no—
959C2×Dic3—32no—
960C2×Dic3—32no—
961C2×Dic3—32no—
962C2×Dic3—32no—
963C2×Dic3—32no—
964C2×Dic3—32no—
965C2×Dic3—32no—
966C2×Dic3—62no—
967C2×Dic3—62no—
968C2×Dic3—62no—
969C2×Dic3—62no—
970C2×Dic3—64no—
971C2×Dic3—64no—
972C2×Dic3—64no—
973C2×Dic3—64no—
974C2×Dic3—64no—
975C2×Dic3—68no—
976C2×Dic3C23×D311yescharacteristic
977C2×Dic3C23×D311yescharacteristic
978C2×Dic3C23×D312yes—
979C2×Dic3C23×D311yescharacteristic
980C2×Dic3C23×D312yes—
981C2×Dic3C23×D312yes—
982C2×Dic3C23×D312yes—
983C2×Dic3C23×D311yescharacteristic
984C2×Dic3C23×D311yescharacteristic
985C2×Dic3C23×D311yescharacteristic
986D12—22no—
987C4×D3—22no—
988C4×D3—22no—
989C4×D3—22no—
990C4×D3—22no—
991C4×D3—64no—
992C4×D3—64no—
993C4×D3—64no—
994Dic6—22no—
995Dic6—22no—
996Dic6—22no—
997Dic6—34no—
998Dic6—34no—
999Dic6—64no—
1000Dic6—64no—
1001Dic6—64no—
1002Dic6—64no—
1003Dic6—64no—
1004Dic6—64no—
1005Dic6—64no—
1006Dic6—64no—
1007Dic6—68no—
1008Dic6—64no—
1009Dic6—62no—
1010Dic6—62no—
1011Dic6—64no—
1012C2×C32—41no—
1013C2×C32C22×#4111yescharacteristic
1014C2×C32C2×2−1+411yescharacteristic
1015C2×C32C2×2−1+411yescharacteristic
1016C3×D3—22no—
1017C3×D3—41no—
1018C2×Q8—31no—
1019C2×Q8—31no—
1020C2×Q8—31no—
1021C2×Q8—92no—
1022C2×Q8—92no—
1023C2×Q8—92no—
1024C2×Q8—91no—
1025C2×Q8—92no—
1026C2×Q8—91no—
1027C2×Q8—184no—
1028C2×Q8—184no—
1029C2×Q8—184no—
1030C2×D4—31no—
1031C2×D4—31no—
1032C2×D4—31no—
1033C22×C4—31no—
1034C22×C4—31no—
1035C22×C4—31no—
1036C22×C4—31no—
1037C22×C4—92no—
1038C22×C4—92no—
1039C22×C4—92no—
1040C22×C4—92no—
1041C22×C4C2×D3211yescharacteristic
1042C4⋊C4—31no—
1043C4⋊C4—32no—
1044C4⋊C4—31no—
1045C4⋊C4—31no—
1046C4⋊C4—31no—
1047C4⋊C4—32no—
1048C4⋊C4—32no—
1049C4⋊C4—32no—
1050C4⋊C4—31no—
1051C4⋊C4—31no—
1052C4⋊C4—31no—
1053C4⋊C4—32no—
1054C4⋊C4—31no—
1055C4⋊C4—31no—
1056C4⋊C4—31no—
1057C4⋊C4—32no—
1058C4⋊C4—32no—
1059C4⋊C4—32no—
1060C4⋊C4—92no—
1061C4⋊C4—92no—
1062C4⋊C4—92no—
1063C4⋊C4—92no—
1064C4⋊C4—92no—
1065C4⋊C4—92no—
1066C4⋊C4—92no—
1067C4⋊C4—92no—
1068C4⋊C4—92no—
1069C4⋊C4—92no—
1070C4⋊C4—92no—
1071C4⋊C4—92no—
1072C4⋊C4—92no—
1073C4⋊C4—92no—
1074C4⋊C4—92no—
1075C4⋊C4—92no—
1076C4⋊C4—92no—
1077C4⋊C4—91no—
1078C4⋊C4—92no—
1079C4⋊C4—91no—
1080C4⋊C4—92no—
1081C4⋊C4—92no—
1082C4⋊C4C2×D3211yescharacteristic
1083C4⋊C4C2×D3211yescharacteristic
1084C22⋊C4—31no—
1085C22⋊C4—31no—
1086C22⋊C4—32no—
1087C22⋊C4—32no—
1088C22⋊C4—31no—
1089C22⋊C4—31no—
1090C22⋊C4—31no—
1091C22⋊C4—31no—
1092C22⋊C4—31no—
1093C22⋊C4—31no—
1094C22⋊C4—92no—
1095C22⋊C4—92no—
1096C22⋊C4—92no—
1097C22⋊C4—92no—
1098C22⋊C4—92no—
1099C22⋊C4—92no—
1100C22⋊C4C2×D3211yescharacteristic
1101C22⋊C4C2×D3211yescharacteristic
1102C42—31no—
1103C42—31no—
1104C42—31no—
1105C42—32no—
1106C42—31no—
1107C42—32no—
1108C42—92no—
1109C42—92no—
1110C42—92no—
1111C42—92no—
1112C42—92no—
1113C42—92no—
1114C42—92no—
1115C42—92no—
1116C42—92no—
1117C42—92no—
1118C42C2×D3211yescharacteristic
1119C42C2×D3211yescharacteristic
1120C22×C3—22no—
1121C22×C3—21no—
1122C22×C3—21no—
1123C22×C3—21no—
1124C22×C3—21no—
1125C22×C3—21no—
1126C22×C3—21no—
1127C22×C3—21no—
1128C22×C3—32no—
1129C22×C3—41no—
1130C22×C3—41no—
1131C22×C3—61no—
1132C22×C3—61no—
1133C22×C3—61no—
1134C22×C3—61no—
1135C22×C3—61no—
1136C22×C3C24×D311yescharacteristic
1137C22×C3C24×D311yescharacteristic
1138C2×D3—21no—
1139C2×D3—21no—
1140C2×D3—21no—
1141C2×D3—21no—
1142C2×D3—21no—
1143C2×D3#101012yes—
1144C3×C4—22no—
1145C3×C4—21no—
1146C3×C4—21no—
1147C3×C4—21no—
1148C3×C4—21no—
1149C3×C4—21no—
1150C3×C4—21no—
1151C3×C4—21no—
1152C3×C4—21no—
1153C3×C4—21no—
1154C3×C4—21no—
1155C3×C4—22no—
1156C3×C4—32no—
1157C3×C4—41no—
1158C3×C4—41no—
1159C3×C4—41no—
1160C3×C4—41no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—62no—
1164C3×C4—62no—
1165C3×C4—62no—
1166C3×C4—62no—
1167C3×C4—61no—
1168C3×C4—61no—
1169C3×C4—61no—
1170C3×C4D3×#4112yes—
1171C3×C4D3×#4112yes—
1172Dic3—22no—
1173Dic3—22no—
1174Dic3—21no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—21no—
1178Dic3—21no—
1179Dic3—22no—
1180Dic3—22no—
1181Dic3—34no—
1182Dic3—34no—
1183Dic3—64no—
1184Dic3—64no—
1185Dic3—62no—
1186Dic3—62no—
1187Dic3—62no—
1188Dic3—62no—
1189Dic3—62no—
1190Dic3—62no—
1191Dic3—122no—
1192Dic3—122no—
1193Dic3#101012yes—
1194C32#352311yescharacteristic, complemented, Sylow
1195C23—31no—
1196C23—31no—
1197C23C22×D3211yescharacteristic
1198Q8—62no—
1199Q8—62no—
1200Q8—62no—
1201Q8—94no—
1202Q8—184no—
1203Q8—184no—
1204Q8—184no—
1205Q8—184no—
1206Q8—182no—
1207D4—62no—
1208D4—62no—
1209D4—62no—
1210C2×C4—22no—
1211C2×C4—31no—
1212C2×C4—31no—
1213C2×C4—31no—
1214C2×C4—31no—
1215C2×C4—32no—
1216C2×C4—31no—
1217C2×C4—32no—
1218C2×C4—32no—
1219C2×C4—32no—
1220C2×C4—31no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—62no—
1224C2×C4—62no—
1225C2×C4—92no—
1226C2×C4—92no—
1227C2×C4—92no—
1228C2×C4—92no—
1229C2×C4—184no—
1230C2×C4—184no—
1231C2×C4—184no—
1232C2×C4—184no—
1233C2×C4C22×D3211yescharacteristic
1234C2×C4C22×D3211yescharacteristic
1235C2×C4C22×D3211yescharacteristic
1236C2×C4C22×D3211yescharacteristic
1237C2×C4C22×D3211yescharacteristic
1238C2×C4C22×D3211yescharacteristic
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—21no—
1242C2×C3—42no—
1243C2×C3—41no—
1244C2×C3—41no—
1245C2×C3—62no—
1246C2×C3—121no—
1247C2×C3C2×D3×#4111yescharacteristic
1248C2×C3C2×D3×#4111yescharacteristic
1249C2×C3C2×#101011yescharacteristic
1250C2×C3C2×#101011yescharacteristic
1251C2×C3D3×2−1+411yescharacteristic
1252C2×C3D3×2−1+411yescharacteristic
1253D3—22no—
1254D3—41no—
1255C22—21no—
1256C22—21no—
1257C22—21no—
1258C22—32no—
1259C22—61no—
1260C22—61no—
1261C22—61no—
1262C22—61no—
1263C22—61no—
1264C22C23×D3211yescharacteristic
1265C4—21no—
1266C4—21no—
1267C4—21no—
1268C4—21no—
1269C4—21no—
1270C4—32no—
1271C4—61no—
1272C4—61no—
1273C4—62no—
1274C4—62no—
1275C4—61no—
1276C4—62no—
1277C4—61no—
1278C4—61no—
1279C4—62no—
1280C4—94no—
1281C4—182no—
1282C4—182no—
1283C4—182no—
1284C4#6430612yes—
1285C3—21no—
1286C3#8612911yescharacteristic, complemented
1287C3#8651411yescharacteristic, complemented
1288C2—41no—
1289C2—62no—
1290C2—121no—
1291C2C2×#6430611yescharacteristic
1292C2D3×#101011yescharacteristic
1293C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC3×#884C22
hypercenter#117D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595987C2semidirect
3. C3×#5518C2semidirect
4. #10594942C2semidirect
5. #10594915C2semidirect
6. #10594915C2semidirect
7. #10594841C2semidirect
8. #10594597C2semidirect
9. #10594474C2semidirect
10. #10594430C2semidirect
11. #10594388C2semidirect
12. #10594249C2semidirect
13. #10594145C2semidirect
14. #10594120C2semidirect
16. #10593920C2semidirect
17. #10593904C2semidirect
18. #10593885C2semidirect
19. C4×D3×Dic6C2semidirect
20. #10593880C2semidirect
21. #10593873C2semidirect
22. #10593861C2semidirect
23. #10593852C2semidirect
165. #5518D3semidirect
1194. C32#3523semidirect
1286. C3#86129semidirect
1287. C3#86514semidirect

Maximal subgroups

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

subgroupindex
#105959872
C3×#55282
C3×#55182
#105949422
#105949152
#105948412
#105945972
#105944742
#105944302
#105943882
#105942492
#105941452
#105941202
#105941122
#105939202
#105939042
#105938852
C4×D3×Dic62
#105938802
#105938732
#105938612
#105938522
#865143
#861293