Finite Group Databasebeta

← #11909936

Subgroups — #11909936

Order 1152.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595989C211yesmaximal, characteristic, complemented
2C3×#5528C211yesmaximal, characteristic
3C3×#5516C211yesmaximal, characteristic, complemented
4#10594939C211yesmaximal, characteristic, complemented
5Dic6×#67C211yesmaximal, characteristic, complemented
6Dic6×#67C211yesmaximal, characteristic, complemented
7#10594840C211yesmaximal, characteristic, complemented
8#10594596C212yesmaximal, complemented
9#10594420C212yesmaximal, complemented
10#10594418C212yesmaximal, complemented
11#10594386C212yesmaximal, complemented
12#10594247C212yesmaximal, complemented
13#10594105C212yesmaximal, complemented
14#10594102C212yesmaximal, complemented
15#10594086C212yesmaximal
16#10593917C211yesmaximal, characteristic, complemented
17Dic6×D12C211yesmaximal, characteristic, complemented
18#10593885C211yesmaximal, characteristic, complemented
19C4×D3×Dic6C211yesmaximal, characteristic, complemented
20#10593880C211yesmaximal, characteristic, complemented
21#10593873C211yesmaximal, characteristic, complemented
22#10593860C211yesmaximal, characteristic, complemented
23#10593851C211yesmaximal, characteristic, complemented
24#86129—31nomaximal
25#85884—31nomaximal
26C22×C3×Dic6C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×#117C2211yescharacteristic
30#64133C2211yescharacteristic
31#64133C2211yescharacteristic
32#64098C2212yes—
33#64098C2212yes—
34#64088C2212yes—
35#64088C2212yes—
36#64079C2211yescharacteristic
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C4×#634C2211yescharacteristic
40C3×C4×#67C2211yescharacteristic
41C3×C4×#67C2211yescharacteristic
42C3×#926C2211yescharacteristic
43C3×#898C2211yescharacteristic
44C3×#896C2211yescharacteristic
45C3×#894C2211yescharacteristic
46C3×#889C2211yescharacteristic
47C3×#887C2212yes—
48C3×#887C2212yes—
49C3×#885C2211yescharacteristic
50C3×#884C2211yescharacteristic
51C3×#883C2211yescharacteristic
52C3×#879C2211yescharacteristic
53C3×#877C2212yes—
54C3×#877C2212yes—
55C3×C4×D12C2211yescharacteristic
56C3×#872C2211yescharacteristic
57C3×C42×D3C2211yescharacteristic
58C3×C4×Dic6C2211yescharacteristic
59C3×C4×Dic6C2211yescharacteristic
60C3×C4×Dic6C2211yescharacteristic
61C3×C4×Dic6C2211yescharacteristic
62C3×C4×Dic6C2211yescharacteristic
63Dic3×#67C2212yes—
64Dic3×#67C2212yes—
65#63969C2212yes—
66#63964C2212yes—
67#63964C2212yes—
68#63959C2212yes—
69#63956C2212yes—
70#63956C2212yes—
71#63918C2211yescharacteristic
72#63918C2212yes—
73C4×#627C2212yes—
74C4×#627C2212yes—
75#63893C2212yes—
76#63893C2212yes—
77Dic3×D12C2212yes—
78D3×C4⋊Dic3C2211yescharacteristic
79#63887C2212yes—
80#63887C2212yes—
81#63884C2212yes—
82#63878C2212yes—
83#63877C2212yes—
84#63877C2212yes—
85#63877C2212yes—
86D3×Dic3⋊C4C2212yes—
87C4×D3×Dic3C2212yes—
88#63870C2212yes—
89#63869C2212yes—
90#63869C2211yescharacteristic
91#63867C2212yes—
92#63867C2212yes—
93#63867C2212yes—
94#63867C2212yes—
95#63866C2211yescharacteristic
96#63866C2211yescharacteristic
97#63862C2212yes—
98#63859C2212yes—
99#63859C2212yes—
100#63859C2212yes—
101#63857C2211yescharacteristic
102#63857C2211yescharacteristic
103#63856C2211yescharacteristic
104#63856C2211yescharacteristic
105#63855C2212yes—
106#63851C2212yes—
107#63847C2212yes—
108#63846C2212yes—
109#63845C2212yes—
110#63845C2212yes—
111#63844C2211yescharacteristic
112#63844C2211yescharacteristic
113Dic3×Dic6C2212yes—
114Dic3×Dic6C2211yescharacteristic
115Dic3×Dic6C2211yescharacteristic
116#63841C2211yescharacteristic
117#63839C2212yes—
118#63839C2212yes—
119#63839C2212yes—
120#63838C2212yes—
121#63837C2212yes—
122#63837C2212yes—
123#63837C2212yes—
124#63837C2212yes—
125C3×#529—31no—
126C3×#519—31no—
127Q8×#67—31no—
128Q8×#67—31no—
129#5701—32no—
130#5701—32no—
131#5685—32no—
132#5671—32no—
133#5650—32no—
134#5650—32no—
135#5622—32no—
136#5600—32no—
137#5583—32no—
138#5583—31no—
139#5581—32no—
140#5581—31no—
141#5578—32no—
142#5578—31no—
143Q8×D12—31no—
144#5572—31no—
145C4×D3×Q8—31no—
146#5570—31no—
147#5569—31no—
148#5567—32no—
149#5567—31no—
150#5567—31no—
151#5542—31no—
152#5541—31no—
153#5541—31no—
154D4×Dic6—31no—
155D4×Dic6—31no—
156D4×Dic6—31no—
157#5533—31no—
158#5533—32no—
159#5529—31no—
160#5529—32no—
161#5528—32no—
162#5528D311yescharacteristic
163#5518—31no—
164#5518—31no—
165#5518—32no—
166#5518—31no—
167#5518—61no—
168#5516—31no—
169#5516D311yescharacteristic, complemented
170#5470—31no—
171C2×C4×Dic6—31no—
172C22×C32×C4C2311yescharacteristic
173C2×#634C2311yescharacteristic
174C2×#634C2311yescharacteristic
175C2×C3×#67C2311yescharacteristic
176C2×C3×#67C2311yescharacteristic
177C22×C3×Dic3C2312yes—
178C2×C3×D12C2311yescharacteristic
179C2×C3×C4×D3C2311yescharacteristic
180C2×C3×C4×D3C2311yescharacteristic
181C2×C3×C4×D3C2311yescharacteristic
182C2×C3×C4×D3C2311yescharacteristic
183C2×C3×Dic6—24no—
184C2×C3×Dic6C2311yescharacteristic
185C2×C3×Dic6C2312yes—
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—
203#3757C2312yes—
204C4⋊(C3⋊Dic3)C2311yescharacteristic
205C4⋊(C3⋊Dic3)C2311yescharacteristic
206C4⋊(C3⋊Dic3)C2312yes—
207C4⋊(C3⋊Dic3)C2312yes—
208#3750C2312yes—
209#3750C2312yes—
210#3750C2312yes—
211#3750C2312yes—
212#3750C2312yes—
213#3750C2312yes—
214C4×C3⋊Dic3C2312yes—
215C4×C3⋊Dic3C2312yes—
216C3×#217C2312yes—
217C3×#217C2311yescharacteristic
218C3×#217C2311yescharacteristic
219C3×(C2×D3)⋊C4C2311yescharacteristic
220C3×(C2×D3)⋊C4C2311yescharacteristic
221C3×(C2×D3)⋊C4C2311yescharacteristic
222C3×(C2×D3)⋊C4C2311yescharacteristic
223C3×(C2×D3)⋊C4C2311yescharacteristic
224C3×(C2×D3)⋊C4C2311yescharacteristic
225C3×C4⋊Dic3C2311yescharacteristic
226C3×C4⋊Dic3C2311yescharacteristic
227C3×C4⋊Dic3C2311yescharacteristic
228C3×C4⋊Dic3C2311yescharacteristic
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2312yes—
233C3×Dic3⋊C4C2311yescharacteristic
234C3×Dic3⋊C4C2311yescharacteristic
235C3×Dic3⋊C4C2311yescharacteristic
236C3×Dic3⋊C4C2311yescharacteristic
237C3×Dic3⋊C4C2311yescharacteristic
238C3×Dic3⋊C4C2311yescharacteristic
239C3×C4×Dic3C2312yes—
240C3×C4×Dic3C2312yes—
241C3×C4×Dic3C2312yes—
242C3×C4×Dic3C2312yes—
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245C3×C4×Dic3C2312yes—
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
275C22×C3×Q8—31no—
276C2×D3×Q8—31no—
277C2×D3×Q8—31no—
278C22×Dic6—31no—
279C22×Dic6—31no—
280C22×Dic6C2×D311yescharacteristic
281C3×#126—31no—
282C3×#126—31no—
283C3×#125—31no—
284C3×#124—31no—
285C3×#123—31no—
286C3×#123—31no—
287C3×C22⋊Q8—31no—
288C3×#121—31no—
289C3×C4×Q8—32no—
290C3×C4×Q8—32no—
291C3×C4×Q8—31no—
292C3×C4×Q8—31no—
293C3×C4×Q8—31no—
294C3×C4×Q8—31no—
295C3×C4×Q8—31no—
296C3×C4×D4—31no—
297C3×C4×D4—31no—
298C3×C4×D4—31no—
299C3×#117—21no—
300C3×#117—31no—
301C3×#117—32no—
302C3×#117—32no—
303C3×#117—31no—
304C3×#117C2×D311yescharacteristic
305C3×#117C2×D311yescharacteristic
306C2×C3×C42—31no—
307#946—31no—
308#946—31no—
309#946—32no—
310#946—32no—
311Q8×Dic3—32no—
312Q8×Dic3—31no—
313Q8×Dic3—31no—
314#944—32no—
315#944—32no—
316#944—32no—
317#944—31no—
318#944—31no—
319#936—32no—
320#935—32no—
321#935—32no—
322D4×Dic3—32no—
323D4×Dic3—32no—
324D4×Dic3—32no—
325C4×#67—32no—
326C4×#67—32no—
327C4×#67C2×D311yescharacteristic
328C4×#67C2×D311yescharacteristic
329#926—31no—
330#926—32no—
331#926C2×D311yescharacteristic
332C2×C4⋊Dic3—31no—
333#924—31no—
334#924—31no—
335#924—31no—
336#924—31no—
337#924—31no—
338#924—31no—
339#924—32no—
340#924—32no—
341#924—31no—
342#924—31no—
343#924—32no—
344#924—61no—
345#924—61no—
346C2×Dic3⋊C4—32no—
347C2×C4×Dic3—32no—
348#898—32no—
349#898C2×D311yescharacteristic
350#897—31no—
351#897—31no—
352#897—32no—
353#897—32no—
354#896—32no—
355#896C2×D311yescharacteristic
356#894—32no—
357#894C2×D311yescharacteristic
358#892—31no—
359#892—32no—
360D3×C4⋊C4—32no—
361D3×C4⋊C4—31no—
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#889—32no—
381#889—32no—
382#889—62no—
383#889—62no—
384#889C2×D311yescharacteristic
385#888—32no—
386#888—32no—
387#888—32no—
388#888—32no—
389#888—31no—
390#887—32no—
391#887—32no—
392#887—32no—
393#887—32no—
394#887—32no—
395#887—32no—
396#887—31no—
397#887—31no—
398#887C2×D312yes—
399#887C2×D312yes—
400#885—32no—
401#885C2×D311yescharacteristic
402#884C2×D311yescharacteristic
403#883—32no—
404#883C2×D311yescharacteristic
405#879—32no—
406#879—32no—
407#879—32no—
408#879—32no—
409#879—32no—
410#879—32no—
411#879—32no—
412#879—32no—
413#879—32no—
414#879—32no—
415#879—32no—
416#879—32no—
417#879—62no—
418#879—62no—
419#879C2×D311yescharacteristic
420#878—32no—
421#878—32no—
422#878—32no—
423#878—32no—
424#878—32no—
425#878—32no—
426#877—32no—
427#877—32no—
428#877—32no—
429#877—32no—
430#877C2×D312yes—
431#877C2×D312yes—
432#876—32no—
433#876—32no—
434#876—32no—
435C4×D12—32no—
436C4×D12C2×D311yescharacteristic
437#872—32no—
438#872—32no—
439#872—32no—
440#872—32no—
441#872C2×D311yescharacteristic
442C42×D3—32no—
443C42×D3C2×D311yescharacteristic
444#870—31no—
445#870—31no—
446#870—31no—
447#870—32no—
448#870—32no—
449#870—32no—
450#870—32no—
451#870—32no—
452#870—61no—
453#869—31no—
454#869—31no—
455#869—31no—
456#869—31no—
457#869—31no—
458#869—32no—
459#869—61no—
460C4×Dic6—31no—
461C4×Dic6—31no—
462C4×Dic6—32no—
463C4×Dic6—31no—
464C4×Dic6—31no—
465C4×Dic6—31no—
466C4×Dic6—31no—
467C4×Dic6—31no—
468C4×Dic6—31no—
469C4×Dic6—32no—
470C4×Dic6—32no—
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×Dic6C2×D311yescharacteristic
480C4×Dic6C2×D311yescharacteristic
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⋊Dic3C2412yes—
495C2×C3⋊Dic3C2412yes—
496C2×C3⋊Dic3C2412yes—
497C2×C3⋊Dic3C2412yes—
498#634—22no—
499#634—22no—
500C3×#67—22no—
501C3×#67—22no—
502C2×C3×Dic3—24no—
503C2×C3×Dic3C2412yes—
504C2×C3×Dic3C2411yescharacteristic
505C2×C3×Dic3C2411yescharacteristic
506C2×C3×Dic3C2411yescharacteristic
507C2×C3×Dic3C2412yes—
508C2×C3×Dic3C2412yes—
509C2×C3×Dic3C2411yescharacteristic
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2412yes—
512C2×C3×Dic3C2411yescharacteristic
513C3×D12—22no—
514C3×C4×D3—22no—
515C3×C4×D3—22no—
516C3×C4×D3—22no—
517C3×C4×D3—22no—
518C3×Dic6—22no—
519C3×Dic6—24no—
520C3×Dic6—22no—
521C3×Dic6#4114yes—
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—92no—
535#552—91no—
536#552—92no—
537D4×Q8—91no—
538D4×Q8—91no—
539D4×Q8—91no—
540#541—91no—
541#541—92no—
542#541—92no—
543#541—91no—
544#533—91no—
545#533—92no—
546#529—31no—
547#529—92no—
548#519—31no—
549#519—91no—
550C2×C4×Q8—91no—
551C2×C3×Q8—31no—
552C2×C3×Q8—31no—
553C2×C3×Q8—32no—
554C2×C3×Q8—31no—
555C2×C3×Q8—64no—
556C2×C3×D4—31no—
557C2×C3×D4—31no—
558C2×C3×D4—31no—
559C22×C3×C4—21no—
560C22×C3×C4—32no—
561C22×C3×C4—31no—
562C22×C3×C4—31no—
563C22×C3×C4—31no—
564C22×C3×C4—31no—
565C22×C3×C4C22×D311yescharacteristic
566C22×C3×C4C22×D311yescharacteristic
567C2×#67C22×D311yescharacteristic
568C2×#67C22×D311yescharacteristic
569C22×Dic3—32no—
570C22×Dic3—32no—
571C22×Dic3—32no—
572C22×Dic3C22×D312yes—
573D3×Q8—64no—
574D3×Q8—64no—
575C2×D12C22×D311yescharacteristic
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3C22×D311yescharacteristic
580C2×C4×D3C22×D311yescharacteristic
581C2×C4×D3C22×D311yescharacteristic
582C2×C4×D3C22×D311yescharacteristic
583C2×Dic6—24no—
584C2×Dic6—31no—
585C2×Dic6—31no—
586C2×Dic6—31no—
587C2×Dic6—31no—
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—64no—
597C2×Dic6—64no—
598C2×Dic6C22×D311yescharacteristic
599C2×Dic6C22×D311yescharacteristic
600C2×Dic6C22×D312yes—
601C2×Dic6C22×D311yescharacteristic
602C3×C4⋊C4—21no—
603C3×C4⋊C4—21no—
604C3×C4⋊C4—31no—
605C3×C4⋊C4—31no—
606C3×C4⋊C4—31no—
607C3×C4⋊C4—31no—
608C3×C4⋊C4—32no—
609C3×C4⋊C4—31no—
610C3×C4⋊C4—31no—
611C3×C4⋊C4—31no—
612C3×C4⋊C4—32no—
613C3×C4⋊C4—31no—
614C3×C4⋊C4—32no—
615C3×C4⋊C4—31no—
616C3×C4⋊C4—31no—
617C3×C4⋊C4—32no—
618C3×C4⋊C4C22×D311yescharacteristic
619C3×C4⋊C4C22×D311yescharacteristic
620C3×C4⋊C4C22×D311yescharacteristic
621C3×C4⋊C4C22×D311yescharacteristic
622C3×C22⋊C4—21no—
623C3×C22⋊C4—21no—
624C3×C22⋊C4—31no—
625C3×C22⋊C4—31no—
626C3×C22⋊C4—32no—
627C3×C22⋊C4—31no—
628C3×C22⋊C4—31no—
629C3×C22⋊C4—31no—
630C3×C22⋊C4—31no—
631C3×C22⋊C4—31no—
632C3×C22⋊C4—31no—
633C3×C22⋊C4C22×D311yescharacteristic
634C3×C22⋊C4C22×D311yescharacteristic
635C3×C22⋊C4C22×D311yescharacteristic
636C3×C22⋊C4C22×D311yescharacteristic
637C3×C42—21no—
638C3×C42—21no—
639C3×C42—31no—
640C3×C42—31no—
641C3×C42—31no—
642C3×C42—31no—
643C3×C42—32no—
644C3×C42—32no—
645C3×C42—32no—
646C3×C42—32no—
647C3×C42—32no—
648C3×C42C22×D311yescharacteristic
649C3×C42C22×D311yescharacteristic
650C3×C42C22×D311yescharacteristic
651C3×C42C22×D311yescharacteristic
652#217—32no—
653#217—32no—
654#217—32no—
655#217—32no—
656#217—32no—
657#217—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—62no—
662#217—62no—
663#217C22×D312yes—
664#217C22×D311yescharacteristic
665#217C22×D311yescharacteristic
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4C22×D311yescharacteristic
672(C2×D3)⋊C4C22×D311yescharacteristic
673(C2×D3)⋊C4C22×D311yescharacteristic
674(C2×D3)⋊C4C22×D311yescharacteristic
675(C2×D3)⋊C4C22×D311yescharacteristic
676(C2×D3)⋊C4C22×D311yescharacteristic
677C4⋊Dic3—31no—
678C4⋊Dic3—31no—
679C4⋊Dic3—32no—
680C4⋊Dic3—31no—
681C4⋊Dic3—31no—
682C4⋊Dic3—32no—
683C4⋊Dic3—32no—
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—32no—
696C4⋊Dic3—61no—
697C4⋊Dic3—61no—
698C4⋊Dic3—62no—
699C4⋊Dic3—62no—
700C4⋊Dic3C22×D311yescharacteristic
701C4⋊Dic3C22×D311yescharacteristic
702C4⋊Dic3C22×D311yescharacteristic
703C4⋊Dic3C22×D311yescharacteristic
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—32no—
733Dic3⋊C4—32no—
734Dic3⋊C4—32no—
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—62no—
738Dic3⋊C4—62no—
739Dic3⋊C4—62no—
740Dic3⋊C4—62no—
741Dic3⋊C4—62no—
742Dic3⋊C4—62no—
743Dic3⋊C4C22×D311yescharacteristic
744Dic3⋊C4C22×D311yescharacteristic
745Dic3⋊C4C22×D311yescharacteristic
746Dic3⋊C4C22×D312yes—
747Dic3⋊C4C22×D311yescharacteristic
748Dic3⋊C4C22×D312yes—
749Dic3⋊C4C22×D312yes—
750Dic3⋊C4C22×D312yes—
751Dic3⋊C4C22×D311yescharacteristic
752Dic3⋊C4C22×D311yescharacteristic
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—62no—
768C4×Dic3—62no—
769C4×Dic3C22×D311yescharacteristic
770C4×Dic3C22×D311yescharacteristic
771C4×Dic3C22×D312yes—
772C4×Dic3C22×D312yes—
773C4×Dic3C22×D311yescharacteristic
774C4×Dic3C22×D311yescharacteristic
775C4×Dic3C22×D312yes—
776C4×Dic3C22×D312yes—
777C4×Dic3C22×D312yes—
778C22×C32—21no—
779C22×C32—21no—
780C22×C32—21no—
781C22×C32C2511yescharacteristic
782C2×C3×D3—21no—
783C2×C3×D3—21no—
784C2×C3×D3—21no—
785C2×C3×D3—21no—
786C2×C3×D3—21no—
787C2×C3×D32−1+412yes—
788C32×C4—21no—
789C32×C4—21no—
790C32×C4—21no—
791C32×C4—21no—
792C32×C4—21no—
793C32×C4C2×#4112yes—
794C3⋊Dic3—22no—
795C3⋊Dic3—22no—
796C3⋊Dic3—22no—
797C3⋊Dic3—22no—
798C3×Dic3—21no—
799C3×Dic3—21no—
800C3×Dic3—22no—
801C3×Dic3—22no—
802C3×Dic3—22no—
803C3×Dic3—21no—
804C3×Dic3—21no—
805C3×Dic3—21no—
806C3×Dic3C2×#4114yes—
807C3×Dic32−1+412yes—
808C22×Q8—31no—
809C22×Q8—91no—
810C22×Q8—91no—
811C4⋊Q8—91no—
812C4⋊Q8—92no—
813C4⋊Q8—91no—
814C4⋊Q8—91no—
815C4⋊Q8—92no—
816C4⋊Q8—92no—
817C4⋊Q8—92no—
818C4⋊Q8—91no—
819#126—31no—
820#126—31no—
821#126—92no—
822#126—92no—
823#126—92no—
824#126—92no—
825#126—92no—
826#126—92no—
827#126—92no—
828#126—92no—
829#125—31no—
830#125—92no—
831#125—92no—
832#125—92no—
833#125—92no—
834#125—92no—
835#125—91no—
836#125—92no—
837#125—92no—
838#125—92no—
839#125—92no—
840#125—92no—
841#125—92no—
842#125—92no—
843#125—91no—
844#124—31no—
845#124—92no—
846#123—31no—
847#123—31no—
848#123—92no—
849#123—92no—
850C22⋊Q8—31no—
851C22⋊Q8—92no—
852C22⋊Q8—92no—
853C22⋊Q8—92no—
854C22⋊Q8—92no—
855C22⋊Q8—92no—
856C22⋊Q8—92no—
857C22⋊Q8—92no—
858C22⋊Q8—91no—
859C22⋊Q8—91no—
860C22⋊Q8—91no—
861C22⋊Q8—91no—
862C22⋊Q8—91no—
863C22⋊Q8—91no—
864#121—31no—
865C4×Q8—32no—
866C4×Q8—32no—
867C4×Q8—31no—
868C4×Q8—31no—
869C4×Q8—31no—
870C4×Q8—31no—
871C4×Q8—31no—
872C4×Q8—92no—
873C4×Q8—92no—
874C4×Q8—91no—
875C4×Q8—92no—
876C4×Q8—92no—
877C4×Q8—91no—
878C4×Q8—92no—
879C4×Q8—92no—
880C4×Q8—91no—
881C4×Q8—91no—
882C4×Q8—92no—
883C4×Q8—92no—
884C4×Q8—91no—
885C4×Q8—91no—
886C4×D4—31no—
887C4×D4—31no—
888C4×D4—31no—
889C4×D4—92no—
890C4×D4—92no—
891C4×D4—92no—
892#117—31no—
893#117—32no—
894#117—32no—
895#117—31no—
896#117—92no—
897#117—92no—
898#117—92no—
899#117—92no—
900#117—92no—
901#117—91no—
902#117D3211yescharacteristic
903C2×C4⋊C4—92no—
904C2×C4⋊C4—91no—
905C2×C42—31no—
906C2×C42—92no—
907C23×C3—21no—
908C23×C3—31no—
909C23×C3—31no—
910C23×C3C23×D311yescharacteristic
911C23×C3C23×D311yescharacteristic
912C22×D3C23×D311yescharacteristic
913C22×D3C23×D311yescharacteristic
914C3×Q8—34no—
915C3×Q8—62no—
916C3×Q8—64no—
917C3×Q8—62no—
918C3×D4—62no—
919C3×D4—62no—
920C3×D4—62no—
921C2×C3×C4—22no—
922C2×C3×C4—22no—
923C2×C3×C4—21no—
924C2×C3×C4—21no—
925C2×C3×C4—21no—
926C2×C3×C4—21no—
927C2×C3×C4—21no—
928C2×C3×C4—21no—
929C2×C3×C4—31no—
930C2×C3×C4—32no—
931C2×C3×C4—32no—
932C2×C3×C4—31no—
933C2×C3×C4—31no—
934C2×C3×C4—31no—
935C2×C3×C4—32no—
936C2×C3×C4—31no—
937C2×C3×C4—31no—
938C2×C3×C4—32no—
939C2×C3×C4—42no—
940C2×C3×C4—62no—
941C2×C3×C4—62no—
942C2×C3×C4—64no—
943C2×C3×C4—62no—
944C2×C3×C4—62no—
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
956C2×C3×C4C23×D311yescharacteristic
957#67—22no—
958#67—22no—
959C2×Dic3—24no—
960C2×Dic3—32no—
961C2×Dic3—32no—
962C2×Dic3—32no—
963C2×Dic3—32no—
964C2×Dic3—32no—
965C2×Dic3—32no—
966C2×Dic3—32no—
967C2×Dic3—32no—
968C2×Dic3—62no—
969C2×Dic3—62no—
970C2×Dic3—62no—
971C2×Dic3—62no—
972C2×Dic3—64no—
973C2×Dic3—64no—
974C2×Dic3—64no—
975C2×Dic3C23×D312yes—
976C2×Dic3C23×D311yescharacteristic
977C2×Dic3C23×D311yescharacteristic
978C2×Dic3C23×D311yescharacteristic
979C2×Dic3C23×D312yes—
980C2×Dic3C23×D311yescharacteristic
981C2×Dic3C23×D311yescharacteristic
982C2×Dic3C23×D312yes—
983C2×Dic3C23×D312yes—
984C2×Dic3C23×D311yescharacteristic
985D12—22no—
986C4×D3—22no—
987C4×D3—22no—
988C4×D3—22no—
989C4×D3—22no—
990C4×D3—64no—
991C4×D3—64no—
992C4×D3—64no—
993Dic6—22no—
994Dic6—24no—
995Dic6—22no—
996Dic6—64no—
997Dic6—64no—
998Dic6—64no—
999Dic6—62no—
1000Dic6—62no—
1001Dic6—62no—
1002Dic6—62no—
1003Dic6—64no—
1004Dic6—64no—
1005Dic6—64no—
1006Dic6—122no—
1007Dic6—122no—
1008Dic6#23514yes—
1009C2×C32—41no—
1010C2×C32C22×#4111yescharacteristic
1011C2×C32C2×2−1+411yescharacteristic
1012C2×C32C2×2−1+411yescharacteristic
1013C3×D3—22no—
1014C3×D3—41no—
1015C2×Q8—31no—
1016C2×Q8—32no—
1017C2×Q8—31no—
1018C2×Q8—31no—
1019C2×Q8—64no—
1020C2×Q8—92no—
1021C2×Q8—92no—
1022C2×Q8—92no—
1023C2×Q8—91no—
1024C2×Q8—91no—
1025C2×Q8—184no—
1026C2×Q8—184no—
1027C2×D4—31no—
1028C2×D4—31no—
1029C2×D4—31no—
1030C22×C4—32no—
1031C22×C4—31no—
1032C22×C4—31no—
1033C22×C4—31no—
1034C22×C4—31no—
1035C22×C4—92no—
1036C22×C4—92no—
1037C22×C4—92no—
1038C22×C4C2×D3211yescharacteristic
1039C4⋊C4—32no—
1040C4⋊C4—31no—
1041C4⋊C4—32no—
1042C4⋊C4—31no—
1043C4⋊C4—32no—
1044C4⋊C4—32no—
1045C4⋊C4—31no—
1046C4⋊C4—31no—
1047C4⋊C4—31no—
1048C4⋊C4—31no—
1049C4⋊C4—31no—
1050C4⋊C4—31no—
1051C4⋊C4—31no—
1052C4⋊C4—31no—
1053C4⋊C4—92no—
1054C4⋊C4—92no—
1055C4⋊C4—92no—
1056C4⋊C4—92no—
1057C4⋊C4—92no—
1058C4⋊C4—92no—
1059C4⋊C4—92no—
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—91no—
1070C4⋊C4—92no—
1071C4⋊C4—91no—
1072C4⋊C4—92no—
1073C4⋊C4—92no—
1074C4⋊C4—92no—
1075C4⋊C4—92no—
1076C4⋊C4—92no—
1077C4⋊C4—92no—
1078C4⋊C4—92no—
1079C4⋊C4C2×D3211yescharacteristic
1080C4⋊C4C2×D3211yescharacteristic
1081C22⋊C4—32no—
1082C22⋊C4—31no—
1083C22⋊C4—31no—
1084C22⋊C4—31no—
1085C22⋊C4—31no—
1086C22⋊C4—31no—
1087C22⋊C4—31no—
1088C22⋊C4—31no—
1089C22⋊C4—31no—
1090C22⋊C4—92no—
1091C22⋊C4—92no—
1092C22⋊C4—92no—
1093C22⋊C4—92no—
1094C22⋊C4—92no—
1095C22⋊C4—92no—
1096C22⋊C4—92no—
1097C22⋊C4C2×D3211yescharacteristic
1098C22⋊C4C2×D3211yescharacteristic
1099C42—31no—
1100C42—31no—
1101C42—31no—
1102C42—32no—
1103C42—32no—
1104C42—32no—
1105C42—32no—
1106C42—31no—
1107C42—32no—
1108C42—92no—
1109C42—92no—
1110C42—92no—
1111C42—92no—
1112C42—92no—
1113C42—92no—
1114C42—92no—
1115C42C2×D3211yescharacteristic
1116C42C2×D3211yescharacteristic
1117C22×C3—21no—
1118C22×C3—21no—
1119C22×C3—21no—
1120C22×C3—21no—
1121C22×C3—21no—
1122C22×C3—21no—
1123C22×C3—21no—
1124C22×C3—32no—
1125C22×C3—41no—
1126C22×C3—41no—
1127C22×C3—41no—
1128C22×C3—61no—
1129C22×C3—61no—
1130C22×C3—61no—
1131C22×C3—61no—
1132C22×C3—61no—
1133C22×C3C24×D311yescharacteristic
1134C22×C3C24×D311yescharacteristic
1135C2×D3—21no—
1136C2×D3—21no—
1137C2×D3—21no—
1138C2×D3—21no—
1139C2×D3—21no—
1140C2×D3#101012yes—
1141C3×C4—21no—
1142C3×C4—21no—
1143C3×C4—21no—
1144C3×C4—21no—
1145C3×C4—21no—
1146C3×C4—21no—
1147C3×C4—21no—
1148C3×C4—21no—
1149C3×C4—21no—
1150C3×C4—21no—
1151C3×C4—22no—
1152C3×C4—34no—
1153C3×C4—32no—
1154C3×C4—41no—
1155C3×C4—41no—
1156C3×C4—41no—
1157C3×C4—41no—
1158C3×C4—41no—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—62no—
1162C3×C4—62no—
1163C3×C4—62no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4C2×#23512yes—
1168C3×C4D3×#4112yes—
1169Dic3—22no—
1170Dic3—21no—
1171Dic3—21no—
1172Dic3—21no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—22no—
1176Dic3—22no—
1177Dic3—62no—
1178Dic3—62no—
1179Dic3—62no—
1180Dic3—62no—
1181Dic3—62no—
1182Dic3—62no—
1183Dic3—62no—
1184Dic3—62no—
1185Dic3—122no—
1186Dic3—122no—
1187Dic3—122no—
1188Dic3—122no—
1189Dic3C2×#23514yes—
1190Dic3#101012yes—
1191C32#352311yescharacteristic, complemented, Sylow
1192C23—31no—
1193C23—31no—
1194C23C22×D3211yescharacteristic
1195Q8—34no—
1196Q8—64no—
1197Q8—62no—
1198Q8—62no—
1199Q8—184no—
1200Q8—184no—
1201Q8—184no—
1202Q8—182no—
1203Q8—182no—
1204D4—62no—
1205D4—62no—
1206D4—62no—
1207C2×C4—22no—
1208C2×C4—31no—
1209C2×C4—32no—
1210C2×C4—32no—
1211C2×C4—32no—
1212C2×C4—31no—
1213C2×C4—31no—
1214C2×C4—32no—
1215C2×C4—31no—
1216C2×C4—31no—
1217C2×C4—31no—
1218C2×C4—62no—
1219C2×C4—62no—
1220C2×C4—64no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—92no—
1224C2×C4—92no—
1225C2×C4—92no—
1226C2×C4—92no—
1227C2×C4—184no—
1228C2×C4—184no—
1229C2×C4—184no—
1230C2×C4C22×D3211yescharacteristic
1231C2×C4C22×D3211yescharacteristic
1232C2×C4C22×D3211yescharacteristic
1233C2×C4C22×D3211yescharacteristic
1234C2×C4C22×D3211yescharacteristic
1235C2×C4C22×D3211yescharacteristic
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—21no—
1239C2×C3—41no—
1240C2×C3—41no—
1241C2×C3—62no—
1242C2×C3—81no—
1243C2×C3—121no—
1244C2×C3C22×#23511yescharacteristic
1245C2×C3C2×D3×#4111yescharacteristic
1246C2×C3C2×#101011yescharacteristic
1247C2×C3C2×#101011yescharacteristic
1248C2×C3D3×2−1+411yescharacteristic
1249C2×C3D3×2−1+411yescharacteristic
1250D3—22no—
1251D3—41no—
1252C22—21no—
1253C22—21no—
1254C22—21no—
1255C22—32no—
1256C22—61no—
1257C22—61no—
1258C22—61no—
1259C22—61no—
1260C22—61no—
1261C22C23×D3211yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—21no—
1265C4—21no—
1266C4—21no—
1267C4—34no—
1268C4—32no—
1269C4—62no—
1270C4—61no—
1271C4—61no—
1272C4—61no—
1273C4—62no—
1274C4—61no—
1275C4—61no—
1276C4—62no—
1277C4—182no—
1278C4—182no—
1279C4—182no—
1280C4—182no—
1281C4D3×#23512yes—
1282C3—21no—
1283C3#8588411yescharacteristic, complemented
1284C3#8612911yescharacteristic, complemented
1285C2—41no—
1286C2—62no—
1287C2—121no—
1288C2C2×D3×#23511yescharacteristic
1289C2D3×#101011yescharacteristic
1290C2D3×#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. #10595989C2semidirect
3. C3×#5516C2semidirect
4. #10594939C2semidirect
5. Dic6×#67C2semidirect
6. Dic6×#67C2semidirect
7. #10594840C2semidirect
8. #10594596C2semidirect
9. #10594420C2semidirect
10. #10594418C2semidirect
11. #10594386C2semidirect
12. #10594247C2semidirect
13. #10594105C2semidirect
14. #10594102C2semidirect
16. #10593917C2semidirect
17. Dic6×D12C2semidirect
18. #10593885C2semidirect
19. C4×D3×Dic6C2semidirect
20. #10593880C2semidirect
21. #10593873C2semidirect
22. #10593860C2semidirect
23. #10593851C2semidirect
169. #5516D3semidirect
1191. C32#3523semidirect
1283. C3#85884semidirect
1284. C3#86129semidirect

Maximal subgroups

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

subgroupindex
#105959892
C3×#55282
C3×#55162
#105949392
Dic6×#672
#105948402
#105945962
#105944202
#105944182
#105943862
#105942472
#105941052
#105941022
#105940862
#105939172
Dic6×D122
#105938852
C4×D3×Dic62
#105938802
#105938732
#105938602
#105938512
#861293
#858843