Finite Group Databasebeta

← #11895687

Subgroups — #11895687

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594566C211yesmaximal, characteristic
2#10594318C211yesmaximal, characteristic, complemented
3#10592551C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4854C211yesmaximal, characteristic, complemented
6#10590879C211yesmaximal, characteristic
7#10590868C211yesmaximal, characteristic, complemented
8#10590813C211yesmaximal, characteristic, complemented
9#10590645C211yesmaximal, characteristic, complemented
10#10590548C211yesmaximal, characteristic
11#10590538C211yesmaximal, characteristic, complemented
12#10590537C211yesmaximal, characteristic, complemented
13#10590481C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81151—31nomaximal
17#81041—31nomaximal
18C2×#3744C2211yescharacteristic
19#64102C2211yescharacteristic
20#64096C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63911C2211yescharacteristic
27C4×#626—21no—
28#63872C2211yescharacteristic
29#63870—21no—
30#63864C2211yescharacteristic
31#63863C2211yescharacteristic
32#63853—21no—
33#63852—21no—
34#63850—21no—
35#63847—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843—21no—
39#63839—21no—
40C2×#3719C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C8×C3⋊Dic3C2211yescharacteristic
44#63637C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63572C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5721—31no—
62#5685—31no—
63#5585—31no—
64#5559—31no—
65C3×#478—31no—
66C3×#475—31no—
67#5088—31no—
68#5068—31no—
69C4×#216—31no—
70C4×#214—31no—
71#4891—31no—
72#4873—31no—
73#4871—31no—
74#4871D311yescharacteristic, complemented
75#4854D311yescharacteristic, complemented
76#4852—31no—
77#4852—31no—
78#4852—31no—
79#4852—61no—
80#4848—31no—
81#4845—31no—
82#4830—31no—
83#4830—31no—
84#4800—31no—
85#4800—31no—
86#4798—31no—
87#4798—31no—
88#4768—31no—
89#4767—31no—
90#4762—31no—
91#4760—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3752—21no—
106#3750—21no—
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110#3744—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3724—21no—
124#3724—21no—
125#3724D411yescharacteristic
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3716—22no—
138#3365—91noSylow
139C3×C4⋊Q8—31no—
140C3×#125—31no—
141C3×C4×Q8—31no—
142C3×C4×D4—31no—
143#947—31no—
144#947—31no—
145Q8×Dic3—61no—
146#944—61no—
147C2×#216—31no—
148#940—31no—
149#936—31no—
150C2×#214—31no—
151#929—61no—
152C4×#67—61no—
153C2×Dic12—31no—
154C2×#204—31no—
155C2×#204—31no—
156C2×#204—31no—
157C2×#204—61no—
158#894—61no—
159#894—61no—
160#893—31no—
161#893—31no—
162#893—61no—
163#893C2×D311yescharacteristic
164#890—31no—
165#890—31no—
166#890C2×D311yescharacteristic
167#889—61no—
168#889—61no—
169#889—61no—
170#889—61no—
171#888—61no—
172#888C2×D311yescharacteristic
173#887—31no—
174#887—31no—
175#887—31no—
176#887—31no—
177#887—61no—
178#887—61no—
179#887C2×D311yescharacteristic
180#885—61no—
181#883—61no—
182#875—31no—
183#875—61no—
184#874—31no—
185C4×D12—61no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic
194C3×#106C2×D311yescharacteristic
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#102—31no—
201#835—31no—
202#832—31no—
203#821—31no—
204#821—31no—
205#821C2×D311yescharacteristic
206#816C2×D311yescharacteristic
207Dic3⋊C8—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8C2×D311yescharacteristic
210Dic3⋊C8C2×D311yescharacteristic
211C8×Dic3—31no—
212C8×Dic3—31no—
213C8×Dic3—31no—
214C8×Dic3—31no—
215C8×Dic3—61no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#810C2×D311yescharacteristic
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809C2×D311yescharacteristic
228#808C2×D311yescharacteristic
229#807C2×D311yescharacteristic
230C4×C3⋊C8—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242C4×C3⋊D3—81no—
243#634—21no—
244#634#4112yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×C4×D3—81no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—42no—
258#627—22no—
259#626—42no—
260#626—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—31no—
271#478—91no—
272#475—31no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C2×#67—61no—
285C2×#67—61no—
286C2×D12—31no—
287C2×D12—31no—
288C2×D12—61no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12C22×D311yescharacteristic
292C2×C4×D3—21no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—121no—
296C2×Dic6—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6C22×D311yescharacteristic
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C22⋊C4—61no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42—61no—
324#217—61no—
325#217—61no—
326#216—62no—
327#214—62no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—121no—
338C4⋊Dic3—21no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—121no—
361C4×Dic3—21no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—121no—
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—61no—
377C2×C3⋊C8C22×D311yescharacteristic
378C2×C3⋊C8C22×D311yescharacteristic
379Dic12—62no—
380#204—62no—
381#204—62no—
382#204—64no—
383#204—62no—
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—21no—
396C3⋊Dic3—22no—
397C3⋊Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13512yes—
405C2×Q16—91no—
406C2×SD16—91no—
407C2×SD16—91no—
408C4⋊Q8—31no—
409C4⋊Q8—181no—
410#127—91no—
411#125—31no—
412#125—91no—
413#125—181no—
414#125—181no—
415#124—91no—
416#124—91no—
417#124—181no—
418#123—181no—
419#123—181no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—181no—
426C4×D4—31no—
427C4×D4—91no—
428C4×D4—181no—
429#107—31no—
430#106—31no—
431#106D3211yescharacteristic
432C4⋊C8—31no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435#103—31no—
436#103—31no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444#102—91no—
445C4×C8—91no—
446C4×C8—91no—
447C4×C8—91no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—121no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—122no—
456C3×D4—61no—
457C3×D4—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—241no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475#67—122no—
476#67—241no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493D12—21no—
494D12—21no—
495D12—62no—
496D12—61no—
497D12—61no—
498D12—61no—
499D12—61no—
500D12—121no—
501D12—122no—
502D12—241no—
503C4×D3—81no—
504C4×D3—241no—
505C4×D3—241no—
506C4×D3—242no—
507Dic6—21no—
508Dic6—21no—
509Dic6—32no—
510Dic6—32no—
511Dic6—42no—
512Dic6—62no—
513Dic6—62no—
514Dic6—61no—
515Dic6—61no—
516Dic6—62no—
517Dic6—121no—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32#54811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57711yescharacteristic
531C3⋊D3—81no—
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—61no—
535C2×Q8—91no—
536C2×Q8—91no—
537C2×D4—31no—
538C2×D4—91no—
539C2×D4—181no—
540C2×D4—181no—
541C22×C4—61no—
542C22×C4—181no—
543Q16—182no—
544SD16—182no—
545SD16—182no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4C2×D3211yescharacteristic
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—61no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—91no—
576C42—181no—
577C42—181no—
578C42—181no—
579C22×C3—21no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—122no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—241no—
596C2×D3—241no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—32no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—81no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4#100711yescharacteristic
613C3×C4#100711yescharacteristic
614C3×C4D3×#4111yescharacteristic
615C3×C4D3×#4111yescharacteristic
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—62no—
623Dic3—62no—
624Dic3—62no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—122no—
630Dic3—121no—
631Dic3#91612yes—
632C32#336511yescharacteristic, complemented, Sylow
633C23—61no—
634C23—181no—
635Q8—61no—
636Q8—61no—
637Q8—92no—
638Q8—122no—
639Q8—182no—
640Q8—181no—
641D4—61no—
642D4—61no—
643D4—181no—
644D4—181no—
645D4—362no—
646D4—721no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—181no—
659C2×C4—241no—
660C2×C4—721no—
661C2×C4C22×D3211yescharacteristic
662C8—21no—
663C8—61no—
664C8—61no—
665C8—181no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—241no—
670C2×C3#563311yescharacteristic
671C2×C3#563311yescharacteristic
672C2×C3C2×#91611yescharacteristic
673C2×C3D3×#13511yescharacteristic
674C2×C3#577511yescharacteristic
675C2×C3#577811yescharacteristic
676D3—81no—
677D3—242no—
678D3—241no—
679D3—241no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—361no—
684C22—361no—
685C22—361no—
686C22D32×D411yescharacteristic
687C4—32no—
688C4—41no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—181no—
697C4—181no—
698C4—182no—
699C4#6430611yescharacteristic
700C4#6431611yescharacteristic
701C3—21no—
702C3#8104111yescharacteristic, complemented
703C3#8115111yescharacteristic, complemented
704C2—241no—
705C2—721no—
706C2#1059452111yescharacteristic
707C2D3×#91611yescharacteristic
708C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#106D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594318C2semidirect
3. #10592551C2semidirect
4. C3×#4871C2semidirect
5. C3×#4854C2semidirect
7. #10590868C2semidirect
8. #10590813C2semidirect
9. #10590645C2semidirect
11. #10590538C2semidirect
12. #10590537C2semidirect
13. #10590481C2semidirect
14. #10590479C2semidirect
15. #10590435C2semidirect
74. #4871D3semidirect
75. #4854D3semidirect
632. C32#3365semidirect
702. C3#81041semidirect
703. C3#81151semidirect

Maximal subgroups

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

subgroupindex
#105945662
#105943182
#105925512
C3×#48712
C3×#48542
#105908792
#105908682
#105908132
#105906452
#105905482
#105905382
#105905372
#105904812
#105904792
#105904352
#811513
#810413