Finite Group Databasebeta

← #11868628

Subgroups — #11868628

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 711 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594448C211yesmaximal, characteristic, complemented
2#10594360C211yesmaximal, characteristic
3#10592579C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590956C211yesmaximal, characteristic
7#10590811C211yesmaximal, characteristic, complemented
8#10590762C211yesmaximal, characteristic, complemented
9#10590658C211yesmaximal, characteristic, complemented
10#10590611C211yesmaximal, characteristic
11#10590574C211yesmaximal, characteristic, complemented
12#10590556C211yesmaximal, characteristic, complemented
13#10590542C211yesmaximal, characteristic, complemented
14#10590491C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#81165—31nomaximal
17#81107—31nomaximal
18C2×#3796C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20#64101C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63918C2211yescharacteristic
27#63904—21no—
28#63895—21no—
29Dic3×D12C2211yescharacteristic
30#63888—21no—
31C4×#624C2211yescharacteristic
32#63880—21no—
33#63878—21no—
34C4×D3×Dic3—21no—
35#63869C2211yescharacteristic
36#63849C2211yescharacteristic
37#63843—21no—
38Dic3×Dic6C2211yescharacteristic
39#63838—21no—
40C2×#3710C2211yescharacteristic
41C32×#107C2211yescharacteristic
42#63645C2211yescharacteristic
43#63635C2211yescharacteristic
44#63635C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#816C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5728—31no—
62#5688—31no—
63C4×#239—31no—
64C4×#237—31no—
65C3×#478—31no—
66C3×#477—31no—
67#5084—31no—
68#5063—31no—
69#5020—31no—
70#5009—31no—
71#4891—31no—
72#4891D311yescharacteristic, complemented
73#4880—31no—
74#4880—31no—
75#4880—31no—
76#4880—61no—
77#4875D311yescharacteristic, complemented
78#4860—31no—
79#4854—31no—
80#4846—31no—
81D3×C4⋊C8—31no—
82D3×C4⋊C8—31no—
83#4829—31no—
84#4804—31no—
85#4804—31no—
86#4796—31no—
87#4796—31no—
88#4772—31no—
89#4772—31no—
90#4761—31no—
91#4759—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#626—21no—
99C2×#624D411yescharacteristic
100C2×#624D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103#3796—22no—
104#3796Q814yescomplemented
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C8×C3⋊D3—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3710—22no—
139#3076—91noSylow
140C2×#239—31no—
141C2×#237—31no—
142C3×C4⋊Q8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146#946—61no—
147Q8×Dic3—31no—
148Q8×Dic3—61no—
149D4×Dic3—31no—
150C4×#67—61no—
151C2×C4×Dic3—61no—
152C2×D3×C8—31no—
153C2×D3×C8—31no—
154C2×D3×C8—31no—
155C2×D3×C8—31no—
156C2×D3×C8—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#893—61no—
161#893C2×D311yescharacteristic
162#892—31no—
163#892—31no—
164#892—31no—
165#892—31no—
166#892—31no—
167#892—31no—
168#892—61no—
169#892—61no—
170#892—61no—
171#890—31no—
172#890C2×D311yescharacteristic
173#888—31no—
174#888C2×D311yescharacteristic
175#887—61no—
176#887—61no—
177#887—61no—
178#887C2×D311yescharacteristic
179#67⋊C4—61no—
180#877—61no—
181C4×D12—31no—
182C4×D12—61no—
183C42×D3—31no—
184C42×D3—31no—
185C42×D3—61no—
186#870—31no—
187#869—31no—
188C4×Dic6—31no—
189C3×#107—21no—
190C3×#107—31no—
191C3×#107C2×D311yescharacteristic
192C3×#107C2×D311yescharacteristic
193C3×#106—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#821—31no—
205#821C2×D311yescharacteristic
206#818—31no—
207#818—31no—
208#818—31no—
209#818—61no—
210#817—31no—
211#816—31no—
212#816C2×D311yescharacteristic
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8C2×D311yescharacteristic
216Dic3⋊C8C2×D311yescharacteristic
217#810—31no—
218#810C2×D311yescharacteristic
219#809—31no—
220#809C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#808—61no—
228#808C2×D311yescharacteristic
229#807—31no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C22×C3⋊D3C2×D411yescharacteristic
234C22×C3×D3—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4×C3⋊D3C2×Q812yes—
242C4×C3⋊D3#4112yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12C2×Q812yes—
252C3×C4×D3—42no—
253C3×Dic6—21no—
254C3×Dic6—42no—
255C3×Dic6C2×Q812yes—
256#627—42no—
257#626—24no—
258#624—22no—
259#624—41no—
260D3×Dic3—24no—
261D3×Dic3—42no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#533—91no—
267C4×#41—91no—
268#479—91no—
269#479—91no—
270#478—31no—
271#478—91no—
272#477—31no—
273#476—91no—
274#475—91no—
275#474—91no—
276#427—91no—
277#427—91no—
278C2×C4⋊C8—91no—
279#416—91no—
280#416—91no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C2×#67—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288#239—34no—
289#239—62no—
290#237—34no—
291#237—62no—
292C2×D12—61no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—31no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×Dic6—21no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6C22×D311yescharacteristic
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C42—31no—
327C3×C42—31no—
328C3×C42—61no—
329#217—61no—
330(C2×D3)⋊C4—21no—
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—61no—
338(C2×D3)⋊C4—121no—
339(C2×D3)⋊C4—121no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360C4×Dic3—21no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—121no—
374C4×Dic3—121no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382D3×C8—62no—
383D3×C8—62no—
384D3×C8—62no—
385D3×C8—62no—
386D3×C8—64no—
387C22×C32C22×D411yescharacteristic
388C2×C3⋊D3—21no—
389C2×C3⋊D3—21no—
390C2×C3⋊D3C22⋊Q812yes—
391C2×C3×D3—22no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C22×Q811yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3⋊Dic3C22⋊Q812yes—
401C3×Dic3—22no—
402C3×Dic3—21no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3#13512yes—
408C2×#41—91no—
409C22×C8—91no—
410C22×C8—91no—
411C4⋊Q8—31no—
412C4⋊Q8—91no—
413#125—31no—
414#125—91no—
415C22⋊Q8—181no—
416C22⋊Q8—181no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—181no—
420C4×Q8—181no—
421C4×D4—31no—
422C4×D4—91no—
423C4×D4—181no—
424C4×D4—181no—
425#117—91no—
426#117—91no—
427#117—91no—
428#117—181no—
429C2×C42—91no—
430C2×C42—181no—
431#107—31no—
432#107—91no—
433#107—91no—
434#107D3211yescharacteristic
435#106—31no—
436#106—91no—
437#106—91no—
438#106—91no—
439C4⋊C8—31no—
440C4⋊C8—31no—
441C4⋊C8—91no—
442C4⋊C8—91no—
443#103—31no—
444#103—31no—
445#103—91no—
446#103—91no—
447#102—31no—
448#102—31no—
449#102—91no—
450#102—91no—
451C23×C3—61no—
452C22×D3—21no—
453C22×D3—31no—
454C22×D3—31no—
455C22×D3—61no—
456C3×Q8—32no—
457C3×Q8—61no—
458C3×Q8—122no—
459C3×D4—32no—
460C3×D4—61no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—122no—
476C2×C3×C4C23×D311yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478#67—64no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—64no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—122no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497D12—21no—
498D12—64no—
499D12D3×Q812yes—
500C4×D3—32no—
501C4×D3—32no—
502C4×D3—32no—
503C4×D3—32no—
504C4×D3—42no—
505C4×D3—62no—
506C4×D3—62no—
507C4×D3—62no—
508C4×D3—64no—
509C4×D3—62no—
510C4×D3—121no—
511C4×D3—121no—
512C4×D3—122no—
513Dic6—21no—
514Dic6—42no—
515Dic6—122no—
516Dic6—122no—
517Dic6D3×Q812yes—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—62no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C2×C32C2×C22⋊Q811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57511yescharacteristic
531C3⋊D3—22no—
532C3×D3—42no—
533#41—94no—
534#41—182no—
535C2×Q8—31no—
536C2×Q8—61no—
537C2×Q8—181no—
538C2×D4—31no—
539C2×D4—181no—
540C22×C4—61no—
541C22×C4—91no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—181no—
545C22×C4—181no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8—182no—
550C2×C8—182no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
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—
571C42—31no—
572C42—31no—
573C42—61no—
574C42—91no—
575C42—91no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—62no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3C2×D3×D411yescharacteristic
585C22×C3C2×D3×D411yescharacteristic
586C2×D3—22no—
587C2×D3—32no—
588C2×D3—32no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—62no—
592C2×D3—61no—
593C2×D3—61no—
594C2×D3—61no—
595C2×D3—61no—
596C2×D3—121no—
597C2×D3—121no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—32no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—62no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4C2×D3×Q811yescharacteristic
614C3×C4C2×D3×Q811yescharacteristic
615C3×C4D3×#4111yescharacteristic
616C3×C4D3×#4111yescharacteristic
617Dic3—21no—
618Dic3—21no—
619Dic3—21no—
620Dic3—22no—
621Dic3—32no—
622Dic3—32no—
623Dic3—41no—
624Dic3—41no—
625Dic3—62no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—121no—
630Dic3—241no—
631Dic3—241no—
632Dic3#91912yes—
633C32#307611yescharacteristic, complemented, Sylow
634C23—61no—
635C23—91no—
636Q8—32no—
637Q8—61no—
638Q8—122no—
639Q8—362no—
640D4—32no—
641D4—61no—
642D4—184no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—91no—
653C2×C4—92no—
654C2×C4—92no—
655C2×C4—122no—
656C2×C4—182no—
657C2×C4—184no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—362no—
661C2×C4—361no—
662C2×C4C22×D3211yescharacteristic
663C8—21no—
664C8—61no—
665C8—61no—
666C8—181no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—122no—
671C2×C3D3×C22⋊Q811yescharacteristic
672C2×C3D3×C22⋊Q811yescharacteristic
673C2×C3C2×#91911yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3#577311yescharacteristic
676C2×C3#577311yescharacteristic
677D3—42no—
678D3—62no—
679D3—62no—
680D3—122no—
681C22—62no—
682C22—92no—
683C22—121no—
684C22—121no—
685C22—181no—
686C22—181no—
687C22D32×D411yescharacteristic
688C4—32no—
689C4—41no—
690C4—41no—
691C4—62no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—92no—
696C4—121no—
697C4—121no—
698C4—361no—
699C4—361no—
700C4#6430611yescharacteristic
701C4D32×Q811yescharacteristic
702C3—21no—
703C3#8110711yescharacteristic, complemented
704C3#8116511yescharacteristic, complemented
705C2—122no—
706C2—182no—
707C2#1059462411yescharacteristic
708C2#1059472811yescharacteristic
709C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
hypercenter#107D32
hypocenterC32#3076
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594448C2semidirect
3. #10592579C2semidirect
4. C3×#4891C2semidirect
5. C3×#4875C2semidirect
7. #10590811C2semidirect
8. #10590762C2semidirect
9. #10590658C2semidirect
11. #10590574C2semidirect
12. #10590556C2semidirect
13. #10590542C2semidirect
14. #10590491C2semidirect
15. #10590465C2semidirect
72. #4891D3semidirect
77. #4875D3semidirect
104. #3796Q8semidirect
633. C32#3076semidirect
703. C3#81107semidirect
704. C3#81165semidirect

Maximal subgroups

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

subgroupindex
#105944482
#105943602
#105925792
C3×#48912
C3×#48752
#105909562
#105908112
#105907622
#105906582
#105906112
#105905742
#105905562
#105905422
#105904912
#105904652
#811653
#811073