Finite Group Databasebeta

← #11868604

Subgroups — #11868604

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594477C211yesmaximal, characteristic, complemented
2#10594362C211yesmaximal, characteristic
3#10592569C211yesmaximal, characteristic, complemented
4C3×#4860C211yesmaximal, characteristic, complemented
5C3×#4857C211yesmaximal, characteristic, complemented
6#10590816C211yesmaximal, characteristic, complemented
7#10590769C211yesmaximal, characteristic, complemented
8#10590690C211yesmaximal, characteristic
9D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
10#10590610C211yesmaximal, characteristic
11#10590571C211yesmaximal, characteristic, complemented
12#10590544C211yesmaximal, characteristic, complemented
13#10590496C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81229—31nomaximal
17#79196—31nomaximal
18C2×#3799C2211yescharacteristic
19#64102C2211yescharacteristic
20#64097C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#892C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63919C2211yescharacteristic
27#63899—21no—
28#63896—21no—
29#63894C2211yescharacteristic
30C4×#624—21no—
31#63881—21no—
32#63880—21no—
33C4×D3×Dic3C2211yescharacteristic
34#63869C2211yescharacteristic
35#63844—21no—
36#63843C2211yescharacteristic
37#63841C2211yescharacteristic
38#63837—21no—
39#63836—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#106C2211yescharacteristic
42#63648C2211yescharacteristic
43#63641C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63572C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5688—31no—
62C4×#239—31no—
63#5522—31no—
64#5517—31no—
65C3×#479—31no—
66C3×#427—31no—
67#5113—31no—
68C2×Dic3⋊C8—31no—
69#5066—31no—
70#5022—31no—
71#5002—31no—
72#4998—31no—
73#4891—31no—
74#4890—31no—
75#4890—31no—
76#4880—31no—
77#4877—31no—
78#4875—31no—
79#4871—31no—
80#4870—31no—
81#4870—31no—
82#4870—61no—
83#4860D311yescharacteristic, complemented
84#4857D311yescharacteristic, complemented
85#4854—31no—
86#4847—31no—
87D3×C4⋊C8—31no—
88#4804—31no—
89#4804—31no—
90#4793—31no—
91#4791—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#626—21no—
99C2×#624—21no—
100C2×#624—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103#3799—22no—
104#3799Q814yescomplemented
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×D3×C8—22no—
128#3724—21no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138D3×C3⋊C8—22no—
139#3076—91noSylow
140C2×#239—31no—
141C2×#235—31no—
142C22×C3×C8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×#117—31no—
146C3×#117—31no—
147Q8×Dic3—31no—
148#926—31no—
149C2×C4×Dic3—31no—
150C22×C3⋊C8—31no—
151C2×D3×C8—31no—
152C2×D3×C8C2×D311yescharacteristic
153#896—61no—
154#896—61no—
155#893—31no—
156#893—31no—
157#893—31no—
158#893—61no—
159#893—61no—
160#892—31no—
161#892—61no—
162#892C2×D311yescharacteristic
163#892C2×D311yescharacteristic
164#890—31no—
165#890C2×D311yescharacteristic
166#888—31no—
167#888—31no—
168#888—31no—
169#888—31no—
170#888—61no—
171#887—31no—
172#887—61no—
173#887—61no—
174#887C2×D311yescharacteristic
175#67⋊C4—61no—
176#67⋊C4—61no—
177#878—61no—
178#878—61no—
179C4×D12—31no—
180C4×D12—61no—
181#872—61no—
182C42×D3—31no—
183C42×D3—61no—
184C42×D3—61no—
185#870—31no—
186C4×Dic6—61no—
187C4×Dic6—61no—
188C3×#107—31no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic
194C3×#106C2×D311yescharacteristic
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198#835—31no—
199#835—31no—
200#821—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—61no—
205#818—31no—
206#817C2×D311yescharacteristic
207#816—31no—
208#816C2×D311yescharacteristic
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—61no—
215Dic3⋊C8C2×D311yescharacteristic
216#810—31no—
217#810C2×D311yescharacteristic
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—61no—
228#807—31no—
229#807C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231#807C2×D311yescharacteristic
232C4⋊(C3⋊C8)—31no—
233C22×C3⋊D3—21no—
234C22×C3×D3C2×D411yescharacteristic
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)C2×Q812yes—
243C4×C3⋊D3—42no—
244#634—42no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6C2×Q812yes—
256#627—42no—
257#626—24no—
258#624—24no—
259#624—42no—
260D3×Dic3—22no—
261D3×Dic3—41no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#533—91no—
267C4×#41—91no—
268#479—31no—
269#479—91no—
270#478—91no—
271#478—91no—
272#477—91no—
273#476—91no—
274#475—91no—
275#474—91no—
276#427—31no—
277#427—91no—
278C2×C4⋊C8—91no—
279#416—91no—
280#416—91no—
281C2×C3×Q8—31no—
282C22×C3×C4—31no—
283C2×#67—61no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286#239—34no—
287#239—62no—
288#235—34no—
289#235—62no—
290C2×D12—31no—
291C2×D12—31no—
292C2×D12—61no—
293C2×D12—61no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—121no—
303C2×C4×D3C22×D311yescharacteristic
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6C22×D311yescharacteristic
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—62no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C22⋊C4—61no—
329C3×C22⋊C4—61no—
330C3×C42—31no—
331C3×C42—61no—
332C3×C42—61no—
333C3×C42—61no—
334#217—61no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—121no—
343C4⋊Dic3—21no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3C22×D311yescharacteristic
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—62no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384D3×C8—22no—
385D3×C8—62no—
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—22no—
388C2×C3⋊D3—41no—
389C2×C3⋊D3—41no—
390C2×C3×D3—21no—
391C2×C3×D3—21no—
392C2×C3×D3C22⋊Q812yes—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4C22×Q811yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—21no—
398C3⋊Dic3—41no—
399C3⋊Dic3#13512yes—
400C3×Dic3—22no—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3C22⋊Q812yes—
407C2×#41—91no—
408C22×C8—31no—
409C22×C8—91no—
410C4⋊Q8—91no—
411C4⋊Q8—91no—
412#125—31no—
413#125—91no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—91no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—181no—
423C4×D4—181no—
424#117—31no—
425#117—31no—
426#117—91no—
427#117—181no—
428C2×C42—91no—
429C2×C42—181no—
430#107—31no—
431#107—31no—
432#107—31no—
433#107—91no—
434#106—31no—
435#106—91no—
436#106—91no—
437#106D3211yescharacteristic
438C4⋊C8—31no—
439C4⋊C8—91no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#102—91no—
447#102—91no—
448#102—91no—
449#102—91no—
450C23×C3—31no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C22×D3D3×D411yescharacteristic
455C3×Q8—32no—
456C3×Q8—61no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
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—61no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475#67—64no—
476C2×Dic3—21no—
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—62no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494D12—32no—
495D12—32no—
496D12—62no—
497D12—64no—
498D12—61no—
499D12—61no—
500D12—121no—
501C4×D3—64no—
502C4×D3—62no—
503C4×D3—64no—
504C4×D3—122no—
505C4×D3—122no—
506C4×D3—122no—
507C4×D3—122no—
508C4×D3—121no—
509C4×D3—242no—
510C4×D3#23512yes—
511C4×D3D3×Q812yes—
512Dic6—21no—
513Dic6—122no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6—242no—
518Dic6D3×Q812yes—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—61no—
523C3×C8—61no—
524C3⋊C8—21no—
525C3⋊C8—21no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C3⋊C8—121no—
529C2×C32C2×C22⋊Q811yescharacteristic
530C2×C32C2×#13511yescharacteristic
531C2×C32#57511yescharacteristic
532C3⋊D3—42no—
533C3×D3—22no—
534#41—94no—
535#41—182no—
536C2×Q8—31no—
537C2×Q8—181no—
538C2×Q8—181no—
539C2×D4—91no—
540C2×D4—181no—
541C22×C4—31no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—181no—
545C22×C4—181no—
546C22×C4—181no—
547C2×C8—31no—
548C2×C8—31no—
549C2×C8—62no—
550C2×C8—91no—
551C2×C8—182no—
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—91no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42—91no—
577C42—91no—
578C42—91no—
579C42—181no—
580C42—181no—
581C22×C3—21no—
582C22×C3—32no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—122no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—241no—
597C2×D3—241no—
598C2×D3#89612yes—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—62no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4C2×#23511yescharacteristic
615C3×C4C2×D3×Q811yescharacteristic
616C3×C4C2×D3×Q811yescharacteristic
617C3×C4D3×#4111yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—22no—
621Dic3—32no—
622Dic3—32no—
623Dic3—41no—
624Dic3—41no—
625Dic3—41no—
626Dic3—62no—
627Dic3—61no—
628Dic3—61no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—241no—
633Dic3#89612yes—
634C32#307611yescharacteristic, complemented, Sylow
635C23—31no—
636C23—181no—
637Q8—32no—
638Q8—61no—
639Q8—362no—
640Q8—362no—
641D4—92no—
642D4—184no—
643D4—181no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—31no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—184no—
658C2×C4—182no—
659C2×C4—181no—
660C2×C4—362no—
661C2×C4—362no—
662C2×C4—361no—
663C2×C4C22×D3211yescharacteristic
664C8—21no—
665C8—61no—
666C8—61no—
667C8—181no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—62no—
672C2×C3C2×#89611yescharacteristic
673C2×C3D3×C22⋊Q811yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3D3×#13511yescharacteristic
676C2×C3#576811yescharacteristic
677C2×C3#577711yescharacteristic
678D3—22no—
679D3—122no—
680D3—122no—
681D3—242no—
682C22—32no—
683C22—61no—
684C22—61no—
685C22—182no—
686C22—361no—
687C22—361no—
688C22D32×D411yescharacteristic
689C4—32no—
690C4—41no—
691C4—41no—
692C4—62no—
693C4—61no—
694C4—61no—
695C4—92no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—181no—
700C4—361no—
701C4D3×#23511yescharacteristic
702C4D32×Q811yescharacteristic
703C3—21no—
704C3#7919611yescharacteristic, complemented
705C3#8122911yescharacteristic, complemented
706C2—62no—
707C2—362no—
708C2D3×#89611yescharacteristic
709C2#1059474611yescharacteristic
710C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
hypercenter#106D32
hypocenterC32#3076
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
1. #10594477C2semidirect
3. #10592569C2semidirect
4. C3×#4860C2semidirect
5. C3×#4857C2semidirect
6. #10590816C2semidirect
7. #10590769C2semidirect
9. D3×Dic3⋊C8C2semidirect
11. #10590571C2semidirect
12. #10590544C2semidirect
13. #10590496C2semidirect
14. #10590468C2semidirect
15. #10590430C2semidirect
83. #4860D3semidirect
84. #4857D3semidirect
104. #3799Q8semidirect
634. C32#3076semidirect
704. C3#79196semidirect
705. C3#81229semidirect

Maximal subgroups

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

subgroupindex
#105944772
#105943622
#105925692
C3×#48602
C3×#48572
#105908162
#105907692
#105906902
D3×Dic3⋊C82
#105906102
#105905712
#105905442
#105904962
#105904682
#105904302
#812293
#791963