Finite Group Databasebeta

← #11868629

Subgroups — #11868629

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594477C211yesmaximal, characteristic, complemented
2#10594358C211yesmaximal, characteristic
3#10592574C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4880C211yesmaximal, characteristic, complemented
6#10590954C211yesmaximal, characteristic
7#10590814C211yesmaximal, characteristic, complemented
8#10590778C211yesmaximal, characteristic, complemented
9D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
10#10590608C211yesmaximal, characteristic
11#10590572C211yesmaximal, characteristic, complemented
12#10590545C211yesmaximal, characteristic, complemented
13#10590490C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590431C211yesmaximal, characteristic, complemented
16#81165—31nomaximal
17#79196—31nomaximal
18C2×#3795C2211yescharacteristic
19#64097C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#890C2211yescharacteristic
26#63919C2211yescharacteristic
27#63902—21no—
28#63899—21no—
29#63898C2211yescharacteristic
30#63896—21no—
31#63879—21no—
32#63877—21no—
33C4×D3×Dic3—21no—
34C4×D3×Dic3C2211yescharacteristic
35#63869C2211yescharacteristic
36#63844—21no—
37#63844C2211yescharacteristic
38#63841C2211yescharacteristic
39#63837—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#107C2211yescharacteristic
42#63643C2211yescharacteristic
43#63641C2211yescharacteristic
44#63637C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54#63573C2211yescharacteristic
55#63572C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5688—31no—
62C4×#237—31no—
63#5522—31no—
64#5517—31no—
65C3×#478—31no—
66C3×#427—31no—
67#5113—31no—
68C2×Dic3⋊C8—31no—
69#5063—31no—
70#5009—31no—
71#5002—31no—
72#4998—31no—
73#4891D311yescharacteristic, complemented
74#4890—31no—
75#4880D311yescharacteristic, complemented
76#4877—31no—
77#4875—31no—
78#4875—31no—
79#4875—61no—
80#4871—31no—
81#4870—31no—
82#4860—31no—
83#4857—31no—
84#4854—31no—
85#4854—31no—
86D3×C4⋊C8—31no—
87#4829—31no—
88#4772—31no—
89#4772—31no—
90#4761—31no—
91#4759—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×#627—21no—
98C2×#625—21no—
99C2×D3×Dic3—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103#3795—22no—
104#3795Q814yescomplemented
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—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—
130#3724—21no—
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138D3×C3⋊C8—22no—
139#3076—91noSylow
140C2×#237—31no—
141C2×#235—31no—
142C22×C3×C8—31no—
143C3×#125—31no—
144C3×C4×D4—31no—
145C3×#117—31no—
146C3×#117—31no—
147D4×Dic3—31no—
148C4×#67—61no—
149#926—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—61no—
152C22×C3⋊C8—31no—
153C2×D3×C8—31no—
154C2×D3×C8C2×D311yescharacteristic
155#896—61no—
156#896—61no—
157#893—31no—
158#893C2×D311yescharacteristic
159#892—31no—
160#892C2×D311yescharacteristic
161#892C2×D311yescharacteristic
162#890—31no—
163#890C2×D311yescharacteristic
164#888—31no—
165#888—31no—
166#888—31no—
167#888—31no—
168#888—61no—
169#887—31no—
170#887—31no—
171#887—31no—
172#887—61no—
173#887—61no—
174#887—61no—
175#67⋊C4—61no—
176#67⋊C4—61no—
177#67⋊C4—61no—
178#878—61no—
179#878—61no—
180#877—61no—
181#872—61no—
182C42×D3—31no—
183C42×D3—61no—
184#870—31no—
185C4×Dic6—31no—
186C4×Dic6—61no—
187C4×Dic6—61no—
188C3×#107—21no—
189C3×#107—31no—
190C3×#107C2×D311yescharacteristic
191C3×#107C2×D311yescharacteristic
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×#102—31no—
197C3×#102—31no—
198#832—31no—
199#832—31no—
200#821—31no—
201#821C2×D311yescharacteristic
202#818C2×D311yescharacteristic
203#817—31no—
204#816—31no—
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
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#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#809—31no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808C2×D311yescharacteristic
225#808C2×D311yescharacteristic
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—61no—
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⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—42no—
244#634C2×Q812yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12C2×Q812yes—
253C3×C4×D3—42no—
254C3×C4×D3C2×Q812yes—
255C3×C4×D3#4112yes—
256#627—42no—
257#625—24no—
258D3×Dic3—22no—
259D3×Dic3—24no—
260D3×Dic3—41no—
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—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×D4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—61no—
284C2×#67—61no—
285C2×#67—61no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290#237—34no—
291#237—62no—
292#235—34no—
293#235—62no—
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3C22×D311yescharacteristic
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×C3×C8—21no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—62no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—61no—
332#217—61no—
333#217—61no—
334(C2×D3)⋊C4—21no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339C4⋊Dic3—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347Dic3⋊C4—21no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
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—21no—
388C2×C3×D3—21no—
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3C22⋊Q812yes—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4C22×Q811yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—22no—
398C3⋊Dic3—21no—
399C3⋊Dic3—41no—
400C3⋊Dic3#13512yes—
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—91no—
417C4×Q8—91no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×D4—31no—
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—91no—
432#107—91no—
433#107D3211yescharacteristic
434#106—31no—
435#106—31no—
436#106—31no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—91no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#102—31no—
447#102—31no—
448#102—91no—
449#102—91no—
450C23×C3—31no—
451C23×C3—61no—
452C22×D3—21no—
453C22×D3D3×D411yescharacteristic
454C3×D4—32no—
455C3×D4—61no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—122no—
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474#67—64no—
475#67—64no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—62no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—64no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—122no—
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498D12—21no—
499D12D3×Q812yes—
500C4×D3—42no—
501C4×D3—62no—
502C4×D3—64no—
503C4×D3—122no—
504C4×D3—121no—
505C4×D3#23512yes—
506C4×D3D3×Q812yes—
507Dic6—32no—
508Dic6—32no—
509Dic6—62no—
510Dic6—61no—
511Dic6—61no—
512Dic6—121no—
513Dic6—122no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6—242no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32C2×C22⋊Q811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57511yescharacteristic
531C3×D3—22no—
532C3×D3—42no—
533#41—94no—
534#41—182no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×Q8—181no—
538C2×D4—31no—
539C2×D4—181no—
540C22×C4—31no—
541C22×C4—61no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—181no—
545C22×C4—181no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—62no—
549C2×C8—91no—
550C2×C8—182no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—91no—
558C4⋊C4—181no—
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—61no—
568C22⋊C4—61no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—61no—
573C42—61no—
574C42—91no—
575C42—91no—
576C42—91no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—32no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—62no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3C2×D3×D411yescharacteristic
588C22×C3C2×D3×D411yescharacteristic
589C2×D3—21no—
590C2×D3—21no—
591C2×D3—22no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3#89612yes—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—32no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×#23511yescharacteristic
610C3×C4C2×D3×Q811yescharacteristic
611C3×C4C2×D3×Q811yescharacteristic
612C3×C4D3×#4111yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—32no—
616Dic3—32no—
617Dic3—41no—
618Dic3—41no—
619Dic3—41no—
620Dic3—62no—
621Dic3—62no—
622Dic3—61no—
623Dic3—61no—
624Dic3—62no—
625Dic3—122no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630Dic3#89612yes—
631C32#307611yescharacteristic, complemented, Sylow
632C23—31no—
633C23—61no—
634Q8—92no—
635Q8—181no—
636Q8—362no—
637Q8—362no—
638D4—32no—
639D4—61no—
640D4—184no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—122no—
654C2×C4—184no—
655C2×C4—182no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—361no—
659C2×C4—362no—
660C2×C4C22×D3211yescharacteristic
661C8—21no—
662C8—61no—
663C8—61no—
664C8—181no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—62no—
669C2×C3—122no—
670C2×C3C2×#89611yescharacteristic
671C2×C3D3×C22⋊Q811yescharacteristic
672C2×C3D3×#13511yescharacteristic
673C2×C3D3×#13511yescharacteristic
674C2×C3#576811yescharacteristic
675C2×C3#577311yescharacteristic
676D3—22no—
677D3—42no—
678C22—32no—
679C22—61no—
680C22—61no—
681C22—62no—
682C22—121no—
683C22—121no—
684C22D32×D411yescharacteristic
685C4—32no—
686C4—41no—
687C4—41no—
688C4—61no—
689C4—61no—
690C4—92no—
691C4—121no—
692C4—121no—
693C4—121no—
694C4—182no—
695C4—181no—
696C4—361no—
697C4D3×#23511yescharacteristic
698C4D32×Q811yescharacteristic
699C3—21no—
700C3#7919611yescharacteristic, complemented
701C3#8116511yescharacteristic, complemented
702C2—62no—
703C2—122no—
704C2D3×#89611yescharacteristic
705C2#1059472911yescharacteristic
706C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
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. #10594477C2semidirect
3. #10592574C2semidirect
4. C3×#4891C2semidirect
5. C3×#4880C2semidirect
7. #10590814C2semidirect
8. #10590778C2semidirect
9. D3×Dic3⋊C8C2semidirect
11. #10590572C2semidirect
12. #10590545C2semidirect
13. #10590490C2semidirect
14. #10590472C2semidirect
15. #10590431C2semidirect
73. #4891D3semidirect
75. #4880D3semidirect
104. #3795Q8semidirect
631. C32#3076semidirect
700. C3#79196semidirect
701. C3#81165semidirect

Maximal subgroups

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

subgroupindex
#105944772
#105943582
#105925742
C3×#48912
C3×#48802
#105909542
#105908142
#105907782
D3×Dic3⋊C82
#105906082
#105905722
#105905452
#105904902
#105904722
#105904312
#811653
#791963