Finite Group Databasebeta

← #11896051

Subgroups — #11896051

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593932C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592415C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic
5C3×#4701C211yesmaximal, characteristic, complemented
6#10590895C211yesmaximal, characteristic
7#10590890C211yesmaximal, characteristic, complemented
8#10590861C211yesmaximal, characteristic
9#10590808C211yesmaximal, characteristic, complemented
10#10590803C211yesmaximal, characteristic, complemented
11#10590794C211yesmaximal, characteristic, complemented
12#10590757C211yesmaximal, characteristic
13#10590744C211yesmaximal, characteristic
14#10590378C211yesmaximal, characteristic
15#10590307C211yesmaximal, characteristic, complemented
16#81671—31nomaximal
17#79981—31nomaximal
18C2×#3746C2211yescharacteristic
19C4×#634C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×#875C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63919—21no—
25#63918C2211yescharacteristic
26#63918C2211yescharacteristic
27Dic3×D12C2211yescharacteristic
28#63887—21no—
29#63878—21no—
30#63866C2211yescharacteristic
31#63862—21no—
32#63860C2211yescharacteristic
33#63858—21no—
34#63844C2211yescharacteristic
35#63844C2211yescharacteristic
36#63843—21no—
37Dic3×Dic6C2211yescharacteristic
38#63839—21no—
39#63839—21no—
40C2×#3719C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C32×#97C2211yescharacteristic
43#63644C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61#5722—31no—
62#5671—31no—
63#5584—31no—
64Q8×Dic6—31no—
65C3×#489—31no—
66C3×#446—31no—
67#5094—31no—
68#5054—31no—
69#4851—31no—
70#4851—31no—
71#4849—31no—
72#4845—31no—
73#4845—31no—
74#4842—31no—
75#4795—31no—
76#4792—31no—
77#4791—31no—
78#4789—31no—
79#4767—31no—
80#4765—31no—
81#4761—31no—
82#4758—31no—
83#4716—31no—
84#4716—31no—
85#4716—31no—
86#4716—61no—
87#4714—31no—
88#4714D311yescharacteristic
89#4701D311yescharacteristic, complemented
90C4×#204—31no—
91#4681—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3—21no—
110#3746—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4D411yescharacteristic
118C3×Dic3⋊C4D411yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3724—21no—
124#3724—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3716—22no—
138#3369—91noSylow
139C3×C4⋊Q8—31no—
140C3×#124—31no—
141C3×C4×Q8—31no—
142#946—61no—
143Q8×Dic3—31no—
144Q8×Dic3—61no—
145#944—31no—
146#944—61no—
147#944—61no—
148C2×#216—31no—
149#936—31no—
150D4×Dic3—31no—
151C2×#214—31no—
152C2×Dic12—31no—
153C2×Dic12—31no—
154C2×Dic12—31no—
155C2×Dic12—61no—
156C2×#204—31no—
157#898—61no—
158#898—61no—
159#892—61no—
160#888—31no—
161#888—31no—
162#888—61no—
163#888—61no—
164#888—61no—
165#888—61no—
166#887—31no—
167#887—31no—
168#887—61no—
169#879—61no—
170#879—61no—
171#878—61no—
172#877—61no—
173#875—31no—
174#875C2×D311yescharacteristic
175C4×D12—31no—
176#869—31no—
177#869—31no—
178#869—31no—
179#869C2×D311yescharacteristic
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C4×Dic6C2×D311yescharacteristic
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#97—21no—
198C3×#97—31no—
199C3×#97C2×D311yescharacteristic
200C3×#97C2×D311yescharacteristic
201C3×C4×C8—31no—
202#835—31no—
203#832—31no—
204#821—31no—
205#821C2×D311yescharacteristic
206#821C2×D311yescharacteristic
207#817—31no—
208#817—31no—
209#817—31no—
210#817—31no—
211#817—61no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—61no—
220#816—61no—
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#815C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226C8×Dic3C2×D311yescharacteristic
227#810—31no—
228#810—31no—
229#808—31no—
230#808—31no—
231C4⋊(C3⋊C8)C2×D311yescharacteristic
232C22×C3×D3—21no—
233C2×C32×C4C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240#634—21no—
241#634—21no—
242#634—21no—
243#634#4112yes—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257#627—81no—
258#627—81no—
259D3×Dic3—42no—
260C32×C8—21no—
261C32×C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—91no—
266#489—31no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—91no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—31no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—31no—
283C22×Dic3—61no—
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—61no—
286C2×Dic6—21no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6D1211yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—21no—
316C3×C42—31no—
317C3×C42—31no—
318C3×C42C22×D311yescharacteristic
319C3×C42C22×D311yescharacteristic
320#217—61no—
321#217—61no—
322#217—61no—
323#216—62no—
324#214—62no—
325(C2×D3)⋊C4—21no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330C4⋊Dic3—21no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3D1211yescharacteristic
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345Dic3⋊C4—61no—
346Dic3⋊C4—61no—
347Dic3⋊C4—61no—
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—121no—
359Dic3⋊C4—121no—
360Dic3⋊C4D1211yescharacteristic
361Dic3⋊C4D1211yescharacteristic
362C4×Dic3—61no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—121no—
373C4×Dic3—121no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378Dic12—62no—
379Dic12—62no—
380Dic12—64no—
381Dic12—62no—
382#204—62no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4C2×#4111yescharacteristic
390C32×C42−1+411yescharacteristic
391C3⋊Dic3—22no—
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3#13712yes—
402C2×Q16—91no—
403C2×Q16—91no—
404C2×SD16—91no—
405C4⋊Q8—31no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411C4⋊Q8—181no—
412#126—181no—
413#126—181no—
414#124—31no—
415#124—91no—
416C22⋊Q8—181no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—181no—
424C4×D4—91no—
425#117—181no—
426#106—91no—
427#106—91no—
428#106—91no—
429C4⋊C8—31no—
430C4⋊C8—31no—
431C4⋊C8—31no—
432#103—31no—
433#103—31no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—31no—
441#102—91no—
442#97—31no—
443#97D3211yescharacteristic
444C4×C8—31no—
445C23×C3—61no—
446C22×D3—21no—
447C3×Q8—62no—
448C3×Q8—61no—
449C3×Q8—61no—
450C3×Q8—241no—
451C3×D4—61no—
452C3×D4—61no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4C2×D1211yescharacteristic
464C2×C3×C4C2×D1211yescharacteristic
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4C23×D311yescharacteristic
468C2×C3×C4C23×D311yescharacteristic
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—122no—
485C2×Dic3C2×D1211yescharacteristic
486C2×Dic3C2×D1211yescharacteristic
487C2×Dic3C2×D1211yescharacteristic
488C2×Dic3C2×D1211yescharacteristic
489D12—21no—
490D12—21no—
491C4×D3—122no—
492Dic6—22no—
493Dic6—21no—
494Dic6—21no—
495Dic6—32no—
496Dic6—32no—
497Dic6—62no—
498Dic6—61no—
499Dic6—61no—
500Dic6—62no—
501Dic6—61no—
502Dic6—61no—
503Dic6—61no—
504Dic6—61no—
505Dic6—81no—
506Dic6—121no—
507Dic6—121no—
508Dic6—241no—
509Dic6—241no—
510Dic6—241no—
511Dic6—241no—
512C3×C8—22no—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C2×C32#54811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57711yescharacteristic
525C3×D3—81no—
526C2×Q8—31no—
527C2×Q8—31no—
528C2×Q8—61no—
529C2×Q8—91no—
530C2×Q8—91no—
531C2×Q8—181no—
532C2×Q8—181no—
533C2×D4—31no—
534C22×C4—181no—
535Q16—182no—
536Q16—182no—
537SD16—182no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8C2×D3211yescharacteristic
541C2×C8C2×D3211yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—61no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C42—31no—
565C42—31no—
566C42—181no—
567C42—181no—
568C42—181no—
569C42—181no—
570C42—181no—
571C42C2×D3211yescharacteristic
572C22×C3—21no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3C22×D1211yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—32no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4#100711yescharacteristic
597C3×C4D3×#4111yescharacteristic
598C3×C4D3×#4111yescharacteristic
599C3×C4#101011yescharacteristic
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—62no—
607Dic3—62no—
608Dic3—122no—
609Dic3—122no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—241no—
617Dic3—241no—
618Dic3#90912yes—
619C32#336911yescharacteristic, complemented, Sylow
620C23—61no—
621Q8—62no—
622Q8—61no—
623Q8—61no—
624Q8—92no—
625Q8—181no—
626Q8—181no—
627Q8—181no—
628Q8—241no—
629Q8—721no—
630Q8—721no—
631D4—61no—
632D4—61no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—362no—
645C2×C4D3×D1211yescharacteristic
646C2×C4D3×D1211yescharacteristic
647C2×C4C22×D3211yescharacteristic
648C8—21no—
649C8—21no—
650C8—61no—
651C8—61no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—241no—
656C2×C3#557611yescharacteristic
657C2×C3#567711yescharacteristic
658C2×C3C2×#90911yescharacteristic
659C2×C3#575111yescharacteristic
660C2×C3#577511yescharacteristic
661C2×C3D3×#13711yescharacteristic
662D3—81no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22C2×D3×D1211yescharacteristic
667C4—21no—
668C4—21no—
669C4—32no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—121no—
674C4—121no—
675C4—121no—
676C4—182no—
677C4—361no—
678C4—361no—
679C4—361no—
680C4#6429711yescharacteristic
681C4#6430611yescharacteristic
682C3—21no—
683C3#7998111yescharacteristic, complemented
684C3#8167111yescharacteristic, complemented
685C2—241no—
686C2#1059390111yescharacteristic
687C2D3×#90911yescharacteristic
688C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#97D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592415C2semidirect
5. C3×#4701C2semidirect
7. #10590890C2semidirect
9. #10590808C2semidirect
10. #10590803C2semidirect
11. #10590794C2semidirect
15. #10590307C2semidirect
89. #4701D3semidirect
619. C32#3369semidirect
683. C3#79981semidirect
684. C3#81671semidirect

Maximal subgroups

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

subgroupindex
#105939322
#105938562
#105924152
C3×#47142
C3×#47012
#105908952
#105908902
#105908612
#105908082
#105908032
#105907942
#105907572
#105907442
#105903782
#105903072
#816713
#799813