Finite Group Databasebeta

← #11895641

Subgroups — #11895641

Order 1152.

752 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#10593978C211yesmaximal, characteristic
2#10593852C211yesmaximal, characteristic, complemented
3#10592544C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590879C211yesmaximal, characteristic
7#10590878C211yesmaximal, characteristic
8#10590863C211yesmaximal, characteristic, complemented
9#10590861C211yesmaximal, characteristic, complemented
10#10590807C211yesmaximal, characteristic, complemented
11#10590802C211yesmaximal, characteristic, complemented
12#10590774C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81151—31nomaximal
17#79935—31nomaximal
18C2×#3746C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20#64084C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#870C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2211yescharacteristic
26#63911C2211yescharacteristic
27#63907—21no—
28#63904—21no—
29#63894C2211yescharacteristic
30#63870—21no—
31#63869C2211yescharacteristic
32#63860C2211yescharacteristic
33#63854—21no—
34#63850—21no—
35#63847—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63839—21no—
40#63838—21no—
41C2×#3716C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43#63648C2211yescharacteristic
44#63643C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5685—31no—
62#5585—31no—
63#5567—31no—
64#5559—31no—
65C3×#478—31no—
66C3×C8×Q8—31no—
67#5068—31no—
68C4×#214—31no—
69#4891—31no—
70#4873—31no—
71#4854—31no—
72#4852—31no—
73#4851—31no—
74#4848—31no—
75#4847—31no—
76#4847D311yescharacteristic, complemented
77#4845—31no—
78#4845—31no—
79#4845—31no—
80#4845—61no—
81#4830D311yescharacteristic, complemented
82#4768—31no—
83#4767—31no—
84#4762—31no—
85#4760—31no—
86C4×Dic12—31no—
87#4697—31no—
88#4697—31no—
89#4694—31no—
90C4×#204—31no—
91C4×#204—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×#627—21no—
99C2×#626—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106#3752—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110#3746—22no—
111#3744—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4D411yescharacteristic
120C3×Dic3⋊C4D411yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3365—91noSylow
139C3×#125—31no—
140C3×C4×Q8—31no—
141C3×C4×D4—31no—
142#947—61no—
143#944—61no—
144#940—31no—
145#936—31no—
146C2×#214—31no—
147#929—61no—
148C4×#67—61no—
149C2×Dic12—31no—
150C2×Dic12—31no—
151C2×Dic12—61no—
152C2×#204—31no—
153C2×#204—31no—
154C2×#204—31no—
155C2×#204—61no—
156#894—61no—
157#894—61no—
158#893—31no—
159#893—61no—
160#890—31no—
161#889—61no—
162#889—61no—
163#889—61no—
164#889—61no—
165#888—31no—
166#888—61no—
167#887—31no—
168#887—31no—
169#887—31no—
170#887—61no—
171#887—61no—
172#885—61no—
173#883—61no—
174#875—31no—
175#875—31no—
176#875—31no—
177#875—61no—
178#874—31no—
179C4×D12—31no—
180C4×D12C2×D311yescharacteristic
181#870—31no—
182#870C2×D311yescharacteristic
183#869—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6C2×D311yescharacteristic
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—21no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8C2×D311yescharacteristic
197C3×C4⋊C8C2×D311yescharacteristic
198C3×#102—31no—
199C3×#102—31no—
200C3×C4×C8—31no—
201C3×C4×C8—31no—
202C3×C4×C8—31no—
203#832—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#821C2×D311yescharacteristic
211#821C2×D311yescharacteristic
212#818C2×D311yescharacteristic
213#817—31no—
214#817C2×D311yescharacteristic
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221Dic3⋊C8C2×D311yescharacteristic
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3C2×D311yescharacteristic
224C8×Dic3C2×D311yescharacteristic
225#810—31no—
226#810—31no—
227#810—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231C4×C3⋊C8C2×D311yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242#634—21no—
243#634—21no—
244#634—21no—
245#634#4112yes—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255C3×C4×D3—81no—
256C3×Dic6—22no—
257#627—42no—
258#626—42no—
259#626—81no—
260#624—81no—
261C32×C8—21no—
262C32×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—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—31no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×D4—31no—
282C22×C3×C4—61no—
283C2×#67—61no—
284C2×#67—61no—
285C2×D12—31no—
286C2×D12—31no—
287C2×D12—61no—
288C2×D12—61no—
289C2×D12—61no—
290C2×D12C22×D311yescharacteristic
291C2×C4×D3—21no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6D1211yescharacteristic
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42C22×D311yescharacteristic
324C3×C42C22×D311yescharacteristic
325#217—61no—
326#217—61no—
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—
338(C2×D3)⋊C4—121no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3D1211yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
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—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363Dic3⋊C4D1211yescharacteristic
364Dic3⋊C4D1211yescharacteristic
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×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378Dic12—62no—
379Dic12—62no—
380Dic12—122no—
381#204—62no—
382#204—62no—
383#204—62no—
384#204—122no—
385C22×C32C22×D411yescharacteristic
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3⋊D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4C2×#4111yescharacteristic
395C32×C42−1+411yescharacteristic
396C3⋊Dic3—22no—
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#13512yes—
406C2×Q16—91no—
407C2×SD16—91no—
408C2×SD16—91no—
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411#127—91no—
412#125—31no—
413#125—91no—
414#125—181no—
415#125—181no—
416#124—91no—
417#124—91no—
418#124—181no—
419#123—181no—
420#123—181no—
421C4×Q8—31no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—31no—
428C4×D4—91no—
429C4×D4—181no—
430#107—31no—
431#106—31no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8D3211yescharacteristic
436#103—91no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—31no—
441#102—31no—
442#102—91no—
443#102—91no—
444#102—91no—
445#102—91no—
446C4×C8—31no—
447C4×C8—31no—
448C4×C8—31no—
449C23×C3—61no—
450C22×D3—21no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C3×Q8—62no—
455C3×D4—61no—
456C3×D4—61no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—241no—
468C2×C3×C4C2×D1211yescharacteristic
469C2×C3×C4C2×D1211yescharacteristic
470C2×C3×C4D3×D411yescharacteristic
471C2×C3×C4D3×D411yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474#67—122no—
475#67—241no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3C2×D1211yescharacteristic
489C2×Dic3C2×D1211yescharacteristic
490C2×Dic3C2×D1211yescharacteristic
491C2×Dic3C2×D1211yescharacteristic
492D12—21no—
493D12—21no—
494D12—61no—
495D12—61no—
496D12—61no—
497D12—61no—
498D12—121no—
499D12—121no—
500D12—122no—
501D12—241no—
502C4×D3—81no—
503C4×D3—241no—
504C4×D3—241no—
505Dic6—22no—
506Dic6—32no—
507Dic6—32no—
508Dic6—62no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—121no—
517Dic6—121no—
518Dic6—122no—
519Dic6—122no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—41no—
525C3×C8—41no—
526C3×C8—61no—
527C3×C8—61no—
528C3⋊C8—21no—
529C3⋊C8—21no—
530C2×C32#54811yescharacteristic
531C2×C32C2×#13511yescharacteristic
532C2×C32#57711yescharacteristic
533C3⋊D3—81no—
534C3×D3—81no—
535C2×Q8—31no—
536C2×Q8—91no—
537C2×Q8—91no—
538C2×Q8—181no—
539C2×D4—31no—
540C2×D4—91no—
541C2×D4—181no—
542C2×D4—181no—
543C22×C4—61no—
544C22×C4—181no—
545Q16—182no—
546SD16—182no—
547SD16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8C2×D3211yescharacteristic
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C22⋊C4—61no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—31no—
575C42—31no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42C2×D3211yescharacteristic
581C22×C3—21no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3C22×D1211yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—241no—
597C2×D3—241no—
598C2×D3—241no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—32no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4#100711yescharacteristic
615C3×C4#100711yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4D3×#4111yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—41no—
622Dic3—41no—
623Dic3—41no—
624Dic3—62no—
625Dic3—62no—
626Dic3—122no—
627Dic3—121no—
628Dic3—121no—
629Dic3—121no—
630Dic3—121no—
631Dic3—241no—
632Dic3—241no—
633Dic3#90412yes—
634C32#336511yescharacteristic, complemented, Sylow
635C23—61no—
636C23—181no—
637Q8—62no—
638Q8—92no—
639Q8—181no—
640Q8—181no—
641Q8—181no—
642Q8—362no—
643D4—61no—
644D4—61no—
645D4—181no—
646D4—181no—
647D4—362no—
648D4—721no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—241no—
660C2×C4—721no—
661C2×C4D3×D1211yescharacteristic
662C2×C4D3×D1211yescharacteristic
663C2×C4C22×D3211yescharacteristic
664C8—21no—
665C8—21no—
666C8—61no—
667C8—61no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—241no—
672C2×C3#557611yescharacteristic
673C2×C3#563311yescharacteristic
674C2×C3C2×#90411yescharacteristic
675C2×C3#575111yescharacteristic
676C2×C3D3×#13511yescharacteristic
677C2×C3#577511yescharacteristic
678D3—81no—
679D3—241no—
680D3—241no—
681D3—481no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22—361no—
686C22—361no—
687C22—361no—
688C22C2×D3×D1211yescharacteristic
689C4—21no—
690C4—21no—
691C4—32no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—182no—
699C4—361no—
700C4—361no—
701C4#6431211yescharacteristic
702C4#6431611yescharacteristic
703C3—21no—
704C3#7993511yescharacteristic, complemented
705C3#8115111yescharacteristic, complemented
706C2—241no—
707C2—721no—
708C2#1059432911yescharacteristic
709C2D3×#90411yescharacteristic
710C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenterC4⋊C8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593852C2semidirect
3. #10592544C2semidirect
4. C3×#4847C2semidirect
5. C3×#4830C2semidirect
8. #10590863C2semidirect
9. #10590861C2semidirect
10. #10590807C2semidirect
11. #10590802C2semidirect
12. #10590774C2semidirect
13. #10590758C2semidirect
14. C4×#3716C2semidirect
15. #10590293C2semidirect
76. #4847D3semidirect
81. #4830D3semidirect
634. C32#3365semidirect
704. C3#79935semidirect
705. C3#81151semidirect

Maximal subgroups

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

subgroupindex
#105939782
#105938522
#105925442
C3×#48472
C3×#48302
#105908792
#105908782
#105908632
#105908612
#105908072
#105908022
#105907742
#105907582
C4×#37162
#105902932
#811513
#799353