Finite Group Databasebeta

← #11895229

Subgroups — #11895229

Order 1152.

762 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593938C211yesmaximal, characteristic, complemented
2#10593850C211yesmaximal, characteristic, complemented
3#10592543C211yesmaximal, characteristic
4C3×#4830C211yesmaximal, characteristic, complemented
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590890C211yesmaximal, characteristic, complemented
7#10590872C211yesmaximal, characteristic, complemented
8#10590814C211yesmaximal, characteristic, complemented
9#10590770C211yesmaximal, characteristic
10#10590763C211yesmaximal, characteristic
11#10590760C211yesmaximal, characteristic, complemented
12#10590759C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81215—31nomaximal
17#79926—31nomaximal
18C2×#3745C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20#64084C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#870C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2211yescharacteristic
26#63895—21no—
27#63894C2211yescharacteristic
28#63894C2211yescharacteristic
29#63894C2211yescharacteristic
30#63888—21no—
31#63888—21no—
32#63883—21no—
33#63869C2211yescharacteristic
34#63868—21no—
35#63866C2211yescharacteristic
36#63865—21no—
37#63864C2211yescharacteristic
38#63848—21no—
39#63844C2211yescharacteristic
40#63836—21no—
41C2×#3717C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43#63648C2211yescharacteristic
44#63643C2211yescharacteristic
45C3×#818C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5690—31no—
62#5584—31no—
63#5579—31no—
64#5568—31no—
65C3×#479—31no—
66C3×C8×Q8—31no—
67#5068—31no—
68C4×#215—31no—
69#4877—31no—
70#4872—31no—
71#4870—31no—
72#4852—31no—
73#4844—31no—
74#4844—31no—
75#4844—31no—
76#4844—61no—
77#4842—31no—
78#4841—31no—
79#4830D311yescharacteristic, complemented
80#4829—31no—
81#4829D311yescharacteristic, complemented
82#4819—31no—
83#4818—31no—
84#4800—31no—
85#4792—31no—
86#4697—31no—
87#4697—31no—
88C4×D24—31no—
89C4×#204—31no—
90C4×#204—31no—
91#4681—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#624—21no—
100C2×#624—21no—
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106#3752—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3745—22no—
110#3744—22no—
111C3×C4⋊Dic3D411yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4D411yescharacteristic
119C3×Dic3⋊C4D411yescharacteristic
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136Dic32—21no—
137#3717—22no—
138#3360—91noSylow
139C3×#125—31no—
140C3×C4×Q8—31no—
141C3×C4×Q8—31no—
142#947—31no—
143#946—61no—
144#946—61no—
145#944—31no—
146C2×#215—31no—
147C2×D24—31no—
148C2×D24—31no—
149C2×D24—61no—
150C2×#204—31no—
151C2×#204—31no—
152C2×#204—31no—
153C2×#204—61no—
154#898—61no—
155#898—61no—
156#898—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#896—61no—
161#896—61no—
162#896—61no—
163#893—31no—
164#893—31no—
165#893—31no—
166#892—61no—
167D3×C4⋊C4—61no—
168D3×C4⋊C4—61no—
169#890—31no—
170#888—31no—
171#887—31no—
172#876—61no—
173#875—31no—
174#875—31no—
175#875—31no—
176#875—61no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—31no—
181C4×D12—31no—
182C4×D12—61no—
183#872—61no—
184#870—31no—
185#870C2×D311yescharacteristic
186#869—31no—
187#869—31no—
188C4×Dic6—31no—
189C4×Dic6C2×D311yescharacteristic
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×#103—31no—
199C3×#103—31no—
200C3×C4×C8—31no—
201C3×C4×C8—31no—
202C3×C4×C8—31no—
203#835—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#818C2×D311yescharacteristic
211#817—31no—
212#817C2×D311yescharacteristic
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—61no—
219#816C2×D311yescharacteristic
220#816C2×D311yescharacteristic
221Dic3⋊C8C2×D311yescharacteristic
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3C2×D311yescharacteristic
224C8×Dic3C2×D311yescharacteristic
225#810—31no—
226#810—31no—
227#809—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—
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)#4112yes—
243C4×C3⋊D3—81no—
244#634—21no—
245#634—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257#627—81no—
258#624—42no—
259#624—42no—
260#624—81no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#556—91no—
266#554—91no—
267#488—91no—
268#488—91no—
269#487—91no—
270#479—31no—
271#479—91no—
272#476—91no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—31no—
277C4×SD16—91no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×D12—31no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—31no—
286C2×D12—61no—
287C2×D12—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—121no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6D1211yescharacteristic
303C2×Dic6C22×D311yescharacteristic
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C22×D311yescharacteristic
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C42—21no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—61no—
325C3×C42C22×D311yescharacteristic
326C3×C42C22×D311yescharacteristic
327#215—62no—
328(C2×D3)⋊C4—61no—
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—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—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—121no—
345(C2×D3)⋊C4—121no—
346(C2×D3)⋊C4—121no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3D1211yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4D1211yescharacteristic
370Dic3⋊C4D1211yescharacteristic
371C4×Dic3—21no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378D24—62no—
379D24—62no—
380D24—122no—
381#204—62no—
382#204—62no—
383#204—62no—
384#204—122no—
385C22×C32C22×D411yescharacteristic
386C2×C3⋊D3—22no—
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—41no—
397C3⋊Dic3—41no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#13512yes—
406C2×SD16—91no—
407C2×SD16—91no—
408C2×D8—91no—
409C4⋊Q8—91no—
410C4⋊Q8—91no—
411#126—181no—
412#126—181no—
413#125—31no—
414#125—91no—
415#124—91no—
416#124—91no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C22⋊Q8—181no—
420C22⋊Q8—181no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×D4—91no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—91no—
428#117—181no—
429C2×C4⋊C4—181no—
430#107—31no—
431#106—31no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8D3211yescharacteristic
436#103—31no—
437#103—31no—
438#103—91no—
439#103—91no—
440#103—91no—
441#103—91no—
442#102—91no—
443#102—91no—
444#102—91no—
445#102—91no—
446C4×C8—31no—
447C4×C8—31no—
448C4×C8—31no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C22×D3—121no—
455C3×Q8—62no—
456C3×Q8—61no—
457C3×Q8—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4C2×D1211yescharacteristic
470C2×C3×C4C2×D1211yescharacteristic
471C2×C3×C4D3×D411yescharacteristic
472C2×C3×C4D3×D411yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3C2×D1211yescharacteristic
486C2×Dic3C2×D1211yescharacteristic
487C2×Dic3C2×D1211yescharacteristic
488C2×Dic3C2×D1211yescharacteristic
489D12—32no—
490D12—32no—
491D12—62no—
492D12—61no—
493D12—61no—
494D12—61no—
495D12—61no—
496D12—61no—
497D12—61no—
498D12—121no—
499D12—121no—
500D12—121no—
501C4×D3—122no—
502C4×D3—122no—
503C4×D3—122no—
504C4×D3—122no—
505C4×D3—241no—
506C4×D3—241no—
507C4×D3—241no—
508C4×D3—241no—
509C4×D3—242no—
510Dic6—22no—
511Dic6—21no—
512Dic6—21no—
513Dic6—61no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—121no—
518Dic6—121no—
519Dic6—241no—
520Dic6—241no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—21no—
525C3×C8—41no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C2×C32#54811yescharacteristic
532C2×C32C2×#13511yescharacteristic
533C2×C32#57711yescharacteristic
534C3⋊D3—42no—
535C3⋊D3—81no—
536C2×Q8—31no—
537C2×Q8—31no—
538C2×Q8—91no—
539C2×Q8—181no—
540C2×D4—91no—
541C2×D4—91no—
542C22×C4—181no—
543C22×C4—181no—
544C22×C4—181no—
545C22×C4—181no—
546SD16—182no—
547SD16—182no—
548D8—182no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8C2×D3211yescharacteristic
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—91no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C22⋊C4—181no—
577C42—31no—
578C42—31no—
579C42—61no—
580C42—181no—
581C42C2×D3211yescharacteristic
582C22×C3—21no—
583C22×C3C22×D1211yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—122no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—241no—
599C2×D3—241no—
600C2×D3—241no—
601C2×D3—241no—
602C2×D3—241no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—32no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4#100711yescharacteristic
620C3×C4#100711yescharacteristic
621C3×C4D3×#4111yescharacteristic
622C3×C4D3×#4111yescharacteristic
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—121no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—241no—
635Dic3—241no—
636Dic3#90412yes—
637C32#336011yescharacteristic, complemented, Sylow
638C23—181no—
639C23—181no—
640Q8—62no—
641Q8—61no—
642Q8—61no—
643Q8—181no—
644Q8—181no—
645Q8—721no—
646D4—92no—
647D4—181no—
648D4—181no—
649D4—181no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—362no—
661C2×C4—362no—
662C2×C4—721no—
663C2×C4—721no—
664C2×C4D3×D1211yescharacteristic
665C2×C4D3×D1211yescharacteristic
666C2×C4C22×D3211yescharacteristic
667C8—21no—
668C8—21no—
669C8—61no—
670C8—61no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3#557611yescharacteristic
675C2×C3#563311yescharacteristic
676C2×C3C2×#90411yescharacteristic
677C2×C3#575111yescharacteristic
678C2×C3D3×#13511yescharacteristic
679C2×C3#577811yescharacteristic
680D3—122no—
681D3—122no—
682D3—242no—
683D3—241no—
684D3—241no—
685D3—481no—
686C22—182no—
687C22—361no—
688C22—361no—
689C22—361no—
690C22—361no—
691C22—361no—
692C22C2×D3×D1211yescharacteristic
693C4—21no—
694C4—21no—
695C4—32no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—121no—
700C4—121no—
701C4—121no—
702C4—121no—
703C4—361no—
704C4—361no—
705C4#6431211yescharacteristic
706C4#6431611yescharacteristic
707C3—21no—
708C3#7992611yescharacteristic, complemented
709C3#8121511yescharacteristic, complemented
710C2—362no—
711C2—721no—
712C2#1059432911yescharacteristic
713C2D3×#90411yescharacteristic
714C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4⋊C8D32
hypocenterC32#3360
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
1. #10593938C2semidirect
2. #10593850C2semidirect
4. C3×#4830C2semidirect
5. C3×#4829C2semidirect
6. #10590890C2semidirect
7. #10590872C2semidirect
8. #10590814C2semidirect
11. #10590760C2semidirect
12. #10590759C2semidirect
13. #10590758C2semidirect
14. C4×#3717C2semidirect
15. #10590293C2semidirect
79. #4830D3semidirect
81. #4829D3semidirect
637. C32#3360semidirect
708. C3#79926semidirect
709. C3#81215semidirect

Maximal subgroups

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

subgroupindex
#105939382
#105938502
#105925432
C3×#48302
C3×#48292
#105908902
#105908722
#105908142
#105907702
#105907632
#105907602
#105907592
#105907582
C4×#37172
#105902932
#812153
#799263