Finite Group Databasebeta

← #11895644

Subgroups — #11895644

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5559C211yesmaximal, characteristic
2#10593852C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic
6#10591478C211yesmaximal, characteristic, complemented
7#10591441C211yesmaximal, characteristic, complemented
8#10591439C211yesmaximal, characteristic
9#10590556C211yesmaximal, characteristic, complemented
10#10590542C211yesmaximal, characteristic, complemented
11#10590481C211yesmaximal, characteristic, complemented
12#10590479C211yesmaximal, characteristic, complemented
13#10590378C211yesmaximal, characteristic, complemented
14#10590278C211yesmaximal, characteristic, complemented
15#10590250C211yesmaximal, characteristic, complemented
16#83717—31nomaximal
17#81151—31nomaximal
18C32×C4×D4C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#936C2211yescharacteristic
23C3×#929—21no—
24C3×C4×#67—21no—
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#885—21no—
28C3×#883—21no—
29C3×#875C2211yescharacteristic
30C3×#870C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63918C2211yescharacteristic
33#63870—21no—
34#63869C2211yescharacteristic
35#63847—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63839—21no—
39#63838—21no—
40C2×#3719C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42#63659C2211yescharacteristic
43#63637C2211yescharacteristic
44#63635C2211yescharacteristic
45C4×C3⋊(C3⋊C8)C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62#5685—31no—
63#5567—31no—
64#5559D311yescharacteristic
65C3×#478—31no—
66#5075—31no—
67#5070—31no—
68#5068—31no—
69#5056—31no—
70#5056—31no—
71#5054—31no—
72#5054—31no—
73C4×#216—31no—
74Q8×C3⋊C8—31no—
75#5020—31no—
76C4×#214—31no—
77C4×#214—31no—
78C4×#214—31no—
79C4×#214—61no—
80#5009—31no—
81#5009D311yescharacteristic, complemented
82#4891—31no—
83#4873—31no—
84#4854—31no—
85#4852—31no—
86#4845—31no—
87#4830—31no—
88#4768—31no—
89#4767—31no—
90#4762—31no—
91#4760—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6D411yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104C32×C42C2311yescharacteristic
105#3754—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3716—22no—
138#3365—91noSylow
139C3×#127—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×#124—31no—
143C3×#124—61no—
144C3×#123—61no—
145C3×#123—61no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×D4—21no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153#944—61no—
154C2×#216—31no—
155#940C2×D311yescharacteristic
156#936C2×D311yescharacteristic
157C2×#214—31no—
158C2×#214—31no—
159C2×#214—31no—
160C2×#214—61no—
161#929—21no—
162C4×#67—21no—
163C2×Dic12—31no—
164C2×#204—31no—
165#893C2×D311yescharacteristic
166#890—31no—
167#889—61no—
168#889—61no—
169#889—61no—
170#889—61no—
171#888—31no—
172#888—61no—
173#887—31no—
174#887—31no—
175#887—61no—
176#887—61no—
177#887C2×D311yescharacteristic
178#885—21no—
179#883—21no—
180#875C2×D311yescharacteristic
181#870—31no—
182#870C2×D311yescharacteristic
183#869—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6C2×D311yescharacteristic
190C3×#107—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#102—31no—
194C3×#102—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#821—31no—
207#816—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—31no—
210C8×Dic3—31no—
211C8×Dic3—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—61no—
217#809—31no—
218#809—31no—
219#808—31no—
220#808—31no—
221#808—61no—
222#808C2×D311yescharacteristic
223#807C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)C2×D311yescharacteristic
227C4×C3⋊C8—31no—
228C4×C3⋊C8—31no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—61no—
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—81no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243#634—21no—
244#634#4112yes—
245C3×#67—42no—
246C3×#67—81no—
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×D12—21no—
255C3×D12—21no—
256C3×C4×D3—81no—
257C3×Dic6—22no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260#627—42no—
261C3⋊(C3⋊C8)—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
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—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—21no—
283C2×C3×D4—31no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
286C2×C3×D4C22×D311yescharacteristic
287C2×C3×D4C22×D311yescharacteristic
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—41no—
291C22×C3×C4—61no—
292C2×#67—21no—
293C2×#67—21no—
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—21no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6#6711yescharacteristic
302C2×Dic6C22×D311yescharacteristic
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C22⋊C4—21no—
317C3×C22⋊C4—21no—
318C3×C22⋊C4—41no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C22⋊C4—61no—
323C3×C22⋊C4—61no—
324C3×C42—21no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—61no—
328C3×C42C22×D311yescharacteristic
329C3×C42C22×D311yescharacteristic
330#217—21no—
331#217—21no—
332#216—62no—
333#214—62no—
334#214—62no—
335#214—62no—
336#214—64no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3#6711yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
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—121no—
362Dic3⋊C4#6711yescharacteristic
363Dic3⋊C4#6711yescharacteristic
364C4×Dic3—21no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—121no—
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382Dic12—62no—
383#204—62no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—41no—
394C32×C4C2×#4111yescharacteristic
395C32×C42−1+411yescharacteristic
396C3⋊Dic3—22no—
397C3⋊Dic3—41no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13512yes—
405C2×Q16—91no—
406C2×SD16—91no—
407C2×SD16—91no—
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410#127—31no—
411#125—31no—
412#125—91no—
413#125—181no—
414#125—181no—
415#124—31no—
416#124—31no—
417#124—61no—
418#123—61no—
419#123—61no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—181no—
426C4×D4—31no—
427C4×D4—61no—
428C4×D4D3211yescharacteristic
429#107—31no—
430#106—31no—
431#106—91no—
432C4⋊C8—31no—
433C4⋊C8—91no—
434C4⋊C8—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444#102—91no—
445C4×C8—91no—
446C4×C8—91no—
447C4×C8—91no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—41no—
451C23×C3—61no—
452C22×D3—21no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×D4—22no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—41no—
462C3×D4—61no—
463C3×D4—61no—
464C3×D4—122no—
465C3×D4—241no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—41no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—81no—
480C2×C3×C4—81no—
481C2×C3×C4—82no—
482C2×C3×C4—241no—
483C2×C3×C4D3×D411yescharacteristic
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4C2×#6711yescharacteristic
486C2×C3×C4C2×#6711yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489#67—42no—
490#67—81no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3C2×#6711yescharacteristic
501C2×Dic3C2×#6711yescharacteristic
502C2×Dic3C2×#6711yescharacteristic
503C2×Dic3C2×#6711yescharacteristic
504D12—21no—
505D12—21no—
506C4×D3—81no—
507Dic6—22no—
508Dic6—21no—
509Dic6—21no—
510Dic6—32no—
511Dic6—32no—
512Dic6—62no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—122no—
517Dic6—122no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—62no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32—81no—
529C2×C32#54811yescharacteristic
530C2×C32C2×#13511yescharacteristic
531C2×C32#57711yescharacteristic
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×D4—31no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4C2×D3211yescharacteristic
541C22×C4—21no—
542C22×C4—61no—
543Q16—182no—
544SD16—182no—
545SD16—182no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8—91no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42C2×D3211yescharacteristic
579C22×C3—21no—
580C22×C3—42no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3C2×D3×D411yescharacteristic
593C22×C3C22×#6711yescharacteristic
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C3×C4—22no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—32no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—81no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4#100711yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4D3×#4111yescharacteristic
618C3×C4#101011yescharacteristic
619Dic3—21no—
620Dic3—21no—
621Dic3—21no—
622Dic3—41no—
623Dic3—41no—
624Dic3—41no—
625Dic3—62no—
626Dic3—62no—
627Dic3—122no—
628Dic3—121no—
629Dic3—121no—
630Dic3—241no—
631Dic3#95012yes—
632C32#336511yescharacteristic, complemented, Sylow
633C23—21no—
634C23—61no—
635Q8—62no—
636Q8—61no—
637Q8—61no—
638Q8—92no—
639Q8—181no—
640Q8—362no—
641D4—21no—
642D4—21no—
643D4—61no—
644D4—61no—
645D4—122no—
646D4—241no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—81no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—241no—
659C2×C4D3×#6711yescharacteristic
660C2×C4D3×#6711yescharacteristic
661C2×C4C22×D3211yescharacteristic
662C8—61no—
663C8—61no—
664C8—181no—
665C8—181no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—82no—
670C2×C3—81no—
671C2×C3—81no—
672C2×C3—241no—
673C2×C3#563311yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3#577511yescharacteristic
676C2×C3C2×#95011yescharacteristic
677C2×C3#583111yescharacteristic
678C2×C3#583611yescharacteristic
679D3—81no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—121no—
684C22—121no—
685C22—121no—
686C22C2×D3×#6711yescharacteristic
687C4—21no—
688C4—21no—
689C4—32no—
690C4—41no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—182no—
698C4—361no—
699C4#6429711yescharacteristic
700C4#6430611yescharacteristic
701C3—21no—
702C3#8115111yescharacteristic, complemented
703C3#8371711yescharacteristic, complemented
704C2—81no—
705C2—241no—
706C2#1059483011yescharacteristic
707C2#1059510611yescharacteristic
708C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC4×D4D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593852C2semidirect
3. C4×#3754C2semidirect
4. C3×#5009C2semidirect
6. #10591478C2semidirect
7. #10591441C2semidirect
9. #10590556C2semidirect
10. #10590542C2semidirect
11. #10590481C2semidirect
12. #10590479C2semidirect
13. #10590378C2semidirect
14. #10590278C2semidirect
15. #10590250C2semidirect
81. #5009D3semidirect
632. C32#3365semidirect
702. C3#81151semidirect
703. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#55592
#105938522
C4×#37542
C3×#50092
#105914872
#105914782
#105914412
#105914392
#105905562
#105905422
#105904812
#105904792
#105903782
#105902782
#105902502
#837173
#811513