Finite Group Databasebeta

← #11895638

Subgroups — #11895638

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
1C3×#5681C211yesmaximal, characteristic
2#10593852C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591614C211yesmaximal, characteristic, complemented
6#10591577C211yesmaximal, characteristic, complemented
7#10591544C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591487C211yesmaximal, characteristic
10#10591439C211yesmaximal, characteristic
11#10591409C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
16#83717—31nomaximal
17#81635—31nomaximal
18C32×#124C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×#886—21no—
27C3×#885—21no—
28C3×#883—21no—
29C3×#67⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63918C2211yescharacteristic
34#63870—21no—
35#63869C2211yescharacteristic
36#63847—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63839—21no—
40#63838—21no—
41C2×#3716C2211yescharacteristic
42#63662C2211yescharacteristic
43#63659C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×C4×C3⋊C8C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62#5685—31no—
63#5681D311yescharacteristic
64#5567—31no—
65C3×#488—31no—
66#5075—31no—
67#5070—31no—
68#5066—31no—
69#5056—31no—
70#5056D311yescharacteristic, complemented
71#5054—31no—
72#5054—31no—
73#5054—31no—
74#5054—61no—
75C4×#216—31no—
76Q8×C3⋊C8—31no—
77#5020—31no—
78C4×#214—31no—
79C4×#214—31no—
80#5009—31no—
81#5009—31no—
82#4800—31no—
83#4798—31no—
84#4791—31no—
85#4790—31no—
86#4763—31no—
87#4762—31no—
88#4760—31no—
89#4758—31no—
90C4×#204—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×Dic6D411yescharacteristic
101C2×#627—21no—
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C42C2311yescharacteristic
105#3756—22no—
106#3754—22no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#217—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3365—91noSylow
139C3×#127—31no—
140C3×#125—31no—
141C3×#124—21no—
142C3×#124—31no—
143C3×#124—61no—
144C3×#124C2×D311yescharacteristic
145C3×#124C2×D311yescharacteristic
146C3×#123—61no—
147C3×#123—61no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153#947C2×D311yescharacteristic
154Q8×Dic3C2×D311yescharacteristic
155#944—61no—
156C2×#216—31no—
157C2×#216—31no—
158C2×#216—61no—
159#940C2×D311yescharacteristic
160D4×Dic3C2×D311yescharacteristic
161C2×#214—31no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—61no—
165C2×#204—31no—
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#886—21no—
178#885—21no—
179#883—21no—
180#67⋊C4—21no—
181C4×D12C2×D311yescharacteristic
182#870—31no—
183#870C2×D311yescharacteristic
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6C2×D311yescharacteristic
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×C4×C8—31no—
196#835—31no—
197#835—31no—
198#835—61no—
199#835C2×D311yescharacteristic
200#835C2×D311yescharacteristic
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#821—31no—
210#817—31no—
211#816—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215C8×Dic3—31no—
216#810—31no—
217#809—31no—
218#809—31no—
219#808—31no—
220#808—31no—
221#808—31no—
222#807—31no—
223#807—31no—
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8C2×D311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244#634—21no—
245#634#4112yes—
246C3×#67—42no—
247C3×#67—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×C4×D3—81no—
259C3×Dic6—22no—
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—31no—
268#488—91no—
269#486—91no—
270#478—91no—
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—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C2×#67—21no—
293C2×#67—21no—
294C22×Dic3—21no—
295C2×D12C22×D311yescharacteristic
296C2×C4×D3—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6#6711yescharacteristic
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C3×C4⋊C4—31no—
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×C22⋊C4—21no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—21no—
317C3×C22⋊C4—21no—
318C3×C22⋊C4—41no—
319C3×C22⋊C4—41no—
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#216—62no—
332#216—62no—
333#216—122no—
334#214—62no—
335#214—62no—
336#214—62no—
337#214—122no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3#6711yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
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—61no—
363Dic3⋊C4—121no—
364Dic3⋊C4#6711yescharacteristic
365Dic3⋊C4#6711yescharacteristic
366C4×Dic3—21no—
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⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384#204—62no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—41no—
395C32×C4C2×#4111yescharacteristic
396C32×C42−1+411yescharacteristic
397C3⋊Dic3—22no—
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—31no—
412#125—31no—
413#125—91no—
414#125—181no—
415#125—181no—
416#124—31no—
417#124—61no—
418#124D3211yescharacteristic
419#123—61no—
420#123—61no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—61no—
430#107—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—91no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
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—91no—
448C4×C8—91no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C23×C3—61no—
453C22×D3—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—62no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—122no—
470C3×D4—241no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—241no—
485C2×C3×C4—241no—
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4C2×#6711yescharacteristic
489C2×C3×C4C2×#6711yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492#67—42no—
493#67—81no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—81no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3C2×#6711yescharacteristic
505C2×Dic3C2×#6711yescharacteristic
506C2×Dic3C2×#6711yescharacteristic
507C2×Dic3C2×#6711yescharacteristic
508D12—21no—
509D12—21no—
510C4×D3—81no—
511Dic6—22no—
512Dic6—32no—
513Dic6—32no—
514Dic6—62no—
515Dic6—61no—
516Dic6—61no—
517Dic6—121no—
518Dic6—122no—
519Dic6—122no—
520C3×C8—61no—
521C3×C8—61no—
522C3⋊C8—21no—
523C3⋊C8—21no—
524C3⋊C8—61no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C3⋊C8—121no—
529C3⋊C8—121no—
530C2×C32—81no—
531C2×C32#54811yescharacteristic
532C2×C32C2×#13511yescharacteristic
533C2×C32#57711yescharacteristic
534C3×D3—81no—
535C2×Q8—31no—
536C2×Q8—91no—
537C2×Q8—181no—
538C2×Q8C2×D3211yescharacteristic
539C2×D4—31no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4C2×D3211yescharacteristic
543C22×C4—61no—
544C22×C4—61no—
545Q16—182no—
546SD16—182no—
547SD16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8—91no—
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—61no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—61no—
574C42—31no—
575C42—31no—
576C42—61no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42C2×D3211yescharacteristic
581C22×C3—21no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3C2×D3×D411yescharacteristic
595C22×C3C22×#6711yescharacteristic
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
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—41no—
609C3×C4—41no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4D3×#4111yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4#101011yescharacteristic
620C3×C4#101011yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3—62no—
628Dic3—62no—
629Dic3—122no—
630Dic3—121no—
631Dic3—121no—
632Dic3—241no—
633Dic3#95012yes—
634C32#336511yescharacteristic, complemented, Sylow
635C23—21no—
636C23—61no—
637Q8—21no—
638Q8—21no—
639Q8—62no—
640Q8—92no—
641Q8—181no—
642Q8—362no—
643D4—21no—
644D4—21no—
645D4—61no—
646D4—61no—
647D4—122no—
648D4—241no—
649C2×C4—21no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—241no—
660C2×C4—241no—
661C2×C4D3×#6711yescharacteristic
662C2×C4D3×#6711yescharacteristic
663C2×C4C22×D3211yescharacteristic
664C8—61no—
665C8—61no—
666C8—181no—
667C8—181no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—81no—
672C2×C3—81no—
673C2×C3—161no—
674C2×C3—241no—
675C2×C3#567711yescharacteristic
676C2×C3D3×#13511yescharacteristic
677C2×C3#577011yescharacteristic
678C2×C3C2×#95011yescharacteristic
679C2×C3#583111yescharacteristic
680C2×C3#583611yescharacteristic
681D3—81no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22C2×D3×#6711yescharacteristic
689C4—21no—
690C4—21no—
691C4—32no—
692C4—41no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—182no—
700C4—361no—
701C4#6430911yescharacteristic
702C4#6431211yescharacteristic
703C3—21no—
704C3#8163511yescharacteristic, complemented
705C3#8371711yescharacteristic, complemented
706C2—81no—
707C2—241no—
708C2#1059523711yescharacteristic
709C2D3×#95011yescharacteristic
710C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenter#124D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593852C2semidirect
3. #10592753C2semidirect
4. C3×#5056C2semidirect
5. #10591614C2semidirect
6. #10591577C2semidirect
7. #10591544C2semidirect
8. #10591537C2semidirect
11. #10591409C2semidirect
12. #10591401C2semidirect
13. C4×#3716C2semidirect
14. #10590270C2semidirect
15. C3⋊C8×Dic6C2semidirect
70. #5056D3semidirect
634. C32#3365semidirect
704. C3#81635semidirect
705. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#56812
#105938522
#105927532
C3×#50562
#105916142
#105915772
#105915442
#105915372
#105914872
#105914392
#105914092
#105914012
C4×#37162
#105902702
C3⋊C8×Dic62
#837173
#816353