Finite Group Databasebeta

← #11887156

Subgroups — #11887156

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591651C212yesmaximal, complemented
6#10591634C212yesmaximal, complemented
7D3×#809C212yesmaximal, complemented
8#10590500C212yesmaximal, complemented
9#10590329C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#83634—31nomaximal
13#80395—31nomaximal
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16C32×C4×Q8C2211yescharacteristic, complemented
17C2×#3755C2211yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C3×#946C2212yescomplemented
20C2×C3×#215C2212yescomplemented
21C3×#896—22no—
22C3×D3×C4⋊C4C2212yescomplemented
23C3×#874C2211yescharacteristic
24C3×C4×D12—21no—
25C3×C4×D12C2211yescharacteristic
26C3×#870—21no—
27C3×#869C2211yescharacteristic, complemented
28#63922—22no—
29#63916—21no—
30#63908C2212yes—
31C2×D3×C3⋊C8C2212yescomplemented
32#63662C2211yescharacteristic, complemented
33#63636C2211yescharacteristic
34#63635C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#809C2212yescomplemented
37C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
38#63573C2212yescomplemented
39#63564C2212yes—
40#63562C2212yescomplemented
41#63562C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×#554—31no—
44#5717—31no—
45#5579D311yescharacteristic, complemented
46D4×D12—31no—
47C3×#460—31no—
48#5171—32no—
49#5169—32no—
50#5088—31no—
51#5084—31no—
52#5070—31no—
53#5048—32no—
54#5046—32no—
55#5027D311yescharacteristic, complemented
56C4×#215—31no—
57C4×#215—31no—
58C4×#215—61no—
59D4×C3⋊C8—31no—
60#4968—32no—
61C2×#809—32no—
62#4842—31no—
63#4834—31no—
64#4777—32no—
65D3×#102—32no—
66C22×D32—22no—
67C2×C32×Q8C2311yescharacteristic
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#625—22no—
79#3802—44no—
80D3×D12—24no—
81D3×D12—42no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C42—21no—
85C32×C42C2311yescharacteristic
86#3755—22no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C3×#215—42no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4D412yes—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C2×C3×C3⋊C8C2312yes—
100(C2×D3)⋊Dic3—22no—
101D3×C3⋊C8—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—61no—
105C2×D3×D4—61no—
106C22×D12—32no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×#127—31no—
110C3×#125—61no—
111C3×C22⋊Q8—32no—
112C3×C22⋊Q8—62no—
113C3×C4×Q8—21no—
114C3×C4×Q8C2×D311yescharacteristic, complemented
115C3×C4×Q8C2×D311yescharacteristic, complemented
116C3×C4×D4—31no—
117C3×C4×D4—61no—
118C2×C3×C4⋊C4—32no—
119#946C2×D312yescomplemented
120C2×#215—31no—
121C2×#215—31no—
122C2×#215—61no—
123C2×#215C2×D312yescomplemented
124#938—32no—
125#938—61no—
126#937—62no—
127#930—32no—
128C22×C3⋊C8—32no—
129C2×D3×C8—32no—
130#896—22no—
131#895—61no—
132D3×C4⋊C4C2×D312yescomplemented
133#882—62no—
134#874C2×D311yescharacteristic
135C4×D12—21no—
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—61no—
139C4×D12C2×D311yescharacteristic
140#870—21no—
141#869C2×D311yescharacteristic, complemented
142C3×C4⋊C8—31no—
143C3×#102—32no—
144#835—31no—
145#835—31no—
146#835—61no—
147#832—32no—
148#832—32no—
149#830—32no—
150#821—32no—
151(C2×D3)⋊C8—32no—
152#817—32no—
153#809—32no—
154#809—32no—
155#809—31no—
156#809—31no—
157#809—32no—
158#809—61no—
159#809C2×D312yescomplemented
160#808—31no—
161#808—31no—
162#808—32no—
163#808—61no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
165C4×C3⋊C8—31no—
166C4×C3⋊C8—31no—
167C4×C3⋊C8—61no—
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3C2×D412yes—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C32×Q8—21no—
175C32×Q8—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)#4112yes—
184C4×C3⋊D3—42no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D412yes—
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—42no—
190C3×D12—81no—
191C3×D12SD1614yescomplemented
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×C4×D3—82no—
195C3×Dic6—81no—
196#626—44no—
197#625—44no—
198C3⋊(C3⋊C8)—21no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—22no—
201#554—31no—
202D42—91no—
203#486—91no—
204#481—92no—
205#476—91no—
206#465—92no—
207#460—31no—
208#450—92no—
209C4×SD16—91no—
210C8×D4—91no—
211C2×#102—92no—
212C23×D3—62no—
213C23×D3—62no—
214C2×C3×Q8—21no—
215C2×C3×Q8—61no—
216C2×C3×Q8C22×D311yescharacteristic
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C22×C3×C4—32no—
223C22×C3×C4—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—62no—
227D3×D4—64no—
228D3×D4—122no—
229D3×D4—124no—
230D3×D4—124no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—61no—
236C2×D12—64no—
237C2×D12—62no—
238C2×D12—122no—
239C2×D12#6711yescharacteristic
240C2×D12C22×D312yes—
241C2×C4×D3—22no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—121no—
245C2×C4×D3C22×D312yes—
246C2×Dic6—21no—
247C3×SD16—122no—
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—41no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C22⋊C4—32no—
261C3×C22⋊C4—62no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—41no—
266C3×C42C22×D311yescharacteristic
267C3×C42C22×D311yescharacteristic
268#217—62no—
269#215—42no—
270#215—62no—
271#215—62no—
272#215—64no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—121no—
278(C2×D3)⋊C4#6712yes—
279C4⋊Dic3—21no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—61no—
283C4⋊Dic3#6711yescharacteristic
284C4⋊Dic3C22×D312yes—
285Dic3⋊C4—22no—
286Dic3⋊C4—22no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—122no—
294C2×C3⋊C8C22×D312yes—
295D3×C8—122no—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3C2×SD1614yes—
306D32—88no—
307C32×C4—21no—
308C32×C4—41no—
309C32×C4—41no—
310C32×C4C2×SD1612yes—
311C32×C4C2×#4111yescharacteristic
312C32×C4H(5,𝔽2)11yescharacteristic
313C3⋊Dic3—41no—
314C3×Dic3—22no—
315C3×Dic3—42no—
316C22×D4—92no—
317C22×D4—181no—
318C2×SD16—32no—
319C2×SD16—91no—
320C22×C8—92no—
321C4⋊Q8—31no—
322#127—31no—
323#125—61no—
324C22⋊Q8—32no—
325C22⋊Q8—62no—
326#121—92no—
327#121—181no—
328#120—182no—
329C4×Q8D3211yescharacteristic, complemented
330C4×D4—31no—
331C4×D4—61no—
332C4×D4—91no—
333C2×C4⋊C4—32no—
334#106—92no—
335#106—91no—
336C4⋊C8—31no—
337#103—91no—
338#102—32no—
339#102—92no—
340#102—92no—
341#102—92no—
342#102—91no—
343C22⋊C8—92no—
344C4×C8—91no—
345C23×C3—32no—
346C23×C3—62no—
347C22×D3—22no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—121no—
351C22×D3—124no—
352C22×D3—124no—
353C22×D3—124no—
354C22×D3—124no—
355C22×D3—242no—
356C22×D3—242no—
357C22×D3C2×#6712yes—
358C3×Q8—22no—
359C3×Q8—21no—
360C3×Q8—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—41no—
364C3×Q8—241no—
365C3×D4—34no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—122no—
369C3×D4—241no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—32no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—242no—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—124no—
391#67—124no—
392#67—124no—
393C2×Dic3—22no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—121no—
397C2×Dic3C2×#6712yes—
398D12—22no—
399D12—22no—
400D12—32no—
401D12—32no—
402D12—42no—
403D12—62no—
404D12—61no—
405D12—61no—
406D12—81no—
407D12—121no—
408D12—124no—
409D12#21514yescomplemented
410C4×D3—22no—
411C4×D3—22no—
412C4×D3—82no—
413C4×D3—122no—
414C4×D3—122no—
415C4×D3—242no—
416Dic6—81no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—61no—
421C3⋊C8—61no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—121no—
425C2×C32#54611yescharacteristic
426C2×C32C22×SD1611yescharacteristic
427C2×C32#57611yescharacteristic
428C3⋊D3—42no—
429C3×D3—24no—
430C3×D3—82no—
431C24—182no—
432C2×Q8—61no—
433C2×Q8C2×D3211yescharacteristic
434C2×D4—32no—
435C2×D4—31no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—91no—
439C2×D4—182no—
440C2×D4—184no—
441C2×D4—182no—
442C2×D4—362no—
443C2×D4—364no—
444C22×C4—32no—
445C22×C4—62no—
446C22×C4—181no—
447SD16—122no—
448SD16—182no—
449C2×C8—32no—
450C2×C8—91no—
451C2×C8—91no—
452C2×C8—362no—
453C4⋊C4—21no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—62no—
457C4⋊C4—62no—
458C4⋊C4—61no—
459C4⋊C4—91no—
460C4⋊C4C2×D3211yescharacteristic
461C22⋊C4—32no—
462C22⋊C4—62no—
463C22⋊C4—182no—
464C22⋊C4—181no—
465C42—21no—
466C42C2×D3211yescharacteristic
467C22×C3—21no—
468C22×C3—34no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C22×#6711yescharacteristic
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—122no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—241no—
489C2×D3—241no—
490C2×D3—248no—
491C2×D3—248no—
492C2×D3C2×#21514yes—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—41no—
499C3×C4—42no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—62no—
505C3×C4—81no—
506C3×C4—122no—
507C3×C4D3×SD1612yes—
508C3×C4C2×#21512yes—
509C3×C4#100411yescharacteristic
510C3×C4D3×#4111yescharacteristic
511C3×C4D3×#4111yescharacteristic
512C3×C4#100911yescharacteristic
513Dic3—22no—
514Dic3—42no—
515Dic3—121no—
516Dic3—121no—
517Dic3—241no—
518C32#329511yescharacteristic, complemented, Sylow
519C23—32no—
520C23—62no—
521C23—181no—
522C23—364no—
523C23—364no—
524C23—722no—
525Q8—21no—
526Q8—21no—
527Q8—241no—
528D4—34no—
529D4—62no—
530D4—62no—
531D4—92no—
532D4—122no—
533D4—181no—
534D4—241no—
535D4—364no—
536D4—364no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—32no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—181no—
544C2×C4—242no—
545C2×C4—362no—
546C2×C4D3×#6711yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—62no—
550C8—181no—
551C8—181no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—64no—
556C2×C3—242no—
557C2×C3#561211yescharacteristic
558C2×C3C2×D3×SD1611yescharacteristic
559C2×C3#577411yescharacteristic
560C2×C3C22×#21511yescharacteristic
561C2×C3#582911yescharacteristic
562C2×C3#583511yescharacteristic
563D3—24no—
564D3—82no—
565D3—122no—
566D3—122no—
567D3—242no—
568C22—34no—
569C22—62no—
570C22—62no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—182no—
575C22—361no—
576C22—361no—
577C22—728no—
578C22C2×D3×#6711yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—62no—
583C4—122no—
584C4—361no—
585C4D3×#21512yes—
586C4#6430611yescharacteristic
587C4#6430711yescharacteristic
588C3—21no—
589C3#8039511yescharacteristic, complemented
590C3#8363411yescharacteristic, complemented
591C2—64no—
592C2—242no—
593C2—362no—
594C2#1059507011yescharacteristic
595C2C2×D3×#21511yescharacteristic
596C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4×Q8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
3. C4×#3755C2semidirect
4. C3×#5027C2semidirect
5. #10591651C2semidirect
6. #10591634C2semidirect
7. D3×#809C2semidirect
8. #10590500C2semidirect
9. #10590329C2semidirect
10. #10590300C2semidirect
11. #10590277C2semidirect
16. C32×C4×Q8C22semidirect
19. C3×#946C22semidirect
20. C2×C3×#215C22semidirect
22. C3×D3×C4⋊C4C22semidirect
27. C3×#869C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63662C22semidirect
34. #63635C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
36. C3×#809C22semidirect
37. C3×C4⋊(C3⋊C8)C22semidirect
38. #63573C22semidirect
40. #63562C22semidirect
41. #63562C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
45. #5579D3semidirect
55. #5027D3semidirect
114. C3×C4×Q8C2×D3semidirect
115. C3×C4×Q8C2×D3semidirect
119. #946C2×D3semidirect
123. C2×#215C2×D3semidirect
132. D3×C4⋊C4C2×D3semidirect
141. #869C2×D3semidirect
159. #809C2×D3semidirect
164. C4⋊(C3⋊C8)C2×D3semidirect
191. C3×D12SD16semidirect
329. C4×Q8D32semidirect
409. D12#215semidirect
518. C32#3295semidirect
589. C3#80395semidirect
590. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
#105940042
C4×#37552
C3×#50272
#105916512
#105916342
D3×#8092
#105905002
#105903292
#105903002
#105902772
#836343
#803953