Finite Group Databasebeta

← #11901735

Subgroups — #11901735

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#540C211yesmaximal, characteristic, complemented
2#10596190C211yesmaximal, characteristic, complemented
3#10596187C211yesmaximal, characteristic, complemented
4#10596169C211yesmaximal, characteristic, complemented
5#10596159C211yesmaximal, characteristic, complemented
6#10596131C214yesmaximal, complemented
7#10596120C214yesmaximal, complemented
8#10596084C214yesmaximal, complemented
9#10596077C212yesmaximal, complemented
10#10596074C212yesmaximal, complemented
11#10596071C214yesmaximal, complemented
12#10596032C212yesmaximal, complemented
13C4×#3830C212yesmaximal, complemented
14C3⋊D3×#117C211yesmaximal, characteristic, complemented
15#10595989C211yesmaximal, characteristic, complemented
16#86467—34nomaximal
17C2×#3830C2212yes—
18C22×C4×C3⋊D3C2211yescharacteristic
19C32×#127C2211yescharacteristic, complemented
20C32×#125C2211yescharacteristic, complemented
21C32×#123C2214yescomplemented
22C32×#121C2214yes—
23C32×#121C2212yes—
24C32×C4×D4C2212yescomplemented
25C32×#117C2211yescharacteristic
26#64148C2214yes—
27#64147C2214yes—
28#64147C2212yes—
29#64146C2214yes—
30#64145C2214yes—
31#64145C2212yescomplemented
32#64144C2214yes—
33#64144C2214yescomplemented
34D4×C3⋊Dic3C2214yes—
35D4×C3⋊Dic3C2214yescomplemented
36D4×C3⋊Dic3C2212yescomplemented
37#64138C2214yes—
38C4×#638C2214yes—
39#64135C2211yescharacteristic
40#64133C2212yes—
41#64133C2214yescomplemented
42C2×C4×C3⋊Dic3C2214yescomplemented
43#64107C2214yes—
44#64106C2212yes—
45#64105C2214yes—
46#64101C2212yes—
47#64101C2212yes—
48C4⋊C4×C3⋊D3C2212yes—
49#64099C2214yescomplemented
50#64098C2214yescomplemented
51#64097C2212yescomplemented
52#64096C2214yescomplemented
53#64096C2212yescomplemented
54#64094C2214yes—
55#64092C2214yes—
56#64090C2214yes—
57#64090C2214yes—
58C22⋊C4×C3⋊D3C2212yes—
59#64088C2214yes—
60#64088C2214yescomplemented
61#64088C2214yescomplemented
62#64087C2214yescomplemented
63#64086C2212yes—
64#64086C2214yescomplemented
65#64081C2211yescharacteristic
66#64081C2211yescharacteristic
67C42×C3⋊D3C2211yescharacteristic
68C42×C3⋊D3C2211yescharacteristic
69#64079C2211yescharacteristic, complemented
70#64078C2211yescharacteristic, complemented
71C4×#634C2212yescomplemented
72C3×#540D314yescomplemented
73#5719—34no—
74#5716—34no—
75#5698—34no—
76#5688—34no—
77#5660—316no—
78#5649—316no—
79#5613—316no—
80#5606—38no—
81#5603—38no—
82#5600—316no—
83#5561—38no—
84C4×#237—38no—
85D3×#117—34no—
86#5518—34no—
87C23×C3⋊D3C2311yescharacteristic
88C2×C32×D4C2312yes—
89C2×C32×D4C2314yes—
90C2×C32×D4C2314yes—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2314yes—
93C2×#638C2314yes—
94C2×#638C2314yes—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2314yes—
97C22×C3⋊Dic3C2314yes—
98#3830—28no—
99C2×C4×C3⋊D3—24no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C4×C3⋊D3C2312yes—
104C2×C4×C3⋊D3C2312yes—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2312yes—
107C2×#634C2314yes—
108C32×C4⋊C4C2312yes—
109C32×C4⋊C4C2314yes—
110C32×C4⋊C4C2312yes—
111C32×C22⋊C4C2312yes—
112C32×C22⋊C4C2314yes—
113C32×C22⋊C4C2314yes—
114C32×C42C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3757C2312yes—
117#3757C2314yes—
118#3757C2314yes—
119#3757C2314yes—
120#3757C2314yes—
121#3757C2314yes—
122#3752C2312yes—
123#3752C2312yes—
124#3752C2314yes—
125#3752C2314yes—
126C4⋊(C3⋊Dic3)C2312yes—
127C4⋊(C3⋊Dic3)C2314yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C4⋊(C3⋊Dic3)C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2312yes—
133#3750C2312yes—
134#3750C2314yes—
135#3750C2314yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2314yes—
138C4×C3⋊Dic3C2311yescharacteristic
139C4×C3⋊Dic3C2311yescharacteristic
140C4×C3⋊Dic3C2312yes—
141C4×C3⋊Dic3C2312yes—
142C4×C3⋊Dic3C2314yes—
143C4×C3⋊Dic3C2314yes—
144#3455—91noSylow
145C2×#237—38no—
146C22×C4×D3—34no—
147C3×#127C2×D314yescomplemented
148C3×#125C2×D314yescomplemented
149C3×#123C2×D3116yescomplemented
150C3×#121C2×D3116yes—
151C3×#121C2×D318yes—
152C3×C4×D4C2×D318yescomplemented
153C3×#117C2×D314yes—
154#939—316no—
155#938—316no—
156#938—38no—
157#937—316no—
158#936—38no—
159#936—316no—
160#935—316no—
161#935—316no—
162D4×Dic3—316no—
163D4×Dic3—38no—
164D4×Dic3—316no—
165#929—316no—
166C4×#67—316no—
167#926—34no—
168#924—316no—
169#924—38no—
170C2×C4×Dic3—316no—
171#898—316no—
172#897—38no—
173#896—316no—
174#892—38no—
175#892—38no—
176D3×C4⋊C4—38no—
177#890—316no—
178#889—316no—
179#888—38no—
180#887—316no—
181#887—38no—
182#885—316no—
183#883—316no—
184#67⋊C4—316no—
185#67⋊C4—316no—
186D3×C22⋊C4—38no—
187#879—316no—
188#879—316no—
189#879—316no—
190#878—316no—
191#877—316no—
192#877—38no—
193#872—34no—
194#872—34no—
195C42×D3—34no—
196C42×D3—34no—
197#870—34no—
198#869—34no—
199C4×Dic6—38no—
200C23×C32C2411yescharacteristic
201C23×C32C2414yes—
202C22×C3⋊D3—22no—
203C22×C3⋊D3—42no—
204C22×C3⋊D3C2411yescharacteristic
205C22×C3⋊D3C2411yescharacteristic
206C32×D4—24no—
207C32×D4—44no—
208C32×D4—44no—
209C2×C32×C4—22no—
210C2×C32×C4—44no—
211C2×C32×C4C2412yes—
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214C2×C32×C4C2411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216#638—28no—
217#638—44no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—28no—
220C2×C3⋊Dic3—44no—
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2414yes—
224C2×C3⋊Dic3C2412yes—
225C2×C3⋊Dic3C2411yescharacteristic
226C2×C3⋊Dic3C2411yescharacteristic
227C4×C3⋊D3—22no—
228C4×C3⋊D3—22no—
229C4×C3⋊D3—22no—
230C4×C3⋊D3—42no—
231C4×C3⋊D3—42no—
232C4×C3⋊D3#4114yes—
233#634—24no—
234#634—44no—
235#542—92no—
236#542—92no—
237#541—91no—
238#541—91no—
239#540—91no—
240#540C3⋊D311yescharacteristic, complemented
241#539—94no—
242#538—94no—
243#533—91no—
244#532—91no—
245#529—94no—
246#529—94no—
247#525—92no—
248C4×#41—92no—
249C2×#117—91no—
250C23×D3—34no—
251C2×C3×D4C22×D318yes—
252C2×C3×D4C22×D3116yes—
253C2×C3×D4C22×D3116yes—
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D3116yes—
256C2×#67—316no—
257C2×#67—316no—
258C22×Dic3—34no—
259C22×Dic3—316no—
260C22×Dic3—316no—
261#237—632no—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—38no—
267C2×C4×D3—38no—
268C2×C4×D3—616no—
269C2×Dic6—38no—
270C2×Dic6—316no—
271C3×C4⋊C4C22×D318yes—
272C3×C4⋊C4C22×D3116yes—
273C3×C4⋊C4C22×D318yes—
274C3×C22⋊C4C22×D318yes—
275C3×C22⋊C4C22×D3116yes—
276C3×C22⋊C4C22×D3116yes—
277C3×C42C22×D314yes—
278C3×C42C22×D314yes—
279#217—316no—
280#217—38no—
281#217—316no—
282#217—316no—
283#217—316no—
284#217—316no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—316no—
288(C2×D3)⋊C4—316no—
289C4⋊Dic3—38no—
290C4⋊Dic3—316no—
291C4⋊Dic3—38no—
292C4⋊Dic3—316no—
293Dic3⋊C4—316no—
294Dic3⋊C4—316no—
295Dic3⋊C4—38no—
296Dic3⋊C4—38no—
297Dic3⋊C4—316no—
298Dic3⋊C4—316no—
299Dic3⋊C4—316no—
300C4×Dic3—316no—
301C4×Dic3—34no—
302C4×Dic3—34no—
303C4×Dic3—38no—
304C4×Dic3—38no—
305C4×Dic3—316no—
306C4×Dic3—316no—
307C22×C32—24no—
308C22×C32—21no—
309C22×C32—24no—
310C22×C32—24no—
311C22×C32—22no—
312C22×C32C2511yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—21no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—44no—
317C2×C3⋊D3C2×#4112yes—
318C32×C4—21no—
319C32×C4—24no—
320C32×C4—22no—
321C32×C4—22no—
322C32×C4C2×#4112yes—
323C3⋊Dic3—24no—
324C3⋊Dic3—21no—
325C3⋊Dic3—22no—
326C3⋊Dic3—24no—
327C3⋊Dic3—22no—
328C3⋊Dic3C2×#4112yes—
329C2×#41—92no—
330C23×C4—91no—
331C4⋊Q8—92no—
332C4⋊Q8—91no—
333#127C2×C3⋊D311yescharacteristic, complemented
334#126—94no—
335#126—94no—
336#126—94no—
337#126—94no—
338#125—94no—
339#125—94no—
340#125—91no—
341#125C2×C3⋊D311yescharacteristic, complemented
342#124—94no—
343#124—92no—
344#124—94no—
345#123—94no—
346#123—94no—
347#123—94no—
348#123—94no—
349#123C2×C3⋊D314yescomplemented
350C22⋊Q8—92no—
351C22⋊Q8—94no—
352C22⋊Q8—92no—
353C22⋊Q8—94no—
354C22⋊Q8—94no—
355#121—92no—
356#121—94no—
357#121—94no—
358#121C2×C3⋊D312yes—
359#121C2×C3⋊D314yes—
360#120—94no—
361C4×Q8—92no—
362C4×Q8—94no—
363C4×Q8—92no—
364C4×D4—92no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369C4×D4—94no—
370C4×D4C2×C3⋊D312yescomplemented
371#117—91no—
372#117—92no—
373#117—92no—
374#117—92no—
375#117—94no—
376#117—91no—
377#117—91no—
378#117C2×C3⋊D311yescharacteristic
379C2×C4⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—94no—
382C2×C42—91no—
383C2×C42—91no—
384C23×C3C23×D314yes—
385C23×C3C23×D3116yes—
386C22×D3—34no—
387C22×D3—34no—
388C22×D3—68no—
389C22×D3—128no—
390C3×D4—216no—
391C3×D4—416no—
392C3×D4—416no—
393C2×C3×C4—28no—
394C2×C3×C4—416no—
395C2×C3×C4C23×D318yes—
396C2×C3×C4C23×D3116yes—
397C2×C3×C4C23×D318yes—
398C2×C3×C4C23×D314yes—
399C2×C3×C4C23×D314yes—
400#67—632no—
401#67—1216no—
402C2×Dic3—34no—
403C2×Dic3—38no—
404C2×Dic3—316no—
405C2×Dic3—316no—
406C2×Dic3—38no—
407C2×Dic3—34no—
408C2×Dic3—68no—
409C2×Dic3—632no—
410C2×Dic3—1216no—
411C4×D3—316no—
412C4×D3—68no—
413C4×D3—68no—
414C4×D3—68no—
415C4×D3—128no—
416C4×D3—128no—
417Dic6—616no—
418Dic6—1216no—
419C2×C32—41no—
420C2×C32—44no—
421C2×C32C22×#4111yescharacteristic
422C2×C32#58512yes—
423C3⋊D3—22no—
424C3⋊D3—41no—
425C24—91no—
426#41—188no—
427C2×Q8—92no—
428C2×Q8—94no—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4C22×C3⋊D312yes—
432C2×D4C22×C3⋊D314yes—
433C2×D4C22×C3⋊D314yes—
434C22×C4—91no—
435C22×C4—94no—
436C22×C4—91no—
437C22×C4—94no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—92no—
442C22×C4—92no—
443C22×C4—184no—
444C22×C4C22×C3⋊D311yescharacteristic
445C22×C4C22×C3⋊D314yes—
446C4⋊C4—92no—
447C4⋊C4—92no—
448C4⋊C4—92no—
449C4⋊C4—92no—
450C4⋊C4—94no—
451C4⋊C4—94no—
452C4⋊C4—94no—
453C4⋊C4—94no—
454C4⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—94no—
457C4⋊C4C22×C3⋊D312yes—
458C4⋊C4C22×C3⋊D312yes—
459C4⋊C4C22×C3⋊D314yes—
460C22⋊C4—92no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—92no—
467C22⋊C4—92no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4C22×C3⋊D312yes—
471C22⋊C4C22×C3⋊D314yes—
472C22⋊C4C22×C3⋊D314yes—
473C42—92no—
474C42—92no—
475C42—94no—
476C42—91no—
477C42—91no—
478C42—94no—
479C42—94no—
480C42C22×C3⋊D311yescharacteristic
481C42C22×C3⋊D311yescharacteristic
482C22×C3—216no—
483C22×C3—24no—
484C22×C3—216no—
485C22×C3—216no—
486C22×C3—28no—
487C22×C3C24×D314yes—
488C2×D3—38no—
489C2×D3—68no—
490C2×D3—64no—
491C2×D3—68no—
492C2×D3—1216no—
493C3×C4—24no—
494C3×C4—216no—
495C3×C4—28no—
496C3×C4—28no—
497C3×C4D3×#4118yes—
498Dic3—38no—
499Dic3—616no—
500Dic3—64no—
501Dic3—68no—
502Dic3—616no—
503Dic3—68no—
504C32#345511yescharacteristic, complemented, Sylow
505C23—91no—
506C23—91no—
507C23—182no—
508C23—362no—
509C23C23×C3⋊D311yescharacteristic
510C23C23×C3⋊D314yes—
511Q8—184no—
512Q8—364no—
513D4—24no—
514D4—44no—
515D4—44no—
516D4—188no—
517D4—364no—
518C2×C4—22no—
519C2×C4—44no—
520C2×C4—91no—
521C2×C4—94no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—94no—
525C2×C4—94no—
526C2×C4—91no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—188no—
531C2×C4—182no—
532C2×C4—362no—
533C2×C4—362no—
534C2×C4—364no—
535C2×C4C23×C3⋊D312yes—
536C2×C4C23×C3⋊D314yes—
537C2×C4C23×C3⋊D312yes—
538C2×C4C23×C3⋊D311yescharacteristic
539C2×C4C23×C3⋊D311yescharacteristic
540C2×C3—44no—
541C2×C3—416no—
542C2×C3C2×D3×#4114yes—
543C2×C3#596618yes—
544D3—68no—
545D3—124no—
546C22—21no—
547C22—24no—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—92no—
552C22—182no—
553C22—181no—
554C22—182no—
555C22—364no—
556C22C24×C3⋊D311yescharacteristic
557C4—21no—
558C4—22no—
559C4—24no—
560C4—22no—
561C4—92no—
562C4—181no—
563C4—184no—
564C4—182no—
565C4—184no—
566C4—182no—
567C4#41×C3⋊D312yes—
568C3#8646714yescomplemented
569C2—41no—
570C2—44no—
571C2—182no—
572C2—361no—
573C2C2×#41×C3⋊D311yescharacteristic
574C2#1059675812yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#540C2
hypercenter#540C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C32×#540C2semidirect
2. #10596190C2semidirect
3. #10596187C2semidirect
4. #10596169C2semidirect
5. #10596159C2semidirect
6. #10596131C2semidirect
7. #10596120C2semidirect
8. #10596084C2semidirect
9. #10596077C2semidirect
10. #10596074C2semidirect
11. #10596071C2semidirect
12. #10596032C2semidirect
13. C4×#3830C2semidirect
14. C3⋊D3×#117C2semidirect
15. #10595989C2semidirect
19. C32×#127C22semidirect
20. C32×#125C22semidirect
21. C32×#123C22semidirect
24. C32×C4×D4C22semidirect
31. #64145C22semidirect
33. #64144C22semidirect
35. D4×C3⋊Dic3C22semidirect
36. D4×C3⋊Dic3C22semidirect
41. #64133C22semidirect
42. C2×C4×C3⋊Dic3C22semidirect
49. #64099C22semidirect
50. #64098C22semidirect
51. #64097C22semidirect
52. #64096C22semidirect
53. #64096C22semidirect
60. #64088C22semidirect
61. #64088C22semidirect
62. #64087C22semidirect
64. #64086C22semidirect
69. #64079C22semidirect
70. #64078C22semidirect
71. C4×#634C22semidirect
72. C3×#540D3semidirect
147. C3×#127C2×D3semidirect
148. C3×#125C2×D3semidirect
149. C3×#123C2×D3semidirect
152. C3×C4×D4C2×D3semidirect
240. #540C3⋊D3semidirect
333. #127C2×C3⋊D3semidirect
341. #125C2×C3⋊D3semidirect
349. #123C2×C3⋊D3semidirect
370. C4×D4C2×C3⋊D3semidirect
504. C32#3455semidirect
568. C3#86467semidirect

Maximal subgroups

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

subgroupindex
C32×#5402
#105961902
#105961872
#105961692
#105961592
#105961312
#105961202
#105960842
#105960772
#105960742
#105960712
#105960322
C4×#38302
C3⋊D3×#1172
#105959892
#864673