Finite Group Databasebeta

← #11910348

Subgroups — #11910348

Order 1152.

3174 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2#10596303C212yesmaximal, complemented
3#10596299C212yesmaximal, complemented
4#10596206C212yesmaximal, complemented
5#10596191C212yesmaximal, complemented
6#10596155C212yesmaximal, complemented
7#10596154C211yesmaximal, characteristic, complemented
8#10596143C211yesmaximal, characteristic, complemented
9#10596092C214yesmaximal, complemented
10#10596091C214yesmaximal, complemented
11#10596018C214yesmaximal, complemented
12#10596009C214yesmaximal, complemented
13#10595950C212yesmaximal, complemented
14#86248—34nomaximal
15C2×C32×#41C2211yescharacteristic
16C2×C32×#41C2211yescharacteristic, complemented
17C2×#3828C2212yes—
18C22×C4×C3⋊D3C2212yescomplemented
19C32×C4⋊Q8C2211yescharacteristic, complemented
20C32×#127C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×#124C2211yescharacteristic, complemented
23C32×#121C2214yescomplemented
24C32×C4×D4C2214yescomplemented
25C2×C32×C42C2211yescharacteristic, complemented
26#64156C2212yes—
27#64155C2214yescomplemented
28#64153C2212yescomplemented
29#64149C2212yes—
30#64148C2214yes—
31#64148C2214yes—
32#64148C2214yescomplemented
33#64148C2214yescomplemented
34#64147C2214yes—
35#64146C2212yes—
36#64146C2214yescomplemented
37#64146C2212yescomplemented
38#64145C2212yescomplemented
39#64144C2212yes—
40#64144C2214yescomplemented
41#64144C2212yescomplemented
42#64139C2212yes—
43#64138C2214yescomplemented
44C4×#638C2214yes—
45C4×#638C2214yescomplemented
46C4×#638C2214yescomplemented
47#64135C2212yescomplemented
48#64133C2212yescomplemented
49C2×C4×C3⋊Dic3C2212yescomplemented
50#64107C2214yescomplemented
51#64105C2214yescomplemented
52#64103C2214yes—
53#64098C2214yescomplemented
54#64095C2214yescomplemented
55#64094C2214yes—
56#64093C2214yes—
57#64092C2214yescomplemented
58#64091C2214yes—
59#64088C2214yescomplemented
60#64087C2214yescomplemented
61#64087C2214yescomplemented
62#64085C2214yescomplemented
63#64084C2212yes—
64C4×C4⋊(C3⋊D3)C2212yes—
65#64081C2214yescomplemented
66#64079C2212yescomplemented
67C4×#634C2212yescomplemented
68C3×#532D314yescomplemented
69#5832—38no—
70#5828—38no—
71#5735—38no—
72#5720—38no—
73#5684—38no—
74#5683—34no—
75#5672—34no—
76#5621—316no—
77#5620—316no—
78#5547—316no—
79#5538—316no—
80#5479—38no—
81C23×C3⋊D3C2312yes—
82C32×#41—42no—
83C32×#41—42no—
84C2×C32×Q8C2311yescharacteristic
85C2×C32×Q8C2311yescharacteristic
86C2×C32×D4C2311yescharacteristic
87C2×C32×D4C2312yes—
88C2×C32×D4C2312yes—
89C2×C32×D4C2311yescharacteristic
90C2×C32×D4C2314yes—
91C22×C32×C4C2312yes—
92C22×C32×C4C2312yes—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2312yes—
95C2×#638C2314yes—
96C2×#638C2314yes—
97C2×#638C2314yes—
98C2×#638C2314yes—
99C22×C3⋊Dic3C2312yes—
100C22×C3⋊Dic3C2314yes—
101#3828—44no—
102C2×C4⋊(C3⋊D3)C2312yes—
103C2×C4⋊(C3⋊D3)C2312yes—
104C2×C4×C3⋊D3—44no—
105C2×C4×C3⋊D3C2314yes—
106C2×C4×C3⋊D3C2314yes—
107C2×#634C2312yes—
108C2×#634C2312yes—
109C32×C4⋊C4C2314yes—
110C32×C22⋊C4C2314yes—
111C32×C22⋊C4C2314yes—
112C32×C42C2312yes—
113C32×C42C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3757C2314yes—
116#3757C2314yes—
117#3757C2312yes—
118#3757C2312yes—
119#3757C2314yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123#3752C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126C4⋊(C3⋊Dic3)C2312yes—
127C4⋊(C3⋊Dic3)C2312yes—
128C4⋊(C3⋊Dic3)C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C4×C3⋊Dic3C2312yes—
137C4×C3⋊Dic3C2312yes—
138#3529—91noSylow
139C2×C3×#41C2×D314yes—
140C2×C3×#41C2×D314yescomplemented
141C2×#235—38no—
142C22×C4×D3—38no—
143C3×C4⋊Q8C2×D314yescomplemented
144C3×#127C2×D314yes—
145C3×#124C2×D314yes—
146C3×#124C2×D314yescomplemented
147C3×#121C2×D3116yescomplemented
148C3×C4×D4C2×D3116yescomplemented
149C2×C3×C42C2×D314yescomplemented
150#947—38no—
151#946—316no—
152#944—38no—
153#940—38no—
154#939—316no—
155#939—316no—
156#939—316no—
157#939—316no—
158#938—316no—
159#937—38no—
160#937—316no—
161#937—38no—
162#936—38no—
163#935—38no—
164#935—316no—
165#935—38no—
166#930—38no—
167#929—316no—
168C4×#67—316no—
169C4×#67—316no—
170C4×#67—316no—
171#926—38no—
172#924—38no—
173C2×C4×Dic3—38no—
174#898—316no—
175#896—316no—
176#894—316no—
177#889—316no—
178#886—316no—
179#885—316no—
180#884—316no—
181#883—316no—
182#882—316no—
183#879—316no—
184#878—316no—
185#878—316no—
186#876—316no—
187#875—38no—
188C4×D12—38no—
189#872—316no—
190#870—38no—
191C4×Dic6—38no—
192C23×C32C2412yes—
193C23×C32C2411yescharacteristic
194C23×C32C2412yes—
195C22×C3⋊D3—44no—
196C22×C3⋊D3—42no—
197C22×C3⋊D3C2414yes—
198C32×Q8—41no—
199C32×Q8—41no—
200C32×D4—44no—
201C32×D4—42no—
202C32×D4—42no—
203C32×D4—41no—
204C32×D4—41no—
205C2×C32×C4—24no—
206C2×C32×C4—24no—
207C2×C32×C4—22no—
208C2×C32×C4—42no—
209C2×C32×C4C2412yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2411yescharacteristic
212C2×C32×C4C2412yes—
213C2×C32×C4C2412yes—
214C2×C32×C4C2411yescharacteristic
215#638—44no—
216#638—44no—
217#638—44no—
218#638—44no—
219C2×C3⋊Dic3—42no—
220C2×C3⋊Dic3—44no—
221C2×C3⋊Dic3C2414yes—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2414yes—
224C4⋊(C3⋊D3)—42no—
225C4⋊(C3⋊D3)—42no—
226C4×C3⋊D3—28no—
227C4×C3⋊D3—44no—
228#634—42no—
229#634—42no—
230#563—92no—
231#563—91no—
232#562—92no—
233#562—94no—
234H(3,𝔽4)—91no—
235#560—92no—
236#560—94no—
237#532—92no—
238#532C3⋊D311yescharacteristic, complemented
239#529—94no—
240#529—92no—
241#525—92no—
242#525—94no—
243C23×D3—38no—
244C3×#41—48no—
245C3×#41—48no—
246C2×C3×Q8C22×D314yes—
247C2×C3×Q8C22×D314yes—
248C2×C3×D4C22×D314yes—
249C2×C3×D4C22×D318yes—
250C2×C3×D4C22×D3116yes—
251C2×C3×D4C22×D318yes—
252C2×C3×D4C22×D314yes—
253C22×C3×C4C22×D318yes—
254C22×C3×C4C22×D318yes—
255C22×C3×C4C22×D314yes—
256C22×C3×C4C22×D318yes—
257C2×#67—316no—
258C2×#67—316no—
259C2×#67—316no—
260C2×#67—316no—
261C22×Dic3—38no—
262C22×Dic3—316no—
263#235—1216no—
264C2×D12—38no—
265C2×D12—38no—
266C2×C4×D3—316no—
267C2×C4×D3—316no—
268C2×C4×D3—1216no—
269C2×Dic6—38no—
270C2×Dic6—38no—
271C3×C4⋊C4C22×D3116yes—
272C3×C22⋊C4C22×D3116yes—
273C3×C22⋊C4C22×D3116yes—
274C3×C42C22×D318yes—
275C3×C42C22×D314yes—
276C3×C42C22×D314yes—
277#217—316no—
278#217—316no—
279#217—38no—
280#217—38no—
281#217—316no—
282(C2×D3)⋊C4—316no—
283(C2×D3)⋊C4—316no—
284(C2×D3)⋊C4—316no—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288C4⋊Dic3—38no—
289C4⋊Dic3—38no—
290C4⋊Dic3—316no—
291Dic3⋊C4—316no—
292Dic3⋊C4—316no—
293Dic3⋊C4—316no—
294Dic3⋊C4—316no—
295Dic3⋊C4—316no—
296Dic3⋊C4—316no—
297C4×Dic3—316no—
298C4×Dic3—38no—
299C4×Dic3—38no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—21no—
303C22×C32—24no—
304C22×C32—22no—
305C22×C32—24no—
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—24no—
308C2×C3⋊D3—24no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—48no—
311C32×C4—22no—
312C32×C4—22no—
313C32×C4—21no—
314C32×C4—22no—
315C32×C4—22no—
316C32×C4H(5,𝔽2)12yes—
317C3⋊Dic3—24no—
318C3⋊Dic3—24no—
319C3⋊Dic3—24no—
320C2×#41—92no—
321C2×#41C2×C3⋊D311yescharacteristic
322C2×#41C2×C3⋊D311yescharacteristic, complemented
323C23×C4—92no—
324C4⋊Q8—92no—
325C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
326#127—92no—
327#127C2×C3⋊D311yescharacteristic
328#126—94no—
329#126—94no—
330#126—94no—
331#125—94no—
332#125—92no—
333#124—92no—
334#124—92no—
335#124—94no—
336#124—92no—
337#124C2×C3⋊D311yescharacteristic
338#124C2×C3⋊D311yescharacteristic, complemented
339#123—92no—
340#123—92no—
341#123—94no—
342#123—94no—
343#123—94no—
344#123—94no—
345#123—94no—
346C22⋊Q8—94no—
347C22⋊Q8—92no—
348C22⋊Q8—94no—
349C22⋊Q8—94no—
350C22⋊Q8—94no—
351#121—94no—
352#121—94no—
353#121—94no—
354#121—94no—
355#121—94no—
356#121—92no—
357#121—94no—
358#121C2×C3⋊D314yescomplemented
359#120—92no—
360#120—94no—
361#120—92no—
362#120—94no—
363C4×Q8—92no—
364C4×D4—94no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—92no—
368C4×D4C2×C3⋊D314yescomplemented
369#117—92no—
370#117—94no—
371C2×C42—92no—
372C2×C42C2×C3⋊D311yescharacteristic, complemented
373C23×C3C23×D318yes—
374C23×C3C23×D314yes—
375C23×C3C23×D318yes—
376C22×D3—316no—
377C22×D3—128no—
378C22×D3—1216no—
379C3×Q8—44no—
380C3×Q8—44no—
381C3×D4—416no—
382C3×D4—48no—
383C3×D4—48no—
384C3×D4—44no—
385C3×D4—44no—
386C2×C3×C4—216no—
387C2×C3×C4—216no—
388C2×C3×C4—28no—
389C2×C3×C4—48no—
390C2×C3×C4C23×D318yes—
391C2×C3×C4C23×D318yes—
392C2×C3×C4C23×D314yes—
393C2×C3×C4C23×D318yes—
394C2×C3×C4C23×D318yes—
395C2×C3×C4C23×D314yes—
396#67—1216no—
397#67—1216no—
398#67—1216no—
399#67—1216no—
400C2×Dic3—316no—
401C2×Dic3—316no—
402C2×Dic3—316no—
403C2×Dic3—128no—
404C2×Dic3—1216no—
405D12—128no—
406D12—128no—
407C4×D3—632no—
408C4×D3—1216no—
409Dic6—128no—
410Dic6—128no—
411C2×C32—42no—
412C2×C32—42no—
413C2×C32—41no—
414C2×C32C2×H(5,𝔽2)11yescharacteristic
415C2×C32#58512yes—
416C3⋊D3—44no—
417C24—92no—
418#41—42no—
419#41—42no—
420#41—364no—
421C2×Q8—92no—
422C2×Q8—92no—
423C2×Q8C22×C3⋊D311yescharacteristic
424C2×Q8C22×C3⋊D311yescharacteristic
425C2×D4—94no—
426C2×D4—94no—
427C2×D4—94no—
428C2×D4—94no—
429C2×D4—92no—
430C2×D4—92no—
431C2×D4C22×C3⋊D314yes—
432C2×D4C22×C3⋊D311yescharacteristic
433C2×D4C22×C3⋊D312yes—
434C2×D4C22×C3⋊D311yescharacteristic
435C2×D4C22×C3⋊D312yes—
436C22×C4—94no—
437C22×C4—92no—
438C22×C4—94no—
439C22×C4—94no—
440C22×C4—364no—
441C22×C4C22×C3⋊D312yes—
442C22×C4C22×C3⋊D311yescharacteristic
443C22×C4C22×C3⋊D312yes—
444C22×C4C22×C3⋊D312yes—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4—94no—
451C4⋊C4—92no—
452C4⋊C4—94no—
453C4⋊C4—92no—
454C4⋊C4C22×C3⋊D314yes—
455C22⋊C4—92no—
456C22⋊C4—92no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4C22×C3⋊D314yes—
467C22⋊C4C22×C3⋊D314yes—
468C42—92no—
469C42—92no—
470C42—94no—
471C42C22×C3⋊D311yescharacteristic
472C42C22×C3⋊D311yescharacteristic
473C42C22×C3⋊D312yes—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—24no—
477C22×C3—216no—
478C22×C3—28no—
479C22×C3—216no—
480C22×C3C24×D314yes—
481C2×D3—616no—
482C2×D3—616no—
483C2×D3—616no—
484C2×D3—1232no—
485C3×C4—28no—
486C3×C4—28no—
487C3×C4—24no—
488C3×C4—28no—
489C3×C4—28no—
490C3×C4#100418yes—
491Dic3—616no—
492Dic3—616no—
493Dic3—616no—
494C32#352911yescharacteristic, complemented, Sylow
495C23—94no—
496C23—362no—
497C23—364no—
498C23C23×C3⋊D312yes—
499C23C23×C3⋊D311yescharacteristic
500C23C23×C3⋊D312yes—
501Q8—41no—
502Q8—41no—
503Q8—362no—
504Q8—362no—
505D4—42no—
506D4—41no—
507D4—41no—
508D4—42no—
509D4—44no—
510D4—362no—
511D4—362no—
512D4—364no—
513D4—364no—
514D4—364no—
515D4—364no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—42no—
520C2×C4—94no—
521C2×C4—94no—
522C2×C4—94no—
523C2×C4—188no—
524C2×C4—364no—
525C2×C4—362no—
526C2×C4—364no—
527C2×C4C23×C3⋊D312yes—
528C2×C4C23×C3⋊D312yes—
529C2×C4C23×C3⋊D311yescharacteristic
530C2×C4C23×C3⋊D312yes—
531C2×C4C23×C3⋊D312yes—
532C2×C4C23×C3⋊D311yescharacteristic
533C2×C3—48no—
534C2×C3—48no—
535C2×C3—44no—
536C2×C3C2×#100414yes—
537C2×C3#596418yes—
538D3—1216no—
539C22—22no—
540C22—21no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—24no—
545C22—184no—
546C22—184no—
547C22—184no—
548C22—368no—
549C22C24×C3⋊D311yescharacteristic
550C4—22no—
551C4—21no—
552C4—22no—
553C4—22no—
554C4—22no—
555C4—184no—
556C4—184no—
557C4—184no—
558C4#6436112yes—
559C3#8624814yescomplemented
560C2—42no—
561C2—41no—
562C2—42no—
563C2—364no—
564C2C2×#6436111yescharacteristic
565C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#532C2
hypercenter#532C3⋊D3
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. #10596303C2semidirect
3. #10596299C2semidirect
4. #10596206C2semidirect
5. #10596191C2semidirect
6. #10596155C2semidirect
7. #10596154C2semidirect
8. #10596143C2semidirect
9. #10596092C2semidirect
10. #10596091C2semidirect
11. #10596018C2semidirect
12. #10596009C2semidirect
13. #10595950C2semidirect
16. C2×C32×#41C22semidirect
18. C22×C4×C3⋊D3C22semidirect
19. C32×C4⋊Q8C22semidirect
22. C32×#124C22semidirect
23. C32×#121C22semidirect
24. C32×C4×D4C22semidirect
25. C2×C32×C42C22semidirect
27. #64155C22semidirect
28. #64153C22semidirect
32. #64148C22semidirect
33. #64148C22semidirect
36. #64146C22semidirect
37. #64146C22semidirect
38. #64145C22semidirect
40. #64144C22semidirect
41. #64144C22semidirect
43. #64138C22semidirect
45. C4×#638C22semidirect
46. C4×#638C22semidirect
47. #64135C22semidirect
48. #64133C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
50. #64107C22semidirect
51. #64105C22semidirect
53. #64098C22semidirect
54. #64095C22semidirect
57. #64092C22semidirect
59. #64088C22semidirect
60. #64087C22semidirect
61. #64087C22semidirect
62. #64085C22semidirect
65. #64081C22semidirect
66. #64079C22semidirect
67. C4×#634C22semidirect
68. C3×#532D3semidirect
140. C2×C3×#41C2×D3semidirect
143. C3×C4⋊Q8C2×D3semidirect
146. C3×#124C2×D3semidirect
147. C3×#121C2×D3semidirect
148. C3×C4×D4C2×D3semidirect
149. C2×C3×C42C2×D3semidirect
238. #532C3⋊D3semidirect
322. C2×#41C2×C3⋊D3semidirect
325. C4⋊Q8C2×C3⋊D3semidirect
338. #124C2×C3⋊D3semidirect
358. #121C2×C3⋊D3semidirect
368. C4×D4C2×C3⋊D3semidirect
372. C2×C42C2×C3⋊D3semidirect
494. C32#3529semidirect
559. C3#86248semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
#105963032
#105962992
#105962062
#105961912
#105961552
#105961542
#105961432
#105960922
#105960912
#105960182
#105960092
#105959502
#862483