Subgroups — #11771321

Order 1152.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#322	C₂	1	1	yes	maximal, characteristic
2	#10588138	C₂	1	1	yes	maximal, characteristic
3	#10588138	C₂	1	1	yes	maximal, characteristic
4	#67442	—	3	1	no	maximal
5	C₄×C₈×C₉	C₄	1	2	yes	—
6	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₉⋊C₁₆	C₄	1	2	yes	—
8	C₂×C₉⋊C₁₆	C₄	1	2	yes	—
9	C₃×#322	D₃	1	1	yes	characteristic
10	#4461	—	3	1	no	—
11	#4461	—	3	1	no	—
12	C₂×C₈×C₉	—	2	2	no	—
13	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉⋊C₁₆	—	2	2	no	—
17	C₉⋊C₁₆	C₈	1	4	yes	complemented
18	#1313	—	9	1	no	Sylow
19	C₃×C₄×C₈	Dic₃	1	2	yes	—
20	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃⋊C₁₆	—	3	2	no	—
22	C₂×C₃⋊C₁₆	—	3	2	no	—
23	C₂×C₄×C₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₉	M₁₆	1	2	yes	—
25	C₈×C₉	—	4	2	no	—
26	C₈×C₉	C₂×C₈	1	2	yes	—
27	C₈×C₉	M₁₆	1	2	yes	—
28	#346	—	9	1	no	—
29	#346	—	9	1	no	—
30	#322	D₉	1	1	yes	characteristic
31	C₂×C₃×C₈	—	2	2	no	—
32	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
33	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
34	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
35	C₃⋊C₁₆	—	3	4	no	—
36	C₃⋊C₁₆	—	6	2	no	—
37	C₂²×C₉	#97	1	1	yes	characteristic
38	C₄×C₉	—	2	2	no	—
39	C₄×C₉	C₄×C₈	1	1	yes	characteristic
40	C₄×C₉	#97	1	1	yes	characteristic
41	C₂×C₁₆	—	9	2	no	—
42	C₂×C₁₆	—	9	2	no	—
43	C₄×C₈	Dic₉	1	2	yes	—
44	C₄×C₈	C₂×D₉	1	1	yes	characteristic
45	C₂×C₃×C₄	#208	1	2	yes	—
46	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
47	C₃×C₈	—	4	2	no	—
48	C₃×C₈	D₃×C₈	1	2	yes	—
49	C₃×C₈	ΓL(1,𝔽₂₅)	1	2	yes	—
50	C₂×C₉	#322	1	1	yes	characteristic
51	C₂×C₉	#347	1	2	yes	—
52	C₂×C₈	—	2	2	no	—
53	C₂×C₈	C₄×D₉	1	1	yes	characteristic
54	C₂×C₈	C₄×D₉	1	1	yes	characteristic
55	C₄²	C₂×Dic₉	1	1	yes	characteristic
56	C₁₆	—	9	4	no	—
57	C₁₆	—	18	2	no	—
58	C₂²×C₃	#803	1	1	yes	characteristic
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	C₈×Dic₃	1	1	yes	characteristic
61	C₃×C₄	#815	1	1	yes	characteristic
62	C₉	#1313	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄	#3667	1	2	yes	—
64	C₂×C₄	C₄×Dic₉	1	1	yes	characteristic
65	C₈	—	4	2	no	—
66	C₈	C₈×D₉	1	2	yes	—
67	C₈	#3663	1	2	yes	—
68	C₂×C₃	#4454	1	1	yes	characteristic
69	C₂×C₃	#4466	1	2	yes	—
70	C₂²	#63362	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	C₈×Dic₉	1	1	yes	characteristic
73	C₄	#63375	1	1	yes	characteristic
74	C₃	#67442	1	1	yes	characteristic
75	C₂	#10588131	1	1	yes	characteristic
76	C₂	#10588143	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₉
commutator	C₄×C₉	C₄×C₈
Frattini	C₃×C₄×C₈	C₂×D₃
Fitting	C₉×#322	C₂
socle, prime radical	C₂²×C₃	#803
cosocle	C₄×C₈×C₉	C₂²
hypercenter	#322	D₉
hypocenter	C₉	#1313
LCS	G ▷ C₄×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #322

Complements

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

N	H ≅ G/N	type
17. C₉⋊C₁₆	C₈	semidirect
62. C₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
C₉×#322	2
#10588138	2
#67442	3