Subgroups — #11772229

Order 1152.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590174	C₂	1	1	yes	maximal, characteristic
2	#10590173	C₂	1	2	yes	maximal
3	C₄⋊#622	—	2	2	no	—
4	C₂×#3708	C₄	1	1	yes	characteristic
5	C₂×#3708	C₄	1	1	yes	characteristic
6	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	C₂×#622	—	4	2	no	—
8	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
9	C₄×C₃⋊Dic₃	D₄	1	1	yes	characteristic
10	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
11	#3708	—	2	1	no	—
12	#3708	C₈	1	2	yes	complemented
13	#1371	—	9	1	no	maximal, Sylow
14	C₈×Dic₃	—	12	1	no	—
15	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₃⋊Dic₃	D₈	1	1	yes	characteristic
17	C₂×C₃⋊Dic₃	Q₁₆	1	1	yes	characteristic
18	#622	—	8	2	no	—
19	C₃²×C₈	—	2	1	no	—
20	C₃⋊(C₃⋊C₈)	C₂×C₈	1	1	yes	characteristic
21	C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
22	C₄×C₁₆	—	9	1	no	—
23	#335	—	9	2	no	—
24	C₂×C₃×C₈	—	4	1	no	—
25	C₄×Dic₃	—	12	1	no	—
26	C₂×C₃⋊C₈	—	12	1	no	—
27	C₂²×C₃²	#107	1	1	yes	characteristic
28	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
29	C₃²×C₄	#108	1	1	yes	characteristic
30	C₃⋊Dic₃	—	2	1	no	—
31	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
32	C₃⋊Dic₃	Q₃₂	1	1	yes	characteristic
33	C₂×C₁₆	—	9	1	no	—
34	C₂×C₁₆	—	9	1	no	—
35	C₄⋊C₈	—	18	2	no	—
36	C₄×C₈	—	9	1	no	—
37	C₂×C₃×C₄	—	4	1	no	—
38	C₂×Dic₃	—	12	1	no	—
39	C₂×Dic₃	—	12	1	no	—
40	C₃×C₈	—	4	2	no	—
41	C₃⋊C₈	—	12	1	no	—
42	C₃⋊C₈	—	12	1	no	—
43	C₂×C₃²	#335	1	1	yes	characteristic
44	C₂×C₃²	#366	1	1	yes	characteristic
45	C₂×C₃²	#368	1	1	yes	characteristic
46	C₂×C₈	—	9	1	no	—
47	C₂×C₈	—	36	2	no	—
48	C₂×C₈	PSU(3,𝔽₂)	1	1	yes	characteristic
49	C₄²	—	9	1	no	—
50	C₁₆	—	9	2	no	—
51	C₁₆	—	18	1	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₃×C₄	—	4	1	no	—
54	C₃×C₄	—	4	1	no	—
55	Dic₃	—	12	1	no	—
56	Dic₃	—	12	1	no	—
57	Dic₃	—	12	2	no	—
58	C₃²	#1371	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄	—	9	1	no	—
60	C₂×C₄	—	9	1	no	—
61	C₂×C₄	#3777	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	—	9	1	no	—
64	C₈	—	9	1	no	—
65	C₈	—	72	2	no	—
66	C₂×C₃	—	4	1	no	—
67	C₂×C₃	—	4	1	no	—
68	C₂×C₃	—	4	1	no	—
69	C₂²	#63746	1	1	yes	characteristic
70	C₄	—	9	1	no	—
71	C₄	—	9	1	no	—
72	C₄	—	18	1	no	—
73	C₄	#63744	1	1	yes	characteristic
74	C₄	#63748	1	1	yes	characteristic
75	C₃	—	4	1	no	—
76	C₂	#10590085	1	1	yes	characteristic
77	C₂	#10590087	1	1	yes	characteristic
78	C₂	#10590089	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63746
commutator	C₃⋊(C₃⋊C₈)	C₂×C₈
Frattini, hypercenter	C₂×C₈	PSU(3,𝔽₂)
Fitting	C₂×C₃²×C₈	Q₈
socle, prime radical	C₂²×C₃²	#107
cosocle	C₈×C₃⋊Dic₃	C₂²
hypocenter	C₃²	#1371
LCS	G ▷ C₃⋊(C₃⋊C₈) ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
12. #3708	C₈	semidirect
58. C₃²	#1371	semidirect

Maximal subgroups

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

subgroup	index
#10590174	2
#10590173	2
#1371	9