Subgroups — #11772125

Order 1152.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593536	C₂	1	1	yes	maximal, characteristic
2	#10593253	C₂	1	1	yes	maximal, characteristic
3	#10590022	C₂	1	1	yes	maximal, characteristic
4	C₄⋊PSU(3,𝔽₂)	—	2	1	no	—
5	C₄⋊AGL(1,𝔽₉)	—	2	1	no	—
6	#63769	—	2	1	no	—
7	C₈×#157	C₂²	1	1	yes	characteristic
8	#63746	C₄	1	2	yes	—
9	#63542	—	2	1	no	—
10	C₂×PSU(3,𝔽₂)	—	4	1	no	—
11	C₂×AGL(1,𝔽₉)	—	4	1	no	—
12	C₄⋊#157	—	2	2	no	—
13	C₄×#157	D₄	1	1	yes	characteristic
14	#3787	C₂×C₄	1	1	yes	characteristic
15	#3777	—	4	1	no	—
16	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
17	C₃×C₃⋊C₁₆	—	4	1	no	—
18	#1364	—	9	1	no	maximal, Sylow
19	D₃×C₁₆	—	12	1	no	—
20	C₂×#157	—	4	2	no	—
21	C₂×#157	D₈	1	1	yes	characteristic
22	C₂×#157	SD₁₆	1	1	yes	characteristic
23	PSU(3,𝔽₂)	—	8	1	no	—
24	PSU(3,𝔽₂)	—	8	1	no	—
25	AGL(1,𝔽₉)	—	8	1	no	—
26	C₄×C₃⋊D₃	C₂²⋊C₄	1	1	yes	characteristic
27	#622	—	2	1	no	—
28	C₃²×C₈	SD₁₆	1	1	yes	characteristic
29	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
30	#500	—	9	1	no	—
31	C₄⋊C₁₆	—	9	1	no	—
32	#335	—	9	1	no	—
33	D₃×C₈	—	12	1	no	—
34	C₃×C₁₆	—	12	1	no	—
35	C₃⋊C₁₆	—	4	1	no	—
36	C₂×C₃⋊D₃	#102	1	1	yes	characteristic
37	#157	—	2	1	no	—
38	#157	—	8	2	no	—
39	#157	D₁₆	1	1	yes	characteristic
40	#157	SD₃₂	1	1	yes	characteristic
41	C₃²×C₄	#103	1	1	yes	characteristic
42	C₃⋊Dic₃	#101	1	1	yes	characteristic
43	C₄⋊Q₈	—	18	1	no	—
44	C₂×C₁₆	—	18	1	no	—
45	#107	—	9	2	no	—
46	#107	—	18	1	no	—
47	C₄⋊C₈	—	18	1	no	—
48	C₄×C₈	—	9	1	no	—
49	C₄×D₃	—	12	1	no	—
50	C₃×C₈	—	4	1	no	—
51	C₃⋊C₈	—	12	1	no	—
52	C₂×C₃²	#332	1	1	yes	characteristic
53	C₃⋊D₃	#357	1	1	yes	characteristic
54	C₃⋊D₃	#362	1	1	yes	characteristic
55	C₂×Q₈	—	36	1	no	—
56	C₂×C₈	—	9	1	no	—
57	C₂×C₈	—	9	1	no	—
58	C₂×C₈	—	36	1	no	—
59	C₄⋊C₄	—	18	2	no	—
60	C₄⋊C₄	—	36	1	no	—
61	C₄²	—	9	1	no	—
62	C₁₆	—	12	1	no	—
63	C₂×D₃	—	12	1	no	—
64	C₃×C₄	—	4	1	no	—
65	Dic₃	—	12	1	no	—
66	C₃²	#1364	1	1	yes	characteristic, complemented, Sylow
67	Q₈	—	72	1	no	—
68	Q₈	—	72	1	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₄	—	9	1	no	—
72	C₂×C₄	—	36	2	no	—
73	C₈	—	9	1	no	—
74	C₈	—	18	1	no	—
75	C₈	—	72	1	no	—
76	C₈	AΓL(1,𝔽₉)	1	1	yes	characteristic
77	C₂×C₃	—	4	1	no	—
78	D₃	—	12	1	no	—
79	D₃	—	12	1	no	—
80	C₂²	—	9	1	no	—
81	C₄	—	9	1	no	—
82	C₄	—	9	1	no	—
83	C₄	—	9	1	no	—
84	C₄	—	18	1	no	—
85	C₄	—	72	2	no	—
86	C₄	PSU(3,𝔽₂)⋊C₄	1	1	yes	characteristic
87	C₃	—	4	1	no	—
88	C₂	—	9	1	no	—
89	C₂	—	9	1	no	—
90	C₂	#10593157	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10593157
commutator	#3787	C₂×C₄
Frattini, hypercenter	C₈	AΓL(1,𝔽₉)
Fitting	C₃²×C₈	SD₁₆
socle	C₂×C₃²	#332
prime radical	C₂×C₃⋊D₃	#102
cosocle	C₈×#157	C₂²
hypocenter	C₃²	#1364
LCS	G ▷ #3787 ▷ C₄×C₃⋊D₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
66. C₃²	#1364	semidirect

Maximal subgroups

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

subgroup	index
#10593536	2
#10593253	2
#10590022	2
#1364	9