Subgroups — #11771327

Order 1152.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590175	C₂	1	1	yes	maximal, characteristic
2	#10590168	C₂	1	1	yes	maximal, characteristic
3	#10589368	C₂	1	1	yes	maximal, characteristic
4	C₄×#622	C₄	1	2	yes	—
5	C₂×#3708	C₄	1	2	yes	—
6	C₂×C₃²×C₁₆	C₄	1	1	yes	characteristic
7	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
9	#4502	—	6	2	no	—
10	C₂×#622	—	2	2	no	—
11	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
12	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
14	#3708	—	2	2	no	—
15	C₃²×C₁₆	C₈	1	2	yes	complemented
16	C₃⋊(C₃⋊C₁₆)	C₈	1	2	yes	complemented
17	#1313	—	9	1	no	maximal, Sylow
18	C₂×C₃×C₁₆	—	2	2	no	—
19	C₈×Dic₃	—	6	2	no	—
20	C₂×C₃⋊C₁₆	—	6	2	no	—
21	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
22	C₂×C₃⋊Dic₃	M₁₆	1	2	yes	—
23	#622	—	4	2	no	—
24	C₃²×C₈	C₂×C₈	1	1	yes	characteristic
25	C₃²×C₈	C₂×C₈	1	1	yes	characteristic
26	C₃⋊(C₃⋊C₈)	M₁₆	1	2	yes	—
27	#346	—	9	1	no	—
28	#346	—	9	1	no	—
29	#322	—	9	1	no	—
30	C₂×C₃×C₈	—	2	2	no	—
31	C₄×Dic₃	—	6	2	no	—
32	C₂×C₃⋊C₈	—	6	2	no	—
33	C₃×C₁₆	—	2	4	no	—
34	C₃⋊C₁₆	—	6	4	no	—
35	C₂²×C₃²	#97	1	1	yes	characteristic
36	C₃²×C₄	C₄×C₈	1	1	yes	characteristic
37	C₃²×C₄	#97	1	1	yes	characteristic
38	C₃⋊Dic₃	—	2	2	no	—
39	C₂×C₁₆	—	9	1	no	—
40	C₂×C₁₆	—	9	2	no	—
41	C₂×C₁₆	#157	1	1	yes	characteristic
42	C₄×C₈	—	9	1	no	—
43	C₄×C₈	—	9	2	no	—
44	C₂×C₃×C₄	—	2	2	no	—
45	C₂×Dic₃	—	6	4	no	—
46	C₃×C₈	—	2	2	no	—
47	C₃×C₈	—	2	2	no	—
48	C₃⋊C₈	—	6	4	no	—
49	C₂×C₃²	#322	1	1	yes	characteristic
50	C₂×C₃²	#347	1	2	yes	—
51	C₂×C₈	—	9	1	no	—
52	C₂×C₈	—	18	2	no	—
53	C₂×C₈	C₂×#157	1	1	yes	characteristic
54	C₄²	—	9	1	no	—
55	C₁₆	—	9	2	no	—
56	C₁₆	—	18	2	no	—
57	C₁₆	#622	1	2	yes	complemented
58	C₂²×C₃	—	2	2	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	2	2	no	—
61	Dic₃	—	12	4	no	—
62	C₃²	#1313	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄	—	9	2	no	—
64	C₂×C₄	C₄×#157	1	1	yes	characteristic
65	C₈	—	9	2	no	—
66	C₈	—	36	2	no	—
67	C₈	#3787	1	1	yes	characteristic
68	C₈	C₂×#622	1	1	yes	characteristic
69	C₂×C₃	—	2	4	no	—
70	C₂×C₃	—	2	2	no	—
71	C₂²	#63767	1	1	yes	characteristic
72	C₄	—	18	2	no	—
73	C₄	#63767	1	1	yes	characteristic
74	C₄	C₄×#622	1	1	yes	characteristic
75	C₃	—	2	2	no	—
76	C₂	#10590136	1	2	yes	—
77	C₂	#10590168	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#157
commutator	C₃²×C₄	C₄×C₈
Frattini	C₂×C₈	C₂×#157
Fitting	C₂×C₃²×C₁₆	C₄
socle, prime radical	C₂²×C₃²	#97
cosocle	C₈×C₃⋊Dic₃	C₂²
hypercenter	C₂×C₁₆	#157
hypocenter	C₃²	#1313
LCS	G ▷ C₃²×C₄ ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₃²×C₁₆	C₈	semidirect
16. C₃⋊(C₃⋊C₁₆)	C₈	semidirect
57. C₁₆	#622	semidirect
62. C₃²	#1313	semidirect

Maximal subgroups

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

subgroup	index
#10590175	2
#10590168	2
#10589368	2
#1313	9