Subgroups — #11771328

Order 1152.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590148	C₂	1	1	yes	maximal, characteristic
2	#10590148	C₂	1	1	yes	maximal, characteristic
3	#10589320	C₂	1	1	yes	maximal, characteristic
4	C₂×#3708	C₄	1	2	yes	—
5	C₂×#3708	C₄	1	2	yes	—
6	C₃²×C₄×C₈	C₄	1	1	yes	characteristic
7	C₄×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
8	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
9	#4454	—	6	2	no	—
10	C₂×C₃²×C₈	—	2	1	no	—
11	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃⋊(C₃⋊C₈)	—	2	1	no	—
13	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
15	#3708	—	2	2	no	—
16	#3708	C₈	1	4	yes	complemented
17	#1313	—	9	1	no	maximal, Sylow
18	C₃×C₄×C₈	—	2	2	no	—
19	C₄×C₃⋊C₈	—	6	2	no	—
20	C₄×C₃⋊C₈	—	6	2	no	—
21	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
22	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
23	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
24	C₃²×C₈	—	4	1	no	—
25	C₃⋊(C₃⋊C₈)	—	4	1	no	—
26	C₃⋊(C₃⋊C₈)	C₂×C₈	1	2	yes	—
27	C₃⋊(C₃⋊C₈)	M₁₆	1	2	yes	—
28	#346	—	9	1	no	—
29	#346	—	9	1	no	—
30	#322	—	9	1	no	—
31	C₂×C₃×C₈	—	2	4	no	—
32	C₃×C₄²	—	2	2	no	—
33	C₂×C₃⋊C₈	—	6	2	no	—
34	C₂×C₃⋊C₈	—	6	2	no	—
35	C₂×C₃⋊C₈	—	6	4	no	—
36	C₂²×C₃²	#97	1	1	yes	characteristic
37	C₃²×C₄	—	2	1	no	—
38	C₃²×C₄	—	2	1	no	—
39	C₃²×C₄	C₄×C₈	1	1	yes	characteristic
40	C₃²×C₄	#97	1	1	yes	characteristic
41	C₂×C₁₆	—	9	2	no	—
42	C₂×C₁₆	—	9	2	no	—
43	C₄×C₈	—	9	1	no	—
44	C₄×C₈	—	9	1	no	—
45	C₄×C₈	#157	1	1	yes	characteristic
46	C₂×C₃×C₄	—	2	2	no	—
47	C₂×C₃×C₄	—	2	2	no	—
48	C₂×C₃×C₄	—	2	2	no	—
49	C₃×C₈	—	4	4	no	—
50	C₃⋊C₈	—	6	4	no	—
51	C₃⋊C₈	—	6	4	no	—
52	C₃⋊C₈	—	12	4	no	—
53	C₂×C₃²	#322	1	1	yes	characteristic
54	C₂×C₃²	#347	1	1	yes	characteristic
55	C₂×C₃²	#347	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	9	1	no	—
58	C₂×C₈	—	9	1	no	—
59	C₂×C₈	—	18	1	no	—
60	C₄²	C₂×#157	1	1	yes	characteristic
61	C₁₆	—	9	4	no	—
62	C₁₆	—	18	2	no	—
63	C₂²×C₃	—	2	2	no	—
64	C₃×C₄	—	2	4	no	—
65	C₃×C₄	—	2	4	no	—
66	C₃×C₄	—	2	2	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃²	#1313	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₄	#3788	1	1	yes	characteristic
70	C₂×C₄	C₄×#157	1	1	yes	characteristic
71	C₂×C₄	#3792	1	1	yes	characteristic
72	C₈	—	4	1	no	—
73	C₈	—	9	2	no	—
74	C₈	—	9	2	no	—
75	C₈	—	36	1	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	2	2	no	—
79	C₂²	#63777	1	1	yes	characteristic
80	C₄	—	2	1	no	—
81	C₄	—	2	1	no	—
82	C₄	C₈×#157	1	1	yes	characteristic
83	C₄	#63767	1	1	yes	characteristic
84	C₃	—	2	2	no	—
85	C₂	#10590149	1	1	yes	characteristic
86	C₂	#10590169	1	1	yes	characteristic
87	C₂	#10590179	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#157
commutator	C₃²×C₄	C₄×C₈
Frattini	C₄²	C₂×#157
Fitting	C₃²×C₄×C₈	C₄
socle, prime radical	C₂²×C₃²	#97
cosocle	C₄×C₃⋊(C₃⋊C₈)	C₂²
hypercenter	C₄×C₈	#157
hypocenter	C₃²	#1313
LCS	G ▷ C₃²×C₄ ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
16. #3708	C₈	semidirect
68. C₃²	#1313	semidirect

Maximal subgroups

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

subgroup	index
#10590148	2
#10589320	2
#1313	9