Subgroups — #11800509

Order 1152.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590234	C₂	1	2	yes	maximal, complemented
2	#10590132	C₂	1	1	yes	maximal, characteristic, complemented
3	#10590024	C₂	1	4	yes	maximal, complemented
4	#63797	—	2	2	no	—
5	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃×D₄₈	—	2	2	no	—
7	#63545	C₂²	1	4	yes	complemented
8	#63540	C₂²	1	2	yes	complemented
9	D₃×D₁₆	—	6	2	no	—
10	#3802	—	4	2	no	—
11	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
12	C₃×D₂₄	—	2	4	no	—
13	#3713	—	4	2	no	—
14	C₃²×C₁₆	D₄	1	1	yes	characteristic
15	C₃⋊(C₃⋊C₁₆)	C₂³	1	1	yes	characteristic
16	C₂×D₃₂	—	9	1	no	maximal, Sylow
17	D₃×D₈	—	6	4	no	—
18	C₃×D₁₆	—	6	2	no	—
19	#826	—	6	4	no	—
20	D₄₈	—	2	2	no	—
21	D₃×C₁₆	—	6	2	no	—
22	C₂×D₃²	—	8	2	no	—
23	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
24	C₃×D₁₂	—	4	4	no	—
25	#625	—	8	2	no	—
26	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
27	C₃⋊(C₃⋊C₈)	D₈	1	1	yes	characteristic
28	C₂×D₁₆	—	9	2	no	—
29	D₃₂	—	9	4	no	—
30	C₂×C₃₂	—	9	1	no	—
31	D₃×D₄	—	12	4	no	—
32	C₃×D₈	—	6	4	no	—
33	#213	—	12	4	no	—
34	D₂₄	—	2	4	no	—
35	D₃×C₈	—	6	2	no	—
36	C₃×C₁₆	—	2	2	no	—
37	C₃⋊C₁₆	—	6	2	no	—
38	C₂×C₃⋊D₃	D₁₆	1	1	yes	characteristic
39	C₂×C₃×D₃	—	8	4	no	—
40	D₃²	—	16	4	no	—
41	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
42	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
43	C₂×D₈	—	18	2	no	—
44	D₁₆	—	6	2	no	—
45	D₁₆	—	9	4	no	—
46	C₂×C₁₆	—	9	1	no	—
47	C₃₂	—	9	2	no	—
48	C₂²×D₃	—	24	4	no	—
49	C₃×D₄	—	12	4	no	—
50	#67	—	24	4	no	—
51	D₁₂	—	4	4	no	—
52	C₄×D₃	—	6	2	no	—
53	C₃×C₈	—	2	2	no	—
54	C₃⋊C₈	—	6	2	no	—
55	C₂×C₃²	C₂×D₁₆	1	1	yes	characteristic
56	C₃⋊D₃	D₃₂	1	2	yes	complemented
57	C₃×D₃	—	16	4	no	—
58	C₂×D₄	—	36	2	no	—
59	D₈	—	6	4	no	—
60	D₈	—	36	2	no	—
61	C₂×C₈	—	9	1	no	—
62	C₁₆	—	9	1	no	—
63	C₁₆	GO⁺(4,𝔽₂)	1	1	yes	characteristic
64	C₂²×C₃	—	24	4	no	—
65	C₂×D₃	—	6	2	no	—
66	C₂×D₃	—	8	4	no	—
67	C₂×D₃	—	48	8	no	—
68	C₃×C₄	—	2	2	no	—
69	Dic₃	—	6	2	no	—
70	C₃²	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	72	2	no	—
72	D₄	—	12	4	no	—
73	D₄	—	72	2	no	—
74	C₂×C₄	—	9	1	no	—
75	C₈	—	9	1	no	—
76	C₈	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	48	4	no	—
79	D₃	—	6	4	no	—
80	D₃	—	16	4	no	—
81	C₂²	—	9	1	no	—
82	C₂²	—	24	4	no	—
83	C₂²	—	144	4	no	—
84	C₄	—	9	1	no	—
85	C₄	#64225	1	1	yes	characteristic
86	C₃	—	2	2	no	—
87	C₂	—	9	2	no	—
88	C₂	—	48	4	no	—
89	C₂	#10593276	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10593276
commutator, cosocle	C₃⋊(C₃⋊C₁₆)	C₂³
Frattini	C₈	C₂×GO⁺(4,𝔽₂)
Fitting	C₃²×C₁₆	D₄
socle	C₂×C₃²	C₂×D₁₆
hypercenter	C₁₆	GO⁺(4,𝔽₂)
hypocenter	C₃²	C₂×D₃₂
LCS	G ▷ C₃⋊(C₃⋊C₁₆) ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
1. #10590234	C₂	semidirect
2. #10590132	C₂	semidirect
3. #10590024	C₂	semidirect
7. #63545	C₂²	semidirect
8. #63540	C₂²	semidirect
56. C₃⋊D₃	D₃₂	semidirect
70. C₃²	C₂×D₃₂	semidirect

Maximal subgroups

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

subgroup	index
#10590234	2
#10590132	2
#10590024	2
C₂×D₃₂	9