Subgroups — #11772705

Order 1152.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63625	C₂	1	1	yes	maximal, characteristic
2	#10590166	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₂×C₃²×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
6	#63625	—	2	2	no	—
7	#63540	—	2	2	no	—
8	C₂×#798	—	6	2	no	—
9	C₂×C₄×C₃⋊D₃	C₈	1	1	yes	characteristic
10	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
12	C₈×C₃⋊D₃	—	2	1	no	—
13	C₈×C₃⋊D₃	—	2	1	no	—
14	C₃²×C₁₆	—	2	1	no	—
15	C₃⋊(C₃⋊C₁₆)	D₄	1	2	yes	—
16	#1400	—	9	1	no	maximal, Sylow
17	C₂×D₃×C₈	—	6	2	no	—
18	C₂×C₃×C₁₆	—	2	2	no	—
19	C₂×C₃⋊C₁₆	—	6	2	no	—
20	#798	—	6	8	no	—
21	C₂²×C₃⋊D₃	C₁₆	1	1	yes	characteristic
22	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
23	C₂×C₃⋊Dic₃	C₁₆	1	1	yes	characteristic
24	C₄×C₃⋊D₃	—	2	1	no	—
25	C₄×C₃⋊D₃	—	2	1	no	—
26	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₃²×C₈	M₁₆	1	1	yes	characteristic
28	C₃⋊(C₃⋊C₈)	—	2	1	no	—
29	C₂×M₃₂	—	9	1	no	—
30	M₆₄	—	9	2	no	—
31	C₂×C₄×D₃	—	6	2	no	—
32	C₂×C₃×C₈	—	2	2	no	—
33	C₂×C₃⋊C₈	—	6	2	no	—
34	D₃×C₈	—	6	4	no	—
35	D₃×C₈	—	6	4	no	—
36	C₃×C₁₆	—	2	4	no	—
37	C₃⋊C₁₆	—	6	4	no	—
38	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
39	C₂×C₃⋊D₃	—	2	1	no	—
40	C₂×C₃⋊D₃	—	4	1	no	—
41	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
42	C₃²×C₄	M₃₂	1	1	yes	characteristic
43	C₃⋊Dic₃	—	2	1	no	—
44	C₂²×C₈	—	9	1	no	—
45	M₃₂	—	18	2	no	—
46	C₂×C₁₆	—	9	1	no	—
47	C₂×C₁₆	#157	1	1	yes	characteristic
48	C₃₂	—	18	2	no	—
49	C₂²×D₃	—	6	2	no	—
50	C₂×C₃×C₄	—	2	2	no	—
51	C₂×Dic₃	—	6	2	no	—
52	C₄×D₃	—	6	4	no	—
53	C₄×D₃	—	6	4	no	—
54	C₃×C₈	—	2	2	no	—
55	C₃×C₈	—	2	2	no	—
56	C₃⋊C₈	—	6	4	no	—
57	C₂×C₃²	—	2	1	no	—
58	C₂×C₃²	C₂²⋊C₁₆	1	1	yes	characteristic
59	C₃⋊D₃	—	4	1	no	—
60	C₂²×C₄	—	9	1	no	—
61	C₂×C₈	—	9	1	no	—
62	C₂×C₈	—	18	1	no	—
63	C₂×C₈	—	18	1	no	—
64	C₂×C₈	C₂×#157	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	9	2	no	—
67	C₂²×C₃	—	2	2	no	—
68	C₂×D₃	—	6	4	no	—
69	C₂×D₃	—	12	4	no	—
70	C₃×C₄	—	2	2	no	—
71	C₃×C₄	—	2	2	no	—
72	Dic₃	—	6	4	no	—
73	C₃²	#1400	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	9	1	no	—
75	C₂×C₄	—	9	1	no	—
76	C₂×C₄	—	18	1	no	—
77	C₂×C₄	—	18	1	no	—
78	C₂×C₄	#3787	1	1	yes	characteristic
79	C₈	—	18	1	no	—
80	C₈	#3788	1	1	yes	characteristic
81	C₈	C₂²⋊#157	1	1	yes	characteristic
82	C₂×C₃	—	2	4	no	—
83	C₂×C₃	—	2	2	no	—
84	D₃	—	12	4	no	—
85	C₂²	—	18	1	no	—
86	C₂²	—	36	1	no	—
87	C₂²	#63764	1	1	yes	characteristic
88	C₄	—	18	1	no	—
89	C₄	#63765	1	1	yes	characteristic
90	C₄	#63778	1	1	yes	characteristic
91	C₃	—	2	2	no	—
92	C₂	—	2	1	no	—
93	C₂	—	36	1	no	—
94	C₂	#10590176	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#157
commutator	C₂²×C₃²	C₂×C₁₆
Frattini	C₂×C₈	C₂×#157
Fitting	C₂×C₃²×C₁₆	C₄
socle	C₂×C₃²	C₂²⋊C₁₆
prime radical	C₂²×C₃⋊D₃	C₁₆
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypercenter	C₂×C₁₆	#157
hypocenter	C₃²	#1400
LCS	G ▷ C₂²×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #10590166	C₂	semidirect
73. C₃²	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63625	2
#10590166	2
#1400	9