Subgroups — #26103991

Order 12032.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688953	C₂	1	2	yes	maximal
2	C₂×C₄₇×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093960	—	2	2	no	—
4	#15688953	—	2	2	no	—
5	#15688953	C₄	1	4	yes	—
6	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
7	C₄₇×M₆₄	—	2	2	no	—
8	C₂×C₃₂×C₄₇	C₄	1	2	yes	—
9	C₂×#10625329	—	4	2	no	—
10	#13093960	—	2	4	no	—
11	#13093960	—	4	2	no	—
12	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	—
15	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
16	C₂×C₁₆×C₄₇	Q₈	1	1	yes	characteristic
17	C₃₂×C₄₇	—	2	2	no	—
18	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	SD₁₆	1	2	yes	—
22	C₂×C₈×C₄₇	Q₁₆	1	1	yes	characteristic
23	#10625329	—	4	4	no	—
24	#10625329	—	8	2	no	—
25	C₂×C₄₇⋊C₈	—	8	2	no	—
26	C₁₆×C₄₇	C₄²	1	1	yes	characteristic
27	C₁₆×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂³×C₄₇	Q₃₂	1	1	yes	characteristic
30	C₂×C₄×C₄₇	#102	1	2	yes	—
31	C₂×C₄×C₄₇	#107	1	1	yes	characteristic
32	C₂×C₄×C₄₇	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₄₇	SD₃₂	1	2	yes	—
34	C₈×C₄₇	#95	1	1	yes	characteristic
35	C₈×C₄₇	#103	1	2	yes	—
36	C₈×C₄₇	#106	1	1	yes	characteristic
37	C₄₇⋊C₈	—	8	4	no	—
38	#7476	—	47	1	no	maximal, Sylow
39	C₂²×C₄₇	—	4	1	no	—
40	C₂²×C₄₇	#358	1	2	yes	—
41	C₂²×C₄₇	#366	1	1	yes	characteristic
42	C₄×C₄₇	#340	1	1	yes	characteristic
43	C₄×C₄₇	#357	1	2	yes	—
44	C₄×C₄₇	#367	1	1	yes	characteristic
45	C₂×M₆₄	D₄₇	1	1	yes	characteristic
46	C₂×#368	—	47	2	no	—
47	C₂×C₄₇	—	2	2	no	—
48	C₂×C₄₇	—	2	1	no	—
49	C₂×C₄₇	#1380	1	1	yes	characteristic
50	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
51	C₂×#108	—	94	2	no	—
52	M₆₄	—	2	2	no	—
53	C₂×C₃₂	Dic₄₇	1	2	yes	—
54	#368	—	47	4	no	—
55	#368	—	94	2	no	—
56	C₄₇	#7476	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	188	2	no	—
58	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
59	C₂×C₁₆	Dic₉₄	1	1	yes	characteristic
60	C₂×C₁₆	C₄×D₄₇	1	2	yes	—
61	C₂×C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
62	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
63	#108	—	94	4	no	—
64	#108	—	188	2	no	—
65	C₃₂	—	2	2	no	—
66	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
67	M₁₆	—	376	2	no	—
68	M₁₆	—	188	4	no	—
69	C₂×C₈	—	376	2	no	—
70	C₂×C₈	#10625325	1	2	yes	—
71	C₂×C₈	Dic₁₈₈	1	1	yes	characteristic
72	C₂×C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
73	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
74	C₁₆	C₄×Dic₄₇	1	1	yes	characteristic
75	C₁₆	Dic₄₇⋊C₄	1	2	yes	—
76	C₁₆	C₂²⋊Dic₄₇	1	1	yes	characteristic
77	C₂³	Dic₃₇₆	1	1	yes	characteristic
78	C₂×C₄	#13093946	1	2	yes	—
79	C₂×C₄	#13093958	1	1	yes	characteristic
80	C₂×C₄	D₇₅₂	1	1	yes	characteristic
81	C₂×C₄	#13093969	1	2	yes	—
82	C₈	—	376	4	no	—
83	C₈	C₄₇⋊#95	1	1	yes	characteristic
84	C₈	#13093949	1	2	yes	—
85	C₈	#13093956	1	1	yes	characteristic
86	C₂²	—	4	1	no	—
87	C₂²	#15688928	1	2	yes	—
88	C₂²	#15688949	1	1	yes	characteristic
89	C₄	#15688886	1	1	yes	characteristic
90	C₄	#15688925	1	2	yes	—
91	C₄	#15688951	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	—	2	1	no	—
94	C₂	#20241480	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688951
commutator	C₁₆×C₄₇	C₄²
Frattini	C₂²×C₁₆	C₂×D₄₇
Fitting	C₂×C₄₇×M₆₄	C₂
socle	C₂×C₄₇	#1380
prime radical	C₂³×C₄₇	Q₃₂
cosocle	C₂²×C₁₆×C₄₇	C₂²
hypercenter	C₂×M₆₄	D₄₇
hypocenter	C₄₇	#7476
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
56. C₄₇	#7476	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688953	2
C₂×C₄₇×M₆₄	2
#7476	47