Subgroups — #15689202

Order 3008.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625324	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₄₇)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₇	C₂²	1	2	yes	—
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
12	C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#10625324	—	2	4	no	—
15	C₂²×D₄₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
20	D₁₈₈	—	2	2	no	—
21	C₄×D₄₇	—	2	2	no	—
22	C₄×D₄₇	—	2	2	no	—
23	C₈×C₄₇	—	2	1	no	—
24	C₈×C₄₇	D₄	1	2	yes	complemented
25	C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₇	—	2	2	no	—
28	C₂×D₄₇	—	2	2	no	—
29	C₂×D₄₇	—	2	2	no	—
30	C₄×C₄₇	—	2	1	no	—
31	C₄×C₄₇	M₁₆	1	2	yes	complemented
32	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₇	#41	1	1	yes	characteristic
34	Dic₄₇	—	2	2	no	—
35	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
36	C₂×C₄₇	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₄₇	#131	1	1	yes	characteristic
38	D₄₇	—	4	2	no	—
39	#436	—	47	1	no	maximal, Sylow
40	C₄₇	#436	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	47	2	no	—
42	C₄×D₄	—	47	1	no	—
43	C₄⋊C₈	—	47	1	no	—
44	C₂²⋊C₈	—	47	2	no	—
45	C₄×C₈	D₄₇	1	1	yes	characteristic, complemented
46	C₂×D₄	—	47	1	no	—
47	C₂²×C₄	—	47	2	no	—
48	M₁₆	—	94	4	no	—
49	C₂×C₈	—	47	2	no	—
50	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
52	C₄⋊C₄	—	47	1	no	—
53	C₂²⋊C₄	—	47	2	no	—
54	C₄²	C₂×D₄₇	1	1	yes	characteristic
55	C₂³	—	47	2	no	—
56	D₄	—	94	2	no	—
57	C₂×C₄	—	47	2	no	—
58	C₂×C₄	—	94	2	no	—
59	C₂×C₄	—	94	2	no	—
60	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
61	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	94	2	no	—
65	C₈	D₁₈₈	1	2	yes	complemented
66	C₂²	—	94	2	no	—
67	C₂²	—	94	2	no	—
68	C₂²	—	94	2	no	—
69	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	94	2	no	—
72	C₄	#10625324	1	2	yes	complemented
73	C₄	C₂×D₁₈₈	1	1	yes	characteristic
74	C₄	#10625350	1	1	yes	characteristic
75	C₂	—	188	2	no	—
76	C₂	C₄×D₁₈₈	1	1	yes	characteristic
77	C₂	C₂×#10625324	1	1	yes	characteristic
78	C₂	#13094030	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₄
Fitting	C₄×C₈×C₄₇	C₂
prime radical	C₂×D₁₈₈	C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	#436
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10625324	C₂	semidirect
3. C₄⋊(C₄₇⋊C₈)	C₂	semidirect
4. (C₂×D₄₇)⋊C₈	C₂	semidirect
5. C₄×C₈×C₄₇	C₂	semidirect
24. C₈×C₄₇	D₄	semidirect
31. C₄×C₄₇	M₁₆	semidirect
40. C₄₇	#436	semidirect
45. C₄×C₈	D₄₇	semidirect
65. C₈	D₁₈₈	semidirect
72. C₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625324	2
C₄×D₁₈₈	2
C₄⋊(C₄₇⋊C₈)	2
(C₂×D₄₇)⋊C₈	2
C₄×C₈×C₄₇	2
#436	47