Subgroups — #15689377

Order 3008.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093999	C₂	1	2	yes	maximal, complemented
4	#13093944	C₂	1	2	yes	maximal, complemented
5	#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₈	—	2	2	no	—
7	C₂×D₁₈₈	C₂²	1	2	yes	—
8	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
11	(C₂×D₄₇)⋊C₄	—	2	2	no	—
12	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	D₃₇₆	—	2	2	no	—
14	#10625324	—	2	2	no	—
15	C₂²×D₄₇	—	2	2	no	—
16	C₂²×D₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	D₄	1	1	yes	characteristic
20	D₁₈₈	—	2	2	no	—
21	D₁₈₈	—	2	2	no	—
22	D₁₈₈	—	4	4	no	—
23	C₄×D₄₇	—	2	1	no	—
24	C₄×D₄₇	—	2	1	no	—
25	C₈×C₄₇	D₄	1	2	yes	complemented
26	C₄₇⋊C₈	—	2	1	no	—
27	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂×D₄₇	—	2	1	no	—
29	C₂×D₄₇	—	2	2	no	—
30	C₂×D₄₇	—	4	2	no	—
31	C₂×D₄₇	—	4	2	no	—
32	C₂×D₄₇	—	4	2	no	—
33	C₄×C₄₇	—	4	2	no	—
34	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₄×C₄₇	#41	1	1	yes	characteristic
36	Dic₄₇	—	2	1	no	—
37	C₂×C₄₇	#121	1	1	yes	characteristic
38	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
39	D₄₇	—	4	1	no	—
40	D₄₇	—	8	2	no	—
41	#469	—	47	1	no	maximal, Sylow
42	C₄₇	#469	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₈	—	47	1	no	—
44	C₂×M₁₆	—	47	1	no	—
45	#121	—	47	2	no	—
46	#106	D₄₇	1	1	yes	characteristic, complemented
47	#102	—	47	2	no	—
48	C₂×D₄	—	47	2	no	—
49	C₂×D₄	—	94	2	no	—
50	C₂²×C₄	—	47	1	no	—
51	D₈	—	94	2	no	—
52	M₁₆	—	94	2	no	—
53	C₂×C₈	—	47	1	no	—
54	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
56	C₂²⋊C₄	—	94	2	no	—
57	C₂³	—	47	1	no	—
58	C₂³	—	94	2	no	—
59	D₄	—	94	2	no	—
60	D₄	—	94	2	no	—
61	D₄	—	188	4	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	47	1	no	—
64	C₂×C₄	—	94	1	no	—
65	C₂×C₄	—	94	1	no	—
66	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
67	C₈	—	94	1	no	—
68	C₈	D₁₈₈	1	2	yes	complemented
69	C₂²	—	94	1	no	—
70	C₂²	—	94	2	no	—
71	C₂²	—	188	2	no	—
72	C₂²	—	188	2	no	—
73	C₂²	—	188	2	no	—
74	C₂²	D₄×D₄₇	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	94	1	no	—
77	C₄	C₂×D₁₈₈	1	1	yes	characteristic
78	C₄	#10625354	1	1	yes	characteristic
79	C₂	—	376	2	no	—
80	C₂	—	188	1	no	—
81	C₂	#13093999	1	1	yes	characteristic
82	C₂	#13094051	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#106×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	#106	D₄₇
hypocenter	C₄₇	#469
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₇₆	C₂	semidirect
2. C₂×#10625324	C₂	semidirect
3. #13093999	C₂	semidirect
4. #13093944	C₂	semidirect
5. #106×C₄₇	C₂	semidirect
25. C₈×C₄₇	D₄	semidirect
42. C₄₇	#469	semidirect
46. #106	D₄₇	semidirect
68. C₈	D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₇₆	2
C₂×#10625324	2
#13093999	2
#13093944	2
#106×C₄₇	2
#469	47