Subgroups — #15689296

Order 3008.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094049	C₂	1	2	yes	maximal, complemented
2	#13094013	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093951	C₂	1	2	yes	maximal, complemented
4	#13093943	C₂	1	1	yes	maximal, characteristic, complemented
5	2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₄₇	—	2	2	no	—
7	#41×C₄₇	—	2	2	no	—
8	#41×C₄₇	C₂²	1	2	yes	—
9	C₂×Q₈×C₄₇	—	2	2	no	—
10	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
12	#10625336	—	2	2	no	—
13	#10625334	—	2	2	no	—
14	(C₂×D₄₇)⋊C₄	—	2	2	no	—
15	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	#10625329	C₂²	1	2	yes	—
17	C₂²×D₄₇	—	2	1	no	—
18	Q₈×C₄₇	—	2	2	no	—
19	Q₈×C₄₇	—	2	2	no	—
20	Q₈×C₄₇	D₄	1	2	yes	—
21	D₄×C₄₇	—	2	2	no	—
22	D₄×C₄₇	—	2	2	no	—
23	D₄×C₄₇	D₄	1	2	yes	—
24	C₂×C₄×C₄₇	—	2	4	no	—
25	C₂×C₄×C₄₇	—	2	2	no	—
26	C₂×C₄×C₄₇	D₄	1	2	yes	—
27	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₄₇	—	2	1	no	—
29	D₁₈₈	—	2	2	no	—
30	C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇	—	2	2	no	—
32	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×D₄₇	—	4	2	no	—
34	C₂×D₄₇	—	4	1	no	—
35	C₄×C₄₇	—	2	2	no	—
36	C₄×C₄₇	—	2	2	no	—
37	C₄×C₄₇	C₂×D₄	1	2	yes	—
38	Dic₄₇	—	4	1	no	—
39	C₂×C₄₇	—	2	1	no	—
40	C₂×C₄₇	—	4	2	no	—
41	C₂×C₄₇	#120	1	1	yes	characteristic
42	D₄₇	—	8	1	no	—
43	#454	—	47	1	no	maximal, Sylow
44	C₄₇	#454	1	1	yes	characteristic, complemented, Sylow
45	2₋¹⁺⁴	D₄₇	1	1	yes	characteristic, complemented
46	AGL(1,ℤ/8)	—	47	2	no	—
47	#124	—	47	1	no	—
48	#104	—	47	2	no	—
49	#101	—	47	1	no	—
50	#41	—	2	2	no	—
51	#41	—	2	2	no	—
52	#41	C₂×D₄₇	1	2	yes	—
53	C₂×Q₈	—	2	2	no	—
54	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
55	C₂×D₄	—	47	1	no	—
56	SD₁₆	—	94	2	no	—
57	D₈	—	94	2	no	—
58	M₁₆	—	47	2	no	—
59	C₂²⋊C₄	—	94	2	no	—
60	C₄²	—	47	1	no	—
61	C₂³	—	94	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	2	2	no	—
64	Q₈	C₂²⋊D₄₇	1	2	yes	—
65	D₄	—	2	2	no	—
66	D₄	—	2	2	no	—
67	D₄	—	94	2	no	—
68	D₄	C₂²⋊D₄₇	1	2	yes	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	—	94	1	no	—
72	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
73	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
74	C₈	—	94	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	188	2	no	—
77	C₂²	—	188	1	no	—
78	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	188	1	no	—
82	C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	4	2	no	—
85	C₂	—	376	1	no	—
86	C₂	#13093993	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093993
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	2₋¹⁺⁴×C₄₇	C₂
socle	C₂×C₄₇	#120
hypercenter	2₋¹⁺⁴	D₄₇
hypocenter	C₄₇	#454
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #13094049	C₂	semidirect
2. #13094013	C₂	semidirect
3. #13093951	C₂	semidirect
4. #13093943	C₂	semidirect
5. 2₋¹⁺⁴×C₄₇	C₂	semidirect
44. C₄₇	#454	semidirect
45. 2₋¹⁺⁴	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094049	2
#13094013	2
#13093951	2
#13093943	2
2₋¹⁺⁴×C₄₇	2
#454	47