Subgroups — #15689306

Order 3008.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094054	C₂	1	2	yes	maximal, complemented
2	#13094022	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
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×Dic₉₄	C₂²	1	1	yes	characteristic
12	#10625337	—	2	2	no	—
13	#10625335	—	2	2	no	—
14	Dic₄₇⋊C₄	—	2	2	no	—
15	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	#10625329	C₂²	1	2	yes	—
17	Q₈×C₄₇	—	2	2	no	—
18	Q₈×C₄₇	—	2	2	no	—
19	Q₈×C₄₇	D₄	1	2	yes	—
20	D₄×C₄₇	—	2	2	no	—
21	D₄×C₄₇	—	2	2	no	—
22	D₄×C₄₇	D₄	1	2	yes	—
23	C₂×C₄×C₄₇	—	2	4	no	—
24	C₂×C₄×C₄₇	—	2	2	no	—
25	C₂×C₄×C₄₇	D₄	1	2	yes	—
26	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₄₇	—	2	1	no	—
28	C₂×Dic₄₇	—	2	1	no	—
29	Dic₉₄	—	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	C₄×C₄₇	—	2	2	no	—
34	C₄×C₄₇	—	2	2	no	—
35	C₄×C₄₇	C₂×D₄	1	2	yes	—
36	Dic₄₇	—	2	2	no	—
37	Dic₄₇	—	4	1	no	—
38	C₂×C₄₇	—	2	1	no	—
39	C₂×C₄₇	—	4	2	no	—
40	C₂×C₄₇	#120	1	1	yes	characteristic
41	#456	—	47	1	no	maximal, Sylow
42	C₄₇	#456	1	1	yes	characteristic, complemented, Sylow
43	2₋¹⁺⁴	D₄₇	1	1	yes	characteristic
44	#137	—	47	2	no	—
45	C₄⋊Q₈	—	47	1	no	—
46	#104	—	47	2	no	—
47	#101	—	47	1	no	—
48	#41	—	2	2	no	—
49	#41	—	2	2	no	—
50	#41	C₂×D₄₇	1	2	yes	—
51	C₂×Q₈	—	2	2	no	—
52	C₂×Q₈	—	47	1	no	—
53	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
54	Q₁₆	—	94	2	no	—
55	SD₁₆	—	94	2	no	—
56	M₁₆	—	47	2	no	—
57	C₄⋊C₄	—	94	2	no	—
58	C₄²	—	47	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	94	2	no	—
62	Q₈	C₂²⋊D₄₇	1	2	yes	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	C₂²⋊D₄₇	1	2	yes	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	94	1	no	—
69	C₂×C₄	—	94	1	no	—
70	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
71	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
72	C₈	—	94	2	no	—
73	C₂²	—	2	2	no	—
74	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	2	no	—
77	C₄	—	94	2	no	—
78	C₄	—	188	1	no	—
79	C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	4	2	no	—
82	C₂	#13093993	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093993
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting, prime radical	2₋¹⁺⁴×C₄₇	C₂
socle	C₂×C₄₇	#120
hypercenter	2₋¹⁺⁴	D₄₇
hypocenter	C₄₇	#456
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. #13094054	C₂	semidirect
2. #13094022	C₂	semidirect
3. #13093951	C₂	semidirect
4. #13093943	C₂	semidirect
42. C₄₇	#456	semidirect

Maximal subgroups

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

subgroup	index
#13094054	2
#13094022	2
#13093951	2
#13093943	2
2₋¹⁺⁴×C₄₇	2
#456	47