Subgroups — #15689301

Order 3008.

152 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	#13094011	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093951	C₂	1	2	yes	maximal, complemented
4	#13093941	C₂	1	1	yes	maximal, characteristic, complemented
5	H(5,𝔽₂)×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#41×C₄₇	—	2	2	no	—
7	#41×C₄₇	C₂²	1	2	yes	—
8	C₂×D₄×C₄₇	—	2	2	no	—
9	C₂×D₄×C₄₇	—	2	2	no	—
10	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
12	C₂²⋊Dic₄₇	—	2	2	no	—
13	#10625337	—	2	2	no	—
14	#10625335	—	2	2	no	—
15	C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
16	#10625329	C₂²	1	2	yes	complemented
17	C₂³×C₄₇	—	2	2	no	—
18	C₂³×C₄₇	D₄	1	2	yes	—
19	Q₈×C₄₇	D₄	1	2	yes	—
20	D₄×C₄₇	—	2	4	no	—
21	D₄×C₄₇	—	2	2	no	—
22	D₄×C₄₇	—	2	2	no	—
23	D₄×C₄₇	D₄	1	2	yes	—
24	C₂×C₄×C₄₇	—	2	2	no	—
25	C₂×C₄×C₄₇	—	2	2	no	—
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	—	2	2	no	—
33	C₂²×C₄₇	—	4	2	no	—
34	C₂²×C₄₇	—	8	2	no	—
35	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₇	—	2	2	no	—
37	C₄×C₄₇	C₂×D₄	1	2	yes	—
38	Dic₄₇	—	4	1	no	—
39	Dic₄₇	—	4	1	no	—
40	C₂×C₄₇	—	2	1	no	—
41	C₂×C₄₇	—	4	2	no	—
42	C₂×C₄₇	—	4	2	no	—
43	C₂×C₄₇	#120	1	1	yes	characteristic
44	#455	—	47	1	no	maximal, Sylow
45	C₄₇	#455	1	1	yes	characteristic, complemented, Sylow
46	H(5,𝔽₂)	D₄₇	1	1	yes	characteristic
47	#137	—	47	2	no	—
48	#124	—	47	1	no	—
49	#104	—	47	2	no	—
50	#100	—	47	1	no	—
51	#41	—	2	2	no	—
52	#41	C₂×D₄₇	1	2	yes	—
53	C₂×Q₈	—	47	1	no	—
54	C₂×D₄	—	2	2	no	—
55	C₂×D₄	—	2	2	no	—
56	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
57	Q₁₆	—	94	2	no	—
58	SD₁₆	—	94	2	no	—
59	M₁₆	—	47	2	no	—
60	C₂²⋊C₄	—	94	2	no	—
61	C₄²	—	47	1	no	—
62	C₂³	—	2	2	no	—
63	C₂³	C₂²⋊D₄₇	1	2	yes	—
64	Q₈	—	94	2	no	—
65	Q₈	C₂²⋊D₄₇	1	2	yes	—
66	D₄	—	2	4	no	—
67	D₄	—	2	2	no	—
68	D₄	—	2	2	no	—
69	D₄	C₂²⋊D₄₇	1	2	yes	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	94	1	no	—
73	C₂×C₄	—	94	1	no	—
74	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
75	C₈	—	94	2	no	—
76	C₂²	—	2	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	—	4	2	no	—
79	C₂²	—	8	2	no	—
80	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	188	1	no	—
83	C₄	—	188	1	no	—
84	C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	4	2	no	—
87	C₂	—	4	2	no	—
88	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	H(5,𝔽₂)×C₄₇	C₂
socle	C₂×C₄₇	#120
hypercenter	H(5,𝔽₂)	D₄₇
hypocenter	C₄₇	#455
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. #13094054	C₂	semidirect
2. #13094011	C₂	semidirect
3. #13093951	C₂	semidirect
4. #13093941	C₂	semidirect
11. C₂×Dic₉₄	C₂²	semidirect
15. C₄×Dic₄₇	C₂²	semidirect
16. #10625329	C₂²	semidirect
45. C₄₇	#455	semidirect

Maximal subgroups

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

subgroup	index
#13094054	2
#13094011	2
#13093951	2
#13093941	2
H(5,𝔽₂)×C₄₇	2
#455	47