Subgroups — #15689290

Order 3008.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094069	C₂	1	1	yes	maximal, characteristic, complemented
2	#13094050	C₂	1	2	yes	maximal, complemented
3	#13093952	C₂	1	2	yes	maximal, complemented
4	#13093941	C₂	1	1	yes	maximal, characteristic, complemented
5	#127×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₄₇	—	2	2	no	—
7	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊D₄₇	—	2	2	no	—
10	#10625352	—	2	2	no	—
11	D₄×D₄₇	—	2	2	no	—
12	#10625350	C₂²	1	2	yes	—
13	C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
14	#10625335	—	2	2	no	—
15	#10625334	—	2	2	no	—
16	#10625329	C₂²	1	2	yes	complemented
17	C₂³×C₄₇	—	2	1	no	—
18	C₂³×C₄₇	D₄	1	2	yes	—
19	C₂²×D₄₇	—	2	2	no	—
20	D₄×C₄₇	—	2	2	no	—
21	D₄×C₄₇	—	2	2	no	—
22	D₄×C₄₇	—	4	4	no	—
23	C₂×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²⋊D₄₇	—	2	4	no	—
26	C₂²⋊D₄₇	—	2	2	no	—
27	C₂×Dic₄₇	—	2	2	no	—
28	D₁₈₈	D₄	1	2	yes	complemented
29	C₄×D₄₇	—	2	2	no	—
30	Dic₉₄	D₄	1	2	yes	complemented
31	C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇	—	2	2	no	—
33	C₂²×C₄₇	—	4	2	no	—
34	C₂²×C₄₇	—	4	2	no	—
35	C₂²×C₄₇	—	4	1	no	—
36	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×D₄₇	—	2	2	no	—
38	C₂×D₄₇	—	8	2	no	—
39	C₄×C₄₇	—	2	2	no	—
40	C₄×C₄₇	C₂×D₄	1	2	yes	—
41	Dic₄₇	—	2	2	no	—
42	C₂×C₄₇	—	2	1	no	—
43	C₂×C₄₇	—	4	2	no	—
44	C₂×C₄₇	—	8	1	no	—
45	C₂×C₄₇	#120	1	1	yes	characteristic
46	D₄₇	—	4	2	no	—
47	#453	—	47	1	no	maximal, Sylow
48	C₄₇	#453	1	1	yes	characteristic, complemented, Sylow
49	H(5,𝔽₂)	—	47	1	no	—
50	AGL(1,ℤ/8)	—	47	2	no	—
51	#127	D₄₇	1	1	yes	characteristic, complemented
52	#104	—	47	2	no	—
53	#100	—	47	1	no	—
54	#41	—	47	2	no	—
55	#41	—	94	2	no	—
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	94	2	no	—
58	C₂×D₄	—	94	2	no	—
59	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
60	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
61	SD₁₆	—	94	2	no	—
62	D₈	—	94	2	no	—
63	M₁₆	—	47	2	no	—
64	C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
65	C₂³	—	2	1	no	—
66	C₂³	—	94	2	no	—
67	C₂³	C₂²⋊D₄₇	1	2	yes	—
68	Q₈	—	47	2	no	—
69	D₄	—	2	2	no	—
70	D₄	—	2	2	no	—
71	D₄	—	4	4	no	—
72	D₄	—	47	2	no	—
73	D₄	—	94	4	no	—
74	D₄	—	94	2	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	94	2	no	—
77	C₂×C₄	—	94	2	no	—
78	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
79	C₈	—	94	2	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	94	2	no	—
85	C₂²	—	376	2	no	—
86	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	—	94	2	no	—
89	C₄	D₄×D₄₇	1	2	yes	—
90	C₂	—	2	1	no	—
91	C₂	—	4	2	no	—
92	C₂	—	8	1	no	—
93	C₂	—	188	2	no	—
94	C₂	#13093992	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093992
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#127×C₄₇	C₂
socle	C₂×C₄₇	#120
hypercenter	#127	D₄₇
hypocenter	C₄₇	#453
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #127

Complements

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

N	H ≅ G/N	type
1. #13094069	C₂	semidirect
2. #13094050	C₂	semidirect
3. #13093952	C₂	semidirect
4. #13093941	C₂	semidirect
5. #127×C₄₇	C₂	semidirect
8. C₂×D₄×C₄₇	C₂²	semidirect
13. C₄²×C₄₇	C₂²	semidirect
16. #10625329	C₂²	semidirect
28. D₁₈₈	D₄	semidirect
30. Dic₉₄	D₄	semidirect
48. C₄₇	#453	semidirect
51. #127	D₄₇	semidirect
60. C₂×D₄	C₂×D₄₇	semidirect
64. C₄²	C₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094069	2
#13094050	2
#13093952	2
#13093941	2
#127×C₄₇	2
#453	47