Subgroups — #15689512

Order 3008.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625325	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₇₆	C₂	1	2	yes	maximal, complemented
3	#13094021	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094012	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₈	—	2	2	no	—
7	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
8	C₂×D₁₈₈	C₂²	1	2	yes	—
9	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂²	1	2	yes	—
11	C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	(C₂×D₄₇)⋊C₄	—	2	2	no	—
13	D₃₇₆	—	2	4	no	—
14	#10625325	—	2	4	no	—
15	C₂²×D₄₇	—	2	1	no	—
16	C₂²×D₄₇	—	2	2	no	—
17	C₂×C₄×C₄₇	D₄	1	2	yes	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	—	2	1	no	—
20	D₁₈₈	—	2	2	no	—
21	D₁₈₈	—	2	2	no	—
22	D₁₈₈	—	2	2	no	—
23	D₁₈₈	—	4	4	no	—
24	Dic₉₄	—	2	2	no	—
25	C₈×C₄₇	D₄	1	4	yes	complemented
26	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄₇	—	4	2	no	—
28	C₂×D₄₇	—	4	1	no	—
29	C₂×D₄₇	—	4	4	no	—
30	C₂×D₄₇	—	4	2	no	—
31	C₄×C₄₇	—	2	2	no	—
32	C₄×C₄₇	C₂×D₄	1	2	yes	—
33	Dic₄₇	—	4	1	no	—
34	C₂×C₄₇	#127	1	1	yes	characteristic
35	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
36	D₄₇	—	8	2	no	—
37	D₄₇	—	8	1	no	—
38	#496	—	47	1	no	maximal, Sylow
39	C₄₇	#496	1	1	yes	characteristic, complemented, Sylow
40	C₂×SD₁₆	—	47	2	no	—
41	C₂×D₈	—	47	2	no	—
42	#127	—	47	1	no	—
43	#124	—	47	1	no	—
44	#97	D₄₇	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	47	1	no	—
46	C₂×D₄	—	47	1	no	—
47	C₂×D₄	—	47	2	no	—
48	C₂×D₄	—	94	2	no	—
49	SD₁₆	—	94	4	no	—
50	D₈	—	94	4	no	—
51	C₂×C₈	C₂×D₄₇	1	2	yes	—
52	C₂²⋊C₄	—	94	2	no	—
53	C₄²	C₂×D₄₇	1	1	yes	characteristic
54	C₂³	—	94	1	no	—
55	C₂³	—	94	2	no	—
56	Q₈	—	94	2	no	—
57	D₄	—	94	2	no	—
58	D₄	—	94	2	no	—
59	D₄	—	94	2	no	—
60	D₄	—	188	4	no	—
61	C₂×C₄	—	94	1	no	—
62	C₂×C₄	D₁₈₈	1	2	yes	—
63	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
64	C₈	D₁₈₈	1	4	yes	complemented
65	C₂²	—	188	1	no	—
66	C₂²	—	188	2	no	—
67	C₂²	—	188	4	no	—
68	C₂²	—	188	2	no	—
69	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	188	1	no	—
72	C₄	C₂×D₁₈₈	1	2	yes	—
73	C₂	—	376	2	no	—
74	C₂	—	376	1	no	—
75	C₂	#13094021	1	1	yes	characteristic
76	C₂	#13094052	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#97×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	#97	D₄₇
hypocenter	C₄₇	#496
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×#10625325	C₂	semidirect
2. C₂×D₃₇₆	C₂	semidirect
3. #13094021	C₂	semidirect
4. #13094012	C₂	semidirect
5. #97×C₄₇	C₂	semidirect
25. C₈×C₄₇	D₄	semidirect
39. C₄₇	#496	semidirect
44. #97	D₄₇	semidirect
64. 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×#10625325	2
C₂×D₃₇₆	2
#13094021	2
#13094012	2
#97×C₄₇	2
#496	47