Subgroups — #15689510

Order 3008.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625335	C₂	1	2	yes	maximal, complemented
2	C₂×#10625334	C₂	1	2	yes	maximal, complemented
3	#13094012	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093935	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	2	yes	—
8	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
10	C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	#10625335	—	2	4	no	—
12	#10625334	—	2	4	no	—
13	(C₂×D₄₇)⋊C₄	—	2	2	no	—
14	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₄₇	—	2	2	no	—
16	C₂²×D₄₇	—	2	1	no	—
17	D₄×C₄₇	—	2	2	no	—
18	D₄×C₄₇	—	2	2	no	—
19	D₄×C₄₇	—	4	4	no	—
20	C₂×C₄×C₄₇	D₄	1	2	yes	—
21	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₇	—	2	1	no	—
23	D₁₈₈	—	2	2	no	—
24	Dic₉₄	—	2	2	no	—
25	C₄₇⋊C₈	D₄	1	4	yes	complemented
26	C₂²×C₄₇	—	4	2	no	—
27	C₂²×C₄₇	—	4	4	no	—
28	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₄₇	—	4	1	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	—	8	2	no	—
35	C₂×C₄₇	#127	1	1	yes	characteristic
36	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
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	D₄₇	1	1	yes	characteristic, complemented
43	#124	—	47	1	no	—
44	#97	—	47	1	no	—
45	C₂×Q₈	—	47	1	no	—
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	—	47	1	no	—
48	C₂×D₄	C₂×D₄₇	1	2	yes	—
49	SD₁₆	—	94	4	no	—
50	D₈	—	94	4	no	—
51	C₂×C₈	—	47	2	no	—
52	C₂²⋊C₄	—	94	2	no	—
53	C₄²	C₂×D₄₇	1	1	yes	characteristic
54	C₂³	—	2	2	no	—
55	C₂³	—	94	1	no	—
56	Q₈	—	94	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	2	2	no	—
59	D₄	—	4	4	no	—
60	D₄	—	94	2	no	—
61	C₂×C₄	—	94	1	no	—
62	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
63	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
64	C₈	—	47	4	no	—
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	188	1	no	—
68	C₂²	—	188	2	no	—
69	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	188	1	no	—
72	C₄	D₄×D₄₇	1	2	yes	—
73	C₂	—	8	2	no	—
74	C₂	—	376	1	no	—
75	C₂	#13094020	1	1	yes	characteristic
76	C₂	#13094050	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#127×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	#127	D₄₇
hypocenter	C₄₇	#496
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10625335	C₂	semidirect
2. C₂×#10625334	C₂	semidirect
3. #13094012	C₂	semidirect
4. #13093935	C₂	semidirect
5. #127×C₄₇	C₂	semidirect
25. C₄₇⋊C₈	D₄	semidirect
39. C₄₇	#496	semidirect
42. #127	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625335	2
C₂×#10625334	2
#13094012	2
#13093935	2
#127×C₄₇	2
#496	47