Subgroups — #15688864

Order 3008.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094016	C₂	1	1	yes	maximal, characteristic
2	#13093935	C₂	1	1	yes	maximal, characteristic
3	#97×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₇	—	2	1	no	—
5	C₄²×C₄₇	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
7	C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
8	Dic₄₇⋊C₄	—	2	1	no	—
9	Dic₄₇⋊C₄	—	2	1	no	—
10	C₂×C₄₇⋊C₈	—	2	1	no	—
11	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂×Dic₄₇	—	2	1	no	—
15	C₂×Dic₄₇	—	2	1	no	—
16	C₈×C₄₇	—	2	2	no	—
17	C₄₇⋊C₈	—	2	2	no	—
18	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₇	—	2	1	no	—
20	C₄×C₄₇	—	2	1	no	—
21	C₄×C₄₇	—	2	1	no	—
22	Dic₄₇	—	4	1	no	—
23	Dic₄₇	—	4	1	no	—
24	C₂×C₄₇	#101	1	1	yes	characteristic
25	C₂×C₄₇	#104	1	1	yes	characteristic
26	C₂×C₄₇	#104	1	1	yes	characteristic
27	#330	—	47	1	no	maximal, Sylow
28	C₄₇	#330	1	1	yes	characteristic, complemented, Sylow
29	#125	—	47	1	no	—
30	#97	—	47	1	no	—
31	#97	D₄₇	1	1	yes	characteristic
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	94	1	no	—
34	C₄⋊C₄	—	47	1	no	—
35	C₄⋊C₄	—	47	1	no	—
36	C₄⋊C₄	—	94	1	no	—
37	C₄⋊C₄	—	94	1	no	—
38	C₄²	C₂×D₄₇	1	1	yes	characteristic
39	C₂×C₄	—	94	1	no	—
40	C₂×C₄	—	94	1	no	—
41	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
42	C₂×C₄	D₁₈₈	1	1	yes	characteristic
43	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₈	—	94	2	no	—
46	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	188	1	no	—
51	C₄	—	188	1	no	—
52	C₂	#13093942	1	1	yes	characteristic
53	C₂	#13093950	1	1	yes	characteristic
54	C₂	#13093952	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄
Frattini	C₄²	C₂×D₄₇
Fitting	#97×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂²
hypercenter	#97	D₄₇
hypocenter	C₄₇	#330
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
28. C₄₇	#330	semidirect

Maximal subgroups

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

subgroup	index
#13094016	2
#13093935	2
#97×C₄₇	2
#330	47