Subgroups — #15689489

Order 3008.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094021	C₂	1	1	yes	maximal, characteristic
2	#13093944	C₂	1	4	yes	maximal, complemented
3	#13093935	C₂	1	1	yes	maximal, characteristic, complemented
4	#125×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₈₈	—	2	2	no	—
6	C₂×D₁₈₈	C₂²	1	2	yes	—
7	C₄⋊C₄×C₄₇	—	2	2	no	—
8	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
11	C₂²×D₄₇	—	2	2	no	—
12	C₂×C₄×C₄₇	—	2	2	no	—
13	C₂×C₄×C₄₇	D₄	1	2	yes	—
14	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
15	D₁₈₈	—	2	4	no	—
16	D₁₈₈	—	4	4	no	—
17	C₄₇⋊C₈	—	2	2	no	—
18	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
19	C₂×D₄₇	—	4	2	no	—
20	C₂×D₄₇	—	4	4	no	—
21	C₄×C₄₇	—	2	2	no	—
22	C₄×C₄₇	—	4	2	no	—
23	C₄×C₄₇	#41	1	2	yes	—
24	C₂×C₄₇	#124	1	1	yes	characteristic
25	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
26	D₄₇	—	8	2	no	—
27	#490	—	47	1	no	maximal, Sylow
28	C₄₇	#490	1	1	yes	characteristic, complemented, Sylow
29	#127	—	47	1	no	—
30	#125	D₄₇	1	1	yes	characteristic, complemented
31	#102	—	47	4	no	—
32	#97	—	47	1	no	—
33	C₂×D₄	—	47	2	no	—
34	C₂×D₄	—	94	2	no	—
35	C₂×C₈	—	47	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
38	C₄²	C₂×D₄₇	1	1	yes	characteristic
39	C₂³	—	94	2	no	—
40	D₄	—	94	4	no	—
41	D₄	—	188	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
44	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
45	C₈	—	94	2	no	—
46	C₂²	—	188	2	no	—
47	C₂²	—	188	4	no	—
48	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	#10625354	1	2	yes	—
52	C₂	—	376	2	no	—
53	C₂	#13094013	1	1	yes	characteristic
54	C₂	#13094049	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#125×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	#13094021	C₂
hypercenter	#125	D₄₇
hypocenter	C₄₇	#490
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #13093944	C₂	semidirect
3. #13093935	C₂	semidirect
4. #125×C₄₇	C₂	semidirect
28. C₄₇	#490	semidirect
30. #125	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094021	2
#13093944	2
#13093935	2
#125×C₄₇	2
#490	47