Subgroups — #15689241

Order 3008.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094046	C₂	1	1	yes	maximal, characteristic
2	#13094030	C₂	1	2	yes	maximal, complemented
3	#13093960	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093952	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625350	C₂²	1	2	yes	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	#10625329	C₂²	1	2	yes	—
11	Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
12	D₃₇₆	C₄	1	1	yes	characteristic, complemented
13	#10625325	C₄	1	2	yes	complemented
14	#10625324	—	2	2	no	—
15	C₈×D₄₇	—	2	2	no	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²⋊D₄₇	—	2	2	no	—
19	D₁₈₈	C₂×C₄	1	2	yes	—
20	C₄×D₄₇	—	2	2	no	—
21	Dic₉₄	C₂×C₄	1	2	yes	—
22	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₄₇	D₄	1	1	yes	characteristic
25	C₈×C₄₇	D₄	1	1	yes	characteristic
26	C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇	#41	1	1	yes	characteristic
28	C₂×D₄₇	—	2	2	no	—
29	C₄×C₄₇	—	2	2	no	—
30	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
32	Dic₄₇	—	2	2	no	—
33	C₂×C₄₇	—	2	1	no	—
34	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
35	D₄₇	—	4	2	no	—
36	#443	—	47	1	no	maximal, Sylow
37	C₄₇	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	—	47	1	no	—
39	#131	—	47	2	no	—
40	#108	—	47	1	no	—
41	#104	—	47	2	no	—
42	C₄×C₈	D₄₇	1	1	yes	characteristic, complemented
43	#41	—	47	2	no	—
44	Q₁₆	—	47	1	no	—
45	SD₁₆	—	47	2	no	—
46	D₈	—	47	1	no	—
47	M₁₆	—	47	2	no	—
48	M₁₆	—	94	2	no	—
49	C₂×C₈	—	94	2	no	—
50	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
52	C₄²	C₂×D₄₇	1	1	yes	characteristic
53	Q₈	—	47	2	no	—
54	D₄	—	47	2	no	—
55	D₄	—	94	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	94	2	no	—
58	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
59	C₈	—	94	2	no	—
60	C₈	C₄×D₄₇	1	1	yes	characteristic
61	C₈	C₄×D₄₇	1	1	yes	characteristic
62	C₈	D₁₈₈	1	1	yes	characteristic
63	C₈	D₁₈₈	1	1	yes	characteristic
64	C₂²	—	94	2	no	—
65	C₂²	#10625350	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	94	2	no	—
68	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
69	C₄	C₂×D₁₈₈	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	188	2	no	—
72	C₂	C₄×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₈₈
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₄×C₈×C₄₇	C₂
socle	C₂×C₄₇	C₄×D₄
prime radical	#13094046	C₂
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	#443
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13094030	C₂	semidirect
3. #13093960	C₂	semidirect
4. #13093952	C₂	semidirect
5. C₄×C₈×C₄₇	C₂	semidirect
11. Dic₁₈₈	C₄	semidirect
12. D₃₇₆	C₄	semidirect
13. #10625325	C₄	semidirect
37. C₄₇	#443	semidirect
42. C₄×C₈	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094046	2
#13094030	2
#13093960	2
#13093952	2
C₄×C₈×C₄₇	2
#443	47