Subgroups — #15689240

Order 3008.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094031	C₂	1	2	yes	maximal, complemented
2	#13093960	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093951	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#41×C₄₇	C₂²	1	2	yes	—
7	Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₄₇	C₄	1	2	yes	complemented
9	D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	#10625329	—	2	2	no	—
13	#10625329	C₂²	1	2	yes	—
14	C₂×C₄₇⋊C₈	—	2	2	no	—
15	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₄₇	C₂×C₄	1	2	yes	—
17	D₄×C₄₇	—	2	2	no	—
18	D₄×C₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₇	—	2	2	no	—
20	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₇	—	2	1	no	—
22	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₄₇⋊C₈	—	2	2	no	—
25	C₄₇⋊C₈	D₄	1	1	yes	characteristic
26	C₄₇⋊C₈	D₄	1	1	yes	characteristic
27	C₂²×C₄₇	—	2	2	no	—
28	C₂²×C₄₇	#41	1	1	yes	characteristic
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	—	4	2	no	—
35	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
36	#443	—	47	1	no	maximal, Sylow
37	C₄₇	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	D₄₇	1	1	yes	characteristic
39	#131	—	47	2	no	—
40	#108	—	47	1	no	—
41	#104	—	47	2	no	—
42	C₄×C₈	—	47	1	no	—
43	#41	C₂×D₄₇	1	2	yes	—
44	Q₁₆	Dic₄₇	1	1	yes	characteristic, complemented
45	SD₁₆	Dic₄₇	1	2	yes	complemented
46	D₈	Dic₄₇	1	1	yes	characteristic, complemented
47	M₁₆	—	47	2	no	—
48	M₁₆	—	94	2	no	—
49	C₂×C₈	—	47	1	no	—
50	C₂×C₈	—	94	2	no	—
51	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
52	C₄²	—	47	1	no	—
53	Q₈	C₂×Dic₄₇	1	2	yes	—
54	D₄	—	2	2	no	—
55	D₄	C₂×Dic₄₇	1	2	yes	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	94	1	no	—
58	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
59	C₈	—	47	1	no	—
60	C₈	—	47	1	no	—
61	C₈	—	94	2	no	—
62	C₈	C₂×Dic₄₇	1	1	yes	characteristic
63	C₈	C₂×Dic₄₇	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#10625352	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	94	2	no	—
68	C₄	D₄×D₄₇	1	1	yes	characteristic
69	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	4	2	no	—
72	C₂	D₄×Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting, prime radical	#135×C₄₇	C₂
socle	C₂×C₄₇	C₄×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#135	D₄₇
hypocenter	C₄₇	#443
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #13094031	C₂	semidirect
2. #13093960	C₂	semidirect
3. #13093951	C₂	semidirect
4. C₈×Dic₄₇	C₂	semidirect
7. Q₁₆×C₄₇	C₄	semidirect
8. SD₁₆×C₄₇	C₄	semidirect
9. D₈×C₄₇	C₄	semidirect
37. C₄₇	#443	semidirect
44. Q₁₆	Dic₄₇	semidirect
45. SD₁₆	Dic₄₇	semidirect
46. D₈	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094031	2
#13093960	2
#13093951	2
C₈×Dic₄₇	2
#135×C₄₇	2
#443	47