Subgroups — #15689404

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094024	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#13093958	C₂	1	2	yes	maximal, complemented
4	#13093946	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄₇	—	2	1	no	—
8	C₂×Dic₉₄	—	2	1	no	—
9	C₂×C₈×C₄₇	C₂²	1	2	yes	—
10	C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	(C₂×D₄₇)⋊C₄	—	2	1	no	—
12	C₄⋊Dic₄₇	—	2	1	no	—
13	C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄₇	—	2	1	no	—
16	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	—	2	2	no	—
20	C₂×Dic₄₇	—	2	1	no	—
21	D₁₈₈	—	2	1	no	—
22	D₁₈₈	Q₈	1	2	yes	complemented
23	C₄×D₄₇	—	4	2	no	—
24	Dic₉₄	—	4	2	no	—
25	C₈×C₄₇	—	2	2	no	—
26	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄₇	—	2	2	no	—
28	C₂×D₄₇	—	4	1	no	—
29	C₂×D₄₇	—	4	1	no	—
30	C₄×C₄₇	—	2	1	no	—
31	C₄×C₄₇	D₈	1	2	yes	—
32	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₄₇	#41	1	1	yes	characteristic
34	Dic₄₇	—	4	2	no	—
35	Dic₄₇	—	4	1	no	—
36	C₂×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
37	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
38	C₂×C₄₇	#137	1	1	yes	characteristic
39	D₄₇	—	4	2	no	—
40	#474	—	47	1	no	maximal, Sylow
41	C₄₇	#474	1	1	yes	characteristic, complemented, Sylow
42	C₄⋊Q₈	—	47	1	no	—
43	C₄×D₄	—	47	1	no	—
44	#107	—	47	2	no	—
45	C₄⋊C₈	D₄₇	1	1	yes	characteristic, complemented
46	#102	—	47	2	no	—
47	C₂×Q₈	—	94	1	no	—
48	C₂×D₄	—	47	1	no	—
49	C₂²×C₄	—	94	1	no	—
50	C₂×C₈	C₂×D₄₇	1	2	yes	—
51	C₄⋊C₄	—	47	2	no	—
52	C₄⋊C₄	—	47	1	no	—
53	C₄⋊C₄	—	94	1	no	—
54	C₂²⋊C₄	—	94	1	no	—
55	C₄²	C₂×D₄₇	1	1	yes	characteristic
56	C₂³	—	94	1	no	—
57	Q₈	—	188	2	no	—
58	D₄	—	47	2	no	—
59	D₄	—	94	1	no	—
60	C₂×C₄	—	94	1	no	—
61	C₂×C₄	—	94	2	no	—
62	C₂×C₄	—	188	2	no	—
63	C₂×C₄	D₁₈₈	1	1	yes	characteristic
64	C₂×C₄	D₁₈₈	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₂²	—	94	2	no	—
68	C₂²	—	188	1	no	—
69	C₂²	—	188	1	no	—
70	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	188	1	no	—
73	C₄	—	188	2	no	—
74	C₄	D₃₇₆	1	2	yes	—
75	C₄	#10625352	1	1	yes	characteristic
76	C₄	Q₈×D₄₇	1	1	yes	characteristic
77	C₂	—	188	2	no	—
78	C₂	#13094004	1	1	yes	characteristic
79	C₂	C₂×D₃₇₆	1	1	yes	characteristic
80	C₂	#13094057	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₄⋊C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂×D₁₈₈	C₂²
hypercenter	C₄⋊C₈	D₄₇
hypocenter	C₄₇	#474
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. #13094024	C₂	semidirect
3. #13093958	C₂	semidirect
5. C₄⋊C₈×C₄₇	C₂	semidirect
22. D₁₈₈	Q₈	semidirect
41. C₄₇	#474	semidirect
45. 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
#13094024	2
C₄×D₁₈₈	2
#13093958	2
#13093946	2
C₄⋊C₈×C₄₇	2
#474	47