Subgroups — #15689262

Order 3008.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625336	C₂	1	2	yes	maximal, complemented
2	#13093998	C₂	1	1	yes	maximal, characteristic
3	#13093948	C₂	1	2	yes	maximal, complemented
4	C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₇	—	2	4	no	—
7	C₂×Q₈×C₄₇	—	2	1	no	—
8	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×C₄₇	—	2	1	no	—
10	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊D₄₇	—	2	1	no	—
12	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
13	#10625336	—	2	4	no	—
14	(C₂×D₄₇)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂³×C₄₇	D₄	1	1	yes	characteristic
18	C₂²×D₄₇	—	2	1	no	—
19	Q₈×C₄₇	—	2	4	no	—
20	Q₈×C₄₇	—	2	2	no	—
21	Q₈×C₄₇	D₄	1	4	yes	complemented
22	C₂×C₄×C₄₇	—	2	4	no	—
23	C₂×C₄×C₄₇	—	2	2	no	—
24	C₂×C₄×C₄₇	—	2	2	no	—
25	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	C₂²⋊D₄₇	—	4	2	no	—
28	C₂×Dic₄₇	—	2	1	no	—
29	D₁₈₈	—	2	2	no	—
30	C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇	—	2	1	no	—
32	C₂²×C₄₇	—	2	1	no	—
33	C₂²×C₄₇	SD₁₆	1	2	yes	complemented
34	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×D₄₇	—	4	1	no	—
36	C₂×D₄₇	—	4	1	no	—
37	C₂×D₄₇	—	4	1	no	—
38	C₄×C₄₇	—	2	4	no	—
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	C₂×D₄	1	2	yes	—
41	Dic₄₇	—	4	1	no	—
42	C₂×C₄₇	—	2	2	no	—
43	C₂×C₄₇	#120	1	1	yes	characteristic
44	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₄₇	#137	1	1	yes	characteristic
46	D₄₇	—	8	1	no	—
47	#448	—	47	1	no	maximal, Sylow
48	C₄₇	#448	1	1	yes	characteristic, complemented, Sylow
49	C₂²×Q₈	D₄₇	1	1	yes	characteristic, complemented
50	C₂×SD₁₆	—	47	2	no	—
51	#121	—	47	1	no	—
52	#103	—	47	2	no	—
53	C₂²⋊C₈	—	47	1	no	—
54	C₂×Q₈	—	2	4	no	—
55	C₂×Q₈	—	2	1	no	—
56	C₂×Q₈	C₂×D₄₇	1	2	yes	—
57	C₂×D₄	—	47	1	no	—
58	C₂×D₄	—	94	1	no	—
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
61	SD₁₆	—	94	4	no	—
62	C₂×C₈	—	47	2	no	—
63	C₄⋊C₄	—	47	1	no	—
64	C₂²⋊C₄	—	94	1	no	—
65	C₂³	—	94	1	no	—
66	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
67	Q₈	—	2	4	no	—
68	Q₈	—	2	2	no	—
69	Q₈	C₂²⋊D₄₇	1	4	yes	complemented
70	D₄	—	94	2	no	—
71	D₄	—	188	2	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	94	1	no	—
76	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₈	—	94	2	no	—
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	188	1	no	—
82	C₂²	—	188	1	no	—
83	C₂²	—	188	1	no	—
84	C₂²	#10625336	1	2	yes	complemented
85	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	2	1	no	—
88	C₄	—	188	1	no	—
89	C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	—	376	1	no	—
92	C₂	#13093993	1	1	yes	characteristic
93	C₂	C₂×#10625336	1	1	yes	characteristic
94	C₂	#13094055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂²×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	#13093998	C₂
hypercenter	C₂²×Q₈	D₄₇
hypocenter	C₄₇	#448
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10625336	C₂	semidirect
3. #13093948	C₂	semidirect
4. C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
5. C₂²×Q₈×C₄₇	C₂	semidirect
21. Q₈×C₄₇	D₄	semidirect
33. C₂²×C₄₇	SD₁₆	semidirect
48. C₄₇	#448	semidirect
49. C₂²×Q₈	D₄₇	semidirect
69. Q₈	C₂²⋊D₄₇	semidirect
84. C₂²	#10625336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625336	2
#13093998	2
#13093948	2
C₂²⋊(C₄₇⋊C₈)	2
C₂²×Q₈×C₄₇	2
#448	47