Subgroups — #15689320

Order 3008.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625335	C₂	1	2	yes	maximal, complemented
2	C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093945	C₂	1	2	yes	maximal, complemented
5	#127×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₇	—	2	1	no	—
7	C₂×D₄×C₄₇	—	2	1	no	—
8	C₂×D₄×C₄₇	C₂²	1	2	yes	—
9	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
10	C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	#10625335	—	2	4	no	—
12	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	Dic₄₇⋊C₄	—	2	1	no	—
14	C₄×Dic₄₇	—	2	1	no	—
15	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₄₇	—	2	2	no	—
17	D₄×C₄₇	—	2	2	no	—
18	D₄×C₄₇	—	2	2	no	—
19	D₄×C₄₇	—	4	2	no	—
20	D₄×C₄₇	—	4	2	no	—
21	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₇	—	2	1	no	—
25	C₂×Dic₄₇	—	2	1	no	—
26	Dic₉₄	—	2	1	no	—
27	Dic₉₄	D₄	1	2	yes	complemented
28	C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇	—	4	2	no	—
30	C₂²×C₄₇	—	4	2	no	—
31	C₂²×C₄₇	—	4	2	no	—
32	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₇	—	2	1	no	—
34	C₄×C₄₇	SD₁₆	1	2	yes	complemented
35	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₇	#41	1	1	yes	characteristic
37	Dic₄₇	—	2	2	no	—
38	Dic₄₇	—	4	1	no	—
39	C₂×C₄₇	—	8	2	no	—
40	C₂×C₄₇	#121	1	1	yes	characteristic
41	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
43	#460	—	47	1	no	maximal, Sylow
44	C₄₇	#460	1	1	yes	characteristic, complemented, Sylow
45	C₂×SD₁₆	—	47	2	no	—
46	#127	D₄₇	1	1	yes	characteristic
47	C₄×Q₈	—	47	1	no	—
48	C₄⋊C₈	—	47	1	no	—
49	#102	—	47	2	no	—
50	C₂×Q₈	—	47	1	no	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂×D₄₇	1	2	yes	—
54	SD₁₆	—	94	4	no	—
55	C₂×C₈	—	47	2	no	—
56	C₄⋊C₄	—	47	1	no	—
57	C₄⋊C₄	—	94	1	no	—
58	C₄²	—	94	1	no	—
59	C₄²	C₂×D₄₇	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	47	2	no	—
62	Q₈	—	94	1	no	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	94	1	no	—
68	C₂×C₄	—	94	1	no	—
69	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
72	C₈	—	94	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	94	2	no	—
79	C₄	—	188	1	no	—
80	C₄	#10625335	1	2	yes	complemented
81	C₄	D₄×D₄₇	1	1	yes	characteristic
82	C₄	#10625352	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#13093995	1	1	yes	characteristic
85	C₂	C₂×#10625335	1	1	yes	characteristic
86	C₂	#13094050	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting, prime radical	#127×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	#127	D₄₇
hypocenter	C₄₇	#460
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10625335	C₂	semidirect
2. C₄×Dic₉₄	C₂	semidirect
3. C₄⋊(C₄₇⋊C₈)	C₂	semidirect
4. #13093945	C₂	semidirect
27. Dic₉₄	D₄	semidirect
34. C₄×C₄₇	SD₁₆	semidirect
44. C₄₇	#460	semidirect
80. C₄	#10625335	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625335	2
C₄×Dic₉₄	2
C₄⋊(C₄₇⋊C₈)	2
#13093945	2
#127×C₄₇	2
#460	47