Subgroups — #15689436

Order 3008.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093998	C₂	1	1	yes	maximal, characteristic
2	#13093957	C₂	1	2	yes	maximal, complemented
3	#13093944	C₂	1	2	yes	maximal, complemented
4	C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₄₇	—	2	1	no	—
7	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₄₇	—	2	1	no	—
9	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₇	—	2	1	no	—
11	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
12	(C₂×D₄₇)⋊C₄	—	2	1	no	—
13	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₄₇	D₄	1	1	yes	characteristic
16	C₂²×D₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	2	2	no	—
19	C₂×C₄×C₄₇	—	4	2	no	—
20	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²⋊D₄₇	—	4	2	no	—
23	C₂×Dic₄₇	—	2	1	no	—
24	D₁₈₈	—	2	2	no	—
25	C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇	—	2	1	no	—
27	C₂²×C₄₇	—	2	1	no	—
28	C₂²×C₄₇	D₈	1	2	yes	—
29	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×D₄₇	—	4	1	no	—
31	C₂×D₄₇	—	4	1	no	—
32	C₂×D₄₇	—	4	1	no	—
33	C₄×C₄₇	—	2	1	no	—
34	C₄×C₄₇	—	4	2	no	—
35	C₄×C₄₇	#41	1	2	yes	—
36	Dic₄₇	—	4	1	no	—
37	C₂×C₄₇	—	2	2	no	—
38	C₂×C₄₇	#123	1	1	yes	characteristic
39	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
40	C₂×C₄₇	#137	1	1	yes	characteristic
41	D₄₇	—	8	1	no	—
42	#480	—	47	1	no	maximal, Sylow
43	C₄₇	#480	1	1	yes	characteristic, complemented, Sylow
44	#121	—	47	1	no	—
45	C₂×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
46	#107	—	47	2	no	—
47	#102	—	47	2	no	—
48	C₂²⋊C₈	—	47	1	no	—
49	C₂×D₄	—	47	1	no	—
50	C₂×D₄	—	94	1	no	—
51	C₂²×C₄	—	2	1	no	—
52	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
53	C₂×C₈	—	47	2	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	47	1	no	—
56	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
57	C₂²⋊C₄	—	94	1	no	—
58	C₂³	—	94	1	no	—
59	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
60	D₄	—	94	2	no	—
61	D₄	—	188	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	94	1	no	—
66	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
68	C₈	—	94	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	188	1	no	—
72	C₂²	—	188	1	no	—
73	C₂²	—	188	1	no	—
74	C₂²	#10625334	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	4	2	no	—
78	C₄	—	188	1	no	—
79	C₄	#10625350	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	376	1	no	—
82	C₂	#13094007	1	1	yes	characteristic
83	C₂	C₂×#10625334	1	1	yes	characteristic
84	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	C₂×C₄⋊C₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	#13093998	C₂
hypercenter	C₂×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#480
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #13093957	C₂	semidirect
3. #13093944	C₂	semidirect
4. C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
5. C₂×C₄⋊C₄×C₄₇	C₂	semidirect
43. C₄₇	#480	semidirect
45. C₂×C₄⋊C₄	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093998	2
#13093957	2
#13093944	2
C₂²⋊(C₄₇⋊C₈)	2
C₂×C₄⋊C₄×C₄₇	2
#480	47