Subgroups — #15689053

Order 3008.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
3	C₄₇⋊#95	C₂	1	2	yes	maximal
4	C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇	C₂²	1	2	yes	—
10	C₂²×Dic₄₇	C₂²	1	2	yes	—
11	C₄⋊C₄×C₄₇	—	2	2	no	—
12	C₄⋊Dic₄₇	—	2	2	no	—
13	Dic₄₇⋊C₄	—	2	4	no	—
14	C₂³×C₄₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₄₇	—	2	1	no	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	2	1	no	—
19	C₂×C₄×C₄₇	—	2	2	no	—
20	C₂×C₄×C₄₇	D₄	1	2	yes	—
21	C₂×C₄×C₄₇	D₄	1	2	yes	—
22	C₂×Dic₄₇	—	2	2	no	—
23	C₂×Dic₄₇	—	2	2	no	—
24	C₂×Dic₄₇	—	2	2	no	—
25	C₂×Dic₄₇	—	2	2	no	—
26	C₂×Dic₄₇	—	2	2	no	—
27	C₂×Dic₄₇	Q₈	1	4	yes	—
28	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₄₇	C₂×Q₈	1	2	yes	—
31	C₂²×C₄₇	#41	1	1	yes	characteristic
32	C₂²×C₄₇	#41	1	2	yes	—
33	C₄×C₄₇	—	2	2	no	—
34	C₄×C₄₇	—	2	2	no	—
35	C₄×C₄₇	—	4	1	no	—
36	Dic₄₇	—	2	4	no	—
37	Dic₄₇	—	4	2	no	—
38	C₂×C₄₇	#121	1	1	yes	characteristic
39	C₂×C₄₇	C₂²⋊Q₈	1	2	yes	—
40	C₂×C₄₇	#123	1	1	yes	characteristic
41	C₂×C₄₇	#125	1	2	yes	—
42	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
43	#398	—	47	1	no	maximal, Sylow
44	C₄₇	#398	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄⋊C₄	—	47	2	no	—
46	C₂×C₄⋊C₄	—	47	1	no	—
47	C₂×C₄⋊C₄	D₄₇	1	1	yes	characteristic
48	#95	—	47	1	no	—
49	#95	—	47	2	no	—
50	C₂²×C₄	—	47	2	no	—
51	C₂²×C₄	—	47	2	no	—
52	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
53	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
54	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	—	94	4	no	—
57	C₄⋊C₄	—	94	2	no	—
58	C₂³	C₂²×D₄₇	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	47	4	no	—
65	C₂×C₄	—	94	2	no	—
66	C₂×C₄	—	94	2	no	—
67	C₂×C₄	—	94	2	no	—
68	C₂×C₄	—	94	2	no	—
69	C₂×C₄	—	94	2	no	—
70	C₂×C₄	D₁₈₈	1	2	yes	—
71	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
72	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
73	C₂²	#10625350	1	1	yes	characteristic
74	C₂²	#10625352	1	2	yes	—
75	C₂²	Q₈×D₄₇	1	2	yes	—
76	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	2	no	—
79	C₄	—	4	1	no	—
80	C₄	—	94	4	no	—
81	C₄	—	188	2	no	—
82	C₂	#13093998	1	1	yes	characteristic
83	C₂	#13094004	1	2	yes	—
84	C₂	#13094005	1	1	yes	characteristic
85	C₂	#13094014	1	2	yes	—
86	C₂	#13094022	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₇
commutator, socle, prime radical, cosocle	C₂³×C₄₇	C₂³
Fitting	C₂×C₄⋊C₄×C₄₇	C₂
hypercenter	C₂×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#398
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
44. C₄₇	#398	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₄₇	2
C₂×Dic₄₇⋊C₄	2
C₄₇⋊#95	2
C₂×C₄⋊C₄×C₄₇	2
#398	47