Subgroups — #15689680

Order 3008.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094024	C₂	1	2	yes	maximal, complemented
2	#13094016	C₂	1	2	yes	maximal, complemented
3	#13094003	C₂	1	4	yes	maximal
4	C₄×Dic₉₄	C₂	1	4	yes	maximal, complemented
5	#13093983	C₂	1	2	yes	maximal
6	C₂×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₄₇	C₂²	1	2	yes	—
8	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₄	C₂²	1	4	yes	—
10	C₄²×C₄₇	C₂²	1	2	yes	—
11	C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₄₇	C₂²	1	4	yes	—
14	C₄⋊Dic₄₇	C₂²	1	4	yes	—
15	C₄⋊Dic₄₇	C₂²	1	4	yes	—
16	Dic₄₇⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂³×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₇	—	2	4	no	—
20	C₂×C₄×C₄₇	Q₈	1	4	yes	complemented
21	C₂×C₄×C₄₇	C₂³	1	2	yes	—
22	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂×C₄×C₄₇	C₂³	1	2	yes	—
24	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₇	C₂³	1	8	yes	—
26	Dic₉₄	—	2	8	no	—
27	C₂²×C₄₇	—	2	2	no	—
28	C₂²×C₄₇	C₂×Q₈	1	2	yes	—
29	C₂²×C₄₇	C₂⁴	1	1	yes	characteristic
30	C₄×C₄₇	—	2	2	no	—
31	C₄×C₄₇	C₂×Q₈	1	2	yes	—
32	C₄×C₄₇	C₂×Q₈	1	2	yes	—
33	C₄×C₄₇	#41	1	4	yes	—
34	Dic₄₇	—	2	8	no	—
35	C₂×C₄₇	—	2	2	no	—
36	C₂×C₄₇	C₂²×Q₈	1	1	yes	characteristic
37	C₂×C₄₇	C₂×#41	1	2	yes	—
38	#533	—	47	1	no	maximal, Sylow
39	C₄₇	#533	1	1	yes	characteristic, complemented, Sylow
40	C₄⋊Q₈	—	47	2	no	—
41	#125	—	47	2	no	—
42	C₂²⋊Q₈	—	47	4	no	—
43	C₄×Q₈	—	47	4	no	—
44	#117	—	47	2	no	—
45	C₂×C₄²	D₄₇	1	1	yes	characteristic
46	C₂×Q₈	—	47	4	no	—
47	C₂²×C₄	C₂×D₄₇	1	2	yes	—
48	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
49	C₄⋊C₄	—	47	8	no	—
50	C₄⋊C₄	—	47	4	no	—
51	C₄⋊C₄	—	47	4	no	—
52	C₂²⋊C₄	—	47	4	no	—
53	C₄²	—	47	4	no	—
54	C₄²	C₂×D₄₇	1	1	yes	characteristic
55	C₄²	C₂×D₄₇	1	1	yes	characteristic
56	C₄²	C₂×D₄₇	1	2	yes	—
57	C₂³	C₂²×D₄₇	1	1	yes	characteristic
58	Q₈	—	94	8	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	47	8	no	—
61	C₂×C₄	Dic₉₄	1	4	yes	complemented
62	C₂×C₄	C₂²×D₄₇	1	2	yes	—
63	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₄₇	1	2	yes	—
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₂²	—	2	2	no	—
67	C₂²	C₂×Dic₉₄	1	2	yes	—
68	C₂²	C₂³×D₄₇	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	94	8	no	—
71	C₄	C₂×Dic₉₄	1	2	yes	—
72	C₄	C₂×Dic₉₄	1	2	yes	—
73	C₄	#10625350	1	4	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂²×Dic₉₄	1	1	yes	characteristic
76	C₂	C₂×#10625350	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁴
Frattini	C₂²	C₂³×D₄₇
Fitting	C₂×C₄²×C₄₇	C₂
prime radical	C₂³×C₄₇	C₂³
hypercenter	C₂×C₄²	D₄₇
hypocenter	C₄₇	#533
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #13094024	C₂	semidirect
2. #13094016	C₂	semidirect
4. C₄×Dic₉₄	C₂	semidirect
20. C₂×C₄×C₄₇	Q₈	semidirect
39. C₄₇	#533	semidirect
61. C₂×C₄	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#13094024	2
#13094016	2
#13094003	2
C₄×Dic₉₄	2
#13093983	2
C₂×C₄²×C₄₇	2
#533	47