Subgroups — #15689679

Order 3008.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094023	C₂	1	2	yes	maximal, complemented
2	#13094016	C₂	1	1	yes	maximal, characteristic, complemented
3	#13094002	C₂	1	4	yes	maximal
4	#13093989	C₂	1	4	yes	maximal, complemented
5	#13093982	C₂	1	2	yes	maximal
6	C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
7	#125×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₇	C₂²	1	2	yes	—
9	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₉₄	C₂²	1	4	yes	—
11	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
12	C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
13	C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
15	C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	Dic₄₇⋊C₄	C₂²	1	4	yes	—
17	Dic₄₇⋊C₄	C₂²	1	4	yes	—
18	C₄×Dic₄₇	C₂²	1	2	yes	—
19	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₄×Dic₄₇	C₂²	1	4	yes	—
21	C₂²×D₄₇	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₄₇	C₂³	1	2	yes	—
23	C₂×C₄×C₄₇	C₂³	1	4	yes	—
24	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₄₇	C₂³	1	4	yes	—
26	C₂×Dic₄₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₄₇	C₂³	1	2	yes	—
28	C₄×D₄₇	—	2	4	no	—
29	C₄×D₄₇	Q₈	1	4	yes	complemented
30	Dic₉₄	—	2	8	no	—
31	C₂²×C₄₇	C₂⁴	1	1	yes	characteristic
32	C₂×D₄₇	—	2	2	no	—
33	C₂×D₄₇	C₂×Q₈	1	2	yes	—
34	C₄×C₄₇	—	2	4	no	—
35	C₄×C₄₇	—	2	2	no	—
36	C₄×C₄₇	C₂×Q₈	1	2	yes	—
37	Dic₄₇	—	2	4	no	—
38	Dic₄₇	C₂×Q₈	1	2	yes	—
39	Dic₄₇	#41	1	4	yes	—
40	C₂×C₄₇	C₂²×Q₈	1	1	yes	characteristic
41	C₂×C₄₇	C₂×#41	1	2	yes	—
42	D₄₇	—	2	2	no	—
43	#533	—	47	1	no	maximal, Sylow
44	C₄₇	#533	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	47	2	no	—
46	#125	—	47	1	no	—
47	#125	D₄₇	1	1	yes	characteristic, complemented
48	C₂²⋊Q₈	—	47	4	no	—
49	C₄×Q₈	—	47	4	no	—
50	#117	—	47	2	no	—
51	C₂×C₄²	—	47	1	no	—
52	C₂×Q₈	—	47	4	no	—
53	C₂²×C₄	—	47	1	no	—
54	C₂²×C₄	—	47	2	no	—
55	C₄⋊C₄	—	47	4	no	—
56	C₄⋊C₄	—	47	4	no	—
57	C₄⋊C₄	—	47	2	no	—
58	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
59	C₄⋊C₄	C₂×D₄₇	1	4	yes	—
60	C₂²⋊C₄	—	47	4	no	—
61	C₄²	—	47	2	no	—
62	C₄²	—	47	1	no	—
63	C₄²	—	47	4	no	—
64	C₄²	C₂×D₄₇	1	1	yes	characteristic
65	C₂³	—	47	1	no	—
66	Q₈	—	94	8	no	—
67	C₂×C₄	—	47	1	no	—
68	C₂×C₄	—	47	2	no	—
69	C₂×C₄	—	47	4	no	—
70	C₂×C₄	—	47	4	no	—
71	C₂×C₄	—	94	4	no	—
72	C₂×C₄	C₂²×D₄₇	1	2	yes	—
73	C₂×C₄	C₂²×D₄₇	1	4	yes	—
74	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
75	C₂²	—	47	2	no	—
76	C₂²	—	94	2	no	—
77	C₂²	C₂³×D₄₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	47	2	no	—
81	C₄	—	47	4	no	—
82	C₄	—	94	4	no	—
83	C₄	Q₈×D₄₇	1	2	yes	—
84	C₂	—	94	2	no	—
85	C₂	C₂×Q₈×D₄₇	1	1	yes	characteristic
86	C₂	#41×D₄₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁴
Fitting	#125×C₄₇	C₂
prime radical	C₂²×D₄₇	C₂³
hypercenter	#125	D₄₇
hypocenter	C₄₇	#533
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #13094023	C₂	semidirect
2. #13094016	C₂	semidirect
4. #13093989	C₂	semidirect
7. #125×C₄₇	C₂	semidirect
29. C₄×D₄₇	Q₈	semidirect
44. C₄₇	#533	semidirect
47. #125	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094023	2
#13094016	2
#13094002	2
#13093989	2
#13093982	2
C₄²×D₄₇	2
#125×C₄₇	2
#533	47