Subgroups — #15688983

Order 3008.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
3	C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
4	C₂³×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₄₇	—	2	4	no	—
7	C₂²×C₄×C₄₇	C₄	1	4	yes	complemented
8	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₇	C₂²	1	4	yes	—
11	C₂²⋊Dic₄₇	—	2	4	no	—
12	C₄⋊Dic₄₇	—	2	4	no	—
13	C₂³×C₄₇	—	2	2	no	—
14	C₂³×C₄₇	—	2	2	no	—
15	C₂³×C₄₇	C₂×C₄	1	2	yes	—
16	C₂³×C₄₇	D₄	1	2	yes	—
17	C₂³×C₄₇	Q₈	1	2	yes	—
18	C₂³×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₇	—	2	2	no	—
20	C₂×C₄×C₄₇	—	2	8	no	—
21	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₄₇	D₄	1	4	yes	—
24	C₂×Dic₄₇	—	2	4	no	—
25	C₂×Dic₄₇	—	2	4	no	—
26	C₂×Dic₄₇	—	2	4	no	—
27	C₂²×C₄₇	—	2	2	no	—
28	C₂²×C₄₇	—	2	2	no	—
29	C₂²×C₄₇	—	2	4	no	—
30	C₂²×C₄₇	—	2	4	no	—
31	C₂²×C₄₇	C₄⋊C₄	1	4	yes	complemented
32	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄₇	C₂×D₄	1	2	yes	—
35	C₂²×C₄₇	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄₇	#41	1	2	yes	—
37	C₄×C₄₇	—	2	2	no	—
38	C₄×C₄₇	C₂²⋊C₄	1	4	yes	complemented
39	Dic₄₇	—	4	4	no	—
40	C₂×C₄₇	—	2	4	no	—
41	C₂×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₄₇	#117	1	1	yes	characteristic
44	C₂×C₄₇	#121	1	2	yes	—
45	C₂×C₄₇	C₂²⋊Q₈	1	2	yes	—
46	#380	—	47	1	no	maximal, Sylow
47	C₄₇	#380	1	1	yes	characteristic, complemented, Sylow
48	C₂³×C₄	D₄₇	1	1	yes	characteristic
49	C₂×C₄⋊C₄	—	47	2	no	—
50	C₂×C₂²⋊C₄	—	47	2	no	—
51	#95	—	47	2	no	—
52	C₂⁴	C₂×D₄₇	1	1	yes	characteristic
53	C₂²×C₄	—	2	4	no	—
54	C₂²×C₄	—	47	4	no	—
55	C₂²×C₄	Dic₄₇	1	4	yes	complemented
56	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
58	C₄⋊C₄	—	94	4	no	—
59	C₂²⋊C₄	—	94	4	no	—
60	C₂³	—	2	2	no	—
61	C₂³	—	2	2	no	—
62	C₂³	Dic₉₄	1	2	yes	—
63	C₂³	D₁₈₈	1	2	yes	—
64	C₂³	C₂×Dic₄₇	1	2	yes	—
65	C₂³	C₂²×D₄₇	1	1	yes	characteristic
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	94	4	no	—
69	C₂×C₄	—	94	4	no	—
70	C₂×C₄	—	94	4	no	—
71	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
72	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
73	C₂×C₄	C₂²⋊D₄₇	1	4	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	C₄⋊Dic₄₇	1	4	yes	complemented
79	C₂²	C₂×Dic₉₄	1	1	yes	characteristic
80	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
81	C₂²	#10625350	1	2	yes	—
82	C₂²	C₂²×Dic₄₇	1	1	yes	characteristic
83	C₂²	C₂×C₂²⋊D₄₇	1	2	yes	—
84	C₄	—	2	2	no	—
85	C₄	—	188	4	no	—
86	C₄	C₂²⋊Dic₄₇	1	4	yes	complemented
87	C₂	—	2	4	no	—
88	C₂	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
89	C₂	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
90	C₂	#13093983	1	1	yes	characteristic
91	C₂	#13093998	1	2	yes	—
92	C₂	#13094003	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄
Fitting	C₂³×C₄×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂³
prime radical	C₂⁴×C₄₇	C₂²
hypercenter	C₂³×C₄	D₄₇
hypocenter	C₄₇	#380
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₄₇	C₂	semidirect
3. C₄₇⋊#95	C₂	semidirect
7. C₂²×C₄×C₄₇	C₄	semidirect
31. C₂²×C₄₇	C₄⋊C₄	semidirect
38. C₄×C₄₇	C₂²⋊C₄	semidirect
47. C₄₇	#380	semidirect
55. C₂²×C₄	Dic₄₇	semidirect
78. C₂²	C₄⋊Dic₄₇	semidirect
86. C₄	C₂²⋊Dic₄₇	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×C₂²⋊Dic₄₇	2
C₄₇⋊#95	2
C₂³×C₄×C₄₇	2
#380	47