Subgroups — C₂×#13093934 #15689071

Order 3008.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093934	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₇	C₄	1	2	yes	—
7	C₂×C₈×C₄₇	C₄	1	4	yes	complemented
8	C₂×C₈×C₄₇	C₂²	1	2	yes	—
9	C₄×Dic₄₇	C₄	1	2	yes	—
10	C₄×Dic₄₇	C₂²	1	2	yes	—
11	C₂×C₄₇⋊C₈	C₄	1	4	yes	complemented
12	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₇	—	2	4	no	—
19	C₂×Dic₄₇	C₂×C₄	1	4	yes	—
20	C₈×C₄₇	C₂×C₄	1	4	yes	complemented
21	C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
22	C₂²×C₄₇	C₄²	1	2	yes	—
23	C₂²×C₄₇	M₁₆	1	4	yes	—
24	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₇	C₄²	1	2	yes	—
26	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₄₇	—	2	4	no	—
29	C₂×C₄₇	#97	1	4	yes	complemented
30	C₂×C₄₇	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄₇	C₂×M₁₆	1	2	yes	—
32	C₂×#97	—	47	1	no	maximal, Sylow
33	C₄₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₈	—	47	1	no	—
35	C₂²×C₈	D₄₇	1	1	yes	characteristic
36	C₂×C₄²	—	47	1	no	—
37	#97	—	47	4	no	—
38	C₂²×C₄	—	47	2	no	—
39	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
40	C₂×C₈	—	47	4	no	—
41	C₂×C₈	—	47	2	no	—
42	C₂×C₈	Dic₄₇	1	4	yes	complemented
43	C₂×C₈	C₂×D₄₇	1	2	yes	—
44	C₄²	—	47	2	no	—
45	C₄²	—	47	2	no	—
46	C₂³	C₄×D₄₇	1	1	yes	characteristic
47	C₂×C₄	—	47	4	no	—
48	C₂×C₄	—	94	4	no	—
49	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
50	C₂×C₄	C₄×D₄₇	1	2	yes	—
51	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
52	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
53	C₈	—	47	4	no	—
54	C₈	C₂×Dic₄₇	1	4	yes	complemented
55	C₂²	#10625324	1	4	yes	—
56	C₂²	C₄×Dic₄₇	1	2	yes	—
57	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
58	C₄	—	94	4	no	—
59	C₄	C₄×Dic₄₇	1	2	yes	—
60	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
61	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
62	C₂	#13093934	1	4	yes	direct product factor
63	C₂	C₂×C₄×Dic₄₇	1	1	yes	characteristic
64	C₂	C₂×#10625324	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂²×C₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	C₂×#97
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #13093934	C₂	direct (N × H)
7. C₂×C₈×C₄₇	C₄	semidirect
11. C₂×C₄₇⋊C₈	C₄	semidirect
20. C₈×C₄₇	C₂×C₄	semidirect
21. C₄₇⋊C₈	C₂×C₄	semidirect
29. C₂×C₄₇	#97	semidirect
33. C₄₇	C₂×#97	semidirect
42. C₂×C₈	Dic₄₇	semidirect
54. C₈	C₂×Dic₄₇	semidirect
62. C₂	#13093934	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄₇⋊C₈	2
C₂×C₄×Dic₄₇	2
#13093934	2
C₂²×C₈×C₄₇	2
C₂×#97	47

Subgroups — C2×#13093934 #15689071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093934 #15689071