Subgroups — C₂×#13093968 #15689547

Order 3008.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093968	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×C₄₇	—	2	1	no	—
6	C₂×Dic₉₄	—	2	1	no	—
7	D₈×C₄₇	—	2	1	no	—
8	D₈×C₄₇	C₂²	1	2	yes	—
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	Dic₁₈₈	—	2	1	no	—
11	Dic₁₈₈	C₂²	1	2	yes	complemented
12	C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂³×C₄₇	—	4	1	no	—
14	D₄×C₄₇	—	2	2	no	—
15	D₄×C₄₇	—	4	1	no	—
16	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂×Dic₄₇	—	4	1	no	—
18	Dic₉₄	—	2	2	no	—
19	Dic₉₄	—	4	1	no	—
20	C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄₇	—	4	2	no	—
23	C₂²×C₄₇	—	8	2	no	—
24	C₂²×C₄₇	D₈	1	1	yes	characteristic
25	C₄×C₄₇	D₈	1	1	yes	characteristic
26	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
27	Dic₄₇	—	4	2	no	—
28	C₂×C₄₇	—	8	2	no	—
29	C₂×C₄₇	SD₃₂	1	2	yes	complemented
30	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
31	C₂×SD₃₂	—	47	1	no	maximal, Sylow
32	C₄₇	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
33	C₂×Q₁₆	—	47	1	no	—
34	C₂×D₈	D₄₇	1	1	yes	characteristic
35	SD₃₂	—	47	4	no	—
36	C₂×C₁₆	—	47	1	no	—
37	C₂×Q₈	—	94	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	47	2	no	—
40	Q₁₆	—	94	1	no	—
41	D₈	—	2	1	no	—
42	D₈	C₂×D₄₇	1	2	yes	—
43	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
44	C₁₆	—	47	2	no	—
45	C₂³	—	4	1	no	—
46	Q₈	—	94	2	no	—
47	Q₈	—	188	1	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	188	1	no	—
51	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
52	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
53	C₈	C₂²×D₄₇	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#10625334	1	1	yes	characteristic
57	C₄	—	188	2	no	—
58	C₄	#10625334	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#13093968	1	2	yes	direct product factor
62	C₂	C₂×#10625334	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625334
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting, prime radical	C₂×D₈×C₄₇	C₂
socle	C₂²×C₄₇	D₈
hypercenter	C₂×D₈	D₄₇
hypocenter	C₄₇	C₂×SD₃₂
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₈₈	C₂	semidirect
2. #13093968	C₂	direct (N × H)
3. C₂×C₄₇⋊C₁₆	C₂	semidirect
11. Dic₁₈₈	C₂²	semidirect
12. C₄₇⋊C₁₆	C₂²	semidirect
29. C₂×C₄₇	SD₃₂	semidirect
32. C₄₇	C₂×SD₃₂	semidirect
61. C₂	#13093968	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₈₈	2
#13093968	2
C₂×C₄₇⋊C₁₆	2
C₂×D₈×C₄₇	2
C₂×SD₃₂	47

Subgroups — C2×#13093968 #15689547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093968 #15689547