Subgroups — C₂×#13093969 #15689548

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	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic
3	#13093969	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₈₈	—	2	1	no	—
6	C₂×Dic₉₄	—	2	1	no	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	Dic₁₈₈	—	2	1	no	—
9	Dic₁₈₈	C₂²	1	2	yes	complemented
10	D₃₇₆	—	2	1	no	—
11	D₃₇₆	C₂²	1	2	yes	—
12	C₁₆×C₄₇	C₂²	1	2	yes	complemented
13	C₂²×D₄₇	—	4	1	no	—
14	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×Dic₄₇	—	4	1	no	—
16	D₁₈₈	—	2	2	no	—
17	D₁₈₈	—	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	D₈	1	1	yes	characteristic
23	C₂×D₄₇	—	4	2	no	—
24	C₂×D₄₇	—	8	2	no	—
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	SD₃₂	1	2	yes	complemented
29	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
30	D₄₇	—	8	2	no	—
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	—	47	1	no	—
35	SD₃₂	—	47	4	no	—
36	C₂×C₁₆	D₄₇	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	94	1	no	—
38	C₂×D₄	—	94	1	no	—
39	Q₁₆	—	47	2	no	—
40	Q₁₆	—	94	1	no	—
41	D₈	—	47	2	no	—
42	D₈	—	94	1	no	—
43	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
44	C₁₆	C₂×D₄₇	1	2	yes	complemented
45	C₂³	—	188	1	no	—
46	Q₈	—	94	2	no	—
47	Q₈	—	188	1	no	—
48	D₄	—	94	2	no	—
49	D₄	—	188	1	no	—
50	C₂×C₄	—	188	1	no	—
51	C₂×C₄	D₁₈₈	1	1	yes	characteristic
52	C₈	D₁₈₈	1	1	yes	characteristic
53	C₈	C₂²×D₄₇	1	1	yes	characteristic
54	C₂²	—	376	2	no	—
55	C₂²	—	188	2	no	—
56	C₂²	D₃₇₆	1	1	yes	characteristic
57	C₄	—	188	2	no	—
58	C₄	D₃₇₆	1	1	yes	characteristic
59	C₄	C₂×D₁₈₈	1	1	yes	characteristic
60	C₂	—	376	2	no	—
61	C₂	#13093969	1	2	yes	direct product factor
62	C₂	C₂×D₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₇₆
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	C₂×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	D₈
prime radical	C₂×D₃₇₆	C₂
hypercenter	C₂×C₁₆	D₄₇
hypocenter	C₄₇	C₂×SD₃₂
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₈₈	C₂	semidirect
3. #13093969	C₂	direct (N × H)
4. C₂×C₁₆×C₄₇	C₂	semidirect
9. Dic₁₈₈	C₂²	semidirect
12. C₁₆×C₄₇	C₂²	semidirect
28. C₂×C₄₇	SD₃₂	semidirect
32. C₄₇	C₂×SD₃₂	semidirect
36. C₂×C₁₆	D₄₇	semidirect
44. C₁₆	C₂×D₄₇	semidirect
61. C₂	#13093969	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
C₂×D₃₇₆	2
#13093969	2
C₂×C₁₆×C₄₇	2
C₂×SD₃₂	47

Subgroups — C2×#13093969 #15689548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093969 #15689548