Subgroups — C₂×#13093970 #15689550

Order 3008.

82 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
2	#13093970	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₄₇	—	2	1	no	—
6	C₂×Dic₉₄	—	2	1	no	—
7	Q₁₆×C₄₇	—	2	1	no	—
8	Q₁₆×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	—
12	C₄₇⋊C₁₆	C₂²	1	2	yes	—
13	Q₈×C₄₇	—	2	2	no	—
14	Q₈×C₄₇	—	4	1	no	—
15	C₂×C₄×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	D₈	1	1	yes	characteristic
23	C₄×C₄₇	—	4	2	no	—
24	C₄×C₄₇	D₈	1	1	yes	characteristic
25	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
26	Dic₄₇	—	4	2	no	—
27	C₂×C₄₇	Q₃₂	1	2	yes	complemented
28	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
29	C₂×Q₃₂	—	47	1	no	maximal, Sylow
30	C₄₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×Q₁₆	—	47	1	no	—
32	C₂×Q₁₆	D₄₇	1	1	yes	characteristic
33	Q₃₂	—	47	4	no	—
34	C₂×C₁₆	—	47	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	94	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	47	2	no	—
39	Q₁₆	—	94	1	no	—
40	Q₁₆	C₂×D₄₇	1	2	yes	—
41	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₁₆	—	47	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	94	2	no	—
46	Q₈	—	188	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	188	1	no	—
49	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
50	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
51	C₈	C₂²×D₄₇	1	1	yes	characteristic
52	C₂²	#10625334	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	188	2	no	—
55	C₄	#10625334	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
57	C₂	#13093970	1	2	yes	direct product factor
58	C₂	C₂×#10625334	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625334
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	D₈
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	C₂×Q₃₂
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13093970	C₂	direct (N × H)
27. C₂×C₄₇	Q₃₂	semidirect
30. C₄₇	C₂×Q₃₂	semidirect
57. C₂	#13093970	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
#13093970	2
C₂×C₄₇⋊C₁₆	2
C₂×Q₁₆×C₄₇	2
C₂×Q₃₂	47

Subgroups — C2×#13093970 #15689550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093970 #15689550