Subgroups — C₂×#16813554 #20298629

Order 7232.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₁₃	C₂	1	2	yes	maximal
2	#16813554	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₁₃	—	2	2	no	—
5	C₄⋊Dic₁₁₃	—	2	2	no	—
6	C₄⋊Dic₁₁₃	C₂²	1	4	yes	—
7	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₁₃	C₄	1	4	yes	complemented
9	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
10	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	Q₈	1	2	yes	—
14	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₁₃	—	2	4	no	—
16	C₂×Dic₁₁₃	—	4	4	no	—
17	C₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₁₁₃	C₄⋊C₄	1	2	yes	—
19	C₂²×C₁₁₃	SD₁₆	1	4	yes	—
20	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
22	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₁₃	—	4	4	no	—
25	C₂×C₁₁₃	#106	1	4	yes	complemented
26	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₁₁₃	C₂×SD₁₆	1	2	yes	—
28	C₁₁₃	C₂×#106	1	1	yes	characteristic, complemented, Sylow
29	C₂×#106	—	113	1	no	maximal, Sylow
30	C₂²×C₈	D₁₁₃	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	113	2	no	—
32	#106	—	113	4	no	—
33	C₂²×C₄	—	226	2	no	—
34	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
35	C₂×C₈	Dic₁₁₃	1	4	yes	complemented
36	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
37	C₄⋊C₄	—	113	4	no	—
38	C₄⋊C₄	—	226	2	no	—
39	C₂³	D₄₅₂	1	1	yes	characteristic
40	C₂×C₄	—	452	4	no	—
41	C₂×C₄	—	226	4	no	—
42	C₂×C₄	Dic₂₂₆	1	2	yes	—
43	C₂×C₄	D₄₅₂	1	1	yes	characteristic
44	C₂×C₄	C₂×Dic₁₁₃	1	2	yes	—
45	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
46	C₈	C₂×Dic₁₁₃	1	4	yes	complemented
47	C₂²	C₄⋊Dic₁₁₃	1	2	yes	—
48	C₂²	#14268636	1	4	yes	—
49	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
50	C₄	—	452	4	no	—
51	C₄	C₄⋊Dic₁₁₃	1	2	yes	—
52	C₄	C₂²×Dic₁₁₃	1	1	yes	characteristic
53	C₄	C₂×Dic₂₂₆	1	1	yes	characteristic
54	C₂	#16813554	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊Dic₁₁₃	1	1	yes	characteristic
56	C₂	C₂×#14268636	1	2	yes	—

	subgroup	G/H
center	C₂³	D₄₅₂
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₂²×C₈×C₁₁₃	C₂
socle	C₂³×C₁₁₃	D₄
hypercenter	C₂²×C₈	D₁₁₃
hypocenter	C₁₁₃	C₂×#106
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #16813554	C₂	direct (N × H)
8. C₂×C₈×C₁₁₃	C₄	semidirect
17. C₈×C₁₁₃	C₂×C₄	semidirect
25. C₂×C₁₁₃	#106	semidirect
28. C₁₁₃	C₂×#106	semidirect
35. C₂×C₈	Dic₁₁₃	semidirect
46. C₈	C₂×Dic₁₁₃	semidirect
54. C₂	#16813554	direct (N × H)

Subgroups — C2×#16813554 #20298629

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813554 #20298629