Subgroups — C₂×#16813616 #20299123

Order 7232.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813616	C₂	1	8	yes	maximal, direct product factor
2	C₂×#14268626	C₂	1	3	yes	maximal, complemented
3	C₂×#14268624	C₂	1	3	yes	maximal
4	C₂×C₄²×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₁₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₁₁₃	C₂²	1	3	yes	—
7	#14268626	C₂²	1	12	yes	complemented
8	#14268624	C₂²	1	12	yes	—
9	C₂²×C₄×C₁₁₃	C₂²	1	3	yes	—
10	C₄²×C₁₁₃	C₂²	1	4	yes	complemented
11	C₂³×C₁₁₃	C₂³	1	1	yes	characteristic
12	C₂²×D₁₁₃	—	2	6	no	—
13	C₂²×D₁₁₃	C₂³	1	2	yes	—
14	C₂×C₄×C₁₁₃	—	2	6	no	—
15	C₂×C₄×C₁₁₃	C₂³	1	6	yes	—
16	C₂×Dic₁₁₃	—	2	6	no	—
17	C₂×Dic₁₁₃	C₂³	1	6	yes	—
18	C₂²×C₁₁₃	#41	1	6	yes	—
19	C₂²×C₁₁₃	C₂⁴	1	1	yes	characteristic
20	C₂×D₁₁₃	—	2	6	no	—
21	C₂×D₁₁₃	—	4	4	no	—
22	C₄×C₁₁₃	—	2	6	no	—
23	Dic₁₁₃	—	2	6	no	—
24	C₂×C₁₁₃	#126	1	4	yes	complemented
25	C₂×C₁₁₃	C₂×#41	1	3	yes	—
26	D₁₁₃	—	4	2	no	—
27	C₁₁₃	C₂×#126	1	1	yes	characteristic, complemented, Sylow
28	C₂×#126	—	113	1	no	maximal, Sylow
29	#126	—	113	8	no	—
30	C₂×C₄⋊C₄	—	113	3	no	—
31	C₂×C₂²⋊C₄	—	113	3	no	—
32	C₂×C₄²	D₁₁₃	1	1	yes	characteristic, complemented
33	C₂⁴	—	113	1	no	—
34	C₂²×C₄	—	113	3	no	—
35	C₂²×C₄	C₂×D₁₁₃	1	3	yes	—
36	C₄⋊C₄	—	113	12	no	—
37	C₂²⋊C₄	—	113	12	no	—
38	C₄²	C₂×D₁₁₃	1	4	yes	complemented
39	C₂³	—	113	2	no	—
40	C₂³	—	226	6	no	—
41	C₂³	C₂²×D₁₁₃	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	113	6	no	—
44	C₂×C₄	—	226	6	no	—
45	C₂×C₄	C₂²×D₁₁₃	1	6	yes	—
46	C₂²	—	452	4	no	—
47	C₂²	—	226	6	no	—
48	C₂²	#14268647	1	6	yes	—
49	C₂²	C₂³×D₁₁₃	1	1	yes	characteristic
50	C₄	—	2	6	no	—
51	C₄	—	226	6	no	—
52	C₂	—	452	2	no	—
53	C₂	#16813616	1	4	yes	direct product factor
54	C₂	C₂×#14268647	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₁₃
commutator	C₂²×C₁₁₃	C₂⁴
Frattini	C₂²	C₂³×D₁₁₃
Fitting	C₂×C₄²×C₁₁₃	C₂
socle	C₂³×C₁₁₃	C₂³
hypercenter	C₂×C₄²	D₁₁₃
hypocenter	C₁₁₃	C₂×#126
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #16813616	C₂	direct (N × H)
2. C₂×#14268626	C₂	semidirect
4. C₂×C₄²×C₁₁₃	C₂	semidirect
7. #14268626	C₂²	semidirect
10. C₄²×C₁₁₃	C₂²	semidirect
24. C₂×C₁₁₃	#126	semidirect
27. C₁₁₃	C₂×#126	semidirect
32. C₂×C₄²	D₁₁₃	semidirect
38. C₄²	C₂×D₁₁₃	semidirect
53. C₂	#16813616	direct (N × H)

Subgroups — C2×#16813616 #20299123

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813616 #20299123