Subgroups — C₂×#16813553 #20298628

Order 7232.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11744751	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813553	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₁₃	—	2	1	no	—
6	C₂×#11744751	C₄	1	4	yes	complemented
7	C₂×#11744751	C₂²	1	2	yes	—
8	C₄⋊Dic₁₁₃	—	2	1	no	—
9	C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₁₃	—	2	1	no	—
11	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₁₃	—	2	1	no	—
13	C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	—	2	2	no	—
16	C₂×C₄×C₁₁₃	—	4	2	no	—
17	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	Q₈	1	2	yes	—
20	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₁₃	—	2	2	no	—
22	C₂×Dic₁₁₃	—	4	2	no	—
23	#11744751	C₂×C₄	1	4	yes	complemented
24	C₂²×C₁₁₃	C₄⋊C₄	1	2	yes	—
25	C₂²×C₁₁₃	SD₁₆	1	2	yes	—
26	C₂²×C₁₁₃	SD₁₆	1	2	yes	—
27	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₁₃	—	4	2	no	—
29	C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₁₃	—	4	2	no	—
33	C₂×C₁₁₃	#106	1	4	yes	complemented
34	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
37	C₁₁₃	C₂×#106	1	1	yes	characteristic, complemented, Sylow
38	C₂×#106	—	113	1	no	maximal, Sylow
39	C₂²×C₈	—	113	1	no	—
40	C₂×C₄⋊C₄	—	113	1	no	—
41	C₂×C₄⋊C₄	D₁₁₃	1	1	yes	characteristic
42	#106	—	113	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	226	1	no	—
45	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
46	C₂×C₈	—	113	4	no	—
47	C₂×C₈	—	113	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	113	2	no	—
50	C₄⋊C₄	—	226	1	no	—
51	C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
52	C₂³	C₂²⋊D₁₁₃	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	452	2	no	—
56	C₂×C₄	—	226	2	no	—
57	C₂×C₄	Dic₂₂₆	1	2	yes	—
58	C₂×C₄	C₄×D₁₁₃	1	2	yes	—
59	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
61	C₈	—	113	4	no	—
62	C₂²	#14268626	1	2	yes	—
63	C₂²	#14268634	1	2	yes	—
64	C₂²	#14268635	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	452	2	no	—
68	C₄	#14268626	1	2	yes	—
69	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
70	C₄	C₂×Dic₂₂₆	1	1	yes	characteristic
71	C₂	#16813553	1	4	yes	direct product factor
72	C₂	C₂×#14268626	1	1	yes	characteristic
73	C₂	C₂×#14268634	1	1	yes	characteristic
74	C₂	C₂×#14268635	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #16813553	C₂	direct (N × H)
6. C₂×#11744751	C₄	semidirect
23. #11744751	C₂×C₄	semidirect
33. C₂×C₁₁₃	#106	semidirect
37. C₁₁₃	C₂×#106	semidirect
71. C₂	#16813553	direct (N × H)

Subgroups — C2×#16813553 #20298628

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813553 #20298628