Subgroups — C₂×#16813547 #20298590

Order 7232.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813547	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₂₆	—	2	1	no	—
6	C₂×Dic₂₂₆	—	2	2	no	—
7	C₂×Dic₂₂₆	C₄	1	4	yes	complemented
8	C₂×Dic₂₂₆	C₂²	1	2	yes	—
9	C₂²×Dic₁₁₃	—	2	1	no	—
10	C₂²×Dic₁₁₃	—	2	1	no	—
11	C₄⋊Dic₁₁₃	—	2	1	no	—
12	C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₁₃	—	2	2	no	—
15	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
20	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₁₃	—	2	4	no	—
22	C₂×Dic₁₁₃	—	2	2	no	—
23	C₂×Dic₁₁₃	—	2	2	no	—
24	C₂×Dic₁₁₃	—	4	2	no	—
25	Dic₂₂₆	—	2	4	no	—
26	Dic₂₂₆	—	2	2	no	—
27	Dic₂₂₆	C₂×C₄	1	4	yes	complemented
28	C₈×C₁₁₃	—	2	2	no	—
29	C₂²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₁₃	SD₁₆	1	2	yes	—
31	C₂²×C₁₁₃	Q₁₆	1	2	yes	—
32	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
34	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
36	Dic₁₁₃	—	2	4	no	—
37	Dic₁₁₃	—	4	2	no	—
38	C₂×C₁₁₃	#103	1	4	yes	complemented
39	C₂×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₁₁₃	C₂×Q₁₆	1	1	yes	characteristic
42	C₁₁₃	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	113	1	no	maximal, Sylow
44	C₂²×Q₈	—	113	1	no	—
45	C₂²×C₈	D₁₁₃	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	113	1	no	—
47	#103	—	113	4	no	—
48	C₂×Q₈	—	113	4	no	—
49	C₂×Q₈	—	113	2	no	—
50	C₂×Q₈	—	226	1	no	—
51	C₂×Q₈	—	226	2	no	—
52	C₂²×C₄	—	226	1	no	—
53	C₂²×C₄	—	226	1	no	—
54	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
57	C₄⋊C₄	—	113	2	no	—
58	C₄⋊C₄	—	226	1	no	—
59	C₂³	D₄₅₂	1	1	yes	characteristic
60	Q₈	—	113	4	no	—
61	Q₈	—	226	4	no	—
62	Q₈	—	226	2	no	—
63	C₂×C₄	—	452	2	no	—
64	C₂×C₄	—	226	2	no	—
65	C₂×C₄	—	226	4	no	—
66	C₂×C₄	—	226	2	no	—
67	C₂×C₄	C₄×D₁₁₃	1	2	yes	—
68	C₂×C₄	D₄₅₂	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₁₁₃	1	2	yes	—
70	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	#14268624	1	2	yes	—
73	C₂²	#14268636	1	2	yes	—
74	C₂²	Dic₄₅₂	1	2	yes	—
75	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
76	C₄	—	452	2	no	—
77	C₄	—	226	4	no	—
78	C₄	#14268624	1	2	yes	—
79	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
81	C₂	#16813547	1	4	yes	direct product factor
82	C₂	C₂×#14268624	1	1	yes	characteristic
83	C₂	C₂×#14268636	1	1	yes	characteristic
84	C₂	C₂×Dic₄₅₂	1	1	yes	characteristic

	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×#103
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
3. #16813547	C₂	direct (N × H)
7. C₂×Dic₂₂₆	C₄	semidirect
27. Dic₂₂₆	C₂×C₄	semidirect
38. C₂×C₁₁₃	#103	semidirect
42. C₁₁₃	C₂×#103	semidirect
81. C₂	#16813547	direct (N × H)

Subgroups — C2×#16813547 #20298590

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813547 #20298590