Subgroups — #20298799

Order 7232.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268636	C₂	1	2	yes	maximal, complemented
2	#16813619	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813544	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₂₆	C₂²	1	1	yes	characteristic
7	C₂×D₄₅₂	—	2	1	no	—
8	C₂×D₄₅₂	—	2	1	no	—
9	C₂×D₄₅₂	C₂²	1	2	yes	—
10	#14268636	—	2	4	no	—
11	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
12	#14268626	—	2	1	no	—
13	C₄×Dic₁₁₃	—	2	1	no	—
14	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
15	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×D₁₁₃	—	2	2	no	—
17	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₁₃	—	2	1	no	—
21	C₂×Dic₁₁₃	—	2	1	no	—
22	D₄₅₂	—	2	2	no	—
23	D₄₅₂	—	2	2	no	—
24	D₄₅₂	—	4	2	no	—
25	D₄₅₂	—	4	2	no	—
26	Dic₂₂₆	—	2	1	no	—
27	Dic₂₂₆	D₄	1	2	yes	complemented
28	C₈×C₁₁₃	—	2	2	no	—
29	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×D₁₁₃	—	4	2	no	—
31	C₂×D₁₁₃	—	4	2	no	—
32	C₂×D₁₁₃	—	4	2	no	—
33	C₄×C₁₁₃	—	2	1	no	—
34	C₄×C₁₁₃	SD₁₆	1	2	yes	complemented
35	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₁₃	#41	1	1	yes	characteristic
37	Dic₁₁₃	—	2	2	no	—
38	Dic₁₁₃	—	4	1	no	—
39	C₂×C₁₁₃	#121	1	1	yes	characteristic
40	C₂×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
42	D₁₁₃	—	8	2	no	—
43	C₁₁₃	#460	1	1	yes	characteristic, complemented, Sylow
44	#460	—	113	1	no	maximal, Sylow
45	C₂×SD₁₆	—	113	2	no	—
46	#127	—	113	1	no	—
47	C₄×Q₈	—	113	1	no	—
48	C₄⋊C₈	D₁₁₃	1	1	yes	characteristic, complemented
49	#102	—	113	2	no	—
50	C₂×Q₈	—	113	1	no	—
51	C₂×D₄	—	113	2	no	—
52	C₂×D₄	—	226	1	no	—
53	C₂×D₄	—	226	1	no	—
54	SD₁₆	—	226	4	no	—
55	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
56	C₄⋊C₄	—	113	1	no	—
57	C₄⋊C₄	—	226	1	no	—
58	C₄²	—	226	1	no	—
59	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
60	C₂³	—	226	2	no	—
61	Q₈	—	113	2	no	—
62	Q₈	—	226	1	no	—
63	D₄	—	452	2	no	—
64	D₄	—	452	2	no	—
65	D₄	—	226	2	no	—
66	D₄	—	226	2	no	—
67	C₂×C₄	—	226	1	no	—
68	C₂×C₄	—	226	1	no	—
69	C₂×C₄	D₄₅₂	1	1	yes	characteristic
70	C₂×C₄	D₄₅₂	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	452	2	no	—
74	C₂²	—	452	2	no	—
75	C₂²	—	452	2	no	—
76	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	452	1	no	—
79	C₄	—	226	2	no	—
80	C₄	#14268636	1	2	yes	complemented
81	C₄	D₄×D₁₁₃	1	1	yes	characteristic
82	C₄	#14268648	1	1	yes	characteristic
83	C₂	—	904	2	no	—
84	C₂	#16813597	1	1	yes	characteristic
85	C₂	C₂×#14268636	1	1	yes	characteristic
86	C₂	#16813650	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₅₂
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄⋊C₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄⋊C₈	D₁₁₃
hypocenter	C₁₁₃	#460
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#14268636	C₂	semidirect
3. C₄×Dic₂₂₆	C₂	semidirect
4. #16813544	C₂	semidirect
5. C₄⋊C₈×C₁₁₃	C₂	semidirect
27. Dic₂₂₆	D₄	semidirect
34. C₄×C₁₁₃	SD₁₆	semidirect
43. C₁₁₃	#460	semidirect
48. C₄⋊C₈	D₁₁₃	semidirect
80. C₄	#14268636	semidirect