Subgroups — #20298402

Order 7232.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268622	C₂	1	1	yes	maximal, characteristic
2	#16813556	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₁₃	—	2	1	no	—
5	#14268622	—	2	1	no	—
6	C₂×Q₈×C₁₁₃	—	2	1	no	—
7	Q₁₆×C₁₁₃	—	2	1	no	—
8	Q₁₆×C₁₁₃	C₄	1	2	yes	complemented
9	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
10	Q₈×C₁₁₃	—	2	2	no	—
11	Q₈×C₁₁₃	—	4	1	no	—
12	C₂×C₄×C₁₁₃	—	4	1	no	—
13	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
14	C₂×Dic₁₁₃	—	4	1	no	—
15	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₁₁₃	D₈	1	1	yes	characteristic
18	C₄×C₁₁₃	—	4	2	no	—
19	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₁₃	SD₁₆	1	1	yes	characteristic
21	Dic₁₁₃	—	8	1	no	—
22	C₂×C₁₁₃	#102	1	1	yes	characteristic
23	C₂×C₁₁₃	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₁₃	Q₃₂	1	1	yes	characteristic
25	C₁₁₃	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	113	1	no	maximal, Sylow
27	C₂×Q₁₆	D₁₁₃	1	1	yes	characteristic
28	C₂×C₁₆	—	113	1	no	—
29	#107	—	113	1	no	—
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	Dic₁₁₃	1	2	yes	complemented
33	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
34	C₄⋊C₄	—	226	1	no	—
35	C₁₆	—	226	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	452	1	no	—
40	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
41	C₈	C₂×Dic₁₁₃	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
43	C₂²	#14268632	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	904	1	no	—
46	C₄	C₂²⋊Dic₁₁₃	1	1	yes	characteristic
47	C₄	#14268635	1	1	yes	characteristic
48	C₂	#16813543	1	1	yes	characteristic
49	C₂	#16813565	1	1	yes	characteristic
50	C₂	#16813568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14268632
commutator	C₈×C₁₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₁₃
Fitting	C₂×Q₁₆×C₁₁₃	C₂
socle	C₂²×C₁₁₃	D₈
hypercenter	C₂×Q₁₆	D₁₁₃
hypocenter	C₁₁₃	#358
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. Q₁₆×C₁₁₃	C₄	semidirect
25. C₁₁₃	#358	semidirect
32. Q₁₆	Dic₁₁₃	semidirect