Subgroups — #20299474

Order 7232.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268657	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#14268657	—	2	2	no	—
4	#14268657	C₄	1	4	yes	—
5	C₂×#11744753	—	2	2	no	—
6	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
7	C₂×#11744751	C₄	1	1	yes	characteristic
8	C₈×D₁₁₃	—	2	2	no	—
9	C₂×C₈×C₁₁₃	C₄	1	1	yes	characteristic
10	C₂²×D₁₁₃	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
13	C₄×D₁₁₃	C₂×C₄	1	2	yes	—
14	C₄×D₁₁₃	D₄	1	2	yes	—
15	#11744753	—	2	4	no	—
16	C₈×C₁₁₃	—	2	1	no	—
17	#11744751	—	2	1	no	—
18	C₂²×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₁₃	—	2	1	no	—
20	C₂×D₁₁₃	—	2	1	no	—
21	C₂×D₁₁₃	C₄⋊C₄	1	2	yes	—
22	C₄×C₁₁₃	C₄²	1	1	yes	characteristic
23	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₁₃	C₂²⋊C₄	1	2	yes	—
25	C₂×C₁₁₃	#95	1	1	yes	characteristic
26	C₂×C₁₁₃	#108	1	1	yes	characteristic
27	C₂×C₁₁₃	#108	1	1	yes	characteristic
28	D₁₁₃	—	2	2	no	—
29	C₁₁₃	#341	1	1	yes	characteristic, complemented, Sylow
30	#341	—	113	1	no	maximal, Sylow
31	C₂×M₁₆	—	113	2	no	—
32	C₂²×C₈	—	113	1	no	—
33	C₂²×C₄	—	113	1	no	—
34	M₁₆	—	113	4	no	—
35	M₁₆	—	226	2	no	—
36	C₂×C₈	—	113	1	no	—
37	C₂×C₈	—	226	2	no	—
38	C₂×C₈	—	226	2	no	—
39	C₂×C₈	#90673	1	1	yes	characteristic
40	C₂³	—	113	1	no	—
41	C₂×C₄	—	113	1	no	—
42	C₂×C₄	—	113	2	no	—
43	C₂×C₄	—	113	2	no	—
44	C₂×C₄	C₂×#90673	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	226	4	no	—
47	C₈	—	226	1	no	—
48	C₂²	—	113	2	no	—
49	C₂²	—	226	1	no	—
50	C₂²	—	226	1	no	—
51	C₂²	C₄⋊#90673	1	1	yes	characteristic
52	C₄	—	113	2	no	—
53	C₄	C₄×#90673	1	1	yes	characteristic
54	C₄	C₂²⋊#90673	1	1	yes	characteristic
55	C₂	—	226	2	no	—
56	C₂	(C₂×#90673)⋊C₄	1	1	yes	characteristic
57	C₂	#16813692	1	1	yes	characteristic
58	C₂	#16813693	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#90673
commutator	C₄×C₁₁₃	C₄²
Frattini	C₂×C₄	C₂×#90673
Fitting	C₂×C₈×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₄⋊C₄
hypercenter	C₂×C₈	#90673
hypocenter	C₁₁₃	#341
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
29. C₁₁₃	#341	semidirect