Subgroups — #28405690

Order 14464.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299530	C₂	1	2	yes	maximal, complemented
2	C₂×#16813561	C₂	1	1	yes	maximal, characteristic
3	#16813672	—	2	2	no	—
4	C₂×C₈×D₁₁₃	C₄	1	1	yes	characteristic
5	#16813561	—	2	2	no	—
6	C₂×#14268622	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₁₃	C₈	1	1	yes	characteristic
9	C₂×#11744751	C₈	1	1	yes	characteristic
10	C₈×D₁₁₃	—	2	1	no	—
11	C₈×D₁₁₃	—	2	1	no	—
12	#14268622	D₄	1	2	yes	—
13	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₁₃	—	2	1	no	—
15	C₂²×D₁₁₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₁₃	C₁₆	1	1	yes	characteristic
18	C₄×D₁₁₃	—	2	1	no	—
19	C₄×D₁₁₃	—	2	1	no	—
20	C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
22	#11744751	—	2	1	no	—
23	C₂²×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₁₁₃	—	2	1	no	—
25	C₂×D₁₁₃	—	4	1	no	—
26	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₁₁₃	M₃₂	1	1	yes	characteristic
28	Dic₁₁₃	—	2	1	no	—
29	C₂×C₁₁₃	—	2	1	no	—
30	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
31	D₁₁₃	—	4	1	no	—
32	#1400	—	113	1	no	maximal, Sylow
33	C₁₁₃	#1400	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₃₂	—	113	1	no	—
35	M₆₄	—	113	2	no	—
36	C₂²×C₈	—	113	1	no	—
37	M₃₂	—	226	2	no	—
38	C₂×C₁₆	—	113	1	no	—
39	C₂×C₁₆	#90673	1	1	yes	characteristic
40	C₃₂	—	226	2	no	—
41	C₂²×C₄	—	113	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	226	1	no	—
44	C₂×C₈	—	226	1	no	—
45	C₂×C₈	C₂×#90673	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	—	113	2	no	—
48	C₂³	—	113	1	no	—
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	226	1	no	—
51	C₂×C₄	—	226	1	no	—
52	C₂×C₄	#14268655	1	1	yes	characteristic
53	C₈	—	226	1	no	—
54	C₈	C₂²⋊#90673	1	1	yes	characteristic
55	C₈	#14268657	1	1	yes	characteristic
56	C₂²	—	452	1	no	—
57	C₂²	—	226	1	no	—
58	C₂²	#16813695	1	1	yes	characteristic
59	C₄	—	226	1	no	—
60	C₄	#16813679	1	1	yes	characteristic
61	C₄	#16813697	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	452	1	no	—
64	C₂	#20299493	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#90673
commutator	C₂²×C₁₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₂²⋊C₁₆
prime radical	C₂²×D₁₁₃	C₁₆
cosocle	C₂×#14268622	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1400
LCS	G ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #20299530	C₂	semidirect
33. C₁₁₃	#1400	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20299530	2
C₂×#16813561	2
#1400	113