Subgroups — #28412339

Order 14656.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301055	C₂	1	2	yes	maximal, complemented
2	#20300984	C₂	1	1	yes	maximal, characteristic
3	C₂×#14270087	—	2	2	no	—
4	C₂×D₉₁₆	C₄	1	1	yes	characteristic
5	C₂×C₂²⋊D₂₂₉	—	2	2	no	—
6	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₂₂₉	C₄	1	1	yes	characteristic
8	#14270087	—	4	2	no	—
9	C₂²×D₂₂₉	—	2	1	no	—
10	D₉₁₆	—	4	1	no	—
11	C₂²⋊D₂₂₉	—	4	2	no	—
12	C₂²⋊D₂₂₉	—	4	2	no	—
13	C₂×Dic₂₂₉	D₄	1	2	yes	—
14	C₂³×C₂₂₉	—	2	1	no	—
15	D₄×C₂₂₉	—	4	1	no	—
16	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₂₂₉	—	4	1	no	—
18	C₂²×C₂₂₉	—	4	2	no	—
19	C₂²×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×D₂₂₉	—	4	1	no	—
21	C₂×D₂₂₉	—	4	2	no	—
22	C₄×C₂₂₉	—	2	1	no	—
23	Dic₂₂₉	D₈	1	2	yes	—
24	Dic₂₂₉	SD₁₆	1	2	yes	—
25	C₂×C₂₂₉	—	8	1	no	—
26	C₂×C₂₂₉	#100	1	1	yes	characteristic
27	C₂×C₂₂₉	#102	1	2	yes	—
28	D₂₂₉	—	8	1	no	—
29	C₂₂₉	#331	1	1	yes	characteristic, complemented, Sylow
30	#331	—	229	1	no	maximal, Sylow
31	#127	—	229	1	no	—
32	C₄⋊C₈	—	229	2	no	—
33	C₂×D₄	—	458	2	no	—
34	C₂×D₄	—	229	1	no	—
35	C₂×D₄	#11745021	1	1	yes	characteristic
36	C₂×C₈	—	458	2	no	—
37	C₄²	—	229	1	no	—
38	C₂³	—	2	1	no	—
39	C₂³	—	458	1	no	—
40	D₄	—	4	1	no	—
41	D₄	—	916	1	no	—
42	D₄	—	916	2	no	—
43	D₄	—	916	2	no	—
44	C₂×C₄	—	229	2	no	—
45	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
46	C₈	—	916	2	no	—
47	C₂²	—	4	1	no	—
48	C₂²	—	4	2	no	—
49	C₂²	—	916	1	no	—
50	C₂²	—	916	2	no	—
51	C₂²	C₂²⋊#11745021	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	229	2	no	—
54	C₄	—	229	2	no	—
55	C₂	—	8	1	no	—
56	C₂	—	1832	1	no	—
57	C₂	#20301048	1	1	yes	characteristic
58	C₂	#20301050	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²⋊#11745021
commutator	C₂×C₄×C₂₂₉	C₂×C₄
Frattini	C₂×C₄	C₂×#11745021
Fitting	C₂×D₄×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₂²⋊C₄
prime radical	#20300984	C₂
cosocle	C₄×Dic₂₂₉	C₂²
hypercenter	C₂×D₄	#11745021
hypocenter	C₂₂₉	#331
LCS	G ▷ C₂×C₄×C₂₂₉ ▷ C₂²×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #20301055	C₂	semidirect
29. C₂₂₉	#331	semidirect

Maximal subgroups

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

subgroup	index
#20301055	2
#20300984	2
#331	229