Subgroups — #28412396

Order 14656.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₂₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20301059	C₂	1	1	yes	maximal, characteristic, complemented
3	#20301011	C₂	1	1	yes	maximal, characteristic
4	#16814676	—	2	1	no	—
5	#16814669	—	2	1	no	—
6	#16814667	—	2	1	no	—
7	#16814653	—	2	1	no	—
8	D₁₈₃₂	C₄	1	1	yes	characteristic
9	C₈×D₂₂₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₂₂₉	C₄	1	1	yes	characteristic
11	#14270087	—	4	1	no	—
12	D₉₁₆	—	2	1	no	—
13	D₉₁₆	—	4	1	no	—
14	C₄×D₂₂₉	—	4	1	no	—
15	C₄×D₂₂₉	D₄	1	1	yes	characteristic
16	#14270080	D₄	1	1	yes	characteristic
17	Q₈×C₂₂₉	—	2	1	no	—
18	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₂₂₉	—	4	1	no	—
20	C₂×D₂₂₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₂₉	—	4	1	no	—
22	C₄×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₂₂₉	D₈	1	1	yes	characteristic
24	C₂×C₂₂₉	#102	1	1	yes	characteristic
25	D₂₂₉	—	2	1	no	—
26	D₂₂₉	—	8	1	no	—
27	C₂₂₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	229	1	no	maximal, Sylow
29	#135	—	229	1	no	—
30	C₂×C₁₆	—	229	1	no	—
31	#108	—	229	1	no	—
32	#41	—	458	1	no	—
33	Q₁₆	#11745021	1	1	yes	characteristic
34	SD₁₆	—	458	1	no	—
35	D₈	—	229	1	no	—
36	M₁₆	—	458	1	no	—
37	C₂×C₈	—	229	1	no	—
38	C₁₆	—	458	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	916	1	no	—
41	D₄	—	458	1	no	—
42	C₂×C₄	—	916	1	no	—
43	C₂×C₄	—	229	1	no	—
44	C₈	—	916	1	no	—
45	C₈	—	229	1	no	—
46	C₈	C₂×#11745021	1	1	yes	characteristic
47	C₂²	—	916	1	no	—
48	C₂²	—	229	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	229	1	no	—
51	C₄	C₂²⋊#11745021	1	1	yes	characteristic
52	C₂	—	1832	1	no	—
53	C₂	—	458	1	no	—
54	C₂	#20301050	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20301050
commutator	C₈×C₂₂₉	C₂×C₄
Frattini	C₈	C₂×#11745021
Fitting	Q₁₆×C₂₂₉	C₄
socle	C₂×C₂₂₉	#102
prime radical	#20301011	C₂
cosocle	C₈×D₂₂₉	C₂²
hypercenter	Q₁₆	#11745021
hypocenter	C₂₂₉	#359
LCS	G ▷ C₈×C₂₂₉ ▷ C₄×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₂₂₉⋊C₁₆	C₂	semidirect
2. #20301059	C₂	semidirect
27. C₂₂₉	#359	semidirect

Maximal subgroups

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

subgroup	index
D₂₂₉⋊C₁₆	2
#20301059	2
#20301011	2
#359	229