Subgroups — #28412402

Order 14656.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814669	C₂	1	2	yes	maximal
2	C₈×Dic₂₂₉	C₂	1	1	yes	maximal, characteristic
3	#16814669	—	2	2	no	—
4	C₂×#14270080	C₂²	1	1	yes	characteristic
5	C₄×Dic₂₂₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₂₂₉	C₄	1	1	yes	characteristic
7	C₂×Dic₂₂₉	C₈	1	1	yes	characteristic
8	C₂×Dic₂₂₉	C₈	1	1	yes	characteristic
9	#14270080	D₄	1	1	yes	characteristic
10	#14270080	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₂₉	—	2	1	no	—
13	C₂²×C₂₂₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₂₉	M₁₆	1	1	yes	characteristic
16	Dic₂₂₉	—	2	1	no	—
17	Dic₂₂₉	C₁₆	1	2	yes	complemented
18	C₂×C₂₂₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₂₂₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₂₂₉	M₃₂	1	1	yes	characteristic
21	C₂₂₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	229	1	no	maximal, Sylow
23	C₂×C₁₆	—	229	2	no	—
24	C₄×C₈	—	229	1	no	—
25	C₂×C₈	—	229	1	no	—
26	C₂×C₈	#11745021	1	1	yes	characteristic
27	C₄²	—	229	1	no	—
28	C₁₆	—	458	2	no	—
29	C₂×C₄	—	229	1	no	—
30	C₂×C₄	—	229	1	no	—
31	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	229	1	no	—
34	C₈	—	229	1	no	—
35	C₂²	D₂₂₉⋊C₈	1	1	yes	characteristic
36	C₄	—	458	1	no	—
37	C₄	—	229	2	no	—
38	C₄	C₄⋊#11745021	1	1	yes	characteristic
39	C₄	#16814675	1	1	yes	characteristic
40	C₂	#20301055	1	1	yes	characteristic
41	C₂	D₂₂₉⋊C₁₆	1	1	yes	characteristic
42	C₂	#20301063	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11745021
commutator	C₂×C₂₂₉	C₂×C₁₆
Fitting	C₂×C₈×C₂₂₉	C₄
socle, prime radical	C₂²×C₂₂₉	C₂×C₈
cosocle	C₂×#14270080	C₂²
hypercenter	C₂×C₈	#11745021
hypocenter	C₂₂₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
17. Dic₂₂₉	C₁₆	semidirect
21. C₂₂₉	C₄⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16814669	2
C₈×Dic₂₂₉	2
C₄⋊C₁₆	229