Subgroups — #28411530

Order 14656.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814650	C₂	1	2	yes	maximal
2	#20300924	C₂	1	4	yes	maximal, complemented
3	C₂×M₁₆×C₂₂₉	C₂	1	1	yes	maximal, characteristic
4	#16814650	—	2	2	no	—
5	#16814650	C₂²	1	4	yes	—
6	C₂×#14270080	—	2	2	no	—
7	C₂²×C₄×C₂₂₉	C₂²	1	1	yes	characteristic
8	M₁₆×C₂₂₉	C₄	1	4	yes	—
9	C₂×C₈×C₂₂₉	C₂²	1	2	yes	—
10	#14270080	—	2	4	no	—
11	C₂³×C₂₂₉	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₂₂₉	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₂₂₉	D₄	1	2	yes	—
14	C₂×C₄×C₂₂₉	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₂₂₉	C₂³	1	1	yes	characteristic
16	C₈×C₂₂₉	C₂×C₄	1	4	yes	—
17	C₂²×C₂₂₉	—	4	1	no	—
18	C₂²×C₂₂₉	C₄⋊C₄	1	2	yes	—
19	C₂²×C₂₂₉	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₂₂₉	C₄⋊C₄	1	2	yes	—
21	C₄×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₂₂₉	C₂×D₄	1	1	yes	characteristic
23	C₂×C₂₂₉	—	2	2	no	—
24	C₂×C₂₂₉	—	2	1	no	—
25	C₂×C₂₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
26	C₂₂₉	#430	1	1	yes	characteristic, complemented, Sylow
27	#430	—	229	1	no	maximal, Sylow
28	C₂×M₁₆	—	229	2	no	—
29	C₂×M₁₆	D₂₂₉	1	1	yes	characteristic
30	#108	—	229	4	no	—
31	C₂²×C₄	C₂×D₂₂₉	1	1	yes	characteristic
32	M₁₆	—	458	2	no	—
33	M₁₆	—	229	4	no	—
34	M₁₆	Dic₂₂₉	1	4	yes	—
35	C₂×C₈	—	458	2	no	—
36	C₂×C₈	C₂×D₂₂₉	1	2	yes	—
37	C₂³	Dic₄₅₈	1	1	yes	characteristic
38	C₂×C₄	C₂×Dic₂₂₉	1	2	yes	—
39	C₂×C₄	D₉₁₆	1	2	yes	—
40	C₂×C₄	Dic₄₅₈	1	1	yes	characteristic
41	C₂×C₄	C₂²×D₂₂₉	1	1	yes	characteristic
42	C₈	—	458	4	no	—
43	C₈	C₂×Dic₂₂₉	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₂₂₉	1	2	yes	—
46	C₂²	C₂×Dic₄₅₈	1	1	yes	characteristic
47	C₄	C₄⋊Dic₂₂₉	1	2	yes	—
48	C₄	C₂²×Dic₂₂₉	1	1	yes	characteristic
49	C₄	C₂×D₉₁₆	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₂₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₉₁₆
commutator	C₄×C₂₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₂₉
Fitting	C₂×M₁₆×C₂₂₉	C₂
socle	C₂×C₂₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₂₉	Q₈
cosocle	C₂×C₄×C₂₂₉	C₂³
hypercenter	C₂×M₁₆	D₂₂₉
hypocenter	C₂₂₉	#430
LCS	G ▷ C₄×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #20300924	C₂	semidirect
26. C₂₂₉	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16814650	2
#20300924	2
C₂×M₁₆×C₂₂₉	2
#430	229