Subgroups — C₂×#20300934 #28411908

Order 14656.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₁₆	C₂	1	1	yes	maximal, characteristic
2	#20300934	C₂	1	4	yes	maximal, direct product factor
3	C₂×#16814641	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₅₈	—	2	1	no	—
6	Dic₉₁₆	—	2	1	no	—
7	Dic₉₁₆	C₂²	1	2	yes	—
8	#16814641	C₂²	1	2	yes	—
9	C₂×Q₈×C₂₂₉	—	2	1	no	—
10	Q₁₆×C₂₂₉	—	2	1	no	—
11	Q₁₆×C₂₂₉	C₂²	1	2	yes	—
12	C₂×C₈×C₂₂₉	C₂²	1	1	yes	characteristic
13	Dic₄₅₈	—	2	2	no	—
14	Dic₄₅₈	—	4	1	no	—
15	C₂×Dic₂₂₉	—	4	1	no	—
16	Q₈×C₂₂₉	—	2	2	no	—
17	Q₈×C₂₂₉	—	4	1	no	—
18	C₂×C₄×C₂₂₉	—	4	1	no	—
19	C₂×C₄×C₂₂₉	D₄	1	1	yes	characteristic
20	C₈×C₂₂₉	D₄	1	1	yes	characteristic
21	C₈×C₂₂₉	C₂³	1	1	yes	characteristic
22	C₂²×C₂₂₉	D₈	1	1	yes	characteristic
23	C₄×C₂₂₉	—	4	2	no	—
24	C₄×C₂₂₉	D₈	1	1	yes	characteristic
25	C₄×C₂₂₉	C₂×D₄	1	1	yes	characteristic
26	Dic₂₂₉	—	4	2	no	—
27	C₂×C₂₂₉	Q₃₂	1	2	yes	complemented
28	C₂×C₂₂₉	C₂×D₈	1	1	yes	characteristic
29	C₂₂₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	229	1	no	maximal, Sylow
31	C₂×Q₁₆	—	229	1	no	—
32	C₂×Q₁₆	D₂₂₉	1	1	yes	characteristic
33	Q₃₂	—	229	4	no	—
34	C₂×C₁₆	—	229	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	458	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	458	1	no	—
39	Q₁₆	—	229	2	no	—
40	Q₁₆	C₂×D₂₂₉	1	2	yes	—
41	C₂×C₈	C₂×D₂₂₉	1	1	yes	characteristic
42	C₁₆	—	229	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	916	1	no	—
46	Q₈	—	458	2	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	916	1	no	—
49	C₂×C₄	C₂²⋊D₂₂₉	1	1	yes	characteristic
50	C₈	C₂²⋊D₂₂₉	1	1	yes	characteristic
51	C₈	C₂²×D₂₂₉	1	1	yes	characteristic
52	C₂²	#16814651	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	916	2	no	—
55	C₄	#16814651	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₂₂₉	1	1	yes	characteristic
57	C₂	#20300934	1	2	yes	direct product factor
58	C₂	C₂×#16814651	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16814651
commutator, cosocle	C₈×C₂₂₉	C₂³
Frattini	C₈	C₂²×D₂₂₉
Fitting	C₂×Q₁₆×C₂₂₉	C₂
socle, prime radical	C₂²×C₂₂₉	D₈
hypercenter	C₂×Q₁₆	D₂₂₉
hypocenter	C₂₂₉	C₂×Q₃₂
LCS	G ▷ C₈×C₂₂₉ ▷ C₄×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #20300934	C₂	direct (N × H)
27. C₂×C₂₂₉	Q₃₂	semidirect
29. C₂₂₉	C₂×Q₃₂	semidirect
57. C₂	#20300934	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₉₁₆	2
#20300934	2
C₂×#16814641	2
C₂×Q₁₆×C₂₂₉	2
C₂×Q₃₂	229

Subgroups — C2×#20300934 #28411908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20300934 #28411908