Subgroups — C₂×#20301049 #28412465

Order 14656.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814675	C₂	1	2	yes	maximal
2	#20301049	C₂	1	4	yes	maximal, direct product factor
3	C₂²×Dic₄₅₈	C₂	1	1	yes	maximal, characteristic
4	#16814675	—	2	2	no	—
5	#16814675	C₂²	1	4	yes	—
6	C₂×#14270087	—	2	2	no	—
7	C₂×Dic₄₅₈	—	2	2	no	—
8	C₂×Dic₄₅₈	—	2	2	no	—
9	C₂×Dic₄₅₈	C₄	1	2	yes	—
10	C₂×Dic₄₅₈	C₂²	1	2	yes	—
11	C₂²×Dic₂₂₉	C₄	1	1	yes	characteristic
12	C₂²×Dic₂₂₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₂₉	C₄	1	1	yes	characteristic
14	#14270087	—	2	4	no	—
15	Dic₄₅₈	—	2	4	no	—
16	Dic₄₅₈	—	2	4	no	—
17	C₂×Dic₂₂₉	—	2	1	no	—
18	C₂×Dic₂₂₉	—	2	1	no	—
19	C₂×Dic₂₂₉	C₂×C₄	1	2	yes	—
20	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₂₉	D₄	1	2	yes	—
22	C₂×Dic₂₂₉	D₄	1	2	yes	—
23	C₂×Dic₂₂₉	C₂³	1	1	yes	characteristic
24	C₂³×C₂₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₂₉	—	2	1	no	—
26	C₂×C₄×C₂₂₉	—	2	1	no	—
27	C₂×C₄×C₂₂₉	C₂×C₄	1	2	yes	—
28	C₂²×C₂₂₉	—	2	2	no	—
29	C₂²×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₂₉	—	2	2	no	—
33	Dic₂₂₉	—	2	2	no	—
34	Dic₂₂₉	C₂²⋊C₄	1	2	yes	—
35	Dic₂₂₉	C₂×D₄	1	2	yes	—
36	C₂×C₂₂₉	—	2	1	no	—
37	C₂×C₂₂₉	—	2	1	no	—
38	C₂×C₂₂₉	#101	1	2	yes	complemented
39	C₂×C₂₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂₂₉	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂×#101	—	229	1	no	maximal, Sylow
42	C₂²×Q₈	—	229	1	no	—
43	C₂×M₁₆	—	229	2	no	—
44	#101	—	229	4	no	—
45	C₂×Q₈	—	458	2	no	—
46	C₂×Q₈	—	458	2	no	—
47	C₂×Q₈	—	229	2	no	—
48	C₂×Q₈	—	229	2	no	—
49	C₂²×C₄	—	229	1	no	—
50	C₂²×C₄	—	229	1	no	—
51	C₂²×C₄	#11745021	1	1	yes	characteristic
52	M₁₆	—	458	2	no	—
53	M₁₆	—	229	4	no	—
54	C₂×C₈	—	458	2	no	—
55	C₂³	C₂×#11745021	1	1	yes	characteristic
56	Q₈	—	458	4	no	—
57	Q₈	—	458	4	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	458	1	no	—
61	C₂×C₄	—	458	1	no	—
62	C₂×C₄	—	229	2	no	—
63	C₂×C₄	—	229	2	no	—
64	C₂×C₄	—	229	2	no	—
65	C₂×C₄	—	229	1	no	—
66	C₂×C₄	—	229	1	no	—
67	C₂×C₄	C₂×#11745021	1	2	yes	—
68	C₈	—	458	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#11745021	1	1	yes	characteristic
71	C₂²	C₂²⋊#11745021	1	1	yes	characteristic
72	C₂²	C₂²×#11745021	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	458	2	no	—
75	C₄	—	229	2	no	—
76	C₄	—	229	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#20301049	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊#11745021	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#11745021
commutator	C₂²×C₂₂₉	C₂²×C₄
Frattini	C₂²	C₂²×#11745021
Fitting	C₂²×C₄×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₂²⋊C₄
prime radical	C₂³×C₂₂₉	C₂×C₄
cosocle	C₂×Dic₂₂₉	C₂³
hypercenter	C₂²×C₄	#11745021
hypocenter	C₂₂₉	C₂×#101
LCS	G ▷ C₂²×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #20301049	C₂	direct (N × H)
38. C₂×C₂₂₉	#101	semidirect
40. C₂₂₉	C₂×#101	semidirect
79. C₂	#20301049	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×#16814675	2
#20301049	2
C₂²×Dic₄₅₈	2
C₂×#101	229

Subgroups — C2×#20301049 #28412465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20301049 #28412465