Subgroups — (C₂×#11745021)⋊C₈ #28412346

Order 14656.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11745021	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11745021	C₄	1	2	yes	—
5	D₂₂₉⋊C₈	—	2	1	no	—
6	D₂₂₉⋊C₈	—	2	1	no	—
7	C₂×#14270087	C₄	1	2	yes	complemented
8	C₄×#11745021	—	2	1	no	—
9	C₄×#11745021	—	2	1	no	—
10	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
11	C₂×#14270080	C₄	1	1	yes	characteristic, complemented
12	C₈×D₂₂₉	—	2	1	no	—
13	C₈×D₂₂₉	—	2	1	no	—
14	C₂×C₈×C₂₂₉	C₄	1	1	yes	characteristic, complemented
15	C₂×#11745021	—	2	2	no	—
16	C₂×#11745021	—	2	2	no	—
17	C₂×#11745021	C₈	1	4	yes	complemented
18	#14270087	—	2	2	no	—
19	C₂²×D₂₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
21	C₄×D₂₂₉	D₄	1	1	yes	characteristic
22	C₄×D₂₂₉	D₄	1	1	yes	characteristic
23	C₄×D₂₂₉	D₄	1	1	yes	characteristic
24	C₄×D₂₂₉	Q₈	1	1	yes	characteristic
25	#14270080	—	2	1	no	—
26	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
27	C₈×C₂₂₉	—	2	1	no	—
28	C₂²×C₂₂₉	C₄²	1	1	yes	characteristic
29	C₂×D₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₂₂₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₂₂₉	C₂×C₈	1	2	yes	—
32	C₂×D₂₂₉	M₁₆	1	2	yes	—
33	#11745021	—	2	4	no	—
34	C₄×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₂₂₉	C₄⋊C₄	1	1	yes	characteristic
36	Dic₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₂₂₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₂₂₉	#95	1	1	yes	characteristic
39	C₂×C₂₂₉	C₄×C₈	1	1	yes	characteristic
40	C₂×C₂₂₉	#97	1	1	yes	characteristic
41	D₂₂₉	C₂²⋊C₈	1	2	yes	—
42	D₂₂₉	C₄⋊C₈	1	2	yes	—
43	C₂₂₉	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	229	1	no	maximal, Sylow
45	C₂²×C₈	—	229	1	no	—
46	C₂²×C₈	—	229	1	no	—
47	C₂×C₄²	—	229	1	no	—
48	C₂²×C₄	—	229	2	no	—
49	C₂²×C₄	—	229	1	no	—
50	C₂×C₈	—	458	1	no	—
51	C₂×C₈	—	458	1	no	—
52	C₂×C₈	—	458	1	no	—
53	C₂×C₈	—	458	1	no	—
54	C₂×C₈	—	229	2	no	—
55	C₂×C₈	—	229	1	no	—
56	C₂×C₈	#11745021	1	1	yes	characteristic, complemented
57	C₄²	—	458	1	no	—
58	C₄²	—	458	1	no	—
59	C₂³	—	229	1	no	—
60	C₂×C₄	—	458	2	no	—
61	C₂×C₄	—	458	2	no	—
62	C₂×C₄	—	229	4	no	—
63	C₂×C₄	—	229	1	no	—
64	C₂×C₄	—	229	1	no	—
65	C₂×C₄	—	229	1	no	—
66	C₂×C₄	—	229	1	no	—
67	C₂×C₄	—	229	1	no	—
68	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	458	2	no	—
71	C₈	—	458	1	no	—
72	C₂²	—	229	1	no	—
73	C₂²	—	229	1	no	—
74	C₂²	—	229	2	no	—
75	C₂²	—	229	2	no	—
76	C₂²	C₄×#11745021	1	1	yes	characteristic
77	C₄	—	458	4	no	—
78	C₄	—	229	1	no	—
79	C₄	—	229	1	no	—
80	C₄	C₂²⋊#11745021	1	1	yes	characteristic
81	C₄	C₄⋊#11745021	1	1	yes	characteristic
82	C₂	—	229	2	no	—
83	C₂	—	229	2	no	—
84	C₂	(C₂×#11745021)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#11745021	1	1	yes	characteristic
86	C₂	#20301042	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#11745021
commutator	C₂×C₂₂₉	C₄×C₈
Fitting	C₂×C₈×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₄²
prime radical	C₂²×D₂₂₉	C₂×C₄
cosocle	C₂×C₄×D₂₂₉	C₂²
hypercenter	C₂×C₈	#11745021
hypocenter	C₂₂₉	#336
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
7. C₂×#14270087	C₄	semidirect
11. C₂×#14270080	C₄	semidirect
14. C₂×C₈×C₂₂₉	C₄	semidirect
17. C₂×#11745021	C₈	semidirect
43. C₂₂₉	#336	semidirect
56. C₂×C₈	#11745021	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₂₉⋊C₈	2
C₂×C₄×#11745021	2
C₂×C₈×D₂₂₉	2
#336	229

Subgroups — (C2×#11745021)⋊C8 #28412346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#11745021)⋊C₈ #28412346