Subgroups — C₂×#11745266 #14271945

Order 1856.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90805	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745266	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90773	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₂₉	—	2	2	no	—
9	#90805	—	2	4	no	—
10	#90805	C₂²	1	8	yes	complemented
11	C₂×D₁₁₆	C₂²	1	2	yes	—
12	C₂×C₄×D₂₉	—	2	2	no	—
13	C₂×Dic₅₈	C₂²	1	2	yes	—
14	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂²	1	4	yes	complemented
17	Dic₁₁₆	C₂²	1	4	yes	complemented
18	D₂₃₂	C₂²	1	4	yes	complemented
19	#90773	C₂²	1	8	yes	complemented
20	C₂³×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×D₂₉	—	2	2	no	—
22	C₂×C₄×C₂₉	D₄	1	2	yes	—
23	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂³	1	2	yes	—
26	C₂²⋊D₂₉	—	2	8	no	—
27	C₂×Dic₂₉	—	2	2	no	—
28	D₁₁₆	—	2	2	no	—
29	D₁₁₆	C₂³	1	4	yes	—
30	C₄×D₂₉	—	2	8	no	—
31	Dic₅₈	—	2	2	no	—
32	Dic₅₈	C₂³	1	4	yes	—
33	C₈×C₂₉	C₂³	1	2	yes	—
34	C₈×C₂₉	C₂³	1	2	yes	—
35	C₂²×C₂₉	—	2	2	no	—
36	C₂²×C₂₉	C₂×D₄	1	2	yes	—
37	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×D₂₉	—	2	4	no	—
39	C₂×D₂₉	—	4	4	no	—
40	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
41	C₄×C₂₉	C₂×D₄	1	2	yes	—
42	C₄×C₂₉	C₂⁴	1	1	yes	characteristic
43	Dic₂₉	—	2	4	no	—
44	C₂×#135	—	29	1	no	maximal, Sylow
45	C₂×C₂₉	—	2	2	no	—
46	C₂×C₂₉	#135	1	2	yes	complemented
47	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
48	D₂₉	—	4	4	no	—
49	C₂×#41	—	29	2	no	—
50	#135	—	29	8	no	—
51	C₂×Q₁₆	—	29	1	no	—
52	C₂×SD₁₆	—	29	2	no	—
53	C₂×D₈	—	29	1	no	—
54	C₂²×C₈	D₂₉	1	1	yes	characteristic, complemented
55	C₂₉	C₂×#135	1	1	yes	characteristic, complemented, Sylow
56	#41	—	29	8	no	—
57	#41	—	58	4	no	—
58	C₂×Q₈	—	29	2	no	—
59	C₂×D₄	—	29	2	no	—
60	C₂×D₄	—	58	2	no	—
61	C₂²×C₄	—	58	2	no	—
62	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
63	Q₁₆	—	29	4	no	—
64	SD₁₆	—	29	8	no	—
65	D₈	—	29	4	no	—
66	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
67	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
68	C₂×C₈	C₂×D₂₉	1	4	yes	complemented
69	C₂³	—	58	2	no	—
70	C₂³	D₁₁₆	1	1	yes	characteristic
71	Q₈	—	29	4	no	—
72	Q₈	—	58	2	no	—
73	D₄	—	29	4	no	—
74	D₄	—	58	8	no	—
75	D₄	—	58	2	no	—
76	C₂×C₄	—	58	2	no	—
77	C₂×C₄	—	58	8	no	—
78	C₂×C₄	D₁₁₆	1	2	yes	—
79	C₂×C₄	D₁₁₆	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₂₉	1	2	yes	—
82	C₈	C₂²×D₂₉	1	2	yes	—
83	C₈	C₂²×D₂₉	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	58	4	no	—
86	C₂²	—	116	4	no	—
87	C₂²	C₂×D₁₁₆	1	2	yes	—
88	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
89	C₄	—	58	4	no	—
90	C₄	C₂×D₁₁₆	1	2	yes	—
91	C₄	C₂×D₁₁₆	1	1	yes	characteristic
92	C₄	C₂³×D₂₉	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	116	4	no	—
95	C₂	#11745266	1	2	yes	direct product factor
96	C₂	C₂²×D₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₁₆
commutator, cosocle	C₄×C₂₉	C₂⁴
Frattini	C₄	C₂³×D₂₉
Fitting	C₂²×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
hypercenter	C₂²×C₈	D₂₉
hypocenter	C₂₉	C₂×#135
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#90805	C₂	semidirect
2. C₂²×C₈×C₂₉	C₂	semidirect
3. C₂×Dic₁₁₆	C₂	semidirect
4. #11745266	C₂	direct (N × H)
5. C₂×D₂₃₂	C₂	semidirect
6. C₂×#90773	C₂	semidirect
10. #90805	C₂²	semidirect
16. C₂×C₈×C₂₉	C₂²	semidirect
17. Dic₁₁₆	C₂²	semidirect
18. D₂₃₂	C₂²	semidirect
19. #90773	C₂²	semidirect
46. C₂×C₂₉	#135	semidirect
54. C₂²×C₈	D₂₉	semidirect
55. C₂₉	C₂×#135	semidirect
68. C₂×C₈	C₂×D₂₉	semidirect
95. C₂	#11745266	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×#90805	2
C₂²×C₈×C₂₉	2
C₂×Dic₁₁₆	2
#11745266	2
C₂×D₂₃₂	2
C₂×#90773	2
C₂×#135	29

Subgroups — C2×#11745266 #14271945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745266 #14271945