Subgroups — C₂×#11745365 #14271996

Order 1856.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745365	C₂	1	16	yes	maximal, direct product factor
3	C₂×Q₈×D₂₉	C₂	1	2	yes	maximal, complemented
4	C₂×#90807	C₂	1	6	yes	maximal, complemented
5	C₂×#90805	C₂	1	3	yes	maximal, complemented
6	C₂²×Dic₅₈	C₂	1	3	yes	maximal, complemented
7	#41×C₂₉	C₂²	1	8	yes	complemented
8	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₂₉	C₂²	1	3	yes	—
10	C₂²×C₄×C₂₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊D₂₉	C₂²	1	6	yes	—
12	C₂²×Dic₂₉	C₂²	1	6	yes	—
13	Q₈×D₂₉	C₂²	1	16	yes	complemented
14	#90807	C₂²	1	48	yes	complemented
15	#90805	C₂²	1	24	yes	complemented
16	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₂₉	C₂²	1	6	yes	—
18	C₂×Dic₅₈	C₂²	1	3	yes	—
19	C₂×Dic₅₈	C₂²	1	6	yes	—
20	C₂×Dic₅₈	C₂²	1	24	yes	complemented
21	C₂³×C₂₉	C₂³	1	3	yes	—
22	C₂²×D₂₉	C₂³	1	2	yes	—
23	Q₈×C₂₉	C₂³	1	4	yes	—
24	D₄×C₂₉	C₂³	1	12	yes	—
25	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂³	1	3	yes	—
27	C₂×C₄×C₂₉	C₂³	1	12	yes	—
28	C₂²⋊D₂₉	C₂³	1	24	yes	—
29	C₂×Dic₂₉	C₂³	1	6	yes	—
30	C₂×Dic₂₉	C₂³	1	24	yes	—
31	D₁₁₆	C₂³	1	4	yes	—
32	C₄×D₂₉	C₂³	1	24	yes	—
33	Dic₅₈	C₂³	1	12	yes	—
34	Dic₅₈	C₂³	1	24	yes	—
35	C₂²×C₂₉	—	2	6	no	—
36	C₂²×C₂₉	C₂⁴	1	6	yes	—
37	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
38	C₂×D₂₉	—	2	4	no	—
39	C₂×D₂₉	C₂⁴	1	4	yes	—
40	C₄×C₂₉	C₂⁴	1	2	yes	—
41	C₄×C₂₉	C₂⁴	1	6	yes	—
42	Dic₂₉	C₂⁴	1	12	yes	—
43	C₂×2₋¹⁺⁴	—	29	1	no	maximal, Sylow
44	C₂×C₂₉	—	2	6	no	—
45	C₂×C₂₉	2₋¹⁺⁴	1	2	yes	complemented
46	C₂×C₂₉	C₂⁵	1	1	yes	characteristic
47	D₂₉	—	2	4	no	—
48	2₋¹⁺⁴	—	29	16	no	—
49	C₂×#41	—	29	6	no	—
50	C₂×#41	—	29	3	no	—
51	C₂×#41	D₂₉	1	1	yes	characteristic, complemented
52	C₂²×Q₈	—	29	2	no	—
53	C₂²×Q₈	—	29	3	no	—
54	C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
55	#41	—	29	48	no	—
56	#41	—	29	24	no	—
57	#41	C₂×D₂₉	1	8	yes	complemented
58	C₂×Q₈	—	29	16	no	—
59	C₂×Q₈	—	29	6	no	—
60	C₂×Q₈	—	29	3	no	—
61	C₂×Q₈	—	29	24	no	—
62	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
63	C₂×D₄	—	29	6	no	—
64	C₂×D₄	—	29	1	no	—
65	C₂×D₄	C₂×D₂₉	1	3	yes	—
66	C₂²×C₄	—	29	6	no	—
67	C₂²×C₄	—	29	6	no	—
68	C₂²×C₄	C₂×D₂₉	1	3	yes	—
69	C₂³	—	29	2	no	—
70	C₂³	C₂²×D₂₉	1	3	yes	—
71	Q₈	—	29	24	no	—
72	Q₈	—	29	12	no	—
73	Q₈	C₂²×D₂₉	1	4	yes	—
74	D₄	—	29	24	no	—
75	D₄	—	29	4	no	—
76	D₄	C₂²×D₂₉	1	12	yes	—
77	C₂×C₄	—	29	24	no	—
78	C₂×C₄	—	29	6	no	—
79	C₂×C₄	—	29	24	no	—
80	C₂×C₄	C₂²×D₂₉	1	12	yes	—
81	C₂×C₄	C₂²×D₂₉	1	3	yes	—
82	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
83	C₂²	—	2	6	no	—
84	C₂²	—	29	4	no	—
85	C₂²	—	58	4	no	—
86	C₂²	C₂³×D₂₉	1	6	yes	—
87	C₂²	C₂³×D₂₉	1	1	yes	characteristic
88	C₄	—	29	12	no	—
89	C₄	C₂³×D₂₉	1	6	yes	—
90	C₄	C₂³×D₂₉	1	2	yes	—
91	C₂	—	2	6	no	—
92	C₂	—	58	4	no	—
93	C₂	#11745365	1	2	yes	direct product factor
94	C₂	C₂⁴×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₉
commutator, cosocle	C₂×C₂₉	C₂⁵
Frattini	C₂	C₂⁴×D₂₉
Fitting	C₂×#41×C₂₉	C₂
socle	C₂²×C₂₉	C₂⁴
hypercenter	C₂×#41	D₂₉
hypocenter	C₂₉	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×C₂₉	C₂	semidirect
2. #11745365	C₂	direct (N × H)
3. C₂×Q₈×D₂₉	C₂	semidirect
4. C₂×#90807	C₂	semidirect
5. C₂×#90805	C₂	semidirect
6. C₂²×Dic₅₈	C₂	semidirect
7. #41×C₂₉	C₂²	semidirect
13. Q₈×D₂₉	C₂²	semidirect
14. #90807	C₂²	semidirect
15. #90805	C₂²	semidirect
20. C₂×Dic₅₈	C₂²	semidirect
45. C₂×C₂₉	2₋¹⁺⁴	semidirect
51. C₂×#41	D₂₉	semidirect
54. C₂₉	C₂×2₋¹⁺⁴	semidirect
57. #41	C₂×D₂₉	semidirect
93. C₂	#11745365	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×#41×C₂₉	2
#11745365	2
C₂×Q₈×D₂₉	2
C₂×#90807	2
C₂×#90805	2
C₂²×Dic₅₈	2
C₂×2₋¹⁺⁴	29

Subgroups — C2×#11745365 #14271996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745365 #14271996