Subgroups — C₂×#11745362 #14271997

Order 1856.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745362	C₂	1	16	yes	maximal, direct product factor
3	C₂×#90809	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×D₂₉	C₂	1	4	yes	maximal, complemented
5	C₂×#90805	C₂	1	6	yes	maximal, complemented
6	C₂×Q₈×C₂₉	C₂²	1	4	yes	—
7	C₂×Q₈×C₂₉	C₂²	1	8	yes	complemented
8	C₂²×C₄×C₂₉	C₂²	1	3	yes	—
9	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	—
10	#90809	C₂²	1	32	yes	complemented
11	Q₈×D₂₉	C₂²	1	32	yes	complemented
12	#90805	C₂²	1	48	yes	complemented
13	C₂×D₁₁₆	C₂²	1	6	yes	—
14	C₂×C₄×D₂₉	C₂²	1	12	yes	—
15	C₂×Dic₅₈	C₂²	1	6	yes	—
16	C₂³×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×D₂₉	C₂³	1	4	yes	—
18	Q₈×C₂₉	C₂³	1	16	yes	—
19	C₂×C₄×C₂₉	C₂³	1	6	yes	—
20	C₂×C₄×C₂₉	C₂³	1	12	yes	—
21	C₂²⋊D₂₉	C₂³	1	16	yes	—
22	C₂×Dic₂₉	C₂³	1	4	yes	—
23	D₁₁₆	C₂³	1	24	yes	—
24	C₄×D₂₉	C₂³	1	48	yes	—
25	Dic₅₈	C₂³	1	24	yes	—
26	C₂²×C₂₉	—	2	2	no	—
27	C₂²×C₂₉	C₂⁴	1	2	yes	—
28	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
29	C₂×D₂₉	—	2	8	no	—
30	C₂×D₂₉	C₂⁴	1	8	yes	—
31	C₄×C₂₉	C₂⁴	1	12	yes	—
32	Dic₂₉	C₂⁴	1	8	yes	—
33	C₂×2₋¹⁺⁴	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	—	2	2	no	—
35	C₂×C₂₉	2₋¹⁺⁴	1	2	yes	complemented
36	C₂×C₂₉	C₂⁵	1	1	yes	characteristic
37	D₂₉	—	2	8	no	—
38	2₋¹⁺⁴	—	29	16	no	—
39	C₂×#41	—	29	4	no	—
40	C₂×#41	—	29	6	no	—
41	C₂²×Q₈	—	29	4	no	—
42	C₂²×Q₈	D₂₉	1	1	yes	characteristic, complemented
43	C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
44	#41	—	29	32	no	—
45	#41	—	29	48	no	—
46	C₂×Q₈	—	29	32	no	—
47	C₂×Q₈	—	29	6	no	—
48	C₂×Q₈	C₂×D₂₉	1	4	yes	—
49	C₂×Q₈	C₂×D₂₉	1	8	yes	complemented
50	C₂×D₄	—	29	4	no	—
51	C₂×D₄	—	29	6	no	—
52	C₂²×C₄	—	29	12	no	—
53	C₂²×C₄	C₂×D₂₉	1	3	yes	—
54	C₂³	—	29	4	no	—
55	C₂³	C₂²×D₂₉	1	1	yes	characteristic
56	Q₈	—	29	24	no	—
57	Q₈	C₂²×D₂₉	1	16	yes	—
58	D₄	—	29	16	no	—
59	D₄	—	29	24	no	—
60	C₂×C₄	—	29	4	no	—
61	C₂×C₄	—	29	48	no	—
62	C₂×C₄	C₂²×D₂₉	1	12	yes	—
63	C₂×C₄	C₂²×D₂₉	1	6	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	—	29	8	no	—
66	C₂²	—	58	8	no	—
67	C₂²	C₂³×D₂₉	1	2	yes	—
68	C₂²	C₂³×D₂₉	1	1	yes	characteristic
69	C₄	—	29	8	no	—
70	C₄	C₂³×D₂₉	1	12	yes	—
71	C₂	—	2	2	no	—
72	C₂	—	58	8	no	—
73	C₂	#11745362	1	2	yes	direct product factor
74	C₂	C₂⁴×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₉
commutator, cosocle	C₂×C₂₉	C₂⁵
Frattini	C₂	C₂⁴×D₂₉
Fitting	C₂²×Q₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂⁴
hypercenter	C₂²×Q₈	D₂₉
hypocenter	C₂₉	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₂₉	C₂	semidirect
2. #11745362	C₂	direct (N × H)
3. C₂×#90809	C₂	semidirect
4. C₂×Q₈×D₂₉	C₂	semidirect
5. C₂×#90805	C₂	semidirect
7. C₂×Q₈×C₂₉	C₂²	semidirect
10. #90809	C₂²	semidirect
11. Q₈×D₂₉	C₂²	semidirect
12. #90805	C₂²	semidirect
35. C₂×C₂₉	2₋¹⁺⁴	semidirect
42. C₂²×Q₈	D₂₉	semidirect
43. C₂₉	C₂×2₋¹⁺⁴	semidirect
49. C₂×Q₈	C₂×D₂₉	semidirect
73. C₂	#11745362	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₂₉	2
#11745362	2
C₂×#90809	2
C₂×Q₈×D₂₉	2
C₂×#90805	2
C₂×2₋¹⁺⁴	29

Subgroups — C2×#11745362 #14271997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745362 #14271997