Subgroups — #14271538

Order 1856.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745302	C₂	1	2	yes	maximal, complemented
3	C₂×#90782	C₂	1	2	yes	maximal, complemented
4	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₂₉	—	2	4	no	—
8	C₂×D₁₁₆	C₂²	1	2	yes	—
9	D₈×C₂₉	—	2	2	no	—
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#90782	—	2	4	no	—
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	D₂₃₂	—	2	2	no	—
15	C₂³×C₂₉	—	2	2	no	—
16	C₂²×D₂₉	—	2	2	no	—
17	D₄×C₂₉	—	2	2	no	—
18	D₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂²⋊D₂₉	—	4	8	no	—
21	C₂×Dic₂₉	D₄	1	2	yes	—
22	D₁₁₆	—	2	2	no	—
23	D₁₁₆	—	2	2	no	—
24	C₈×C₂₉	D₄	1	2	yes	complemented
25	#6597	D₄	1	2	yes	complemented
26	C₂²×C₂₉	—	4	2	no	—
27	C₂²×C₂₉	—	4	4	no	—
28	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×D₂₉	—	4	2	no	—
30	C₂×D₂₉	—	4	4	no	—
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	Dic₂₉	D₈	1	4	yes	complemented
34	#493	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	—	8	2	no	—
36	C₂×C₂₉	#127	1	1	yes	characteristic
37	C₂×C₂₉	C₂×D₈	1	2	yes	—
38	D₂₉	—	8	2	no	—
39	C₂×D₈	—	29	2	no	—
40	C₂×D₈	—	29	1	no	—
41	C₂×D₈	D₂₉	1	1	yes	characteristic, complemented
42	#127	—	29	2	no	—
43	C₄×C₈	—	29	1	no	—
44	C₂₉	#493	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₄	—	29	2	no	—
46	C₂×D₄	—	58	4	no	—
47	C₂×D₄	C₂×D₂₉	1	2	yes	—
48	D₈	—	2	2	no	—
49	D₈	—	58	4	no	—
50	D₈	—	58	2	no	—
51	C₂×C₈	—	29	1	no	—
52	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
53	C₄²	—	29	1	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	58	2	no	—
56	D₄	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	58	2	no	—
59	D₄	—	58	2	no	—
60	D₄	—	116	8	no	—
61	C₂×C₄	—	29	2	no	—
62	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
63	C₈	—	29	2	no	—
64	C₈	C₂²⋊D₂₉	1	2	yes	complemented
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	116	2	no	—
68	C₂²	—	116	4	no	—
69	C₂²	D₄×D₂₉	1	1	yes	characteristic
70	C₄	—	29	4	no	—
71	C₄	D₄×D₂₉	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
73	C₂	—	8	2	no	—
74	C₂	—	232	2	no	—
75	C₂	D₈×D₂₉	1	2	yes	—
76	C₂	#11745302	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×D₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
hypercenter	C₂×D₈	D₂₉
hypocenter	C₂₉	#493
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₂₉	C₂	semidirect
2. #11745302	C₂	semidirect
3. C₂×#90782	C₂	semidirect
4. C₂×D₂₃₂	C₂	semidirect
5. C₈×Dic₂₉	C₂	semidirect
24. C₈×C₂₉	D₄	semidirect
25. #6597	D₄	semidirect
33. Dic₂₉	D₈	semidirect
41. C₂×D₈	D₂₉	semidirect
44. C₂₉	#493	semidirect
64. C₈	C₂²⋊D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₂₉	2
#11745302	2
C₂×#90782	2
C₂×D₂₃₂	2
C₈×Dic₂₉	2
#493	29