Subgroups — #14271539

Order 1856.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#90782	C₂	1	4	yes	maximal, complemented
3	#11745236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₂₉	—	2	2	no	—
6	C₂×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂×D₁₁₆	—	2	2	no	—
8	C₂×D₁₁₆	C₂²	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	#90782	—	2	8	no	—
11	C₂×#6597	C₂²	1	2	yes	—
12	C₂³×C₂₉	—	2	2	no	—
13	C₂²×D₂₉	—	2	2	no	—
14	D₄×C₂₉	—	2	4	no	—
15	D₄×C₂₉	—	4	4	no	—
16	C₂×C₄×C₂₉	D₄	1	2	yes	—
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	D₁₁₆	—	2	4	no	—
19	D₁₁₆	—	4	4	no	—
20	#6597	D₄	1	4	yes	complemented
21	C₂²×C₂₉	—	4	2	no	—
22	C₂²×C₂₉	—	4	4	no	—
23	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₂₉	—	4	2	no	—
25	C₂×D₂₉	—	4	4	no	—
26	C₄×C₂₉	D₈	1	4	yes	complemented
27	C₄×C₂₉	C₂×D₄	1	2	yes	—
28	#493	—	29	1	no	maximal, Sylow
29	C₂×C₂₉	—	8	2	no	—
30	C₂×C₂₉	#127	1	1	yes	characteristic
31	C₂×C₂₉	C₂×D₈	1	2	yes	—
32	D₂₉	—	8	2	no	—
33	C₂×D₈	—	29	4	no	—
34	#127	—	29	1	no	—
35	#127	D₂₉	1	1	yes	characteristic, complemented
36	C₄×C₈	—	29	1	no	—
37	C₂₉	#493	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₄	—	2	2	no	—
39	C₂×D₄	—	29	2	no	—
40	C₂×D₄	—	58	2	no	—
41	C₂×D₄	C₂×D₂₉	1	2	yes	—
42	D₈	—	58	8	no	—
43	C₂×C₈	—	29	2	no	—
44	C₄²	C₂×D₂₉	1	1	yes	characteristic
45	C₂³	—	2	2	no	—
46	C₂³	—	58	2	no	—
47	D₄	—	2	4	no	—
48	D₄	—	4	4	no	—
49	D₄	—	58	4	no	—
50	D₄	—	116	4	no	—
51	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
52	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
53	C₈	—	29	4	no	—
54	C₂²	—	4	4	no	—
55	C₂²	—	4	2	no	—
56	C₂²	—	116	4	no	—
57	C₂²	—	116	2	no	—
58	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
59	C₄	#90782	1	4	yes	complemented
60	C₄	D₄×D₂₉	1	2	yes	—
61	C₂	—	8	2	no	—
62	C₂	—	232	2	no	—
63	C₂	C₂×#90782	1	2	yes	—
64	C₂	#11745302	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#127	C₂
socle	C₂²×C₂₉	C₂×D₄
hypercenter	#127	D₂₉
hypocenter	C₂₉	#493
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂₉×#127	C₂	semidirect
2. C₂×#90782	C₂	semidirect
3. #11745236	C₂	semidirect
4. C₄×#6597	C₂	semidirect
20. #6597	D₄	semidirect
26. C₄×C₂₉	D₈	semidirect
35. #127	D₂₉	semidirect
37. C₂₉	#493	semidirect
59. C₄	#90782	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#127	2
C₂×#90782	2
#11745236	2
C₄×#6597	2
#493	29