Subgroups — #14270952

Order 1856.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745297	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#99	C₂	1	1	yes	maximal, characteristic
3	#11745181	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₉	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊C₄×C₂₉	—	2	1	no	—
7	C₂²⋊Dic₂₉	—	2	1	no	—
8	C₂²⋊Dic₂₉	C₄	1	1	yes	characteristic, complemented
9	#90779	—	2	1	no	—
10	#90777	—	2	1	no	—
11	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₂₉	D₄	1	1	yes	characteristic
13	D₄×C₂₉	—	4	1	no	—
14	C₂×C₄×C₂₉	—	4	1	no	—
15	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂×Dic₂₉	—	2	1	no	—
17	C₂×Dic₂₉	—	2	1	no	—
18	C₂×Dic₂₉	—	4	1	no	—
19	#6597	—	4	1	no	—
20	C₂²×C₂₉	—	2	1	no	—
21	C₂²×C₂₉	—	2	1	no	—
22	C₂²×C₂₉	—	4	1	no	—
23	C₂²×C₂₉	—	4	1	no	—
24	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₂₉	—	2	1	no	—
26	C₄×C₂₉	—	8	1	no	—
27	Dic₂₉	—	4	1	no	—
28	Dic₂₉	—	4	1	no	—
29	#352	—	29	1	no	maximal, Sylow
30	C₂×C₂₉	—	2	1	no	—
31	C₂×C₂₉	—	4	1	no	—
32	C₂×C₂₉	—	4	1	no	—
33	C₂×C₂₉	#99	1	1	yes	characteristic
34	#123	—	29	1	no	—
35	#100	—	29	1	no	—
36	#99	D₂₉	1	1	yes	characteristic
37	C₂₉	#352	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₄	C₂×D₂₉	1	1	yes	characteristic
39	C₂²×C₄	—	29	1	no	—
40	M₁₆	—	58	1	no	—
41	C₄⋊C₄	—	58	1	no	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₂²⋊C₄	—	29	1	no	—
44	C₂²⋊C₄	—	58	1	no	—
45	C₂³	C₄×D₂₉	1	1	yes	characteristic
46	C₂³	C₂²⋊D₂₉	1	1	yes	characteristic
47	D₄	—	4	1	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	—	58	1	no	—
50	C₂×C₄	—	58	1	no	—
51	C₂×C₄	—	116	1	no	—
52	C₂×C₄	D₁₁₆	1	1	yes	characteristic
53	C₈	—	116	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	#90781	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	8	1	no	—
61	C₄	—	116	1	no	—
62	C₄	—	116	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	#11745154	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745154
commutator	C₂³×C₂₉	C₂×C₄
Frattini	C₂×D₄	C₂×D₂₉
Fitting	C₂₉×#99	C₂
socle	C₂×C₂₉	#99
prime radical, cosocle	C₂×D₄×C₂₉	C₂²
hypercenter	#99	D₂₉
hypocenter	C₂₉	#352
LCS	G ▷ C₂³×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #99

Complements

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

N	H ≅ G/N	type
5. C₂²×Dic₂₉	C₄	semidirect
8. C₂²⋊Dic₂₉	C₄	semidirect
37. C₂₉	#352	semidirect

Maximal subgroups

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

subgroup	index
#11745297	2
C₂₉×#99	2
#11745181	2
#352	29