Subgroups — #14271287

Order 1856.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#11745162	C₂	1	2	yes	maximal
4	C₈×Dic₂₉	C₂	1	2	yes	maximal
5	C₄×#6597	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₉	C₂²	1	2	yes	—
8	C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₉	C₄	1	1	yes	characteristic
10	#90779	C₄	1	2	yes	—
11	C₄×Dic₂₉	C₂²	1	2	yes	—
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
19	Dic₅₈	C₈	1	4	yes	complemented
20	C₈×C₂₉	—	2	2	no	—
21	#6597	—	2	1	no	—
22	#6597	Q₈	1	2	yes	complemented
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉	—	2	1	no	—
25	C₄×C₂₉	C₂×C₈	1	2	yes	—
26	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₂₉	#41	1	1	yes	characteristic
28	Dic₂₉	—	2	2	no	—
29	Dic₂₉	C₂×C₈	1	4	yes	—
30	C₈×Q₈	—	29	1	no	maximal, Sylow
31	C₂×C₂₉	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₂₉	#131	1	1	yes	characteristic
34	C₄×Q₈	—	29	1	no	—
35	C₄⋊C₈	—	29	2	no	—
36	C₄⋊C₈	D₂₉	1	1	yes	characteristic
37	C₄×C₈	—	29	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	29	1	no	—
41	C₂×C₈	—	29	1	no	—
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	C₂×D₂₉	1	2	yes	—
44	C₄⋊C₄	—	29	2	no	—
45	C₄⋊C₄	—	29	1	no	—
46	C₄²	—	29	2	no	—
47	C₄²	C₂×D₂₉	1	1	yes	characteristic
48	Q₈	—	29	4	no	—
49	C₂×C₄	—	29	2	no	—
50	C₂×C₄	—	29	2	no	—
51	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
52	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	29	2	no	—
56	C₈	—	58	1	no	—
57	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	29	4	no	—
60	C₄	—	58	2	no	—
61	C₄	C₈×D₂₉	1	2	yes	—
62	C₄	#90807	1	1	yes	characteristic
63	C₄	Q₈×D₂₉	1	1	yes	characteristic
64	C₂	#11745249	1	1	yes	characteristic
65	C₂	C₂×C₈×D₂₉	1	1	yes	characteristic
66	C₂	#11745269	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₈
Fitting	C₂₉×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₂₉	C₂²×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	C₈×Q₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
19. Dic₅₈	C₈	semidirect
22. #6597	Q₈	semidirect
39. C₂₉	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₅₈	2
C₂₉×C₄⋊C₈	2
#11745162	2
C₈×Dic₂₉	2
C₄×#6597	2
C₈×Q₈	29