Subgroups — #14271405

Order 1856.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745259	C₂	1	2	yes	maximal
4	C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745158	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	#90781	—	2	2	no	—
11	C₄⋊Dic₂₉	—	2	2	no	—
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	Dic₁₁₆	—	2	2	no	—
14	C₈×D₂₉	—	2	2	no	—
15	C₂²×D₂₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₉	—	2	2	no	—
19	C₂×Dic₂₉	D₄	1	1	yes	characteristic
20	C₄×D₂₉	—	2	1	no	—
21	C₄×D₂₉	—	2	1	no	—
22	Dic₅₈	—	2	2	no	—
23	Dic₅₈	—	2	2	no	—
24	C₈×C₂₉	D₄	1	2	yes	—
25	#6597	—	2	1	no	—
26	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₉	—	2	1	no	—
28	C₂×D₂₉	—	2	1	no	—
29	C₂×D₂₉	Q₁₆	1	2	yes	complemented
30	C₄×C₂₉	—	4	2	no	—
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	#41	1	1	yes	characteristic
33	Dic₂₉	—	2	1	no	—
34	Dic₂₉	—	4	2	no	—
35	#467	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	#121	1	1	yes	characteristic
37	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₂₉	#135	1	1	yes	characteristic
39	D₂₉	—	2	2	no	—
40	C₂×Q₁₆	—	29	1	no	—
41	C₂²×C₈	—	29	1	no	—
42	C₂²⋊Q₈	—	29	2	no	—
43	#107	D₂₉	1	1	yes	characteristic, complemented
44	#103	—	29	2	no	—
45	C₂₉	#467	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₈	—	29	2	no	—
47	C₂²×C₄	—	29	1	no	—
48	Q₁₆	—	58	2	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	58	2	no	—
51	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
52	C₄⋊C₄	—	58	2	no	—
53	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
54	C₂²⋊C₄	—	58	2	no	—
55	C₂³	—	29	1	no	—
56	Q₈	—	58	2	no	—
57	Q₈	—	58	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	58	1	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	—	58	2	no	—
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	—	58	1	no	—
65	C₈	D₁₁₆	1	2	yes	—
66	C₂²	—	29	2	no	—
67	C₂²	—	58	1	no	—
68	C₂²	—	58	1	no	—
69	C₂²	D₄×D₂₉	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	58	1	no	—
72	C₄	—	116	2	no	—
73	C₄	C₂×D₁₁₆	1	1	yes	characteristic
74	C₄	#90809	1	1	yes	characteristic
75	C₂	—	58	2	no	—
76	C₂	#11745257	1	1	yes	characteristic
77	C₂	#11745274	1	1	yes	characteristic
78	C₂	Q₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#107	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂²×D₂₉	D₄
hypercenter	#107	D₂₉
hypocenter	C₂₉	#467
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₆	C₂	semidirect
4. C₂₉×#107	C₂	semidirect
5. #11745158	C₂	semidirect
29. C₂×D₂₉	Q₁₆	semidirect
43. #107	D₂₉	semidirect
45. C₂₉	#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆	2
C₂×C₈×D₂₉	2
#11745259	2
C₂₉×#107	2
#11745158	2
#467	29