Subgroups — #14271422

Order 1856.

110 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×#90772	C₂	1	1	yes	maximal, characteristic
3	#11745259	C₂	1	2	yes	maximal
4	C₂₉×#106	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	#90772	—	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	2	no	—
29	C₄×C₂₉	—	4	2	no	—
30	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₉	#41	1	1	yes	characteristic
32	Dic₂₉	—	2	1	no	—
33	Dic₂₉	—	4	2	no	—
34	#470	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	#121	1	1	yes	characteristic
36	C₂×C₂₉	#137	1	2	yes	—
37	D₂₉	—	4	1	no	—
38	C₂×Q₁₆	—	29	1	no	—
39	C₂×M₁₆	—	29	1	no	—
40	C₂²⋊Q₈	—	29	2	no	—
41	#106	D₂₉	1	1	yes	characteristic, complemented
42	#103	—	29	2	no	—
43	C₂₉	#470	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	29	2	no	—
45	C₂²×C₄	—	29	1	no	—
46	Q₁₆	—	58	2	no	—
47	M₁₆	—	58	2	no	—
48	C₂×C₈	—	29	1	no	—
49	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
50	C₄⋊C₄	—	58	2	no	—
51	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
52	C₂²⋊C₄	—	58	2	no	—
53	C₂³	—	29	1	no	—
54	Q₈	—	58	2	no	—
55	Q₈	—	58	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	58	1	no	—
59	C₂×C₄	—	58	1	no	—
60	C₂×C₄	—	58	2	no	—
61	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
62	C₈	—	58	1	no	—
63	C₈	D₁₁₆	1	2	yes	—
64	C₂²	—	58	1	no	—
65	C₂²	—	58	2	no	—
66	C₂²	D₄×D₂₉	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	58	1	no	—
69	C₄	—	116	2	no	—
70	C₄	C₂×D₁₁₆	1	1	yes	characteristic
71	C₄	#90809	1	1	yes	characteristic
72	C₂	—	116	1	no	—
73	C₂	#11745257	1	1	yes	characteristic
74	C₂	#11745277	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#106	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂²×D₂₉	D₄
hypercenter	#106	D₂₉
hypocenter	C₂₉	#470
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₆	C₂	semidirect
4. C₂₉×#106	C₂	semidirect
5. #11745158	C₂	semidirect
41. #106	D₂₉	semidirect
43. C₂₉	#470	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×#90772	2
#11745259	2
C₂₉×#106	2
#11745158	2
#470	29