Subgroups — #14271370

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#90785	C₂	1	2	yes	maximal
3	C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
4	#11745183	C₂	1	2	yes	maximal
5	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
7	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₄⋊C₄×C₂₉	—	2	1	no	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90785	—	2	4	no	—
12	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	#90779	—	2	1	no	—
14	C₄×Dic₂₉	—	2	1	no	—
15	C₂×#6597	C₂²	1	2	yes	—
16	Q₈×C₂₉	—	2	2	no	—
17	Q₈×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₉	—	2	1	no	—
23	C₂×Dic₂₉	—	2	1	no	—
24	Dic₅₈	—	2	1	no	—
25	Dic₅₈	D₄	1	2	yes	—
26	#6597	—	2	2	no	—
27	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₉	—	2	1	no	—
29	C₄×C₂₉	—	4	2	no	—
30	C₄×C₂₉	Q₁₆	1	2	yes	complemented
31	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	#41	1	1	yes	characteristic
33	Dic₂₉	—	2	2	no	—
34	Dic₂₉	—	4	1	no	—
35	#462	—	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	#137	1	1	yes	characteristic
39	C₂×Q₁₆	—	29	2	no	—
40	C₄⋊Q₈	D₂₉	1	1	yes	characteristic
41	C₄×Q₈	—	29	1	no	—
42	C₄⋊C₈	—	29	1	no	—
43	#103	—	29	2	no	—
44	C₂₉	#462	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	29	1	no	—
46	C₂×Q₈	C₂×D₂₉	1	2	yes	—
47	Q₁₆	—	58	4	no	—
48	C₂×C₈	—	29	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	29	1	no	—
52	C₄⋊C₄	—	58	1	no	—
53	C₄²	—	58	1	no	—
54	C₄²	C₂×D₂₉	1	1	yes	characteristic
55	Q₈	—	2	2	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	29	2	no	—
58	Q₈	—	58	1	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	58	1	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
65	C₈	—	58	2	no	—
66	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	4	2	no	—
69	C₄	—	58	2	no	—
70	C₄	—	116	1	no	—
71	C₄	#90785	1	2	yes	complemented
72	C₄	D₄×D₂₉	1	1	yes	characteristic
73	C₄	#90807	1	1	yes	characteristic
74	C₂	#11745300	1	1	yes	characteristic
75	C₂	#11745304	1	1	yes	characteristic
76	C₂	C₂×#90785	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×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#462
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
30. C₄×C₂₉	Q₁₆	semidirect
44. C₂₉	#462	semidirect
71. C₄	#90785	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₄⋊Q₈	2
C₂×#90785	2
C₄×Dic₅₈	2
#11745183	2
C₄⋊#6597	2
#462	29