Subgroups — #14271440

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, complemented
2	C₄×D₁₁₆	C₂	1	1	yes	maximal, characteristic
3	#11745157	C₂	1	2	yes	maximal
4	#11745155	C₂	1	2	yes	maximal, complemented
5	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₂₉	—	2	1	no	—
7	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₂₉	—	2	1	no	—
9	C₄⋊C₄×C₂₉	—	2	1	no	—
10	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
11	C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	#90781	—	2	1	no	—
13	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂²×D₂₉	—	2	1	no	—
16	Q₈×C₂₉	—	4	2	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₉	—	2	1	no	—
22	D₁₁₆	—	2	1	no	—
23	D₁₁₆	Q₈	1	2	yes	complemented
24	C₄×D₂₉	—	4	2	no	—
25	#6597	—	2	2	no	—
26	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₉	—	2	2	no	—
28	C₂×D₂₉	—	4	1	no	—
29	C₂×D₂₉	—	4	1	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	—	4	2	no	—
32	C₄×C₂₉	D₈	1	2	yes	—
33	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₂₉	#41	1	1	yes	characteristic
35	Dic₂₉	—	4	1	no	—
36	#474	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
38	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
39	C₂×C₂₉	#137	1	1	yes	characteristic
40	D₂₉	—	4	2	no	—
41	C₄⋊Q₈	D₂₉	1	1	yes	characteristic, complemented
42	C₄×D₄	—	29	1	no	—
43	#107	—	29	2	no	—
44	C₄⋊C₈	—	29	1	no	—
45	#102	—	29	2	no	—
46	C₂₉	#474	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₈	—	2	1	no	—
48	C₂×D₄	—	29	1	no	—
49	C₂²×C₄	—	58	1	no	—
50	C₂×C₈	—	29	2	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	29	1	no	—
53	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
54	C₂²⋊C₄	—	58	1	no	—
55	C₄²	C₂×D₂₉	1	1	yes	characteristic
56	C₂³	—	58	1	no	—
57	Q₈	—	4	2	no	—
58	D₄	—	29	2	no	—
59	D₄	—	58	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	—	116	2	no	—
63	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
66	C₈	—	58	2	no	—
67	C₂²	—	58	2	no	—
68	C₂²	—	116	1	no	—
69	C₂²	—	116	1	no	—
70	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	4	2	no	—
73	C₄	—	116	1	no	—
74	C₄	#90782	1	2	yes	—
75	C₄	Q₈×D₂₉	1	1	yes	characteristic
76	C₄	#90809	1	1	yes	characteristic
77	C₂	—	116	2	no	—
78	C₂	C₂×#90782	1	1	yes	characteristic
79	C₂	#11745304	1	1	yes	characteristic
80	C₂	#11745308	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	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₁₁₆	C₂²
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#474
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
1. C₂₉×C₄⋊Q₈	C₂	semidirect
4. #11745155	C₂	semidirect
5. C₄⋊#6597	C₂	semidirect
23. D₁₁₆	Q₈	semidirect
41. C₄⋊Q₈	D₂₉	semidirect
46. C₂₉	#474	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
C₄×D₁₁₆	2
#11745157	2
#11745155	2
C₄⋊#6597	2
#474	29