Subgroups — #16817533

Order 3712.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270984	C₂	1	2	yes	maximal, complemented
2	C₂₉×#492	C₂	1	1	yes	maximal, characteristic
3	C₂×SD₁₆×C₂₉	—	2	2	no	—
4	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₂₉×#127	C₄	1	1	yes	characteristic
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745160	—	2	2	no	—
8	C₂×Q₈×C₂₉	—	2	1	no	—
9	C₂×D₄×C₂₉	—	2	1	no	—
10	C₂×D₄×C₂₉	—	4	1	no	—
11	SD₁₆×C₂₉	—	4	2	no	—
12	SD₁₆×C₂₉	—	4	2	no	—
13	C₂×C₈×C₂₉	D₄	1	2	yes	—
14	C₄⋊C₄×C₂₉	—	4	1	no	—
15	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
16	#90768	—	4	2	no	—
17	C₂³×C₂₉	—	4	1	no	—
18	Q₈×C₂₉	—	4	2	no	—
19	D₄×C₂₉	—	4	2	no	—
20	D₄×C₂₉	—	8	2	no	—
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₂₉	D₈	1	2	yes	—
25	C₈×C₂₉	SD₁₆	1	2	yes	—
26	#1359	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	—	8	2	no	—
28	C₂²×C₂₉	—	8	1	no	—
29	C₂²×C₂₉	#100	1	1	yes	characteristic
30	C₄×C₂₉	—	2	2	no	—
31	C₄×C₂₉	—	8	1	no	—
32	C₄×C₂₉	#102	1	2	yes	—
33	#492	D₂₉	1	1	yes	characteristic
34	#364	—	29	2	no	—
35	C₂×C₂₉	—	2	1	no	—
36	C₂×C₂₉	—	16	1	no	—
37	C₂×C₂₉	#331	1	1	yes	characteristic
38	C₂×SD₁₆	—	2	2	no	—
39	C₄⋊Q₈	Dic₂₉	1	1	yes	characteristic
40	#127	Dic₂₉	1	1	yes	characteristic
41	M₃₂	—	58	2	no	—
42	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
43	C₂₉	#1359	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	2	1	no	—
46	C₂×D₄	—	4	1	no	—
47	SD₁₆	—	4	2	no	—
48	SD₁₆	—	4	2	no	—
49	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
52	C₁₆	—	116	2	no	—
53	C₂³	—	4	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	4	2	no	—
56	D₄	—	8	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
60	C₈	#90782	1	2	yes	—
61	C₈	#90783	1	2	yes	—
62	C₂²	—	8	2	no	—
63	C₂²	—	8	1	no	—
64	C₂²	#11745181	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#11745180	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	#14270907	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270907
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#492	C₂
socle	C₂×C₂₉	#331
prime radical	C₂₉×#127	C₄
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#492	D₂₉
hypocenter	C₂₉	#1359
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14270984	C₂	semidirect
43. C₂₉	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14270984	2
C₂₉×#492	2
#1359	29