Subgroups — #16817545

Order 3712.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271565	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#334	C₂	1	1	yes	maximal, characteristic
4	#11745232	—	2	1	no	—
5	C₂₉×C₄⋊C₈	—	2	1	no	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745166	C₄	1	1	yes	characteristic
8	#11745166	C₄	1	1	yes	characteristic
9	#11745165	—	2	1	no	—
10	C₂×#90768	—	2	1	no	—
11	C₂×C₈×C₂₉	—	4	1	no	—
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₉	—	2	1	no	—
16	C₄⋊Dic₂₉	—	2	1	no	—
17	#90779	—	4	1	no	—
18	#90779	—	4	1	no	—
19	#90768	—	4	1	no	—
20	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
23	C₂×Dic₂₉	—	4	1	no	—
24	C₂×Dic₂₉	—	4	1	no	—
25	C₈×C₂₉	—	2	1	no	—
26	C₈×C₂₉	—	8	1	no	—
27	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
28	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
29	#1363	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	#102	1	1	yes	characteristic
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	—	2	1	no	—
33	C₄×C₂₉	#101	1	1	yes	characteristic
34	C₄×C₂₉	#103	1	1	yes	characteristic
35	Dic₂₉	—	8	1	no	—
36	Dic₂₉	—	8	1	no	—
37	#499	—	29	1	no	—
38	C₄⋊C₁₆	—	29	1	no	—
39	#334	D₂₉	1	1	yes	characteristic
40	C₂×C₂₉	#332	1	1	yes	characteristic
41	C₂×C₂₉	#359	1	1	yes	characteristic
42	C₂×C₂₉	#360	1	1	yes	characteristic
43	#125	—	58	1	no	—
44	C₂×C₁₆	—	58	1	no	—
45	#107	—	29	1	no	—
46	#107	—	29	1	no	—
47	#106	—	58	1	no	—
48	C₄⋊C₈	—	2	1	no	—
49	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
50	C₂₉	#1363	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	4	1	no	—
52	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
53	C₂×C₈	D₁₁₆	1	1	yes	characteristic
54	C₄⋊C₄	—	58	1	no	—
55	C₄⋊C₄	—	58	1	no	—
56	C₄⋊C₄	—	116	1	no	—
57	C₄⋊C₄	—	116	1	no	—
58	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₁₆	—	116	1	no	—
60	C₂×C₄	—	116	1	no	—
61	C₂×C₄	—	116	1	no	—
62	C₂×C₄	#90781	1	1	yes	characteristic
63	C₂×C₄	#90782	1	1	yes	characteristic
64	C₂×C₄	#90784	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	8	1	no	—
67	C₈	#90773	1	1	yes	characteristic
68	C₈	Dic₁₁₆	1	1	yes	characteristic
69	C₂²	#11745157	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	232	1	no	—
73	C₄	—	232	1	no	—
74	C₄	#11745164	1	1	yes	characteristic
75	C₄	#11745172	1	1	yes	characteristic
76	C₂	#14270910	1	1	yes	characteristic
77	C₂	#14270969	1	1	yes	characteristic
78	C₂	#14270972	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745157
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#334	C₂
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#334	D₂₉
hypocenter	C₂₉	#1363
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
50. C₂₉	#1363	semidirect

Maximal subgroups

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

subgroup	index
#14271565	2
C₄⋊#90768	2
C₂₉×#334	2
#1363	29