Subgroups — #16821768

Order 3712.

116 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	#14270990	C₂	1	2	yes	maximal
3	#14270988	C₂	1	2	yes	maximal
4	C₄×#90768	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#499	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#125	—	2	1	no	—
7	#11745232	—	2	1	no	—
8	C₂₉×#107	C₂²	1	2	yes	—
9	C₂₉×#106	—	2	1	no	—
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	C₂²	1	2	yes	—
12	#11745165	—	2	1	no	—
13	C₂×#90768	C₂²	1	1	yes	characteristic
14	C₂×#90768	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₂₉	—	2	2	no	—
18	C₄⋊C₄×C₂₉	—	4	2	no	—
19	C₄²×C₂₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₂₉	—	2	2	no	—
21	#90779	—	4	2	no	—
22	#90768	Q₈	1	2	yes	—
23	#90768	Q₈	1	2	yes	—
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	D₈	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₉	—	4	2	no	—
28	C₈×C₂₉	Q₁₆	1	2	yes	—
29	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
31	#2253	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
33	C₄×C₂₉	—	2	2	no	—
34	C₄×C₂₉	—	8	2	no	—
35	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
36	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₂₉	—	8	2	no	—
38	#499	—	29	1	no	—
39	#499	D₂₉	1	1	yes	characteristic
40	#367	—	29	2	no	—
41	#366	—	29	2	no	—
42	C₄×C₁₆	—	29	1	no	—
43	C₂×C₂₉	#500	1	1	yes	characteristic
44	C₂×C₂₉	#508	1	2	yes	—
45	#125	—	2	1	no	—
46	#125	—	58	1	no	—
47	C₂×C₁₆	—	29	1	no	—
48	C₂×C₁₆	—	29	1	no	—
49	#107	—	29	2	no	—
50	#107	C₂×D₂₉	1	2	yes	—
51	#106	—	2	1	no	—
52	#106	—	58	1	no	—
53	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂₉	#2253	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	58	2	no	—
60	C₄⋊C₄	—	116	2	no	—
61	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
62	C₁₆	—	29	2	no	—
63	C₁₆	—	29	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	116	2	no	—
66	C₂×C₄	#90782	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
68	C₈	#90785	1	2	yes	—
69	C₈	Q₈×D₂₉	1	1	yes	characteristic
70	C₈	Q₈×D₂₉	1	1	yes	characteristic
71	C₂²	C₂×#90782	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	232	2	no	—
75	C₄	C₂×#90785	1	1	yes	characteristic
76	C₄	#11745306	1	1	yes	characteristic
77	C₂	#14271566	1	1	yes	characteristic
78	C₂	#14271593	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#90782
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#499	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	#499	D₂₉
hypocenter	C₂₉	#2253
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
54. C₂₉	#2253	semidirect

Maximal subgroups

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

subgroup	index
#14271565	2
#14270990	2
#14270988	2
C₄×#90768	2
C₂₉×#499	2
#2253	29