Subgroups — #16817551

Order 3712.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#335	C₂	1	1	yes	maximal, characteristic
4	#11745231	—	2	1	no	—
5	C₂₉×C₄⋊C₈	—	2	1	no	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745166	—	2	1	no	—
8	#11745166	C₄	1	2	yes	—
9	C₂×#90768	—	2	1	no	—
10	C₂×Dic₅₈	—	4	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	2	no	—
16	C₄⋊Dic₂₉	—	4	1	no	—
17	#90768	—	4	1	no	—
18	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₂₉	—	4	2	no	—
22	Dic₅₈	—	8	2	no	—
23	C₈×C₂₉	—	2	1	no	—
24	C₈×C₂₉	—	8	1	no	—
25	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
26	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
27	#1365	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	#102	1	1	yes	characteristic
29	C₄×C₂₉	—	2	1	no	—
30	C₄×C₂₉	#101	1	1	yes	characteristic
31	C₄×C₂₉	#103	1	1	yes	characteristic
32	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
33	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
34	Dic₂₉	—	8	2	no	—
35	#500	—	29	1	no	—
36	C₄⋊C₁₆	—	29	1	no	—
37	#335	D₂₉	1	1	yes	characteristic
38	C₂×C₂₉	#332	1	1	yes	characteristic
39	C₂×C₂₉	#358	1	1	yes	characteristic
40	C₂×C₂₉	#361	1	1	yes	characteristic
41	C₄⋊Q₈	—	58	1	no	—
42	C₂×C₁₆	—	58	1	no	—
43	#107	—	29	2	no	—
44	#107	—	58	1	no	—
45	C₄⋊C₈	—	2	1	no	—
46	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
47	C₂₉	#1365	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	116	1	no	—
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
51	C₂×C₈	D₁₁₆	1	1	yes	characteristic
52	C₄⋊C₄	—	58	2	no	—
53	C₄⋊C₄	—	116	1	no	—
54	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
55	C₁₆	—	116	1	no	—
56	Q₈	—	232	2	no	—
57	C₂×C₄	—	116	2	no	—
58	C₂×C₄	#90781	1	1	yes	characteristic
59	C₂×C₄	#90782	1	1	yes	characteristic
60	C₂×C₄	#90784	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	#90773	1	1	yes	characteristic
64	C₈	Dic₁₁₆	1	1	yes	characteristic
65	C₂²	#11745157	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	232	2	no	—
68	C₄	#11745164	1	1	yes	characteristic
69	C₄	#11745172	1	1	yes	characteristic
70	C₄	#11745175	1	1	yes	characteristic
71	C₄	#11745177	1	1	yes	characteristic
72	C₂	#14270910	1	1	yes	characteristic
73	C₂	#14270966	1	1	yes	characteristic
74	C₂	#14270975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745157
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#335	C₂
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#335	D₂₉
hypocenter	C₂₉	#1365
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
47. C₂₉	#1365	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
C₄⋊#90768	2
C₂₉×#335	2
#1365	29