Subgroups — #16817548

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	1	no	—
23	Dic₅₈	—	8	1	no	—
24	C₈×C₂₉	—	2	1	no	—
25	C₈×C₂₉	—	8	1	no	—
26	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
28	#1364	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	#102	1	1	yes	characteristic
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	#101	1	1	yes	characteristic
32	C₄×C₂₉	#103	1	1	yes	characteristic
33	C₄×C₂₉	D₁₆	1	1	yes	characteristic
34	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
35	Dic₂₉	—	8	2	no	—
36	#500	—	29	1	no	—
37	C₄⋊C₁₆	—	29	1	no	—
38	#335	D₂₉	1	1	yes	characteristic
39	C₂×C₂₉	#332	1	1	yes	characteristic
40	C₂×C₂₉	#357	1	1	yes	characteristic
41	C₂×C₂₉	#362	1	1	yes	characteristic
42	C₄⋊Q₈	—	58	1	no	—
43	C₂×C₁₆	—	58	1	no	—
44	#107	—	29	2	no	—
45	#107	—	58	1	no	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
48	C₂₉	#1364	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	116	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
52	C₂×C₈	D₁₁₆	1	1	yes	characteristic
53	C₄⋊C₄	—	58	2	no	—
54	C₄⋊C₄	—	116	1	no	—
55	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
56	C₁₆	—	116	1	no	—
57	Q₈	—	232	1	no	—
58	Q₈	—	232	1	no	—
59	C₂×C₄	—	116	2	no	—
60	C₂×C₄	#90781	1	1	yes	characteristic
61	C₂×C₄	#90782	1	1	yes	characteristic
62	C₂×C₄	#90784	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	#90773	1	1	yes	characteristic
66	C₈	Dic₁₁₆	1	1	yes	characteristic
67	C₂²	#11745157	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	232	2	no	—
70	C₄	#11745164	1	1	yes	characteristic
71	C₄	#11745172	1	1	yes	characteristic
72	C₄	#11745174	1	1	yes	characteristic
73	C₄	#11745176	1	1	yes	characteristic
74	C₂	#14270910	1	1	yes	characteristic
75	C₂	#14270963	1	1	yes	characteristic
76	C₂	#14270978	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	#1364
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
48. C₂₉	#1364	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
#1364	29