Subgroups — #16817455

Order 3712.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₁₆	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	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic
5	C₄×Dic₅₈	—	2	1	no	—
6	C₂₉×C₄⋊C₈	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745166	C₄	1	1	yes	characteristic
9	#11745164	—	2	1	no	—
10	C₂×#90768	—	2	1	no	—
11	C₂×Dic₅₈	—	2	1	no	—
12	C₂×C₈×C₂₉	—	4	1	no	—
13	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₄²×C₂₉	D₄	1	1	yes	characteristic
16	C₄⋊Dic₂₉	—	2	1	no	—
17	#90779	—	4	1	no	—
18	C₄×Dic₂₉	—	4	1	no	—
19	Dic₁₁₆	—	2	1	no	—
20	Dic₁₁₆	C₈	1	2	yes	complemented
21	#90768	—	2	2	no	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₂₉	—	4	1	no	—
26	C₂×Dic₂₉	—	4	1	no	—
27	Dic₅₈	—	2	2	no	—
28	Dic₅₈	—	4	1	no	—
29	C₈×C₂₉	—	2	1	no	—
30	C₈×C₂₉	—	8	1	no	—
31	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
32	C₈×C₂₉	M₁₆	1	1	yes	characteristic
33	#1332	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	#102	1	1	yes	characteristic
35	C₄×C₂₉	—	2	1	no	—
36	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₂₉	#104	1	1	yes	characteristic
38	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
39	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
40	Dic₂₉	—	4	2	no	—
41	Dic₂₉	—	8	1	no	—
42	C₄×Q₁₆	—	29	1	no	—
43	C₄×C₁₆	—	29	1	no	—
44	#335	D₂₉	1	1	yes	characteristic
45	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₂₉	#358	1	1	yes	characteristic
47	C₂×C₂₉	#359	1	1	yes	characteristic
48	C₂×Q₁₆	—	29	1	no	—
49	C₄×Q₈	—	58	1	no	—
50	C₂×C₁₆	—	58	1	no	—
51	#107	—	29	1	no	—
52	C₄⋊C₈	—	2	1	no	—
53	#103	—	58	1	no	—
54	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂₉	#1332	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	58	1	no	—
57	Q₁₆	—	29	2	no	—
58	Q₁₆	—	58	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
61	C₂×C₈	D₁₁₆	1	1	yes	characteristic
62	C₄⋊C₄	—	58	1	no	—
63	C₄⋊C₄	—	116	1	no	—
64	C₄²	—	116	1	no	—
65	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
66	C₁₆	—	58	2	no	—
67	Q₈	—	58	2	no	—
68	Q₈	—	116	1	no	—
69	C₂×C₄	—	116	1	no	—
70	C₂×C₄	—	116	1	no	—
71	C₂×C₄	#90781	1	1	yes	characteristic
72	C₂×C₄	#90782	1	1	yes	characteristic
73	C₂×C₄	#90784	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₈×D₂₉	1	1	yes	characteristic
77	C₈	#90772	1	1	yes	characteristic
78	C₂²	#11745157	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	116	2	no	—
81	C₄	—	232	1	no	—
82	C₄	#11745168	1	1	yes	characteristic
83	C₄	#11745173	1	1	yes	characteristic
84	C₄	#11745175	1	1	yes	characteristic
85	C₄	#11745177	1	1	yes	characteristic
86	C₂	#14270890	1	1	yes	characteristic
87	C₂	#14270966	1	1	yes	characteristic
88	C₂	#14270969	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#90782
commutator	C₈×C₂₉	C₂×C₈
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	#1332
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
20. Dic₁₁₆	C₈	semidirect
55. C₂₉	#1332	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₁₁₆	2
C₄×#90768	2
C₂₉×#335	2
#1332	29