Subgroups — #16821248

Order 3712.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745160	C₂	1	2	yes	maximal
2	C₄⋊#90768	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
7	C₄×C₈×C₂₉	C₄	1	2	yes	—
8	C₄×C₈×C₂₉	C₂²	1	2	yes	—
9	#11745160	—	2	4	no	—
10	C₂×#90768	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₉	C₈	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	—	2	2	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	D₄	1	2	yes	—
17	C₂×C₈×C₂₉	Q₈	1	2	yes	—
18	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
19	C₄²×C₂₉	C₈	1	1	yes	characteristic
20	C₄²×C₂₉	C₈	1	1	yes	characteristic
21	C₄²×C₂₉	C₂×C₄	1	2	yes	—
22	#90768	—	2	4	no	—
23	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	2	4	no	—
25	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₈×C₂₉	—	2	2	no	—
32	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
33	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
35	#2150	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	2	2	no	—
37	C₂²×C₂₉	C₄⋊C₈	1	2	yes	—
38	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₂₉	—	2	2	no	—
40	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
41	C₄×C₂₉	M₃₂	1	4	yes	complemented
42	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₃₂	—	29	2	no	—
45	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
46	C₄⋊C₁₆	—	29	4	no	—
47	C₂×C₂₉	—	2	2	no	—
48	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₂₉	C₂×M₃₂	1	2	yes	—
50	C₂²×C₈	Dic₂₉	1	1	yes	characteristic
51	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
52	C₂×C₄²	Dic₂₉	1	1	yes	characteristic
53	M₃₂	—	58	4	no	—
54	C₂×C₁₆	—	29	4	no	—
55	C₄×C₈	Dic₂₉	1	2	yes	—
56	C₄×C₈	C₂×D₂₉	1	2	yes	—
57	C₂₉	#2150	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	#6597	1	2	yes	—
59	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	Dic₅₈	1	2	yes	—
62	C₂×C₈	D₁₁₆	1	2	yes	—
63	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
64	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
65	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
66	C₄²	#6597	1	1	yes	characteristic
67	C₄²	#6597	1	1	yes	characteristic
68	C₄²	C₂×Dic₂₉	1	2	yes	—
69	C₁₆	—	58	4	no	—
70	C₂³	C₂×#6597	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	C₂×#6597	1	2	yes	—
73	C₂×C₄	C₂×#6597	1	1	yes	characteristic
74	C₂×C₄	C₂×#6597	1	2	yes	—
75	C₂×C₄	#90777	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₂₉	1	2	yes	—
77	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₈	C₄⋊Dic₂₉	1	2	yes	—
80	C₈	C₂×Dic₅₈	1	1	yes	characteristic
81	C₈	C₂×D₁₁₆	1	1	yes	characteristic
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊#6597	1	2	yes	—
84	C₂²	C₂²×#6597	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	C₄⋊#6597	1	2	yes	—
87	C₄	#11745160	1	4	yes	complemented
88	C₄	C₂×#90777	1	1	yes	characteristic
89	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#6597	1	1	yes	characteristic
92	C₂	C₂×#11745160	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₄×C₈×C₂₉	C₂
prime radical	C₂³×C₂₉	C₂×C₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#2150
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊#90768	C₂	semidirect
41. C₄×C₂₉	M₃₂	semidirect
57. C₂₉	#2150	semidirect
87. C₄	#11745160	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745160	2
C₄⋊#90768	2
C₂×C₄×C₈×C₂₉	2
#2150	29