Subgroups — #16834686

Order 3712.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₂₉⋊C₈	C₂	1	2	yes	maximal
2	#14272004	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×D₂₉⋊C₈	C₄	1	4	yes	—
5	C₂×C₈×D₂₉	C₄	1	2	yes	—
6	C₄²×D₂₉	C₂²	1	1	yes	characteristic
7	C₄×#6599	C₄	1	4	yes	—
8	C₄×#6599	C₂²	1	4	yes	—
9	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
10	C₈×Dic₂₉	C₂²	1	2	yes	—
11	C₄×#6597	C₄	1	1	yes	characteristic
12	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
14	C₂×#6599	C₂×C₄	1	8	yes	—
15	D₂₉⋊C₈	—	2	8	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
19	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
20	C₂×#6597	C₂×C₄	1	2	yes	—
21	C₈×D₂₉	C₈	1	8	yes	complemented
22	C₂²×D₂₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄²	1	2	yes	—
24	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
26	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
27	C₄×D₂₉	C₂×C₈	1	4	yes	—
28	C₄×D₂₉	M₁₆	1	8	yes	—
29	#6599	—	2	8	no	—
30	C₈×C₂₉	C₂×C₈	1	4	yes	complemented
31	#6597	C₂×C₈	1	4	yes	complemented
32	C₂×#322	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
34	C₂×D₂₉	C₄×C₈	1	2	yes	—
35	C₂×D₂₉	#97	1	4	yes	—
36	C₄×C₂₉	#97	1	4	yes	—
37	C₄×C₂₉	C₂²×C₈	1	2	yes	—
38	Dic₂₉	C₄×C₈	1	2	yes	—
39	Dic₂₉	C₂×M₁₆	1	4	yes	—
40	C₂×C₄×C₈	—	29	2	no	—
41	C₂×C₄×C₈	—	29	1	no	—
42	#322	—	29	4	no	—
43	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
44	C₂×C₂₉	C₂×#97	1	2	yes	—
45	D₂₉	#322	1	4	yes	complemented
46	C₂²×C₈	—	29	2	no	—
47	C₂²×C₈	—	29	4	no	—
48	C₂×C₄²	—	29	1	no	—
49	C₄×C₈	—	29	4	no	—
50	C₄×C₈	—	29	4	no	—
51	C₄×C₈	—	29	2	no	—
52	C₄×C₈	—	29	1	no	—
53	C₄×C₈	#1181	1	1	yes	characteristic
54	C₂₉	C₂×#322	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	—	29	2	no	—
56	C₂²×C₄	—	29	1	no	—
57	C₂×C₈	—	29	2	no	—
58	C₂×C₈	—	29	8	no	—
59	C₂×C₈	—	29	8	no	—
60	C₂×C₈	—	58	8	no	—
61	C₂×C₈	C₂×#1181	1	2	yes	—
62	C₄²	—	29	2	no	—
63	C₄²	—	29	1	no	—
64	C₄²	C₂×#1181	1	1	yes	characteristic
65	C₂³	—	29	1	no	—
66	C₂×C₄	—	29	2	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	4	no	—
69	C₂×C₄	—	29	8	no	—
70	C₂×C₄	C₄×#1181	1	2	yes	—
71	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
72	C₈	—	29	4	no	—
73	C₈	—	58	8	no	—
74	C₈	D₂₉⋊C₈	1	4	yes	complemented
75	C₂²	—	29	2	no	—
76	C₂²	—	29	4	no	—
77	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
78	C₄	—	29	2	no	—
79	C₄	—	29	4	no	—
80	C₄	#11745208	1	4	yes	—
81	C₄	C₂×D₂₉⋊C₈	1	2	yes	—
82	C₂	—	29	4	no	—
83	C₂	C₄×D₂₉⋊C₈	1	1	yes	characteristic
84	C₂	C₂×#11745208	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×#1181
commutator	C₂×C₂₉	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₄²
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	C₂×#322
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14272004	C₂	semidirect
21. C₈×D₂₉	C₈	semidirect
30. C₈×C₂₉	C₂×C₈	semidirect
31. #6597	C₂×C₈	semidirect
45. D₂₉	#322	semidirect
54. C₂₉	C₂×#322	semidirect
74. C₈	D₂₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₂₉⋊C₈	2
#14272004	2
C₄×C₈×D₂₉	2
C₂×#322	29