Subgroups — #16834706

Order 3712.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272181	C₂	1	2	yes	maximal
2	#6599⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₂₉	C₄	1	2	yes	—
5	C₄²×D₂₉	C₂²	1	1	yes	characteristic
6	#11745220	C₄	1	4	yes	—
7	#11745219	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	2	yes	—
13	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×#6599	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
16	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
19	C₂×#6597	C₂×C₄	1	2	yes	—
20	C₈×D₂₉	—	2	4	no	—
21	C₂²×D₂₉	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₄²	1	2	yes	—
23	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
25	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
26	C₄×D₂₉	—	2	4	no	—
27	C₄×D₂₉	M₁₆	1	4	yes	—
28	#6599	—	2	8	no	—
29	C₈×C₂₉	—	2	2	no	—
30	#6597	—	2	2	no	—
31	#1452	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
33	C₂×D₂₉	—	2	2	no	—
34	C₂×D₂₉	#97	1	2	yes	—
35	C₄×C₂₉	—	2	2	no	—
36	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
37	Dic₂₉	#97	1	2	yes	—
38	Dic₂₉	#131	1	4	yes	—
39	#431	—	29	2	no	—
40	C₂×C₄×C₈	—	29	1	no	—
41	#322	—	29	4	no	—
42	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
43	C₂×C₂₉	#405	1	2	yes	—
44	D₂₉	—	2	2	no	—
45	C₂²×C₈	—	29	2	no	—
46	C₂×C₄²	—	29	1	no	—
47	C₄⋊C₈	—	29	4	no	—
48	C₂²⋊C₈	—	29	4	no	—
49	C₄×C₈	—	29	4	no	—
50	C₄×C₈	—	29	2	no	—
51	C₄×C₈	—	29	1	no	—
52	C₄×C₈	#1181	1	1	yes	characteristic
53	C₂₉	#1452	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	—	29	1	no	—
55	C₂²×C₄	—	29	2	no	—
56	C₂×C₈	—	29	8	no	—
57	C₂×C₈	—	29	2	no	—
58	C₂×C₈	—	58	4	no	—
59	C₂×C₈	C₂×#1181	1	2	yes	—
60	C₄²	—	29	2	no	—
61	C₄²	—	29	1	no	—
62	C₄²	C₂×#1181	1	1	yes	characteristic
63	C₂³	—	29	1	no	—
64	C₂×C₄	—	29	2	no	—
65	C₂×C₄	—	29	1	no	—
66	C₂×C₄	—	29	4	no	—
67	C₂×C₄	—	58	4	no	—
68	C₂×C₄	C₄×#1181	1	2	yes	—
69	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	58	8	no	—
72	C₈	—	58	2	no	—
73	C₂²	—	29	2	no	—
74	C₂²	—	58	2	no	—
75	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	29	2	no	—
78	C₄	—	29	4	no	—
79	C₄	D₂₉⋊M₁₆	1	2	yes	—
80	C₂	—	58	2	no	—
81	C₂	#14272122	1	1	yes	characteristic
82	C₂	#14272126	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₄×C₈×C₂₉	C₄
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1452
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #6599⋊C₈	C₂	semidirect
53. C₂₉	#1452	semidirect

Maximal subgroups

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

subgroup	index
#14272181	2
#6599⋊C₈	2
C₄×C₈×D₂₉	2
#1452	29