Subgroups — #16817663

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270956	C₂	1	2	yes	maximal
2	C₂₉×#490	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#127	C₂²	1	1	yes	characteristic
4	C₂₉×#125	C₄	1	1	yes	characteristic, complemented
5	C₂₉×#102	—	2	2	no	—
6	C₂₉×#97	C₄	1	1	yes	characteristic, complemented
7	#11745182	—	2	2	no	—
8	C₂×D₄×C₂₉	—	4	1	no	—
9	C₂×D₄×C₂₉	D₄	1	2	yes	—
10	C₂×C₈×C₂₉	—	2	1	no	—
11	C₄⋊C₄×C₂₉	—	2	1	no	—
12	C₄⋊C₄×C₂₉	—	4	1	no	—
13	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂²⋊Dic₂₉	—	4	2	no	—
15	C₂³×C₂₉	—	2	2	no	—
16	D₄×C₂₉	—	4	2	no	—
17	D₄×C₂₉	—	8	2	no	—
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	—	4	1	no	—
20	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	—	8	2	no	—
22	C₈×C₂₉	—	4	1	no	—
23	#1412	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	—	4	2	no	—
25	C₂²×C₂₉	—	8	2	no	—
26	C₂²×C₂₉	#99	1	1	yes	characteristic
27	C₄×C₂₉	—	2	1	no	—
28	C₄×C₂₉	—	4	1	no	—
29	C₄×C₂₉	—	8	1	no	—
30	Dic₂₉	—	16	2	no	—
31	#490	D₂₉	1	1	yes	characteristic
32	#353	—	29	2	no	—
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	—	8	2	no	—
35	C₂×C₂₉	#354	1	1	yes	characteristic
36	#127	C₂×D₂₉	1	1	yes	characteristic
37	#125	Dic₂₉	1	1	yes	characteristic, complemented
38	#102	—	2	2	no	—
39	#99	—	58	2	no	—
40	#97	Dic₂₉	1	1	yes	characteristic, complemented
41	C₂₉	#1412	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₄	—	4	1	no	—
43	C₂×D₄	C₂²⋊D₂₉	1	2	yes	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	116	2	no	—
48	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
49	C₂³	—	2	2	no	—
50	D₄	—	4	2	no	—
51	D₄	—	8	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	232	2	no	—
55	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
56	C₈	—	4	1	no	—
57	C₂²	—	4	2	no	—
58	C₂²	—	8	2	no	—
59	C₂²	#11745182	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	464	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	8	2	no	—
66	C₂	#14270958	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270958
commutator	C₄²×C₂₉	C₂×C₄
Frattini	#127	C₂×D₂₉
Fitting	C₂₉×#490	C₂
socle	C₂×C₂₉	#354
prime radical, cosocle	C₂₉×#127	C₂²
hypercenter	#490	D₂₉
hypocenter	C₂₉	#1412
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #490

Complements

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

N	H ≅ G/N	type
4. C₂₉×#125	C₄	semidirect
6. C₂₉×#97	C₄	semidirect
37. #125	Dic₂₉	semidirect
40. #97	Dic₂₉	semidirect
41. C₂₉	#1412	semidirect

Maximal subgroups

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

subgroup	index
#14270956	2
C₂₉×#490	2
#1412	29