Group #16818795 — subgroups

Subgroups — #16818795

Order 3712.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271529	C₂	1	1	yes	maximal, characteristic
3	#14271528	C₂	1	2	yes	maximal
4	#14270904	C₂	1	2	yes	maximal, complemented
5	C₂₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#125	C₂²	1	1	yes	characteristic
7	#11745252	—	2	2	no	—
8	#11745251	—	2	2	no	—
9	#11745251	—	2	2	no	—
10	#11745236	C₂²	1	1	yes	characteristic
11	#11745232	C₂²	1	2	yes	—
12	C₂₉×#97	C₂²	1	2	yes	—
13	#11745169	—	2	2	no	—
14	#11745169	—	2	2	no	—
15	#11745157	—	2	2	no	—
16	#11745151	C₂²	1	1	yes	characteristic
17	C₂×D₁₁₆	—	2	1	no	—
18	C₂×D₁₁₆	—	2	2	no	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₄⋊C₄×C₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
22	C₄²×C₂₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	D₄	1	2	yes	—
25	C₄⋊Dic₂₉	D₄	1	2	yes	—
26	#90779	—	2	2	no	—
27	#90779	—	2	2	no	—
28	#90779	—	2	2	no	—
29	#90779	—	2	2	no	—
30	C₄×Dic₂₉	—	2	2	no	—
31	C₂×#6597	—	2	1	no	—
32	C₂²×D₂₉	—	4	1	no	—
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
36	C₂×Dic₂₉	—	2	2	no	—
37	C₂×Dic₂₉	—	2	2	no	—
38	D₁₁₆	—	4	2	no	—
39	D₁₁₆	—	4	4	no	—
40	C₈×C₂₉	—	4	2	no	—
41	#6597	—	4	1	no	—
42	#1658	—	29	1	no	maximal, Sylow
43	C₂²×C₂₉	#120	1	1	yes	characteristic
44	C₂×D₂₉	—	8	2	no	—
45	C₂×D₂₉	—	8	1	no	—
46	C₄×C₂₉	—	2	1	no	—
47	C₄×C₂₉	—	2	2	no	—
48	C₄×C₂₉	—	4	2	no	—
49	Dic₂₉	—	4	2	no	—
50	Dic₂₉	—	4	2	no	—
51	#564	—	29	1	no	—
52	#490	—	29	1	no	—
53	#490	—	29	2	no	—
54	#330	—	29	2	no	—
55	#330	D₂₉	1	1	yes	characteristic, complemented
56	C₂×C₂₉	#454	1	2	yes	—
57	C₂×C₂₉	#454	1	1	yes	characteristic
58	D₂₉	—	16	1	no	—
59	#127	—	29	1	no	—
60	#125	—	29	2	no	—
61	#125	—	58	2	no	—
62	#125	—	58	2	no	—
63	#125	—	58	2	no	—
64	#125	C₂×D₂₉	1	1	yes	characteristic
65	#102	—	58	2	no	—
66	#102	—	58	2	no	—
67	#102	—	58	2	no	—
68	#97	—	29	1	no	—
69	#97	C₂×D₂₉	1	2	yes	—
70	C₂₉	#1658	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₄	—	58	1	no	—
72	C₂×D₄	—	58	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	58	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	29	2	no	—
77	C₄⋊C₄	—	29	2	no	—
78	C₄⋊C₄	—	58	2	no	—
79	C₄⋊C₄	—	58	2	no	—
80	C₄⋊C₄	—	58	2	no	—
81	C₄⋊C₄	—	58	2	no	—
82	C₄⋊C₄	—	58	2	no	—
83	C₄⋊C₄	D₁₁₆	1	2	yes	—
84	C₄²	—	58	2	no	—
85	C₄²	C₂²×D₂₉	1	1	yes	characteristic
86	C₂³	—	116	1	no	—
87	D₄	—	116	4	no	—
88	D₄	—	116	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	58	2	no	—
91	C₂×C₄	—	58	2	no	—
92	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
93	C₂×C₄	D₄×D₂₉	1	2	yes	—
94	C₈	—	4	2	no	—
95	C₈	—	116	1	no	—
96	C₂²	—	232	2	no	—
97	C₂²	—	232	1	no	—
98	C₂²	#11745244	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	116	2	no	—
103	C₄	—	116	2	no	—
104	C₂	—	464	1	no	—
105	C₂	#14271337	1	2	yes	—
106	C₂	#14271338	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉⋊#564

C₂

yes

maximal, characteristic, complemented

#14271529

C₂

yes

maximal, characteristic

#14271528

C₂

yes

maximal

#14270904

C₂

yes

maximal, complemented

C₂₉×#330

C₂

yes

maximal, characteristic, complemented

C₂₉×#125

C₂²

yes

—

—

—

C₂²

yes

characteristic

#11745232

C₂²

yes

—

C₂₉×#97

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄⋊Dic₂₉

D₄

yes

—

—

—

—

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂²×D₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₂×C₂₉

#454

yes

—

C₂×C₂₉

#454

yes

characteristic

D₂₉

—

—

—

—

—

—

C₂×D₂₉

yes

—

—

—

—

C₂×D₂₉

yes

—

C₂₉

#1658

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₁₆

yes

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

116

—

D₄

—

116

—

D₄

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

—

C₈

—

C₈

—

116

—

C₂²

—

232

—

C₂²

—

232

—

C₂²

#11745244

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

116

—

103

C₄

—

116

—

104

C₂

—

464

—

105

C₂

#14271337

yes

—

106

C₂

#14271338

yes

characteristic

	subgroup	G/H
center	C₂²	#11745244
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#330	C₂
socle	C₂²×C₂₉	#120
prime radical	#11745236	C₂²
hypercenter	#330	D₂₉
hypocenter	C₂₉	#1658
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#11745244

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#330

C₂

C₂²×C₂₉

C₂²

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₂₉⋊#564	C₂	semidirect
4. #14270904	C₂	semidirect
5. C₂₉×#330	C₂	semidirect
55. #330	D₂₉	semidirect
70. C₂₉	#1658	semidirect

H ≅ G/N

type

1. C₂₉⋊#564

C₂

semidirect

4. #14270904

C₂

semidirect

5. C₂₉×#330

C₂

semidirect

55. #330

D₂₉

semidirect

70. C₂₉

#1658

semidirect

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

subgroup	index
C₂₉⋊#564	2
#14271529	2
#14271528	2
#14270904	2
C₂₉×#330	2
#1658	29

subgroup

index

C₂₉⋊#564

C₂₉×#330

Subgroups — #16818795

Conjugacy classes of subgroups

Complements

Maximal subgroups