Group #16834696 — subgroups

Subgroups — #16834696

Order 3712.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	#14272181	C₂	1	2	yes	maximal
2	#14272004	C₂	1	2	yes	maximal, complemented
3	C₈×#6599	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
6	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
7	C₄²×D₂₉	C₂²	1	1	yes	characteristic
8	#11745220	C₄	1	4	yes	—
9	#11745219	C₄	1	4	yes	—
10	C₄×#6599	C₂²	1	4	yes	—
11	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
12	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₄×#6597	C₄	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×#6599	C₂×C₄	1	8	yes	—
18	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
23	C₂×#6597	C₂×C₄	1	1	yes	characteristic
24	C₂×#6597	C₂×C₄	1	1	yes	characteristic
25	C₈×D₂₉	C₈	1	4	yes	complemented
26	C₈×D₂₉	C₈	1	4	yes	complemented
27	C₂²×D₂₉	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₄²	1	2	yes	—
29	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
31	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
32	C₄×D₂₉	—	2	4	no	—
33	C₄×D₂₉	C₂×C₈	1	2	yes	—
34	C₄×D₂₉	C₂×C₈	1	2	yes	—
35	#6599	—	2	8	no	—
36	C₈×C₂₉	C₂×C₈	1	2	yes	—
37	C₈×C₂₉	C₂×C₈	1	2	yes	—
38	#6597	C₂×C₈	1	2	yes	—
39	#6597	C₂×C₈	1	2	yes	—
40	#1450	—	29	1	no	maximal, Sylow
41	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
42	C₂×D₂₉	—	2	2	no	—
43	C₂×D₂₉	C₄×C₈	1	2	yes	—
44	C₄×C₂₉	—	2	2	no	—
45	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
46	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
47	Dic₂₉	C₄×C₈	1	2	yes	—
48	Dic₂₉	#131	1	4	yes	—
49	#431	—	29	2	no	—
50	C₂×C₄×C₈	—	29	1	no	—
51	#322	—	29	2	no	—
52	C₈²	—	29	2	no	—
53	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
54	C₂×C₂₉	#405	1	2	yes	—
55	D₂₉	—	2	2	no	—
56	C₂²×C₈	—	29	1	no	—
57	C₂²×C₈	—	29	1	no	—
58	C₂×C₄²	—	29	1	no	—
59	C₄⋊C₈	—	29	4	no	—
60	C₂²⋊C₈	—	29	4	no	—
61	C₄×C₈	—	29	4	no	—
62	C₄×C₈	—	29	1	no	—
63	C₄×C₈	—	29	1	no	—
64	C₄×C₈	—	29	1	no	—
65	C₄×C₈	#1181	1	1	yes	characteristic
66	C₂₉	#1450	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	29	1	no	—
68	C₂²×C₄	—	29	2	no	—
69	C₂×C₈	—	29	1	no	—
70	C₂×C₈	—	29	1	no	—
71	C₂×C₈	—	29	4	no	—
72	C₂×C₈	—	29	4	no	—
73	C₂×C₈	—	29	8	no	—
74	C₂×C₈	C₂×#1181	1	1	yes	characteristic
75	C₂×C₈	C₂×#1181	1	1	yes	characteristic
76	C₄²	—	29	2	no	—
77	C₄²	—	29	1	no	—
78	C₄²	C₂×#1181	1	1	yes	characteristic
79	C₂³	—	29	1	no	—
80	C₂×C₄	—	29	2	no	—
81	C₂×C₄	—	29	1	no	—
82	C₂×C₄	—	29	2	no	—
83	C₂×C₄	—	29	2	no	—
84	C₂×C₄	—	58	4	no	—
85	C₂×C₄	C₄×#1181	1	2	yes	—
86	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
87	C₈	—	29	2	no	—
88	C₈	—	29	2	no	—
89	C₈	—	58	8	no	—
90	C₈	D₂₉⋊C₈	1	2	yes	—
91	C₈	D₂₉⋊C₈	1	2	yes	—
92	C₂²	—	29	2	no	—
93	C₂²	—	58	2	no	—
94	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	29	2	no	—
97	C₄	—	29	4	no	—
98	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
99	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
100	C₂	—	58	2	no	—
101	C₂	C₄×D₂₉⋊C₈	1	1	yes	characteristic
102	C₂	#14272126	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272181

C₂

yes

maximal

#14272004

C₂

yes

maximal, complemented

C₈×#6599

C₂

yes

maximal, complemented

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×C₈×D₂₉

C₄

yes

characteristic

C₂×C₈×D₂₉

C₄

yes

characteristic

C₄²×D₂₉

C₂²

yes

characteristic

#11745220

C₄

yes

—

#11745219

C₄

yes

—

C₄×#6599

C₂²

yes

—

C₄×C₈×C₂₉

C₄

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

C₄×#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×#6599

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

C₈

yes

complemented

C₈×D₂₉

C₈

yes

complemented

C₂²×D₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄²

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

C₂×C₈

yes

—

C₄×D₂₉

C₂×C₈

yes

—

#6599

—

C₈×C₂₉

C₂×C₈

yes

—

C₈×C₂₉

C₂×C₈

yes

—

#6597

C₂×C₈

yes

—

#6597

C₂×C₈

yes

—

#1450

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₄×C₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂²×C₈

yes

characteristic

C₄×C₂₉

C₂²×C₈

yes

characteristic

Dic₂₉

C₄×C₈

yes

—

Dic₂₉

#131

yes

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂×C₂₉

C₂×C₄×C₈

yes

characteristic

C₂×C₂₉

#405

yes

—

D₂₉

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#1181

yes

characteristic

C₂₉

#1450

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×#1181

yes

—

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

D₂₉⋊C₈

yes

—

C₈

D₂₉⋊C₈

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#1181

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂×D₂₉⋊C₈

yes

characteristic

C₄

C₂×D₂₉⋊C₈

yes

characteristic

100

C₂

—

101

C₂

C₄×D₂₉⋊C₈

yes

characteristic

102

C₂

#14272126

yes

—

	subgroup	G/H
center	C₂×C₈	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	#1450
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

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

C₄×C₈

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #14272004	C₂	semidirect
3. C₈×#6599	C₂	semidirect
25. C₈×D₂₉	C₈	semidirect
26. C₈×D₂₉	C₈	semidirect
66. C₂₉	#1450	semidirect

H ≅ G/N

type

2. #14272004

C₂

semidirect

3. C₈×#6599

C₂

semidirect

25. C₈×D₂₉

C₈

semidirect

26. C₈×D₂₉

C₈

semidirect

66. C₂₉

#1450

semidirect

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

subgroup	index
#14272181	2
#14272004	2
C₈×#6599	2
C₄×C₈×D₂₉	2
#1450	29

subgroup

index

C₄×C₈×D₂₉

Subgroups — #16834696

Conjugacy classes of subgroups

Complements

Maximal subgroups