Group #16833640 — subgroups

Subgroups — #16833640

Order 3712.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#14271917	C₂	1	10	yes	maximal, complemented
2	#14271911	C₂	1	5	yes	maximal, complemented
3	#14271719	C₂	1	5	yes	maximal, complemented
4	#14271698	C₂	1	10	yes	maximal, complemented
5	C₂₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#125	C₂²	1	5	yes	—
7	C₂₉×#125	C₂²	1	10	yes	—
8	#11745260	C₂²	1	20	yes	—
9	#11745259	C₂²	1	10	yes	—
10	#11745258	C₂²	1	20	yes	—
11	#11745257	C₂²	1	10	yes	—
12	#11745256	C₂²	1	20	yes	—
13	#11745255	C₂²	1	10	yes	—
14	#11745254	C₂²	1	10	yes	—
15	#11745250	C₂²	1	10	yes	—
16	#11745249	C₂²	1	10	yes	—
17	#11745237	C₂²	1	10	yes	—
18	C₄²×D₂₉	C₂²	1	5	yes	—
19	#11745232	C₂²	1	5	yes	—
20	C₂×D₁₁₆	C₂³	1	10	yes	—
21	C₂×C₄×D₂₉	C₂³	1	5	yes	—
22	C₂×C₄×D₂₉	C₂³	1	10	yes	—
23	C₂×Dic₅₈	C₂³	1	10	yes	—
24	C₄⋊C₄×C₂₉	C₂³	1	10	yes	—
25	C₄⋊C₄×C₂₉	C₂³	1	10	yes	—
26	C₄⋊C₄×C₂₉	C₂³	1	10	yes	—
27	C₄²×C₂₉	C₂³	1	5	yes	—
28	#90781	C₂³	1	20	yes	—
29	#90781	C₂³	1	20	yes	—
30	C₄⋊Dic₂₉	C₂³	1	10	yes	—
31	#90779	C₂³	1	20	yes	—
32	C₄×Dic₂₉	C₂³	1	10	yes	—
33	C₄×Dic₂₉	C₂³	1	5	yes	—
34	C₂²×D₂₉	C₂⁴	1	5	yes	—
35	C₂×C₄×C₂₉	C₂⁴	1	10	yes	—
36	C₂×C₄×C₂₉	C₂⁴	1	5	yes	—
37	C₂×Dic₂₉	C₂⁴	1	10	yes	—
38	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
39	D₁₁₆	—	4	10	no	—
40	C₄×D₂₉	—	2	10	no	—
41	C₄×D₂₉	—	4	10	no	—
42	Dic₅₈	—	4	10	no	—
43	#3531	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
45	C₂×D₂₉	—	2	5	no	—
46	C₂×D₂₉	—	2	10	no	—
47	C₄×C₂₉	—	2	5	no	—
48	C₄×C₂₉	—	2	10	no	—
49	Dic₂₉	—	2	10	no	—
50	Dic₂₉	2₋¹⁺⁴	1	2	yes	—
51	#564	D₂₉	1	1	yes	characteristic, complemented
52	#563	—	29	10	no	—
53	#562	—	29	5	no	—
54	#533	—	29	5	no	—
55	#529	—	29	10	no	—
56	C₂×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
57	C₂×C₂₉	#585	1	2	yes	—
58	D₂₉	—	4	5	no	—
59	C₄⋊Q₈	—	29	10	no	—
60	#126	—	29	20	no	—
61	#125	—	29	5	no	—
62	#125	C₂×D₂₉	1	10	yes	—
63	#125	C₂×D₂₉	1	5	yes	—
64	#124	—	29	10	no	—
65	#123	—	29	20	no	—
66	C₂²⋊Q₈	—	29	10	no	—
67	C₂²⋊Q₈	—	29	20	no	—
68	#121	—	29	10	no	—
69	C₄×Q₈	—	29	10	no	—
70	C₄×D₄	—	29	10	no	—
71	#117	—	29	10	no	—
72	C₂×C₄²	—	29	5	no	—
73	C₂₉	#3531	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	29	10	no	—
75	C₂×D₄	—	29	10	no	—
76	C₂²×C₄	—	29	5	no	—
77	C₂²×C₄	—	29	10	no	—
78	C₄⋊C₄	—	29	10	no	—
79	C₄⋊C₄	—	29	20	no	—
80	C₄⋊C₄	C₂²×D₂₉	1	10	yes	—
81	C₄⋊C₄	C₂²×D₂₉	1	10	yes	—
82	C₄⋊C₄	C₂²×D₂₉	1	10	yes	—
83	C₂²⋊C₄	—	29	20	no	—
84	C₂²⋊C₄	—	29	20	no	—
85	C₄²	—	29	10	no	—
86	C₄²	—	29	5	no	—
87	C₄²	C₂²×D₂₉	1	5	yes	—
88	C₂³	—	29	5	no	—
89	Q₈	—	116	10	no	—
90	D₄	—	116	10	no	—
91	C₂×C₄	—	29	1	no	—
92	C₂×C₄	—	29	10	no	—
93	C₂×C₄	—	58	10	no	—
94	C₂×C₄	—	116	10	no	—
95	C₂×C₄	C₂³×D₂₉	1	5	yes	—
96	C₂×C₄	C₂³×D₂₉	1	10	yes	—
97	C₂²	—	58	10	no	—
98	C₂²	—	58	5	no	—
99	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
100	C₄	—	2	10	no	—
101	C₄	—	2	5	no	—
102	C₄	—	29	2	no	—
103	C₄	—	58	10	no	—
104	C₂	—	116	5	no	—
105	C₂	2₋¹⁺⁴×D₂₉	1	1	yes	characteristic
106	C₂	#14272000	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271917

C₂

yes

maximal, complemented

#14271911

C₂

yes

maximal, complemented

#14271719

C₂

yes

maximal, complemented

#14271698

C₂

yes

maximal, complemented

C₂₉×#564

C₂

yes

maximal, characteristic, complemented

C₂₉×#125

C₂²

yes

—

C₂₉×#125

C₂²

yes

—

#11745260

C₂²

yes

—

#11745259

C₂²

yes

—

#11745258

C₂²

yes

—

#11745257

C₂²

yes

—

#11745256

C₂²

yes

—

#11745255

C₂²

yes

—

#11745254

C₂²

yes

—

#11745250

C₂²

yes

—

#11745249

C₂²

yes

—

#11745237

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

—

#11745232

C₂²

yes

—

C₂×D₁₁₆

C₂³

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

C₂×Dic₅₈

C₂³

yes

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₄²×C₂₉

C₂³

yes

—

#90781

C₂³

yes

—

#90781

C₂³

yes

—

C₄⋊Dic₂₉

C₂³

yes

—

#90779

C₂³

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂²×D₂₉

C₂⁴

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

—

C₂×Dic₂₉

C₂⁴

yes

—

C₂×Dic₂₉

C₂⁴

yes

characteristic

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

#3531

—

maximal, Sylow

C₂²×C₂₉

C₂⁵

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

2₋¹⁺⁴

yes

—

#564

D₂₉

yes

characteristic, complemented

—

—

—

—

C₂×C₂₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₂₉

#585

yes

—

D₂₉

—

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₂₉

yes

—

#125

C₂×D₂₉

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂₉

#3531

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₂₉

yes

—

C₄⋊C₄

C₂²×D₂₉

yes

—

C₄⋊C₄

C₂²×D₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

—

C₂³

—

Q₈

—

116

—

D₄

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂³×D₂₉

yes

—

C₂×C₄

C₂³×D₂₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₂₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

—

116

—

105

C₂

2₋¹⁺⁴×D₂₉

yes

characteristic

106

C₂

#14272000

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#564	C₂
hypercenter	#564	D₂₉
hypocenter	C₂₉	#3531
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁵

Fitting

C₂₉×#564

C₂

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. #14271917	C₂	semidirect
2. #14271911	C₂	semidirect
3. #14271719	C₂	semidirect
4. #14271698	C₂	semidirect
5. C₂₉×#564	C₂	semidirect
51. #564	D₂₉	semidirect
73. C₂₉	#3531	semidirect

H ≅ G/N

type

1. #14271917

C₂

semidirect

2. #14271911

C₂

semidirect

3. #14271719

C₂

semidirect

4. #14271698

C₂

semidirect

5. C₂₉×#564

C₂

semidirect

51. #564

D₂₉

semidirect

73. C₂₉

#3531

semidirect

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

subgroup	index
#14271917	2
#14271911	2
#14271719	2
#14271698	2
C₂₉×#564	2
#3531	29

subgroup

index

C₂₉×#564

Subgroups — #16833640

Conjugacy classes of subgroups

Complements

Maximal subgroups