Group #16831296 — subgroups

Subgroups — #16831296

Order 3712.

444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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	#14271976	C₂	1	4	yes	maximal, complemented
2	#14271435	C₂	1	4	yes	maximal, complemented
3	#14271345	C₂	1	4	yes	maximal, complemented
4	#14271281	C₂	1	2	yes	maximal, complemented
5	C₂₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745362	C₂²	1	4	yes	—
7	C₂×Q₁₆×C₂₉	C₂²	1	4	yes	—
8	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
9	#11745304	C₂²	1	8	yes	—
10	#11745281	—	2	4	no	—
11	#11745280	—	2	8	no	—
12	Q₁₆×D₂₉	—	2	4	no	—
13	#11745266	C₂²	1	2	yes	—
14	#11745263	C₂²	1	4	yes	—
15	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	#11745184	C₂²	1	4	yes	—
17	#11745167	C₂²	1	2	yes	—
18	#11745153	C₂²	1	4	yes	—
19	C₂×Q₈×C₂₉	C₂³	1	4	yes	—
20	#90809	—	2	8	no	—
21	Q₈×D₂₉	—	2	8	no	—
22	#90805	—	4	4	no	—
23	#90805	C₂³	1	4	yes	—
24	Q₁₆×C₂₉	—	2	4	no	—
25	Q₁₆×C₂₉	—	2	4	no	—
26	C₂×C₈×C₂₉	C₂³	1	2	yes	—
27	C₄⋊C₄×C₂₉	—	4	2	no	—
28	C₄²×C₂₉	C₂³	1	1	yes	characteristic
29	#90785	—	2	8	no	—
30	#90784	—	2	8	no	—
31	#90777	C₂³	1	4	yes	—
32	Dic₁₁₆	D₄	1	2	yes	—
33	D₂₃₂	D₄	1	2	yes	—
34	#90773	D₄	1	4	yes	—
35	#90772	—	2	4	no	—
36	C₈×D₂₉	—	2	4	no	—
37	Q₈×C₂₉	—	2	8	no	—
38	C₂×C₄×C₂₉	—	2	1	no	—
39	C₂×C₄×C₂₉	—	2	4	no	—
40	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
41	C₂²⋊D₂₉	—	2	4	no	—
42	D₁₁₆	—	4	4	no	—
43	D₁₁₆	C₂×D₄	1	4	yes	—
44	C₄×D₂₉	—	2	4	no	—
45	C₄×D₂₉	—	4	8	no	—
46	Dic₅₈	—	4	4	no	—
47	Dic₅₈	C₂×D₄	1	4	yes	—
48	C₈×C₂₉	C₂×D₄	1	2	yes	—
49	C₈×C₂₉	C₂×D₄	1	2	yes	—
50	#6597	—	2	4	no	—
51	#3293	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
53	C₂×D₂₉	—	2	4	no	—
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	—	4	4	no	—
56	C₄×C₂₉	C₂²×D₄	1	2	yes	—
57	Dic₂₉	—	2	4	no	—
58	#578	—	29	4	no	—
59	#494	D₂₉	1	1	yes	characteristic, complemented
60	#473	—	29	4	no	—
61	#456	—	29	4	no	—
62	#443	—	29	2	no	—
63	C₂×C₂₉	—	2	1	no	—
64	C₂×C₂₉	D₄²	1	1	yes	characteristic
65	D₂₉	—	4	4	no	—
66	2₋¹⁺⁴	—	29	4	no	—
67	#137	—	29	8	no	—
68	#137	—	58	8	no	—
69	#135	—	29	2	no	—
70	#135	—	58	4	no	—
71	C₂×Q₁₆	—	58	4	no	—
72	C₂×Q₁₆	C₂×D₂₉	1	4	yes	—
73	#131	—	29	4	no	—
74	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
75	#108	—	29	2	no	—
76	#104	—	29	4	no	—
77	#101	—	29	4	no	—
78	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
79	C₂₉	#3293	1	1	yes	characteristic, complemented, Sylow
80	#41	—	29	4	no	—
81	#41	—	58	8	no	—
82	#41	—	116	4	no	—
83	C₂×Q₈	—	58	8	no	—
84	C₂×Q₈	C₂²×D₂₉	1	4	yes	—
85	Q₁₆	—	2	4	no	—
86	Q₁₆	—	2	4	no	—
87	Q₁₆	—	29	2	no	—
88	Q₁₆	—	58	8	no	—
89	SD₁₆	—	29	4	no	—
90	SD₁₆	—	58	8	no	—
91	D₈	—	29	2	no	—
92	M₁₆	—	29	4	no	—
93	M₁₆	—	58	4	no	—
94	C₂×C₈	—	58	4	no	—
95	C₂×C₈	C₂²×D₂₉	1	2	yes	—
96	C₄⋊C₄	—	4	2	no	—
97	C₄²	C₂²×D₂₉	1	1	yes	characteristic
98	Q₈	—	2	8	no	—
99	Q₈	—	29	4	no	—
100	Q₈	—	116	4	no	—
101	D₄	—	29	4	no	—
102	D₄	—	58	4	no	—
103	D₄	—	116	4	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	116	8	no	—
108	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
109	C₈	—	58	4	no	—
110	C₈	D₄×D₂₉	1	2	yes	—
111	C₈	D₄×D₂₉	1	2	yes	—
112	C₂²	—	58	4	no	—
113	C₂²	#11745359	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	—	58	4	no	—
117	C₄	C₂×D₄×D₂₉	1	2	yes	—
118	C₂	—	2	1	no	—
119	C₂	—	116	4	no	—
120	C₂	#14271798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271976

C₂

yes

maximal, complemented

#14271435

C₂

yes

maximal, complemented

#14271345

C₂

yes

maximal, complemented

#14271281

C₂

yes

maximal, complemented

C₂₉×#494

C₂

yes

maximal, characteristic, complemented

#11745362

C₂²

yes

—

C₂×Q₁₆×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₂²

yes

—

#11745304

C₂²

yes

—

#11745281

—

#11745280

—

Q₁₆×D₂₉

—

#11745266

C₂²

yes

—

#11745263

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745184

C₂²

yes

—

#11745167

C₂²

yes

—

#11745153

C₂²

yes

—

C₂×Q₈×C₂₉

C₂³

yes

—

#90809

—

Q₈×D₂₉

—

#90805

—

#90805

C₂³

yes

—

Q₁₆×C₂₉

—

Q₁₆×C₂₉

—

C₂×C₈×C₂₉

C₂³

yes

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

—

—

C₂³

yes

—

Dic₁₁₆

D₄

yes

—

D₂₃₂

D₄

yes

—

#90773

D₄

yes

—

#90772

—

C₈×D₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂²⋊D₂₉

—

D₁₁₆

—

D₁₁₆

C₂×D₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

Dic₅₈

C₂×D₄

yes

—

C₈×C₂₉

C₂×D₄

yes

—

C₈×C₂₉

C₂×D₄

yes

—

—

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²×D₄

yes

—

Dic₂₉

—

#578

—

#494

D₂₉

yes

characteristic, complemented

#473

—

#456

—

#443

—

C₂×C₂₉

—

C₂×C₂₉

D₄²

yes

characteristic

D₂₉

—

2₋¹⁺⁴

—

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₂₉

yes

—

#131

—

C₄⋊Q₈

C₂×D₂₉

yes

—

#108

—

#104

—

#101

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#3293

yes

characteristic, complemented, Sylow

#41

—

#41

—

#41

—

116

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₂₉

yes

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₂₉

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

116

—

101

D₄

—

102

D₄

—

103

D₄

—

116

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

116

—

108

C₂×C₄

C₂³×D₂₉

yes

characteristic

109

C₈

—

110

C₈

D₄×D₂₉

yes

—

111

C₈

D₄×D₂₉

yes

—

112

C₂²

—

113

C₂²

#11745359

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×D₄×D₂₉

yes

—

118

C₂

—

119

C₂

—

116

—

120

C₂

#14271798

yes

characteristic

	subgroup	G/H
center	C₂	#14271798
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#494	C₂
socle	C₂×C₂₉	D₄²
hypercenter	#494	D₂₉
hypocenter	C₂₉	#3293
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

subgroup

G/H

center

C₂

#14271798

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂₉×#494

C₂

socle

C₂×C₂₉

D₄²

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

N	H ≅ G/N	type
1. #14271976	C₂	semidirect
2. #14271435	C₂	semidirect
3. #14271345	C₂	semidirect
4. #14271281	C₂	semidirect
5. C₂₉×#494	C₂	semidirect
59. #494	D₂₉	semidirect
79. C₂₉	#3293	semidirect

H ≅ G/N

type

1. #14271976

C₂

semidirect

2. #14271435

C₂

semidirect

3. #14271345

C₂

semidirect

4. #14271281

C₂

semidirect

5. C₂₉×#494

C₂

semidirect

59. #494

D₂₉

semidirect

79. C₂₉

#3293

semidirect

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

subgroup	index
#14271976	2
#14271435	2
#14271345	2
#14271281	2
C₂₉×#494	2
#3293	29

subgroup

index

C₂₉×#494

Subgroups — #16831296

Conjugacy classes of subgroups

Complements

Maximal subgroups