Group #14271792 — subgroups

Subgroups — #14271792

Order 1856.

206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#11745306	C₂	1	2	yes	maximal, complemented
3	#11745286	C₂	1	1	yes	maximal, characteristic
4	C₂×#90779	C₂	1	1	yes	maximal, characteristic
5	#11745251	C₂	1	2	yes	maximal, complemented
6	#11745251	C₂	1	2	yes	maximal, complemented
7	#11745250	C₂	1	2	yes	maximal, complemented
8	#11745240	C₂	1	2	yes	maximal
9	#11745239	C₂	1	2	yes	maximal
10	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₈	C₂²	1	2	yes	—
16	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
17	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
19	C₂²⋊Dic₂₉	C₂²	1	2	yes	—
20	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
21	C₄⋊Dic₂₉	C₂²	1	2	yes	—
22	#90779	C₂²	1	2	yes	—
23	#90779	C₂²	1	2	yes	—
24	#90779	C₂²	1	2	yes	—
25	#90779	C₂²	1	2	yes	—
26	#90779	C₂²	1	2	yes	—
27	#90779	C₂²	1	2	yes	—
28	#90779	C₂²	1	2	yes	—
29	C₄×Dic₂₉	C₂²	1	2	yes	—
30	C₄×Dic₂₉	C₂²	1	2	yes	—
31	C₂³×C₂₉	C₂³	1	1	yes	characteristic
32	Q₈×C₂₉	—	4	1	no	—
33	C₂×C₄×C₂₉	—	4	1	no	—
34	C₂×C₄×C₂₉	C₂³	1	2	yes	—
35	C₂×C₄×C₂₉	C₂³	1	2	yes	—
36	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
38	C₂×Dic₂₉	—	4	1	no	—
39	C₂×Dic₂₉	Q₈	1	4	yes	complemented
40	C₂×Dic₂₉	C₂³	1	2	yes	—
41	C₂×Dic₂₉	C₂³	1	2	yes	—
42	C₂×Dic₂₉	C₂³	1	2	yes	—
43	C₂×Dic₂₉	C₂³	1	2	yes	—
44	Dic₅₈	—	4	1	no	—
45	Dic₅₈	—	4	2	no	—
46	C₂²×C₂₉	—	2	1	no	—
47	C₂²×C₂₉	—	2	1	no	—
48	C₂²×C₂₉	C₂×Q₈	1	2	yes	—
49	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	2	no	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	—	2	2	no	—
54	Dic₂₉	—	2	2	no	—
55	Dic₂₉	—	2	2	no	—
56	Dic₂₉	—	2	2	no	—
57	Dic₂₉	C₂×Q₈	1	4	yes	—
58	#544	—	29	1	no	maximal, Sylow
59	C₂×C₂₉	—	2	2	no	—
60	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
61	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
62	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
63	C₄⋊Q₈	—	29	2	no	—
64	C₄⋊Q₈	—	29	2	no	—
65	#125	—	29	2	no	—
66	#125	—	29	2	no	—
67	C₂²⋊Q₈	—	29	1	no	—
68	C₂²⋊Q₈	—	29	2	no	—
69	C₂²⋊Q₈	D₂₉	1	1	yes	characteristic
70	#117	—	29	2	no	—
71	C₂×C₄⋊C₄	—	29	1	no	—
72	C₂₉	#544	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	29	1	no	—
74	C₂×Q₈	—	29	2	no	—
75	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
76	C₂²×C₄	—	29	1	no	—
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
79	C₄⋊C₄	—	29	2	no	—
80	C₄⋊C₄	—	29	2	no	—
81	C₄⋊C₄	—	29	2	no	—
82	C₄⋊C₄	—	29	2	no	—
83	C₄⋊C₄	—	29	2	no	—
84	C₄⋊C₄	—	29	1	no	—
85	C₄⋊C₄	—	29	2	no	—
86	C₄⋊C₄	—	29	2	no	—
87	C₄⋊C₄	—	29	2	no	—
88	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
89	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
90	C₂²⋊C₄	—	29	2	no	—
91	C₂²⋊C₄	C₂×D₂₉	1	2	yes	—
92	C₄²	—	29	2	no	—
93	C₄²	—	29	2	no	—
94	C₂³	C₂²×D₂₉	1	1	yes	characteristic
95	Q₈	—	4	1	no	—
96	Q₈	—	116	1	no	—
97	Q₈	—	116	2	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	29	4	no	—
100	C₂×C₄	—	29	2	no	—
101	C₂×C₄	—	29	2	no	—
102	C₂×C₄	—	29	2	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	116	1	no	—
105	C₂×C₄	C₂²×D₂₉	1	2	yes	—
106	C₂×C₄	C₂²×D₂₉	1	2	yes	—
107	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
108	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
109	C₂²	—	2	1	no	—
110	C₂²	—	2	1	no	—
111	C₂²	Q₈×D₂₉	1	2	yes	—
112	C₂²	C₂³×D₂₉	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	2	2	no	—
116	C₄	—	2	2	no	—
117	C₄	—	29	4	no	—
118	C₄	—	58	2	no	—
119	C₄	—	58	2	no	—
120	C₄	—	58	2	no	—
121	C₂	—	2	2	no	—
122	C₂	#11745359	1	1	yes	characteristic
123	C₂	C₂×Q₈×D₂₉	1	1	yes	characteristic
124	C₂	#11745365	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×C₂²⋊Q₈

C₂

yes

maximal, characteristic

#11745306

C₂

yes

maximal, complemented

#11745286

C₂

yes

maximal, characteristic

C₂×#90779

C₂

yes

maximal, characteristic

#11745251

C₂

yes

maximal, complemented

#11745251

C₂

yes

maximal, complemented

#11745250

C₂

yes

maximal, complemented

#11745240

C₂

yes

maximal

#11745239

C₂

yes

maximal

C₂×Q₈×C₂₉

C₂²

yes

characteristic

C₂²×C₄×C₂₉

C₂²

yes

characteristic

C₂²×Dic₂₉

C₂²

yes

characteristic

C₂²×Dic₂₉

C₂²

yes

characteristic

C₂×Dic₅₈

C₂²

yes

characteristic

C₂×Dic₅₈

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂²⋊C₄×C₂₉

C₂²

yes

—

C₂²⋊Dic₂₉

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

—

C₂³×C₂₉

C₂³

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

Q₈

yes

complemented

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

Dic₅₈

—

Dic₅₈

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×Q₈

yes

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂×Q₈

yes

—

#544

—

maximal, Sylow

C₂×C₂₉

—

C₂×C₂₉

C₂²×Q₈

yes

characteristic

C₂×C₂₉

H(5,𝔽₂)

yes

characteristic

C₂×C₂₉

2₋¹⁺⁴

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

D₂₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

C₂₉

#544

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×D₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

C₂×D₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₂₉

yes

—

C₄²

—

C₄²

—

C₂³

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

116

—

105

C₂×C₄

C₂²×D₂₉

yes

—

106

C₂×C₄

C₂²×D₂₉

yes

—

107

C₂×C₄

C₂²×D₂₉

yes

characteristic

108

C₂×C₄

C₂²×D₂₉

yes

characteristic

109

C₂²

—

110

C₂²

—

111

C₂²

Q₈×D₂₉

yes

—

112

C₂²

C₂³×D₂₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₂

—

122

C₂

#11745359

yes

characteristic

123

C₂

C₂×Q₈×D₂₉

yes

characteristic

124

C₂

#11745365

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×C₂²⋊Q₈	C₂
prime radical	C₂³×C₂₉	C₂³
hypercenter	C₂²⋊Q₈	D₂₉
hypocenter	C₂₉	#544
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×C₂²⋊Q₈

C₂

prime radical

C₂³×C₂₉

C₂³

hypercenter

C₂²⋊Q₈

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₂²⋊Q₈

N	H ≅ G/N	type
2. #11745306	C₂	semidirect
5. #11745251	C₂	semidirect
6. #11745251	C₂	semidirect
7. #11745250	C₂	semidirect
39. C₂×Dic₂₉	Q₈	semidirect
72. C₂₉	#544	semidirect

H ≅ G/N

type

2. #11745306

C₂

semidirect

5. #11745251

C₂

semidirect

6. #11745251

C₂

semidirect

7. #11745250

C₂

semidirect

39. C₂×Dic₂₉

Q₈

semidirect

72. C₂₉

#544

semidirect

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

subgroup	index
C₂₉×C₂²⋊Q₈	2
#11745306	2
#11745286	2
C₂×#90779	2
#11745251	2
#11745250	2
#11745240	2
#11745239	2
#544	29

subgroup

index

C₂₉×C₂²⋊Q₈

Subgroups — #14271792

Conjugacy classes of subgroups

Complements

Maximal subgroups