Group #16836037 — subgroups

Subgroups — #16836037

Order 3712.

424 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 152 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	(C₂×#1181)⋊Q₈	C₂	1	4	yes	maximal
2	#14272112	C₂	1	8	yes	maximal
3	#14272108	C₂	1	2	yes	maximal
4	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×D₂₉	C₂²	1	2	yes	—
6	C₂×C₄⋊#1181	C₂²	1	4	yes	—
7	C₂×C₄×#1181	C₂²	1	4	yes	—
8	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	#11745306	C₄	1	2	yes	complemented
10	C₄⋊C₄×D₂₉	C₂²	1	4	yes	—
11	#11745250	C₄	1	4	yes	complemented
12	C₄²×D₂₉	C₂²	1	1	yes	characteristic
13	#11745231	C₄	1	1	yes	characteristic, complemented
14	(C₂×#1181)⋊C₄	C₂²	1	8	yes	—
15	(C₂×#1181)⋊C₄	C₂²	1	4	yes	—
16	(C₂×#1181)⋊C₄	C₂²	1	8	yes	—
17	C₂²×#1181	C₂³	1	8	yes	—
18	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
19	Q₈×D₂₉	—	4	2	no	—
20	Q₈×D₂₉	—	4	2	no	—
21	C₂×C₄×D₂₉	C₂³	1	4	yes	—
22	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
23	C₂×C₄×D₂₉	C₂³	1	2	yes	—
24	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
25	C₂×Dic₅₈	C₂×C₄	1	4	yes	—
26	C₄⋊#1181	—	4	4	no	—
27	C₄×#1181	—	4	4	no	—
28	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
29	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
31	#90779	C₂×C₄	1	8	yes	—
32	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
33	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
34	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
35	C₂×#1181	—	2	8	no	—
36	C₂×#1181	—	2	16	no	—
37	Q₈×C₂₉	—	4	2	no	—
38	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
41	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
42	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
44	C₄×D₂₉	—	2	4	no	—
45	C₄×D₂₉	—	2	4	no	—
46	C₄×D₂₉	—	2	2	no	—
47	C₄×D₂₉	—	2	4	no	—
48	Dic₅₈	—	4	4	no	—
49	Dic₅₈	—	4	2	no	—
50	#2381	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
52	C₂×D₂₉	H(5,𝔽₂)	1	2	yes	—
53	C₂×D₂₉	2₋¹⁺⁴	1	4	yes	—
54	#1181	—	4	8	no	—
55	C₄×C₂₉	—	2	1	no	—
56	C₄×C₂₉	—	2	4	no	—
57	C₄×C₂₉	—	2	2	no	—
58	Dic₂₉	—	2	1	no	—
59	Dic₂₉	—	2	4	no	—
60	Dic₂₉	—	2	2	no	—
61	C₂×C₄⋊Q₈	—	29	1	no	—
62	#391	—	29	4	no	—
63	#387	—	29	8	no	—
64	#383	—	29	2	no	—
65	C₂×C₂₉	#518	1	1	yes	characteristic
66	C₂×C₂₉	#519	1	2	yes	—
67	D₂₉	#563	1	4	yes	—
68	C₂²×Q₈	—	29	2	no	—
69	C₄⋊Q₈	—	29	2	no	—
70	C₄⋊Q₈	—	29	4	no	—
71	C₄⋊Q₈	—	29	1	no	—
72	C₄⋊Q₈	#1181	1	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄	—	29	4	no	—
74	C₂×C₄⋊C₄	—	29	4	no	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	—	29	4	no	—
77	#95	—	29	8	no	—
78	#95	—	29	4	no	—
79	#95	—	29	8	no	—
80	C₂₉	#2381	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	29	4	no	—
82	C₂×Q₈	—	29	2	no	—
83	C₂×Q₈	—	116	2	no	—
84	C₂×Q₈	—	116	2	no	—
85	C₂×Q₈	C₂×#1181	1	2	yes	—
86	C₂²×C₄	—	29	2	no	—
87	C₂²×C₄	—	29	1	no	—
88	C₂²×C₄	—	29	4	no	—
89	C₂²×C₄	—	29	8	no	—
90	C₄⋊C₄	—	29	8	no	—
91	C₄⋊C₄	—	29	4	no	—
92	C₄⋊C₄	—	116	4	no	—
93	C₄⋊C₄	C₂×#1181	1	4	yes	—
94	C₄²	—	29	1	no	—
95	C₄²	—	29	2	no	—
96	C₄²	—	116	4	no	—
97	C₄²	C₂×#1181	1	1	yes	characteristic
98	C₂³	—	29	1	no	—
99	Q₈	—	4	2	no	—
100	Q₈	—	116	2	no	—
101	Q₈	—	116	4	no	—
102	C₂×C₄	—	29	2	no	—
103	C₂×C₄	—	29	1	no	—
104	C₂×C₄	—	29	4	no	—
105	C₂×C₄	—	58	4	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	58	2	no	—
108	C₂×C₄	—	58	4	no	—
109	C₂×C₄	—	58	8	no	—
110	C₂×C₄	—	58	16	no	—
111	C₂×C₄	C₂²×#1181	1	2	yes	—
112	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
113	C₂×C₄	C₂²×#1181	1	4	yes	—
114	C₂²	—	29	2	no	—
115	C₂²	—	29	4	no	—
116	C₂²	C₂³×#1181	1	1	yes	characteristic
117	C₄	—	2	1	no	—
118	C₄	—	2	4	no	—
119	C₄	—	2	2	no	—
120	C₄	—	58	1	no	—
121	C₄	—	58	4	no	—
122	C₄	—	58	2	no	—
123	C₄	—	116	8	no	—
124	C₂	—	29	4	no	—
125	C₂	#14272230	1	1	yes	characteristic
126	C₂	#14272231	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

(C₂×#1181)⋊Q₈

C₂

yes

maximal

#14272112

C₂

yes

maximal

#14272108

C₂

yes

maximal

C₄⋊Q₈×D₂₉

C₂

yes

maximal, characteristic

C₂×Q₈×D₂₉

C₂²

yes

—

C₂×C₄⋊#1181

C₂²

yes

—

C₂×C₄×#1181

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic, complemented

#11745306

C₄

yes

complemented

C₄⋊C₄×D₂₉

C₂²

yes

—

#11745250

C₄

yes

complemented

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₄

yes

characteristic, complemented

(C₂×#1181)⋊C₄

C₂²

yes

—

(C₂×#1181)⋊C₄

C₂²

yes

—

(C₂×#1181)⋊C₄

C₂²

yes

—

C₂²×#1181

C₂³

yes

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

Q₈×D₂₉

—

Q₈×D₂₉

—

C₂×C₄×D₂₉

C₂³

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×C₄×D₂₉

C₂³

yes

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₄⋊#1181

—

C₄×#1181

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

—

C₂²×D₂₉

C₂⁴

yes

characteristic

C₂×#1181

—

C₂×#1181

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

Dic₅₈

—

#2381

—

maximal, Sylow

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

H(5,𝔽₂)

yes

—

C₂×D₂₉

2₋¹⁺⁴

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

C₂×C₄⋊Q₈

—

#391

—

#387

—

#383

—

C₂×C₂₉

#518

yes

characteristic

C₂×C₂₉

#519

yes

—

D₂₉

#563

yes

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

#1181

yes

characteristic, complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

#95

—

#95

—

#95

—

C₂₉

#2381

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

116

—

C₂×Q₈

—

116

—

C₂×Q₈

C₂×#1181

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄⋊C₄

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

116

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

Q₈

—

100

Q₈

—

116

—

101

Q₈

—

116

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂²×#1181

yes

—

112

C₂×C₄

C₂²×#1181

yes

characteristic

113

C₂×C₄

C₂²×#1181

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

C₂³×#1181

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

116

—

124

C₂

—

125

C₂

#14272230

yes

characteristic

126

C₂

#14272231

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×C₄⋊Q₈	C₄
prime radical, cosocle	C₂²×D₂₉	C₂⁴
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#2381
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×#1181

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂₉×C₄⋊Q₈

C₄

prime radical, cosocle

C₂²×D₂₉

C₂⁴

C₄⋊Q₈

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₄⋊Q₈

N	H ≅ G/N	type
8. C₂₉×C₄⋊Q₈	C₄	semidirect
9. #11745306	C₄	semidirect
11. #11745250	C₄	semidirect
13. #11745231	C₄	semidirect
72. C₄⋊Q₈	#1181	semidirect
80. C₂₉	#2381	semidirect

H ≅ G/N

type

8. C₂₉×C₄⋊Q₈

C₄

semidirect

9. #11745306

C₄

semidirect

11. #11745250

C₄

semidirect

13. #11745231

C₄

semidirect

72. C₄⋊Q₈

#1181

semidirect

80. C₂₉

#2381

semidirect

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

subgroup	index
(C₂×#1181)⋊Q₈	2
#14272112	2
#14272108	2
C₄⋊Q₈×D₂₉	2
#2381	29

subgroup

index

C₄⋊Q₈×D₂₉

Subgroups — #16836037

Conjugacy classes of subgroups

Complements

Maximal subgroups