Group #16835678 — subgroups

Subgroups — #16835678

Order 3712.

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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	#14272168	C₂	1	1	yes	maximal, characteristic
2	C₄²×#1181	C₂	1	1	yes	maximal, characteristic
3	#14272033	C₂	1	4	yes	maximal
4	#14271719	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#1181	—	2	2	no	—
6	C₂×C₄×#1181	C₂²	1	2	yes	—
7	C₂×#90796	C₂²	1	2	yes	—
8	C₂₉×#125	C₄	1	1	yes	characteristic, complemented
9	#11745258	—	2	2	no	—
10	#11745254	C₂²	1	2	yes	—
11	#11745250	C₄	1	2	yes	complemented
12	#11745249	—	2	2	no	—
13	C₄²×D₂₉	C₂²	1	1	yes	characteristic
14	#11745232	C₄	1	1	yes	characteristic, complemented
15	#11745220	—	2	2	no	—
16	C₂²×#1181	—	2	2	no	—
17	C₂×C₄×D₂₉	D₄	1	2	yes	—
18	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₅₈	—	2	2	no	—
20	C₂×#6599	—	2	2	no	—
21	C₄×#1181	—	2	8	no	—
22	C₄×#1181	—	2	2	no	—
23	C₄×#1181	Q₈	1	4	yes	complemented
24	#90796	—	2	4	no	—
25	C₄⋊C₄×C₂₉	—	2	2	no	—
26	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
27	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
28	#90781	—	2	2	no	—
29	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
30	#90779	—	2	2	no	—
31	#90779	—	2	2	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₂₉	D₄	1	2	yes	—
35	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
36	C₂×#1181	—	2	8	no	—
37	C₂×#1181	—	2	4	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
43	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
44	C₄×D₂₉	—	2	4	no	—
45	C₄×D₂₉	C₂×Q₈	1	2	yes	—
46	C₄×D₂₉	#41	1	2	yes	—
47	Dic₅₈	—	4	4	no	—
48	#6599	—	4	2	no	—
49	#1994	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×D₂₉	—	2	2	no	—
52	C₂×D₂₉	C₂²⋊Q₈	1	2	yes	—
53	#1181	—	2	8	no	—
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	—	4	2	no	—
56	C₄×C₂₉	C₄×Q₈	1	2	yes	—
57	Dic₂₉	—	4	2	no	—
58	Dic₂₉	#104	1	4	yes	—
59	Dic₂₉	#124	1	1	yes	characteristic
60	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
61	#533	—	29	1	no	—
62	#423	—	29	1	no	—
63	C₄³	—	29	1	no	—
64	#339	—	29	4	no	—
65	C₂×C₂₉	#391	1	1	yes	characteristic
66	C₂×C₂₉	C₂×#104	1	2	yes	—
67	D₂₉	—	2	2	no	—
68	C₂×M₁₆	—	29	2	no	—
69	C₄⋊Q₈	—	29	2	no	—
70	#125	—	29	1	no	—
71	#125	#1181	1	1	yes	characteristic, complemented
72	C₂²⋊Q₈	—	58	2	no	—
73	C₄×Q₈	—	58	2	no	—
74	#117	—	29	2	no	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	—	29	2	no	—
77	C₂×C₄²	—	58	2	no	—
78	C₄⋊C₈	—	58	2	no	—
79	C₂₉	#1994	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₈	—	58	2	no	—
81	C₂²×C₄	—	29	1	no	—
82	C₂²×C₄	—	29	2	no	—
83	C₂²×C₄	—	58	2	no	—
84	M₁₆	—	58	4	no	—
85	C₂×C₈	—	58	2	no	—
86	C₄⋊C₄	—	2	2	no	—
87	C₄⋊C₄	—	29	2	no	—
88	C₄⋊C₄	—	58	2	no	—
89	C₄⋊C₄	—	58	2	no	—
90	C₄⋊C₄	C₂×#1181	1	2	yes	—
91	C₂²⋊C₄	—	58	2	no	—
92	C₄²	—	29	2	no	—
93	C₄²	—	29	1	no	—
94	C₄²	—	29	4	no	—
95	C₄²	—	58	2	no	—
96	C₄²	—	58	2	no	—
97	C₄²	—	58	8	no	—
98	C₄²	C₂×#1181	1	1	yes	characteristic
99	C₂³	—	29	1	no	—
100	Q₈	—	116	4	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	29	1	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	29	2	no	—
105	C₂×C₄	—	29	2	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	58	4	no	—
108	C₂×C₄	—	58	8	no	—
109	C₂×C₄	—	58	2	no	—
110	C₂×C₄	C₂²⋊#1181	1	2	yes	—
111	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
112	C₈	—	116	2	no	—
113	C₂²	—	29	2	no	—
114	C₂²	—	58	2	no	—
115	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
116	C₄	—	2	2	no	—
117	C₄	—	4	2	no	—
118	C₄	—	29	1	no	—
119	C₄	—	29	1	no	—
120	C₄	—	29	4	no	—
121	C₄	—	58	8	no	—
122	C₄	—	116	2	no	—
123	C₄	Q₈×#1181	1	2	yes	—
124	C₂	—	58	2	no	—
125	C₂	(C₂×#1181)⋊Q₈	1	1	yes	characteristic
126	C₂	D₂₉⋊#104	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272168

C₂

yes

maximal, characteristic

C₄²×#1181

C₂

yes

maximal, characteristic

#14272033

C₂

yes

maximal

#14271719

C₂

yes

maximal, characteristic

C₂×C₄×#1181

—

C₂×C₄×#1181

C₂²

yes

—

C₂×#90796

C₂²

yes

—

C₂₉×#125

C₄

yes

characteristic, complemented

#11745258

—

#11745254

C₂²

yes

—

#11745250

C₄

yes

complemented

#11745249

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₄

yes

characteristic, complemented

#11745220

—

C₂²×#1181

—

C₂×C₄×D₂₉

D₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

—

—

—

Q₈

yes

complemented

#90796

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂²×D₂₉

C₂×D₄

yes

characteristic

C₂×#1181

—

C₂×#1181

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

C₂×Q₈

yes

—

C₄×D₂₉

#41

yes

—

Dic₅₈

—

#6599

—

#1994

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₂²⋊Q₈

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

Dic₂₉

—

Dic₂₉

#104

yes

—

Dic₂₉

#124

yes

characteristic

Dic₂₉

C₄⋊Q₈

yes

characteristic

#533

—

#423

—

C₄³

—

#339

—

C₂×C₂₉

#391

yes

characteristic

C₂×C₂₉

C₂×#104

yes

—

D₂₉

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

#1181

yes

characteristic, complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂₉

#1994

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

100

Q₈

—

116

—

101

C₂×C₄

—

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

C₂²⋊#1181

yes

—

111

C₂×C₄

C₂²×#1181

yes

characteristic

112

C₈

—

116

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₂²⋊#1181

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

116

—

123

C₄

Q₈×#1181

yes

—

124

C₂

—

125

C₂

(C₂×#1181)⋊Q₈

yes

characteristic

126

C₂

D₂₉⋊#104

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#125	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂×D₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#125	#1181
hypocenter	C₂₉	#1994
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#125

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂×D₄

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
8. C₂₉×#125	C₄	semidirect
11. #11745250	C₄	semidirect
14. #11745232	C₄	semidirect
23. C₄×#1181	Q₈	semidirect
71. #125	#1181	semidirect
79. C₂₉	#1994	semidirect

H ≅ G/N

type

8. C₂₉×#125

C₄

semidirect

11. #11745250

C₄

semidirect

14. #11745232

C₄

semidirect

23. C₄×#1181

Q₈

semidirect

71. #125

#1181

semidirect

79. C₂₉

#1994

semidirect

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

subgroup	index
#14272168	2
C₄²×#1181	2
#14272033	2
#14271719	2
#1994	29

subgroup

index

C₄²×#1181

Subgroups — #16835678

Conjugacy classes of subgroups

Complements

Maximal subgroups