Group #16834558 — subgroups

Subgroups — #16834558

Order 3712.

136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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	D₂₉⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745209	C₂	1	1	yes	maximal, characteristic
3	#108×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#1181	—	2	1	no	—
5	M₁₆×D₂₉	—	2	1	no	—
6	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
7	#11745214	—	2	1	no	—
8	#11745209	—	2	1	no	—
9	#11745209	C₄	1	2	yes	—
10	#11745206	—	2	1	no	—
11	D₂₉⋊C₁₆	C₄	1	2	yes	complemented
12	C₂₉×#108	C₄	1	1	yes	characteristic, complemented
13	#11745170	—	2	1	no	—
14	#11745167	C₄	1	1	yes	characteristic, complemented
15	C₂²×#1181	—	4	1	no	—
16	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
17	C₄⋊#1181	—	2	2	no	—
18	C₄⋊#1181	—	4	1	no	—
19	M₁₆×C₂₉	—	2	1	no	—
20	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
21	#90777	—	2	1	no	—
22	C₂×#6597	D₄	1	1	yes	characteristic
23	#90772	—	4	1	no	—
24	C₈×D₂₉	—	4	1	no	—
25	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
26	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
27	C₈×D₂₉	D₄	1	1	yes	characteristic
28	C₈×D₂₉	Q₈	1	1	yes	characteristic
29	#90770	—	2	2	no	—
30	C₂²×D₂₉	SD₁₆	1	1	yes	characteristic
31	C₂×#1181	—	4	2	no	—
32	C₂×#1181	—	8	2	no	—
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₂₉	Q₁₆	1	1	yes	characteristic
35	C₄×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₂₉	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₂₉	D₈	1	1	yes	characteristic
38	C₄×D₂₉	SD₁₆	1	1	yes	characteristic
39	C₈×C₂₉	—	4	1	no	—
40	C₈×C₂₉	C₄²	1	1	yes	characteristic
41	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
42	#6597	—	4	1	no	—
43	#6597	C₂²⋊C₄	1	1	yes	characteristic
44	#6597	C₄⋊C₄	1	1	yes	characteristic
45	#1383	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	#103	1	1	yes	characteristic
47	C₂×D₂₉	—	2	2	no	—
48	C₂×D₂₉	#102	1	1	yes	characteristic
49	C₂×D₂₉	#106	1	1	yes	characteristic
50	#1181	—	8	2	no	—
51	C₄×C₂₉	#95	1	1	yes	characteristic
52	C₄×C₂₉	#102	1	1	yes	characteristic
53	Dic₂₉	#103	1	1	yes	characteristic
54	Dic₂₉	#107	1	1	yes	characteristic
55	C₂×M₃₂	—	29	1	no	—
56	C₂×#108	—	29	1	no	—
57	C₂×#106	—	29	1	no	—
58	C₂×C₂₉	—	2	1	no	—
59	C₂×C₂₉	#340	1	1	yes	characteristic
60	D₂₉	—	2	1	no	—
61	D₂₉	#365	1	2	yes	—
62	C₂×M₁₆	—	58	1	no	—
63	C₂²×C₈	—	29	1	no	—
64	C₂×C₄⋊C₄	—	58	1	no	—
65	M₃₂	—	58	1	no	—
66	M₃₂	—	58	1	no	—
67	C₂×C₁₆	—	29	2	no	—
68	#108	—	29	1	no	—
69	#108	—	58	1	no	—
70	#108	#1181	1	1	yes	characteristic, complemented
71	#106	—	29	2	no	—
72	#106	—	58	1	no	—
73	C₂₉	#1383	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	—	29	1	no	—
75	C₂²×C₄	—	116	1	no	—
76	M₁₆	—	2	1	no	—
77	M₁₆	—	58	1	no	—
78	M₁₆	—	116	1	no	—
79	C₂×C₈	—	29	1	no	—
80	C₂×C₈	—	29	1	no	—
81	C₂×C₈	—	29	1	no	—
82	C₂×C₈	—	29	1	no	—
83	C₂×C₈	—	29	1	no	—
84	C₂×C₈	—	116	1	no	—
85	C₂×C₈	C₂×#1181	1	1	yes	characteristic
86	C₄⋊C₄	—	58	2	no	—
87	C₄⋊C₄	—	116	1	no	—
88	C₁₆	—	58	2	no	—
89	C₂³	—	29	1	no	—
90	C₂×C₄	—	29	1	no	—
91	C₂×C₄	—	29	1	no	—
92	C₂×C₄	—	29	1	no	—
93	C₂×C₄	—	29	1	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	116	2	no	—
96	C₂×C₄	—	232	2	no	—
97	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
98	C₈	—	4	1	no	—
99	C₈	—	29	1	no	—
100	C₈	—	29	1	no	—
101	C₈	—	116	1	no	—
102	C₈	C₄×#1181	1	1	yes	characteristic
103	C₈	C₄⋊#1181	1	1	yes	characteristic
104	C₂²	—	29	1	no	—
105	C₂²	—	29	1	no	—
106	C₂²	—	58	2	no	—
107	C₂²	#11745225	1	1	yes	characteristic
108	C₄	—	29	1	no	—
109	C₄	—	29	1	no	—
110	C₄	—	232	2	no	—
111	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
112	C₄	#11745223	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	29	2	no	—
115	C₂	—	58	1	no	—
116	C₂	#14272036	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₂₉⋊M₃₂

C₂

yes

maximal, characteristic

C₂×#11745209

C₂

yes

maximal, characteristic

#108×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄⋊#1181

—

M₁₆×D₂₉

—

C₂×C₈×D₂₉

C₂²

yes

—

—

C₄

yes

—

#11745206

—

D₂₉⋊C₁₆

C₄

yes

complemented

C₂₉×#108

C₄

yes

characteristic, complemented

#11745170

—

#11745167

C₄

yes

characteristic, complemented

C₂²×#1181

—

C₂×C₄×D₂₉

D₄

yes

characteristic

C₄⋊#1181

—

C₄⋊#1181

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

#90777

—

C₂×#6597

D₄

yes

characteristic

#90772

—

C₈×D₂₉

—

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

D₄

yes

characteristic

C₈×D₂₉

Q₈

yes

characteristic

#90770

—

C₂²×D₂₉

SD₁₆

yes

characteristic

C₂×#1181

—

C₂×#1181

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

Q₁₆

yes

characteristic

C₄×D₂₉

C₂²⋊C₄

yes

characteristic

C₄×D₂₉

C₄⋊C₄

yes

characteristic

C₄×D₂₉

D₈

yes

characteristic

C₄×D₂₉

SD₁₆

yes

characteristic

C₈×C₂₉

—

C₈×C₂₉

C₄²

yes

characteristic

C₈×C₂₉

C₄⋊C₄

yes

characteristic

#6597

—

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₄⋊C₄

yes

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

yes

C₂×D₂₉

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

yes

Dic₂₉

yes

C₂×M₃₂

—

C₂×#108

—

C₂×#106

—

C₂×C₂₉

—

C₂×C₂₉

#340

yes

characteristic

D₂₉

—

D₂₉

#365

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

yes

characteristic, complemented

#106

—

#106

—

C₂₉

#1383

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

116

—

M₁₆

—

M₁₆

—

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

116

—

C₂×C₈

C₂×#1181

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

232

—

C₂×C₄

C₂²⋊#1181

yes

characteristic

C₈

—

C₈

—

100

C₈

—

101

C₈

—

116

—

102

C₈

C₄×#1181

yes

characteristic

103

C₈

C₄⋊#1181

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

#11745225

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

232

—

111

C₄

(C₂×#1181)⋊C₄

yes

characteristic

112

C₄

#11745223

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#14272036

yes

characteristic

	subgroup	G/H
center	C₂	#14272036
commutator	C₈×C₂₉	C₄²
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#108	C₄
socle	C₂×C₂₉	#340
prime radical	C₂²×D₂₉	SD₁₆
cosocle	C₂×C₈×D₂₉	C₂²
hypercenter	#108	#1181
hypocenter	C₂₉	#1383
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

subgroup

G/H

center

C₂

#14272036

commutator

C₈×C₂₉

C₄²

Frattini

C₂×C₈

C₂×#1181

Fitting

C₂₉×#108

C₄

socle

C₂×C₂₉

#340

prime radical

C₂²×D₂₉

SD₁₆

cosocle

C₂×C₈×D₂₉

C₂²

C₂₉

G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

N	H ≅ G/N	type
11. D₂₉⋊C₁₆	C₄	semidirect
12. C₂₉×#108	C₄	semidirect
14. #11745167	C₄	semidirect
70. #108	#1181	semidirect
73. C₂₉	#1383	semidirect

H ≅ G/N

type

11. D₂₉⋊C₁₆

C₄

semidirect

12. C₂₉×#108

C₄

semidirect

14. #11745167

C₄

semidirect

70. #108

#1181

semidirect

73. C₂₉

#1383

semidirect

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

subgroup	index
D₂₉⋊M₃₂	2
C₂×#11745209	2
#108×D₂₉	2
#1383	29

subgroup

index

D₂₉⋊M₃₂

C₂×#11745209

#108×D₂₉

#1383

Subgroups — #16834558

Conjugacy classes of subgroups

Complements

Maximal subgroups