Group #16834559 — subgroups

Subgroups — #16834559

Order 3712.

132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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	#14272173	C₂	1	1	yes	maximal, characteristic
3	#14271198	C₂	1	1	yes	maximal, characteristic
4	#11745345	—	2	1	no	—
5	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
6	#11745254	—	2	1	no	—
7	#11745214	—	2	1	no	—
8	#11745210	—	2	1	no	—
9	#11745209	C₄	1	2	yes	complemented
10	#11745206	—	2	1	no	—
11	D₂₉⋊C₁₆	C₄	1	2	yes	complemented
12	C₂₉×#106	C₄	1	1	yes	characteristic, complemented
13	#11745165	C₄	1	1	yes	characteristic, complemented
14	#11745155	—	2	1	no	—
15	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
16	C₂²⋊#1181	—	4	1	no	—
17	C₄⋊#1181	—	2	2	no	—
18	C₄×#1181	—	4	1	no	—
19	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₂₉	—	2	1	no	—
21	#90781	—	4	1	no	—
22	C₄⋊Dic₂₉	—	2	1	no	—
23	C₄×Dic₂₉	—	4	1	no	—
24	C₂×#6597	D₄	1	1	yes	characteristic
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	D₈	1	1	yes	characteristic
31	C₂×#1181	—	4	2	no	—
32	C₂×C₄×C₂₉	—	4	1	no	—
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₂₉	—	4	1	no	—
35	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
36	C₄×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₂₉	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₂₉	SD₁₆	1	1	yes	characteristic
39	C₄×D₂₉	Q₁₆	1	1	yes	characteristic
40	C₈×C₂₉	C₄²	1	1	yes	characteristic
41	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
42	#6597	C₂²⋊C₄	1	1	yes	characteristic
43	#6597	C₄⋊C₄	1	1	yes	characteristic
44	#1384	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	#102	1	1	yes	characteristic
46	C₂×D₂₉	—	4	1	no	—
47	C₂×D₂₉	#102	1	1	yes	characteristic
48	C₂×D₂₉	#107	1	1	yes	characteristic
49	#1181	—	8	2	no	—
50	C₄×C₂₉	—	8	1	no	—
51	C₄×C₂₉	#95	1	1	yes	characteristic
52	C₄×C₂₉	#103	1	1	yes	characteristic
53	Dic₂₉	—	8	1	no	—
54	Dic₂₉	#103	1	1	yes	characteristic
55	Dic₂₉	#106	1	1	yes	characteristic
56	C₂×M₃₂	—	29	1	no	—
57	#427	—	29	1	no	—
58	#427	—	29	1	no	—
59	C₂×C₂₉	—	2	1	no	—
60	C₂×C₂₉	#340	1	1	yes	characteristic
61	D₂₉	—	2	1	no	—
62	D₂₉	—	2	1	no	—
63	C₂²×C₈	—	29	1	no	—
64	#117	—	58	1	no	—
65	#117	—	58	1	no	—
66	M₃₂	—	58	1	no	—
67	M₃₂	—	58	1	no	—
68	C₂×C₁₆	—	29	2	no	—
69	#107	—	58	1	no	—
70	#107	—	58	1	no	—
71	#106	—	29	2	no	—
72	#106	—	29	1	no	—
73	#106	#1181	1	1	yes	characteristic, complemented
74	C₂₉	#1384	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	29	1	no	—
76	C₂×C₈	—	29	1	no	—
77	C₂×C₈	—	29	1	no	—
78	C₂×C₈	—	29	1	no	—
79	C₂×C₈	—	29	1	no	—
80	C₂×C₈	—	29	1	no	—
81	C₂×C₈	C₂×#1181	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄⋊C₄	—	58	1	no	—
85	C₂²⋊C₄	—	116	1	no	—
86	C₂²⋊C₄	—	116	1	no	—
87	C₄²	—	116	1	no	—
88	C₄²	—	116	1	no	—
89	C₁₆	—	58	2	no	—
90	C₂³	—	29	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	—	29	1	no	—
93	C₂×C₄	—	29	1	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	29	1	no	—
97	C₂×C₄	—	116	2	no	—
98	C₂×C₄	—	116	1	no	—
99	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
100	C₈	—	29	1	no	—
101	C₈	—	29	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	—	116	1	no	—
107	C₂²	#11745223	1	1	yes	characteristic
108	C₄	—	8	1	no	—
109	C₄	—	29	1	no	—
110	C₄	—	29	1	no	—
111	C₄	—	232	1	no	—
112	C₄	—	232	2	no	—
113	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
114	C₄	#11745225	1	1	yes	characteristic
115	C₂	—	2	1	no	—
116	C₂	—	58	1	no	—
117	C₂	—	58	1	no	—
118	C₂	#14272036	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₂₉⋊M₃₂

C₂

yes

maximal, characteristic

#14272173

C₂

yes

maximal, characteristic

#14271198

C₂

yes

maximal, characteristic

#11745345

—

C₂×C₈×D₂₉

C₂²

yes

—

—

—

C₄

yes

complemented

#11745206

—

D₂₉⋊C₁₆

C₄

yes

complemented

C₂₉×#106

C₄

yes

characteristic, complemented

#11745165

C₄

yes

characteristic, complemented

#11745155

—

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂²⋊#1181

—

C₄⋊#1181

—

C₄×#1181

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

—

#90781

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₂×#6597

D₄

yes

characteristic

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

D₈

yes

characteristic

C₂×#1181

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

SD₁₆

yes

characteristic

C₄×D₂₉

C₂²⋊C₄

yes

characteristic

C₄×D₂₉

C₄⋊C₄

yes

characteristic

C₄×D₂₉

SD₁₆

yes

characteristic

C₄×D₂₉

Q₁₆

yes

characteristic

C₈×C₂₉

C₄²

yes

characteristic

C₈×C₂₉

C₄⋊C₄

yes

characteristic

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₄⋊C₄

yes

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

yes

C₂×D₂₉

yes

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

yes

Dic₂₉

yes

C₂×M₃₂

—

#427

—

#427

—

C₂×C₂₉

—

C₂×C₂₉

#340

yes

characteristic

D₂₉

—

D₂₉

—

C₂²×C₈

—

#117

—

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

—

yes

characteristic, complemented

C₂₉

#1384

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

116

—

C₂²⋊C₄

—

116

—

C₄²

—

116

—

C₄²

—

116

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

C₂²⋊#1181

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

C₄×#1181

yes

characteristic

103

C₈

C₄⋊#1181

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

116

—

107

C₂²

#11745223

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

232

—

112

C₄

—

232

—

113

C₄

(C₂×#1181)⋊C₄

yes

characteristic

114

C₄

#11745225

yes

characteristic

115

C₂

—

116

C₂

—

117

C₂

—

118

C₂

#14272036

yes

characteristic

	subgroup	G/H
center	C₂	#14272036
commutator	C₈×C₂₉	C₄²
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#106	C₄
socle	C₂×C₂₉	#340
prime radical	C₂²×D₂₉	D₈
cosocle	C₂×C₈×D₂₉	C₂²
hypercenter	#106	#1181
hypocenter	C₂₉	#1384
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

subgroup

G/H

center

C₂

#14272036

commutator

C₈×C₂₉

C₄²

Frattini

C₂×C₈

C₂×#1181

Fitting

C₂₉×#106

C₄

socle

C₂×C₂₉

#340

prime radical

C₂²×D₂₉

D₈

cosocle

C₂×C₈×D₂₉

C₂²

C₂₉

G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

N	H ≅ G/N	type
9. #11745209	C₄	semidirect
11. D₂₉⋊C₁₆	C₄	semidirect
12. C₂₉×#106	C₄	semidirect
13. #11745165	C₄	semidirect
73. #106	#1181	semidirect
74. C₂₉	#1384	semidirect

H ≅ G/N

type

9. #11745209

C₄

semidirect

11. D₂₉⋊C₁₆

C₄

semidirect

12. C₂₉×#106

C₄

semidirect

13. #11745165

C₄

semidirect

73. #106

#1181

semidirect

74. C₂₉

#1384

semidirect

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

subgroup	index
D₂₉⋊M₃₂	2
#14272173	2
#14271198	2
#1384	29

subgroup

index

D₂₉⋊M₃₂

#14272173

#14271198

#1384

Subgroups — #16834559

Conjugacy classes of subgroups

Complements

Maximal subgroups