Group #16835432 — subgroups

Subgroups — #16835432

Order 3712.

220 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11745212	C₂	1	2	yes	maximal
2	C₂×#11745211	C₂	1	2	yes	maximal
3	#14272168	C₂	1	2	yes	maximal
4	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#90796	C₂²	1	4	yes	—
6	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
8	C₄²×D₂₉	C₂²	1	1	yes	characteristic
9	#11745220	—	2	4	no	—
10	#11745212	—	2	4	no	—
11	#11745211	—	2	4	no	—
12	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
13	C₈×Dic₂₉	C₄	1	1	yes	characteristic
14	C₈×Dic₂₉	C₄	1	1	yes	characteristic
15	C₄×#6597	C₄	1	1	yes	characteristic
16	C₂×C₄×D₂₉	Q₈	1	2	yes	—
17	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
18	C₂×#6599	—	2	4	no	—
19	#90796	—	2	4	no	—
20	#90796	—	2	4	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₂₉	D₄	1	2	yes	—
26	C₂×#6597	C₂×C₄	1	1	yes	characteristic
27	C₂×#6597	C₂×C₄	1	1	yes	characteristic
28	C₈×D₂₉	D₄	1	2	yes	—
29	C₈×D₂₉	D₄	1	2	yes	—
30	C₈×D₂₉	Q₈	1	2	yes	—
31	C₈×D₂₉	Q₈	1	2	yes	—
32	C₂²×D₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
37	C₄×D₂₉	—	2	4	no	—
38	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
39	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
40	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
42	#6599	—	4	4	no	—
43	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
44	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
45	#6597	C₄⋊C₄	1	2	yes	—
46	#6597	C₄⋊C₄	1	2	yes	—
47	#1848	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×D₂₉	—	2	2	no	—
50	C₂×D₂₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₂×D₂₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₄×C₂₉	—	2	2	no	—
53	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	Dic₂₉	#108	1	4	yes	complemented
56	Dic₂₉	#127	1	1	yes	characteristic
57	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₂×#108	—	29	2	no	—
59	C₂×#108	—	29	2	no	—
60	#423	—	29	2	no	—
61	C₂×C₄×C₈	—	29	1	no	—
62	C₂×C₂₉	#384	1	1	yes	characteristic
63	C₂×C₂₉	C₂×#108	1	2	yes	—
64	D₂₉	—	2	1	no	—
65	D₂₉	—	2	1	no	—
66	C₂×M₁₆	—	29	4	no	—
67	C₂²×C₈	—	29	1	no	—
68	C₂²×C₈	—	29	1	no	—
69	C₂×C₄²	—	29	1	no	—
70	#108	—	58	4	no	—
71	#108	—	58	4	no	—
72	C₄⋊C₈	—	58	4	no	—
73	C₄×C₈	—	29	1	no	—
74	C₄×C₈	—	29	1	no	—
75	C₄×C₈	—	29	1	no	—
76	C₄×C₈	#1181	1	1	yes	characteristic
77	C₂₉	#1848	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	29	1	no	—
79	C₂²×C₄	—	29	2	no	—
80	M₁₆	—	58	4	no	—
81	M₁₆	—	58	4	no	—
82	C₂×C₈	—	29	1	no	—
83	C₂×C₈	—	29	1	no	—
84	C₂×C₈	—	29	2	no	—
85	C₂×C₈	—	29	2	no	—
86	C₂×C₈	—	29	2	no	—
87	C₂×C₈	—	29	2	no	—
88	C₂×C₈	—	58	4	no	—
89	C₂×C₈	C₂×#1181	1	1	yes	characteristic
90	C₂×C₈	C₂×#1181	1	1	yes	characteristic
91	C₄²	—	29	2	no	—
92	C₄²	—	29	1	no	—
93	C₄²	C₂×#1181	1	1	yes	characteristic
94	C₂³	—	29	1	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	29	2	no	—
97	C₂×C₄	—	29	1	no	—
98	C₂×C₄	—	29	1	no	—
99	C₂×C₄	—	29	1	no	—
100	C₂×C₄	—	29	1	no	—
101	C₂×C₄	—	58	4	no	—
102	C₂×C₄	C₄⋊#1181	1	2	yes	—
103	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
104	C₈	—	29	2	no	—
105	C₈	—	29	2	no	—
106	C₈	—	116	4	no	—
107	C₈	C₄⋊#1181	1	2	yes	—
108	C₈	C₄⋊#1181	1	2	yes	—
109	C₂²	—	29	1	no	—
110	C₂²	—	29	1	no	—
111	C₂²	—	58	2	no	—
112	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	29	1	no	—
115	C₄	—	29	1	no	—
116	C₄	—	29	4	no	—
117	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
118	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
119	C₂	—	58	1	no	—
120	C₂	—	58	1	no	—
121	C₂	#14272109	1	1	yes	characteristic
122	C₂	D₂₉⋊#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745212

C₂

yes

maximal

C₂×#11745211

C₂

yes

maximal

#14272168

C₂

yes

maximal

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×#90796

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₄²×D₂₉

C₂²

yes

—

—

—

C₄×C₈×C₂₉

C₄

yes

characteristic

C₈×Dic₂₉

C₄

yes

characteristic

C₈×Dic₂₉

C₄

yes

characteristic

C₄×#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

—

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

D₄

yes

—

C₈×D₂₉

D₄

yes

—

C₈×D₂₉

Q₈

yes

—

C₈×D₂₉

Q₈

yes

—

C₂²×D₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

characteristic

#6599

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

#6597

C₄⋊C₄

yes

—

#6597

C₄⋊C₄

yes

—

#1848

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₄⋊Q₈

yes

characteristic

C₂×D₂₉

C₄⋊Q₈

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

Dic₂₉

yes

Dic₂₉

yes

Dic₂₉

C₄⋊Q₈

yes

—

—

—

C₂×C₄×C₈

—

C₂×C₂₉

#384

yes

characteristic

C₂×C₂₉

C₂×#108

yes

—

D₂₉

—

D₂₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#1181

yes

characteristic

C₂₉

#1848

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄⋊#1181

yes

—

103

C₂×C₄

C₂²×#1181

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

116

—

107

C₈

C₄⋊#1181

yes

—

108

C₈

C₄⋊#1181

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×C₄⋊#1181

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄⋊#1181

yes

characteristic

118

C₄

C₂×C₄⋊#1181

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#14272109

yes

characteristic

122

C₂

D₂₉⋊#108

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₂×Q₈
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1848
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₄×C₈×C₂₉

C₄

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂²×D₂₉

C₂×Q₈

cosocle

C₂×C₄×D₂₉

C₂³

C₄×C₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
55. Dic₂₉	#108	semidirect
77. C₂₉	#1848	semidirect

H ≅ G/N

type

55. Dic₂₉

#108

semidirect

77. C₂₉

#1848

semidirect

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

subgroup	index
C₂×#11745212	2
C₂×#11745211	2
#14272168	2
C₄×C₈×D₂₉	2
#1848	29

subgroup

index

C₄×C₈×D₂₉

Subgroups — #16835432

Conjugacy classes of subgroups

Complements

Maximal subgroups