Group #16819654 — subgroups

Subgroups — #16819654

Order 3712.

248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745155	C₂	1	2	yes	maximal
2	C₂×#11745156	C₂	1	2	yes	maximal
3	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic
4	#14271029	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#382	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
9	C₂²×#6597	C₂²	1	1	yes	characteristic
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	C₂₉×#95	—	2	2	no	—
12	#11745179	—	2	2	no	—
13	#11745156	—	2	4	no	—
14	#11745155	—	2	4	no	—
15	C₄×#6597	C₄	1	4	yes	complemented
16	C₂²×C₄×C₂₉	—	2	2	no	—
17	C₂²×C₄×C₂₉	D₄	1	2	yes	—
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₂₉	—	2	2	no	—
20	C₄⋊C₄×C₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄²×C₂₉	C₂×C₄	1	2	yes	—
23	C₄²×C₂₉	Q₈	1	2	yes	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	C₄⋊Dic₂₉	—	2	2	no	—
26	C₂×#6597	C₂×C₄	1	2	yes	—
27	C₂×#6597	C₂×C₄	1	2	yes	—
28	C₂×#6597	D₄	1	2	yes	—
29	C₂×#6597	D₄	1	2	yes	—
30	C₂×#6597	Q₈	1	2	yes	—
31	C₂×#6597	Q₈	1	2	yes	—
32	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	4	no	—
34	C₂×C₄×C₂₉	—	4	2	no	—
35	C₂×C₄×C₂₉	—	4	4	no	—
36	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×Dic₂₉	—	4	2	no	—
44	C₂×Dic₂₉	—	4	4	no	—
45	#6597	C₄⋊C₄	1	4	yes	—
46	#6597	C₄⋊C₄	1	4	yes	—
47	#1846	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₂₉	#127	1	1	yes	characteristic
50	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₂²×C₂₉	#135	1	4	yes	—
52	C₄×C₂₉	—	2	4	no	—
53	C₄×C₂₉	—	8	2	no	—
54	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
57	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
58	Dic₂₉	—	8	2	no	—
59	C₂×#107	—	29	2	no	—
60	C₂×#106	—	29	2	no	—
61	C₂×C₄×C₈	—	29	1	no	—
62	#382	—	29	1	no	—
63	#382	D₂₉	1	1	yes	characteristic
64	C₂×C₂₉	#384	1	1	yes	characteristic
65	C₂×C₂₉	#427	1	2	yes	—
66	C₂×C₂₉	#495	1	2	yes	—
67	C₂×C₂₉	#499	1	2	yes	—
68	C₂²×C₈	—	29	1	no	—
69	C₂²×C₈	—	29	1	no	—
70	C₂×C₄⋊C₄	—	29	2	no	—
71	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
72	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
73	#107	—	58	4	no	—
74	#106	—	58	4	no	—
75	C₄×C₈	—	29	4	no	—
76	#95	—	2	2	no	—
77	#95	—	58	2	no	—
78	C₂₉	#1846	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	58	2	no	—
81	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
82	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
83	C₂×C₈	—	29	2	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	—	29	2	no	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	58	2	no	—
92	C₄⋊C₄	—	58	2	no	—
93	C₄²	Dic₅₈	1	2	yes	—
94	C₄²	C₄×D₂₉	1	2	yes	—
95	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	4	4	no	—
99	C₂×C₄	—	116	2	no	—
100	C₂×C₄	—	116	4	no	—
101	C₂×C₄	#90779	1	4	yes	—
102	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
104	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
105	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
108	C₈	—	29	4	no	—
109	C₈	—	29	4	no	—
110	C₂²	C₂×#90779	1	1	yes	characteristic
111	C₂²	#11745302	1	1	yes	characteristic
112	C₂²	#11745306	1	1	yes	characteristic
113	C₂²	#11745312	1	4	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	8	2	no	—
116	C₄	—	232	2	no	—
117	C₄	#11745250	1	1	yes	characteristic
118	C₄	#11745250	1	1	yes	characteristic
119	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
120	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
121	C₂	#14271032	1	1	yes	characteristic
122	C₂	#14271199	1	2	yes	—
123	C₂	#14271545	1	2	yes	—
124	C₂	#14271562	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745155

C₂

yes

maximal

C₂×#11745156

C₂

yes

maximal

C₂×C₄×#6597

C₂

yes

maximal, characteristic

#14271029

C₂

yes

maximal, characteristic

C₂₉×#382

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#95

—

—

—

—

C₄

yes

complemented

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂×#6597

Q₈

yes

—

C₂×#6597

Q₈

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

C₄⋊C₄

yes

—

#6597

C₄⋊C₄

yes

—

#1846

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#127

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

#135

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

—

#382

—

#382

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#495

yes

—

C₂×C₂₉

#499

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#107

—

#106

—

C₄×C₈

—

#95

—

#95

—

C₂₉

#1846

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₅₈

yes

—

C₄²

C₄×D₂₉

yes

—

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

100

C₂×C₄

—

116

—

101

C₂×C₄

#90779

yes

—

102

C₂×C₄

C₂×Dic₅₈

yes

characteristic

103

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

104

C₂×C₄

D₄×D₂₉

yes

characteristic

105

C₂×C₄

D₄×D₂₉

yes

characteristic

106

C₂×C₄

Q₈×D₂₉

yes

characteristic

107

C₂×C₄

Q₈×D₂₉

yes

characteristic

108

C₈

—

109

C₈

—

110

C₂²

C₂×#90779

yes

characteristic

111

C₂²

#11745302

yes

characteristic

112

C₂²

#11745306

yes

characteristic

113

C₂²

#11745312

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

232

—

117

C₄

#11745250

yes

characteristic

118

C₄

#11745250

yes

characteristic

119

C₄

C₄⋊C₄×D₂₉

yes

characteristic

120

C₄

C₄⋊C₄×D₂₉

yes

characteristic

121

C₂

#14271032

yes

characteristic

122

C₂

#14271199

yes

—

123

C₂

#14271545

yes

—

124

C₂

#14271562

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#382	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#382	D₂₉
hypocenter	C₂₉	#1846
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#382

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
15. C₄×#6597	C₄	semidirect
78. C₂₉	#1846	semidirect

H ≅ G/N

type

15. C₄×#6597

C₄

semidirect

78. C₂₉

#1846

semidirect

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

subgroup	index
C₂×#11745155	2
C₂×#11745156	2
C₂×C₄×#6597	2
#14271029	2
C₂₉×#382	2
#1846	29

subgroup

index

C₂×C₄×#6597

C₂₉×#382

Subgroups — #16819654

Conjugacy classes of subgroups

Complements

Maximal subgroups