Group #16819658 — subgroups

Subgroups — #16819658

Order 3712.

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

normal subgroups only

This group has 256 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×#11745151	C₂	1	1	yes	maximal, characteristic
4	#14271029	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂²×#6597	C₂²	1	2	yes	—
12	#11745179	—	2	2	no	—
13	#11745156	—	2	4	no	—
14	#11745155	—	2	4	no	—
15	#11745151	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	1	no	—
20	C₂²×Dic₂₉	—	2	1	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	4	4	no	—
24	C₄²×C₂₉	C₂×C₄	1	2	yes	—
25	C₄²×C₂₉	Q₈	1	2	yes	—
26	C₄⋊Dic₂₉	—	2	2	no	—
27	C₄⋊Dic₂₉	—	2	2	no	—
28	C₂×#6597	C₂×C₄	1	4	yes	—
29	C₂×#6597	D₄	1	4	yes	—
30	C₂×#6597	Q₈	1	4	yes	—
31	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	—	2	2	no	—
33	C₂×C₄×C₂₉	—	2	2	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	2	yes	—
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
41	C₂×Dic₂₉	—	4	1	no	—
42	C₂×Dic₂₉	—	4	1	no	—
43	C₂×Dic₂₉	—	4	2	no	—
44	C₂×Dic₂₉	—	4	2	no	—
45	#6597	C₄⋊C₄	1	8	yes	complemented
46	#1847	—	29	1	no	maximal, Sylow
47	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₂₉	#127	1	1	yes	characteristic
49	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
50	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
51	C₂²×C₂₉	#137	1	2	yes	—
52	C₄×C₂₉	—	2	4	no	—
53	C₄×C₂₉	—	8	2	no	—
54	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
55	C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
56	Dic₂₉	—	8	1	no	—
57	Dic₂₉	—	8	1	no	—
58	C₂×#107	—	29	2	no	—
59	C₂×#106	—	29	2	no	—
60	C₂×#97	—	29	1	no	—
61	#384	D₂₉	1	1	yes	characteristic
62	#382	—	29	1	no	—
63	C₂×C₂₉	#384	1	1	yes	characteristic
64	C₂×C₂₉	#428	1	2	yes	—
65	C₂×C₂₉	#496	1	1	yes	characteristic
66	C₂×C₂₉	#497	1	1	yes	characteristic
67	C₂×C₂₉	#501	1	2	yes	—
68	C₂²×C₈	—	29	2	no	—
69	C₂×C₄⋊C₄	—	2	2	no	—
70	C₂×C₄⋊C₄	—	29	1	no	—
71	C₂×C₄⋊C₄	—	29	1	no	—
72	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
73	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
74	#107	—	58	4	no	—
75	#106	—	58	4	no	—
76	#97	—	29	4	no	—
77	#95	—	58	2	no	—
78	C₂₉	#1847	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	58	1	no	—
81	C₂²×C₄	—	58	1	no	—
82	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	C₂×C₈	—	29	4	no	—
85	C₂×C₈	—	29	4	no	—
86	C₂×C₈	—	29	4	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	4	4	no	—
90	C₄⋊C₄	—	58	2	no	—
91	C₄⋊C₄	—	58	2	no	—
92	C₄²	Dic₅₈	1	2	yes	—
93	C₄²	C₄×D₂₉	1	2	yes	—
94	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	4	4	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	—	116	2	no	—
100	C₂×C₄	—	116	1	no	—
101	C₂×C₄	—	116	1	no	—
102	C₂×C₄	—	116	2	no	—
103	C₂×C₄	#90779	1	4	yes	—
104	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
105	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
106	C₂×C₄	D₄×D₂₉	1	2	yes	—
107	C₂×C₄	Q₈×D₂₉	1	2	yes	—
108	C₈	—	29	8	no	—
109	C₂²	C₂×#90779	1	1	yes	characteristic
110	C₂²	#11745294	1	2	yes	—
111	C₂²	#11745302	1	1	yes	characteristic
112	C₂²	#11745304	1	2	yes	—
113	C₂²	#11745306	1	1	yes	characteristic
114	C₄	—	2	4	no	—
115	C₄	—	8	2	no	—
116	C₄	—	232	1	no	—
117	C₄	—	232	1	no	—
118	C₄	#11745250	1	2	yes	—
119	C₄	C₄⋊C₄×D₂₉	1	2	yes	—
120	C₂	#14271032	1	1	yes	characteristic
121	C₂	#14271203	1	2	yes	—
122	C₂	#14271550	1	1	yes	characteristic
123	C₂	#14271555	1	1	yes	characteristic
124	C₂	#14271569	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745155

C₂

yes

maximal

C₂×#11745156

C₂

yes

maximal

C₂×#11745151

C₂

yes

maximal, characteristic

#14271029

C₂

yes

maximal, characteristic

C₂₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

—

—

—

—

C₄

yes

complemented

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

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

D₄

yes

—

C₂×#6597

Q₈

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

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

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

C₄⋊C₄

yes

complemented

#1847

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#127

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

—

C₄×C₂₉

C₄⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×#107

—

C₂×#106

—

C₂×#97

—

#384

D₂₉

yes

characteristic

#382

—

C₂×C₂₉

#384

yes

characteristic

C₂×C₂₉

#428

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

—

C₂₉

#1847

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

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

—

C₂×C₄

—

116

—

100

C₂×C₄

—

116

—

101

C₂×C₄

—

116

—

102

C₂×C₄

—

116

—

103

C₂×C₄

#90779

yes

—

104

C₂×C₄

C₂×Dic₅₈

yes

characteristic

105

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

106

C₂×C₄

D₄×D₂₉

yes

—

107

C₂×C₄

Q₈×D₂₉

yes

—

108

C₈

—

109

C₂²

C₂×#90779

yes

characteristic

110

C₂²

#11745294

yes

—

111

C₂²

#11745302

yes

characteristic

112

C₂²

#11745304

yes

—

113

C₂²

#11745306

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

232

—

117

C₄

—

232

—

118

C₄

#11745250

yes

—

119

C₄

C₄⋊C₄×D₂₉

yes

—

120

C₂

#14271032

yes

characteristic

121

C₂

#14271203

yes

—

122

C₂

#14271550

yes

characteristic

123

C₂

#14271555

yes

characteristic

124

C₂

#14271569

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#384	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#384	D₂₉
hypocenter	C₂₉	#1847
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#384

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 ◁ #384

N	H ≅ G/N	type
15. #11745151	C₄	semidirect
45. #6597	C₄⋊C₄	semidirect
78. C₂₉	#1847	semidirect

H ≅ G/N

type

15. #11745151

C₄

semidirect

45. #6597

C₄⋊C₄

semidirect

78. C₂₉

#1847

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×#11745151	2
#14271029	2
C₂₉×#384	2
#1847	29

subgroup

index

C₂₉×#384

Subgroups — #16819658

Conjugacy classes of subgroups

Complements

Maximal subgroups