Group #18069196 — subgroups

Subgroups — #18069196

Order 4864.

140 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 57 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	C₈×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	#14561553	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1367	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃₈	—	2	1	no	—
5	C₄×Dic₇₆	C₄	1	1	yes	characteristic
6	C₄×C₁₉⋊C₁₆	—	2	1	no	—
7	#11926297	C₄	1	1	yes	characteristic
8	#11926276	—	2	1	no	—
9	C₁₉×C₄⋊C₁₆	—	2	1	no	—
10	C₈²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	C₈	1	1	yes	characteristic
12	C₄×Dic₃₈	—	2	1	no	—
13	C₂×C₁₆×C₁₉	—	4	1	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	#10597275	C₈	1	1	yes	characteristic
18	#10597273	—	2	1	no	—
19	Dic₁₉⋊C₈	—	4	1	no	—
20	C₈×Dic₁₉	—	4	1	no	—
21	C₂×C₁₉⋊C₁₆	—	2	2	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₄⋊Dic₁₉	—	2	1	no	—
31	Dic₁₉⋊C₄	—	4	1	no	—
32	C₄×Dic₁₉	—	4	1	no	—
33	C₂×C₁₉⋊C₈	—	4	1	no	—
34	Dic₇₆	—	2	1	no	—
35	Dic₇₆	C₁₆	1	2	yes	complemented
36	C₁₆×C₁₉	—	8	1	no	—
37	C₁₉⋊C₁₆	—	4	2	no	—
38	#7071	—	19	1	no	maximal, Sylow
39	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	Dic₃₈	—	2	2	no	—
45	Dic₃₈	—	4	1	no	—
46	C₈×C₁₉	—	2	2	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	2	1	no	—
49	C₈×C₁₉	—	2	1	no	—
50	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
51	C₈×C₁₉	M₃₂	1	1	yes	characteristic
52	C₁₉⋊C₈	—	8	1	no	—
53	C₈×Q₁₆	—	19	1	no	—
54	#1367	D₁₉	1	1	yes	characteristic
55	#1312	—	19	1	no	—
56	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
57	C₄×C₁₉	—	2	1	no	—
58	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
59	C₄×C₁₉	#350	1	1	yes	characteristic
60	C₄×C₁₉	#360	1	1	yes	characteristic
61	C₄×C₁₉	#362	1	1	yes	characteristic
62	Dic₁₉	—	4	2	no	—
63	Dic₁₉	—	8	1	no	—
64	C₈×Q₈	—	38	1	no	—
65	C₄×Q₁₆	—	19	1	no	—
66	C₄⋊C₁₆	—	2	1	no	—
67	C₄×C₁₆	—	38	1	no	—
68	#335	—	19	1	no	—
69	Q₈⋊C₈	—	38	1	no	—
70	C₈²	C₂×D₁₉	1	1	yes	characteristic
71	C₂×C₁₉	D₄⋊C₁₆	1	1	yes	characteristic
72	C₂×C₁₉	#1334	1	1	yes	characteristic
73	C₂×C₁₉	#1336	1	1	yes	characteristic
74	C₂×Q₁₆	—	19	1	no	—
75	C₄×Q₈	—	38	1	no	—
76	C₂×C₁₆	—	4	1	no	—
77	C₂×C₁₆	—	38	2	no	—
78	#107	—	19	1	no	—
79	C₄⋊C₈	—	38	1	no	—
80	C₄⋊C₈	—	76	1	no	—
81	#103	—	38	1	no	—
82	C₄×C₈	—	76	1	no	—
83	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
84	C₄×C₈	D₇₆	1	1	yes	characteristic
85	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
86	C₁₉	#7071	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	38	1	no	—
88	Q₁₆	—	19	2	no	—
89	Q₁₆	—	38	1	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	76	1	no	—
92	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
93	C₂×C₈	#64515	1	1	yes	characteristic
94	C₂×C₈	#64525	1	1	yes	characteristic
95	C₂×C₈	#64527	1	1	yes	characteristic
96	C₄⋊C₄	—	38	1	no	—
97	C₄⋊C₄	—	76	1	no	—
98	C₄²	—	76	1	no	—
99	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
100	C₁₆	—	8	1	no	—
101	C₁₆	—	76	2	no	—
102	Q₈	—	38	2	no	—
103	Q₈	—	76	1	no	—
104	C₂×C₄	—	76	1	no	—
105	C₂×C₄	—	76	1	no	—
106	C₂×C₄	#10597266	1	1	yes	characteristic
107	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
108	C₂×C₄	#10597282	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	—	2	1	no	—
111	C₈	—	2	1	no	—
112	C₈	—	2	1	no	—
113	C₈	—	152	1	no	—
114	C₈	C₁₆×D₁₉	1	1	yes	characteristic
115	C₈	#10597255	1	1	yes	characteristic
116	C₂²	#11926271	1	1	yes	characteristic
117	C₄	—	2	1	no	—
118	C₄	—	76	2	no	—
119	C₄	—	152	1	no	—
120	C₄	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
121	C₄	#11926329	1	1	yes	characteristic
122	C₄	#11926353	1	1	yes	characteristic
123	C₄	#11926359	1	1	yes	characteristic
124	C₂	#14561589	1	1	yes	characteristic
125	C₂	#14561604	1	1	yes	characteristic
126	C₂	#14561610	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₇₆

C₂

yes

maximal, characteristic

#14561553

C₂

yes

maximal, characteristic

C₁₉×#1367

C₂

yes

maximal, characteristic

C₈×Dic₃₈

—

C₄×Dic₇₆

C₄

yes

characteristic

C₄×C₁₉⋊C₁₆

—

#11926297

C₄

yes

characteristic

#11926276

—

C₁₉×C₄⋊C₁₆

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

C₈

yes

characteristic

C₄×Dic₃₈

—

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597275

C₈

yes

characteristic

#10597273

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

Dic₇₆

C₁₆

yes

complemented

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7071

—

maximal, Sylow

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂×C₁₆

yes

characteristic

C₈×C₁₉

M₃₂

yes

characteristic

C₁₉⋊C₈

—

C₈×Q₁₆

—

#1367

D₁₉

yes

characteristic

#1312

—

C₂²×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊C₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₈×Q₈

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

C₄×C₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

C₂×D₁₉

yes

characteristic

C₂×C₁₉

D₄⋊C₁₆

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7071

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₉

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

100

C₁₆

—

101

C₁₆

—

102

Q₈

—

103

Q₈

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#10597266

yes

characteristic

107

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

108

C₂×C₄

#10597282

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

152

—

114

C₈

C₁₆×D₁₉

yes

characteristic

115

C₈

#10597255

yes

characteristic

116

C₂²

#11926271

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

152

—

120

C₄

(C₂×D₁₉)⋊C₁₆

yes

characteristic

121

C₄

#11926329

yes

characteristic

122

C₄

#11926353

yes

characteristic

123

C₄

#11926359

yes

characteristic

124

C₂

#14561589

yes

characteristic

125

C₂

#14561604

yes

characteristic

126

C₂

#14561610

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597266
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1367	C₂
socle, prime radical	C₂²×C₁₉	D₄⋊C₈
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1367	D₁₉
hypocenter	C₁₉	#7071
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1367

subgroup

G/H

center

C₂×C₄

#10597266

commutator

C₈×C₁₉

C₂×C₁₆

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1367

C₂

socle, prime radical

C₂²×C₁₉

D₄⋊C₈

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1367

N	H ≅ G/N	type
35. Dic₇₆	C₁₆	semidirect
86. C₁₉	#7071	semidirect

H ≅ G/N

type

35. Dic₇₆

C₁₆

semidirect

86. C₁₉

#7071

semidirect

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

subgroup	index
C₈×Dic₇₆	2
#14561553	2
C₁₉×#1367	2
#7071	19

subgroup

index

C₈×Dic₇₆

#14561553

C₁₉×#1367

#7071

Subgroups — #18069196

Conjugacy classes of subgroups

Complements

Maximal subgroups