Group #18069259 — subgroups

Subgroups — #18069259

Order 4864.

152 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14563241	C₂	1	1	yes	maximal, characteristic
2	#14561699	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1367	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926924	C₄	1	1	yes	characteristic
5	#11926921	C₄	1	1	yes	characteristic
6	#11926891	—	2	1	no	—
7	#11926891	—	2	1	no	—
8	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
9	C₁₉×C₄⋊C₁₆	—	2	1	no	—
10	C₈²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	—	4	1	no	—
12	C₂×D₁₅₂	—	4	1	no	—
13	#10597320	—	2	1	no	—
14	#10597315	—	2	1	no	—
15	C₂×C₁₆×C₁₉	—	4	1	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	#10597278	—	4	1	no	—
20	#10597278	—	4	1	no	—
21	#10597278	—	4	1	no	—
22	#10597278	—	4	1	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₂×D₇₆	—	4	1	no	—
25	C₂×D₇₆	—	4	1	no	—
26	C₂×D₇₆	—	4	1	no	—
27	C₂×Dic₃₈	—	4	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
31	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₄⋊Dic₁₉	—	4	1	no	—
35	C₄⋊Dic₁₉	—	4	1	no	—
36	Dic₇₆	—	8	2	no	—
37	D₁₅₂	—	8	2	no	—
38	C₁₆×C₁₉	—	8	1	no	—
39	C₁₉⋊C₁₆	—	8	1	no	—
40	#7092	—	19	1	no	maximal, Sylow
41	C₂²×D₁₉	—	8	1	no	—
42	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
45	C₂×Dic₁₉	—	8	1	no	—
46	D₇₆	—	8	2	no	—
47	D₇₆	—	8	1	no	—
48	D₇₆	—	8	1	no	—
49	D₇₆	—	8	1	no	—
50	D₇₆	—	8	1	no	—
51	Dic₃₈	—	8	2	no	—
52	C₈×C₁₉	—	2	2	no	—
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	—	2	1	no	—
56	C₈×C₁₉	—	2	1	no	—
57	#1709	—	19	1	no	—
58	#1367	—	19	1	no	—
59	#1367	D₁₉	1	1	yes	characteristic, complemented
60	C₂²×C₁₉	#331	1	1	yes	characteristic
61	C₂×D₁₉	—	16	1	no	—
62	C₂×D₁₉	—	16	1	no	—
63	C₂×D₁₉	—	16	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	#359	1	1	yes	characteristic
66	C₄×C₁₉	#359	1	1	yes	characteristic
67	C₄×C₁₉	#360	1	1	yes	characteristic
68	C₄×C₁₉	#360	1	1	yes	characteristic
69	Dic₁₉	—	16	1	no	—
70	#494	—	19	1	no	—
71	#493	—	19	1	no	—
72	#486	—	38	1	no	—
73	#486	—	38	1	no	—
74	C₄⋊C₁₆	—	2	1	no	—
75	C₄⋊C₁₆	—	38	1	no	—
76	C₈²	C₂×D₁₉	1	1	yes	characteristic
77	C₂×C₁₉	#1357	1	1	yes	characteristic
78	C₂×C₁₉	#1360	1	1	yes	characteristic
79	C₂×C₁₉	#1360	1	1	yes	characteristic
80	D₁₉	—	32	1	no	—
81	C₂×Q₁₆	—	76	1	no	—
82	C₂×D₈	—	76	1	no	—
83	C₄⋊Q₈	—	38	1	no	—
84	#127	—	38	1	no	—
85	C₂×C₁₆	—	4	1	no	—
86	C₂×C₁₆	—	76	1	no	—
87	#102	—	76	1	no	—
88	#102	—	76	1	no	—
89	#102	—	76	1	no	—
90	#102	—	76	1	no	—
91	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
92	C₄×C₈	D₇₆	1	1	yes	characteristic
93	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
94	C₁₉	#7092	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	76	1	no	—
96	C₂×D₄	—	76	1	no	—
97	C₂×D₄	—	76	1	no	—
98	C₂×D₄	—	76	1	no	—
99	Q₁₆	—	152	2	no	—
100	D₈	—	152	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	#64516	1	1	yes	characteristic
103	C₂×C₈	D₁₅₂	1	1	yes	characteristic
104	C₂×C₈	#64525	1	1	yes	characteristic
105	C₂×C₈	#64527	1	1	yes	characteristic
106	C₄⋊C₄	—	76	1	no	—
107	C₄⋊C₄	—	76	1	no	—
108	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
109	C₁₆	—	8	1	no	—
110	C₁₆	—	152	1	no	—
111	C₂³	—	152	1	no	—
112	Q₈	—	152	2	no	—
113	D₄	—	152	2	no	—
114	D₄	—	152	1	no	—
115	D₄	—	152	1	no	—
116	D₄	—	152	1	no	—
117	D₄	—	152	1	no	—
118	C₂×C₄	—	152	1	no	—
119	C₂×C₄	#10597266	1	1	yes	characteristic
120	C₂×C₄	#10597278	1	1	yes	characteristic
121	C₂×C₄	#10597280	1	1	yes	characteristic
122	C₈	—	2	2	no	—
123	C₈	—	2	1	no	—
124	C₈	—	2	1	no	—
125	C₈	—	2	1	no	—
126	C₈	—	2	1	no	—
127	C₂²	—	304	1	no	—
128	C₂²	—	304	1	no	—
129	C₂²	—	304	1	no	—
130	C₂²	#11926287	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	304	1	no	—
133	C₄	#11926350	1	1	yes	characteristic
134	C₄	#11926352	1	1	yes	characteristic
135	C₄	#11926353	1	1	yes	characteristic
136	C₄	#11926355	1	1	yes	characteristic
137	C₂	—	608	1	no	—
138	C₂	#14561671	1	1	yes	characteristic
139	C₂	#14561677	1	1	yes	characteristic
140	C₂	#14561679	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563241

C₂

yes

maximal, characteristic

#14561699

C₂

yes

maximal, characteristic, complemented

C₁₉×#1367

C₂

yes

maximal, characteristic, complemented

#11926924

C₄

yes

characteristic

#11926921

C₄

yes

characteristic

#11926891

—

#11926891

—

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×C₄⋊C₁₆

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×D₁₅₂

—

#10597320

—

#10597315

—

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

—

—

—

C₂×C₁₉⋊C₁₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7092

—

maximal, Sylow

C₂²×D₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1709

—

#1367

—

#1367

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#331

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7092

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

152

—

100

D₈

—

152

—

101

C₂×C₈

—

102

C₂×C₈

#64516

yes

characteristic

103

C₂×C₈

D₁₅₂

yes

characteristic

104

C₂×C₈

#64525

yes

characteristic

105

C₂×C₈

#64527

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

109

C₁₆

—

110

C₁₆

—

152

—

111

C₂³

—

152

—

112

Q₈

—

152

—

113

D₄

—

152

—

114

D₄

—

152

—

115

D₄

—

152

—

116

D₄

—

152

—

117

D₄

—

152

—

118

C₂×C₄

—

152

—

119

C₂×C₄

#10597266

yes

characteristic

120

C₂×C₄

#10597278

yes

characteristic

121

C₂×C₄

#10597280

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₂²

—

304

—

128

C₂²

—

304

—

129

C₂²

—

304

—

130

C₂²

#11926287

yes

characteristic

131

C₄

—

132

C₄

—

304

—

133

C₄

#11926350

yes

characteristic

134

C₄

#11926352

yes

characteristic

135

C₄

#11926353

yes

characteristic

136

C₄

#11926355

yes

characteristic

137

C₂

—

608

—

138

C₂

#14561671

yes

characteristic

139

C₂

#14561677

yes

characteristic

140

C₂

#14561679

yes

characteristic

	subgroup	G/H
center	C₂²	#11926287
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1367	C₂
socle	C₂²×C₁₉	#331
prime radical	#11926921	C₄
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1367	D₁₉
hypocenter	C₁₉	#7092
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1367

subgroup

G/H

center

C₂²

#11926287

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1367

C₂

C₂²×C₁₉

C₄

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1367

N	H ≅ G/N	type
2. #14561699	C₂	semidirect
3. C₁₉×#1367	C₂	semidirect
59. #1367	D₁₉	semidirect
94. C₁₉	#7092	semidirect

H ≅ G/N

type

2. #14561699

C₂

semidirect

3. C₁₉×#1367

C₂

semidirect

59. #1367

D₁₉

semidirect

94. C₁₉

#7092

semidirect

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

subgroup	index
#14563241	2
#14561699	2
C₁₉×#1367	2
#7092	19

subgroup

index

#14563241

#14561699

C₁₉×#1367

#7092

Subgroups — #18069259

Conjugacy classes of subgroups

Complements

Maximal subgroups