Group #18070390 — subgroups

Subgroups — #18070390

Order 4864.

164 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14563299	C₂	1	1	yes	maximal, characteristic
2	#14561802	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1409	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926921	C₄	1	1	yes	characteristic, complemented
5	#11926920	—	2	1	no	—
6	#11926892	—	2	1	no	—
7	#11926343	—	2	1	no	—
8	#11926265	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#492	C₂²	1	1	yes	characteristic
10	C₁₉×#353	—	2	1	no	—
11	C₂×SD₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
13	C₁₉×#127	D₄	1	1	yes	characteristic
14	C₂×#64525	—	4	2	no	—
15	C₂×D₁₅₂	—	4	1	no	—
16	#10597320	—	2	1	no	—
17	C₁₉×#99	—	4	1	no	—
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	#10597293	—	4	1	no	—
20	#10597266	—	4	2	no	—
21	C₄×C₁₉⋊C₈	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₇₆	—	4	1	no	—
26	C₂×D₇₆	—	4	1	no	—
27	C₂×D₇₆	—	4	1	no	—
28	SD₁₆×C₁₉	—	8	2	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₂²⋊C₄×C₁₉	—	8	1	no	—
32	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	#64525	—	8	4	no	—
34	#64520	—	8	1	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	D₁₅₂	—	8	2	no	—
37	#7527	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	—	4	1	no	—
39	C₂²×D₁₉	—	8	1	no	—
40	Q₈×C₁₉	—	8	1	no	—
41	D₄×C₁₉	—	8	1	no	—
42	D₄×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	16	1	no	—
46	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
47	D₇₆	—	8	2	no	—
48	D₇₆	—	8	2	no	—
49	D₇₆	—	8	2	no	—
50	C₈×C₁₉	—	2	2	no	—
51	C₁₉⋊C₈	—	4	2	no	—
52	C₁₉⋊C₈	—	16	1	no	—
53	#1721	—	19	1	no	—
54	#1410	—	19	1	no	—
55	#1409	D₁₉	1	1	yes	characteristic, complemented
56	C₂²×C₁₉	—	8	1	no	—
57	C₂²×C₁₉	—	16	1	no	—
58	C₂²×C₁₉	#353	1	1	yes	characteristic
59	C₂×D₁₉	—	16	1	no	—
60	C₂×D₁₉	—	16	1	no	—
61	C₂×D₁₉	—	16	1	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	8	1	no	—
65	C₄×C₁₉	—	32	1	no	—
66	#493	—	19	1	no	—
67	#493	—	38	1	no	—
68	#492	C₂×D₁₉	1	1	yes	characteristic
69	#486	—	38	1	no	—
70	#356	—	38	1	no	—
71	#353	—	2	1	no	—
72	#322	—	19	1	no	—
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	—	16	1	no	—
75	C₂×C₁₉	#1408	1	1	yes	characteristic
76	D₁₉	—	32	1	no	—
77	C₂×SD₁₆	—	4	1	no	—
78	C₂×D₈	—	76	1	no	—
79	C₂×D₈	—	76	2	no	—
80	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
81	#127	—	38	1	no	—
82	#127	C₂²⋊D₁₉	1	1	yes	characteristic
83	#102	—	76	2	no	—
84	#101	—	76	1	no	—
85	#99	—	4	1	no	—
86	C₄×C₈	—	38	1	no	—
87	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
88	C₁₉	#7527	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	2	1	no	—
90	C₂×D₄	—	2	1	no	—
91	C₂×D₄	—	4	1	no	—
92	C₂×D₄	—	76	1	no	—
93	C₂×D₄	—	76	1	no	—
94	C₂×D₄	—	76	1	no	—
95	SD₁₆	—	8	2	no	—
96	D₈	—	152	2	no	—
97	D₈	—	152	4	no	—
98	M₁₆	—	152	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	38	2	no	—
101	C₄⋊C₄	—	4	1	no	—
102	C₂²⋊C₄	—	8	1	no	—
103	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
104	C₂³	—	4	1	no	—
105	C₂³	—	152	1	no	—
106	Q₈	—	8	1	no	—
107	D₄	—	8	1	no	—
108	D₄	—	8	2	no	—
109	D₄	—	152	2	no	—
110	D₄	—	152	2	no	—
111	D₄	—	152	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	16	1	no	—
115	C₂×C₄	#10597263	1	1	yes	characteristic
116	C₈	—	2	2	no	—
117	C₈	—	304	1	no	—
118	C₈	—	76	2	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	16	1	no	—
121	C₂²	—	304	1	no	—
122	C₂²	—	304	1	no	—
123	C₂²	—	304	1	no	—
124	C₂²	#11926336	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	2	1	no	—
127	C₄	—	8	1	no	—
128	C₄	—	32	1	no	—
129	C₂	—	2	1	no	—
130	C₂	—	16	1	no	—
131	C₂	—	608	1	no	—
132	C₂	#14561797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563299

C₂

yes

maximal, characteristic

#14561802

C₂

yes

maximal, characteristic, complemented

C₁₉×#1409

C₂

yes

maximal, characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

—

—

—

C₄

yes

characteristic, complemented

C₁₉×#492

C₂²

yes

characteristic

C₁₉×#353

—

C₂×SD₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₂×#64525

—

C₂×D₁₅₂

—

#10597320

—

C₁₉×#99

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597293

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

#64525

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

#7527

—

maximal, Sylow

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1721

—

#1410

—

#1409

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#353

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#493

—

#493

—

#492

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

D₇₆

yes

characteristic

#127

—

#127

C₂²⋊D₁₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₁₉

#7527

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

152

—

D₈

—

152

—

M₁₆

—

152

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

104

C₂³

—

105

C₂³

—

152

—

106

Q₈

—

107

D₄

—

108

D₄

—

109

D₄

—

152

—

110

D₄

—

152

—

111

D₄

—

152

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

#10597263

yes

characteristic

116

C₈

—

117

C₈

—

304

—

118

C₈

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

304

—

122

C₂²

—

304

—

123

C₂²

—

304

—

124

C₂²

#11926336

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₂

—

130

C₂

—

131

C₂

—

608

—

132

C₂

#14561797

yes

characteristic

	subgroup	G/H
center	C₂	#14561797
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#492	C₂×D₁₉
Fitting	C₁₉×#1409	C₂
socle	C₂×C₁₉	#1408
prime radical	#14563299	C₂
cosocle	C₁₉×#492	C₂²
hypercenter	#1409	D₁₉
hypocenter	C₁₉	#7527
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1409

subgroup

G/H

center

C₂

#14561797

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#492

C₂×D₁₉

Fitting

C₁₉×#1409

C₂

C₂×C₁₉

C₂

C₁₉×#492

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1409

N	H ≅ G/N	type
2. #14561802	C₂	semidirect
3. C₁₉×#1409	C₂	semidirect
4. #11926921	C₄	semidirect
8. #11926265	C₄	semidirect
55. #1409	D₁₉	semidirect
88. C₁₉	#7527	semidirect

H ≅ G/N

type

2. #14561802

C₂

semidirect

3. C₁₉×#1409

C₂

semidirect

4. #11926921

C₄

semidirect

8. #11926265

C₄

semidirect

55. #1409

D₁₉

semidirect

88. C₁₉

#7527

semidirect

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

subgroup	index
#14563299	2
#14561802	2
C₁₉×#1409	2
#7527	19

subgroup

index

#14563299

#14561802

C₁₉×#1409

#7527

Subgroups — #18070390

Conjugacy classes of subgroups

Complements

Maximal subgroups