Group #19136208 — subgroups

Subgroups — #19136208

Order 5504.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13063331	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₃)⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10621898	C₄	1	1	yes	characteristic
6	#13063331	—	2	2	no	—
7	#13063331	—	2	2	no	—
8	C₂×#10621877	C₄	1	1	yes	characteristic
9	C₂×#10621872	C₄	1	2	yes	—
10	C₂×C₈×D₄₃	C₂²	1	2	yes	—
11	#13063265	—	2	2	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	—	2	2	no	—
15	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₄₃	C₈	1	2	yes	—
18	#10621898	—	2	2	no	—
19	#10621898	—	2	2	no	—
20	C₂×D₁₇₂	C₈	1	1	yes	characteristic
21	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
22	C₂×Dic₈₆	C₈	1	1	yes	characteristic
23	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	D₄	1	2	yes	—
25	C₂×C₈×C₄₃	D₄	1	2	yes	—
26	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
27	#10621877	—	2	2	no	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
29	#10621872	—	2	4	no	—
30	C₈×D₄₃	—	2	2	no	—
31	C₈×D₄₃	—	2	2	no	—
32	C₁₆×C₄₃	—	2	2	no	—
33	C₄₃⋊C₁₆	—	2	2	no	—
34	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₄₃	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₄₃	M₁₆	1	2	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₄₃	—	2	4	no	—
41	C₂×Dic₄₃	C₂×C₈	1	2	yes	—
42	D₁₇₂	—	2	2	no	—
43	C₄×D₄₃	—	2	2	no	—
44	C₄×D₄₃	—	2	2	no	—
45	Dic₈₆	—	2	2	no	—
46	C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
47	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₄₃⋊C₈	—	2	2	no	—
50	C₂²×C₄₃	—	2	2	no	—
51	C₂²×C₄₃	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₄₃	—	2	2	no	—
54	C₂×D₄₃	—	2	4	no	—
55	C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
56	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
58	Dic₄₃	—	2	2	no	—
59	#2113	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	—	2	2	no	—
61	C₂×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
62	C₂×C₄₃	#504	1	2	yes	—
63	D₄₃	—	4	2	no	—
64	C₂×#131	—	43	1	no	—
65	C₂×M₃₂	—	43	1	no	—
66	C₂²×C₁₆	D₄₃	1	1	yes	characteristic, complemented
67	C₂²⋊C₁₆	—	43	4	no	—
68	C₄₃	#2113	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	—	43	1	no	—
70	#131	—	86	2	no	—
71	#131	—	86	2	no	—
72	C₂×M₁₆	—	43	1	no	—
73	C₂×M₁₆	—	43	2	no	—
74	C₂²×C₈	—	43	2	no	—
75	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
76	M₃₂	—	86	2	no	—
77	C₂×C₁₆	—	2	2	no	—
78	C₂×C₁₆	—	43	2	no	—
79	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
80	#41	—	86	2	no	—
81	#41	—	86	2	no	—
82	C₂×Q₈	—	43	1	no	—
83	C₂×D₄	—	43	2	no	—
84	C₂×D₄	—	43	1	no	—
85	C₂²×C₄	—	43	2	no	—
86	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
87	M₁₆	—	86	2	no	—
88	M₁₆	—	86	4	no	—
89	C₂×C₈	—	43	2	no	—
90	C₂×C₈	—	86	2	no	—
91	C₂×C₈	—	86	2	no	—
92	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
93	C₂×C₈	D₁₇₂	1	2	yes	—
94	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
95	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	86	2	no	—
98	C₂³	—	43	2	no	—
99	C₂³	C₈×D₄₃	1	1	yes	characteristic
100	Q₈	—	86	2	no	—
101	D₄	—	86	4	no	—
102	D₄	—	86	2	no	—
103	C₂×C₄	—	43	2	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	—	86	2	no	—
106	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
107	C₂×C₄	#10621872	1	2	yes	—
108	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
110	C₈	—	86	2	no	—
111	C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
112	C₈	C₂×D₁₇₂	1	1	yes	characteristic
113	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	86	4	no	—
116	C₂²	—	86	2	no	—
117	C₂²	(C₂×D₄₃)⋊C₈	1	2	yes	—
118	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
119	C₄	—	86	2	no	—
120	C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
121	C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
122	C₄	C₂×#10621872	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	172	2	no	—
125	C₂	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
126	C₂	#14583315	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063331

C₂

yes

maximal, characteristic

C₂×#13063265

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₃)⋊C₁₆

C₂

yes

maximal, complemented

C₂²×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₄

yes

—

—

C₄

yes

characteristic

C₂×#10621872

C₄

yes

—

C₂×C₈×D₄₃

C₂²

yes

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

C₈

yes

—

#10621898

—

#10621898

—

C₂×D₁₇₂

C₈

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×Dic₈₆

C₈

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

#10621872

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂²×D₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

C₂×C₈

yes

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

C₂²⋊C₄

yes

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

C₂²⋊C₈

yes

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

Dic₄₃

—

#2113

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₄₃

#504

yes

—

D₄₃

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

D₄₃

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₄₃

#2113

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂³

C₈×D₄₃

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₄₃

yes

characteristic

107

C₂×C₄

#10621872

yes

—

108

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

110

C₈

—

111

C₈

(C₂×D₄₃)⋊C₄

yes

—

112

C₈

C₂×D₁₇₂

yes

characteristic

113

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

(C₂×D₄₃)⋊C₈

yes

—

118

C₂²

C₂×C₈×D₄₃

yes

characteristic

119

C₄

—

120

C₄

(C₂×D₄₃)⋊C₈

yes

—

121

C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

122

C₄

C₂×#10621872

yes

characteristic

123

C₂

—

124

C₂

—

172

—

125

C₂

C₂×(C₂×D₄₃)⋊C₈

yes

characteristic

126

C₂

#14583315

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₈
Fitting	C₂²×C₁₆×C₄₃	C₂
hypercenter	C₂²×C₁₆	D₄₃
hypocenter	C₄₃	#2113
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂²×C₈

Fitting

C₂²×C₁₆×C₄₃

C₂

hypercenter

C₂²×C₁₆

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. C₂×#13063265	C₂	semidirect
3. (C₂×D₄₃)⋊C₁₆	C₂	semidirect
4. C₂²×C₁₆×C₄₃	C₂	semidirect
66. C₂²×C₁₆	D₄₃	semidirect
68. C₄₃	#2113	semidirect

H ≅ G/N

type

2. C₂×#13063265

C₂

semidirect

3. (C₂×D₄₃)⋊C₁₆

C₂

semidirect

4. C₂²×C₁₆×C₄₃

C₂

semidirect

66. C₂²×C₁₆

D₄₃

semidirect

68. C₄₃

#2113

semidirect

Subgroups — #19136208

Conjugacy classes of subgroups

Complements