Group #19135419 — subgroups

Subgroups — #19135419

Order 5504.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13063322	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063247	C₂	1	4	yes	maximal, complemented
3	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₇₂	—	2	2	no	—
6	C₂²×D₁₇₂	C₂²	1	2	yes	—
7	#13063322	—	2	2	no	—
8	#13063322	C₄	1	4	yes	complemented
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	#13063247	—	2	8	no	—
11	C₄₃⋊#95	—	2	2	no	—
12	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	#97×C₄₃	—	2	2	no	—
15	C₂³×D₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	D₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	2	no	—
19	C₂×D₁₇₂	—	2	8	no	—
20	C₂×D₁₇₂	—	2	2	no	—
21	C₂×D₁₇₂	—	2	4	no	—
22	C₂×D₁₇₂	—	2	4	no	—
23	C₂×D₁₇₂	—	4	8	no	—
24	C₂×D₁₇₂	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	D₄	1	4	yes	complemented
28	C₄²×C₄₃	C₂×C₄	1	2	yes	—
29	C₄²×C₄₃	D₄	1	2	yes	—
30	C₄⋊Dic₄₃	—	2	4	no	—
31	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂²×D₄₃	—	2	4	no	—
33	C₂²×D₄₃	—	4	2	no	—
34	C₂²×D₄₃	—	4	2	no	—
35	C₂²×D₄₃	—	4	8	no	—
36	C₂×C₄×C₄₃	—	2	4	no	—
37	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
38	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	#41	1	2	yes	—
42	C₂×Dic₄₃	—	4	2	no	—
43	C₂×Dic₄₃	—	4	4	no	—
44	D₁₇₂	—	2	8	no	—
45	D₁₇₂	—	4	16	no	—
46	D₁₇₂	—	4	4	no	—
47	C₈×C₄₃	—	2	4	no	—
48	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄₃	#124	1	1	yes	characteristic
50	C₂²×C₄₃	#127	1	1	yes	characteristic
51	C₂²×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
52	C₂×D₄₃	—	4	4	no	—
53	C₂×D₄₃	—	4	8	no	—
54	C₂×D₄₃	—	8	4	no	—
55	C₂×D₄₃	—	8	4	no	—
56	C₄×C₄₃	—	2	4	no	—
57	C₄×C₄₃	C₄×D₄	1	2	yes	—
58	C₄×C₄₃	#121	1	2	yes	—
59	Dic₄₃	—	8	2	no	—
60	#1961	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	#390	1	1	yes	characteristic
62	C₂×C₄₃	#418	1	2	yes	—
63	C₂×C₄₃	#490	1	2	yes	—
64	C₂×C₄₃	#496	1	2	yes	—
65	D₄₃	—	8	4	no	—
66	C₂×#127	—	43	1	no	—
67	C₂×#102	—	43	4	no	—
68	C₂×#97	D₄₃	1	1	yes	characteristic, complemented
69	#382	—	43	1	no	—
70	C₄₃	#1961	1	1	yes	characteristic, complemented, Sylow
71	C₂²×D₄	—	43	2	no	—
72	C₂²×D₄	—	86	2	no	—
73	C₂²×C₈	C₂×D₄₃	1	2	yes	—
74	#127	—	43	4	no	—
75	#127	—	86	2	no	—
76	C₂×C₄⋊C₄	—	43	2	no	—
77	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
78	#102	—	86	8	no	—
79	#97	—	2	2	no	—
80	#95	—	86	2	no	—
81	C₂⁴	—	86	2	no	—
82	C₂×D₄	—	43	4	no	—
83	C₂×D₄	—	86	8	no	—
84	C₂×D₄	—	86	4	no	—
85	C₂×D₄	—	86	4	no	—
86	C₂×D₄	—	86	2	no	—
87	C₂×D₄	—	172	8	no	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	D₁₇₂	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	D₁₇₂	1	4	yes	complemented
94	C₄⋊C₄	—	86	4	no	—
95	C₄²	C₄×D₄₃	1	2	yes	—
96	C₄²	C₂²⋊D₄₃	1	2	yes	—
97	C₂³	—	86	4	no	—
98	C₂³	—	172	2	no	—
99	C₂³	—	172	2	no	—
100	C₂³	—	172	8	no	—
101	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
102	D₄	—	86	8	no	—
103	D₄	—	172	16	no	—
104	D₄	—	172	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	172	2	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
110	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
111	C₂×C₄	#10621898	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
113	C₈	—	2	4	no	—
114	C₂²	—	344	4	no	—
115	C₂²	—	344	4	no	—
116	C₂²	—	172	4	no	—
117	C₂²	—	172	8	no	—
118	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
119	C₂²	#13063313	1	1	yes	characteristic
120	C₂²	#13063322	1	1	yes	characteristic
121	C₂²	#13063353	1	4	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	344	2	no	—
124	C₄	C₄×D₁₇₂	1	2	yes	—
125	C₄	#13063299	1	2	yes	—
126	C₂	—	344	4	no	—
127	C₂	#14582801	1	1	yes	characteristic
128	C₂	#14582905	1	2	yes	—
129	C₂	#14583264	1	2	yes	—
130	C₂	#14583288	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063322

C₂

yes

maximal, characteristic

C₂×#13063247

C₂

yes

maximal, complemented

#14582765

C₂

yes

maximal, characteristic, complemented

C₂×#97×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

—

C₂²×D₁₇₂

C₂²

yes

—

#13063322

—

#13063322

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063247

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

complemented

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

D₄

yes

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#490

yes

—

C₂×C₄₃

#496

yes

—

D₄₃

—

C₂×#127

—

C₂×#102

—

C₂×#97

D₄₃

yes

characteristic, complemented

#382

—

C₄₃

#1961

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

C₂×D₄₃

yes

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

complemented

C₄⋊C₄

—

C₄²

C₄×D₄₃

yes

—

C₄²

C₂²⋊D₄₃

yes

—

C₂³

—

C₂³

—

172

—

C₂³

—

172

—

100

C₂³

—

172

—

101

C₂³

C₂×D₁₇₂

yes

characteristic

102

D₄

—

103

D₄

—

172

—

104

D₄

—

172

—

105

C₂×C₄

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

110

C₂×C₄

C₂×D₁₇₂

yes

—

111

C₂×C₄

#10621898

yes

—

112

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

113

C₈

—

114

C₂²

—

344

—

115

C₂²

—

344

—

116

C₂²

—

172

—

117

C₂²

—

172

—

118

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

119

C₂²

#13063313

yes

characteristic

120

C₂²

#13063322

yes

characteristic

121

C₂²

#13063353

yes

—

122

C₄

—

123

C₄

—

344

—

124

C₄

C₄×D₁₇₂

yes

—

125

C₄

#13063299

yes

—

126

C₂

—

344

—

127

C₂

#14582801

yes

characteristic

128

C₂

#14582905

yes

—

129

C₂

#14583264

yes

—

130

C₂

#14583288

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#1961
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#97×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×#97

D₄₃

hypocenter

C₄₃

#1961

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
2. C₂×#13063247	C₂	semidirect
3. #14582765	C₂	semidirect
4. C₂×#97×C₄₃	C₂	semidirect
8. #13063322	C₄	semidirect
27. C₂×C₈×C₄₃	D₄	semidirect
68. C₂×#97	D₄₃	semidirect
70. C₄₃	#1961	semidirect
93. C₂×C₈	D₁₇₂	semidirect

H ≅ G/N

type

2. C₂×#13063247

C₂

semidirect

3. #14582765

C₂

semidirect

4. C₂×#97×C₄₃

C₂

semidirect

8. #13063322

C₄

semidirect

27. C₂×C₈×C₄₃

D₄

semidirect

68. C₂×#97

D₄₃

semidirect

70. C₄₃

#1961

semidirect

93. C₂×C₈

D₁₇₂

semidirect

Subgroups — #19135419

Conjugacy classes of subgroups

Complements