Group #19145041 — subgroups

Subgroups — #19145041

Order 5504.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063347	C₂	1	4	yes	maximal, complemented
2	#14583449	C₂	1	2	yes	maximal, complemented
3	#14583293	C₂	1	4	yes	maximal, complemented
4	#14583288	C₂	1	4	yes	maximal, complemented
5	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	C₂²	1	4	yes	—
7	#13063347	—	2	16	no	—
8	C₂×Dic₁₇₂	C₂²	1	4	yes	—
9	C₂×#10621873	C₂²	1	8	yes	—
10	C₂×D₃₄₄	C₂²	1	4	yes	—
11	#13063325	C₂²	1	2	yes	—
12	#13063322	C₂²	1	2	yes	—
13	#13063313	C₂²	1	4	yes	—
14	#13063299	—	2	4	no	—
15	C₄×D₁₇₂	—	2	4	no	—
16	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	#97×C₄₃	C₂²	1	4	yes	—
19	C₂²×C₄×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₄₃	—	2	4	no	—
22	#10621898	—	2	16	no	—
23	C₂×D₁₇₂	—	2	4	no	—
24	C₂×D₁₇₂	C₂³	1	4	yes	—
25	C₂×C₄×D₄₃	—	2	4	no	—
26	C₂×Dic₈₆	C₂³	1	4	yes	—
27	C₂×C₈×C₄₃	D₄	1	8	yes	complemented
28	C₂×C₈×C₄₃	C₂³	1	4	yes	—
29	C₄²×C₄₃	D₄	1	2	yes	—
30	C₄²×C₄₃	C₂³	1	2	yes	—
31	(C₂×D₄₃)⋊C₄	—	2	8	no	—
32	C₄⋊Dic₄₃	—	2	4	no	—
33	Dic₁₇₂	—	2	8	no	—
34	D₃₄₄	—	2	8	no	—
35	#10621873	—	2	16	no	—
36	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×D₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	4	2	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
43	C₂²⋊D₄₃	—	4	8	no	—
44	C₂×Dic₄₃	—	2	4	no	—
45	D₁₇₂	—	2	8	no	—
46	D₁₇₂	—	4	8	no	—
47	C₄×D₄₃	—	4	8	no	—
48	Dic₈₆	—	2	8	no	—
49	C₈×C₄₃	C₂×D₄	1	8	yes	—
50	C₂²×C₄₃	—	2	2	no	—
51	C₂²×C₄₃	#127	1	2	yes	—
52	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
53	C₂×D₄₃	—	4	4	no	—
54	C₂×D₄₃	—	4	8	no	—
55	C₄×C₄₃	—	2	4	no	—
56	C₄×C₄₃	#127	1	2	yes	—
57	C₄×C₄₃	C₂²×D₄	1	2	yes	—
58	Dic₄₃	—	4	4	no	—
59	#3150	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	—	2	2	no	—
61	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
62	C₂×C₄₃	#575	1	2	yes	—
63	D₄₃	—	8	4	no	—
64	C₂×#135	—	43	4	no	—
65	#532	—	43	2	no	—
66	#497	—	43	4	no	—
67	#496	—	43	4	no	—
68	C₂×#97	D₄₃	1	1	yes	characteristic, complemented
69	C₄₃	#3150	1	1	yes	characteristic, complemented, Sylow
70	C₂×#41	—	43	4	no	—
71	#135	—	86	16	no	—
72	C₂×Q₁₆	—	43	4	no	—
73	C₂×SD₁₆	—	43	8	no	—
74	C₂×D₈	—	43	4	no	—
75	C₂²×C₈	C₂×D₄₃	1	2	yes	—
76	C₄⋊Q₈	—	43	2	no	—
77	#127	—	43	2	no	—
78	#124	—	43	4	no	—
79	#121	—	86	4	no	—
80	C₄×D₄	—	86	4	no	—
81	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
82	#97	C₂×D₄₃	1	4	yes	—
83	#41	—	86	16	no	—
84	C₂×Q₈	—	43	4	no	—
85	C₂×D₄	—	43	4	no	—
86	C₂×D₄	—	86	4	no	—
87	C₂×D₄	—	86	4	no	—
88	C₂²×C₄	—	86	4	no	—
89	C₂²×C₄	D₁₇₂	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	Q₁₆	—	86	8	no	—
92	SD₁₆	—	86	16	no	—
93	D₈	—	86	8	no	—
94	C₂×C₈	D₁₇₂	1	8	yes	complemented
95	C₂×C₈	C₂²×D₄₃	1	4	yes	—
96	C₄⋊C₄	—	86	4	no	—
97	C₂²⋊C₄	—	86	8	no	—
98	C₄²	D₁₇₂	1	2	yes	—
99	C₄²	C₂²×D₄₃	1	2	yes	—
100	C₂³	—	86	4	no	—
101	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
102	Q₈	—	86	8	no	—
103	D₄	—	86	8	no	—
104	D₄	—	172	8	no	—
105	D₄	—	172	8	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	86	4	no	—
108	C₂×C₄	—	172	8	no	—
109	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
110	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
111	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
112	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
113	C₈	C₂×D₁₇₂	1	8	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	172	4	no	—
116	C₂²	—	172	8	no	—
117	C₂²	#13063322	1	2	yes	—
118	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	172	4	no	—
121	C₄	#13063322	1	2	yes	—
122	C₄	C₂²×D₁₇₂	1	2	yes	—
123	C₂	—	2	2	no	—
124	C₂	—	344	4	no	—
125	C₂	C₂×#13063322	1	1	yes	characteristic
126	C₂	#14583699	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063347

C₂

yes

maximal, complemented

#14583449

C₂

yes

maximal, complemented

#14583293

C₂

yes

maximal, complemented

#14583288

C₂

yes

maximal, complemented

C₂×#97×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₂²

yes

—

#13063347

—

C₂×Dic₁₇₂

C₂²

yes

—

C₂×#10621873

C₂²

yes

—

C₂×D₃₄₄

C₂²

yes

—

#13063325

C₂²

yes

—

#13063322

C₂²

yes

—

#13063313

C₂²

yes

—

#13063299

—

C₄×D₁₇₂

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

C₂³

yes

—

C₂×C₈×C₄₃

D₄

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

D₃₄₄

—

#10621873

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

#127

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

—

C₄×C₄₃

C₂²×D₄

yes

—

Dic₄₃

—

#3150

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#127

yes

characteristic

C₂×C₄₃

#575

yes

—

D₄₃

—

—

—

—

—

C₂×#97

D₄₃

yes

characteristic, complemented

C₄₃

#3150

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#97

C₂×D₄₃

yes

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

D₁₇₂

yes

complemented

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₁₇₂

yes

—

C₄²

C₂²×D₄₃

yes

—

100

C₂³

—

101

C₂³

C₂×D₁₇₂

yes

characteristic

102

Q₈

—

103

D₄

—

104

D₄

—

172

—

105

D₄

—

172

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

172

—

109

C₂×C₄

C₂×D₁₇₂

yes

—

110

C₂×C₄

C₂×D₁₇₂

yes

—

111

C₂×C₄

C₂×D₁₇₂

yes

characteristic

112

C₂×C₄

C₂³×D₄₃

yes

characteristic

113

C₈

C₂×D₁₇₂

yes

—

114

C₂²

—

115

C₂²

—

172

—

116

C₂²

—

172

—

117

C₂²

#13063322

yes

—

118

C₂²

C₂²×D₁₇₂

yes

characteristic

119

C₄

—

120

C₄

—

172

—

121

C₄

#13063322

yes

—

122

C₄

C₂²×D₁₇₂

yes

—

123

C₂

—

124

C₂

—

344

—

125

C₂

C₂×#13063322

yes

characteristic

126

C₂

#14583699

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#3150
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×#97×C₄₃

C₂

socle

C₂²×C₄₃

C₂²×D₄

hypercenter

C₂×#97

D₄₃

hypocenter

C₄₃

#3150

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
1. C₂×#13063347	C₂	semidirect
2. #14583449	C₂	semidirect
3. #14583293	C₂	semidirect
4. #14583288	C₂	semidirect
5. C₂×#97×C₄₃	C₂	semidirect
27. C₂×C₈×C₄₃	D₄	semidirect
68. C₂×#97	D₄₃	semidirect
69. C₄₃	#3150	semidirect
94. C₂×C₈	D₁₇₂	semidirect

H ≅ G/N

type

1. C₂×#13063347

C₂

semidirect

2. #14583449

C₂

semidirect

3. #14583293

C₂

semidirect

4. #14583288

C₂

semidirect

5. C₂×#97×C₄₃

C₂

semidirect

27. C₂×C₈×C₄₃

D₄

semidirect

68. C₂×#97

D₄₃

semidirect

69. C₄₃

#3150

semidirect

94. C₂×C₈

D₁₇₂

semidirect

Subgroups — #19145041

Conjugacy classes of subgroups

Complements