Group #19136861 — subgroups

Subgroups — #19136861

Order 5504.

198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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×#13063270	C₂	1	2	yes	maximal, complemented
2	C₂×D₆₈₈	C₂	1	2	yes	maximal, complemented
3	#14583283	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583276	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×#10621873	—	2	1	no	—
8	C₂×D₃₄₄	—	2	1	no	—
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	C₂×D₃₄₄	C₂²	1	2	yes	—
11	#13063322	—	2	1	no	—
12	#13063313	—	2	1	no	—
13	#13063270	—	2	4	no	—
14	D₆₈₈	—	2	4	no	—
15	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₁₇₂	—	2	1	no	—
18	C₂×D₁₇₂	—	2	2	no	—
19	C₂×D₁₇₂	—	4	2	no	—
20	C₂×Dic₈₆	—	2	1	no	—
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
23	C₄²×C₄₃	D₄	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	4	2	no	—
25	Dic₁₇₂	—	2	2	no	—
26	D₃₄₄	—	2	2	no	—
27	D₃₄₄	—	2	2	no	—
28	D₃₄₄	—	2	2	no	—
29	D₃₄₄	—	4	2	no	—
30	#10621873	—	4	2	no	—
31	C₁₆×C₄₃	D₄	1	4	yes	complemented
32	C₂²×D₄₃	—	4	1	no	—
33	C₂²×D₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	D₈	1	2	yes	—
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₄₃	—	4	1	no	—
37	D₁₇₂	—	4	1	no	—
38	D₁₇₂	—	4	2	no	—
39	D₁₇₂	—	4	1	no	—
40	D₁₇₂	—	4	2	no	—
41	D₁₇₂	—	8	4	no	—
42	Dic₈₆	—	4	1	no	—
43	Dic₈₆	—	4	1	no	—
44	C₈×C₄₃	D₈	1	2	yes	—
45	C₈×C₄₃	C₂×D₄	1	2	yes	—
46	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
47	C₂×D₄₃	—	8	1	no	—
48	C₂×D₄₃	—	8	2	no	—
49	C₂×D₄₃	—	8	2	no	—
50	C₂×D₄₃	—	8	4	no	—
51	C₄×C₄₃	—	2	2	no	—
52	C₄×C₄₃	#127	1	1	yes	characteristic
53	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
54	Dic₄₃	—	8	1	no	—
55	#2250	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	#493	1	1	yes	characteristic
57	C₂×C₄₃	#509	1	2	yes	—
58	D₄₃	—	16	1	no	—
59	D₄₃	—	16	2	no	—
60	C₂×SD₃₂	—	43	2	no	—
61	C₂×D₁₆	—	43	2	no	—
62	#495	—	43	1	no	—
63	#493	—	43	1	no	—
64	#346	D₄₃	1	1	yes	characteristic, complemented
65	C₄₃	#2250	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₁₆	—	43	1	no	—
67	C₂×SD₁₆	—	86	1	no	—
68	C₂×D₈	—	43	2	no	—
69	C₂×D₈	—	43	1	no	—
70	C₂×D₈	—	86	1	no	—
71	#127	—	86	1	no	—
72	#124	—	86	1	no	—
73	SD₃₂	—	86	4	no	—
74	D₁₆	—	86	4	no	—
75	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
76	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₂×Q₈	—	86	1	no	—
78	C₂×D₄	—	86	1	no	—
79	C₂×D₄	—	86	2	no	—
80	C₂×D₄	—	172	2	no	—
81	Q₁₆	—	86	2	no	—
82	SD₁₆	—	172	2	no	—
83	D₈	—	86	2	no	—
84	D₈	—	86	2	no	—
85	D₈	—	86	2	no	—
86	D₈	—	172	2	no	—
87	C₂×C₈	D₁₇₂	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
89	C₂²⋊C₄	—	172	2	no	—
90	C₄²	D₁₇₂	1	1	yes	characteristic
91	C₁₆	D₁₇₂	1	4	yes	complemented
92	C₂³	—	172	1	no	—
93	C₂³	—	172	2	no	—
94	Q₈	—	172	1	no	—
95	Q₈	—	172	1	no	—
96	D₄	—	344	4	no	—
97	D₄	—	172	1	no	—
98	D₄	—	172	2	no	—
99	D₄	—	172	2	no	—
100	D₄	—	172	1	no	—
101	C₂×C₄	—	172	1	no	—
102	C₂×C₄	D₃₄₄	1	2	yes	—
103	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
104	C₈	D₃₄₄	1	2	yes	—
105	C₈	C₂×D₁₇₂	1	2	yes	—
106	C₂²	—	344	4	no	—
107	C₂²	—	344	2	no	—
108	C₂²	—	344	2	no	—
109	C₂²	—	344	1	no	—
110	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	344	1	no	—
113	C₄	#13063322	1	1	yes	characteristic
114	C₄	C₂×D₃₄₄	1	1	yes	characteristic
115	C₂	—	688	2	no	—
116	C₂	—	688	1	no	—
117	C₂	#14583276	1	1	yes	characteristic
118	C₂	#14583337	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063270

C₂

yes

maximal, complemented

C₂×D₆₈₈

C₂

yes

maximal, complemented

#14583283

C₂

yes

maximal, characteristic, complemented

#14583276

C₂

yes

maximal, characteristic, complemented

C₄₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂²

yes

characteristic

C₂×D₃₄₄

C₂²

yes

—

#13063322

—

#13063313

—

#13063270

—

D₆₈₈

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

#10621873

—

C₁₆×C₄₃

D₄

yes

complemented

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

D₄₃

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

#493

—

#346

D₄₃

yes

characteristic, complemented

C₄₃

#2250

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

#124

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

Q₁₆

—

SD₁₆

—

172

—

D₈

—

D₈

—

D₈

—

D₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

D₁₇₂

yes

complemented

C₂³

—

172

—

C₂³

—

172

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

D₄

—

172

—

100

D₄

—

172

—

101

C₂×C₄

—

172

—

102

C₂×C₄

D₃₄₄

yes

—

103

C₂×C₄

C₂×D₁₇₂

yes

characteristic

104

C₈

D₃₄₄

yes

—

105

C₈

C₂×D₁₇₂

yes

—

106

C₂²

—

344

—

107

C₂²

—

344

—

108

C₂²

—

344

—

109

C₂²

—

344

—

110

C₂²

C₂×D₃₄₄

yes

characteristic

111

C₄

—

112

C₄

—

344

—

113

C₄

#13063322

yes

characteristic

114

C₄

C₂×D₃₄₄

yes

characteristic

115

C₂

—

688

—

116

C₂

—

688

—

117

C₂

#14583276

yes

characteristic

118

C₂

#14583337

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	#2250
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#346

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
1. C₂×#13063270	C₂	semidirect
2. C₂×D₆₈₈	C₂	semidirect
3. #14583283	C₂	semidirect
4. #14583276	C₂	semidirect
5. C₄₃×#346	C₂	semidirect
31. C₁₆×C₄₃	D₄	semidirect
64. #346	D₄₃	semidirect
65. C₄₃	#2250	semidirect
91. C₁₆	D₁₇₂	semidirect

H ≅ G/N

type

1. C₂×#13063270

C₂

semidirect

2. C₂×D₆₈₈

C₂

semidirect

3. #14583283

C₂

semidirect

4. #14583276

C₂

semidirect

5. C₄₃×#346

C₂

semidirect

31. C₁₆×C₄₃

D₄

semidirect

64. #346

D₄₃

semidirect

65. C₄₃

#2250

semidirect

91. C₁₆

D₁₇₂

semidirect

Subgroups — #19136861

Conjugacy classes of subgroups

Complements