Group #19136866 — subgroups

Subgroups — #19136866

Order 5504.

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

normal subgroups only

This group has 178 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×Dic₃₄₄	C₂	1	2	yes	maximal, complemented
2	C₂×#13063270	C₂	1	2	yes	maximal
3	#14583283	C₂	1	1	yes	maximal, characteristic
4	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	—	2	1	no	—
7	C₂×Dic₁₇₂	C₂²	1	2	yes	—
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621873	—	2	1	no	—
10	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
11	#13063325	—	2	1	no	—
12	#13063313	—	2	1	no	—
13	Dic₃₄₄	—	2	4	no	—
14	#13063270	—	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×Dic₈₆	—	2	1	no	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	(C₂×D₄₃)⋊C₄	—	4	2	no	—
24	C₄⋊Dic₄₃	—	4	2	no	—
25	Dic₁₇₂	—	2	2	no	—
26	Dic₁₇₂	—	2	2	no	—
27	Dic₁₇₂	—	2	2	no	—
28	Dic₁₇₂	—	4	2	no	—
29	D₃₄₄	—	2	2	no	—
30	#10621873	—	4	2	no	—
31	C₁₆×C₄₃	D₄	1	4	yes	—
32	C₂²×D₄₃	—	4	1	no	—
33	C₂×C₄×C₄₃	D₈	1	2	yes	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₄₃	—	4	2	no	—
36	C₂×Dic₄₃	—	4	1	no	—
37	D₁₇₂	—	4	1	no	—
38	D₁₇₂	—	4	1	no	—
39	Dic₈₆	—	4	2	no	—
40	Dic₈₆	—	4	1	no	—
41	Dic₈₆	—	4	1	no	—
42	Dic₈₆	—	4	2	no	—
43	C₈×C₄₃	D₈	1	2	yes	—
44	C₈×C₄₃	C₂×D₄	1	2	yes	—
45	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
46	C₂×D₄₃	—	8	1	no	—
47	C₂×D₄₃	—	8	2	no	—
48	C₄×C₄₃	—	2	2	no	—
49	C₄×C₄₃	#127	1	1	yes	characteristic
50	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
51	Dic₄₃	—	8	1	no	—
52	Dic₄₃	—	8	2	no	—
53	#2251	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	#493	1	1	yes	characteristic
55	C₂×C₄₃	#510	1	2	yes	—
56	D₄₃	—	16	1	no	—
57	C₂×Q₃₂	—	43	2	no	—
58	C₂×SD₃₂	—	43	2	no	—
59	#495	—	43	1	no	—
60	#494	—	43	1	no	—
61	#346	D₄₃	1	1	yes	characteristic, complemented
62	C₄₃	#2251	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	43	2	no	—
64	C₂×Q₁₆	—	43	1	no	—
65	C₂×Q₁₆	—	86	1	no	—
66	C₂×SD₁₆	—	86	1	no	—
67	C₂×D₈	—	43	1	no	—
68	C₄⋊Q₈	—	86	1	no	—
69	#124	—	86	1	no	—
70	Q₃₂	—	86	4	no	—
71	SD₃₂	—	86	4	no	—
72	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
73	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	C₂×Q₈	—	86	1	no	—
75	C₂×Q₈	—	86	2	no	—
76	C₂×D₄	—	86	1	no	—
77	Q₁₆	—	86	2	no	—
78	Q₁₆	—	86	2	no	—
79	Q₁₆	—	86	2	no	—
80	Q₁₆	—	172	2	no	—
81	SD₁₆	—	172	2	no	—
82	D₈	—	86	2	no	—
83	C₂×C₈	D₁₇₂	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
85	C₄⋊C₄	—	172	2	no	—
86	C₂²⋊C₄	—	172	2	no	—
87	C₄²	D₁₇₂	1	1	yes	characteristic
88	C₁₆	D₁₇₂	1	4	yes	—
89	C₂³	—	172	1	no	—
90	Q₈	—	172	2	no	—
91	Q₈	—	172	1	no	—
92	Q₈	—	172	1	no	—
93	Q₈	—	172	2	no	—
94	D₄	—	172	1	no	—
95	D₄	—	172	1	no	—
96	C₂×C₄	—	172	1	no	—
97	C₂×C₄	—	172	2	no	—
98	C₂×C₄	D₃₄₄	1	2	yes	—
99	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
100	C₈	D₃₄₄	1	2	yes	—
101	C₈	C₂×D₁₇₂	1	2	yes	—
102	C₂²	—	344	2	no	—
103	C₂²	—	344	1	no	—
104	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	344	1	no	—
107	C₄	—	344	2	no	—
108	C₄	#13063322	1	1	yes	characteristic
109	C₄	C₂×D₃₄₄	1	1	yes	characteristic
110	C₂	—	688	1	no	—
111	C₂	#14583276	1	1	yes	characteristic
112	C₂	#14583342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₄₄

C₂

yes

maximal, complemented

C₂×#13063270

C₂

yes

maximal

#14583283

C₂

yes

maximal, characteristic

#14583279

C₂

yes

maximal, characteristic, complemented

C₄₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₂²

yes

characteristic

#13063325

—

#13063313

—

Dic₃₄₄

—

#13063270

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

#10621873

—

C₁₆×C₄₃

D₄

yes

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

#494

—

#346

D₄₃

yes

characteristic, complemented

C₄₃

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#124

—

Q₃₂

—

SD₃₂

—

C₂×C₁₆

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

172

—

SD₁₆

—

172

—

D₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

D₁₇₂

yes

—

C₂³

—

172

—

Q₈

—

172

—

Q₈

—

172

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

D₃₄₄

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

100

C₈

D₃₄₄

yes

—

101

C₈

C₂×D₁₇₂

yes

—

102

C₂²

—

344

—

103

C₂²

—

344

—

104

C₂²

C₂×D₃₄₄

yes

characteristic

105

C₄

—

106

C₄

—

344

—

107

C₄

—

344

—

108

C₄

#13063322

yes

characteristic

109

C₄

C₂×D₃₄₄

yes

characteristic

110

C₂

—

688

—

111

C₂

#14583276

yes

characteristic

112

C₂

#14583342

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	#2251
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×Dic₃₄₄	C₂	semidirect
4. #14583279	C₂	semidirect
5. C₄₃×#346	C₂	semidirect
61. #346	D₄₃	semidirect
62. C₄₃	#2251	semidirect

H ≅ G/N

type

1. C₂×Dic₃₄₄

C₂

semidirect

4. #14583279

C₂

semidirect

5. C₄₃×#346

C₂

semidirect

61. #346

D₄₃

semidirect

62. C₄₃

#2251

semidirect

Subgroups — #19136866

Conjugacy classes of subgroups

Complements