Group #19136316 — subgroups

Subgroups — #19136316

Order 5504.

220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#14582937	C₂	1	1	yes	maximal, characteristic
3	#14582704	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₈₆	—	2	1	no	—
6	C₂×Dic₁₇₂	—	2	1	no	—
7	C₂×Dic₁₇₂	—	2	2	no	—
8	C₂×Dic₁₇₂	C₄	1	4	yes	complemented
9	C₂×Dic₁₇₂	C₂²	1	2	yes	—
10	#13063284	—	2	1	no	—
11	#13063259	C₂²	1	2	yes	—
12	#13063257	—	2	1	no	—
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₃	—	2	2	no	—
15	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×Dic₄₃	—	4	1	no	—
18	C₂×Dic₈₆	—	2	4	no	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×Dic₈₆	—	4	1	no	—
21	C₂×Dic₈₆	—	4	2	no	—
22	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	D₄	1	2	yes	—
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²⋊Dic₄₃	—	4	1	no	—
27	C₄⋊Dic₄₃	—	2	2	no	—
28	C₄×Dic₄₃	—	4	1	no	—
29	Dic₁₇₂	—	2	4	no	—
30	Dic₁₇₂	—	2	2	no	—
31	Dic₁₇₂	C₂×C₄	1	4	yes	—
32	C₁₆×C₄₃	—	2	2	no	—
33	C₂³×C₄₃	D₈	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
36	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₃	—	4	4	no	—
39	C₂×Dic₄₃	—	4	2	no	—
40	C₂×Dic₄₃	—	4	2	no	—
41	Dic₈₆	—	2	4	no	—
42	Dic₈₆	—	4	4	no	—
43	Dic₈₆	—	4	2	no	—
44	C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
45	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄₃	—	2	2	no	—
48	C₂²×C₄₃	#102	1	2	yes	—
49	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
50	C₄×C₄₃	#102	1	2	yes	—
51	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
53	Dic₄₃	—	4	4	no	—
54	Dic₄₃	—	8	2	no	—
55	#2141	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
58	C₂×C₄₃	#510	1	2	yes	—
59	C₂²×Q₁₆	—	43	1	no	—
60	C₂×M₃₂	D₄₃	1	1	yes	characteristic
61	#427	—	43	1	no	—
62	#358	—	43	4	no	—
63	C₄₃	#2141	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	86	1	no	—
65	C₂×Q₁₆	—	43	2	no	—
66	C₂×Q₁₆	—	43	4	no	—
67	C₂×Q₁₆	—	86	1	no	—
68	C₂×Q₁₆	—	86	2	no	—
69	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
70	#117	—	86	1	no	—
71	M₃₂	—	2	2	no	—
72	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
73	#107	—	43	2	no	—
74	#106	—	86	1	no	—
75	C₂×Q₈	—	86	4	no	—
76	C₂×Q₈	—	86	2	no	—
77	C₂×Q₈	—	172	2	no	—
78	C₂×Q₈	—	172	1	no	—
79	C₂²×C₄	—	172	1	no	—
80	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
81	Q₁₆	—	43	4	no	—
82	Q₁₆	—	86	4	no	—
83	Q₁₆	—	86	2	no	—
84	C₂×C₈	C₄×D₄₃	1	2	yes	—
85	C₂×C₈	D₁₇₂	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
87	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
88	C₄⋊C₄	—	86	2	no	—
89	C₂²⋊C₄	—	172	1	no	—
90	C₄²	—	172	1	no	—
91	C₁₆	—	2	2	no	—
92	C₂³	D₃₄₄	1	1	yes	characteristic
93	Q₈	—	86	4	no	—
94	Q₈	—	172	4	no	—
95	Q₈	—	172	2	no	—
96	C₂×C₄	—	172	2	no	—
97	C₂×C₄	—	172	4	no	—
98	C₂×C₄	—	172	2	no	—
99	C₂×C₄	#10621873	1	2	yes	—
100	C₂×C₄	D₃₄₄	1	1	yes	characteristic
101	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
102	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
103	C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
104	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
105	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
106	C₂²	—	2	2	no	—
107	C₂²	#13063247	1	2	yes	—
108	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
109	C₄	—	344	2	no	—
110	C₄	—	172	4	no	—
111	C₄	#13063247	1	2	yes	—
112	C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
113	C₄	C₂×#10621873	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	C₂×#13063247	1	1	yes	characteristic
116	C₂	#14583342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic

#14582937

C₂

yes

maximal, characteristic

#14582704

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₄

yes

complemented

C₂×Dic₁₇₂

C₂²

yes

—

#13063284

—

#13063259

C₂²

yes

—

#13063257

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

C₂×C₄

yes

—

C₁₆×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂²⋊C₄

yes

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

#102

yes

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2141

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#102

yes

characteristic

C₂×C₄₃

#510

yes

—

C₂²×Q₁₆

—

C₂×M₃₂

D₄₃

yes

characteristic

#427

—

#358

—

C₄₃

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

C₂×D₄₃

yes

—

#107

—

#106

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

D₁₇₂

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

172

—

C₁₆

—

C₂³

D₃₄₄

yes

characteristic

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

—

100

C₂×C₄

D₃₄₄

yes

characteristic

101

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

102

C₂×C₄

C₂×D₁₇₂

yes

characteristic

103

C₈

(C₂×D₄₃)⋊C₄

yes

—

104

C₈

C₂×C₄×D₄₃

yes

characteristic

105

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

106

C₂²

—

107

C₂²

#13063247

yes

—

108

C₂²

C₂×D₃₄₄

yes

characteristic

109

C₄

—

344

—

110

C₄

—

172

—

111

C₄

#13063247

yes

—

112

C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

113

C₄

C₂×#10621873

yes

characteristic

114

C₂

—

115

C₂

C₂×#13063247

yes

characteristic

116

C₂

#14583342

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	#2141
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₃₄₄

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×M₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×M₃₂

D₄₃

hypocenter

C₄₃

#2141

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #14582704	C₂	semidirect
8. C₂×Dic₁₇₂	C₄	semidirect
63. C₄₃	#2141	semidirect

H ≅ G/N

type

3. #14582704

C₂

semidirect

8. C₂×Dic₁₇₂

C₄

semidirect

63. C₄₃

#2141

semidirect

Subgroups — #19136316

Conjugacy classes of subgroups

Complements