Group #19136642 — subgroups

Subgroups — #19136642

Order 5504.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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×#13063271	C₂	1	2	yes	maximal
2	C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#14582703	C₂	1	2	yes	maximal
5	C₄₃×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₄×Dic₈₆	—	2	1	no	—
8	#13063271	—	2	4	no	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	#13063259	C₂²	1	1	yes	characteristic
11	#13063250	—	2	1	no	—
12	C₂×Q₁₆×C₄₃	—	2	1	no	—
13	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄⋊Q₈×C₄₃	—	2	1	no	—
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₃	—	2	2	no	—
17	C₂×Dic₈₆	—	2	1	no	—
18	Q₁₆×C₄₃	—	2	2	no	—
19	Q₁₆×C₄₃	—	2	2	no	—
20	Q₁₆×C₄₃	—	4	2	no	—
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₄₃	—	4	1	no	—
24	C₄⋊C₄×C₄₃	—	4	1	no	—
25	C₄²×C₄₃	D₄	1	1	yes	characteristic
26	C₄⋊Dic₄₃	—	2	1	no	—
27	Dic₄₃⋊C₄	—	4	1	no	—
28	C₄×Dic₄₃	—	4	1	no	—
29	Dic₁₇₂	—	2	1	no	—
30	Dic₁₇₂	D₄	1	2	yes	—
31	C₄₃⋊C₁₆	—	2	2	no	—
32	Q₈×C₄₃	—	4	2	no	—
33	Q₈×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	—	4	2	no	—
35	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
36	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₃	—	4	1	no	—
39	C₂×Dic₄₃	—	4	1	no	—
40	Dic₈₆	—	2	2	no	—
41	Dic₈₆	—	4	1	no	—
42	C₈×C₄₃	—	2	1	no	—
43	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₈×C₄₃	#41	1	1	yes	characteristic
45	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	8	2	no	—
48	C₄×C₄₃	Q₃₂	1	2	yes	complemented
49	C₄×C₄₃	#121	1	1	yes	characteristic
50	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
51	Dic₄₃	—	4	2	no	—
52	Dic₄₃	—	8	1	no	—
53	#2209	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	#459	1	1	yes	characteristic
55	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₄₃	#510	1	1	yes	characteristic
57	C₂×Q₃₂	—	43	2	no	—
58	#494	D₄₃	1	1	yes	characteristic
59	C₄×Q₁₆	—	43	1	no	—
60	C₄⋊C₁₆	—	43	1	no	—
61	#358	—	43	2	no	—
62	C₄₃	#2209	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	2	1	no	—
64	C₂×Q₁₆	—	43	1	no	—
65	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
66	C₄⋊Q₈	—	2	1	no	—
67	C₄×Q₈	—	86	1	no	—
68	Q₃₂	—	86	4	no	—
69	C₂×C₁₆	—	43	2	no	—
70	#107	—	43	1	no	—
71	#103	—	86	1	no	—
72	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	86	1	no	—
75	Q₁₆	—	2	2	no	—
76	Q₁₆	—	2	2	no	—
77	Q₁₆	—	4	2	no	—
78	Q₁₆	—	43	2	no	—
79	Q₁₆	—	86	1	no	—
80	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
82	C₄⋊C₄	—	4	1	no	—
83	C₄⋊C₄	—	4	1	no	—
84	C₄⋊C₄	—	86	1	no	—
85	C₄⋊C₄	—	172	1	no	—
86	C₄²	—	172	1	no	—
87	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
88	C₁₆	—	86	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	86	2	no	—
92	Q₈	—	172	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	—	172	1	no	—
95	C₂×C₄	—	172	1	no	—
96	C₂×C₄	#10621882	1	1	yes	characteristic
97	C₂×C₄	#10621882	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	D₄×D₄₃	1	1	yes	characteristic
101	C₈	#10621900	1	1	yes	characteristic
102	C₂²	C₂×#10621882	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	2	no	—
105	C₄	—	344	1	no	—
106	C₄	—	172	2	no	—
107	C₄	#13063271	1	2	yes	complemented
108	C₄	#13063296	1	1	yes	characteristic
109	C₄	#13063351	1	1	yes	characteristic
110	C₂	#14583091	1	1	yes	characteristic
111	C₂	C₂×#13063271	1	1	yes	characteristic
112	C₂	#14583340	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063271

C₂

yes

maximal

C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic

#14582703

C₂

yes

maximal

C₄₃×#494

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₄×Dic₈₆

—

#13063271

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

#13063259

C₂²

yes

characteristic

#13063250

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

Q₃₂

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×Q₃₂

yes

characteristic

C₂×C₄₃

#510

yes

characteristic

C₂×Q₃₂

—

#494

D₄₃

yes

characteristic

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

C₄₃

#2209

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

—

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

#107

—

#103

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

100

C₈

D₄×D₄₃

yes

characteristic

101

C₈

#10621900

yes

characteristic

102

C₂²

C₂×#10621882

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

344

—

106

C₄

—

172

—

107

C₄

#13063271

yes

complemented

108

C₄

#13063296

yes

characteristic

109

C₄

#13063351

yes

characteristic

110

C₂

#14583091

yes

characteristic

111

C₂

C₂×#13063271

yes

characteristic

112

C₂

#14583340

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#494	D₄₃
hypocenter	C₄₃	#2209
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#494

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
48. C₄×C₄₃	Q₃₂	semidirect
62. C₄₃	#2209	semidirect
107. C₄	#13063271	semidirect

H ≅ G/N

type

48. C₄×C₄₃

Q₃₂

semidirect

62. C₄₃

#2209

semidirect

107. C₄

#13063271

semidirect

Subgroups — #19136642

Conjugacy classes of subgroups

Complements