Group #19133990 — subgroups

Subgroups — #19133990

Order 5504.

156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583304	C₂	1	1	yes	maximal, characteristic
2	#14583110	C₂	1	2	yes	maximal
3	C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#14582646	C₂	1	2	yes	maximal
5	C₄₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	—	2	2	no	—
7	#13063325	C₂²	1	2	yes	—
8	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
9	#13063259	—	2	1	no	—
10	#13063259	—	2	1	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₄₃⋊C₈	—	2	1	no	—
13	#13063250	—	2	2	no	—
14	C₈×Dic₄₃	—	2	1	no	—
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₈₆	—	2	2	no	—
18	C₂×Dic₈₆	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
26	Dic₄₃⋊C₄	—	2	1	no	—
27	C₄×Dic₄₃	—	2	1	no	—
28	C₂×C₄₃⋊C₈	—	2	1	no	—
29	Dic₁₇₂	—	4	4	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
33	C₂×Dic₄₃	—	2	1	no	—
34	C₂×Dic₄₃	—	2	1	no	—
35	C₂×Dic₄₃	—	4	2	no	—
36	Dic₈₆	—	2	1	no	—
37	Dic₈₆	—	4	2	no	—
38	Dic₈₆	—	4	2	no	—
39	Dic₈₆	D₈	1	2	yes	—
40	C₈×C₄₃	—	2	1	no	—
41	C₈×C₄₃	—	4	2	no	—
42	C₈×C₄₃	Q₁₆	1	2	yes	complemented
43	C₄₃⋊C₈	—	4	1	no	—
44	C₂²×C₄₃	#121	1	1	yes	characteristic
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
47	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₄×C₄₃	#135	1	1	yes	characteristic
49	C₄×C₄₃	#137	1	1	yes	characteristic
50	Dic₄₃	—	2	2	no	—
51	Dic₄₃	—	4	1	no	—
52	Dic₄₃	—	8	2	no	—
53	#1674	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	#462	1	1	yes	characteristic
55	C₂×C₄₃	#466	1	1	yes	characteristic
56	C₂×C₄₃	#473	1	1	yes	characteristic
57	#500	—	43	1	no	—
58	#462	—	43	2	no	—
59	C₈×Q₈	—	43	1	no	—
60	#335	D₄₃	1	1	yes	characteristic
61	#332	—	43	2	no	—
62	C₄₃	#1674	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	86	2	no	—
64	C₄⋊Q₈	—	43	2	no	—
65	C₄×Q₈	—	43	1	no	—
66	#107	—	86	1	no	—
67	#107	—	86	1	no	—
68	C₄⋊C₈	—	43	1	no	—
69	C₄⋊C₈	—	86	1	no	—
70	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
71	#103	—	86	2	no	—
72	C₄×C₈	—	86	1	no	—
73	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	C₂×Q₈	—	43	1	no	—
75	C₂×Q₈	—	86	2	no	—
76	Q₁₆	—	172	4	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	86	1	no	—
79	C₂×C₈	D₁₇₂	1	1	yes	characteristic
80	C₂×C₈	D₁₇₂	1	1	yes	characteristic
81	C₄⋊C₄	—	43	1	no	—
82	C₄⋊C₄	—	86	1	no	—
83	C₄⋊C₄	—	86	2	no	—
84	C₄⋊C₄	—	86	2	no	—
85	C₄²	—	86	1	no	—
86	C₄²	C₂²×D₄₃	1	1	yes	characteristic
87	Q₈	—	43	2	no	—
88	Q₈	—	86	1	no	—
89	Q₈	—	172	2	no	—
90	Q₈	—	172	2	no	—
91	C₂×C₄	—	86	1	no	—
92	C₂×C₄	—	86	1	no	—
93	C₂×C₄	—	172	2	no	—
94	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
95	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
96	C₂×C₄	#10621902	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	4	2	no	—
99	C₈	—	172	1	no	—
100	C₈	Dic₁₇₂	1	2	yes	complemented
101	C₂²	#13063300	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	86	2	no	—
104	C₄	—	344	2	no	—
105	C₄	—	172	1	no	—
106	C₄	D₈×D₄₃	1	1	yes	characteristic
107	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
108	C₄	#13063348	1	1	yes	characteristic
109	C₄	#13063358	1	1	yes	characteristic
110	C₂	#14583110	1	1	yes	characteristic
111	C₂	#14583136	1	1	yes	characteristic
112	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic

#14583110

C₂

yes

maximal

C₈×Dic₈₆

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal

C₄₃×#335

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

—

#13063325

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

characteristic

#13063259

—

#13063259

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

C₈×Dic₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

D₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

Q₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₈×Q₈

—

#335

D₄₃

yes

characteristic

#332

—

C₄₃

#1674

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621902

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

100

C₈

Dic₁₇₂

yes

complemented

101

C₂²

#13063300

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

344

—

105

C₄

—

172

—

106

C₄

D₈×D₄₃

yes

characteristic

107

C₄

C₂×Dic₁₇₂

yes

characteristic

108

C₄

#13063348

yes

characteristic

109

C₄

#13063358

yes

characteristic

110

C₂

#14583110

yes

characteristic

111

C₂

#14583136

yes

characteristic

112

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#335	C₂
socle	C₂²×C₄₃	#121
hypercenter	#335	D₄₃
hypocenter	C₄₃	#1674
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #335

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#335

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #335

N	H ≅ G/N	type
42. C₈×C₄₃	Q₁₆	semidirect
62. C₄₃	#1674	semidirect
100. C₈	Dic₁₇₂	semidirect

H ≅ G/N

type

42. C₈×C₄₃

Q₁₆

semidirect

62. C₄₃

#1674

semidirect

100. C₈

Dic₁₇₂

semidirect

Subgroups — #19133990

Conjugacy classes of subgroups

Complements