Group #19133735 — subgroups

Subgroups — #19133735

Order 5504.

206 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14583278	C₂	1	1	yes	maximal, characteristic
2	#14583194	C₂	1	2	yes	maximal
3	#14582648	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
5	Q₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621885	—	2	2	no	—
7	#13063325	C₂²	1	1	yes	characteristic
8	#13063258	—	2	2	no	—
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	#13063249	—	2	2	no	—
11	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Q₈×C₄₃	—	2	2	no	—
13	C₄⋊Q₈×C₄₃	—	2	2	no	—
14	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×Q₈×C₄₃	—	2	2	no	—
16	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×Q₈×C₄₃	—	2	2	no	—
18	C₂×Q₈×C₄₃	D₄	1	2	yes	—
19	C₂×Q₈×C₄₃	D₄	1	2	yes	—
20	C₂×Dic₈₆	—	2	1	no	—
21	C₄⋊C₄×C₄₃	—	2	4	no	—
22	C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
25	C₄²×C₄₃	—	2	2	no	—
26	C₄²×C₄₃	—	2	2	no	—
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	#10621885	—	4	4	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₂×C₄₃⋊C₈	—	2	1	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	Q₈×C₄₃	—	2	2	no	—
33	Q₈×C₄₃	—	4	2	no	—
34	Q₈×C₄₃	—	8	2	no	—
35	Q₈×C₄₃	Q₁₆	1	4	yes	complemented
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
41	C₂×Dic₄₃	—	4	1	no	—
42	Dic₈₆	—	4	2	no	—
43	C₄₃⋊C₈	—	2	2	no	—
44	C₄₃⋊C₈	—	4	2	no	—
45	C₂²×C₄₃	#120	1	1	yes	characteristic
46	C₄×C₄₃	—	2	4	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	4	2	no	—
49	C₄×C₄₃	—	4	2	no	—
50	C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
51	C₄×C₄₃	#137	1	2	yes	—
52	Dic₄₃	—	8	1	no	—
53	#1633	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	#451	1	2	yes	—
55	C₂×C₄₃	#453	1	1	yes	characteristic
56	Q₈²	D₄₃	1	1	yes	characteristic
57	#494	—	43	1	no	—
58	#477	—	43	2	no	—
59	#333	—	43	1	no	—
60	Q₈⋊C₈	—	43	2	no	—
61	C₄₃	#1633	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	86	2	no	—
63	C₄⋊Q₈	—	2	2	no	—
64	C₄⋊Q₈	—	2	2	no	—
65	C₄⋊Q₈	—	43	1	no	—
66	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
67	C₄×Q₈	—	2	2	no	—
68	C₄×Q₈	C₂×D₄₃	1	2	yes	—
69	#107	—	86	2	no	—
70	C₄⋊C₈	—	43	2	no	—
71	#103	—	86	2	no	—
72	C₄×C₈	—	43	1	no	—
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	86	1	no	—
75	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
76	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
77	Q₁₆	—	172	4	no	—
78	C₂×C₈	—	86	1	no	—
79	C₂×C₈	—	86	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	86	2	no	—
84	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
85	C₄²	—	2	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	C₂²×D₄₃	1	1	yes	characteristic
88	Q₈	—	2	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	8	2	no	—
91	Q₈	—	172	2	no	—
92	Q₈	#10621885	1	4	yes	complemented
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	172	1	no	—
97	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
99	C₈	—	86	2	no	—
100	C₈	—	172	2	no	—
101	C₂²	#13063294	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	2	no	—
106	C₄	—	344	1	no	—
107	C₄	C₂×#10621885	1	2	yes	—
108	C₄	#13063356	1	2	yes	—
109	C₂	#14583055	1	2	yes	—
110	C₂	#14583067	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583278

C₂

yes

maximal, characteristic

#14583194

C₂

yes

maximal

#14582648

C₂

yes

maximal, characteristic

Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal

Q₈²×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621885

—

#13063325

C₂²

yes

characteristic

#13063258

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063249

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621885

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

Q₁₆

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

—

C₄×C₄₃

#137

yes

—

Dic₄₃

—

#1633

—

maximal, Sylow

C₂×C₄₃

#451

yes

—

C₂×C₄₃

#453

yes

characteristic

Q₈²

D₄₃

yes

—

—

—

Q₈⋊C₈

—

C₄₃

#1633

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

C₂×D₄₃

yes

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₄₃

yes

—

C₂×Q₈

C₂²⋊D₄₃

yes

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

172

—

Q₈

#10621885

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

C₈

—

100

C₈

—

172

—

101

C₂²

#13063294

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

344

—

107

C₄

C₂×#10621885

yes

—

108

C₄

#13063356

yes

—

109

C₂

#14583055

yes

—

110

C₂

#14583067

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	Q₈²×C₄₃	C₂
socle	C₂²×C₄₃	#120
hypercenter	Q₈²	D₄₃
hypocenter	C₄₃	#1633
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

subgroup

G/H

center

C₂²

#13063294

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

Q₈²×C₄₃

C₂

socle

C₂²×C₄₃

#120

hypercenter

Q₈²

D₄₃

hypocenter

C₄₃

#1633

LCS

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

N	H ≅ G/N	type
35. Q₈×C₄₃	Q₁₆	semidirect
61. C₄₃	#1633	semidirect
92. Q₈	#10621885	semidirect

H ≅ G/N

type

35. Q₈×C₄₃

Q₁₆

semidirect

61. C₄₃

#1633

semidirect

92. Q₈

#10621885

semidirect

Subgroups — #19133735

Conjugacy classes of subgroups

Complements