Group #19134124 — subgroups

Subgroups — #19134124

Order 5504.

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

normal subgroups only

This group has 140 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	#14583304	C₂	1	1	yes	maximal, characteristic
2	#14583195	C₂	1	2	yes	maximal
3	#14583029	C₂	1	1	yes	maximal, characteristic
4	#14582647	C₂	1	2	yes	maximal
5	C₄₃×#334	C₂	1	1	yes	maximal, characteristic
6	#13063325	C₂²	1	2	yes	—
7	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
8	#13063259	—	2	1	no	—
9	#13063259	—	2	1	no	—
10	#13063259	—	2	2	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₄₃⋊C₈	—	2	1	no	—
13	#13063250	—	2	2	no	—
14	#13063235	—	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	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
32	C₂×Dic₄₃	—	2	1	no	—
33	C₂×Dic₄₃	—	2	1	no	—
34	C₂×Dic₄₃	—	4	2	no	—
35	Dic₈₆	—	2	2	no	—
36	Dic₈₆	—	8	2	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₈×C₄₃	—	4	2	no	—
39	C₈×C₄₃	Q₁₆	1	2	yes	—
40	C₄₃⋊C₈	—	4	1	no	—
41	C₂²×C₄₃	#121	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
44	C₄×C₄₃	#137	1	2	yes	—
45	C₄×C₄₃	#137	1	1	yes	characteristic
46	Dic₄₃	—	4	1	no	—
47	Dic₄₃	—	4	1	no	—
48	Dic₄₃	—	8	2	no	—
49	#1696	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	#462	1	1	yes	characteristic
51	C₂×C₄₃	#470	1	1	yes	characteristic
52	C₂×C₄₃	#472	1	1	yes	characteristic
53	#500	—	43	1	no	—
54	#477	—	43	2	no	—
55	#446	—	43	1	no	—
56	#334	D₄₃	1	1	yes	characteristic
57	#333	—	43	2	no	—
58	C₄₃	#1696	1	1	yes	characteristic, complemented, Sylow
59	C₄⋊Q₈	—	43	2	no	—
60	C₄×Q₈	—	43	1	no	—
61	#107	—	86	2	no	—
62	#107	—	86	1	no	—
63	#107	—	86	1	no	—
64	C₄⋊C₈	—	43	1	no	—
65	C₄⋊C₈	—	86	1	no	—
66	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
67	#103	—	86	2	no	—
68	#97	—	86	1	no	—
69	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
70	C₂×Q₈	—	43	1	no	—
71	C₂×Q₈	—	86	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	86	1	no	—
74	C₂×C₈	D₁₇₂	1	1	yes	characteristic
75	C₂×C₈	D₁₇₂	1	1	yes	characteristic
76	C₄⋊C₄	—	43	1	no	—
77	C₄⋊C₄	—	86	1	no	—
78	C₄⋊C₄	—	86	2	no	—
79	C₄⋊C₄	—	86	2	no	—
80	C₄²	—	86	1	no	—
81	C₄²	C₂²×D₄₃	1	1	yes	characteristic
82	Q₈	—	86	2	no	—
83	Q₈	—	344	2	no	—
84	C₂×C₄	—	86	1	no	—
85	C₂×C₄	—	86	1	no	—
86	C₂×C₄	—	172	2	no	—
87	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
88	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
89	C₂×C₄	#10621902	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	4	2	no	—
92	C₈	—	172	1	no	—
93	C₈	Dic₁₇₂	1	2	yes	—
94	C₂²	#13063300	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	344	2	no	—
97	C₄	—	172	1	no	—
98	C₄	—	172	1	no	—
99	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
100	C₄	#13063354	1	2	yes	—
101	C₄	#13063358	1	1	yes	characteristic
102	C₂	#14583110	1	1	yes	characteristic
103	C₂	#14583158	1	1	yes	characteristic
104	C₂	#14583170	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic

#14583195

C₂

yes

maximal

#14583029

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal

C₄₃×#334

C₂

yes

maximal, characteristic

#13063325

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

—

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

#13063235

—

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

—

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

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

Q₁₆

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

#137

yes

—

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

D₄₃

yes

characteristic

#333

—

C₄₃

#1696

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

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

—

344

—

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

—

C₈

Dic₁₇₂

yes

—

C₂²

#13063300

yes

characteristic

C₄

—

C₄

—

344

—

C₄

—

172

—

C₄

—

172

—

C₄

C₂×Dic₁₇₂

yes

characteristic

100

C₄

#13063354

yes

—

101

C₄

#13063358

yes

characteristic

102

C₂

#14583110

yes

characteristic

103

C₂

#14583158

yes

characteristic

104

C₂

#14583170

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1696
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
58. C₄₃	#1696	semidirect

H ≅ G/N

type

58. C₄₃

#1696

semidirect

Subgroups — #19134124

Conjugacy classes of subgroups

Complements