Group #19132608 — subgroups

Subgroups — #19132608

Order 5504.

116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14583140	C₂	1	1	yes	maximal, characteristic
2	#14582662	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
5	#13063304	—	2	1	no	—
6	C₂×C₄⋊Dic₄₃	—	2	1	no	—
7	#13063259	C₄	1	1	yes	characteristic, complemented
8	#13063250	—	2	1	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂²×Dic₄₃	—	4	1	no	—
13	C₂×Dic₈₆	—	2	1	no	—
14	C₂×C₈×C₄₃	—	4	1	no	—
15	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₂²⋊Dic₄₃	—	4	1	no	—
18	C₄⋊Dic₄₃	—	2	2	no	—
19	C₄⋊Dic₄₃	—	2	1	no	—
20	C₄⋊Dic₄₃	—	4	1	no	—
21	Dic₄₃⋊C₄	—	4	1	no	—
22	Dic₁₇₂	—	4	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₂³×C₄₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
29	C₂×Dic₄₃	—	4	2	no	—
30	C₂×Dic₄₃	—	4	1	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	C₂×Dic₄₃	—	8	1	no	—
33	C₂×Dic₄₃	—	8	1	no	—
34	Dic₈₆	—	4	1	no	—
35	Dic₈₆	—	4	1	no	—
36	C₈×C₄₃	—	2	1	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₂²×C₄₃	—	2	1	no	—
39	C₂²×C₄₃	—	2	1	no	—
40	C₂²×C₄₃	#102	1	1	yes	characteristic
41	C₂²×C₄₃	SD₃₂	1	1	yes	characteristic
42	C₂²×C₄₃	Q₃₂	1	1	yes	characteristic
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	#99	1	1	yes	characteristic
45	C₄×C₄₃	#104	1	1	yes	characteristic
46	Dic₄₃	—	8	2	no	—
47	Dic₄₃	—	8	1	no	—
48	Dic₄₃	—	8	1	no	—
49	#1348	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	#327	1	1	yes	characteristic
53	C₂×C₄₃	#358	1	1	yes	characteristic
54	C₂×C₄₃	#360	1	1	yes	characteristic
55	#467	—	43	1	no	—
56	C₂²⋊C₁₆	D₄₃	1	1	yes	characteristic
57	#340	—	43	1	no	—
58	C₄₃	#1348	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	43	1	no	—
60	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₂²⋊Q₈	—	86	1	no	—
62	C₂×C₄⋊C₄	—	86	1	no	—
63	C₂×C₁₆	—	2	1	no	—
64	#107	—	43	1	no	—
65	#103	—	86	1	no	—
66	C₂×Q₈	—	86	1	no	—
67	C₂²×C₄	—	172	1	no	—
68	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
69	Q₁₆	—	172	1	no	—
70	C₂×C₈	—	4	1	no	—
71	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
72	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
73	C₄⋊C₄	—	86	2	no	—
74	C₄⋊C₄	—	86	1	no	—
75	C₄⋊C₄	—	172	1	no	—
76	C₄⋊C₄	—	172	1	no	—
77	C₂²⋊C₄	—	172	1	no	—
78	C₁₆	—	4	1	no	—
79	C₂³	D₃₄₄	1	1	yes	characteristic
80	Q₈	—	172	1	no	—
81	Q₈	—	172	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	344	1	no	—
85	C₂×C₄	—	344	1	no	—
86	C₂×C₄	—	172	2	no	—
87	C₂×C₄	—	172	1	no	—
88	C₂×C₄	—	172	1	no	—
89	C₂×C₄	#10621873	1	1	yes	characteristic
90	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	—	2	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	#13063247	1	1	yes	characteristic
96	C₂²	#13063270	1	1	yes	characteristic
97	C₂²	Dic₃₄₄	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	344	2	no	—
100	C₄	—	344	1	no	—
101	C₄	—	344	1	no	—
102	C₄	#13063239	1	1	yes	characteristic
103	C₄	#13063251	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	2	1	no	—
106	C₂	#14582634	1	1	yes	characteristic
107	C₂	#14582704	1	1	yes	characteristic
108	C₂	#14582710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583140

C₂

yes

maximal, characteristic

#14582662

C₂

yes

maximal, characteristic

C₄₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₄

yes

characteristic, complemented

#13063304

—

C₂×C₄⋊Dic₄₃

—

#13063259

C₄

yes

characteristic, complemented

#13063250

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

characteristic

C₂²×C₄₃

SD₃₂

yes

characteristic

C₂²×C₄₃

Q₃₂

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1348

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂²⋊C₁₆

D₄₃

yes

characteristic

#340

—

C₄₃

#1348

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₁₆

—

#107

—

#103

—

C₂×Q₈

—

C₂²×C₄

—

172

—

C₂²×C₄

D₁₇₂

yes

characteristic

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₂³

D₃₄₄

yes

characteristic

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

Dic₃₄₄

yes

characteristic

C₄

—

C₄

—

344

—

100

C₄

—

344

—

101

C₄

—

344

—

102

C₄

#13063239

yes

characteristic

103

C₄

#13063251

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#14582634

yes

characteristic

107

C₂

#14582704

yes

characteristic

108

C₂

#14582710

yes

characteristic

	subgroup	G/H
center	C₂²	#13063247
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₄₃×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₃	#102
hypercenter	C₂²⋊C₁₆	D₄₃
hypocenter	C₄₃	#1348
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#13063247

commutator

C₂×C₈×C₄₃

C₂×C₄

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₄₃×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₃

#102

hypercenter

C₂²⋊C₁₆

D₄₃

hypocenter

C₄₃

#1348

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
4. C₂×Dic₁₇₂	C₄	semidirect
7. #13063259	C₄	semidirect
58. C₄₃	#1348	semidirect

H ≅ G/N

type

4. C₂×Dic₁₇₂

C₄

semidirect

7. #13063259

C₄

semidirect

58. C₄₃

#1348

semidirect

Subgroups — #19132608

Conjugacy classes of subgroups

Complements