Group #19135587 — subgroups

Subgroups — #19135587

Order 5504.

228 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13063317	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621877	C₂	1	1	yes	maximal, characteristic
3	#14582667	C₂	1	4	yes	maximal
4	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	C₂²	1	2	yes	—
6	#13063317	—	2	1	no	—
7	#13063317	—	2	1	no	—
8	#13063317	—	2	2	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×Dic₄₃⋊C₄	C₄	1	4	yes	—
11	#13063236	—	2	1	no	—
12	C₄×C₄₃⋊C₈	—	2	1	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₄⋊C₈×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	C₂×C₄	1	4	yes	—
19	M₁₆×C₄₃	—	2	4	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	D₄	1	2	yes	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	Dic₄₃⋊C₄	—	2	4	no	—
27	Dic₄₃⋊C₄	—	2	4	no	—
28	#10621877	—	2	2	no	—
29	#10621877	Q₈	1	4	yes	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₄₃	#41	1	2	yes	—
39	C₂×Dic₄₃	—	2	4	no	—
40	C₂×Dic₄₃	—	4	4	no	—
41	C₈×C₄₃	—	4	2	no	—
42	C₄₃⋊C₈	—	2	4	no	—
43	C₂²×C₄₃	—	2	2	no	—
44	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₄₃	#124	1	1	yes	characteristic
50	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
51	Dic₄₃	—	4	4	no	—
52	#1998	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	2	no	—
54	C₂×C₄₃	#391	1	1	yes	characteristic
55	C₂×C₄₃	#413	1	2	yes	—
56	C₂×#125	—	43	1	no	—
57	#423	D₄₃	1	1	yes	characteristic
58	C₄×M₁₆	—	43	1	no	—
59	#343	—	43	4	no	—
60	C₄₃	#1998	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	43	2	no	—
62	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
63	#125	—	86	1	no	—
64	#125	—	86	1	no	—
65	#125	—	86	2	no	—
66	C₂×C₄⋊C₄	—	43	2	no	—
67	C₂×C₄⋊C₄	—	43	4	no	—
68	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
69	C₄⋊C₈	—	2	2	no	—
70	#97	—	86	1	no	—
71	C₄×C₈	—	86	1	no	—
72	C₂²×C₄	—	43	4	no	—
73	C₂²×C₄	C₄×D₄₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
75	M₁₆	—	2	4	no	—
76	M₁₆	—	43	4	no	—
77	M₁₆	—	86	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	86	2	no	—
80	C₄⋊C₄	—	86	4	no	—
81	C₄⋊C₄	—	86	4	no	—
82	C₄⋊C₄	—	86	2	no	—
83	C₄⋊C₄	—	86	2	no	—
84	C₄²	D₁₇₂	1	1	yes	characteristic
85	C₄²	D₁₇₂	1	1	yes	characteristic
86	C₄²	C₂²⋊D₄₃	1	2	yes	—
87	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	86	4	no	—
90	C₂×C₄	—	172	4	no	—
91	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
92	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
93	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
94	C₂×C₄	#10621900	1	2	yes	—
95	C₂×C₄	Q₈×D₄₃	1	2	yes	—
96	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
97	C₈	—	4	2	no	—
98	C₈	—	86	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
101	C₂²	#13063290	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	172	4	no	—
105	C₄	#13063305	1	2	yes	—
106	C₄	#13063312	1	1	yes	characteristic
107	C₄	#13063323	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#14582804	1	1	yes	characteristic
110	C₂	#14582881	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal, characteristic

C₄×#10621877

C₂

yes

maximal, characteristic

#14582667

C₂

yes

maximal

C₄₃×#423

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063317

—

#13063317

—

#13063317

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

#10621877

—

#10621877

Q₈

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

Dic₄₃

—

#1998

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#391

yes

characteristic

C₂×C₄₃

#413

yes

—

C₂×#125

—

#423

D₄₃

yes

characteristic

C₄×M₁₆

—

#343

—

C₄₃

#1998

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₁₇₂

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

—

C₂³

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621900

yes

—

C₂×C₄

Q₈×D₄₃

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

—

100

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

101

C₂²

#13063290

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

172

—

105

C₄

#13063305

yes

—

106

C₄

#13063312

yes

characteristic

107

C₄

#13063323

yes

characteristic

108

C₂

—

109

C₂

#14582804

yes

characteristic

110

C₂

#14582881

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#1998
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
60. C₄₃	#1998	semidirect

H ≅ G/N

type

60. C₄₃

#1998

semidirect

Subgroups — #19135587

Conjugacy classes of subgroups

Complements