Group #19133231 — subgroups

Subgroups — #19133231

Order 5504.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14583455	C₂	1	1	yes	maximal, characteristic
2	#14582954	C₂	1	2	yes	maximal
3	#14582641	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582640	C₂	1	2	yes	maximal, complemented
5	C₄₃×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063324	C₄	1	2	yes	—
7	#13063317	C₂²	1	1	yes	characteristic
8	#13063303	—	2	2	no	—
9	#13063290	—	2	2	no	—
10	#13063283	C₄	1	2	yes	—
11	C₄²×D₄₃	C₂²	1	1	yes	characteristic
12	Dic₄₃⋊C₈	—	2	2	no	—
13	(C₂×D₄₃)⋊C₈	—	2	2	no	—
14	#13063236	C₂²	1	2	yes	—
15	#125×C₄₃	C₂²	1	1	yes	characteristic
16	#97×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₄₃	D₄	1	2	yes	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
26	Dic₄₃⋊C₄	—	2	2	no	—
27	Dic₄₃⋊C₄	—	2	2	no	—
28	C₄×Dic₄₃	—	2	2	no	—
29	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₄₃	D₄	1	2	yes	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
36	C₂×Dic₄₃	—	2	2	no	—
37	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₄₃	—	2	2	no	—
40	C₄×D₄₃	—	4	2	no	—
41	Dic₈₆	—	4	4	no	—
42	C₈×C₄₃	—	4	2	no	—
43	C₄₃⋊C₈	—	4	2	no	—
44	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₄₃	—	2	1	no	—
46	C₂×D₄₃	—	2	2	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	2	no	—
49	C₄×C₄₃	—	4	2	no	—
50	Dic₄₃	—	2	2	no	—
51	Dic₄₃	—	4	2	no	—
52	Dic₄₃	#101	1	2	yes	—
53	#1537	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	C₂×#101	1	1	yes	characteristic
55	C₂×C₄₃	#421	1	2	yes	—
56	D₄₃	—	4	1	no	—
57	#533	—	43	1	no	—
58	#432	—	43	2	no	—
59	#330	—	43	1	no	—
60	#330	—	43	2	no	—
61	#330	D₄₃	1	1	yes	characteristic, complemented
62	C₄₃	#1537	1	1	yes	characteristic, complemented, Sylow
63	C₄⋊Q₈	—	43	2	no	—
64	#125	—	43	1	no	—
65	#125	C₂×D₄₃	1	1	yes	characteristic
66	C₂²⋊Q₈	—	86	2	no	—
67	C₄×Q₈	—	86	2	no	—
68	#117	—	43	2	no	—
69	C₂×C₄²	—	43	1	no	—
70	C₄⋊C₈	—	86	2	no	—
71	C₂²⋊C₈	—	86	2	no	—
72	#97	—	43	2	no	—
73	#97	C₂×D₄₃	1	2	yes	—
74	C₂×Q₈	—	86	2	no	—
75	C₂²×C₄	—	43	1	no	—
76	C₂²×C₄	—	43	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	86	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	43	2	no	—
81	C₄⋊C₄	—	86	2	no	—
82	C₄⋊C₄	—	86	2	no	—
83	C₄⋊C₄	C₄×D₄₃	1	2	yes	—
84	C₂²⋊C₄	—	86	2	no	—
85	C₄²	—	43	1	no	—
86	C₄²	—	43	2	no	—
87	C₄²	—	86	2	no	—
88	C₄²	C₂²×D₄₃	1	1	yes	characteristic
89	C₂³	—	43	1	no	—
90	Q₈	—	172	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	43	1	no	—
93	C₂×C₄	—	43	2	no	—
94	C₂×C₄	—	86	2	no	—
95	C₂×C₄	—	86	2	no	—
96	C₂×C₄	—	172	2	no	—
97	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
98	C₂×C₄	D₄×D₄₃	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	172	2	no	—
101	C₂²	—	86	1	no	—
102	C₂²	—	86	2	no	—
103	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	43	2	no	—
108	C₄	—	86	2	no	—
109	C₄	—	172	2	no	—
110	C₂	—	172	1	no	—
111	C₂	#101×D₄₃	1	1	yes	characteristic
112	C₂	#14582914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583455

C₂

yes

maximal, characteristic

#14582954

C₂

yes

maximal

#14582641

C₂

yes

maximal, characteristic, complemented

#14582640

C₂

yes

maximal, complemented

C₄₃×#330

C₂

yes

maximal, characteristic, complemented

#13063324

C₄

yes

—

#13063317

C₂²

yes

—

—

C₄

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

#13063236

C₂²

yes

—

#125×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#101

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1537

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

—

C₈

—

100

C₈

—

172

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

172

—

110

C₂

—

172

—

111

C₂

#101×D₄₃

yes

characteristic

112

C₂

#14582914

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#330	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#330	D₄₃
hypocenter	C₄₃	#1537
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#330

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #14582641	C₂	semidirect
4. #14582640	C₂	semidirect
5. C₄₃×#330	C₂	semidirect
61. #330	D₄₃	semidirect
62. C₄₃	#1537	semidirect

H ≅ G/N

type

3. #14582641

C₂

semidirect

4. #14582640

C₂

semidirect

5. C₄₃×#330

C₂

semidirect

61. #330

D₄₃

semidirect

62. C₄₃

#1537

semidirect

Subgroups — #19133231

Conjugacy classes of subgroups

Complements