Group #19133674 — subgroups

Subgroups — #19133674

Order 5504.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583629	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583273	C₂	1	1	yes	maximal, characteristic
3	#14583100	C₂	1	2	yes	maximal
4	#14582629	C₂	1	2	yes	maximal, complemented
5	C₄₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621873	—	2	2	no	—
7	C₂×#10621884	—	2	2	no	—
8	#13063324	—	2	2	no	—
9	#13063323	—	2	2	no	—
10	#13063322	C₂²	1	1	yes	characteristic
11	C₄×Dic₈₆	C₂²	1	2	yes	—
12	#13063290	—	2	2	no	—
13	#13063247	—	2	2	no	—
14	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
17	C₂×Q₈×C₄₃	D₄	1	2	yes	—
18	C₂×D₁₇₂	—	2	2	no	—
19	C₂×D₁₇₂	—	2	1	no	—
20	C₂×Dic₈₆	—	2	2	no	—
21	C₂×Dic₈₆	D₄	1	2	yes	—
22	C₂×C₈×C₄₃	—	2	2	no	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	#10621884	—	4	4	no	—
26	C₄⋊Dic₄₃	D₄	1	2	yes	—
27	Dic₄₃⋊C₄	—	2	4	no	—
28	Dic₄₃⋊C₄	—	2	2	no	—
29	C₄×Dic₄₃	—	2	2	no	—
30	C₄×Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	#10621873	—	4	4	no	—
33	C₂²×D₄₃	—	4	1	no	—
34	Q₈×C₄₃	—	4	2	no	—
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
38	C₂×Dic₄₃	—	2	2	no	—
39	C₂×Dic₄₃	—	2	2	no	—
40	D₁₇₂	—	4	2	no	—
41	D₁₇₂	—	4	2	no	—
42	D₁₇₂	—	4	2	no	—
43	Dic₈₆	—	2	2	no	—
44	Dic₈₆	—	8	2	no	—
45	Dic₈₆	SD₁₆	1	4	yes	complemented
46	C₈×C₄₃	—	4	2	no	—
47	C₄₃⋊C₈	—	2	2	no	—
48	C₂²×C₄₃	#120	1	1	yes	characteristic
49	C₂×D₄₃	—	8	2	no	—
50	C₂×D₄₃	—	8	1	no	—
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	—	4	2	no	—
53	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
54	C₄×C₄₃	#137	1	2	yes	—
55	Dic₄₃	—	2	4	no	—
56	Dic₄₃	—	4	2	no	—
57	#1623	—	43	1	no	maximal, Sylow
58	C₂×C₄₃	#448	1	2	yes	—
59	C₂×C₄₃	#453	1	1	yes	characteristic
60	D₄₃	—	16	1	no	—
61	Q₈²	—	43	1	no	—
62	#492	—	43	1	no	—
63	#460	—	43	2	no	—
64	#333	D₄₃	1	1	yes	characteristic, complemented
65	Q₈⋊C₈	—	43	2	no	—
66	C₄₃	#1623	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	86	2	no	—
68	C₂×SD₁₆	—	86	2	no	—
69	C₄⋊Q₈	—	86	2	no	—
70	C₄⋊Q₈	—	86	2	no	—
71	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
72	#127	—	43	1	no	—
73	C₄×Q₈	—	43	2	no	—
74	C₄×Q₈	—	86	2	no	—
75	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
76	#102	—	86	2	no	—
77	C₄×C₈	—	43	1	no	—
78	C₂×Q₈	—	43	2	no	—
79	C₂×Q₈	—	86	2	no	—
80	C₂×Q₈	D₁₇₂	1	2	yes	—
81	C₂×D₄	—	86	1	no	—
82	C₂×D₄	—	86	2	no	—
83	SD₁₆	—	172	4	no	—
84	SD₁₆	—	172	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	86	1	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	43	2	no	—
89	C₄⋊C₄	—	86	4	no	—
90	C₄⋊C₄	—	86	2	no	—
91	C₄²	—	86	2	no	—
92	C₄²	—	86	2	no	—
93	C₄²	C₂²×D₄₃	1	1	yes	characteristic
94	C₂³	—	172	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	43	4	no	—
97	Q₈	—	86	2	no	—
98	Q₈	—	344	2	no	—
99	D₄	—	172	2	no	—
100	D₄	—	172	2	no	—
101	D₄	—	172	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	86	2	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
106	C₂×C₄	D₄×D₄₃	1	2	yes	—
107	C₈	—	4	2	no	—
108	C₈	—	86	2	no	—
109	C₂²	—	344	1	no	—
110	C₂²	—	344	2	no	—
111	C₂²	#13063295	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	86	4	no	—
115	C₄	—	172	2	no	—
116	C₄	SD₁₆×D₄₃	1	2	yes	—
117	C₄	#13063357	1	2	yes	—
118	C₂	—	688	1	no	—
119	C₂	#14583039	1	2	yes	—
120	C₂	#14583069	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583629

C₂

yes

maximal, characteristic, complemented

#14583273

C₂

yes

maximal, characteristic

#14583100

C₂

yes

maximal

#14582629

C₂

yes

maximal, complemented

C₄₃×#333

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

#13063290

—

#13063247

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

#10621873

—

C₂²×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

SD₁₆

yes

complemented

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

—

C₄×C₄₃

#137

yes

—

Dic₄₃

—

Dic₄₃

—

#1623

—

maximal, Sylow

C₂×C₄₃

#448

yes

—

C₂×C₄₃

#453

yes

characteristic

D₄₃

—

Q₈²

—

#492

—

#460

—

#333

D₄₃

yes

characteristic, complemented

Q₈⋊C₈

—

C₄₃

#1623

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

#127

—

C₄×Q₈

—

C₄×Q₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#102

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₇₂

yes

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

172

—

SD₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

172

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

344

—

D₄

—

172

—

100

D₄

—

172

—

101

D₄

—

172

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×D₁₇₂

yes

characteristic

106

C₂×C₄

D₄×D₄₃

yes

—

107

C₈

—

108

C₈

—

109

C₂²

—

344

—

110

C₂²

—

344

—

111

C₂²

#13063295

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

172

—

116

C₄

SD₁₆×D₄₃

yes

—

117

C₄

#13063357

yes

—

118

C₂

—

688

—

119

C₂

#14583039

yes

—

120

C₂

#14583069

yes

characteristic

	subgroup	G/H
center	C₂²	#13063295
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#333	C₂
socle	C₂²×C₄₃	#120
hypercenter	#333	D₄₃
hypocenter	C₄₃	#1623
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#13063295

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#333

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #14583629	C₂	semidirect
4. #14582629	C₂	semidirect
5. C₄₃×#333	C₂	semidirect
45. Dic₈₆	SD₁₆	semidirect
64. #333	D₄₃	semidirect
66. C₄₃	#1623	semidirect

H ≅ G/N

type

1. #14583629

C₂

semidirect

4. #14582629

C₂

semidirect

5. C₄₃×#333

C₂

semidirect

45. Dic₈₆

SD₁₆

semidirect

64. #333

D₄₃

semidirect

66. C₄₃

#1623

semidirect

Subgroups — #19133674

Conjugacy classes of subgroups

Complements