Group #19133955 — subgroups

Subgroups — #19133955

Order 5504.

188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14583276	C₂	1	1	yes	maximal, characteristic
2	#14583099	C₂	1	2	yes	maximal, complemented
3	#14582652	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582642	C₂	1	2	yes	maximal, complemented
5	C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621884	—	2	2	no	—
7	C₂×D₃₄₄	—	2	1	no	—
8	C₂×D₃₄₄	—	2	1	no	—
9	#13063322	C₂²	1	2	yes	—
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
11	#13063245	—	2	2	no	—
12	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₃	—	2	1	no	—
14	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	—	2	1	no	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×D₁₇₂	—	2	2	no	—
19	C₂×D₁₇₂	—	2	2	no	—
20	C₂×D₁₇₂	—	2	2	no	—
21	C₂×C₈×C₄₃	—	2	1	no	—
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₃	—	2	1	no	—
25	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
26	C₄²×C₄₃	—	2	1	no	—
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	#10621884	—	4	4	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	D₃₄₄	—	4	2	no	—
31	D₃₄₄	—	4	2	no	—
32	C₂²×D₄₃	—	4	2	no	—
33	Q₈×C₄₃	—	2	1	no	—
34	Q₈×C₄₃	D₈	1	2	yes	complemented
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
40	D₁₇₂	—	4	2	no	—
41	D₁₇₂	—	4	2	no	—
42	D₁₇₂	—	4	2	no	—
43	D₁₇₂	—	4	2	no	—
44	D₁₇₂	—	8	2	no	—
45	C₈×C₄₃	—	2	1	no	—
46	C₈×C₄₃	—	4	1	no	—
47	C₈×C₄₃	SD₁₆	1	2	yes	complemented
48	C₄₃⋊C₈	—	4	2	no	—
49	C₂²×C₄₃	#121	1	1	yes	characteristic
50	C₂×D₄₃	—	8	2	no	—
51	C₂×D₄₃	—	8	2	no	—
52	C₂×D₄₃	—	8	2	no	—
53	C₄×C₄₃	—	2	2	no	—
54	C₄×C₄₃	—	2	1	no	—
55	C₄×C₄₃	—	4	1	no	—
56	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
57	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
58	C₄×C₄₃	#135	1	1	yes	characteristic
59	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
60	#1668	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	#460	1	1	yes	characteristic
62	C₂×C₄₃	#466	1	1	yes	characteristic
63	C₂×C₄₃	#472	1	1	yes	characteristic
64	D₄₃	—	16	2	no	—
65	#493	—	43	1	no	—
66	#460	—	43	2	no	—
67	C₈×Q₈	D₄₃	1	1	yes	characteristic, complemented
68	#335	—	43	1	no	—
69	#331	—	43	2	no	—
70	C₄₃	#1668	1	1	yes	characteristic, complemented, Sylow
71	C₂×SD₁₆	—	86	2	no	—
72	C₂×D₈	—	86	1	no	—
73	C₂×D₈	—	86	1	no	—
74	#127	—	43	2	no	—
75	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
76	C₄⋊C₈	—	2	1	no	—
77	C₄⋊C₈	—	43	2	no	—
78	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
79	#102	—	86	2	no	—
80	C₄×C₈	—	2	1	no	—
81	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
82	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
83	C₂×D₄	—	86	2	no	—
84	C₂×D₄	—	86	2	no	—
85	C₂×D₄	—	86	2	no	—
86	SD₁₆	—	172	4	no	—
87	D₈	—	172	2	no	—
88	D₈	—	172	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	86	2	no	—
91	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
92	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
95	C₄²	—	2	1	no	—
96	C₄²	C₂²×D₄₃	1	1	yes	characteristic
97	C₂³	—	172	2	no	—
98	Q₈	—	2	1	no	—
99	Q₈	D₃₄₄	1	2	yes	complemented
100	D₄	—	344	2	no	—
101	D₄	—	172	2	no	—
102	D₄	—	172	2	no	—
103	D₄	—	172	2	no	—
104	D₄	—	172	2	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
108	C₂×C₄	#10621898	1	1	yes	characteristic
109	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	4	1	no	—
112	C₈	—	172	2	no	—
113	C₈	#10621884	1	2	yes	complemented
114	C₂²	—	344	2	no	—
115	C₂²	—	344	2	no	—
116	C₂²	—	344	2	no	—
117	C₂²	#13063299	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	1	no	—
120	C₄	—	4	1	no	—
121	C₄	C₂×D₃₄₄	1	1	yes	characteristic
122	C₄	C₂×#10621884	1	1	yes	characteristic
123	C₄	#13063347	1	1	yes	characteristic
124	C₄	#13063350	1	1	yes	characteristic
125	C₂	—	688	2	no	—
126	C₂	#14583099	1	1	yes	characteristic
127	C₂	#14583135	1	1	yes	characteristic
128	C₂	#14583169	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583276

C₂

yes

maximal, characteristic

#14583099

C₂

yes

maximal, complemented

#14582652

C₂

yes

maximal, characteristic, complemented

#14582642

C₂

yes

maximal, complemented

C₈×Q₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

#13063322

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063245

—

C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

D₃₄₄

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

D₈

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#493

—

#460

—

C₈×Q₈

D₄₃

yes

characteristic, complemented

#335

—

#331

—

C₄₃

#1668

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

#127

—

C₄×Q₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

D₁₇₂

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

172

—

D₈

—

172

—

D₈

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

D₁₇₂

yes

characteristic

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

172

—

Q₈

—

Q₈

D₃₄₄

yes

complemented

100

D₄

—

344

—

101

D₄

—

172

—

102

D₄

—

172

—

103

D₄

—

172

—

104

D₄

—

172

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂×D₁₇₂

yes

characteristic

108

C₂×C₄

#10621898

yes

characteristic

109

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

172

—

113

C₈

#10621884

yes

complemented

114

C₂²

—

344

—

115

C₂²

—

344

—

116

C₂²

—

344

—

117

C₂²

#13063299

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂×D₃₄₄

yes

characteristic

122

C₄

C₂×#10621884

yes

characteristic

123

C₄

#13063347

yes

characteristic

124

C₄

#13063350

yes

characteristic

125

C₂

—

688

—

126

C₂

#14583099

yes

characteristic

127

C₂

#14583135

yes

characteristic

128

C₂

#14583169

yes

characteristic

	subgroup	G/H
center	C₂²	#13063299
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈×Q₈×C₄₃	C₂
socle	C₂²×C₄₃	#121
hypercenter	C₈×Q₈	D₄₃
hypocenter	C₄₃	#1668
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

subgroup

G/H

center

C₂²

#13063299

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₈×Q₈×C₄₃

C₂

socle

C₂²×C₄₃

#121

hypercenter

C₈×Q₈

D₄₃

hypocenter

C₄₃

#1668

LCS

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

N	H ≅ G/N	type
2. #14583099	C₂	semidirect
3. #14582652	C₂	semidirect
4. #14582642	C₂	semidirect
5. C₈×Q₈×C₄₃	C₂	semidirect
34. Q₈×C₄₃	D₈	semidirect
47. C₈×C₄₃	SD₁₆	semidirect
67. C₈×Q₈	D₄₃	semidirect
70. C₄₃	#1668	semidirect
99. Q₈	D₃₄₄	semidirect
113. C₈	#10621884	semidirect

H ≅ G/N

type

2. #14583099

C₂

semidirect

3. #14582652

C₂

semidirect

4. #14582642

C₂

semidirect

5. C₈×Q₈×C₄₃

C₂

semidirect

34. Q₈×C₄₃

D₈

semidirect

47. C₈×C₄₃

SD₁₆

semidirect

67. C₈×Q₈

D₄₃

semidirect

70. C₄₃

#1668

semidirect

99. Q₈

D₃₄₄

semidirect

113. C₈

#10621884

semidirect

Subgroups — #19133955

Conjugacy classes of subgroups

Complements