Group #19134208 — subgroups

Subgroups — #19134208

Order 5504.

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

normal subgroups only

This group has 178 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	#14583251	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583249	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583247	C₂	1	1	yes	maximal, characteristic
4	#14583247	C₂	1	1	yes	maximal, characteristic
5	#14583246	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063325	C₂²	1	1	yes	characteristic
9	#13063322	C₂²	1	1	yes	characteristic
10	#13063249	—	2	2	no	—
11	#13063248	—	2	2	no	—
12	#13063247	—	2	2	no	—
13	#13063245	—	2	2	no	—
14	#13063245	—	2	2	no	—
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	#103×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	C₂×C₈×C₄₃	D₄	1	2	yes	—
28	C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
36	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
37	C₂²×D₄₃	—	4	1	no	—
38	Q₈×C₄₃	—	4	2	no	—
39	Q₈×C₄₃	—	4	2	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	—	4	1	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₄₃	—	4	1	no	—
46	D₁₇₂	—	4	2	no	—
47	D₁₇₂	—	4	2	no	—
48	D₁₇₂	—	4	2	no	—
49	Dic₈₆	—	4	2	no	—
50	C₈×C₄₃	—	2	2	no	—
51	C₄₃⋊C₈	—	2	2	no	—
52	C₄₃⋊C₈	—	2	2	no	—
53	C₂²×C₄₃	#127	1	1	yes	characteristic
54	C₂×D₄₃	—	8	1	no	—
55	C₂×D₄₃	—	8	1	no	—
56	C₂×D₄₃	—	8	1	no	—
57	C₄×C₄₃	—	8	1	no	—
58	C₄×C₄₃	—	8	1	no	—
59	C₄×C₄₃	#135	1	2	yes	—
60	C₄×C₄₃	#135	1	2	yes	—
61	C₄×C₄₃	#135	1	2	yes	—
62	Dic₄₃	—	8	1	no	—
63	#1711	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	#495	1	1	yes	characteristic
65	C₂×C₄₃	#495	1	1	yes	characteristic
66	C₂×C₄₃	#495	1	1	yes	characteristic
67	D₄₃	—	16	1	no	—
68	#487	—	43	1	no	—
69	#487	—	43	1	no	—
70	#487	D₄₃	1	1	yes	characteristic, complemented
71	#486	—	43	1	no	—
72	#486	—	43	1	no	—
73	#486	—	43	1	no	—
74	C₈²	—	43	1	no	—
75	C₄₃	#1711	1	1	yes	characteristic, complemented, Sylow
76	C₄⋊Q₈	—	43	1	no	—
77	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
78	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
79	#127	—	43	1	no	—
80	#103	—	2	2	no	—
81	#103	—	86	2	no	—
82	#103	—	86	2	no	—
83	#102	—	86	2	no	—
84	#102	—	86	2	no	—
85	#102	—	86	2	no	—
86	C₄×C₈	—	43	1	no	—
87	C₄×C₈	—	43	1	no	—
88	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
89	C₂×Q₈	—	2	1	no	—
90	C₂×Q₈	—	2	1	no	—
91	C₂×Q₈	—	86	1	no	—
92	C₂×D₄	—	86	1	no	—
93	C₂×D₄	—	86	1	no	—
94	C₂×D₄	—	86	1	no	—
95	C₂×C₈	—	43	2	no	—
96	C₂×C₈	—	43	2	no	—
97	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
98	C₄⋊C₄	—	2	1	no	—
99	C₄⋊C₄	—	2	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	86	1	no	—
103	C₄⋊C₄	—	86	1	no	—
104	C₄²	C₂²×D₄₃	1	1	yes	characteristic
105	C₂³	—	172	1	no	—
106	Q₈	—	4	2	no	—
107	Q₈	—	4	2	no	—
108	Q₈	—	172	2	no	—
109	D₄	—	172	2	no	—
110	D₄	—	172	2	no	—
111	D₄	—	172	2	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	172	1	no	—
115	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
116	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
118	C₈	—	2	2	no	—
119	C₈	—	86	2	no	—
120	C₈	—	86	2	no	—
121	C₂²	—	344	1	no	—
122	C₂²	—	344	1	no	—
123	C₂²	—	344	1	no	—
124	C₂²	#13063321	1	1	yes	characteristic
125	C₄	—	8	1	no	—
126	C₄	—	8	1	no	—
127	C₄	—	344	1	no	—
128	C₄	#13063345	1	2	yes	—
129	C₄	#13063346	1	2	yes	—
130	C₄	#13063348	1	2	yes	—
131	C₂	—	688	1	no	—
132	C₂	#14583280	1	1	yes	characteristic
133	C₂	#14583281	1	1	yes	characteristic
134	C₂	#14583284	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583251

C₂

yes

maximal, characteristic, complemented

#14583249

C₂

yes

maximal, characteristic, complemented

#14583247

C₂

yes

maximal, characteristic

#14583247

C₂

yes

maximal, characteristic

#14583246

C₂

yes

maximal, characteristic

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄₃×#487

C₂

yes

maximal, characteristic, complemented

#13063325

C₂²

yes

characteristic

#13063322

C₂²

yes

—

—

—

—

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

#135

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#487

—

#487

—

#487

D₄₃

yes

characteristic, complemented

#486

—

#486

—

#486

—

C₈²

—

C₄₃

#1711

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

C₂×D₄₃

yes

—

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄²

C₂²×D₄₃

yes

characteristic

105

C₂³

—

172

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

172

—

109

D₄

—

172

—

110

D₄

—

172

—

111

D₄

—

172

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

172

—

115

C₂×C₄

D₄×D₄₃

yes

characteristic

116

C₂×C₄

D₄×D₄₃

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₂²

—

344

—

122

C₂²

—

344

—

123

C₂²

—

344

—

124

C₂²

#13063321

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

344

—

128

C₄

#13063345

yes

—

129

C₄

#13063346

yes

—

130

C₄

#13063348

yes

—

131

C₂

—

688

—

132

C₂

#14583280

yes

characteristic

133

C₂

#14583281

yes

characteristic

134

C₂

#14583284

yes

characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#487	C₂
socle	C₂²×C₄₃	#127
hypercenter	#487	D₄₃
hypocenter	C₄₃	#1711
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#13063321

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#487

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
1. #14583251	C₂	semidirect
2. #14583249	C₂	semidirect
6. C₈×C₄₃⋊C₈	C₂	semidirect
7. C₄₃×#487	C₂	semidirect
70. #487	D₄₃	semidirect
75. C₄₃	#1711	semidirect

H ≅ G/N

type

1. #14583251

C₂

semidirect

2. #14583249

C₂

semidirect

6. C₈×C₄₃⋊C₈

C₂

semidirect

7. C₄₃×#487

C₂

semidirect

70. #487

D₄₃

semidirect

75. C₄₃

#1711

semidirect

Subgroups — #19134208

Conjugacy classes of subgroups

Complements