Finite Group Databasebeta

← #19132910

Subgroups — #19132910

Order 5504.

332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22⋊C8×D43C212yesmaximal, complemented
3#14582624C212yesmaximal, complemented
4#14582623C211yesmaximal, characteristic, complemented
5C43×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D43C411yescharacteristic
7C23×Dic43C411yescharacteristic
8C22×C4×D43C2211yescharacteristic
9C2×C8×D43—22no—
10(C22⋊D43)⋊C4—22no—
11(C22⋊D43)⋊C4—22no—
12C2×Dic43⋊C4C2211yescharacteristic
13C2×(C2×D43)⋊C4C411yescharacteristic
14C2×C4×Dic43C411yescharacteristic
15C22⋊(C43⋊C8)C2212yes—
16(C2×D43)⋊C8—22no—
17C2×C22⋊C4×C43C2211yescharacteristic
18C22⋊C8×C43C2212yes—
19C24×C43C2×C411yescharacteristic
20C23×D43C2×C411yescharacteristic
21C22×C4×C43C2×C411yescharacteristic
22C22×C4×C43C2311yescharacteristic
23C2×C22⋊D43—22no—
24C2×C22⋊D43—22no—
25C2×C22⋊D43C814yescomplemented
26C22×Dic43—21no—
27C22×Dic43—21no—
28C22×Dic43—42no—
29C22×Dic43C2×C411yescharacteristic
30C22×Dic43C2×C411yescharacteristic
31C22×Dic43C2×C411yescharacteristic
32C2×C4×D43—42no—
33C2×C4×D43D412yes—
34C2×C4×D43D412yes—
35C2×C8×C43—22no—
36C22⋊C4×C43—22no—
37(C2×D43)⋊C4—22no—
38Dic43⋊C4—22no—
39C4×Dic43—21no—
40C4×Dic43—21no—
41C2×C43⋊C8—22no—
42C8×D43—44no—
43C23×C43—21no—
44C23×C43—21no—
45C23×C43—41no—
46C23×C43—41no—
47C23×C43C2×C812yescomplemented
48C23×C43C22×C411yescharacteristic
49C22×D43—41no—
50C22×D43—41no—
51C22×D43C22⋊C412yes—
52C22×D43C2×C812yes—
53C22×D43M1612yes—
54C2×C4×C43—21no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43C2×D412yes—
58C22⋊D43—28no—
59C2×Dic43—21no—
60C2×Dic43—21no—
61C2×Dic43—22no—
62C2×Dic43—21no—
63C2×Dic43—42no—
64C2×Dic43—42no—
65C2×Dic43—41no—
66C2×Dic43C22⋊C411yescharacteristic
67C2×Dic43C22⋊C411yescharacteristic
68C2×Dic43C2×C812yescomplemented
69C4×D43—24no—
70C4×D43—42no—
71C8×C43—42no—
72C43⋊C8—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—22no—
76C22×C43—42no—
77C22×C43—42no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43C2×C22⋊C411yescharacteristic
81C22×C43C22×C811yescharacteristic
82C22×C43C2×M1611yescharacteristic
83C2×D43—22no—
84C2×D43—22no—
85C2×D43—42no—
86C2×D43—42no—
87C2×D43C22⋊C814yes—
88C4×C43—22no—
89C4×C43—41no—
90Dic43—22no—
91Dic43—21no—
92Dic43—41no—
93Dic43#9912yes—
94#1459—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—21no—
97C2×C43—42no—
98C2×C43C2×C22⋊C811yescharacteristic
99C2×C43C2×#9911yescharacteristic
100C2×C43#41311yescharacteristic
101D43—24no—
102C2×C4×D4—431no—
103C2×C22⋊C8—432no—
104#324—432no—
105#323—431no—
106#323D4311yescharacteristic, complemented
107C43#145911yescharacteristic, complemented, Sylow
108C22×D4—431no—
109C23×C4—431no—
110C23×C4—431no—
111C22×C8—862no—
112C4×D4—862no—
113C4×D4—862no—
114C2×C4⋊C4—431no—
115C2×C22⋊C4—431no—
116C2×C22⋊C4C2×D4311yescharacteristic
117C2×C42—431no—
118C22⋊C8—432no—
119C22⋊C8—862no—
120C22⋊C8C2×D4312yes—
121C24—431no—
122C24C4×D4311yescharacteristic
123C2×D4—434no—
124C2×D4—862no—
125C2×D4—862no—
126C22×C4—431no—
127C22×C4—431no—
128C22×C4—432no—
129C22×C4—432no—
130C22×C4—431no—
131C22×C4—861no—
132C22×C4—861no—
133C22×C4—1722no—
134C22×C4—1722no—
135C22×C4C4×D4311yescharacteristic
136C22×C4C22×D4311yescharacteristic
137C2×C8—22no—
138C2×C8—862no—
139C2×C8—1724no—
140C4⋊C4—862no—
141C22⋊C4—22no—
142C22⋊C4—862no—
143C42—861no—
144C42—861no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—432no—
150C23—432no—
151C23—432no—
152C23—1721no—
153C23—1721no—
154C23C8×D4312yescomplemented
155C23C2×C4×D4311yescharacteristic
156D4—868no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—431no—
161C2×C4—431no—
162C2×C4—432no—
163C2×C4—864no—
164C2×C4—862no—
165C2×C4—861no—
166C2×C4—861no—
167C2×C4—861no—
168C2×C4—1722no—
169C2×C4—1722no—
170C2×C4—1722no—
171C2×C4—1721no—
172C2×C4D4×D4312yes—
173C8—42no—
174C8—1722no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—434no—
183C22—862no—
184C22—862no—
185C22—1722no—
186C22—1722no—
187C22C22⋊C4×D4311yescharacteristic
188C22C2×C8×D4311yescharacteristic
189C22M16×D4311yescharacteristic
190C4—22no—
191C4—41no—
192C4—432no—
193C4—862no—
194C4—861no—
195C4—1721no—
196C2—21no—
197C2—21no—
198C2—42no—
199C2—864no—
200C2C22⋊C8×D4311yescharacteristic
201C2#99×D4311yescharacteristic
202C2#1458288011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC22×C43C22×C8
FrattiniC22×C4C22×D43
FittingC43×#323C2
socleC22×C43C2×C22⋊C4
hypercenter#323D43
hypocenterC43#1459
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22⋊C8×D43C2semidirect
3. #14582624C2semidirect
4. #14582623C2semidirect
5. C43×#323C2semidirect
25. C2×C22⋊D43C8semidirect
47. C23×C43C2×C8semidirect
68. C2×Dic43C2×C8semidirect
106. #323D43semidirect
107. C43#1459semidirect
154. C23C8×D43semidirect