Finite Group Databasebeta

← #19132932

Subgroups — #19132932

Order 5504.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13063287C211yesmaximal, characteristic
2#14582861C212yesmaximal, complemented
3#14582625C211yesmaximal, characteristic, complemented
4#14582622C212yesmaximal, complemented
5C43×#324C211yesmaximal, characteristic, complemented
6C22×D172C411yescharacteristic
7C22×C4×D43C411yescharacteristic
8C22×C4×D43C2211yescharacteristic
9C2×#10621872—22no—
10#13063287—22no—
11#13063287—22no—
12C2×(C2×D43)⋊C4C411yescharacteristic
13C2×(C2×D43)⋊C4C2211yescharacteristic
14C2×C4×Dic43C411yescharacteristic
15C22⋊(C43⋊C8)C2212yes—
16(C2×D43)⋊C8—22no—
17C2×C4⋊C4×C43C2211yescharacteristic
18C22⋊C8×C43C2212yes—
19C23×D43C2×C411yescharacteristic
20C23×D43C2×C411yescharacteristic
21C22×C4×C43C2×C411yescharacteristic
22C22×C4×C43C2×C411yescharacteristic
23C22×C4×C43C2311yescharacteristic
24C22×Dic43C2×C411yescharacteristic
25C22×Dic43C2×C411yescharacteristic
26C2×D172—22no—
27C2×D172—22no—
28C2×D172—22no—
29C2×C4×D43—21no—
30C2×C4×D43—21no—
31C2×C4×D43—42no—
32C2×C4×D43—42no—
33C2×C4×D43D412yes—
34C2×C4×D43D412yes—
35C2×C8×C43—22no—
36C4⋊C4×C43—22no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—22no—
39C4×Dic43—21no—
40C4×Dic43—21no—
41C2×C43⋊C8—22no—
42#10621872—44no—
43C23×C43C22×C411yescharacteristic
44C22×D43—21no—
45C22×D43—21no—
46C22×D43—21no—
47C22×D43—21no—
48C22×D43—41no—
49C22×D43—41no—
50C22×D43—41no—
51C22×D43—41no—
52C22×D43C22⋊C412yes—
53C22×D43M1612yescomplemented
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43M1612yescomplemented
60C2×C4×C43C2×D412yes—
61C2×Dic43—22no—
62C2×Dic43—21no—
63C2×Dic43—41no—
64C2×Dic43C22⋊C411yescharacteristic
65C2×Dic43C22⋊C411yescharacteristic
66D172—28no—
67C4×D43—24no—
68C4×D43—42no—
69C4×D43—42no—
70C4×D43—42no—
71C8×C43—42no—
72C43⋊C8—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43C2×C22⋊C411yescharacteristic
76C22×C43C2×M1611yescharacteristic
77C22×C43C2×M1611yescharacteristic
78C2×D43—22no—
79C2×D43—22no—
80C2×D43—22no—
81C2×D43—22no—
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—42no—
85C2×D43—41no—
86C2×D43—41no—
87C2×D43—42no—
88C4×C43—22no—
89C4×C43—22no—
90C4×C43—41no—
91Dic43—21no—
92Dic43—41no—
93Dic43#9912yes—
94#1465—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—21no—
97C2×C43#40711yescharacteristic
98C2×C43C2×#9911yescharacteristic
99C2×C43#41311yescharacteristic
100D43—42no—
101D43—42no—
102C2×C4×D4—431no—
103#407—432no—
104#324—431no—
105#324D4311yescharacteristic, complemented
106#323—432no—
107C43#146511yescharacteristic, complemented, Sylow
108C22×D4—431no—
109C23×C4—431no—
110C23×C4—431no—
111C2×M16—862no—
112C4×D4—862no—
113C4×D4—862no—
114C2×C4⋊C4C2×D4311yescharacteristic
115C2×C22⋊C4—431no—
116C2×C22⋊C4—431no—
117C2×C42—431no—
118C22⋊C8—432no—
119C22⋊C8—862no—
120C22⋊C8C2×D4312yes—
121C24—431no—
122C24—431no—
123C2×D4—862no—
124C2×D4—862no—
125C2×D4—862no—
126C22×C4—431no—
127C22×C4—432no—
128C22×C4—432no—
129C22×C4—431no—
130C22×C4—861no—
131C22×C4—861no—
132C22×C4—1722no—
133C22×C4—1722no—
134C22×C4C4×D4311yescharacteristic
135C22×C4C4×D4311yescharacteristic
136C22×C4C22×D4311yescharacteristic
137M16—1724no—
138C2×C8—22no—
139C2×C8—862no—
140C4⋊C4—22no—
141C22⋊C4—862no—
142C22⋊C4—862no—
143C42—861no—
144C42—861no—
145C23—432no—
146C23—432no—
147C23—861no—
148C23—861no—
149C23—861no—
150C23—861no—
151C23—1721no—
152C23—1721no—
153C23—1721no—
154C23—1721no—
155C23C2×C4×D4311yescharacteristic
156D4—868no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—431no—
163C2×C4—431no—
164C2×C4—864no—
165C2×C4—862no—
166C2×C4—861no—
167C2×C4—1722no—
168C2×C4—1722no—
169C2×C4—1722no—
170C2×C4—1721no—
171C2×C4#1062187212yescomplemented
172C2×C4D4×D4312yes—
173C8—42no—
174C8—1722no—
175C22—21no—
176C22—21no—
177C22—862no—
178C22—862no—
179C22—862no—
180C22—862no—
181C22—1722no—
182C22—1722no—
183C22—1722no—
184C22—1722no—
185C22—1721no—
186C22—1721no—
187C22C22⋊C4×D4311yescharacteristic
188C22M16×D4311yescharacteristic
189C22C2×#1062187211yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—432no—
194C4—861no—
195C4—1721no—
196C2—21no—
197C2—21no—
198C2—1722no—
199C2—1722no—
200C2#1458286111yescharacteristic
201C2#99×D4311yescharacteristic
202C2#1458288211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#324C2
socleC22×C43C2×C22⋊C4
hypercenter#324D43
hypocenterC43#1465
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14582861C2semidirect
3. #14582625C2semidirect
4. #14582622C2semidirect
5. C43×#324C2semidirect
53. C22×D43M16semidirect
59. C2×C4×C43M16semidirect
105. #324D43semidirect
107. C43#1465semidirect
171. C2×C4#10621872semidirect