Finite Group Databasebeta

← #19135010

Subgroups — #19135010

Order 5504.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#14583665C211yesmaximal, characteristic, complemented
2#14583410C211yesmaximal, characteristic
3#14582881C211yesmaximal, characteristic, complemented
4#14582863C211yesmaximal, characteristic, complemented
5#14582671C211yesmaximal, characteristic, complemented
6#14582670C211yesmaximal, characteristic, complemented
7C43×#407C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063333—22no—
10#13063331—22no—
11C2×#10621877C2211yescharacteristic
12C2×#10621877C2211yescharacteristic
13M16×D43—22no—
14#13063308C412yes—
15#13063304—21no—
16#13063299—21no—
17#13063294C412yes—
18C4×C22⋊D43—22no—
19#13063284C2211yescharacteristic
20#13063243—21no—
21#13063241—21no—
22C22⋊(C43⋊C8)—22no—
23C23×C4×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25C2×M16×C43C2211yescharacteristic
26C22⋊C8×C43—22no—
27C24×C43C2×C411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43C2×C411yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—22no—
37C2×C22⋊D43C2×C412yes—
38#10621898—21no—
39#10621898—21no—
40#10621898—21no—
41#10621898—21no—
42C2×D172D411yescharacteristic
43C2×C4×D43D412yes—
44C2×Dic86D411yescharacteristic
45M16×C43—21no—
46M16×C43—21no—
47M16×C43—21no—
48M16×C43—21no—
49C2×C8×C43—21no—
50C2×C8×C43D412yescomplemented
51C22⋊Dic43—22no—
52C22⋊Dic43C2×C412yes—
53(C2×D43)⋊C4—22no—
54C4⋊Dic43—21no—
55Dic43⋊C4—22no—
56C4×Dic43—21no—
57#10621877—21no—
58#10621877—21no—
59#10621877—21no—
60#10621877—21no—
61C2×C43⋊C8—21no—
62C2×C43⋊C8D412yescomplemented
63#10621872—24no—
64C8×D43—24no—
65C23×C43—21no—
66C23×C43—21no—
67C23×C43—21no—
68C23×C43—42no—
69C23×C43C22×C411yescharacteristic
70C22×D43C22⋊C412yes—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C2×C4×C43#4111yescharacteristic
84C22⋊D43—22no—
85C22⋊D43—22no—
86C22⋊D43—44no—
87C2×Dic43—22no—
88C2×Dic43C22⋊C412yes—
89D172—21no—
90D172—21no—
91C4×D43—22no—
92C4×D43—22no—
93Dic86—21no—
94Dic86—21no—
95C8×C43—22no—
96C8×C43—41no—
97C43⋊C8—22no—
98C43⋊C8—41no—
99C22×C43—22no—
100C22×C43—22no—
101C22×C43—22no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43C2×C22⋊C411yescharacteristic
108C22×C43C4×D411yescharacteristic
109C22×C43C4×D411yescharacteristic
110C2×D43—22no—
111C2×D43—42no—
112C4×C43—41no—
113C4×C43#12011yescharacteristic
114C4×C43#12111yescharacteristic
115C4×C43#12111yescharacteristic
116C4×C43#12311yescharacteristic
117Dic43—22no—
118Dic43—42no—
119#1891—431nomaximal, Sylow
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43—42no—
124C2×C43#38611yescharacteristic
125D43—42no—
126#568—431no—
127#525—431no—
128#413—431no—
129#407—431no—
130#407D4311yescharacteristic, complemented
131#344—431no—
132#344—431no—
133C43#189111yescharacteristic, complemented, Sylow
134C2×#41—431no—
135C23×C4C2×D4311yescharacteristic
136#131—862no—
137#131—862no—
138C2×M16—431no—
139C2×M16—431no—
140C2×M16—862no—
141C2×M16C2×D4311yescharacteristic
142C2×M16C2×D4311yescharacteristic
143#123—432no—
144C22⋊Q8—861no—
145#121—861no—
146#120—432no—
147C4×D4—862no—
148#117—431no—
149#101—861no—
150#100—861no—
151C22⋊C8—22no—
152C22⋊C8—862no—
153C24C4×D4311yescharacteristic
154#41—861no—
155#41—861no—
156#41—861no—
157#41—861no—
158C2×Q8—431no—
159C2×D4—432no—
160C2×D4—431no—
161C2×D4—862no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—432no—
169C22×C4C4×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—864no—
176M16—861no—
177M16—861no—
178M16—861no—
179M16—861no—
180C2×C8—21no—
181C2×C8—432no—
182C2×C8—864no—
183C2×C8—861no—
184C2×C8C22⋊D4312yescomplemented
185C4⋊C4—862no—
186C4⋊C4—861no—
187C22⋊C4—432no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C42—861no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—432no—
196C23C2×C4×D4311yescharacteristic
197Q8—861no—
198Q8—861no—
199D4—862no—
200D4—862no—
201D4—861no—
202D4—861no—
203D4—1724no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—432no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4#1062189811yescharacteristic
216C2×C4D4×D4311yescharacteristic
217C2×C4D4×D4311yescharacteristic
218C2×C4D4×D4311yescharacteristic
219C2×C4#1062190011yescharacteristic
220C2×C4C2×C22⋊D4311yescharacteristic
221C8—22no—
222C8—41no—
223C8—862no—
224C8—1721no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—862no—
234C22—1722no—
235C22C22⋊C4×D4311yescharacteristic
236C22(C22⋊D43)⋊C411yescharacteristic
237C22C4×C22⋊D4311yescharacteristic
238C4—41no—
239C4—862no—
240C4—1722no—
241C4#1306329311yescharacteristic
242C4#1306329611yescharacteristic
243C4#1306329811yescharacteristic
244C4#1306330711yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—1722no—
250C2#1458277511yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#407C2
socleC2×C43#386
hypercenter#407D43
hypocenterC43#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14583665C2semidirect
3. #14582881C2semidirect
4. #14582863C2semidirect
5. #14582671C2semidirect
6. #14582670C2semidirect
7. C43×#407C2semidirect
50. C2×C8×C43D4semidirect
62. C2×C43⋊C8D4semidirect
130. #407D43semidirect
133. C43#1891semidirect
184. C2×C8C22⋊D43semidirect