Finite Group Databasebeta

← #19141637

Subgroups — #19141637

Order 5504.

552 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 121 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#14582828C212yesmaximal, complemented
2#14582824C211yesmaximal, characteristic, complemented
3#14582821C212yesmaximal, complemented
4#14582789C212yesmaximal, complemented
5#14582789C212yesmaximal, complemented
6#14582787C212yesmaximal, complemented
7#14582754C212yesmaximal
8#14582754C211yesmaximal, characteristic
9C43×#399C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic, complemented
12C2×Dic43⋊C4C2212yescomplemented
13C2×C22⋊Dic43C2212yes—
14C2×C22⋊Dic43C2211yescharacteristic
15C2×(C2×D43)⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×C4×Dic43C2212yescomplemented
22C43⋊#95C2212yescomplemented
23C43⋊#95C2212yescomplemented
24C43⋊#95C2211yescharacteristic, complemented
25C43⋊#95C2212yescomplemented
26C2×C4⋊C4×C43C2211yescharacteristic, complemented
27C2×C4⋊C4×C43C2212yescomplemented
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2211yescharacteristic
30#95×C43C2211yescharacteristic, complemented
31C24×C43C2311yescharacteristic
32C23×D43—22no—
33C23×D43—24no—
34C23×D43—41no—
35C23×D43—42no—
36C23×D43—41no—
37C23×D43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C4⋊C4×C43—41no—
46C4⋊C4×C43—42no—
47C22⋊C4×C43—42no—
48C22⋊C4×C43—41no—
49C22⋊Dic43—24no—
50C22⋊Dic43—41no—
51(C2×D43)⋊C4—24no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—42no—
54(C2×D43)⋊C4—42no—
55(C2×D43)⋊C4—42no—
56(C2×D43)⋊C4—42no—
57C4⋊Dic43—41no—
58Dic43⋊C4—42no—
59C4×Dic43—42no—
60C23×C43—22no—
61C23×C43—21no—
62C23×C43—21no—
63C23×C43—22no—
64C23×C43#4112yes—
65C23×C43C2411yescharacteristic
66C22×D43—22no—
67C22×D43—22no—
68C22×D43—22no—
69C22×D43—22no—
70C22×D43—22no—
71C22×D43—22no—
72C22×D43—44no—
73C22×D43—48no—
74C22×D43—48no—
75C22×D43—44no—
76C22×D43—44no—
77C22×D43#4114yes—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C22×C43—22no—
98C22×C43—24no—
99C22×C43—42no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43C2×#4112yes—
103C22×C43C2×#4111yescharacteristic
104C22×C43H(5,𝔽2)12yes—
105C22×C43H(5,𝔽2)11yescharacteristic
106C22×C43H(5,𝔽2)11yescharacteristic
107C2×D43—24no—
108C2×D43—24no—
109C2×D43—24no—
110C2×D43—416no—
111C2×D43—42no—
112C2×D43—42no—
113C2×D43—42no—
114C2×D43—42no—
115C4×C43—42no—
116C4×C43—41no—
117C4×C43—42no—
118C4×C43—41no—
119Dic43—42no—
120Dic43—42no—
121Dic43—42no—
122#2735—431nomaximal, Sylow
123C2×C43—42no—
124C2×C43#53812yes—
125C2×C43#53811yescharacteristic
126C2×C43#55112yes—
127C2×C43#55111yescharacteristic
128C2×C43#56011yescharacteristic
129D43—44no—
130#399D4311yescharacteristic, complemented
131#397—431no—
132#397—432no—
133#396—432no—
134#388—432no—
135#388—432no—
136#388—432no—
137#379—432no—
138#379—431no—
139C43#273511yescharacteristic, complemented, Sylow
140C25—431no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4C2×D4311yescharacteristic, complemented
144C2×C4⋊C4C2×D4312yescomplemented
145C2×C22⋊C4—432no—
146C2×C22⋊C4—432no—
147C2×C22⋊C4—432no—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—432no—
150C2×C22⋊C4—432no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C22⋊C4C2×D4312yes—
154C2×C22⋊C4C2×D4311yescharacteristic
155C2×C42—432no—
156#95—432no—
157#95—431no—
158#95—432no—
159#95—432no—
160#95C2×D4311yescharacteristic, complemented
161C24—432no—
162C24—864no—
163C24—862no—
164C24—1722no—
165C24—1721no—
166C24—1721no—
167C24C22×D4311yescharacteristic
168C22×C4—432no—
169C22×C4—432no—
170C22×C4—432no—
171C22×C4C22×D4311yescharacteristic
172C22×C4C22×D4312yes—
173C22×C4C22×D4312yes—
174C22×C4C22×D4311yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—1722no—
178C4⋊C4—1721no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—864no—
182C22⋊C4—864no—
183C22⋊C4—864no—
184C22⋊C4—1722no—
185C22⋊C4—1722no—
186C22⋊C4—1722no—
187C22⋊C4—1722no—
188C22⋊C4—1721no—
189C42—1722no—
190C23—22no—
191C23—22no—
192C23—21no—
193C23—21no—
194C23—434no—
195C23—862no—
196C23—862no—
197C23—862no—
198C23—862no—
199C23—862no—
200C23—862no—
201C23—1728no—
202C23—1724no—
203C23—1724no—
204C23—1728no—
205C23—1724no—
206C23#1062190212yes—
207C23C23×D4311yescharacteristic
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C22—24no—
228C22—22no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—864no—
233C22—864no—
234C22—864no—
235C22—17216no—
236C22—1722no—
237C22—1722no—
238C22—1722no—
239C22—1722no—
240C22#41×D4312yes—
241C22C2×#1062190211yescharacteristic
242C22#1306337012yes—
243C22#1306337011yescharacteristic
244C22#1306337111yescharacteristic
245C4—41no—
246C4—42no—
247C4—41no—
248C4—42no—
249C4—1722no—
250C4—1722no—
251C4—1722no—
252C2—42no—
253C2—1724no—
254C2#1458348512yes—
255C2#1458348911yescharacteristic
256C2#1458357612yes—
257C2#1458357711yescharacteristic
258C2#1458363611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2735
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #14582828C2semidirect
2. #14582824C2semidirect
3. #14582821C2semidirect
4. #14582789C2semidirect
5. #14582789C2semidirect
6. #14582787C2semidirect
9. C43×#399C2semidirect
11. C2×C4⋊Dic43C22semidirect
12. C2×Dic43⋊C4C22semidirect
21. C2×C4×Dic43C22semidirect
22. C43⋊#95C22semidirect
23. C43⋊#95C22semidirect
24. C43⋊#95C22semidirect
25. C43⋊#95C22semidirect
26. C2×C4⋊C4×C43C22semidirect
27. C2×C4⋊C4×C43C22semidirect
30. #95×C43C22semidirect
130. #399D43semidirect
139. C43#2735semidirect
143. C2×C4⋊C4C2×D43semidirect
144. C2×C4⋊C4C2×D43semidirect
160. #95C2×D43semidirect