Finite Group Databasebeta

← #19137859

Subgroups — #19137859

Order 5504.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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
2C2×#13063283C211yesmaximal, characteristic, complemented
3#14582838C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, characteristic, complemented
5#14582826C212yesmaximal, complemented
6#14582825C211yesmaximal, characteristic, complemented
7#14582816C212yesmaximal
8C4⋊C4×Dic43C212yesmaximal, complemented
9#14582746C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063287—24no—
16#13063283—24no—
17C2×C4⋊Dic43C2212yes—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×C4×Dic43C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C2×C4×Dic43C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—22no—
50C2×D172—22no—
51C2×C4×D43—24no—
52C2×C4×D43—22no—
53C2×C4×D43—24no—
54C2×C4×D43D414yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—24no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—24no—
64C4⋊Dic43—22no—
65C4⋊Dic43—24no—
66C4×Dic43—24no—
67C4×Dic43—22no—
68C4×Dic43—24no—
69C23×C43C2411yescharacteristic
70C22×D43—21no—
71C22×D43—22no—
72C22×D43—22no—
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—21no—
76C22×D43—21no—
77C22×D43—21no—
78C22×D43C2×D412yes—
79C22×D43#4112yes—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43C2×D412yes—
91C2×C4×C43#4112yes—
92C2×C4×C43#4114yes—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43C2×D412yes—
102C2×Dic43#4114yes—
103D172—28no—
104C4×D43—28no—
105C4×D43—44no—
106C22×C43C22×D411yescharacteristic
107C22×C43C2×#4112yes—
108C22×C43C2×#4111yescharacteristic
109C22×C43C2×#4111yescharacteristic
110C22×C43C2×#4112yes—
111C2×D43—22no—
112C2×D43—22no—
113C2×D43—22no—
114C2×D43—24no—
115C2×D43—22no—
116C2×D43—41no—
117C2×D43—42no—
118C2×D43—42no—
119C2×D43—42no—
120C2×D43—41no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—24no—
124C4×C43—41no—
125C4×C43—42no—
126Dic43—42no—
127Dic43—42no—
128Dic43—41no—
129Dic43#12314yes—
130#2395—431nomaximal, Sylow
131C2×C43C2×#12311yescharacteristic
132C2×C43#52511yescharacteristic
133C2×C43#52912yes—
134C2×C43#52912yes—
135C2×C43#53211yescharacteristic
136D43—42no—
137D43—42no—
138C2×C4×D4—431no—
139C2×#117—431no—
140#400—431no—
141#399—431no—
142#398D4311yescharacteristic, complemented
143#397—431no—
144#397—432no—
145#394—432no—
146C4×C4⋊C4—432no—
147C4×C22⋊C4—432no—
148C4×C22⋊C4—431no—
149C43#239511yescharacteristic, complemented, Sylow
150C22×D4—431no—
151C23×C4—431no—
152C23×C4—431no—
153C4×D4—864no—
154#117—864no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4C2×D4311yescharacteristic
158C2×C4⋊C4C2×D4311yescharacteristic
159C2×C4⋊C4C2×D4312yes—
160C2×C22⋊C4—432no—
161C2×C22⋊C4—431no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—432no—
166C2×C42—432no—
167C2×C42—431no—
168C2×C42—432no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95C2×D4312yes—
174#95C2×D4311yescharacteristic
175C24—431no—
176C24—431no—
177C2×D4—862no—
178C2×D4—862no—
179C2×D4—862no—
180C22×C4—431no—
181C22×C4—434no—
182C22×C4—432no—
183C22×C4—431no—
184C22×C4—432no—
185C22×C4—864no—
186C22×C4—862no—
187C22×C4—864no—
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4312yes—
190C22×C4C22×D4311yescharacteristic
191C22×C4C22×D4311yescharacteristic
192C22×C4C22×D4312yes—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—24no—
196C4⋊C4—862no—
197C4⋊C4—864no—
198C22⋊C4—864no—
199C22⋊C4—862no—
200C22⋊C4—864no—
201C22⋊C4—862no—
202C22⋊C4—864no—
203C22⋊C4—864no—
204C42—864no—
205C42—862no—
206C42—864no—
207C23—432no—
208C23—432no—
209C23—861no—
210C23—862no—
211C23—862no—
212C23—861no—
213C23—861no—
214C23—861no—
215C23—862no—
216C23—862no—
217C23C23×D4311yescharacteristic
218D4—868no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—432no—
230C2×C4—434no—
231C2×C4—868no—
232C2×C4—861no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—1724no—
241C2×C4D4×D4312yes—
242C2×C4#1062190012yes—
243C2×C4#1062190214yes—
244C22—862no—
245C22—862no—
246C22—862no—
247C22—864no—
248C22—862no—
249C22—1721no—
250C22—1722no—
251C22—1722no—
252C22—1722no—
253C22—1721no—
254C22C2×D4×D4311yescharacteristic
255C22#41×D4312yes—
256C22#41×D4311yescharacteristic
257C22C2×#1062190011yescharacteristic
258C22C2×#1062190212yes—
259C4—22no—
260C4—22no—
261C4—24no—
262C4—41no—
263C4—42no—
264C4—434no—
265C4—1722no—
266C4—1721no—
267C4—1722no—
268C2—1722no—
269C2—1722no—
270C2#123×D4311yescharacteristic
271C2#1458340911yescharacteristic
272C2#1458343412yes—
273C2#1458343512yes—
274C2#1458345011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2395
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#13063283C2semidirect
3. #14582838C2semidirect
4. #14582836C2semidirect
5. #14582826C2semidirect
6. #14582825C2semidirect
8. C4⋊C4×Dic43C2semidirect
9. #14582746C2semidirect
10. #14582746C2semidirect
11. C43×#398C2semidirect
142. #398D43semidirect
149. C43#2395semidirect