Finite Group Databasebeta

← #21449138

Subgroups — #21449138

Order 7808.

1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519746C212yesmaximal, complemented
3#16839674C212yesmaximal, complemented
4#16839671C212yesmaximal, complemented
5#16839641C212yesmaximal, complemented
6#16839638C214yesmaximal, complemented
7#16839625C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
9C2×#11758222—24no—
10C2×#11758222—28no—
11C22×Dic122C2211yescharacteristic, complemented
12C22×D244C2211yescharacteristic, complemented
13C22×C22⋊D61C2214yes—
14C22×C22⋊D61C2212yes—
15C22×C4×D61C2212yescomplemented
16#14519746—28no—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2214yes—
19C2×#11758198C2214yescomplemented
20#14519684C2212yescomplemented
21#14519684C2212yescomplemented
22#14519684C2214yescomplemented
23C25×C61C2211yescharacteristic
24C23×C4×C61C2211yescharacteristic
25C23×C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61—24no—
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2212yes—
29C24×C61—22no—
30C24×C61—24no—
31C24×C61—24no—
32C24×C61—42no—
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35C23×D61C2312yes—
36C22×C4×C61—24no—
37C22×C4×C61—22no—
38C22×C4×C61—42no—
39C22×C4×C61D414yescomplemented
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—28no—
46C2×C22⋊D61—28no—
47C2×C22⋊D61—44no—
48C2×C22⋊D61D418yescomplemented
49C22×Dic61C2314yes—
50C22×Dic61C2312yes—
51#11758222—232no—
52C2×D244—24no—
53C2×D244—22no—
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×Dic122—22no—
58C2×Dic122—24no—
59C22⋊C4×C61—24no—
60C22⋊C4×C61—24no—
61C22⋊Dic61—24no—
62C22⋊Dic61—28no—
63#11758198—44no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—28no—
67C23×C61—24no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—24no—
71C23×C61—416no—
72C23×C61—44no—
73C23×C61—44no—
74C23×C61C2×D414yes—
75C23×C61C2×D412yes—
76C23×C61#4114yescomplemented
77C23×C61C2411yescharacteristic
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—24no—
81C22×D61—24no—
82C22×D61C2×D414yes—
83C2×C4×C61—28no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—24no—
88C2×C4×C61—44no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2×D412yes—
91C22⋊D61—216no—
92C22⋊D61—416no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—24no—
96C2×Dic61—24no—
97C2×Dic61—24no—
98C2×Dic61C2×D414yes—
99D244—28no—
100C4×D61—216no—
101Dic122—28no—
102C22×C61—22no—
103C22×C61—22no—
104C22×C61—28no—
105C22×C61—24no—
106C22×C61—28no—
107C22×C61—416no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—44no—
111C22×C61#12014yes—
112C22×C61C22×D412yes—
113C22×C61C22×D411yescharacteristic
114C22×C61C2×#4112yes—
115C22×C61H(5,𝔽2)12yes—
116C2×D61—24no—
117C2×D61—28no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—44no—
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—42no—
124Dic61—24no—
125Dic61—44no—
126#2404—611nomaximal, Sylow
127C2×C61—24no—
128C2×C61—44no—
129C2×C61C2×#12011yescharacteristic
130C2×C61#52511yescharacteristic
131C2×C61#53511yescharacteristic
132C2×C61#54614yes—
133D61—44no—
134C22×#41—611no—
135C2×#120—612no—
136C22×C22⋊C4D6111yescharacteristic, complemented
137#393—612no—
138#392—612no—
139#386—612no—
140#386—614no—
141#381—611no—
142C61#240411yescharacteristic, complemented, Sylow
143C25C2×D6111yescharacteristic
144C2×#41—1228no—
145C2×#41—1224no—
146C22×Q8—611no—
147C22×D4—612no—
148C22×D4—614no—
149C22×D4—611no—
150C23×C4—612no—
151C23×C4C2×D6111yescharacteristic
152C23×C4C2×D6111yescharacteristic
153#120—1228no—
154C2×C22⋊C4—24no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—614no—
157C2×C22⋊C4—614no—
158C2×C22⋊C4C2×D6112yes—
159C2×C22⋊C4C2×D6112yes—
160#95—612no—
161#95—612no—
162#95—614no—
163C24—24no—
164C24—22no—
165C24—24no—
166C24—42no—
167C24—612no—
168C24C22×D6112yes—
169C24C22×D6111yescharacteristic
170#41—12232no—
171C2×Q8—1224no—
172C2×Q8—1222no—
173C2×D4—618no—
174C2×D4—1224no—
175C2×D4—1224no—
176C2×D4—1224no—
177C2×D4—1228no—
178C2×D4—1228no—
179C2×D4—1222no—
180C2×D4—2444no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—612no—
185C22×C4—614no—
186C22×C4—1224no—
187C22×C4—1224no—
188C22×C4—1224no—
189C22×C4C22⋊D6114yescomplemented
190C22×C4C22×D6112yes—
191C22×C4C22×D6111yescharacteristic
192C22×C4C22×D6111yescharacteristic
193C22⋊C4—24no—
194C22⋊C4—24no—
195C22⋊C4—1228no—
196C22⋊C4—1224no—
197C22⋊C4—2444no—
198C23—22no—
199C23—22no—
200C23—28no—
201C23—24no—
202C23—22no—
203C23—22no—
204C23—24no—
205C23—416no—
206C23—44no—
207C23—44no—
208C23—614no—
209C23—1222no—
210C23—1222no—
211C23—1224no—
212C23—1224no—
213C23#1175822214yescomplemented
214C23D4×D6114yes—
215C23C2×C22⋊D6112yes—
216C23C23×D6111yescharacteristic
217Q8—1228no—
218D4—1228no—
219D4—12216no—
220D4—24416no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—28no—
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—614no—
228C2×C4—12216no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1224no—
232C2×C4—1224no—
233C2×C4—1224no—
234C2×C4C2×C22⋊D6112yes—
235C2×C4C2×C22⋊D6112yes—
236C22—22no—
237C22—22no—
238C22—28no—
239C22—24no—
240C22—28no—
241C22—416no—
242C22—42no—
243C22—42no—
244C22—44no—
245C22—1224no—
246C22—1228no—
247C22—2442no—
248C22—2442no—
249C22—2444no—
250C22#1451974514yes—
251C22C2×D4×D6112yes—
252C22C22×C22⋊D6111yescharacteristic
253C22C2×#1175822212yes—
254C22#1451982212yes—
255C4—22no—
256C4—22no—
257C4—42no—
258C4—1224no—
259C4—2444no—
260C2—24no—
261C2—44no—
262C2—2444no—
263C2C2×#1451974511yescharacteristic
264C2#1684027311yescharacteristic
265C2#1684032911yescharacteristic
266C2#1684040214yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C22⋊C4×C61C2
hypercenterC22×C22⋊C4D61
hypocenterC61#2404
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519746C2semidirect
3. #16839674C2semidirect
4. #16839671C2semidirect
5. #16839641C2semidirect
6. #16839638C2semidirect
7. #16839625C2semidirect
8. C22×C22⋊C4×C61C2semidirect
11. C22×Dic122C22semidirect
12. C22×D244C22semidirect
15. C22×C4×D61C22semidirect
19. C2×#11758198C22semidirect
20. #14519684C22semidirect
21. #14519684C22semidirect
22. #14519684C22semidirect
39. C22×C4×C61D4semidirect
48. C2×C22⋊D61D4semidirect
76. C23×C61#41semidirect
136. C22×C22⋊C4D61semidirect
142. C61#2404semidirect
189. C22×C4C22⋊D61semidirect
213. C23#11758222semidirect