Finite Group Databasebeta

← #21456803

Subgroups — #21456803

Order 7808.

444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840307C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic, complemented
3#16840150C212yesmaximal, complemented
4#16840120C212yesmaximal, complemented
5#16839976C212yesmaximal, complemented
6#16839975C212yesmaximal, complemented
7#16839903C211yesmaximal, characteristic, complemented
8#16839900C211yesmaximal, characteristic, complemented
9#16839896C211yesmaximal, characteristic, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C22×Dic122C2211yescharacteristic
14C2×#11758190C2212yescomplemented
15C2×#11758200C2212yescomplemented
16C2×#11758199C2212yes—
17#14519776C2211yescharacteristic, complemented
18#14519773C2211yescharacteristic, complemented
19#14519764—21no—
20#14519764—21no—
21#14519764C2212yes—
22#14519764C2212yes—
23#14519763—21no—
24#14519751C2211yescharacteristic
25#14519749—21no—
26D4×Dic61C2211yescharacteristic, complemented
27#14519739C2211yescharacteristic, complemented
28#14519737—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×D8×C61C2212yes—
40#121×C61C2211yescharacteristic
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61—42no—
47C2×D4×C61C2312yes—
48C2×D4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C2×C22⋊D61—21no—
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61D411yescharacteristic
56C22×Dic61D411yescharacteristic
57#11758224—44no—
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×Dic122—21no—
61C2×Dic122—21no—
62C2×Dic122—42no—
63C2×Dic122C2312yes—
64D8×C61—42no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—22no—
69C22⋊Dic61—22no—
70C22⋊Dic61—22no—
71C22⋊Dic61—22no—
72C22⋊Dic61—21no—
73#11758200—42no—
74#11758199—42no—
75#11758198—21no—
76#11758198—21no—
77C4⋊Dic61C2311yescharacteristic
78#11758196—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C4×Dic61C2311yescharacteristic
83C2×#92418C2312yes—
84#11758190—42no—
85C23×C61—22no—
86C23×C61—21no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61C2×D411yescharacteristic
91C22×D61—21no—
92D4×C61—22no—
93D4×C61—22no—
94D4×C61—22no—
95D4×C61—42no—
96D4×C61—42no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—42no—
102C22⋊D61—42no—
103C22⋊D61—42no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113C2×Dic61C2×D411yescharacteristic
114D244—22no—
115C4×D61—42no—
116Dic122—22no—
117Dic122—22no—
118Dic122—42no—
119Dic122—42no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61—84no—
131C22×C61AGL(1,ℤ/8)12yes—
132C22×C61C22×D411yescharacteristic
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61H(5,𝔽2)12yes—
139Dic61—21no—
140Dic61—21no—
141Dic61—21no—
142Dic61—21no—
143Dic61—42no—
144Dic61—41no—
145#3213—611nomaximal, Sylow
146C2×C61—22no—
147C2×C61—81no—
148C2×C61—82no—
149C2×C61#53511yescharacteristic
150C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
151C2×C61#57511yescharacteristic
152D61—81no—
153#532—611no—
154C2×#124—611no—
155#496—612no—
156#489—612no—
157#463—612no—
158#463—612no—
159#448—611no—
160#448—611no—
161#447—611no—
162#447D6111yescharacteristic, complemented
163#432—611no—
164C61#321311yescharacteristic, complemented, Sylow
165C2×#41—1221no—
166C22×Q8—611no—
167C22×D4C2×D6111yescharacteristic
168C2×SD16—612no—
169C2×SD16—612no—
170C2×D8—612no—
171C2×D8C2×D6112yes—
172C4⋊Q8—611no—
173#127—611no—
174#124—612no—
175#124—612no—
176#124—1221no—
177#124—1221no—
178#124—1221no—
179#121—611no—
180#121—1221no—
181#121C2×D6111yescharacteristic
182C4×D4—611no—
183C4×D4—611no—
184C4×D4—1221no—
185C2×C22⋊C4—1221no—
186C2×C22⋊C4—1221no—
187C2×C42—611no—
188C4⋊C8—612no—
189#103—612no—
190#103—612no—
191#102—612no—
192#102C2×D6112yes—
193C22⋊C8—611no—
194C22⋊C8C2×D6111yescharacteristic
195#97—612no—
196C24—21no—
197#41—2444no—
198C2×Q8—612no—
199C2×Q8—1221no—
200C2×Q8—1221no—
201C2×Q8—2442no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—42no—
205C2×D4—611no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4C22×D6112yes—
210C2×D4C22×D6111yescharacteristic
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4C22×D6111yescharacteristic
217SD16—2442no—
218SD16—2442no—
219D8—42no—
220D8—2442no—
221C2×C8—612no—
222C2×C8C22×D6112yes—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4C22×D6111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—1221no—
228C22⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42—611no—
238C23—21no—
239C23—22no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—1221no—
244C23D4×D6111yescharacteristic
245Q8—1222no—
246Q8—1222no—
247Q8—2442no—
248Q8—2442no—
249D4—22no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—1222no—
255D4—2442no—
256D4—2442no—
257D4—2442no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—2442no—
268C2×C4—2441no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4D4×D6111yescharacteristic
272C2×C4C23×D6111yescharacteristic
273C8—22no—
274C8—1222no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—42no—
281C22—42no—
282C22—41no—
283C22—84no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22#1451980112yes—
288C22C2×D4×D6111yescharacteristic
289C4—21no—
290C4—41no—
291C4—1221no—
292C4—1221no—
293C4—1221no—
294C4—1221no—
295C4—2441no—
296C4—2442no—
297C4#1451982212yes—
298C2—22no—
299C2—82no—
300C2—81no—
301C2—4881no—
302C2#1684032711yescharacteristic
303C2C2×#1451980111yescharacteristic
304C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840307C2semidirect
2. C2×#14519764C2semidirect
3. #16840150C2semidirect
4. #16840120C2semidirect
5. #16839976C2semidirect
6. #16839975C2semidirect
7. #16839903C2semidirect
8. #16839900C2semidirect
9. #16839896C2semidirect
10. #16839816C2semidirect
11. C61×#447C2semidirect
14. C2×#11758190C22semidirect
15. C2×#11758200C22semidirect
17. #14519776C22semidirect
18. #14519773C22semidirect
26. D4×Dic61C22semidirect
27. #14519739C22semidirect
32. #14519706C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
37. #14519687C22semidirect
162. #447D61semidirect
164. C61#3213semidirect