Finite Group Databasebeta

← #21456807

Subgroups — #21456807

Order 7808.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#16840313C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic, complemented
5#16840124C211yesmaximal, characteristic, complemented
6#16839980C212yesmaximal, complemented
7#16839976C212yesmaximal, complemented
8#16839902C212yesmaximal, complemented
9#16839897C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×Q8×D61C2211yescharacteristic
14C2×D4×D61C2211yescharacteristic
15C2×#11758190C2212yescomplemented
16C2×#11758201C2212yescomplemented
17C2×D488C2212yes—
18C2×#11758199C2212yes—
19#14519774C2211yescharacteristic, complemented
20#14519766—21no—
21#14519766C2211yescharacteristic
22#14519765C2211yescharacteristic
23#14519764C2211yescharacteristic
24#14519763—21no—
25#14519763—21no—
26#14519752—21no—
27#14519752C2212yes—
28#14519739—21no—
29#14519739C2212yescomplemented
30C22⋊C4×D61—21no—
31C22⋊C4×D61—21no—
32C42×D61C2211yescharacteristic
33#14519706C2212yescomplemented
34#14519700C2212yescomplemented
35#14519697C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic, complemented
38C4⋊Q8×C61C2211yescharacteristic, complemented
39#124×C61C2211yescharacteristic
40#103×C61C2212yescomplemented
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C2×Q8×C61—21no—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48#11758226—44no—
49Q8×D61—42no—
50D4×D61—42no—
51C2×D244—22no—
52C2×D244—21no—
53C2×D244—21no—
54C2×D244C2311yescharacteristic
55C2×D244C2312yes—
56C2×C4×D61—21no—
57C2×C4×D61—22no—
58C2×C4×D61D411yescharacteristic
59C2×C4×D61D411yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×Dic122—21no—
62C2×Dic122C2311yescharacteristic
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71#11758201—42no—
72#11758199—42no—
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76#11758198—21no—
77#11758198—22no—
78#11758198—22no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83D488—42no—
84#11758190—42no—
85C23×C61—21no—
86C22×D61—21no—
87C22×D61—22no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61C2×D411yescharacteristic
92Q8×C61—22no—
93Q8×C61—42no—
94D4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2411yescharacteristic
100C22⋊D61—42no—
101C2×Dic61—21no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105D244—22no—
106D244—22no—
107D244—22no—
108D244—42no—
109D244—42no—
110D244—44no—
111C4×D61—22no—
112C4×D61—22no—
113C4×D61—41no—
114C4×D61—44no—
115C4×D61—42no—
116Dic122—22no—
117Dic122—42no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C22×D411yescharacteristic
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—41no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61—41no—
132C2×D61—84no—
133C2×D61AGL(1,ℤ/8)12yes—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61H(5,𝔽2)12yes—
139Dic61—21no—
140Dic61—21no—
141Dic61—21no—
142Dic61—41no—
143#3213—611nomaximal, Sylow
144C2×C61—81no—
145C2×C61#53511yescharacteristic
146C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C61#57511yescharacteristic
148D61—22no—
149D61—82no—
150D61—81no—
151#532—611no—
152C2×#124—611no—
153#496—611no—
154#496—611no—
155#489—611no—
156#489D6111yescharacteristic, complemented
157#463—612no—
158#463—612no—
159#448—612no—
160#447—612no—
161#432—611no—
162C61#321311yescharacteristic, complemented, Sylow
163C2×#41—1221no—
164C22×Q8—611no—
165C22×D4—611no—
166C2×SD16—612no—
167C2×SD16—612no—
168C2×D8—612no—
169C2×D8—612no—
170C4⋊Q8C2×D6111yescharacteristic, complemented
171#127—611no—
172#124—611no—
173#124—611no—
174#124—611no—
175#124—1221no—
176#124—1221no—
177#124—1221no—
178#124C2×D6111yescharacteristic
179#121—612no—
180#121—1221no—
181C4×D4—612no—
182C4×D4—1221no—
183C2×C22⋊C4—1221no—
184C2×C22⋊C4—1221no—
185C2×C42—611no—
186C4⋊C8—612no—
187#103—612no—
188#103C2×D6112yescomplemented
189#102—612no—
190#102C2×D6112yes—
191C22⋊C8—612no—
192#97—611no—
193#97C2×D6111yescharacteristic, complemented
194C24—1221no—
195#41—2444no—
196C2×Q8—21no—
197C2×Q8—611no—
198C2×Q8—1221no—
199C2×Q8—2442no—
200C2×Q8C22×D6111yescharacteristic
201C2×D4—611no—
202C2×D4—612no—
203C2×D4—1222no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4—2442no—
208C2×D4C22×D6111yescharacteristic
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1222no—
213C22×C4—1221no—
214SD16—2442no—
215SD16—2442no—
216D8—2442no—
217D8—2442no—
218C2×C8—612no—
219C2×C8C22×D6112yes—
220C4⋊C4—21no—
221C4⋊C4C22×D6112yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1222no—
227C22⋊C4—1222no—
228C22⋊C4—1221no—
229C22⋊C4—1221no—
230C22⋊C4—1221no—
231C22⋊C4—1221no—
232C42—611no—
233C42—611no—
234C42—611no—
235C42C22×D6111yescharacteristic
236C23—21no—
237C23—611no—
238C23—1221no—
239C23—1222no—
240C23—2442no—
241C23—2442no—
242C23—2442no—
243Q8—22no—
244Q8—42no—
245Q8—1222no—
246Q8—2442no—
247D4—22no—
248D4—1222no—
249D4—1222no—
250D4—1222no—
251D4—2442no—
252D4—2442no—
253D4—2444no—
254D4—2442no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1221no—
263C2×C4—2441no—
264C2×C4—2444no—
265C2×C4—2442no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—1222no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—612no—
275C22—1221no—
276C22—1221no—
277C22—4884no—
278C22—2442no—
279C22—2441no—
280C22—2442no—
281C22—2441no—
282C22—2441no—
283C22—2442no—
284C22C2×D4×D6111yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—1221no—
290C4—1221no—
291C4—1221no—
292C4—2441no—
293C4#1451982312yes—
294C2—81no—
295C2—1222no—
296C2—4881no—
297C2—4882no—
298C2#1684033011yescharacteristic
299C2AGL(1,ℤ/8)×D6111yescharacteristic
300C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #124×D61C2semidirect
3. #16840152C2semidirect
4. #16840151C2semidirect
5. #16840124C2semidirect
6. #16839980C2semidirect
7. #16839976C2semidirect
8. #16839902C2semidirect
9. #16839897C2semidirect
10. #16839817C2semidirect
11. C61×#489C2semidirect
15. C2×#11758190C22semidirect
16. C2×#11758201C22semidirect
19. #14519774C22semidirect
29. #14519739C22semidirect
33. #14519706C22semidirect
34. #14519700C22semidirect
37. #14519688C22semidirect
38. C4⋊Q8×C61C22semidirect
40. #103×C61C22semidirect
42. #97×C61C22semidirect
156. #489D61semidirect
162. C61#3213semidirect
170. C4⋊Q8C2×D61semidirect
188. #103C2×D61semidirect
193. #97C2×D61semidirect