Finite Group Databasebeta

← #21457422

Subgroups — #21457422

Order 7808.

546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519804C212yesmaximal, complemented
2#16840415C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840136C211yesmaximal, characteristic, complemented
5#16840011C212yesmaximal, complemented
6#16839958C211yesmaximal, characteristic, complemented
7#16839911C212yesmaximal, complemented
8#16839910C212yesmaximal, complemented
9C4×#11758199C211yesmaximal, characteristic, complemented
10#16839839C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yescomplemented
13C22×D244—21no—
14C2×D4×D61C2212yes—
15#14519804—28no—
16C2×#11758201C2212yescomplemented
17C2×#11758201C2212yescomplemented
18C2×D488C2212yescomplemented
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2212yescomplemented
21#14519774C2211yescharacteristic
22#14519762—22no—
23#14519753C2212yescomplemented
24#14519752—21no—
25#14519752C2212yes—
26#14519751—21no—
27#14519747—22no—
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30C4⋊C4×D61—21no—
31#14519710C2211yescharacteristic, complemented
32#14519699C2212yescomplemented
33#14519698C2211yescharacteristic
34#14519697C2211yescharacteristic, complemented
35#14519689C2212yescomplemented
36C4×#92418C2211yescharacteristic, complemented
37C2×SD16×C61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic, complemented
39C4×D4×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic, complemented
41#103×C61C2212yescomplemented
42C23×D61—22no—
43C2×Q8×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—22no—
47#11758226—24no—
48#11758226—42no—
49D4×D61—24no—
50D4×D61—42no—
51C2×D244—22no—
52C2×D244—22no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244—44no—
56C2×D244D411yescharacteristic
57C2×D244C2312yes—
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61C2312yes—
62SD16×C61—24no—
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69#11758201—24no—
70#11758201—42no—
71#11758199D414yescomplemented
72#11758198—22no—
73#11758198—21no—
74#11758198—22no—
75#11758198D412yes—
76C4⋊Dic61D411yescharacteristic
77C4⋊Dic61C2311yescharacteristic
78#11758196—22no—
79C2×#92418C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81D488—24no—
82#11758189—24no—
83C23×C61—21no—
84C22×D61—21no—
85C22×D61—22no—
86C22×D61—44no—
87C22×D61—44no—
88C22×D61—82no—
89C22×D61C2×D412yes—
90Q8×C61—22no—
91Q8×C61—22no—
92D4×C61—21no—
93D4×C61C2×D412yes—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2411yescharacteristic
100C22⋊D61—44no—
101C2×Dic61—21no—
102C2×Dic61C2×D412yes—
103D244—22no—
104D244—22no—
105D244—21no—
106D244—22no—
107D244—44no—
108D244—44no—
109D244—42no—
110D244—81no—
111D244C2×D412yescomplemented
112C4×D61—22no—
113C4×D61—22no—
114C4×D61—44no—
115C4×D61—42no—
116C8×C61—22no—
117#92418—21no—
118#92418C2×D412yescomplemented
119C22×C61—22no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61C22×D411yescharacteristic
123C2×D61—22no—
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—88no—
133C4×C61—21no—
134C4×C61—42no—
135C4×C61—41no—
136C4×C61AGL(1,ℤ/8)12yescomplemented
137C4×C61C22×D411yescharacteristic
138C4×C61H(5,𝔽2)11yescharacteristic
139Dic61—22no—
140Dic61—41no—
141#3272—611nomaximal, Sylow
142C2×C61—42no—
143C2×C61D4211yescharacteristic
144C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C61#57711yescharacteristic
146D61—42no—
147D61—42no—
148D61—82no—
149C2×AGL(1,ℤ/8)—612no—
150#547—611no—
151D42—611no—
152#492—611no—
153#468—612no—
154#461D6111yescharacteristic, complemented
155#459—611no—
156#450—612no—
157#449—612no—
158C4×D8—611no—
159#436—611no—
160C61#327211yescharacteristic, complemented, Sylow
161C2×#41—612no—
162C22×D4—612no—
163C22×D4—1221no—
164AGL(1,ℤ/8)—1228no—
165C2×SD16—612no—
166C2×SD16—612no—
167C2×SD16C2×D6112yes—
168C2×D8—611no—
169C2×D8—612no—
170C2×M16—612no—
171C4⋊Q8C2×D6111yescharacteristic, complemented
172#127—611no—
173#123—1222no—
174C22⋊Q8—612no—
175#121—612no—
176#121—1221no—
177#121—1221no—
178#120—1222no—
179C4×D4—611no—
180C4×D4—611no—
181C4×D4C2×D6111yescharacteristic
182C2×C4⋊C4—1221no—
183#107—611no—
184C4⋊C8C2×D6111yescharacteristic, complemented
185#103C2×D6112yescomplemented
186#102—611no—
187#102—612no—
188#102—611no—
189C22⋊C8—612no—
190C4×C8—611no—
191C24—1222no—
192#41—1224no—
193#41—2442no—
194C2×Q8C22×D6112yes—
195C2×D4—611no—
196C2×D4—611no—
197C2×D4—612no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—1224no—
202C2×D4—1221no—
203C2×D4—1221no—
204C2×D4—2444no—
205C2×D4—2442no—
206C2×D4C22×D6111yescharacteristic
207C22×C4—21no—
208C22×C4—612no—
209C22×C4—1222no—
210C22×C4—1221no—
211SD16—24no—
212SD16—1224no—
213SD16—2442no—
214D8—614no—
215D8—1224no—
216M16—1224no—
217C2×C8—611no—
218C2×C8—611no—
219C2×C8C22×D6112yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—611no—
223C4⋊C4—611no—
224C4⋊C4—1222no—
225C4⋊C4C22×D6111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—612no—
228C22⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4—1221no—
231C42C22×D6111yescharacteristic
232C23—21no—
233C23—612no—
234C23—1221no—
235C23—1222no—
236C23—4882no—
237C23—2444no—
238C23—2444no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—612no—
243D4—1222no—
244D4—1221no—
245D4—1222no—
246D4—1222no—
247D4—4881no—
248D4—2444no—
249D4—2444no—
250D4—2444no—
251D4—2442no—
252D4D4×D6112yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—612no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—1221no—
260C2×C4—2444no—
261C2×C4—2442no—
262C2×C4D4×D6111yescharacteristic
263C2×C4D4×D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—22no—
266C8—612no—
267C8—1221no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—1222no—
272C22—1222no—
273C22—1222no—
274C22—1222no—
275C22—4888no—
276C22—2442no—
277C22—2442no—
278C22—2442no—
279C22—2441no—
280C22—2441no—
281C22C2×D4×D6111yescharacteristic
282C4—21no—
283C4—41no—
284C4—42no—
285C4—1222no—
286C4—2441no—
287C4#1451980412yescomplemented
288C4C2×D4×D6111yescharacteristic
289C4#1451982311yescharacteristic
290C2—42no—
291C2—4882no—
292C2—2442no—
293C2—2442no—
294C2#1684039611yescharacteristic
295C2C2×#1451980411yescharacteristic
296C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3272
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. #16840415C2semidirect
3. D4×D244C2semidirect
4. #16840136C2semidirect
5. #16840011C2semidirect
6. #16839958C2semidirect
7. #16839911C2semidirect
8. #16839910C2semidirect
9. C4×#11758199C2semidirect
10. #16839839C2semidirect
11. C61×#461C2semidirect
12. C2×#11758226C22semidirect
16. C2×#11758201C22semidirect
17. C2×#11758201C22semidirect
18. C2×D488C22semidirect
20. C2×#11758189C22semidirect
23. #14519753C22semidirect
29. C4×D244C22semidirect
31. #14519710C22semidirect
32. #14519699C22semidirect
34. #14519697C22semidirect
35. #14519689C22semidirect
36. C4×#92418C22semidirect
38. C4⋊Q8×C61C22semidirect
40. C4⋊C8×C61C22semidirect
41. #103×C61C22semidirect
71. #11758199D4semidirect
111. D244C2×D4semidirect
118. #92418C2×D4semidirect
136. C4×C61AGL(1,ℤ/8)semidirect
154. #461D61semidirect
160. C61#3272semidirect
171. C4⋊Q8C2×D61semidirect
184. C4⋊C8C2×D61semidirect
185. #103C2×D61semidirect
287. C4#14519804semidirect