Finite Group Databasebeta

← #21455360

Subgroups — #21455360

Order 7808.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic, complemented
3#16840331C211yesmaximal, characteristic, complemented
4#16840242C211yesmaximal, characteristic, complemented
5#16839985C212yesmaximal, complemented
6#16839978C212yesmaximal, complemented
7#16839963C212yesmaximal, complemented
8#16839958C212yesmaximal, complemented
9#16839764C211yesmaximal, characteristic, complemented
10C2×#14519699C211yesmaximal, characteristic, complemented
11C61×#424C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C22×D244C2211yescharacteristic
15#14519805—24no—
16#14519799—24no—
17C2×Dic244C2211yescharacteristic, complemented
18C2×#11758190C2212yes—
19C2×#11758190C2211yescharacteristic, complemented
20C2×#11758190C2211yescharacteristic, complemented
21C2×D488C2212yes—
22C2×D488C2211yescharacteristic, complemented
23#14519774C2212yes—
24#14519765C2212yes—
25#14519752—21no—
26#14519752—21no—
27#14519747—22no—
28C4×Dic122C2212yescomplemented
29C4×D244C2212yescomplemented
30#14519737—22no—
31#14519735—21no—
32C2×C4⋊Dic61C2211yescharacteristic
33C4⋊C4×D61—21no—
34#14519702C2212yescomplemented
35#14519699C2212yes—
36#14519699C2212yes—
37#14519699C2212yescomplemented
38C2×M16×C61C2211yescharacteristic
39C22×C8×C61C2211yescharacteristic
40#117×C61C2211yescharacteristic
41C4⋊C8×C61C2212yescomplemented
42C4⋊C8×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48#11758222—22no—
49#11758222—22no—
50#11758222—22no—
51#11758222D414yescomplemented
52C2×D244—22no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—22no—
56C2×D244—22no—
57C2×D244C2312yes—
58C2×D244C2311yescharacteristic
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×Dic122C2311yescharacteristic
64C2×Dic122C2311yescharacteristic
65M16×C61—22no—
66C2×C8×C61—22no—
67C2×C8×C61C2311yescharacteristic
68C2×C8×C61C2311yescharacteristic
69C2×C8×C61C2312yes—
70C4⋊C4×C61D411yescharacteristic
71C4⋊C4×C61D411yescharacteristic
72C22⋊C4×C61D412yes—
73C42×C61C2312yes—
74#11758198—22no—
75#11758198—22no—
76#11758198—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61C2312yes—
79#11758196—22no—
80C4×Dic61—22no—
81Dic244—22no—
82D488—24no—
83D488—22no—
84#11758190—22no—
85#11758190—24no—
86#11758190—22no—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89C22×D61—22no—
90C22×D61—21no—
91C22×D61—42no—
92C22×D61—81no—
93C22×D61—81no—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D412yes—
98C2×C4×C61#4112yes—
99C2×C4×C61C2411yescharacteristic
100C22⋊D61—24no—
101C22⋊D61—42no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—81no—
106D244—22no—
107D244—21no—
108D244—21no—
109D244—22no—
110D244—21no—
111D244—42no—
112D244—82no—
113D244—82no—
114D244C2×D412yes—
115C4×D61—24no—
116C4×D61—42no—
117C4×D61—82no—
118Dic122—21no—
119Dic122—21no—
120Dic122—21no—
121Dic122C2×D412yes—
122C8×C61—21no—
123C8×C61—22no—
124C8×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61#12112yes—
128C22×C61C22×D411yescharacteristic
129C2×D61—22no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61—84no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61#12112yes—
142C4×C61C22×D411yescharacteristic
143C4×C61C2×#4111yescharacteristic
144Dic61—22no—
145Dic61—41no—
146Dic61—42no—
147#3045—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61C2×#12111yescharacteristic
150C2×C61#57611yescharacteristic
151C2×C61#57711yescharacteristic
152D61—42no—
153D61—81no—
154D61—82no—
155C2×AGL(1,ℤ/8)—611no—
156C2×#135—611no—
157#535—611no—
158#520—611no—
159#464—612no—
160#463—612no—
161#460—612no—
162#459—612no—
163#424D6111yescharacteristic, complemented
164#417—611no—
165C2×#102—611no—
166C61#304511yescharacteristic, complemented, Sylow
167C2×#41—611no—
168C2×#41—611no—
169C22×D4—611no—
170AGL(1,ℤ/8)—1224no—
171#135—1224no—
172C2×Q16—611no—
173C2×SD16—611no—
174C2×SD16—611no—
175C2×SD16—612no—
176C2×D8—611no—
177C2×D8—612no—
178C2×M16C2×D6111yescharacteristic
179C22×C8C2×D6111yescharacteristic
180#127—612no—
181#124—612no—
182#121—1221no—
183#121—1221no—
184#120—1222no—
185C4×Q8—612no—
186C4×D4—612no—
187C4×D4—1222no—
188#117—1221no—
189#117C2×D6111yescharacteristic
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C4⋊C8C2×D6112yescomplemented
193C4⋊C8C2×D6112yescomplemented
194#103—612no—
195#102—612no—
196#102—612no—
197#102—612no—
198C24—1221no—
199#41—614no—
200#41—1222no—
201#41—1222no—
202#41—1222no—
203C2×Q8—611no—
204C2×Q8—611no—
205C2×D4—611no—
206C2×D4—612no—
207C2×D4—611no—
208C2×D4—1221no—
209C2×D4—1221no—
210C2×D4—1222no—
211C2×D4—1222no—
212C2×D4—1221no—
213C2×D4—1222no—
214C2×D4—1222no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1222no—
218C22×C4—1221no—
219C22×C4C22×D6111yescharacteristic
220Q16—1222no—
221SD16—1222no—
222SD16—1222no—
223SD16—1224no—
224D8—1222no—
225D8—1224no—
226M16—22no—
227C2×C8—22no—
228C2×C8C22×D6111yescharacteristic
229C2×C8C22×D6111yescharacteristic
230C2×C8C22×D6112yes—
231C4⋊C4—612no—
232C4⋊C4—1221no—
233C4⋊C4—1222no—
234C4⋊C4D24411yescharacteristic
235C4⋊C4D24411yescharacteristic
236C22⋊C4—1222no—
237C22⋊C4—1222no—
238C22⋊C4—1222no—
239C22⋊C4D24412yes—
240C42—1222no—
241C42C22×D6112yes—
242C23—1221no—
243C23—1222no—
244C23—1221no—
245C23—4881no—
246C23—4881no—
247C23—2442no—
248C23C2×D24411yescharacteristic
249Q8—612no—
250Q8—1221no—
251Q8—1221no—
252Q8—1221no—
253D4—612no—
254D4—1224no—
255D4—1222no—
256D4—1221no—
257D4—1221no—
258D4—1222no—
259D4—1221no—
260D4—4882no—
261D4—4882no—
262D4—2442no—
263D4—2442no—
264C2×C4—1221no—
265C2×C4—1224no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—4882no—
269C2×C4—4881no—
270C2×C4—2442no—
271C2×C4C2×D24412yes—
272C2×C4C2×D24412yes—
273C2×C4C2×D24411yescharacteristic
274C2×C4D4×D6112yes—
275C2×C4#1175822612yes—
276C2×C4C23×D6111yescharacteristic
277C8—21no—
278C8—21no—
279C8—22no—
280C22—21no—
281C22—21no—
282C22—1222no—
283C22—4884no—
284C22—2441no—
285C22—2442no—
286C22—2441no—
287C22—2442no—
288C22—2441no—
289C22—2442no—
290C22—2441no—
291C22—2441no—
292C22#1451975212yes—
293C22C22×D24411yescharacteristic
294C4—22no—
295C4—22no—
296C4—1222no—
297C4—2441no—
298C4—2442no—
299C4#1451975212yes—
300C4C2×D4×D6111yescharacteristic
301C4C2×#1175822611yescharacteristic
302C2—22no—
303C2—4882no—
304C2—4881no—
305C2—2442no—
306C2C2×#1451975211yescharacteristic
307C2#1684056711yescharacteristic
308C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3045
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519799C2semidirect
3. #16840331C2semidirect
4. #16840242C2semidirect
5. #16839985C2semidirect
6. #16839978C2semidirect
7. #16839963C2semidirect
8. #16839958C2semidirect
9. #16839764C2semidirect
10. C2×#14519699C2semidirect
11. C61×#424C2semidirect
17. C2×Dic244C22semidirect
19. C2×#11758190C22semidirect
20. C2×#11758190C22semidirect
22. C2×D488C22semidirect
28. C4×Dic122C22semidirect
29. C4×D244C22semidirect
34. #14519702C22semidirect
37. #14519699C22semidirect
41. C4⋊C8×C61C22semidirect
42. C4⋊C8×C61C22semidirect
51. #11758222D4semidirect
163. #424D61semidirect
166. C61#3045semidirect
192. C4⋊C8C2×D61semidirect
193. C4⋊C8C2×D61semidirect