Finite Group Databasebeta

← #21455500

Subgroups — #21455500

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×#14519785C211yesmaximal, characteristic, complemented
3#16840343C211yesmaximal, characteristic, complemented
4#16840331C211yesmaximal, characteristic, complemented
5#16840016C212yesmaximal, complemented
6#16840009C212yesmaximal, complemented
7#16839999C212yesmaximal, complemented
8#16839992C212yesmaximal, complemented
9#16839756C211yesmaximal, characteristic, complemented
10C2×#14519697C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C22×D244C2211yescharacteristic
15#14519805—24no—
16C2×#11758190C2212yes—
17C2×D488C2212yes—
18#14519785—24no—
19C2×#11758189C2212yescomplemented
20C22×#92418C2211yescharacteristic
21C2×C8×D61C2212yescomplemented
22#14519774—21no—
23#14519765—21no—
24#14519757—21no—
25#14519757C2212yescomplemented
26#14519752—21no—
27#14519752C2212yes—
28#14519752C2212yes—
29#14519752C2212yescomplemented
30#14519751—22no—
31#14519747—22no—
32#14519700C2211yescharacteristic, complemented
33#14519700C2211yescharacteristic, complemented
34#14519697C2212yes—
35#14519697C2212yes—
36#14519697C2211yescharacteristic, complemented
37#14519697C2211yescharacteristic, complemented
38C2×M16×C61C2211yescharacteristic
39#117×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#107×C61C2212yescomplemented
42#106×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61D412yes—
48#11758222—22no—
49#11758222—22no—
50#11758222—22no—
51#11758222—22no—
52C2×D244—22no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—22no—
56C2×D244—22no—
57C2×D244—22no—
58C2×D244D411yescharacteristic
59C2×D244C2312yes—
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61C2312yes—
63C2×Dic122D411yescharacteristic
64C2×Dic122C2311yescharacteristic
65M16×C61D414yescomplemented
66C2×C8×C61C2312yes—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2311yescharacteristic
69C4⋊C4×C61C2312yes—
70C4⋊C4×C61C2311yescharacteristic
71C22⋊C4×C61—21no—
72C42×C61—21no—
73#11758198—22no—
74#11758198—22no—
75#11758198—22no—
76#11758198—22no—
77C4⋊Dic61—22no—
78C2×#92418—22no—
79C2×#92418C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81D488—24no—
82#11758190—24no—
83#11758189—24no—
84C8×D61—24no—
85C23×C61C2×D411yescharacteristic
86C22×D61—21no—
87C22×D61—22no—
88C22×D61—42no—
89C22×D61—81no—
90C22×D61—81no—
91C22×D61C2×D412yes—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—81no—
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×Dic61C2×D412yes—
104D244—22no—
105D244—22no—
106D244—21no—
107D244—22no—
108D244—21no—
109D244—42no—
110D244—82no—
111D244—82no—
112D244—82no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—42no—
116Dic122—22no—
117Dic122—21no—
118Dic122—21no—
119C8×C61C2×D414yes—
120#92418—21no—
121#92418—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#12112yes—
125C22×C61C22×D411yescharacteristic
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61—41no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—41no—
135C2×D61—84no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61—41no—
139C4×C61#12112yes—
140C4×C61C22×D411yescharacteristic
141C4×C61C2×#4111yescharacteristic
142Dic61—22no—
143Dic61—41no—
144#3062—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61C2×#12111yescharacteristic
147C2×C61#57611yescharacteristic
148C2×C61#57711yescharacteristic
149D61—42no—
150D61—81no—
151D61—82no—
152C2×AGL(1,ℤ/8)—611no—
153C2×#131—611no—
154#537—611no—
155#535—611no—
156#469—612no—
157#468—612no—
158#466—612no—
159#465—612no—
160#428D6111yescharacteristic, complemented
161#416—611no—
162C2×#102—611no—
163C61#306211yescharacteristic, complemented, Sylow
164C2×#41—611no—
165C2×#41—611no—
166C22×D4—611no—
167AGL(1,ℤ/8)—1224no—
168C2×SD16—612no—
169C2×D8—612no—
170#131—1224no—
171C2×M16—612no—
172C2×M16C2×D6111yescharacteristic
173C22×C8—611no—
174C22×C8—612no—
175#127—1221no—
176#124—1221no—
177C22⋊Q8—612no—
178C22⋊Q8—1221no—
179#121—612no—
180#121—612no—
181#121—612no—
182#121—1221no—
183#121—1222no—
184#120—1222no—
185#117C2×D6111yescharacteristic
186C2×C4⋊C4C2×D6111yescharacteristic
187#107C2×D6112yescomplemented
188#106C2×D6112yescomplemented
189#103—611no—
190#103—611no—
191#102—612no—
192#102—612no—
193#102—611no—
194#102—611no—
195C24—1221no—
196#41—1222no—
197#41—1222no—
198#41—1222no—
199#41—1222no—
200C2×Q8—611no—
201C2×Q8—611no—
202C2×D4—612no—
203C2×D4—611no—
204C2×D4—611no—
205C2×D4—612no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C2×D4—1221no—
212C2×D4—1222no—
213C22×C4—21no—
214C22×C4—612no—
215C22×C4—1221no—
216C22×C4C22×D6111yescharacteristic
217SD16—1224no—
218D8—1224no—
219M16—1224no—
220M16D24414yescomplemented
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—1222no—
224C2×C8—1224no—
225C2×C8C22×D6112yes—
226C4⋊C4—21no—
227C4⋊C4—1222no—
228C4⋊C4C22×D6112yes—
229C4⋊C4C22×D6111yescharacteristic
230C4⋊C4C22×D6111yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—1222no—
233C22⋊C4—1222no—
234C22⋊C4—1222no—
235C22⋊C4—1222no—
236C42—21no—
237C23—612no—
238C23—1221no—
239C23—1222no—
240C23—4881no—
241C23—4881no—
242C23—2442no—
243C23D4×D6111yescharacteristic
244Q8—1222no—
245Q8—1221no—
246Q8—1221no—
247D4—1224no—
248D4—1221no—
249D4—1222no—
250D4—1222no—
251D4—1221no—
252D4—1222no—
253D4—4882no—
254D4—4882no—
255D4—4882no—
256D4—2442no—
257D4—2442no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—81no—
262C2×C4—612no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—2442no—
267C2×C4C2×D24412yes—
268C2×C4D4×D6111yescharacteristic
269C2×C4#1175822612yes—
270C2×C4C23×D6111yescharacteristic
271C8—1221no—
272C8—1221no—
273C8C2×D24414yes—
274C22—21no—
275C22—21no—
276C22—1222no—
277C22—1222no—
278C22—1222no—
279C22—4884no—
280C22—2441no—
281C22—2442no—
282C22—2441no—
283C22—2442no—
284C22—2442no—
285C22—2441no—
286C22#1451975212yes—
287C22C2×D4×D6111yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—1222no—
292C4—2441no—
293C4#1451975212yes—
294C4C22×D24411yescharacteristic
295C4C2×#1175822611yescharacteristic
296C2—22no—
297C2—4882no—
298C2—4881no—
299C2—2442no—
300C2C2×#1451975211yescharacteristic
301C2#1684056611yescharacteristic
302C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3062
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519785C2semidirect
3. #16840343C2semidirect
4. #16840331C2semidirect
5. #16840016C2semidirect
6. #16840009C2semidirect
7. #16839999C2semidirect
8. #16839992C2semidirect
9. #16839756C2semidirect
10. C2×#14519697C2semidirect
11. C61×#428C2semidirect
19. C2×#11758189C22semidirect
21. C2×C8×D61C22semidirect
25. #14519757C22semidirect
29. #14519752C22semidirect
32. #14519700C22semidirect
33. #14519700C22semidirect
36. #14519697C22semidirect
37. #14519697C22semidirect
41. #107×C61C22semidirect
42. #106×C61C22semidirect
65. M16×C61D4semidirect
160. #428D61semidirect
163. C61#3062semidirect
187. #107C2×D61semidirect
188. #106C2×D61semidirect
220. M16D244semidirect