Finite Group Databasebeta

← #21455953

Subgroups — #21455953

Order 7808.

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

normal subgroups only

This group has 450 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×C4×D244C211yesmaximal, characteristic, complemented
2#16840090C211yesmaximal, characteristic, complemented
3#16840073C211yesmaximal, characteristic, complemented
4#16840059C212yesmaximal, complemented
5#16839974C212yesmaximal, complemented
6#16839912C211yesmaximal, characteristic, complemented
7#16839895C211yesmaximal, characteristic
8#16839872C212yesmaximal, complemented
9#16839860C212yesmaximal, complemented
10#16839819C211yesmaximal, characteristic, complemented
11C61×#529C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C4×D61—21no—
14C2×#11758201C2212yes—
15C2×#11758199C2212yes—
16C4×D244—21no—
17C4×D244—21no—
18C4×D244C2212yes—
19C4×D244C2212yes—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758198—21no—
22#14519710C2212yescomplemented
23#14519708C2212yescomplemented
24C4⋊#92418C2212yescomplemented
25#14519701C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yes—
28#14519697C2212yes—
29C22⋊#92418C2211yescharacteristic
30C22⋊#92418C2211yescharacteristic
31#14519688C2212yescomplemented
32#126×C61—21no—
33#125×C61C2211yescharacteristic, complemented
34#124×C61C2211yescharacteristic, complemented
35#123×C61—21no—
36C22⋊Q8×C61C2211yescharacteristic
37#121×C61C2211yescharacteristic
38C4×Q8×C61C2211yescharacteristic, complemented
39C4×D4×C61—21no—
40C4×D4×C61C2211yescharacteristic, complemented
41#117×C61—21no—
42C2×C42×C61C2211yescharacteristic
43C23×D61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61D411yescharacteristic
49C22×C4×C61D411yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C22×Dic61—21no—
52C2×D244—21no—
53C2×D244—24no—
54C2×D244C2312yes—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—44no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2311yescharacteristic
63C4⋊C4×C61C2311yescharacteristic
64C22⋊C4×C61—21no—
65C22⋊C4×C61—21no—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—21no—
68C22⋊C4×C61—21no—
69C42×C61—21no—
70C42×C61D411yescharacteristic
71C42×C61D411yescharacteristic
72C42×C61C2311yescharacteristic
73C42×C61C2311yescharacteristic
74#11758201—24no—
75#11758199—24no—
76#11758198—22no—
77#11758198—22no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2312yes—
80C2×#92418C2312yes—
81C2×#92418C2312yes—
82C23×C61—21no—
83C23×C61C2×D411yescharacteristic
84C22×D61—24no—
85C22×D61—22no—
86C22×D61—42no—
87C22×D61—42no—
88Q8×C61—22no—
89D4×C61—22no—
90D4×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—42no—
106D244—24no—
107D244—22no—
108D244#4114yes—
109C4×D61—44no—
110C4×D61—44no—
111#92418—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61AGL(1,ℤ/8)12yes—
119C22×C61C22×D411yescharacteristic
120C2×D61—24no—
121C2×D61—48no—
122C2×D61—42no—
123C2×D61—42no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61C2×#4112yes—
133Dic61—42no—
134#3114—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—81no—
137C2×C61#52511yescharacteristic
138C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C61#57511yescharacteristic
140D61—44no—
141#529D6111yescharacteristic, complemented
142C2×C4×D4—611no—
143#483—611no—
144#480—611no—
145#478—612no—
146#463—612no—
147#450—611no—
148#447—611no—
149#442—612no—
150#440—612no—
151#432—611no—
152C61#311411yescharacteristic, complemented, Sylow
153C22×D4—611no—
154C23×C4—1221no—
155C2×SD16—612no—
156C2×D8—612no—
157#126—21no—
158#125C2×D6111yescharacteristic, complemented
159#124C2×D6111yescharacteristic, complemented
160#123—21no—
161C22⋊Q8C2×D6111yescharacteristic
162#121C2×D6111yescharacteristic
163C4×Q8C2×D6111yescharacteristic, complemented
164C4×D4—21no—
165C4×D4—612no—
166C4×D4—612no—
167C4×D4—1221no—
168C4×D4—1221no—
169C4×D4C2×D6111yescharacteristic, complemented
170#117—21no—
171C2×C4⋊C4—611no—
172C2×C22⋊C4—1221no—
173C2×C42C2×D6111yescharacteristic
174#107—612no—
175#106—612no—
176C4⋊C8—612no—
177#103—612no—
178#102—612no—
179#102—612no—
180#102—612no—
181C22⋊C8—611no—
182C22⋊C8—611no—
183#97—612no—
184C24—1221no—
185C2×Q8C22×D6111yescharacteristic
186C2×D4—21no—
187C2×D4—612no—
188C2×D4—1224no—
189C2×D4—1221no—
190C2×D4C22×D6111yescharacteristic
191C22×C4—21no—
192C22×C4—1221no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4—2444no—
196C22×C4C22⋊D6111yescharacteristic
197C22×C4C22⋊D6111yescharacteristic
198C22×C4C22×D6111yescharacteristic
199SD16—1224no—
200D8—1224no—
201C2×C8—612no—
202C2×C8—612no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—612no—
208C4⋊C4—1221no—
209C4⋊C4C22×D6111yescharacteristic
210C4⋊C4C22×D6111yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—1222no—
217C22⋊C4—1222no—
218C42—21no—
219C42C22⋊D6111yescharacteristic
220C42C22⋊D6111yescharacteristic
221C42C22×D6111yescharacteristic
222C42C22×D6111yescharacteristic
223C23—21no—
224C23—1224no—
225C23—1222no—
226C23—2442no—
227C23—2442no—
228C23C2×C22⋊D6111yescharacteristic
229Q8—22no—
230D4—22no—
231D4—42no—
232D4—614no—
233D4—1224no—
234D4—1222no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—1222no—
243C2×C4—2444no—
244C2×C4—2444no—
245C2×C4—2442no—
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C2×C4C2×C22⋊D6111yescharacteristic
249C2×C4C2×C22⋊D6111yescharacteristic
250C2×C4C2×C22⋊D6111yescharacteristic
251C2×C4C23×D6111yescharacteristic
252C8—1222no—
253C8—1222no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—1224no—
260C22—2448no—
261C22—2442no—
262C22—2442no—
263C22#1451980212yes—
264C22C22×C22⋊D6111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—2442no—
274C4#41×D6112yes—
275C2—22no—
276C2—81no—
277C2—2444no—
278C2#1684026911yescharacteristic
279C2C2×#1451980211yescharacteristic
280C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#529C2
socleC22×C61C22×D4
hypercenter#529D61
hypocenterC61#3114
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D244C2semidirect
2. #16840090C2semidirect
3. #16840073C2semidirect
4. #16840059C2semidirect
5. #16839974C2semidirect
6. #16839912C2semidirect
8. #16839872C2semidirect
9. #16839860C2semidirect
10. #16839819C2semidirect
11. C61×#529C2semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
25. #14519701C22semidirect
26. #14519698C22semidirect
31. #14519688C22semidirect
33. #125×C61C22semidirect
34. #124×C61C22semidirect
38. C4×Q8×C61C22semidirect
40. C4×D4×C61C22semidirect
141. #529D61semidirect
152. C61#3114semidirect
158. #125C2×D61semidirect
159. #124C2×D61semidirect
163. C4×Q8C2×D61semidirect
169. C4×D4C2×D61semidirect