Finite Group Databasebeta

← #21456780

Subgroups — #21456780

Order 7808.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14519765C211yesmaximal, characteristic, complemented
2#16840144C212yesmaximal, complemented
3#16840119C212yesmaximal, complemented
4#16839984C212yesmaximal, complemented
5#16839977C212yesmaximal, complemented
6#16839917C211yesmaximal, characteristic, complemented
7#16839912C211yesmaximal, characteristic, complemented
8#16839900C211yesmaximal, characteristic, complemented
9#16839895C211yesmaximal, characteristic
10#16839815C211yesmaximal, characteristic, complemented
11C61×#529C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×#11758202C2212yescomplemented
15C2×#11758200C2212yescomplemented
16C2×#11758201C2212yes—
17C2×#11758199C2212yes—
18#14519765—21no—
19#14519765—21no—
20#14519765C2212yes—
21#14519765C2212yes—
22C2×#11758198—21no—
23C2×#11758198—21no—
24C4⋊#92418C2212yescomplemented
25#14519700C2212yescomplemented
26#14519700C2212yescomplemented
27#14519697C2212yes—
28#14519697C2212yes—
29C22⋊#92418C2211yescharacteristic
30C22⋊#92418C2211yescharacteristic
31C4×#92418C2212yescomplemented
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—42no—
54C2×D244C2312yes—
55C2×Dic122—21no—
56C2×Dic122—42no—
57C2×Dic122C2312yes—
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#11758202—42no—
75#11758201—42no—
76#11758200—42no—
77#11758199—42no—
78#11758198—22no—
79#11758198—22no—
80#11758198—22no—
81#11758198—22no—
82C2×#92418C2312yes—
83C2×#92418C2312yes—
84C23×C61—21no—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—42no—
90Q8×C61—22no—
91D4×C61—22no—
92D4×C61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2411yescharacteristic
106C2×Dic61—22no—
107C2×Dic61—42no—
108D244—22no—
109D244—22no—
110D244—42no—
111Dic122—22no—
112Dic122—22no—
113Dic122—42no—
114#92418—22no—
115#92418—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61#13512yes—
122C22×C61C22×D411yescharacteristic
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—84no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61H(5,𝔽2)12yes—
136Dic61—42no—
137#3211—611nomaximal, Sylow
138C2×C61—22no—
139C2×C61—81no—
140C2×C61#53511yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57511yescharacteristic
143D61—82no—
144#529D6111yescharacteristic, complemented
145C2×#124—611no—
146#495—612no—
147#488—612no—
148#464—612no—
149#463—612no—
150#451—611no—
151#450—611no—
152#448—611no—
153#447—611no—
154#431—611no—
155C61#321111yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4—611no—
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×D8—612no—
162#126—21no—
163#125C2×D6111yescharacteristic, complemented
164#124—612no—
165#124—612no—
166#124—1221no—
167#124—1221no—
168#124C2×D6111yescharacteristic, complemented
169#123—21no—
170C22⋊Q8C2×D6111yescharacteristic
171#121C2×D6111yescharacteristic
172C4×Q8C2×D6111yescharacteristic, complemented
173C4×D4—21no—
174C4×D4C2×D6111yescharacteristic, complemented
175#117—21no—
176C2×C22⋊C4—1221no—
177C2×C22⋊C4—1221no—
178C2×C42C2×D6111yescharacteristic
179C4⋊C8—612no—
180#103—612no—
181#103—612no—
182#102—612no—
183#102—612no—
184C22⋊C8—611no—
185C22⋊C8—611no—
186C4×C8—612no—
187C24—1221no—
188C2×Q8—612no—
189C2×Q8—1221no—
190C2×Q8—2442no—
191C2×Q8C22×D6111yescharacteristic
192C2×D4—21no—
193C2×D4—612no—
194C2×D4—1221no—
195C2×D4—2442no—
196C2×D4C22×D6111yescharacteristic
197C22×C4—21no—
198C22×C4—1221no—
199C22×C4C22⋊D6111yescharacteristic
200C22×C4C22⋊D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202Q16—2442no—
203SD16—2442no—
204SD16—2442no—
205D8—2442no—
206C2×C8—612no—
207C2×C8—612no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4C22×D6111yescharacteristic
213C4⋊C4C22×D6111yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—21no—
218C22⋊C4—21no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C42—21no—
224C42C22⋊D6111yescharacteristic
225C42C22⋊D6111yescharacteristic
226C42C22×D6111yescharacteristic
227C42C22×D6111yescharacteristic
228C23—21no—
229C23—1222no—
230C23—2442no—
231C23—2442no—
232C23—2442no—
233C23C2×C22⋊D6111yescharacteristic
234Q8—22no—
235Q8—1222no—
236Q8—1222no—
237Q8—2442no—
238D4—22no—
239D4—42no—
240D4—1222no—
241D4—1222no—
242D4—2442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—1222no—
251C2×C4—2442no—
252C2×C4C2×C22⋊D6111yescharacteristic
253C2×C4C2×C22⋊D6111yescharacteristic
254C2×C4C2×C22⋊D6111yescharacteristic
255C2×C4C2×C22⋊D6111yescharacteristic
256C2×C4C2×C22⋊D6111yescharacteristic
257C2×C4C23×D6111yescharacteristic
258C8—1222no—
259C8—1222no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—4884no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22#1451979712yes—
270C22C22×C22⋊D6111yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—2442no—
280C4#1451982312yes—
281C2—22no—
282C2—81no—
283C2—4882no—
284C2#1684032611yescharacteristic
285C2C2×#1451979711yescharacteristic
286C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#529C2
socleC22×C61C22×D4
hypercenter#529D61
hypocenterC61#3211
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×#14519765C2semidirect
2. #16840144C2semidirect
3. #16840119C2semidirect
4. #16839984C2semidirect
5. #16839977C2semidirect
6. #16839917C2semidirect
7. #16839912C2semidirect
8. #16839900C2semidirect
10. #16839815C2semidirect
11. C61×#529C2semidirect
14. C2×#11758202C22semidirect
15. C2×#11758200C22semidirect
24. C4⋊#92418C22semidirect
25. #14519700C22semidirect
26. #14519700C22semidirect
31. C4×#92418C22semidirect
33. #125×C61C22semidirect
34. #124×C61C22semidirect
38. C4×Q8×C61C22semidirect
40. C4×D4×C61C22semidirect
144. #529D61semidirect
155. C61#3211semidirect
163. #125C2×D61semidirect
168. #124C2×D61semidirect
172. C4×Q8C2×D61semidirect
174. C4×D4C2×D61semidirect