Finite Group Databasebeta

← #21456786

Subgroups — #21456786

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
1#16840296C211yesmaximal, characteristic, complemented
2C2×#14519765C211yesmaximal, characteristic, complemented
3#16840146C212yesmaximal, complemented
4#16840117C212yesmaximal, complemented
5#16839985C212yesmaximal, complemented
6#16839978C212yesmaximal, complemented
7#16839920C211yesmaximal, characteristic, complemented
8#16839915C211yesmaximal, characteristic, complemented
9#16839903C211yesmaximal, characteristic, complemented
10#16839898C211yesmaximal, characteristic
11C61×#431C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×Dic244C2212yescomplemented
15C2×#11758190C2212yes—
16C2×#11758190C2212yescomplemented
17C2×D488C2212yes—
18#14519771—21no—
19#14519769C2211yescharacteristic, complemented
20#14519765—21no—
21#14519765—21no—
22#14519765C2212yes—
23#14519765C2212yes—
24#14519765C2211yescharacteristic, complemented
25#14519760—21no—
26#14519756C2211yescharacteristic
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic, complemented
30C4×C22⋊D61—21no—
31#14519734—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34#14519702C2212yescomplemented
35#14519702C2212yescomplemented
36#14519699C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yescomplemented
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42C4×C8×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61D411yescharacteristic
45C22×C4×C61D411yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48C22×Dic61—21no—
49C2×D244—21no—
50C2×D244—42no—
51C2×D244C2312yes—
52C2×D244C2311yescharacteristic
53C2×C4×D61—21no—
54C2×Dic122—21no—
55C2×Dic122—42no—
56C2×Dic122C2312yes—
57C2×Dic122C2311yescharacteristic
58C2×C8×C61C2312yes—
59C2×C8×C61C2312yes—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—22no—
66#11758198—22no—
67#11758198—22no—
68#11758198—22no—
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80Dic244—42no—
81D488—42no—
82#11758190—42no—
83#11758190—42no—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—42no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—42no—
105D244—22no—
106D244—22no—
107D244—22no—
108D244—42no—
109C4×D61—42no—
110Dic122—22no—
111Dic122—22no—
112Dic122—22no—
113Dic122—42no—
114C8×C61—22no—
115C8×C61—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61#13512yes—
119C22×C61C22×D411yescharacteristic
120C2×D61—42no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—41no—
125C2×D61—42no—
126C2×D61—84no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61H(5,𝔽2)12yes—
133Dic61—42no—
134Dic61—41no—
135Dic61—41no—
136Dic61—41no—
137#3211—611nomaximal, Sylow
138C2×C61—22no—
139C2×C61#53511yescharacteristic
140C2×C61C2×#13511yescharacteristic
141C2×C61#57511yescharacteristic
142D61—81no—
143D61—82no—
144#529—611no—
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#431D6111yescharacteristic, complemented
155C61#321111yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4—611no—
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×D8—612no—
162#126—1221no—
163#125—611no—
164#124—612no—
165#124—612no—
166#124—611no—
167#124—1221no—
168#124—1221no—
169#123—1221no—
170C22⋊Q8—611no—
171#121—611no—
172C4×Q8—611no—
173C4×D4—611no—
174C4×D4—1221no—
175#117—1221no—
176C2×C22⋊C4—1221no—
177C2×C22⋊C4—1221no—
178C2×C42C2×D6111yescharacteristic
179C4⋊C8C2×D6112yescomplemented
180#103—612no—
181#103—612no—
182#102—612no—
183#102—612no—
184C22⋊C8C2×D6111yescharacteristic
185C22⋊C8C2×D6111yescharacteristic
186C4×C8C2×D6112yescomplemented
187C24—1221no—
188C2×Q8—612no—
189C2×Q8—611no—
190C2×Q8—1221no—
191C2×Q8—2442no—
192C2×D4—612no—
193C2×D4—611no—
194C2×D4—1221no—
195C2×D4—1221no—
196C2×D4—2442no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4D24411yescharacteristic
200C22×C4D24411yescharacteristic
201C22×C4C22×D6111yescharacteristic
202Q16—2442no—
203SD16—2442no—
204SD16—2442no—
205D8—2442no—
206C2×C8C22×D6112yes—
207C2×C8C22×D6112yes—
208C4⋊C4—611no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1222no—
216C22⋊C4—1222no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C22⋊C4—1221no—
223C42—1221no—
224C42D24411yescharacteristic
225C42D24411yescharacteristic
226C42C22×D6111yescharacteristic
227C42C22×D6111yescharacteristic
228C23—1221no—
229C23—1222no—
230C23—2442no—
231C23—2442no—
232C23—2442no—
233C23C2×D24411yescharacteristic
234Q8—1222no—
235Q8—1222no—
236Q8—1222no—
237Q8—2442no—
238D4—1222no—
239D4—1222no—
240D4—1222no—
241D4—2442no—
242D4—2442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4C2×D24411yescharacteristic
253C2×C4C2×D24411yescharacteristic
254C2×C4C2×D24411yescharacteristic
255C2×C4C2×D24411yescharacteristic
256C2×C4C2×D24411yescharacteristic
257C2×C4C23×D6111yescharacteristic
258C8—22no—
259C8—22no—
260C22—21no—
261C22—21no—
262C22—4884no—
263C22—2441no—
264C22—2442no—
265C22—2441no—
266C22—2442no—
267C22—2442no—
268C22—2441no—
269C22#1451979912yes—
270C22C22×D24411yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—2441no—
277C4—2441no—
278C4—2442no—
279C4—2441no—
280C4#1451982312yes—
281C2—22no—
282C2—4882no—
283C2—4881no—
284C2#1684033111yescharacteristic
285C2C2×#1451979911yescharacteristic
286C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840296C2semidirect
2. C2×#14519765C2semidirect
3. #16840146C2semidirect
4. #16840117C2semidirect
5. #16839985C2semidirect
6. #16839978C2semidirect
7. #16839920C2semidirect
8. #16839915C2semidirect
9. #16839903C2semidirect
11. C61×#431C2semidirect
14. C2×Dic244C22semidirect
16. C2×#11758190C22semidirect
19. #14519769C22semidirect
24. #14519765C22semidirect
28. C4×Dic122C22semidirect
29. C4×D244C22semidirect
34. #14519702C22semidirect
35. #14519702C22semidirect
39. C4⋊C8×C61C22semidirect
42. C4×C8×C61C22semidirect
154. #431D61semidirect
155. C61#3211semidirect
179. C4⋊C8C2×D61semidirect
186. C4×C8C2×D61semidirect