Finite Group Databasebeta

← #21455753

Subgroups — #21455753

Order 7808.

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

normal subgroups only

This group has 414 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
1#16840274C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16840106C212yesmaximal, complemented
4#16840105C212yesmaximal, complemented
5#16840089C212yesmaximal, complemented
6#16840088C212yesmaximal, complemented
7#16839805C211yesmaximal, characteristic, complemented
8#16839764C211yesmaximal, characteristic, complemented
9#16839761C211yesmaximal, characteristic, complemented
10#16839725C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519761—21no—
16#14519757C2211yescharacteristic
17#14519757C2211yescharacteristic
18#14519752C2211yescharacteristic
19#14519752C2211yescharacteristic
20#14519747—21no—
21C4×D244—21no—
22C4×D244—21no—
23#14519735—21no—
24#14519735—21no—
25#14519735C2212yes—
26#14519735C2212yes—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×#11758198—21no—
29C2×C4×Dic61—21no—
30#14519710C2212yescomplemented
31#14519708C2212yescomplemented
32#14519702C2212yescomplemented
33#14519700C2212yescomplemented
34#14519699C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yes—
37#14519689C2212yes—
38C2×M16×C61C2211yescharacteristic
39#117×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#107×C61C2212yescomplemented
42#106×C61C2212yescomplemented
43C23×D61D411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C22×Dic61D411yescharacteristic
49#11758222—22no—
50#11758222—22no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244C2311yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—21no—
57C2×C4×D61D411yescharacteristic
58C2×C4×D61D411yescharacteristic
59C2×C4×D61C2311yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×Dic122C2311yescharacteristic
62M16×C61—22no—
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2311yescharacteristic
66C4⋊C4×C61C2312yes—
67C4⋊C4×C61C2311yescharacteristic
68C22⋊C4×C61—21no—
69C42×C61—21no—
70#11758198—22no—
71#11758198—22no—
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2312yes—
80C4×Dic61—22no—
81C4×Dic61—22no—
82#11758194—22no—
83C2×#92418C2312yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61C2×D411yescharacteristic
90C22×D61C2×D411yescharacteristic
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61#4112yes—
97C2×C4×C61#4112yes—
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—42no—
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106D244—21no—
107D244—21no—
108D244—42no—
109D244—42no—
110C4×D61—22no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—42no—
117Dic122—21no—
118Dic122—21no—
119C8×C61—22no—
120#92418—22no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#12312yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—44no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61#12312yes—
139C4×C61C2×#4111yescharacteristic
140C4×C61C2×#4111yescharacteristic
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61—42no—
145#3093—611nomaximal, Sylow
146C2×C61—22no—
147C2×C61C2×#12311yescharacteristic
148C2×C61#57511yescharacteristic
149C2×C61#57511yescharacteristic
150D61—41no—
151D61—41no—
152D61—81no—
153#525—611no—
154C2×#117—611no—
155#485—612no—
156#485—612no—
157#482—612no—
158#482—612no—
159#428—611no—
160#428D6111yescharacteristic, complemented
161#417—611no—
162#417—611no—
163#407—611no—
164C61#309311yescharacteristic, complemented, Sylow
165C2×#41—611no—
166C23×C4—611no—
167C2×M16—611no—
168C2×M16C2×D6111yescharacteristic
169#123—1221no—
170C22⋊Q8—611no—
171C22⋊Q8—611no—
172#121—611no—
173#121—611no—
174#120—1221no—
175C4×D4—1221no—
176C4×D4—1221no—
177#117—612no—
178#117—612no—
179#117—1221no—
180#117—1221no—
181#117C2×D6111yescharacteristic
182C2×C4⋊C4—611no—
183C2×C4⋊C4C2×D6111yescharacteristic
184C2×C22⋊C4—1221no—
185C2×C42—1221no—
186#107—612no—
187#107C2×D6112yescomplemented
188#106—612no—
189#106C2×D6112yescomplemented
190#103—612no—
191#103—612no—
192#102—612no—
193#102—612no—
194C22⋊C8—612no—
195C22⋊C8—612no—
196C24—611no—
197#41—1222no—
198#41—1222no—
199C2×Q8—611no—
200C2×D4—611no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—1221no—
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4C22×D6111yescharacteristic
215M16—22no—
216M16—1222no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—21no—
220C4⋊C4—612no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4C22×D6112yes—
225C4⋊C4C22×D6111yescharacteristic
226C4⋊C4C22×D6111yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—1221no—
229C22⋊C4—1221no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—21no—
235C42—1222no—
236C42—1222no—
237C23—611no—
238C23—611no—
239C23—1222no—
240C23—1221no—
241C23—2441no—
242C23—2441no—
243C23D4×D6111yescharacteristic
244Q8—1221no—
245Q8—1221no—
246D4—1221no—
247D4—1221no—
248D4—2442no—
249D4—2442no—
250D4—2442no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4#1175822212yes—
269C2×C4D4×D6111yescharacteristic
270C2×C4#1175822612yes—
271C2×C4C23×D6111yescharacteristic
272C8—22no—
273C8—1222no—
274C22—21no—
275C22—21no—
276C22—1221no—
277C22—1221no—
278C22—1221no—
279C22—1221no—
280C22—1221no—
281C22—1221no—
282C22—2444no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22#1451976212yes—
287C22C2×D4×D6111yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—1221no—
292C4—1221no—
293C4—2441no—
294C4—2442no—
295C4#1451976212yes—
296C4C2×#1175822211yescharacteristic
297C4C2×#1175822611yescharacteristic
298C2—22no—
299C2—4881no—
300C2—2441no—
301C2—2441no—
302C2C2×#1451976211yescharacteristic
303C2#1684055811yescharacteristic
304C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3093
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
2. C2×#14519735C2semidirect
3. #16840106C2semidirect
4. #16840105C2semidirect
5. #16840089C2semidirect
6. #16840088C2semidirect
7. #16839805C2semidirect
8. #16839764C2semidirect
9. #16839761C2semidirect
10. #16839725C2semidirect
11. C61×#428C2semidirect
30. #14519710C22semidirect
31. #14519708C22semidirect
32. #14519702C22semidirect
33. #14519700C22semidirect
34. #14519699C22semidirect
35. #14519697C22semidirect
41. #107×C61C22semidirect
42. #106×C61C22semidirect
160. #428D61semidirect
164. C61#3093semidirect
187. #107C2×D61semidirect
189. #106C2×D61semidirect