Finite Group Databasebeta

← #21455761

Subgroups — #21455761

Order 7808.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14519752C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic, complemented
3#16840089C212yesmaximal, complemented
4#16840088C212yesmaximal, complemented
5#16840082C212yesmaximal, complemented
6#16840077C212yesmaximal, complemented
7#16839802C211yesmaximal, characteristic, complemented
8#16839768C211yesmaximal, characteristic, complemented
9#16839766C211yesmaximal, characteristic, complemented
10#16839725C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C22×D244—21no—
13C22×D244C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519752—21no—
17#14519752—21no—
18#14519752C2212yes—
19#14519752C2212yes—
20#14519736C2211yescharacteristic
21#14519735C2211yescharacteristic, complemented
22#14519735C2211yescharacteristic, complemented
23#14519734—21no—
24#14519733—21no—
25C4⋊C4×D61C2211yescharacteristic, complemented
26C4⋊C4×D61C2211yescharacteristic, complemented
27C2×#11758198—21no—
28C22⋊C4×D61—21no—
29C42×D61—21no—
30#14519710C2212yescomplemented
31#14519708C2212yescomplemented
32#14519699C2212yescomplemented
33#14519699C2212yescomplemented
34#14519697C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yescomplemented
37#14519689C2212yescomplemented
38C2×M16×C61C2211yescharacteristic
39#117×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#107×C61C2212yescomplemented
42#106×C61C2212yescomplemented
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61D411yescharacteristic
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—22no—
51C2×D244—22no—
52C2×D244—21no—
53C2×D244—44no—
54C2×D244C2312yes—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61D411yescharacteristic
60C2×C4×D61D411yescharacteristic
61C2×C4×D61C2311yescharacteristic
62C2×C4×D61C2311yescharacteristic
63M16×C61—22no—
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2311yescharacteristic
67C4⋊C4×C61C2312yes—
68C4⋊C4×C61C2311yescharacteristic
69C22⋊C4×C61—21no—
70C42×C61—21no—
71C22⋊Dic61—21no—
72#11758198—21no—
73#11758198—21no—
74#11758198—22no—
75#11758198—22no—
76C4⋊Dic61C2311yescharacteristic
77C4⋊Dic61C2311yescharacteristic
78#11758196—21no—
79#11758196—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83#11758194—22no—
84C2×#92418C2312yes—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—41no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61C2×D411yescharacteristic
94C22×D61C2×D411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—42no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61#4112yes—
101C2×C4×C61#4112yes—
102C2×C4×C61C2411yescharacteristic
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108D244—22no—
109D244—22no—
110D244—44no—
111D244—44no—
112D244—42no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—42no—
120C4×D61—42no—
121C8×C61—22no—
122#92418—22no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#12312yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—84no—
137C2×D61AGL(1,ℤ/8)12yes—
138C4×C61—41no—
139C4×C61—42no—
140C4×C61—41no—
141C4×C61#12312yes—
142C4×C61C2×#4111yescharacteristic
143C4×C61C2×#4111yescharacteristic
144Dic61—21no—
145Dic61—21no—
146Dic61—41no—
147Dic61—41no—
148#3094—611nomaximal, Sylow
149C2×C61—22no—
150C2×C61C2×#12311yescharacteristic
151C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C61#57511yescharacteristic
153D61—22no—
154D61—41no—
155D61—82no—
156C2×#121—611no—
157C2×#117—611no—
158#482—612no—
159#482—612no—
160#481—612no—
161#480—612no—
162#428—611no—
163#428D6111yescharacteristic, complemented
164#418—611no—
165#418—611no—
166#407—611no—
167C61#309411yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C22×D4—1221no—
170C23×C4—611no—
171C2×M16—611no—
172C2×M16C2×D6111yescharacteristic
173#121—612no—
174#121—612no—
175#121—1221no—
176#121—1221no—
177#117—611no—
178#117—611no—
179#117—611no—
180#117—1221no—
181#117—1221no—
182#117C2×D6111yescharacteristic
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4C2×D6111yescharacteristic
186C2×C22⋊C4—1221no—
187C2×C22⋊C4—1221no—
188C2×C42—1221no—
189#107—612no—
190#107C2×D6112yescomplemented
191#106—612no—
192#106C2×D6112yescomplemented
193#102—612no—
194#102—612no—
195#102—612no—
196#102—612no—
197C22⋊C8—612no—
198C22⋊C8—612no—
199C24—611no—
200C24—1221no—
201C2×D4—612no—
202C2×D4—1222no—
203C2×D4—1222no—
204C2×D4—1222no—
205C2×D4—1221no—
206C2×D4—1222no—
207C2×D4—2444no—
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1222no—
217C22×C4—1222no—
218C22×C4C22×D6111yescharacteristic
219M16—22no—
220M16—1222no—
221C2×C8—612no—
222C2×C8C22×D6112yes—
223C4⋊C4—21no—
224C4⋊C4—611no—
225C4⋊C4—611no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4C22×D6111yescharacteristic
229C4⋊C4C22×D6111yescharacteristic
230C4⋊C4C22×D6112yes—
231C22⋊C4—21no—
232C22⋊C4—1222no—
233C22⋊C4—1222no—
234C22⋊C4—1221no—
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C42—21no—
238C42—1221no—
239C42—1221no—
240C42—1221no—
241C23—611no—
242C23—611no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—2441no—
247C23—2442no—
248C23—2442no—
249C23—2442no—
250C23D4×D6111yescharacteristic
251D4—1222no—
252D4—1222no—
253D4—2444no—
254D4—2444no—
255D4—2442no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4#1175822212yes—
274C2×C4D4×D6111yescharacteristic
275C2×C4#1175822612yes—
276C2×C4C23×D6111yescharacteristic
277C8—22no—
278C8—1222no—
279C22—21no—
280C22—21no—
281C22—612no—
282C22—1221no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22—1221no—
287C22—4884no—
288C22—2444no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22#1451976212yes—
293C22C2×D4×D6111yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—1221no—
298C4—1221no—
299C4—2441no—
300C4—2441no—
301C4#1451976212yes—
302C4C2×#1175822211yescharacteristic
303C4C2×#1175822611yescharacteristic
304C2—22no—
305C2—1222no—
306C2—4882no—
307C2—2441no—
308C2C2×#1451976211yescharacteristic
309C2AGL(1,ℤ/8)×D6111yescharacteristic
310C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3094
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. #117×D61C2semidirect
3. #16840089C2semidirect
4. #16840088C2semidirect
5. #16840082C2semidirect
6. #16840077C2semidirect
7. #16839802C2semidirect
8. #16839768C2semidirect
9. #16839766C2semidirect
10. #16839725C2semidirect
11. C61×#428C2semidirect
21. #14519735C22semidirect
22. #14519735C22semidirect
25. C4⋊C4×D61C22semidirect
26. C4⋊C4×D61C22semidirect
30. #14519710C22semidirect
31. #14519708C22semidirect
32. #14519699C22semidirect
33. #14519699C22semidirect
34. #14519697C22semidirect
35. #14519697C22semidirect
36. #14519689C22semidirect
37. #14519689C22semidirect
41. #107×C61C22semidirect
42. #106×C61C22semidirect
163. #428D61semidirect
167. C61#3094semidirect
190. #107C2×D61semidirect
192. #106C2×D61semidirect