Finite Group Databasebeta

← #21456758

Subgroups — #21456758

Order 7808.

488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840314C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic
3#16840133C212yesmaximal, complemented
4#16840107C212yesmaximal, complemented
5#16839961C212yesmaximal, complemented
6#16839960C212yesmaximal, complemented
7#16839915C211yesmaximal, characteristic, complemented
8#16839913C211yesmaximal, characteristic, complemented
9#16839912C211yesmaximal, characteristic, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61—21no—
14C22×C22⋊D61—21no—
15C2×#11758190C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×#11758201C2212yescomplemented
18#14519776C2211yescharacteristic, complemented
19#14519775C2211yescharacteristic, complemented
20#14519773—21no—
21#14519773—21no—
22#14519773C2212yes—
23#14519773C2212yes—
24#14519767—21no—
25#14519756C2211yescharacteristic
26#14519754—21no—
27Q8×Dic61C2211yescharacteristic, complemented
28#14519742—21no—
29#14519742C2211yescharacteristic, complemented
30#14519733—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×SD16×C61C2212yescomplemented
40C22⋊Q8×C61C2211yescharacteristic
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61—21no—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—44no—
55C2×C22⋊D61—44no—
56C22×Dic61D411yescharacteristic
57C22×Dic61D411yescharacteristic
58C2×D244—21no—
59C2×D244—42no—
60C2×D244C2312yes—
61C2×Dic122—21no—
62C2×Dic122C2311yescharacteristic
63SD16×C61—42no—
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—21no—
69#11758201—42no—
70#11758200—42no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61D411yescharacteristic
81C4×Dic61D411yescharacteristic
82C4×Dic61C2311yescharacteristic
83C4×Dic61C2311yescharacteristic
84C2×#92418C2312yes—
85#11758190—42no—
86C23×C61—22no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61C2×D411yescharacteristic
91C22×D61—22no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95Q8×C61—22no—
96D4×C61—22no—
97D4×C61—22no—
98D4×C61—42no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—44no—
105C22⋊D61—44no—
106C22⋊D61—44no—
107C22⋊D61—44no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61SD1614yescomplemented
112C2×Dic61C2×D411yescharacteristic
113C2×Dic61C2×D411yescharacteristic
114C2×Dic61C2×D411yescharacteristic
115C2×Dic61C2×D411yescharacteristic
116D244—22no—
117D244—22no—
118D244—42no—
119Dic122—22no—
120Dic122—42no—
121C8×C61—22no—
122#92418—22no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—84no—
129C22×C61C2×SD1612yes—
130C22×C61C22×D411yescharacteristic
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—84no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61H(5,𝔽2)12yes—
139Dic61—21no—
140Dic61—41no—
141Dic61—41no—
142Dic61C2×SD1612yes—
143Dic61C2×SD1612yes—
144Dic61AGL(1,ℤ/8)12yes—
145#3208—611nomaximal, Sylow
146C2×C61—22no—
147C2×C61—82no—
148C2×C61#53511yescharacteristic
149C2×C61C22×SD1611yescharacteristic
150C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
151D61—82no—
152#533—611no—
153C2×#127—611no—
154#492—612no—
155#486—612no—
156#460—612no—
157#460—612no—
158#450—611no—
159#450—611no—
160#450—611no—
161#450D6111yescharacteristic, complemented
162#431—611no—
163C61#320811yescharacteristic, complemented, Sylow
164C22×D4—611no—
165C22×D4—1221no—
166C22×D4—1221no—
167C22×D4C2×D6111yescharacteristic
168C2×SD16—612no—
169C2×SD16—612no—
170C2×SD16—612no—
171C2×SD16C2×D6112yescomplemented
172C4⋊Q8—611no—
173C4⋊Q8—611no—
174#127—612no—
175#127—612no—
176#127—1221no—
177#127—1221no—
178#125—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—1221no—
181C22⋊Q8C2×D6111yescharacteristic
182C4×Q8—611no—
183C4×Q8—611no—
184C4×Q8—1221no—
185#117—1221no—
186C2×C42—611no—
187C4⋊C8—612no—
188#102—612no—
189#102—612no—
190#102—612no—
191#102C2×D6112yescomplemented
192C22⋊C8—611no—
193C22⋊C8C2×D6111yescharacteristic
194C4×C8—612no—
195C24—21no—
196C24—1221no—
197C2×Q8—611no—
198C2×Q8—1221no—
199C2×Q8C22×D6111yescharacteristic
200C2×D4—21no—
201C2×D4—42no—
202C2×D4—612no—
203C2×D4—1222no—
204C2×D4—1222no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1221no—
208C2×D4—2442no—
209C2×D4—2444no—
210C2×D4—2444no—
211C2×D4C22×D6112yes—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4C22×D6111yescharacteristic
215SD16—42no—
216SD16—2442no—
217SD16—2442no—
218SD16—2442no—
219C2×C8—612no—
220C2×C8C22×D6112yes—
221C4⋊C4—21no—
222C4⋊C4—611no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4C22×D6111yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—1221no—
232C42—611no—
233C42—611no—
234C42—611no—
235C42—611no—
236C42—1221no—
237C42—1221no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—1222no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23D4×D6111yescharacteristic
247Q8—22no—
248Q8—1222no—
249Q8—2442no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—1222no—
254D4—1222no—
255D4—2442no—
256D4—2444no—
257D4—2444no—
258D4—2444no—
259D4—2444no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—614no—
267C2×C4—611no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4D4×D6111yescharacteristic
272C2×C4C23×D6111yescharacteristic
273C8—22no—
274C8—1222no—
275C22—21no—
276C22—21no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—84no—
281C22—4884no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22SD16×D6112yes—
286C22C2×D4×D6111yescharacteristic
287C4—21no—
288C4—41no—
289C4—41no—
290C4—612no—
291C4—612no—
292C4—612no—
293C4—1221no—
294C4—2441no—
295C4—2441no—
296C4#1451982212yes—
297C2—22no—
298C2—82no—
299C2—4882no—
300C2#1684032711yescharacteristic
301C2C2×SD16×D6111yescharacteristic
302C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3208
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840314C2semidirect
3. #16840133C2semidirect
4. #16840107C2semidirect
5. #16839961C2semidirect
6. #16839960C2semidirect
7. #16839915C2semidirect
8. #16839913C2semidirect
9. #16839912C2semidirect
10. #16839812C2semidirect
11. C61×#450C2semidirect
15. C2×#11758190C22semidirect
16. C2×#11758200C22semidirect
17. C2×#11758201C22semidirect
18. #14519776C22semidirect
19. #14519775C22semidirect
27. Q8×Dic61C22semidirect
29. #14519742C22semidirect
32. #14519706C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
37. C8×Dic61C22semidirect
39. C2×SD16×C61C22semidirect
41. #102×C61C22semidirect
111. C2×Dic61SD16semidirect
161. #450D61semidirect
163. C61#3208semidirect
171. C2×SD16C2×D61semidirect
191. #102C2×D61semidirect