Finite Group Databasebeta

← #21457442

Subgroups — #21457442

Order 7808.

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

normal subgroups only

This group has 556 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
1C2×#14519801C212yesmaximal, complemented
2#16840432C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840138C211yesmaximal, characteristic, complemented
5#16840014C212yesmaximal, complemented
6#16839963C211yesmaximal, characteristic, complemented
7#16839908C212yesmaximal, complemented
8#16839894C212yesmaximal, complemented
9C4×#11758200C211yesmaximal, characteristic, complemented
10#16839839C211yesmaximal, characteristic, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yescomplemented
13C22×D244—21no—
14C2×D4×D61C2212yes—
15#14519801—28no—
16C2×#11758190C2212yescomplemented
17C2×#11758200C2211yescharacteristic
18C2×#11758199C2212yescomplemented
19C2×#11758199C2212yescomplemented
20C2×#11758189C2212yescomplemented
21#14519774C2211yescharacteristic
22#14519773—21no—
23#14519752C2212yes—
24#14519751—21no—
25#14519749—22no—
26#14519748C2212yescomplemented
27#14519747—22no—
28C4×Dic122C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic
30D4×Dic61—21no—
31#14519708C2211yescharacteristic, complemented
32#14519700C2211yescharacteristic, complemented
33#14519699C2212yescomplemented
34#14519698C2211yescharacteristic
35#14519689C2212yescomplemented
36C4×#92418C2211yescharacteristic, complemented
37C2×D8×C61C2212yes—
38#127×C61C2211yescharacteristic, complemented
39C4×D4×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic, complemented
41#102×C61C2212yescomplemented
42C23×D61—22no—
43C2×D4×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61C2312yes—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—22no—
51C22×Dic61—22no—
52#11758224—24no—
53#11758224—42no—
54D4×D61—24no—
55D4×D61—42no—
56C2×D244—22no—
57C2×D244—21no—
58C2×D244—21no—
59C2×D244—44no—
60C2×D244D411yescharacteristic
61C2×D244C2312yes—
62C2×C4×D61C2312yes—
63C2×Dic122C2311yescharacteristic
64D8×C61—24no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—22no—
70#11758200D414yescomplemented
71#11758199—24no—
72#11758199—42no—
73#11758198—22no—
74#11758198D412yes—
75C4⋊Dic61D411yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77#11758196—21no—
78C4×Dic61—21no—
79C2×#92418C2311yescharacteristic
80C2×#92418C2311yescharacteristic
81#11758190—24no—
82#11758189—24no—
83C23×C61—21no—
84C23×C61—22no—
85C22×D61—22no—
86C22×D61—44no—
87C22×D61—44no—
88C22×D61—82no—
89C22×D61C2×D412yes—
90D4×C61—22no—
91D4×C61—21no—
92D4×C61—22no—
93D4×C61—42no—
94D4×C61—81no—
95D4×C61C2×D412yes—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—44no—
102C22⋊D61—44no—
103C22⋊D61—82no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—44no—
107C2×Dic61C2×D412yes—
108D244—22no—
109D244—22no—
110D244—22no—
111D244—44no—
112D244—42no—
113D244—81no—
114C4×D61—22no—
115C4×D61—22no—
116Dic122—21no—
117Dic122C2×D412yescomplemented
118C8×C61—22no—
119#92418—21no—
120#92418C2×D412yescomplemented
121C22×C61—22no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61C22×D411yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—88no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61AGL(1,ℤ/8)12yescomplemented
138C4×C61C22×D411yescharacteristic
139C4×C61H(5,𝔽2)11yescharacteristic
140Dic61—22no—
141Dic61—22no—
142Dic61—41no—
143#3274—611nomaximal, Sylow
144C2×C61—42no—
145C2×C61—82no—
146C2×C61D4211yescharacteristic
147C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C61#57611yescharacteristic
149D61—42no—
150D61—82no—
151C2×AGL(1,ℤ/8)—612no—
152#550—611no—
153D42—611no—
154#493—611no—
155#469—612no—
156#460—611no—
157#459D6111yescharacteristic, complemented
158#449—612no—
159#447—612no—
160C4×SD16—611no—
161#436—611no—
162C61#327411yescharacteristic, complemented, Sylow
163C2×#41—612no—
164C22×D4—612no—
165C22×D4—1221no—
166AGL(1,ℤ/8)—1228no—
167C2×SD16—611no—
168C2×SD16—612no—
169C2×D8—612no—
170C2×D8—612no—
171C2×D8C2×D6112yes—
172C2×M16—612no—
173#127—611no—
174#127—1221no—
175#127C2×D6111yescharacteristic, complemented
176#121—612no—
177#121—612no—
178#121—1222no—
179#121—1221no—
180#120—1222no—
181C4×Q8—611no—
182C4×D4—611no—
183C4×D4—1221no—
184C4×D4C2×D6111yescharacteristic
185#106—611no—
186C4⋊C8C2×D6111yescharacteristic, complemented
187#103—611no—
188#102—611no—
189#102—612no—
190#102C2×D6112yescomplemented
191C22⋊C8—612no—
192C4×C8—611no—
193C24—1222no—
194#41—1224no—
195#41—2442no—
196C2×Q8—611no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—611no—
200C2×D4—612no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—1224no—
204C2×D4—1222no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—2444no—
209C2×D4—2442no—
210C2×D4C22×D6112yes—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—612no—
214C22×C4—1222no—
215SD16—614no—
216SD16—1224no—
217D8—24no—
218D8—1224no—
219D8—2442no—
220M16—1224no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8C22×D6112yes—
224C4⋊C4—611no—
225C4⋊C4—611no—
226C4⋊C4—1221no—
227C4⋊C4C22×D6111yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—612no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C42—1221no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—22no—
236C23—612no—
237C23—1222no—
238C23—4882no—
239C23—2444no—
240C23—2444no—
241Q8—612no—
242Q8—1221no—
243D4—22no—
244D4—21no—
245D4—22no—
246D4—42no—
247D4—81no—
248D4—1222no—
249D4—1222no—
250D4—1222no—
251D4—4881no—
252D4—4882no—
253D4—2444no—
254D4—2444no—
255D4—2444no—
256D4—2442no—
257D4D4×D6112yes—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—612no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1221no—
265C2×C4—2444no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—612no—
271C8—1221no—
272C22—22no—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—1222no—
279C22—1222no—
280C22—1222no—
281C22—4888no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22C2×D4×D6111yescharacteristic
286C4—21no—
287C4—41no—
288C4—1222no—
289C4—1222no—
290C4—2441no—
291C4#1451980112yescomplemented
292C4C2×D4×D6111yescharacteristic
293C4#1451982311yescharacteristic
294C2—42no—
295C2—82no—
296C2—4882no—
297C2—2442no—
298C2#1684039611yescharacteristic
299C2C2×#1451980111yescharacteristic
300C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3274
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. #16840432C2semidirect
3. D4×D244C2semidirect
4. #16840138C2semidirect
5. #16840014C2semidirect
6. #16839963C2semidirect
7. #16839908C2semidirect
8. #16839894C2semidirect
9. C4×#11758200C2semidirect
10. #16839839C2semidirect
11. C61×#459C2semidirect
12. C2×#11758224C22semidirect
16. C2×#11758190C22semidirect
18. C2×#11758199C22semidirect
19. C2×#11758199C22semidirect
20. C2×#11758189C22semidirect
26. #14519748C22semidirect
28. C4×Dic122C22semidirect
31. #14519708C22semidirect
32. #14519700C22semidirect
33. #14519699C22semidirect
35. #14519689C22semidirect
36. C4×#92418C22semidirect
38. #127×C61C22semidirect
40. C4⋊C8×C61C22semidirect
41. #102×C61C22semidirect
70. #11758200D4semidirect
117. Dic122C2×D4semidirect
120. #92418C2×D4semidirect
137. C4×C61AGL(1,ℤ/8)semidirect
157. #459D61semidirect
162. C61#3274semidirect
175. #127C2×D61semidirect
186. C4⋊C8C2×D61semidirect
190. #102C2×D61semidirect
291. C4#14519801semidirect