Finite Group Databasebeta

← #21456759

Subgroups — #21456759

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#16840316C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic
3#16840133C212yesmaximal, complemented
4#16840107C212yesmaximal, complemented
5#16839963C211yesmaximal, characteristic, complemented
6#16839962C211yesmaximal, characteristic, complemented
7#16839959C211yesmaximal, characteristic, complemented
8#16839914C212yesmaximal, complemented
9#16839911C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#460C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2212yes—
15C2×#11758190C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×#11758201C2212yescomplemented
18#14519776C2211yescharacteristic, complemented
19#14519775C2211yescharacteristic, complemented
20#14519774C2211yescharacteristic
21#14519773—21no—
22#14519773—21no—
23#14519773C2212yes—
24#14519767—21no—
25#14519757C2211yescharacteristic
26#14519755—21no—
27#14519753C2211yescharacteristic
28C4×Dic122—21no—
29C4×Dic122C2211yescharacteristic, complemented
30#14519734—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic, complemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yes—
37C8×Dic61C2212yescomplemented
38C2×SD16×C61C2212yescomplemented
39#127×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic, complemented
41C4⋊C8×C61C2211yescharacteristic, complemented
42#102×C61C2212yescomplemented
43C23×D61—22no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2312yes—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—22no—
51D4×D61—42no—
52D4×D61—42no—
53D4×D61—44no—
54D4×D61—44no—
55C2×D244—21no—
56C2×D244—21no—
57C2×D244C2312yes—
58C2×C4×D61D411yescharacteristic
59C2×C4×D61D411yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×Dic122—21no—
62C2×Dic122C2311yescharacteristic
63SD16×C61—42no—
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2311yescharacteristic
67C42×C61—21no—
68C42×C61C2311yescharacteristic
69#11758201—42no—
70#11758200—42no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79#11758196—21no—
80C4×Dic61—21no—
81C4×Dic61D411yescharacteristic
82C4×Dic61D411yescharacteristic
83C4×Dic61C2311yescharacteristic
84C2×#92418C2312yes—
85#11758190—42no—
86C23×C61—22no—
87C22×D61—22no—
88C22×D61—44no—
89C22×D61—44no—
90C22×D61—44no—
91C22×D61C2×D411yescharacteristic
92Q8×C61—21no—
93Q8×C61—21no—
94D4×C61—22no—
95D4×C61—22no—
96D4×C61—42no—
97D4×C61—42no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—44no—
104C22⋊D61—44no—
105C22⋊D61—44no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110C2×Dic61C2×D411yescharacteristic
111D244—22no—
112D244—22no—
113D244—42no—
114D244—42no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—22no—
118C4×D61SD1614yescomplemented
119Dic122—21no—
120Dic122—21no—
121Dic122—42no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61C22×D411yescharacteristic
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—88no—
134C2×D61C2×SD1612yes—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61C2×SD1612yes—
139C4×C61H(5,𝔽2)11yescharacteristic
140C4×C61H(5,𝔽2)11yescharacteristic
141Dic61—21no—
142Dic61—41no—
143Dic61—41no—
144Dic61C2×SD1612yes—
145Dic61AGL(1,ℤ/8)12yes—
146#3208—611nomaximal, Sylow
147C2×C61—82no—
148C2×C61#53511yescharacteristic
149C2×C61C22×SD1611yescharacteristic
150C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
151D61—22no—
152D61—82no—
153#533—611no—
154C2×#127—611no—
155#492—612no—
156#486—612no—
157#460—611no—
158#460—611no—
159#460—611no—
160#460D6111yescharacteristic, complemented
161#450—612no—
162#450—612no—
163#431—611no—
164C61#320811yescharacteristic, complemented, Sylow
165C22×D4—612no—
166C22×D4—1221no—
167C22×D4—1221no—
168C2×SD16—612no—
169C2×SD16—612no—
170C2×SD16—612no—
171C2×SD16C2×D6112yescomplemented
172C4⋊Q8—611no—
173C4⋊Q8—611no—
174#127—612no—
175#127—611no—
176#127—1221no—
177#127—1221no—
178#127C2×D6111yescharacteristic
179#125—1221no—
180C22⋊Q8—611no—
181C22⋊Q8—611no—
182C22⋊Q8—1221no—
183C4×Q8—611no—
184C4×Q8—1221no—
185C4×Q8C2×D6111yescharacteristic, complemented
186#117—1221no—
187C2×C42—611no—
188C4⋊C8—611no—
189C4⋊C8C2×D6111yescharacteristic, complemented
190#102—612no—
191#102—612no—
192#102—612no—
193#102C2×D6112yescomplemented
194C22⋊C8—612no—
195C4×C8—612no—
196C24—1222no—
197C2×Q8—611no—
198C2×Q8—1221no—
199C2×Q8C22×D6111yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—612no—
203C2×D4—1222no—
204C2×D4—1222no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—2444no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2444no—
212C2×D4C22×D6112yes—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216SD16—42no—
217SD16—2442no—
218SD16—2442no—
219SD16—2442no—
220C2×C8—612no—
221C2×C8C22×D6112yes—
222C4⋊C4—21no—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4C22×D6111yescharacteristic
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C42—21no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42—1221no—
238C42C22×D6111yescharacteristic
239C23—22no—
240C23—611no—
241C23—1222no—
242C23—2444no—
243C23—2444no—
244C23—2444no—
245Q8—21no—
246Q8—21no—
247Q8—1221no—
248Q8—1221no—
249Q8—2442no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—1222no—
255D4—1222no—
256D4—2442no—
257D4—2444no—
258D4—2444no—
259D4—2444no—
260D4—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—614no—
266C2×C4—611no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4D4×D6111yescharacteristic
273C2×C4D4×D6111yescharacteristic
274C2×C4C23×D6111yescharacteristic
275C8—22no—
276C8—1222no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—612no—
281C22—1221no—
282C22—1221no—
283C22—4888no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22C2×D4×D6111yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—612no—
292C4—612no—
293C4—1221no—
294C4—2441no—
295C4—2441no—
296C4SD16×D6112yes—
297C4#1451982211yescharacteristic
298C4#1451982311yescharacteristic
299C2—82no—
300C2—1222no—
301C2—4882no—
302C2#1684032811yescharacteristic
303C2C2×SD16×D6111yescharacteristic
304C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#460C2
socleC22×C61C22×D4
hypercenter#460D61
hypocenterC61#3208
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840133C2semidirect
4. #16840107C2semidirect
5. #16839963C2semidirect
6. #16839962C2semidirect
7. #16839959C2semidirect
8. #16839914C2semidirect
9. #16839911C2semidirect
10. #16839814C2semidirect
11. C61×#460C2semidirect
15. C2×#11758190C22semidirect
16. C2×#11758200C22semidirect
17. C2×#11758201C22semidirect
18. #14519776C22semidirect
19. #14519775C22semidirect
29. C4×Dic122C22semidirect
32. C4⋊#92418C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
37. C8×Dic61C22semidirect
38. C2×SD16×C61C22semidirect
40. C4×Q8×C61C22semidirect
41. C4⋊C8×C61C22semidirect
42. #102×C61C22semidirect
118. C4×D61SD16semidirect
160. #460D61semidirect
164. C61#3208semidirect
171. C2×SD16C2×D61semidirect
185. C4×Q8C2×D61semidirect
189. C4⋊C8C2×D61semidirect
193. #102C2×D61semidirect