Finite Group Databasebeta

← #21456578

Subgroups — #21456578

Order 7808.

468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14519757C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic
3#16840094C212yesmaximal, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16839992C212yesmaximal, complemented
6#16839990C212yesmaximal, complemented
7#16839914C212yesmaximal, complemented
8#16839903C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10C22⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#481C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic, complemented
13C2×D4×D61—21no—
14C2×D4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C2×#11758190C2212yescomplemented
17C2×#11758200C2212yescomplemented
18C2×C8×D61C2212yescomplemented
19#14519757—21no—
20#14519757—21no—
21#14519757C2212yes—
22#14519757C2212yescomplemented
23#14519752C2211yescharacteristic
24#14519751C2211yescharacteristic
25#14519750—21no—
26#14519749—21no—
27#14519748C2211yescharacteristic
28C2×C4⋊Dic61—21no—
29C4⋊C4×D61C2211yescharacteristic
30C2×#11758198—21no—
31C22⋊C4×D61—21no—
32#14519708C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic, complemented
37#14519689C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic, complemented
40#106×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C22×Dic61—21no—
53C22×Dic61D411yescharacteristic
54D4×D61—42no—
55D4×D61—44no—
56C2×D244—21no—
57C2×D244C2311yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—42no—
60C2×C4×D61D411yescharacteristic
61C2×C4×D61D411yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×C4×D61C2311yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—42no—
66C2×Dic122C2312yes—
67C2×C8×C61C2312yes—
68C4⋊C4×C61—21no—
69C4⋊C4×C61C2312yes—
70C4⋊C4×C61C2311yescharacteristic
71C22⋊C4×C61—21no—
72C22⋊Dic61—21no—
73#11758200—42no—
74#11758198—22no—
75#11758198—22no—
76#11758198—21no—
77#11758198—21no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61C2311yescharacteristic
81#11758196—21no—
82C2×#92418C2312yes—
83#11758190—42no—
84C8×D61—42no—
85C23×C61—21no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88C22×D61—41no—
89C22×D61—41no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61SD1614yescomplemented
94C22×D61C2×D411yescharacteristic
95C22×D61C2×D411yescharacteristic
96D4×C61—22no—
97D4×C61—42no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—42no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—42no—
105C22⋊D61—42no—
106C22⋊D61—42no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—41no—
110C2×Dic61—42no—
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113D244—22no—
114D244—42no—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—42no—
120Dic122—22no—
121Dic122—22no—
122Dic122—42no—
123C8×C61—22no—
124#92418—22no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61C2×SD1612yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—44no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—84no—
141C2×D61C2×SD1612yes—
142C2×D61C2×SD1612yes—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—42no—
146C4×C61H(5,𝔽2)12yes—
147Dic61—21no—
148Dic61—21no—
149Dic61—42no—
150Dic61—41no—
151#3187—611nomaximal, Sylow
152C2×C61—22no—
153C2×C61—81no—
154C2×C61#53411yescharacteristic
155C2×C61C22×SD1611yescharacteristic
156C2×C61#57511yescharacteristic
157D61—22no—
158D61—22no—
159D61—81no—
160C2×C22⋊Q8—611no—
161C2×#121—611no—
162#483—612no—
163#481—611no—
164#481D6111yescharacteristic, complemented
165#465—612no—
166#465—612no—
167#450—612no—
168#448—611no—
169#448—611no—
170C2×C22⋊C8—611no—
171C61#318711yescharacteristic, complemented, Sylow
172C22×Q8—611no—
173C22×D4—611no—
174C22×D4—1221no—
175C23×C4—611no—
176C2×SD16—612no—
177C2×SD16—612no—
178C22×C8—612no—
179C22⋊Q8—612no—
180C22⋊Q8—612no—
181C22⋊Q8—1221no—
182C22⋊Q8—1221no—
183#121—611no—
184#121—611no—
185#121—611no—
186#121—1221no—
187#121—1221no—
188#121C2×D6111yescharacteristic
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4C2×D6111yescharacteristic, complemented
192C2×C22⋊C4—1221no—
193C2×C22⋊C4—1221no—
194#106—612no—
195#106C2×D6112yescomplemented
196#103—612no—
197#103—612no—
198#102—612no—
199#102C2×D6112yescomplemented
200C22⋊C8—611no—
201C22⋊C8—612no—
202C22⋊C8C2×D6111yescharacteristic, complemented
203C24—611no—
204C24—1221no—
205C2×Q8—612no—
206C2×Q8—1221no—
207C2×Q8—2442no—
208C2×D4—21no—
209C2×D4—611no—
210C2×D4—1221no—
211C2×D4—1221no—
212C2×D4—1221no—
213C2×D4—1221no—
214C2×D4—2442no—
215C2×D4—2444no—
216C2×D4C22×D6111yescharacteristic
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—2442no—
226C22×C4C22×D6111yescharacteristic
227SD16—2442no—
228SD16—2442no—
229C2×C8—612no—
230C2×C8—2442no—
231C2×C8C22×D6112yes—
232C4⋊C4—21no—
233C4⋊C4—611no—
234C4⋊C4—1221no—
235C4⋊C4—1222no—
236C4⋊C4—1222no—
237C4⋊C4C22×D6112yes—
238C4⋊C4C22×D6111yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—1221no—
241C22⋊C4—1222no—
242C22⋊C4—1222no—
243C22⋊C4—1221no—
244C22⋊C4—1221no—
245C23—21no—
246C23—611no—
247C23—611no—
248C23—614no—
249C23—1221no—
250C23—2441no—
251C23—2441no—
252C23—2442no—
253C23—2442no—
254C23—2442no—
255C23D4×D6111yescharacteristic
256Q8—1222no—
257Q8—1222no—
258Q8—2442no—
259D4—22no—
260D4—42no—
261D4—1222no—
262D4—2442no—
263D4—2442no—
264D4—2442no—
265D4—2442no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1221no—
275C2×C4—1222no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2442no—
279C2×C4—2441no—
280C2×C4—2442no—
281C2×C4D4×D6111yescharacteristic
282C2×C4C23×D6111yescharacteristic
283C8—22no—
284C8—1222no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—612no—
291C22—612no—
292C22—1221no—
293C22—1221no—
294C22—1221no—
295C22—1221no—
296C22—4884no—
297C22—2444no—
298C22—2441no—
299C22—2441no—
300C22—2441no—
301C22SD16×D6112yes—
302C22C2×D4×D6111yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—1221no—
307C4—1221no—
308C4—2441no—
309C4—2442no—
310C4#1451982312yes—
311C2—22no—
312C2—81no—
313C2—1222no—
314C2—1222no—
315C2—4881no—
316C2#1684032311yescharacteristic
317C2C2×SD16×D6111yescharacteristic
318C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3187
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
3. #16840094C2semidirect
4. #16840080C2semidirect
5. #16839992C2semidirect
6. #16839990C2semidirect
7. #16839914C2semidirect
8. #16839903C2semidirect
9. #16839900C2semidirect
10. C22⋊C8×D61C2semidirect
11. C61×#481C2semidirect
12. C22×Dic122C22semidirect
16. C2×#11758190C22semidirect
17. C2×#11758200C22semidirect
18. C2×C8×D61C22semidirect
22. #14519757C22semidirect
32. #14519708C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
35. #14519697C22semidirect
36. C22⋊#92418C22semidirect
39. C2×C4⋊C4×C61C22semidirect
40. #106×C61C22semidirect
41. #102×C61C22semidirect
42. C22⋊C8×C61C22semidirect
93. C22×D61SD16semidirect
164. #481D61semidirect
171. C61#3187semidirect
191. C2×C4⋊C4C2×D61semidirect
195. #106C2×D61semidirect
199. #102C2×D61semidirect
202. C22⋊C8C2×D61semidirect