Finite Group Databasebeta

← #21456635

Subgroups — #21456635

Order 7808.

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

normal subgroups only

This group has 466 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
1#16840273C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic, complemented
3#16840093C211yesmaximal, characteristic, complemented
4#16840087C212yesmaximal, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840015C212yesmaximal, complemented
7#16840008C212yesmaximal, complemented
8#16839915C211yesmaximal, characteristic, complemented
9#16839909C212yesmaximal, complemented
10#16839898C211yesmaximal, characteristic, complemented
11C61×#407C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic, complemented
13C22×D244C2211yescharacteristic
14C22×C22⋊D61—21no—
15C2×#11758190C2212yescomplemented
16C2×D488C2212yescomplemented
17#14519760—21no—
18#14519756C2211yescharacteristic
19#14519756C2211yescharacteristic, complemented
20#14519751—21no—
21#14519751—21no—
22#14519751C2212yes—
23#14519751C2212yes—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic, complemented
26#14519746—21no—
27C4×C22⋊D61—21no—
28C4×C22⋊D61—21no—
29#14519736C2211yescharacteristic, complemented
30C2×C4⋊Dic61C2211yescharacteristic
31C2×#11758198—21no—
32#14519711C2212yescomplemented
33#14519709C2212yescomplemented
34#14519702C2212yescomplemented
35#14519699C2212yescomplemented
36#14519699C2212yescomplemented
37#14519699C2212yescomplemented
38C23×C4×C61C2211yescharacteristic
39C2×M16×C61C2212yescomplemented
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42C22⋊C8×C61C2212yescomplemented
43C24×C61D411yescharacteristic
44C23×D61—21no—
45C22×C4×C61—42no—
46C22×C4×C61D411yescharacteristic
47C22×C4×C61D411yescharacteristic
48C22×C4×C61D411yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—21no—
55C2×C22⋊D61—21no—
56C2×C22⋊D61—21no—
57C2×C22⋊D61—44no—
58C22×Dic61—21no—
59#11758222—42no—
60C2×D244—21no—
61C2×D244—42no—
62C2×D244C2312yes—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×Dic122C2311yescharacteristic
66M16×C61—42no—
67C2×C8×C61C2312yes—
68C2×C8×C61C2312yes—
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—21no—
72#11758198—22no—
73#11758198—22no—
74#11758198—21no—
75#11758198—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2311yescharacteristic
78C4⋊Dic61C2311yescharacteristic
79C4⋊Dic61C2312yes—
80#11758196—21no—
81#11758196—21no—
82C4×Dic61—21no—
83D488—42no—
84#11758190—42no—
85C23×C61—22no—
86C23×C61—41no—
87C23×C61—41no—
88C23×C61C2×D411yescharacteristic
89C23×C61C2×D411yescharacteristic
90C23×C61C2×D411yescharacteristic
91C22×D61—21no—
92C22×D61—22no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—42no—
107C22⋊D61—42no—
108C22⋊D61—44no—
109C22⋊D61—44no—
110C22⋊D61—42no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—42no—
116D244—22no—
117D244—22no—
118D244—22no—
119D244—42no—
120C4×D61—42no—
121Dic122—22no—
122C8×C61—22no—
123C8×C61—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—44no—
133C22×C61AGL(1,ℤ/8)12yes—
134C22×C61C22×D411yescharacteristic
135C2×D61—41no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—42no—
141C2×D61—84no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61H(5,𝔽2)12yes—
146Dic61—41no—
147Dic61—42no—
148Dic61—41no—
149Dic61—41no—
150#3194—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—41no—
153C2×C61—41no—
154C2×C61#53411yescharacteristic
155C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C61#57511yescharacteristic
157D61—81no—
158D61—82no—
159#525—611no—
160C2×#121—611no—
161#483—611no—
162#482—612no—
163#480—611no—
164#469—612no—
165#468—612no—
166#450—611no—
167#449—612no—
168#447—611no—
169#407D6111yescharacteristic, complemented
170C61#319411yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C22×D4—611no—
173C22×D4—1221no—
174C23×C4C2×D6111yescharacteristic
175C2×SD16—612no—
176C2×D8—612no—
177C2×M16C2×D6112yescomplemented
178#123—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—611no—
181#121—612no—
182#121—612no—
183#121—611no—
184#121—611no—
185#121—1221no—
186#121—1221no—
187#120—1221no—
188C4×D4—1221no—
189C4×D4—1221no—
190#117—611no—
191C2×C4⋊C4—611no—
192C2×C22⋊C4—1221no—
193#107—612no—
194#106—612no—
195#103—612no—
196#102—612no—
197#102—612no—
198#102—612no—
199C22⋊C8C2×D6111yescharacteristic
200C22⋊C8C2×D6111yescharacteristic
201C22⋊C8C2×D6112yescomplemented
202C24—1221no—
203C24D24411yescharacteristic
204#41—2442no—
205C2×Q8—611no—
206C2×D4—611no—
207C2×D4—612no—
208C2×D4—1221no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—1222no—
212C2×D4—1222no—
213C2×D4—1221no—
214C2×D4—2442no—
215C2×D4—2444no—
216C22×C4—42no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4D24411yescharacteristic
220C22×C4D24411yescharacteristic
221C22×C4D24411yescharacteristic
222C22×C4C22×D6111yescharacteristic
223C22×C4C22×D6111yescharacteristic
224C22×C4C22×D6111yescharacteristic
225SD16—2442no—
226D8—2442no—
227M16—42no—
228C2×C8C22×D6112yes—
229C2×C8C22×D6112yes—
230C4⋊C4—611no—
231C4⋊C4—611no—
232C4⋊C4—612no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1222no—
240C22⋊C4—1222no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C42—1221no—
244C23—22no—
245C23—41no—
246C23—41no—
247C23—1221no—
248C23—1222no—
249C23—2442no—
250C23—2442no—
251C23—2442no—
252C23C2×D24411yescharacteristic
253C23C2×D24411yescharacteristic
254C23C2×D24411yescharacteristic
255Q8—1222no—
256D4—1222no—
257D4—1222no—
258D4—1222no—
259D4—2442no—
260D4—2442no—
261D4—2444no—
262D4—2444no—
263D4—2442no—
264D4—2442no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1222no—
274C2×C4—1221no—
275C2×C4—2442no—
276C2×C4—2442no—
277C2×C4C2×D24411yescharacteristic
278C2×C4C2×D24411yescharacteristic
279C2×C4C2×D24411yescharacteristic
280C2×C4C23×D6111yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—4884no—
293C22—2442no—
294C22—2441no—
295C22—2441no—
296C22—2442no—
297C22—2441no—
298C22—2442no—
299C22#1451980512yes—
300C22C22×D24411yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—2442no—
305C4—2441no—
306C4—2441no—
307C4—2441no—
308C4#1451982212yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—4882no—
313C2—4881no—
314C2#1684032411yescharacteristic
315C2C2×#1451980511yescharacteristic
316C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #16840273C2semidirect
2. C2×#14519751C2semidirect
3. #16840093C2semidirect
4. #16840087C2semidirect
5. #16840076C2semidirect
6. #16840015C2semidirect
7. #16840008C2semidirect
8. #16839915C2semidirect
9. #16839909C2semidirect
10. #16839898C2semidirect
11. C61×#407C2semidirect
12. C2×#11758222C22semidirect
15. C2×#11758190C22semidirect
16. C2×D488C22semidirect
19. #14519756C22semidirect
25. #14519751C22semidirect
29. #14519736C22semidirect
32. #14519711C22semidirect
33. #14519709C22semidirect
34. #14519702C22semidirect
35. #14519699C22semidirect
36. #14519699C22semidirect
37. #14519699C22semidirect
39. C2×M16×C61C22semidirect
42. C22⋊C8×C61C22semidirect
169. #407D61semidirect
170. C61#3194semidirect
177. C2×M16C2×D61semidirect
201. C22⋊C8C2×D61semidirect