Finite Group Databasebeta

← #21455073

Subgroups — #21455073

Order 7808.

806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519805C212yesmaximal, complemented
3C2×#14519751C211yesmaximal, characteristic, complemented
4#16839909C214yesmaximal, complemented
5#16839903C212yesmaximal, complemented
6#16839898C212yesmaximal, complemented
7#16839764C212yesmaximal, complemented
8C61×#407C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10C2×#11758222—21no—
11C2×#11758222—28no—
12C2×#11758222C2212yes—
13C2×#11758222C2212yescomplemented
14C22×Dic122C2211yescharacteristic, complemented
15C22×D244C2211yescharacteristic, complemented
16C22×D244C2211yescharacteristic, complemented
17C22×C22⋊D61—21no—
18C22×C22⋊D61—21no—
19C22×C4×D61—21no—
20#14519805—28no—
21C2×#11758190C2214yescomplemented
22C2×D488C2214yescomplemented
23#14519751—21no—
24#14519751—21no—
25#14519751C2212yes—
26#14519751C2212yescomplemented
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C2×#11758198—21no—
29#14519702C2214yescomplemented
30#14519699C2214yescomplemented
31C23×C4×C61C2211yescharacteristic
32C2×M16×C61C2212yescomplemented
33C22⋊C8×C61C2212yescomplemented
34C22⋊C8×C61C2212yescomplemented
35C24×C61D411yescharacteristic
36C23×D61—21no—
37C23×D61—21no—
38C22×C4×C61—24no—
39C22×C4×C61D411yescharacteristic
40C22×C4×C61D411yescharacteristic
41C22×C4×C61D411yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—28no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—44no—
51C22×Dic61—21no—
52C22×Dic61—21no—
53#11758222—28no—
54#11758222—28no—
55#11758222—24no—
56#11758222—24no—
57#11758222—24no—
58#11758222D418yescomplemented
59C2×D244—21no—
60C2×D244—24no—
61C2×D244—24no—
62C2×D244—21no—
63C2×D244C2312yes—
64C2×D244C2312yes—
65C2×C4×D61—28no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×Dic122—21no—
69C2×Dic122—24no—
70C2×Dic122C2312yes—
71M16×C61—24no—
72C2×C8×C61C2314yes—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61—21no—
76C4⋊Dic61C2312yes—
77D488—28no—
78#11758190—28no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—41no—
82C23×C61C2×D411yescharacteristic
83C23×C61C2×D411yescharacteristic
84C23×C61C2×D411yescharacteristic
85C22×D61—24no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D414yes—
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—28no—
104C22⋊D61—28no—
105C22⋊D61—44no—
106C22⋊D61—44no—
107C2×Dic61—24no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—42no—
111D244—24no—
112D244—22no—
113D244—24no—
114D244—42no—
115D244C2×D414yescomplemented
116C4×D61—28no—
117C4×D61—28no—
118Dic122—24no—
119Dic122—22no—
120Dic122C2×D414yescomplemented
121C8×C61—24no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—44no—
130C22×C61#12012yes—
131C22×C61AGL(1,ℤ/8)12yescomplemented
132C22×C61C22×D411yescharacteristic
133C2×D61—24no—
134C2×D61—48no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—84no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61#12012yes—
144C4×C61C22×D412yes—
145Dic61—24no—
146Dic61—42no—
147#3006—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61—22no—
150C2×C61—41no—
151C2×C61C2×#12011yescharacteristic
152C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C61#57511yescharacteristic
154D61—44no—
155D61—82no—
156C22×#41—611no—
157C2×AGL(1,ℤ/8)—612no—
158C2×#121—611no—
159#449—614no—
160#448—612no—
161#447—612no—
162#417—612no—
163#407D6111yescharacteristic, complemented
164C61#300611yescharacteristic, complemented, Sylow
165C2×#41—612no—
166C2×#41—612no—
167C2×#41—1228no—
168C2×#41—1221no—
169C2×#41—1221no—
170C22×Q8—611no—
171C22×D4—611no—
172C22×D4—611no—
173C22×D4—1221no—
174C22×D4—1221no—
175C23×C4—1221no—
176C23×C4C2×D6111yescharacteristic
177AGL(1,ℤ/8)—1228no—
178C2×SD16—614no—
179C2×D8—614no—
180C2×M16C2×D6112yescomplemented
181#121—612no—
182#121—612no—
183#121—1221no—
184#121—1221no—
185C2×C4⋊C4—611no—
186C2×C22⋊C4—1221no—
187#103—614no—
188#102—614no—
189C22⋊C8C2×D6112yescomplemented
190C22⋊C8C2×D6112yescomplemented
191C24—1221no—
192C24—1221no—
193C24D24411yescharacteristic
194#41—618no—
195#41—1224no—
196#41—1224no—
197#41—1228no—
198#41—1228no—
199#41—1224no—
200C2×Q8—612no—
201C2×Q8—1224no—
202C2×Q8—1221no—
203C2×D4—612no—
204C2×D4—612no—
205C2×D4—1224no—
206C2×D4—1228no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1222no—
211C2×D4—1221no—
212C2×D4—1221no—
213C2×D4—1224no—
214C2×D4—2444no—
215C22×C4—24no—
216C22×C4—1228no—
217C22×C4—1221no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4—1221no—
221C22×C4D24411yescharacteristic
222C22×C4D24411yescharacteristic
223C22×C4D24411yescharacteristic
224C22×C4C22×D6111yescharacteristic
225C22×C4C22×D6111yescharacteristic
226C22×C4C22×D6111yescharacteristic
227SD16—1228no—
228D8—1228no—
229M16—24no—
230C2×C8C22×D6114yes—
231C4⋊C4—612no—
232C4⋊C4—1221no—
233C22⋊C4—1222no—
234C22⋊C4—1222no—
235C23—22no—
236C23—22no—
237C23—41no—
238C23—1224no—
239C23—1222no—
240C23—1222no—
241C23—2442no—
242C23—2442no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23C2×D24411yescharacteristic
247C23C2×D24411yescharacteristic
248C23C2×D24411yescharacteristic
249Q8—614no—
250Q8—1224no—
251Q8—1222no—
252D4—614no—
253D4—1224no—
254D4—1228no—
255D4—1228no—
256D4—1222no—
257D4—1224no—
258D4—2444no—
259D4—2444no—
260D4—2442no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—1228no—
267C2×C4—1224no—
268C2×C4—1222no—
269C2×C4—1228no—
270C2×C4—1222no—
271C2×C4—2442no—
272C2×C4C2×D24411yescharacteristic
273C2×C4C2×D24411yescharacteristic
274C2×C4C2×D24411yescharacteristic
275C2×C4D4×D6114yes—
276C2×C4C23×D6111yescharacteristic
277C8—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22—1224no—
287C22—4884no—
288C22—2448no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22—2442no—
293C22—2442no—
294C22#1451974712yes—
295C22#1451980512yescomplemented
296C22C22×D24411yescharacteristic
297C4—21no—
298C4—21no—
299C4—1224no—
300C4—2442no—
301C4#1451974712yes—
302C4C2×D4×D6112yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—4882no—
307C2—2444no—
308C2C2×#1451974711yescharacteristic
309C2C2×#1451980511yescharacteristic
310C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3006
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. C22×#11758222C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519751C2semidirect
4. #16839909C2semidirect
5. #16839903C2semidirect
6. #16839898C2semidirect
7. #16839764C2semidirect
8. C61×#407C2semidirect
13. C2×#11758222C22semidirect
14. C22×Dic122C22semidirect
15. C22×D244C22semidirect
16. C22×D244C22semidirect
21. C2×#11758190C22semidirect
22. C2×D488C22semidirect
26. #14519751C22semidirect
27. C2×C4⋊Dic61C22semidirect
29. #14519702C22semidirect
30. #14519699C22semidirect
32. C2×M16×C61C22semidirect
33. C22⋊C8×C61C22semidirect
34. C22⋊C8×C61C22semidirect
58. #11758222D4semidirect
115. D244C2×D4semidirect
120. Dic122C2×D4semidirect
131. C22×C61AGL(1,ℤ/8)semidirect
163. #407D61semidirect
164. C61#3006semidirect
180. C2×M16C2×D61semidirect
189. C22⋊C8C2×D61semidirect
190. C22⋊C8C2×D61semidirect
295. C22#14519805semidirect