Finite Group Databasebeta

← #21455071

Subgroups — #21455071

Order 7808.

806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14519802C212yesmaximal, complemented
2C2×#14519751C211yesmaximal, characteristic, complemented
3#16839907C214yesmaximal, complemented
4#16839901C212yesmaximal, complemented
5#16839896C212yesmaximal, complemented
6#16839763C212yesmaximal, complemented
7#16839726C211yesmaximal, characteristic, complemented
8C22×#41×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic, complemented
10C22×C22⋊D61—21no—
11#14519802—28no—
12C2×#11758201C2214yescomplemented
13C2×#11758199C2214yescomplemented
14C2×#11758194C2212yescomplemented
15#14519751—21no—
16#14519751—21no—
17#14519751C2212yes—
18#14519751C2212yescomplemented
19C2×C4⋊Dic61C2211yescharacteristic, complemented
20C2×#11758198—21no—
21#14519701C2214yescomplemented
22#14519698C2214yescomplemented
23C22⋊#92418C2212yescomplemented
24C22⋊#92418C2212yescomplemented
25C2×#41×C61—28no—
26C2×#41×C61—21no—
27C2×#41×C61—21no—
28C2×#41×C61C2212yes—
29C2×#41×C61C2212yescomplemented
30C22×Q8×C61C2211yescharacteristic, complemented
31C22×D4×C61—21no—
32C22×D4×C61C2211yescharacteristic, complemented
33C23×C4×C61—21no—
34C23×C4×C61C2211yescharacteristic
35C24×C61—21no—
36C24×C61D411yescharacteristic
37C23×D61—21no—
38#41×C61—28no—
39#41×C61—28no—
40#41×C61—24no—
41#41×C61—24no—
42#41×C61—24no—
43#41×C61D418yescomplemented
44C2×Q8×C61—24no—
45C2×Q8×C61—21no—
46C2×Q8×C61C2312yes—
47C2×D4×C61—28no—
48C2×D4×C61—22no—
49C2×D4×C61—22no—
50C2×D4×C61—24no—
51C2×D4×C61—21no—
52C2×D4×C61C2312yes—
53C22×C4×C61—28no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—24no—
58C22×C4×C61D411yescharacteristic
59C22×C4×C61D411yescharacteristic
60C22×C4×C61D411yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—22no—
65C2×C22⋊D61—22no—
66C2×C22⋊D61—44no—
67C22×Dic61—21no—
68C2×D244—24no—
69C2×D244—21no—
70C2×D244C2312yes—
71#11758201—28no—
72#11758199—28no—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61—21no—
76C4⋊Dic61C2312yes—
77#11758194—24no—
78C2×#92418C2314yes—
79C23×C61—24no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—41no—
84C23×C61—42no—
85C23×C61—42no—
86C23×C61C2×D411yescharacteristic
87C23×C61C2×D411yescharacteristic
88C23×C61C2×D411yescharacteristic
89C22×D61—22no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93Q8×C61—24no—
94Q8×C61—22no—
95Q8×C61C2×D414yescomplemented
96D4×C61—28no—
97D4×C61—24no—
98D4×C61—28no—
99D4×C61—22no—
100D4×C61C2×D414yescomplemented
101C2×C4×C61—24no—
102C2×C4×C61—28no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61—28no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×D414yes—
114C2×C4×C61C2411yescharacteristic
115C22⋊D61—44no—
116C22⋊D61—44no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119D244—24no—
120D244—42no—
121#92418—24no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—24no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—44no—
131C22×C61—48no—
132C22×C61—42no—
133C22×C61—42no—
134C22×C61#12012yes—
135C22×C61AGL(1,ℤ/8)12yescomplemented
136C22×C61C22×D411yescharacteristic
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—84no—
141C4×C61—21no—
142C4×C61—24no—
143C4×C61—21no—
144C4×C61#12012yes—
145C4×C61C22×D412yes—
146Dic61—42no—
147#3006—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61—22no—
150C2×C61—41no—
151C2×C61—44no—
152C2×C61C2×#12011yescharacteristic
153C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C61#57511yescharacteristic
155D61—82no—
156C22×#41D6111yescharacteristic, complemented
157C2×AGL(1,ℤ/8)—612no—
158C2×#121—611no—
159#449—614no—
160#448—612no—
161#447—612no—
162#417—612no—
163#407—611no—
164C61#300611yescharacteristic, complemented, Sylow
165C2×#41—28no—
166C2×#41—21no—
167C2×#41—21no—
168C2×#41C2×D6112yes—
169C2×#41C2×D6112yescomplemented
170C22×Q8C2×D6111yescharacteristic, complemented
171C22×D4—21no—
172C22×D4—611no—
173C22×D4—1221no—
174C22×D4C2×D6111yescharacteristic, complemented
175C23×C4—21no—
176C23×C4C2×D6111yescharacteristic
177AGL(1,ℤ/8)—1228no—
178C2×SD16—614no—
179C2×D8—614no—
180C2×M16—612no—
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⋊C8—612no—
190C22⋊C8—612no—
191C24—21no—
192C24—1221no—
193C24C22⋊D6111yescharacteristic
194#41—28no—
195#41—28no—
196#41—24no—
197#41—24no—
198#41—24no—
199#41C22⋊D6118yescomplemented
200C2×Q8—24no—
201C2×Q8—21no—
202C2×Q8C22×D6112yes—
203C2×D4—28no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—24no—
207C2×D4—21no—
208C2×D4—612no—
209C2×D4—1222no—
210C2×D4—1222no—
211C2×D4—1224no—
212C2×D4—1221no—
213C2×D4—2444no—
214C2×D4C22×D6112yes—
215C22×C4—28no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—1221no—
221C22×C4C22⋊D6111yescharacteristic
222C22×C4C22⋊D6111yescharacteristic
223C22×C4C22⋊D6111yescharacteristic
224C22×C4C22×D6111yescharacteristic
225C22×C4C22×D6111yescharacteristic
226C22×C4C22×D6111yescharacteristic
227SD16—1228no—
228D8—1228no—
229M16—1224no—
230C2×C8—614no—
231C4⋊C4—612no—
232C4⋊C4—1221no—
233C22⋊C4—1222no—
234C22⋊C4—1222no—
235C23—24no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—41no—
240C23—42no—
241C23—42no—
242C23—1222no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23C2×C22⋊D6111yescharacteristic
247C23C2×C22⋊D6111yescharacteristic
248C23C2×C22⋊D6111yescharacteristic
249Q8—24no—
250Q8—22no—
251Q8C2×C22⋊D6114yescomplemented
252D4—28no—
253D4—24no—
254D4—28no—
255D4—22no—
256D4—1224no—
257D4—2444no—
258D4—2444no—
259D4—2442no—
260D4C2×C22⋊D6114yescomplemented
261C2×C4—24no—
262C2×C4—28no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—28no—
269C2×C4—22no—
270C2×C4—1222no—
271C2×C4—2442no—
272C2×C4C2×C22⋊D6111yescharacteristic
273C2×C4C2×C22⋊D6111yescharacteristic
274C2×C4C2×C22⋊D6114yes—
275C2×C4C2×C22⋊D6111yescharacteristic
276C2×C4C23×D6111yescharacteristic
277C8—1224no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—48no—
288C22—42no—
289C22—42no—
290C22—4884no—
291C22—2442no—
292C22—2442no—
293C22—2442no—
294C22#1451974612yes—
295C22#1451980212yescomplemented
296C22C22×C22⋊D6111yescharacteristic
297C4—21no—
298C4—24no—
299C4—21no—
300C4—2442no—
301C4#1451974612yes—
302C4C22×C22⋊D6112yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—44no—
307C2—4882no—
308C2C2×#1451974611yescharacteristic
309C2C2×#1451980211yescharacteristic
310C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×#41×C61C2
socleC22×C61C22×D4
hypercenterC22×#41D61
hypocenterC61#3006
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C2×#14519751C2semidirect
3. #16839907C2semidirect
4. #16839901C2semidirect
5. #16839896C2semidirect
6. #16839763C2semidirect
7. #16839726C2semidirect
8. C22×#41×C61C2semidirect
9. C22×D244C22semidirect
12. C2×#11758201C22semidirect
13. C2×#11758199C22semidirect
14. C2×#11758194C22semidirect
18. #14519751C22semidirect
19. C2×C4⋊Dic61C22semidirect
21. #14519701C22semidirect
22. #14519698C22semidirect
23. C22⋊#92418C22semidirect
24. C22⋊#92418C22semidirect
29. C2×#41×C61C22semidirect
30. C22×Q8×C61C22semidirect
32. C22×D4×C61C22semidirect
43. #41×C61D4semidirect
95. Q8×C61C2×D4semidirect
100. D4×C61C2×D4semidirect
135. C22×C61AGL(1,ℤ/8)semidirect
156. C22×#41D61semidirect
164. C61#3006semidirect
169. C2×#41C2×D61semidirect
170. C22×Q8C2×D61semidirect
174. C22×D4C2×D61semidirect
199. #41C22⋊D61semidirect
251. Q8C2×C22⋊D61semidirect
260. D4C2×C22⋊D61semidirect
295. C22#14519802semidirect