Finite Group Databasebeta

← #21455087

Subgroups — #21455087

Order 7808.

784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519802C211yesmaximal, characteristic, complemented
2C22×#11758199C211yesmaximal, characteristic, complemented
3#16840326C211yesmaximal, characteristic, complemented
4#16839907C214yesmaximal, complemented
5#16839896C214yesmaximal, complemented
6#16839767C211yesmaximal, characteristic, complemented
7#16839758C211yesmaximal, characteristic, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic, complemented
11#14519802—24no—
12C2×#11758201C2212yescomplemented
13C2×#11758199—24no—
14C2×#11758199C2214yescomplemented
15C2×#11758199C2212yescomplemented
16C2×#11758194C2211yescharacteristic, complemented
17C22×#92418C2211yescharacteristic, complemented
18#14519773—21no—
19#14519766—21no—
20#14519751C2214yescomplemented
21#14519745—22no—
22#14519736C2211yescharacteristic, complemented
23#14519701C2212yescomplemented
24#14519698C2212yescomplemented
25#14519698C2214yescomplemented
26C22⋊#92418C2214yescomplemented
27H(5,𝔽2)×C61—24no—
28H(5,𝔽2)×C61—24no—
29C2×#41×C61—21no—
30C2×#41×C61C2211yescharacteristic
31C2×#41×C61C2211yescharacteristic
32C2×#41×C61C2212yescomplemented
33C22×D4×C61—21no—
34C22×D4×C61—22no—
35C22×D4×C61C2211yescharacteristic
36C22×D4×C61C2212yescomplemented
37C24×C61—21no—
38C24×C61—22no—
39C23×D61—21no—
40#41×C61—28no—
41#41×C61—24no—
42#41×C61—24no—
43#41×C61—22no—
44#41×C61—22no—
45#41×C61—22no—
46#41×C61D414yescomplemented
47C2×Q8×C61D411yescharacteristic
48C2×Q8×C61C2311yescharacteristic
49C2×D4×C61—216no—
50C2×D4×C61—28no—
51C2×D4×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—24no—
54C2×D4×C61—24no—
55C2×D4×C61—21no—
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C2×D4×C61D412yes—
59C2×D4×C61D411yescharacteristic
60C2×D4×C61D414yescomplemented
61C2×D4×C61C2312yes—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61C2312yes—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—24no—
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—21no—
71C2×D244C2312yes—
72C22⋊Dic61—21no—
73#11758201—24no—
74#11758199—28no—
75#11758199—24no—
76#11758198—24no—
77C4⋊Dic61C2312yes—
78C4×Dic61—21no—
79#11758194—22no—
80C2×#92418—22no—
81C2×#92418C2312yes—
82C2×#92418C2312yes—
83C23×C61—28no—
84C23×C61—21no—
85C23×C61—22no—
86C23×C61—24no—
87C23×C61—82no—
88C23×C61—84no—
89C23×C61C2×D412yes—
90C23×C61C2×D411yescharacteristic
91C22×D61—22no—
92C22×D61—42no—
93C22×D61—82no—
94Q8×C61—22no—
95Q8×C61—21no—
96Q8×C61C2×D412yes—
97D4×C61—28no—
98D4×C61—28no—
99D4×C61—24no—
100D4×C61—24no—
101D4×C61—22no—
102D4×C61—24no—
103D4×C61—22no—
104D4×C61—21no—
105D4×C61C2×D412yes—
106D4×C61C2×D414yes—
107C2×C4×C61—28no—
108C2×C4×C61—21no—
109C2×C4×C61—24no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61C2×D412yes—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D412yes—
115C2×C4×C61C2×D412yes—
116C2×C4×C61C2411yescharacteristic
117C22⋊D61—84no—
118C2×Dic61—22no—
119D244—22no—
120D244—22no—
121D244—42no—
122#92418—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—24no—
127C22×C61—22no—
128C22×C61—24no—
129C22×C61—44no—
130C22×C61—42no—
131C22×C61—84no—
132C22×C61—88no—
133C22×C61#12012yes—
134C22×C61C22×D411yescharacteristic
135C2×D61—42no—
136C2×D61—44no—
137C2×D61—84no—
138C4×C61—22no—
139C4×C61—22no—
140C4×C61#12012yes—
141C4×C61C22×D411yescharacteristic
142C4×C61C22×D411yescharacteristic
143Dic61—42no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61—44no—
148C2×C61—42no—
149C2×C61C2×#12011yescharacteristic
150C2×C61#57612yes—
151D61—82no—
152C2×H(5,𝔽2)D6111yescharacteristic, complemented
153C2×AGL(1,ℤ/8)—611no—
154C22×D8—611no—
155#535—611no—
156#449—614no—
157#447—614no—
158#418—611no—
159#416—611no—
160#408—611no—
161C61#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—24no—
163H(5,𝔽2)—24no—
164C2×#41—21no—
165C2×#41C2×D6111yescharacteristic
166C2×#41C2×D6111yescharacteristic
167C2×#41C2×D6112yescomplemented
168C22×D4—21no—
169C22×D4—22no—
170C22×D4—611no—
171C22×D4C2×D6111yescharacteristic
172C22×D4C2×D6112yescomplemented
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—614no—
176C2×D8—612no—
177C2×D8—1224no—
178C2×M16—611no—
179C22×C8—611no—
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117—611no—
185#103—612no—
186#102—612no—
187#102—614no—
188C22⋊C8—614no—
189C24—21no—
190C24—22no—
191C24—1221no—
192#41—28no—
193#41—24no—
194#41—24no—
195#41—22no—
196#41—22no—
197#41—22no—
198#41C22⋊D6114yescomplemented
199C2×Q8C22⋊D6111yescharacteristic
200C2×Q8C22×D6111yescharacteristic
201C2×D4—216no—
202C2×D4—28no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—24no—
206C2×D4—24no—
207C2×D4—21no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—612no—
211C2×D4—1224no—
212C2×D4—1222no—
213C2×D4—1222no—
214C2×D4—1221no—
215C2×D4C22⋊D6112yes—
216C2×D4C22⋊D6111yescharacteristic
217C2×D4C22⋊D6114yescomplemented
218C2×D4C22×D6112yes—
219C2×D4C22×D6111yescharacteristic
220C22×C4—21no—
221C22×C4—22no—
222C22×C4C22×D6112yes—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—1228no—
226D8—1224no—
227M16—1222no—
228C2×C8—612no—
229C2×C8—612no—
230C2×C8—1222no—
231C4⋊C4—612no—
232C22⋊C4—1221no—
233C22⋊C4—1224no—
234C42—1221no—
235C23—28no—
236C23—21no—
237C23—22no—
238C23—24no—
239C23—82no—
240C23—84no—
241C23—1222no—
242C23—4882no—
243C23—2442no—
244C23C2×C22⋊D6112yes—
245C23C2×C22⋊D6111yescharacteristic
246Q8—21no—
247Q8—22no—
248Q8C2×C22⋊D6112yes—
249D4—28no—
250D4—28no—
251D4—24no—
252D4—24no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—24no—
257D4—1222no—
258D4—1222no—
259D4—4884no—
260D4—2442no—
261D4C2×C22⋊D6112yes—
262D4C2×C22⋊D6114yes—
263C2×C4—28no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—1222no—
269C2×C4C2×C22⋊D6112yes—
270C2×C4C2×C22⋊D6112yes—
271C2×C4C2×C22⋊D6112yes—
272C2×C4C2×C22⋊D6111yescharacteristic
273C2×C4C23×D6111yescharacteristic
274C8—1222no—
275C8—1222no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—22no—
280C22—24no—
281C22—44no—
282C22—42no—
283C22—84no—
284C22—88no—
285C22—4884no—
286C22—2442no—
287C22—2444no—
288C22#1451974612yes—
289C22C22×C22⋊D6111yescharacteristic
290C4—22no—
291C4—22no—
292C4—2442no—
293C4#1451974612yes—
294C4C22×C22⋊D6111yescharacteristic
295C4C22×C22⋊D6111yescharacteristic
296C2—22no—
297C2—42no—
298C2—44no—
299C2—42no—
300C2—4882no—
301C2C2×#1451974611yescharacteristic
302C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×H(5,𝔽2)×C61C2
socleC22×C61C22×D4
hypercenterC2×H(5,𝔽2)D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C22×#11758199C2semidirect
3. #16840326C2semidirect
4. #16839907C2semidirect
5. #16839896C2semidirect
6. #16839767C2semidirect
7. #16839758C2semidirect
8. #16839729C2semidirect
9. C2×H(5,𝔽2)×C61C2semidirect
10. C22×D244C22semidirect
12. C2×#11758201C22semidirect
14. C2×#11758199C22semidirect
15. C2×#11758199C22semidirect
16. C2×#11758194C22semidirect
17. C22×#92418C22semidirect
20. #14519751C22semidirect
22. #14519736C22semidirect
23. #14519701C22semidirect
24. #14519698C22semidirect
25. #14519698C22semidirect
26. C22⋊#92418C22semidirect
32. C2×#41×C61C22semidirect
36. C22×D4×C61C22semidirect
46. #41×C61D4semidirect
60. C2×D4×C61D4semidirect
152. C2×H(5,𝔽2)D61semidirect
161. C61#3008semidirect
167. C2×#41C2×D61semidirect
172. C22×D4C2×D61semidirect
198. #41C22⋊D61semidirect
217. C2×D4C22⋊D61semidirect