Finite Group Databasebeta

← #21458050

Subgroups — #21458050

Order 7808.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840482C211yesmaximal, characteristic, complemented
2#16840108C211yesmaximal, characteristic, complemented
3#16840083C212yesmaximal, complemented
4#16840042C211yesmaximal, characteristic, complemented
5#16840006C212yesmaximal, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839913C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9#16839840C211yesmaximal, characteristic, complemented
10#16839767C212yesmaximal, complemented
11D42×C61C211yesmaximal, characteristic
12C2×#11758200C2211yescharacteristic
13C2×#11758200C2212yescomplemented
14C2×#11758194C2212yescomplemented
15#14519777C2211yescharacteristic, complemented
16#14519770—22no—
17#14519764—21no—
18#14519756C2212yescomplemented
19C4×Dic122C2211yescharacteristic, complemented
20#14519742—21no—
21#14519736C2212yescomplemented
22#14519710C2212yescomplemented
23#14519708C2211yescharacteristic, complemented
24C4⋊#92418C2211yescharacteristic, complemented
25#14519700C2211yescharacteristic, complemented
26#14519698C2211yescharacteristic
27#14519698C2212yes—
28#14519698C2212yescomplemented
29#14519698C2212yescomplemented
30#14519698C2212yescomplemented
31C22⋊#92418C2212yescomplemented
32C4×#92418C2211yescharacteristic, complemented
33C22×D4×C61—21no—
34C22×D4×C61C2212yes—
35#127×C61C2211yescharacteristic
36#121×C61—21no—
37#121×C61C2212yes—
38#120×C61—22no—
39C4×D4×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C24×C61—22no—
42C2×D4×C61—24no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61—44no—
49C2×D4×C61D411yescharacteristic
50C2×D4×C61C2312yes—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61C2312yes—
54C2×Dic122—21no—
55C2×Dic122C2311yescharacteristic
56C4⋊C4×C61D411yescharacteristic
57C4⋊C4×C61C2311yescharacteristic
58C22⋊C4×C61—21no—
59C22⋊C4×C61—22no—
60C22⋊C4×C61D412yes—
61C42×C61C2311yescharacteristic
62C22⋊Dic61—22no—
63C22⋊Dic61—22no—
64#11758200—22no—
65#11758200—42no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2312yes—
69#11758196—22no—
70#11758196—21no—
71C4×Dic61—22no—
72C4×Dic61—21no—
73#11758194—42no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76C2×#92418C2312yes—
77C23×C61—21no—
78C23×C61—22no—
79C23×C61—44no—
80C23×C61—44no—
81C23×C61—82no—
82C23×C61C2×D412yes—
83D4×C61—22no—
84D4×C61—22no—
85D4×C61—21no—
86D4×C61—22no—
87D4×C61—44no—
88D4×C61—44no—
89D4×C61—42no—
90D4×C61—81no—
91D4×C61#4112yes—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2411yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103Dic122—21no—
104Dic122—21no—
105Dic122—42no—
106#92418—21no—
107#92418—21no—
108#92418—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—88no—
119C22×C61C22×D411yescharacteristic
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61AGL(1,ℤ/8)12yes—
124C4×C61C2×#4111yescharacteristic
125C4×C61H(5,𝔽2)11yescharacteristic
126Dic61—41no—
127Dic61—42no—
128Dic61—41no—
129#3324—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61—42no—
132C2×C61—82no—
133C2×C61#54611yescharacteristic
134C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C61#57711yescharacteristic
136#556—611no—
137D42D6111yescharacteristic
138#486—611no—
139#482—612no—
140#474—611no—
141#468—612no—
142#460—611no—
143#450—612no—
144C4×SD16—611no—
145#436—611no—
146#418—612no—
147C61#332411yescharacteristic, complemented, Sylow
148C22×D4—21no—
149C22×D4C2×D6112yes—
150C2×SD16—611no—
151C2×SD16—612no—
152C2×M16—612no—
153C4⋊Q8—611no—
154#127C2×D6111yescharacteristic
155#126—1222no—
156#124—1221no—
157C22⋊Q8—612no—
158#121—21no—
159#121C2×D6112yes—
160#120—22no—
161C4×Q8—611no—
162C4×Q8—1221no—
163C4×D4C2×D6111yescharacteristic
164C4×D4C2×D6111yescharacteristic
165#117—612no—
166#107—612no—
167#106—611no—
168C4⋊C8—611no—
169#103—611no—
170#102—611no—
171#102—612no—
172#102—612no—
173#102—612no—
174#102—612no—
175C22⋊C8—612no—
176C4×C8—611no—
177C24—22no—
178C2×Q8—611no—
179C2×Q8—1221no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—42no—
186C2×D4—44no—
187C2×D4C22⋊D6111yescharacteristic
188C2×D4C22×D6112yes—
189C2×D4C22×D6111yescharacteristic
190C22×C4—21no—
191C22×C4C22×D6112yes—
192SD16—1222no—
193SD16—2442no—
194M16—2442no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—612no—
198C4⋊C4—611no—
199C4⋊C4—612no—
200C4⋊C4—1221no—
201C4⋊C4—1222no—
202C4⋊C4—1221no—
203C4⋊C4C22⋊D6111yescharacteristic
204C4⋊C4C22×D6111yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—22no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4C22⋊D6112yes—
210C42—1222no—
211C42—1221no—
212C42C22×D6111yescharacteristic
213C23—21no—
214C23—22no—
215C23—44no—
216C23—44no—
217C23—82no—
218C23C2×C22⋊D6112yes—
219Q8—1221no—
220Q8—1221no—
221Q8—2442no—
222D4—22no—
223D4—21no—
224D4—22no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1175822412yes—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4C2×C22⋊D6112yes—
239C2×C4C2×C22⋊D6111yescharacteristic
240C2×C4C2×C22⋊D6111yescharacteristic
241C2×C4C23×D6111yescharacteristic
242C8—1221no—
243C8—1221no—
244C8—1222no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—88no—
255C22C22×C22⋊D6111yescharacteristic
256C4—21no—
257C4—22no—
258C4—41no—
259C4—2442no—
260C4—2441no—
261C4—2441no—
262C4#1451980312yes—
263C4C2×#1175822411yescharacteristic
264C4#1451982211yescharacteristic
265C2—42no—
266C2—42no—
267C2—82no—
268C2#1684040611yescharacteristic
269C2C2×#1451980311yescharacteristic
270C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #16840482C2semidirect
2. #16840108C2semidirect
3. #16840083C2semidirect
4. #16840042C2semidirect
5. #16840006C2semidirect
6. #16839959C2semidirect
7. #16839913C2semidirect
8. C4×#11758200C2semidirect
9. #16839840C2semidirect
10. #16839767C2semidirect
13. C2×#11758200C22semidirect
14. C2×#11758194C22semidirect
15. #14519777C22semidirect
18. #14519756C22semidirect
19. C4×Dic122C22semidirect
21. #14519736C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
25. #14519700C22semidirect
28. #14519698C22semidirect
29. #14519698C22semidirect
30. #14519698C22semidirect
31. C22⋊#92418C22semidirect
32. C4×#92418C22semidirect
147. C61#3324semidirect