Finite Group Databasebeta

← #21457643

Subgroups — #21457643

Order 7808.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840469C211yesmaximal, characteristic, complemented
2#16840108C211yesmaximal, characteristic, complemented
3#16840078C212yesmaximal, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16839989C212yesmaximal, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839913C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9D4×#92418C211yesmaximal, characteristic, complemented
10C2×#14519698C212yesmaximal, complemented
11D42×C61C211yesmaximal, characteristic
12C2×#11758200C2211yescharacteristic
13C2×#11758200C2212yescomplemented
14C22×#92418C2212yescomplemented
15#14519777C2211yescharacteristic, complemented
16#14519768—21no—
17#14519756C2212yescomplemented
18#14519754—22no—
19C4×Dic122C2211yescharacteristic, complemented
20D4×Dic61—21no—
21C2×C4⋊Dic61C2212yescomplemented
22#14519708C2212yescomplemented
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—
54C22×Dic61—22no—
55C2×Dic122—21no—
56C2×Dic122C2311yescharacteristic
57C4⋊C4×C61D411yescharacteristic
58C4⋊C4×C61C2311yescharacteristic
59C22⋊C4×C61—21no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61D412yes—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64#11758200—22no—
65#11758200—42no—
66C4⋊Dic61—22no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2312yes—
70#11758196—21no—
71#11758196—22no—
72C4×Dic61—21no—
73C2×#92418—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—21no—
85D4×C61—22no—
86D4×C61—44no—
87D4×C61—44no—
88D4×C61—42no—
89D4×C61—81no—
90D4×C61SD1614yescomplemented
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—
103C2×Dic61—82no—
104Dic122—21no—
105Dic122—21no—
106Dic122—81no—
107#92418—21no—
108#92418—21no—
109#92418—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×C61C2×SD1614yes—
120C22×C61C22×D411yescharacteristic
121C4×C61—22no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61C2×SD1612yes—
125C4×C61C2×#4111yescharacteristic
126C4×C61H(5,𝔽2)11yescharacteristic
127Dic61—41no—
128Dic61—42no—
129Dic61—41no—
130#3295—611nomaximal, Sylow
131C2×C61—24no—
132C2×C61—42no—
133C2×C61—82no—
134C2×C61#54611yescharacteristic
135C2×C61C22×SD1611yescharacteristic
136C2×C61#57611yescharacteristic
137#554—611no—
138D42D6111yescharacteristic
139#486—611no—
140#481—612no—
141#476—611no—
142#465—612no—
143#460—611no—
144#450—612no—
145C4×SD16—611no—
146C8×D4—611no—
147C2×#102—612no—
148C61#329511yescharacteristic, complemented, Sylow
149C22×D4—21no—
150C22×D4C2×D6112yes—
151C2×SD16—611no—
152C2×SD16—612no—
153C22×C8—612no—
154C4⋊Q8—611no—
155#127C2×D6111yescharacteristic
156#125—1221no—
157C22⋊Q8—612no—
158C22⋊Q8—1222no—
159#121—21no—
160#121C2×D6112yes—
161#120—22no—
162C4×Q8—611no—
163C4×D4—1221no—
164C4×D4C2×D6111yescharacteristic
165C4×D4C2×D6111yescharacteristic
166C2×C4⋊C4—612no—
167#106—611no—
168#106—612no—
169C4⋊C8—611no—
170#103—611no—
171#102—611no—
172#102—612no—
173#102—612no—
174#102—612no—
175#102—612no—
176C22⋊C8—612no—
177C4×C8—611no—
178C24—22no—
179C2×Q8—611no—
180C2×Q8—1221no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D6111yescharacteristic
189C2×D4C22×D6112yes—
190C2×D4C22×D6111yescharacteristic
191C22×C4—21no—
192C22×C4—1222no—
193C22×C4C22×D6112yes—
194SD16—1222no—
195SD16—2442no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—612no—
199C2×C8—2442no—
200C4⋊C4—611no—
201C4⋊C4—612no—
202C4⋊C4—1222no—
203C4⋊C4—1221no—
204C4⋊C4—1222no—
205C4⋊C4—1221no—
206C4⋊C4C22⋊D6111yescharacteristic
207C4⋊C4C22×D6111yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—1222no—
211C22⋊C4C22⋊D6112yes—
212C42—1221no—
213C42C22×D6111yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D6112yes—
220Q8—1221no—
221Q8—1221no—
222Q8—4881no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1175820014yescomplemented
231D4#1175822412yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1222no—
239C2×C4—4882no—
240C2×C4C2×C22⋊D6111yescharacteristic
241C2×C4C2×C22⋊D6112yes—
242C2×C4C2×C22⋊D6111yescharacteristic
243C2×C4C23×D6111yescharacteristic
244C8—1221no—
245C8—1221no—
246C8—1222no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1175820014yes—
257C22C22×C22⋊D6111yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—2441no—
262C4—2442no—
263C4—2441no—
264C4C2×#1175820012yes—
265C4C2×#1175822411yescharacteristic
266C4#1451982211yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#1684040611yescharacteristic
271C2C22×#1175820011yescharacteristic
272C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3295
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. #16840469C2semidirect
2. #16840108C2semidirect
3. #16840078C2semidirect
4. #16840052C2semidirect
5. #16839989C2semidirect
6. #16839959C2semidirect
7. #16839913C2semidirect
8. C4×#11758200C2semidirect
9. D4×#92418C2semidirect
10. C2×#14519698C2semidirect
13. C2×#11758200C22semidirect
14. C22×#92418C22semidirect
15. #14519777C22semidirect
17. #14519756C22semidirect
19. C4×Dic122C22semidirect
21. C2×C4⋊Dic61C22semidirect
22. #14519708C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
25. #14519700C22semidirect
28. #14519698C22semidirect
29. #14519698C22semidirect
30. #14519698C22semidirect
31. C22⋊#92418C22semidirect
32. C4×#92418C22semidirect
90. D4×C61SD16semidirect
148. C61#3295semidirect
230. D4#11758200semidirect