Finite Group Databasebeta

← #21456681

Subgroups — #21456681

Order 7808.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840328C212yesmaximal, complemented
2#16840088C212yesmaximal, complemented
3#16840085C212yesmaximal, complemented
4#16840015C211yesmaximal, characteristic, complemented
5#16839996C212yesmaximal, complemented
6#16839897C212yesmaximal, complemented
7#16839894C212yesmaximal, complemented
8#16839730C211yesmaximal, characteristic, complemented
9C61×#469C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C2×D4×D61C2212yescomplemented
12C2×D488C2211yescharacteristic
13C2×#11758199C2212yes—
14C22×#92418C2211yescharacteristic, complemented
15#14519773—22no—
16#14519763—22no—
17#14519752C2212yes—
18#14519751C2212yescomplemented
19#14519748C2212yes—
20#14519747—22no—
21#14519745—22no—
22#14519735C2212yescomplemented
23#14519710C2212yescomplemented
24#14519709C2211yescharacteristic, complemented
25#14519699C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yescomplemented
28#14519689C2212yescomplemented
29#14519689C2212yescomplemented
30C2×D8×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic, complemented
32#121×C61C2212yescomplemented
33#106×C61C2211yescharacteristic, complemented
34#102×C61C2212yescomplemented
35C23×D61—22no—
36C2×D4×C61—22no—
37C2×D4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61D412yes—
43D4×D61—42no—
44D4×D61—42no—
45#11758222—41no—
46#11758222—41no—
47C2×D244—22no—
48C2×D244D411yescharacteristic
49C2×D244C2312yes—
50C2×C4×D61C2312yes—
51C2×Dic122D411yescharacteristic
52D8×C61—41no—
53M16×C61—41no—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C4⋊C4×C61C2312yes—
57C22⋊C4×C61—22no—
58C22⋊Dic61—22no—
59#11758199—42no—
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61C2312yes—
64C4×Dic61—22no—
65C2×#92418—41no—
66C2×#92418C2312yes—
67D488—41no—
68C23×C61—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71C22×D61—44no—
72C22×D61—82no—
73C22×D61—82no—
74C22×D61C2×D412yes—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—82no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C22⋊D61—44no—
85C22⋊D61—82no—
86C22⋊D61—82no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89D244—22no—
90D244—22no—
91D244—41no—
92D244—82no—
93C4×D61—22no—
94C4×D61—22no—
95Dic122—41no—
96C8×C61—21no—
97C8×C61—21no—
98#92418—22no—
99C22×C61—21no—
100C22×C61—22no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C2×D61—22no—
106C2×D61—22no—
107C2×D61—22no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—88no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61H(5,𝔽2)11yescharacteristic
115C4×C61H(5,𝔽2)11yescharacteristic
116Dic61—22no—
117Dic61—42no—
118#3199—611nomaximal, Sylow
119C2×C61—41no—
120C2×C61—82no—
121C2×C61#53411yescharacteristic
122C2×C61#57612yes—
123D61—42no—
124D61—82no—
125#535—612no—
126#482—612no—
127#482—612no—
128#469—611no—
129#469D6111yescharacteristic, complemented
130#466—612no—
131#447—612no—
132#447—612no—
133#408—611no—
134C61#319911yescharacteristic, complemented, Sylow
135C2×#41—611no—
136C22×D4—612no—
137C2×D8—612no—
138C2×D8—611no—
139C2×D8C2×D6111yescharacteristic
140C2×M16C2×D6111yescharacteristic, complemented
141C22×C8—611no—
142#127—1222no—
143#124—1222no—
144#121—612no—
145#121—612no—
146#121—612no—
147#121C2×D6112yescomplemented
148#120—1222no—
149#120—1222no—
150#117—612no—
151#107—612no—
152#106—611no—
153#106C2×D6111yescharacteristic, complemented
154#102—612no—
155#102—612no—
156#102—612no—
157#102C2×D6112yescomplemented
158C22⋊C8—612no—
159C22⋊C8—612no—
160C24—1222no—
161#41—2441no—
162#41—2441no—
163C2×Q8—611no—
164C2×D4—22no—
165C2×D4—612no—
166C2×D4—611no—
167C2×D4—612no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—2442no—
173C2×D4—2442no—
174C2×D4C22×D6112yes—
175C22×C4—612no—
176C22×C4C22×D6111yescharacteristic
177D8—41no—
178D8—2441no—
179D8—2442no—
180M16—41no—
181C2×C8—612no—
182C2×C8—2441no—
183C2×C8C22×D6111yescharacteristic
184C2×C8C22×D6111yescharacteristic
185C4⋊C4—612no—
186C4⋊C4C22×D6112yes—
187C22⋊C4—22no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C42—1222no—
193C23—22no—
194C23—612no—
195C23—1222no—
196C23—4882no—
197C23—4882no—
198C23—2444no—
199C23D4×D6111yescharacteristic
200Q8—2441no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—1222no—
205D4—1222no—
206D4—4882no—
207D4—4882no—
208D4—4882no—
209D4—2441no—
210D4—2442no—
211D4—2444no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—612no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4D4×D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—21no—
222C8—21no—
223C8—1222no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—1222no—
230C22—1222no—
231C22—1222no—
232C22—4888no—
233C22—2442no—
234C22—2442no—
235C22—2442no—
236C22C2×D4×D6111yescharacteristic
237C4—21no—
238C4—42no—
239C4—1222no—
240C4—2442no—
241C4#1451982211yescharacteristic
242C4#1451982311yescharacteristic
243C2—41no—
244C2—82no—
245C2—4882no—
246C2—2442no—
247C2#1684032011yescharacteristic
248C2#1684056612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3199
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #16840328C2semidirect
2. #16840088C2semidirect
3. #16840085C2semidirect
4. #16840015C2semidirect
5. #16839996C2semidirect
6. #16839897C2semidirect
7. #16839894C2semidirect
8. #16839730C2semidirect
9. C61×#469C2semidirect
11. C2×D4×D61C22semidirect
14. C22×#92418C22semidirect
18. #14519751C22semidirect
22. #14519735C22semidirect
23. #14519710C22semidirect
24. #14519709C22semidirect
25. #14519699C22semidirect
26. #14519698C22semidirect
27. #14519697C22semidirect
28. #14519689C22semidirect
29. #14519689C22semidirect
31. C2×M16×C61C22semidirect
32. #121×C61C22semidirect
33. #106×C61C22semidirect
34. #102×C61C22semidirect
129. #469D61semidirect
134. C61#3199semidirect
140. C2×M16C2×D61semidirect
147. #121C2×D61semidirect
153. #106C2×D61semidirect
157. #102C2×D61semidirect