Finite Group Databasebeta

← #21455779

Subgroups — #21455779

Order 7808.

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

normal subgroups only

This group has 418 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#16840331C211yesmaximal, characteristic
2#16840243C211yesmaximal, characteristic, complemented
3#16840089C212yesmaximal, complemented
4#16840088C212yesmaximal, complemented
5#16840082C212yesmaximal, complemented
6#16840077C212yesmaximal, complemented
7#16839798C211yesmaximal, characteristic, complemented
8#16839768C211yesmaximal, characteristic, complemented
9C2×#14519697C211yesmaximal, characteristic, complemented
10#16839730C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×#92418C2211yescharacteristic
15#14519774—21no—
16#14519765—21no—
17#14519752C2212yes—
18#14519752C2212yes—
19#14519747—22no—
20#14519742—21no—
21#14519739—21no—
22C4×C22⋊D61—22no—
23#14519736C2211yescharacteristic
24#14519735C2212yescomplemented
25C4⋊C4×D61C2212yescomplemented
26#14519710C2211yescharacteristic, complemented
27#14519710C2211yescharacteristic, complemented
28#14519708C2211yescharacteristic, complemented
29#14519708C2211yescharacteristic, complemented
30#14519699C2212yes—
31#14519699C2212yes—
32#14519697C2212yes—
33#14519697C2212yes—
34#14519689C2212yescomplemented
35#14519689C2212yescomplemented
36C2×M16×C61C2211yescharacteristic
37#117×C61C2211yescharacteristic
38C2×C4⋊C4×C61C2211yescharacteristic
39#107×C61C2212yescomplemented
40#106×C61C2212yescomplemented
41C23×D61—21no—
42C22×C4×C61—21no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61D412yes—
45#11758222—22no—
46#11758222—22no—
47C2×D244—22no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244—22no—
51C2×D244—22no—
52C2×D244D411yescharacteristic
53C2×D244C2312yes—
54C2×C4×D61—22no—
55C2×C4×D61C2312yes—
56C2×Dic122D411yescharacteristic
57M16×C61—22no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C4⋊C4×C61C2312yes—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61—21no—
65C22⋊Dic61—21no—
66#11758198—22no—
67#11758198—22no—
68#11758198—22no—
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C2×#92418—22no—
75C2×#92418C2311yescharacteristic
76C2×#92418C2311yescharacteristic
77C23×C61C2×D411yescharacteristic
78C22×D61—22no—
79C22×D61—42no—
80C22×D61—81no—
81C22×D61—81no—
82C22×D61C2×D412yes—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—81no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61#4112yes—
89C2×C4×C61#4112yes—
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—24no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61C2×D412yes—
95D244—22no—
96D244—22no—
97D244—22no—
98D244—42no—
99D244—82no—
100D244—82no—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—82no—
104Dic122—22no—
105C8×C61—22no—
106#92418—21no—
107#92418—21no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#12312yes—
111C22×C61C22×D411yescharacteristic
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—84no—
119C4×C61—42no—
120C4×C61—41no—
121C4×C61—41no—
122C4×C61#12312yes—
123C4×C61C2×#4111yescharacteristic
124C4×C61C2×#4111yescharacteristic
125Dic61—22no—
126Dic61—41no—
127Dic61—41no—
128#3096—611nomaximal, Sylow
129C2×C61—22no—
130C2×C61C2×#12311yescharacteristic
131C2×C61#57611yescharacteristic
132C2×C61#57711yescharacteristic
133D61—42no—
134D61—82no—
135#535—611no—
136#520—611no—
137#482—612no—
138#482—612no—
139#481—612no—
140#480—612no—
141#428D6111yescharacteristic, complemented
142#427—611no—
143#418—611no—
144C2×#102—611no—
145#408—611no—
146C61#309611yescharacteristic, complemented, Sylow
147C2×#41—611no—
148C22×D4—611no—
149C2×M16C2×D6111yescharacteristic
150C22×C8—611no—
151#127—1221no—
152#124—1221no—
153#121—612no—
154#121—612no—
155#120—1222no—
156C4×Q8—1221no—
157C4×D4—1221no—
158C4×D4—1222no—
159#117—611no—
160#117—612no—
161#117C2×D6111yescharacteristic
162C2×C4⋊C4—612no—
163C2×C4⋊C4C2×D6111yescharacteristic
164#107—611no—
165#107—611no—
166#107C2×D6112yescomplemented
167#106—611no—
168#106—611no—
169#106C2×D6112yescomplemented
170#102—612no—
171#102—612no—
172#102—612no—
173#102—612no—
174C22⋊C8—612no—
175C22⋊C8—612no—
176C24—1221no—
177#41—1222no—
178#41—1222no—
179C2×Q8—611no—
180C2×D4—612no—
181C2×D4—611no—
182C2×D4—612no—
183C2×D4—1222no—
184C2×D4—1222no—
185C2×D4—1222no—
186C2×D4—1221no—
187C2×D4—1222no—
188C22×C4—21no—
189C22×C4—612no—
190C22×C4—1222no—
191C22×C4C22×D6111yescharacteristic
192M16—22no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—1222no—
196C2×C8C22×D6112yes—
197C4⋊C4—21no—
198C4⋊C4—611no—
199C4⋊C4—611no—
200C4⋊C4—1222no—
201C4⋊C4C22×D6112yes—
202C4⋊C4C22×D6111yescharacteristic
203C4⋊C4C22×D6111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—1222no—
206C22⋊C4—1222no—
207C22⋊C4—1222no—
208C22⋊C4—1221no—
209C42—21no—
210C42—1222no—
211C42—1221no—
212C23—612no—
213C23—1222no—
214C23—4881no—
215C23—4881no—
216C23—2442no—
217C23D4×D6111yescharacteristic
218Q8—1222no—
219D4—1224no—
220D4—1222no—
221D4—1222no—
222D4—1222no—
223D4—4882no—
224D4—4882no—
225D4—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—81no—
230C2×C4—612no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—4882no—
236C2×C4#1175822212yes—
237C2×C4D4×D6111yescharacteristic
238C2×C4#1175822612yes—
239C2×C4C23×D6111yescharacteristic
240C8—22no—
241C8—1221no—
242C8—1221no—
243C22—21no—
244C22—21no—
245C22—1222no—
246C22—1222no—
247C22—1222no—
248C22—4884no—
249C22—2442no—
250C22—2442no—
251C22—2442no—
252C22#1451976212yes—
253C22C2×D4×D6111yescharacteristic
254C4—42no—
255C4—41no—
256C4—41no—
257C4—1222no—
258C4—2441no—
259C4—2441no—
260C4#1451976212yes—
261C4C2×#1175822211yescharacteristic
262C4C2×#1175822611yescharacteristic
263C2—22no—
264C2—4882no—
265C2—2442no—
266C2C2×#1451976211yescharacteristic
267C2#1684056611yescharacteristic
268C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3096
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #16840243C2semidirect
3. #16840089C2semidirect
4. #16840088C2semidirect
5. #16840082C2semidirect
6. #16840077C2semidirect
7. #16839798C2semidirect
8. #16839768C2semidirect
9. C2×#14519697C2semidirect
10. #16839730C2semidirect
11. C61×#428C2semidirect
24. #14519735C22semidirect
25. C4⋊C4×D61C22semidirect
26. #14519710C22semidirect
27. #14519710C22semidirect
28. #14519708C22semidirect
29. #14519708C22semidirect
34. #14519689C22semidirect
35. #14519689C22semidirect
39. #107×C61C22semidirect
40. #106×C61C22semidirect
141. #428D61semidirect
146. C61#3096semidirect
166. #107C2×D61semidirect
169. #106C2×D61semidirect