Finite Group Databasebeta

← #21455778

Subgroups — #21455778

Order 7808.

418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840326C211yesmaximal, characteristic
2#16840245C211yesmaximal, characteristic, complemented
3#16840087C212yesmaximal, complemented
4#16840087C212yesmaximal, complemented
5#16840081C212yesmaximal, complemented
6#16840076C212yesmaximal, complemented
7#16839804C211yesmaximal, characteristic, complemented
8#16839800C211yesmaximal, characteristic, complemented
9#16839768C211yesmaximal, characteristic, complemented
10C2×#14519699C211yesmaximal, characteristic, complemented
11C61×#408C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13#14519773—21no—
14#14519766—21no—
15#14519751C2212yes—
16#14519751C2212yes—
17#14519745—22no—
18Q8×Dic61—21no—
19D4×Dic61—21no—
20D4×Dic61—22no—
21#14519736C2211yescharacteristic
22#14519736C2211yescharacteristic
23#14519736C2212yescomplemented
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2212yescomplemented
26#14519711C2211yescharacteristic, complemented
27#14519711C2211yescharacteristic, complemented
28#14519711C2212yescomplemented
29#14519709C2211yescharacteristic, complemented
30#14519709C2211yescharacteristic, complemented
31#14519709C2212yescomplemented
32#14519699C2212yes—
33#14519699C2212yes—
34#14519699C2212yes—
35#14519699C2212yes—
36C2×#41×C61C2211yescharacteristic
37C2×M16×C61C2211yescharacteristic
38C22×C8×C61C2211yescharacteristic
39C22⋊C8×C61C2212yescomplemented
40C22⋊C8×C61C2212yescomplemented
41C23×D61—21no—
42#41×C61—22no—
43#41×C61—22no—
44C2×Q8×C61D411yescharacteristic
45C2×D4×C61D412yes—
46C2×D4×C61D411yescharacteristic
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—22no—
50C2×C22⋊D61—22no—
51C22×Dic61—21no—
52C22×Dic61—22no—
53C2×D244—22no—
54C2×D244—22no—
55C2×D244—21no—
56C2×D244C2312yes—
57M16×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61C2311yescharacteristic
60C2×C8×C61C2311yescharacteristic
61C2×C8×C61C2312yes—
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64C22⋊Dic61—22no—
65#11758198—22no—
66#11758198—22no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72C4⋊Dic61C2311yescharacteristic
73C4⋊Dic61C2311yescharacteristic
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—22no—
77C23×C61C2×D412yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—22no—
80C22×D61—42no—
81C22×D61—81no—
82C22×D61—81no—
83Q8×C61—22no—
84D4×C61—24no—
85D4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61#4112yes—
91C2×C4×C61#4112yes—
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—82no—
94C22⋊D61—82no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—81no—
101C2×Dic61—82no—
102D244—22no—
103D244—22no—
104D244—42no—
105C8×C61—21no—
106C8×C61—21no—
107C8×C61—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61#12312yes—
114C22×C61C22×D411yescharacteristic
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—84no—
119C4×C61—22no—
120C4×C61#12312yes—
121C4×C61C2×#4111yescharacteristic
122C4×C61C2×#4111yescharacteristic
123Dic61—41no—
124Dic61—42no—
125Dic61—41no—
126Dic61—41no—
127Dic61—41no—
128#3096—611nomaximal, Sylow
129C2×C61—22no—
130C2×C61—42no—
131C2×C61C2×#12311yescharacteristic
132C2×C61#57611yescharacteristic
133C2×C61#57711yescharacteristic
134D61—82no—
135#535—611no—
136#520—611no—
137#482—612no—
138#482—612no—
139#481—612no—
140#480—612no—
141#428—611no—
142#427—611no—
143#418—611no—
144C2×#102—611no—
145#408D6111yescharacteristic, complemented
146C61#309611yescharacteristic, complemented, Sylow
147C2×#41C2×D6111yescharacteristic
148C22×D4—611no—
149C2×M16C2×D6111yescharacteristic
150C22×C8C2×D6111yescharacteristic
151#127—1221no—
152#124—1221no—
153#121—612no—
154#121—612no—
155#120—1222no—
156C4×Q8—1221no—
157C4×D4—1222no—
158C4×D4—1221no—
159#117—611no—
160#117—612no—
161#117—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—612no—
164#107—611no—
165#107—611no—
166#107—612no—
167#106—611no—
168#106—611no—
169#106—612no—
170#102—612no—
171#102—612no—
172#102—612no—
173#102—612no—
174C22⋊C8C2×D6112yescomplemented
175C22⋊C8C2×D6112yescomplemented
176C24—1221no—
177#41—22no—
178#41—22no—
179C2×Q8D24411yescharacteristic
180C2×D4—612no—
181C2×D4—1222no—
182C2×D4—1222no—
183C2×D4—1221no—
184C2×D4—1222no—
185C2×D4—1222no—
186C2×D4D24412yes—
187C2×D4D24411yescharacteristic
188C22×C4—1222no—
189C22×C4—1221no—
190C22×C4C22×D6112yes—
191C22×C4C22×D6111yescharacteristic
192M16—22no—
193C2×C8—22no—
194C2×C8C22×D6111yescharacteristic
195C2×C8C22×D6112yes—
196C2×C8C22×D6111yescharacteristic
197C4⋊C4—612no—
198C4⋊C4—611no—
199C4⋊C4—611no—
200C4⋊C4—611no—
201C4⋊C4—611no—
202C4⋊C4—1222no—
203C4⋊C4—1221no—
204C22⋊C4—1222no—
205C22⋊C4—1221no—
206C22⋊C4—1221no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C42—1222no—
210C42—1221no—
211C42—1221no—
212C23—1222no—
213C23—4881no—
214C23—4881no—
215C23—2442no—
216C23C2×D24412yes—
217C23C2×D24411yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—1222no—
222D4—1222no—
223D4—4882no—
224D4—4882no—
225D4—2442no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—4881no—
234C2×C4—4882no—
235C2×C4C2×D24412yes—
236C2×C4C2×D24411yescharacteristic
237C2×C4#1175822412yes—
238C2×C4#1175822412yes—
239C2×C4C23×D6111yescharacteristic
240C8—21no—
241C8—21no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—4884no—
249C22—2442no—
250C22—2442no—
251C22—2442no—
252C22#1451976112yes—
253C22C22×D24411yescharacteristic
254C4—22no—
255C4—2442no—
256C4—2441no—
257C4—2441no—
258C4—2441no—
259C4—2441no—
260C4#1451976112yes—
261C4C2×#1175822411yescharacteristic
262C4C2×#1175822411yescharacteristic
263C2—22no—
264C2—42no—
265C2—4882no—
266C2C2×#1451976111yescharacteristic
267C2#1684056711yescharacteristic
268C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3096
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #16840245C2semidirect
3. #16840087C2semidirect
4. #16840087C2semidirect
5. #16840081C2semidirect
6. #16840076C2semidirect
7. #16839804C2semidirect
8. #16839800C2semidirect
9. #16839768C2semidirect
10. C2×#14519699C2semidirect
11. C61×#408C2semidirect
23. #14519736C22semidirect
25. C2×C4⋊Dic61C22semidirect
26. #14519711C22semidirect
27. #14519711C22semidirect
28. #14519711C22semidirect
29. #14519709C22semidirect
30. #14519709C22semidirect
31. #14519709C22semidirect
39. C22⋊C8×C61C22semidirect
40. C22⋊C8×C61C22semidirect
145. #408D61semidirect
146. C61#3096semidirect
174. C22⋊C8C2×D61semidirect
175. C22⋊C8C2×D61semidirect