Finite Group Databasebeta

← #21455749

Subgroups — #21455749

Order 7808.

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

normal subgroups only

This group has 414 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#16840269C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16840102C212yesmaximal, complemented
4#16840101C212yesmaximal, complemented
5#16840085C212yesmaximal, complemented
6#16840084C212yesmaximal, complemented
7#16839804C211yesmaximal, characteristic, complemented
8#16839802C211yesmaximal, characteristic, complemented
9#16839763C211yesmaximal, characteristic, complemented
10#16839725C211yesmaximal, characteristic, complemented
11C61×#417C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14#14519758—21no—
15#14519753C2211yescharacteristic
16#14519753C2211yescharacteristic
17#14519748C2211yescharacteristic
18#14519748C2211yescharacteristic
19#14519745—21no—
20C4×C22⋊D61—21no—
21C4×C22⋊D61—21no—
22#14519736C2211yescharacteristic
23#14519735—21no—
24#14519735—21no—
25#14519735C2212yes—
26#14519735C2212yes—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×#11758198—21no—
29C2×C4×Dic61—21no—
30#14519711C2212yescomplemented
31#14519710C2212yescomplemented
32#14519709C2212yescomplemented
33#14519708C2212yescomplemented
34#14519701C2212yescomplemented
35#14519698C2212yescomplemented
36#14519689C2212yes—
37#14519689C2212yes—
38C2×#41×C61C2211yescharacteristic
39C2×M16×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#103×C61C2212yescomplemented
42#102×C61C2212yescomplemented
43C23×D61D411yescharacteristic
44#41×C61—22no—
45#41×C61—22no—
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—21no—
48C2×D4×C61C2311yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C22×Dic61—21no—
55C22×Dic61D411yescharacteristic
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61D411yescharacteristic
59C2×C4×D61D411yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×C4×D61C2311yescharacteristic
62M16×C61—22no—
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C22⋊Dic61—21no—
67C22⋊Dic61—21no—
68C22⋊Dic61—21no—
69#11758198—22no—
70#11758198—22no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2312yes—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82#11758194—22no—
83C2×#92418C2312yes—
84C23×C61—21no—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61C2×D411yescharacteristic
90C22×D61C2×D411yescharacteristic
91Q8×C61—21no—
92Q8×C61—21no—
93D4×C61—21no—
94D4×C61—21no—
95D4×C61—42no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61#4112yes—
102C2×C4×C61#4112yes—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—42no—
105C22⋊D61—42no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—42no—
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C8×C61—22no—
120#92418—22no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61#12312yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—44no—
135C4×C61—41no—
136C4×C61—42no—
137C4×C61#12312yes—
138C4×C61C2×#4111yescharacteristic
139C4×C61C2×#4111yescharacteristic
140Dic61—21no—
141Dic61—21no—
142Dic61—42no—
143Dic61—41no—
144Dic61—41no—
145#3093—611nomaximal, Sylow
146C2×C61—22no—
147C2×C61—81no—
148C2×C61C2×#12311yescharacteristic
149C2×C61#57511yescharacteristic
150C2×C61#57511yescharacteristic
151D61—41no—
152D61—41no—
153#525—611no—
154C2×#117—611no—
155#485—612no—
156#485—612no—
157#482—612no—
158#482—612no—
159#428—611no—
160#428—611no—
161#417—611no—
162#417D6111yescharacteristic, complemented
163#407—611no—
164C61#309311yescharacteristic, complemented, Sylow
165C2×#41C2×D6111yescharacteristic
166C23×C4—611no—
167C2×M16—611no—
168C2×M16C2×D6111yescharacteristic
169#123—1221no—
170C22⋊Q8—611no—
171C22⋊Q8—611no—
172#121—611no—
173#121—611no—
174#120—1221no—
175C4×D4—1221no—
176C4×D4—1221no—
177#117—611no—
178#117—612no—
179#117—612no—
180#117—1221no—
181#117—1221no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4C2×D6111yescharacteristic
184C2×C22⋊C4—1221no—
185C2×C42—1221no—
186#107—612no—
187#107—612no—
188#106—612no—
189#106—612no—
190#103—612no—
191#103C2×D6112yescomplemented
192#102—612no—
193#102C2×D6112yescomplemented
194C22⋊C8—612no—
195C22⋊C8—612no—
196C24—611no—
197#41—22no—
198#41—22no—
199C2×Q8C22×D6111yescharacteristic
200C2×D4—21no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4C22×D6111yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—1221no—
214C22×C4C22×D6111yescharacteristic
215M16—22no—
216M16—1222no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—21no—
220C4⋊C4—612no—
221C4⋊C4—611no—
222C4⋊C4—611no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4C22×D6112yes—
227C22⋊C4—1222no—
228C22⋊C4—1222no—
229C22⋊C4—1221no—
230C22⋊C4—1221no—
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—1222no—
235C42—1222no—
236C42—1221no—
237C23—21no—
238C23—611no—
239C23—611no—
240C23—1222no—
241C23—2441no—
242C23—2441no—
243C23D4×D6111yescharacteristic
244Q8—21no—
245Q8—21no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—2442no—
250D4—2442no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—2442no—
268C2×C4#1175822212yes—
269C2×C4D4×D6111yescharacteristic
270C2×C4#1175822412yes—
271C2×C4C23×D6111yescharacteristic
272C8—22no—
273C8—1222no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—1221no—
280C22—1221no—
281C22—1221no—
282C22—1221no—
283C22—1221no—
284C22—1221no—
285C22—2444no—
286C22#1451975912yes—
287C22C2×D4×D6111yescharacteristic
288C4—41no—
289C4—42no—
290C4—1221no—
291C4—1221no—
292C4—2441no—
293C4—2442no—
294C4—2441no—
295C4#1451975912yes—
296C4C2×#1175822411yescharacteristic
297C4C2×#1175822211yescharacteristic
298C2—22no—
299C2—81no—
300C2—2441no—
301C2—2441no—
302C2C2×#1451975911yescharacteristic
303C2#1684055811yescharacteristic
304C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3093
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#14519735C2semidirect
3. #16840102C2semidirect
4. #16840101C2semidirect
5. #16840085C2semidirect
6. #16840084C2semidirect
7. #16839804C2semidirect
8. #16839802C2semidirect
9. #16839763C2semidirect
10. #16839725C2semidirect
11. C61×#417C2semidirect
30. #14519711C22semidirect
31. #14519710C22semidirect
32. #14519709C22semidirect
33. #14519708C22semidirect
34. #14519701C22semidirect
35. #14519698C22semidirect
41. #103×C61C22semidirect
42. #102×C61C22semidirect
162. #417D61semidirect
164. C61#3093semidirect
191. #103C2×D61semidirect
193. #102C2×D61semidirect