Finite Group Databasebeta

← #21455427

Subgroups — #21455427

Order 7808.

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

normal subgroups only

This group has 500 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
1C2×#14519797C211yesmaximal, characteristic, complemented
2C22×#11758189C211yesmaximal, characteristic, complemented
3#16840274C211yesmaximal, characteristic, complemented
4#16840269C211yesmaximal, characteristic, complemented
5#16840019C212yesmaximal, complemented
6#16840014C212yesmaximal, complemented
7#16840011C212yesmaximal, complemented
8#16840007C212yesmaximal, complemented
9#16839798C211yesmaximal, characteristic, complemented
10#16839759C211yesmaximal, characteristic, complemented
11C61×#416C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14#14519797—24no—
15C2×#11758202C2211yescharacteristic, complemented
16C2×#11758200C2211yescharacteristic, complemented
17C2×#11758201C2211yescharacteristic, complemented
18C2×#11758199C2211yescharacteristic, complemented
19C2×#11758189—24no—
20C2×#11758189C2212yes—
21C2×#11758189C2212yes—
22C22×#92418C2211yescharacteristic
23#14519761—21no—
24#14519758—21no—
25#14519757C2212yes—
26#14519753C2212yes—
27#14519752C2212yes—
28#14519748C2212yes—
29#14519747—21no—
30#14519745—21no—
31C4×D244—22no—
32C4×C22⋊D61—22no—
33#14519736C2211yescharacteristic
34#14519710C2212yescomplemented
35#14519708C2212yescomplemented
36#14519702C2212yescomplemented
37#14519699C2212yescomplemented
38C2×#41×C61C2211yescharacteristic
39C22×C8×C61C2211yescharacteristic
40#117×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×C61C2311yescharacteristic
51C2×C22⋊D61—21no—
52C2×C22⋊D61—22no—
53C22×Dic61D411yescharacteristic
54#11758222—22no—
55#11758222—22no—
56C2×D244—22no—
57C2×D244C2311yescharacteristic
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—21no—
61C2×C4×D61D412yes—
62C2×C4×D61C2312yes—
63C2×Dic122C2311yescharacteristic
64C2×C8×C61—22no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2312yes—
67C22⋊C4×C61—21no—
68C42×C61—21no—
69C22⋊Dic61—21no—
70C22⋊Dic61—22no—
71#11758202—22no—
72#11758201—22no—
73#11758200—22no—
74#11758199—22no—
75#11758198—22no—
76#11758198—22no—
77#11758198—22no—
78C4⋊Dic61—22no—
79C4⋊Dic61C2312yes—
80#11758196—22no—
81C4×Dic61—21no—
82C2×#92418D414yescomplemented
83C2×#92418C2311yescharacteristic
84C2×#92418C2311yescharacteristic
85#11758189—24no—
86#11758189—24no—
87C23×C61—21no—
88C23×C61C2×D411yescharacteristic
89C22×D61—22no—
90C22×D61—21no—
91C22×D61—42no—
92C22×D61C2×D412yes—
93Q8×C61—21no—
94Q8×C61—21no—
95D4×C61—21no—
96D4×C61—21no—
97D4×C61—42no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—42no—
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D412yes—
103C2×C4×C61#4112yes—
104C2×C4×C61C2411yescharacteristic
105C22⋊D61—44no—
106C22⋊D61—42no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61C2×D412yes—
111D244—21no—
112D244—21no—
113D244—44no—
114C4×D61—24no—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—42no—
118Dic122—21no—
119Dic122—21no—
120C8×C61—22no—
121#92418C2×D412yes—
122#92418C2×D412yes—
123C22×C61—22no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61#12112yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—44no—
132C2×D61—41no—
133C2×D61—42no—
134C4×C61—41no—
135C4×C61—42no—
136C4×C61#12112yes—
137C4×C61C22×D411yescharacteristic
138C4×C61C2×#4111yescharacteristic
139Dic61—22no—
140Dic61—41no—
141Dic61—42no—
142#3054—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61C2×#12111yescharacteristic
146C2×C61#57512yes—
147D61—42no—
148D61—81no—
149C2×#135—611no—
150C22×M16—611no—
151#525—611no—
152#525—611no—
153#470—612no—
154#469—612no—
155#468—612no—
156#468—612no—
157#427—611no—
158#416—611no—
159#416D6111yescharacteristic, complemented
160C61#305411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C2×#41C2×D6111yescharacteristic
163C23×C4—611no—
164#135—1224no—
165C2×Q16—611no—
166C2×SD16—611no—
167C2×SD16—611no—
168C2×D8—611no—
169C2×M16—612no—
170C2×M16—612no—
171C2×M16—1224no—
172C22×C8—611no—
173C22×C8C2×D6111yescharacteristic
174#123—1221no—
175#123—1221no—
176C22⋊Q8—612no—
177C22⋊Q8—612no—
178#121—612no—
179#121—612no—
180#120—1221no—
181#120—1221no—
182C4×D4—1222no—
183C4×D4—1222no—
184#117—611no—
185#117C2×D6111yescharacteristic
186#107—612no—
187#106—612no—
188#103—612no—
189#103C2×D6112yescomplemented
190#102—612no—
191#102C2×D6112yescomplemented
192C24—611no—
193#41—22no—
194#41—22no—
195#41—1222no—
196#41—1222no—
197C2×Q8—611no—
198C2×Q8C22×D6111yescharacteristic
199C2×D4—21no—
200C2×D4—611no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—1221no—
204C2×D4C22×D6111yescharacteristic
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—612no—
208C22×C4—612no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—1221no—
212C22×C4C22×D6111yescharacteristic
213Q16—1222no—
214SD16—1222no—
215SD16—1222no—
216D8—1222no—
217M16—1224no—
218M16—1224no—
219C2×C8—22no—
220C2×C8—614no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8C22×D6112yes—
224C4⋊C4—612no—
225C4⋊C4—1222no—
226C4⋊C4—1222no—
227C4⋊C4C22×D6112yes—
228C22⋊C4—21no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1222no—
233C22⋊C4—1221no—
234C42—21no—
235C42—1221no—
236C23—21no—
237C23—612no—
238C23—1222no—
239C23—1221no—
240C23—2442no—
241C23D4×D6111yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—1221no—
245Q8—1221no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—1221no—
250D4—1221no—
251D4—2444no—
252D4—2444no—
253D4—2442no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—612no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1224no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—2442no—
265C2×C4#1175822212yes—
266C2×C4D4×D6112yes—
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—612no—
271C8—612no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—1222no—
276C22—1222no—
277C22—1222no—
278C22—2444no—
279C22—2441no—
280C22—2442no—
281C22#1451975012yes—
282C22C2×D4×D6111yescharacteristic
283C4—41no—
284C4—42no—
285C4—1222no—
286C4—2441no—
287C4—2442no—
288C4#1451975012yes—
289C4C2×D4×D6111yescharacteristic
290C4C2×#1175822211yescharacteristic
291C2—22no—
292C2—81no—
293C2—4881no—
294C2—2442no—
295C2C2×#1451975011yescharacteristic
296C2#1684055912yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14519797C2semidirect
2. C22×#11758189C2semidirect
3. #16840274C2semidirect
4. #16840269C2semidirect
5. #16840019C2semidirect
6. #16840014C2semidirect
7. #16840011C2semidirect
8. #16840007C2semidirect
9. #16839798C2semidirect
10. #16839759C2semidirect
11. C61×#416C2semidirect
15. C2×#11758202C22semidirect
16. C2×#11758200C22semidirect
17. C2×#11758201C22semidirect
18. C2×#11758199C22semidirect
34. #14519710C22semidirect
35. #14519708C22semidirect
36. #14519702C22semidirect
37. #14519699C22semidirect
41. #103×C61C22semidirect
42. #102×C61C22semidirect
82. C2×#92418D4semidirect
159. #416D61semidirect
160. C61#3054semidirect
189. #103C2×D61semidirect
191. #102C2×D61semidirect