Finite Group Databasebeta

← #21455425

Subgroups — #21455425

Order 7808.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11758194C211yesmaximal, characteristic, complemented
3#16840273C211yesmaximal, characteristic, complemented
4#16840018C212yesmaximal, complemented
5#16840013C212yesmaximal, complemented
6#16840010C212yesmaximal, complemented
7#16840006C212yesmaximal, complemented
8#16839798C211yesmaximal, characteristic, complemented
9#16839758C211yesmaximal, characteristic, complemented
10#16839756C211yesmaximal, characteristic, complemented
11C61×#525C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13#14519797—24no—
14C2×#11758202C2211yescharacteristic, complemented
15C2×#11758200C2211yescharacteristic, complemented
16C2×#11758201C2211yescharacteristic, complemented
17C2×#11758199C2211yescharacteristic, complemented
18C2×#11758194—24no—
19C2×#11758194C2212yes—
20C2×#11758194C2212yes—
21C22×#92418C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519760—21no—
24#14519756C2212yes—
25#14519751C2212yes—
26#14519746—21no—
27C4×C22⋊D61—22no—
28#14519736C2211yescharacteristic
29#14519710C2212yescomplemented
30#14519708C2212yescomplemented
31#14519701C2212yescomplemented
32#14519700C2212yescomplemented
33#14519698C2212yescomplemented
34#14519697C2212yescomplemented
35C2×#41×C61C2211yescharacteristic
36C23×C4×C61C2211yescharacteristic
37#123×C61—21no—
38C22⋊Q8×C61C2212yes—
39#121×C61C2212yes—
40#120×C61—21no—
41C4×D4×C61—22no—
42#117×C61C2211yescharacteristic
43C24×C61D411yescharacteristic
44#41×C61—22no—
45#41×C61—22no—
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—22no—
48C2×D4×C61—21no—
49C2×D4×C61C2311yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—21no—
53C22×C4×C61D412yes—
54C22×C4×C61D411yescharacteristic
55C22×C4×C61C2312yes—
56C22×C4×C61C2311yescharacteristic
57C2×C22⋊D61—21no—
58C2×C22⋊D61—22no—
59#11758222—22no—
60#11758222—22no—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×Dic122C2311yescharacteristic
64C4⋊C4×C61—22no—
65C4⋊C4×C61C2312yes—
66C22⋊C4×C61—21no—
67C22⋊C4×C61—22no—
68C22⋊C4×C61—22no—
69C42×C61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—22no—
72#11758202—22no—
73#11758201—22no—
74#11758200—22no—
75#11758199—22no—
76#11758198—22no—
77C4⋊Dic61C2312yes—
78#11758196—22no—
79C4×Dic61—21no—
80#11758194—24no—
81#11758194—24no—
82C2×#92418—22no—
83C2×#92418D414yescomplemented
84C2×#92418C2312yes—
85C2×#92418C2311yescharacteristic
86C2×#92418C2311yescharacteristic
87C23×C61—22no—
88C23×C61—21no—
89C23×C61—42no—
90C23×C61C2×D412yes—
91C23×C61C2×D411yescharacteristic
92C22×D61—21no—
93Q8×C61—21no—
94Q8×C61—21no—
95D4×C61—21no—
96D4×C61—21no—
97D4×C61—44no—
98D4×C61—42no—
99C2×C4×C61—22no—
100C2×C4×C61—24no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2×D411yescharacteristic
108C2×C4×C61C2×D412yes—
109C2×C4×C61#4112yes—
110C2×C4×C61C2411yescharacteristic
111C22⋊D61—44no—
112C22⋊D61—42no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115D244—21no—
116D244—21no—
117C4×D61—42no—
118Dic122—21no—
119Dic122—21no—
120#92418—22no—
121#92418C2×D412yes—
122#92418C2×D412yes—
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—44no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61#12112yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—41no—
133C2×D61—42no—
134C4×C61—22no—
135C4×C61—41no—
136C4×C61—42no—
137C4×C61#12112yes—
138C4×C61C22×D411yescharacteristic
139C4×C61C2×#4111yescharacteristic
140Dic61—41no—
141Dic61—42no—
142#3054—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—42no—
145C2×C61—81no—
146C2×C61C2×#12111yescharacteristic
147C2×C61#57512yes—
148D61—81no—
149C2×#135—611no—
150C22×M16—611no—
151#525—611no—
152#525D6111yescharacteristic, complemented
153#470—612no—
154#469—612no—
155#468—612no—
156#468—612no—
157#427—611no—
158#416—611no—
159#416—611no—
160C61#305411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C2×#41C2×D6111yescharacteristic
163C23×C4C2×D6111yescharacteristic
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×C8—611no—
174#123—21no—
175#123—1221no—
176C22⋊Q8—612no—
177C22⋊Q8C2×D6112yes—
178#121—612no—
179#121C2×D6112yes—
180#120—21no—
181#120—1221no—
182C4×D4—22no—
183C4×D4—1222no—
184#117—611no—
185#117C2×D6111yescharacteristic
186#107—612no—
187#106—612no—
188#103—612no—
189#103—612no—
190#102—612no—
191#102—612no—
192C24C22⋊D6111yescharacteristic
193#41—22no—
194#41—22no—
195#41—1222no—
196#41—1222no—
197C2×Q8—611no—
198C2×Q8C22×D6111yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—611no—
202C2×D4—1222no—
203C2×D4—1221no—
204C2×D4C22×D6111yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—1221no—
209C22×C4C22⋊D6111yescharacteristic
210C22×C4C22⋊D6112yes—
211C22×C4C22×D6112yes—
212C22×C4C22×D6111yescharacteristic
213Q16—1222no—
214SD16—1222no—
215SD16—1222no—
216D8—1222no—
217M16—1224no—
218M16—1224no—
219C2×C8—614no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—612no—
223C2×C8—1222no—
224C4⋊C4—22no—
225C4⋊C4—612no—
226C4⋊C4—1222no—
227C4⋊C4C22×D6112yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—1221no—
232C22⋊C4—1222no—
233C22⋊C4—1222no—
234C42—21no—
235C42—1221no—
236C23—22no—
237C23—21no—
238C23—42no—
239C23—1221no—
240C23C2×C22⋊D6112yes—
241C23C2×C22⋊D6111yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—1221no—
245Q8—1221no—
246D4—21no—
247D4—21no—
248D4—44no—
249D4—42no—
250D4—1221no—
251D4—1221no—
252D4—2444no—
253D4—2442no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—1222no—
262C2×C4—1221no—
263C2×C4—2442no—
264C2×C4D4×D6112yes—
265C2×C4#1175822412yes—
266C2×C4C2×C22⋊D6112yes—
267C2×C4C2×C22⋊D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—612no—
270C8—612no—
271C8—1222no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—44no—
277C22—41no—
278C22—42no—
279C22—2441no—
280C22—2442no—
281C22#1451974912yes—
282C22C22×C22⋊D6111yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—2441no—
287C4—2442no—
288C4#1451974912yes—
289C4C2×D4×D6111yescharacteristic
290C4C2×#1175822411yescharacteristic
291C2—22no—
292C2—42no—
293C2—81no—
294C2—4881no—
295C2C2×#1451974911yescharacteristic
296C2#1684056012yes—
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#525C2
socleC22×C61C22×D4
hypercenter#525D61
hypocenterC61#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#14519797C2semidirect
2. C22×#11758194C2semidirect
3. #16840273C2semidirect
4. #16840018C2semidirect
5. #16840013C2semidirect
6. #16840010C2semidirect
7. #16840006C2semidirect
8. #16839798C2semidirect
9. #16839758C2semidirect
10. #16839756C2semidirect
11. C61×#525C2semidirect
14. C2×#11758202C22semidirect
15. C2×#11758200C22semidirect
16. C2×#11758201C22semidirect
17. C2×#11758199C22semidirect
29. #14519710C22semidirect
30. #14519708C22semidirect
31. #14519701C22semidirect
32. #14519700C22semidirect
33. #14519698C22semidirect
34. #14519697C22semidirect
83. C2×#92418D4semidirect
152. #525D61semidirect
160. C61#3054semidirect