Finite Group Databasebeta

← #21456580

Subgroups — #21456580

Order 7808.

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

normal subgroups only

This group has 472 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
1C2×#14519751C211yesmaximal, characteristic, complemented
2#16840095C211yesmaximal, characteristic, complemented
3#16840086C212yesmaximal, complemented
4#16840078C211yesmaximal, characteristic, complemented
5#16839996C212yesmaximal, complemented
6#16839993C212yesmaximal, complemented
7#16839912C211yesmaximal, characteristic, complemented
8#16839907C212yesmaximal, complemented
9#16839895C211yesmaximal, characteristic, complemented
10C2×C22⋊#92418C211yesmaximal, characteristic, complemented
11C61×#525C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61—21no—
14C2×#11758201C2212yescomplemented
15C2×#11758199C2212yescomplemented
16C22×#92418C2212yescomplemented
17#14519751—21no—
18#14519751—21no—
19#14519751C2212yes—
20#14519751C2212yes—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758198—21no—
23#14519710C2212yescomplemented
24#14519708C2212yescomplemented
25#14519701C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yescomplemented
28#14519697C2212yescomplemented
29C22⋊#92418C2211yescharacteristic
30C22⋊#92418C2211yescharacteristic
31C22⋊#92418C2212yescomplemented
32C2×#41×C61C2211yescharacteristic, complemented
33C23×C4×C61C2211yescharacteristic
34#123×C61—21no—
35C22⋊Q8×C61C2211yescharacteristic
36C22⋊Q8×C61C2211yescharacteristic, complemented
37#121×C61C2211yescharacteristic
38#121×C61C2211yescharacteristic, complemented
39#120×C61—21no—
40C4×D4×C61—21no—
41C4×D4×C61—21no—
42#117×C61C2211yescharacteristic, complemented
43C24×C61D411yescharacteristic
44C23×D61—21no—
45#41×C61—42no—
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—21no—
48C2×D4×C61—21no—
49C2×D4×C61—21no—
50C2×D4×C61C2311yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—42no—
53C22×C4×C61D411yescharacteristic
54C22×C4×C61D411yescharacteristic
55C22×C4×C61D411yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C2×C22⋊D61—22no—
60C2×C22⋊D61—22no—
61C2×C22⋊D61—44no—
62C22×Dic61—21no—
63C2×D244—21no—
64C2×D244—42no—
65C2×D244C2312yes—
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2311yescharacteristic
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C22⋊C4×C61—21no—
72C22⋊C4×C61—21no—
73C22⋊C4×C61—21no—
74C22⋊C4×C61—21no—
75C42×C61—21no—
76#11758201—42no—
77#11758199—42no—
78#11758198—22no—
79#11758198—22no—
80C4⋊Dic61—21no—
81C4⋊Dic61C2312yes—
82C2×#92418—42no—
83C2×#92418C2312yes—
84C2×#92418C2312yes—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—21no—
88C23×C61—41no—
89C23×C61C2×D411yescharacteristic
90C23×C61C2×D411yescharacteristic
91C23×C61C2×D411yescharacteristic
92C22×D61—22no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96Q8×C61—22no—
97D4×C61—22no—
98D4×C61—42no—
99D4×C61—42no—
100D4×C61—42no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2411yescharacteristic
115C22⋊D61—44no—
116C22⋊D61—44no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119D244—22no—
120D244—22no—
121D244—42no—
122#92418—22no—
123#92418—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—44no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61#13512yes—
136C22×C61AGL(1,ℤ/8)12yes—
137C22×C61C22×D411yescharacteristic
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—84no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61H(5,𝔽2)12yes—
149Dic61—42no—
150#3188—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—22no—
153C2×C61—41no—
154C2×C61—81no—
155C2×C61#53411yescharacteristic
156C2×C61C2×#13511yescharacteristic
157C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
158D61—82no—
159#525D6111yescharacteristic, complemented
160C2×#121—611no—
161#484—611no—
162#482—612no—
163#481—611no—
164#466—612no—
165#465—612no—
166#450—611no—
167#449—612no—
168#447—611no—
169C2×C22⋊C8—611no—
170C61#318811yescharacteristic, complemented, Sylow
171C2×#41C2×D6111yescharacteristic, complemented
172C22×D4—611no—
173C22×D4—1221no—
174C23×C4C2×D6111yescharacteristic
175C2×SD16—612no—
176C2×D8—612no—
177C22×C8—612no—
178#123—21no—
179C22⋊Q8C2×D6111yescharacteristic
180C22⋊Q8C2×D6111yescharacteristic, complemented
181#121—612no—
182#121—612no—
183#121—1221no—
184#121—1221no—
185#121C2×D6111yescharacteristic
186#121C2×D6111yescharacteristic, complemented
187#120—21no—
188C4×D4—21no—
189C4×D4—21no—
190#117C2×D6111yescharacteristic, complemented
191C2×C4⋊C4—611no—
192C2×C22⋊C4—1221no—
193#107—612no—
194#106—612no—
195#103—612no—
196#102—612no—
197#102—612no—
198#102—612no—
199C22⋊C8—611no—
200C22⋊C8—611no—
201C22⋊C8—612no—
202C24—1221no—
203C24C22⋊D6111yescharacteristic
204#41—42no—
205C2×Q8C22×D6111yescharacteristic
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—612no—
210C2×D4—1222no—
211C2×D4—1222no—
212C2×D4—1221no—
213C2×D4—2442no—
214C2×D4—2444no—
215C2×D4C22×D6111yescharacteristic
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—1221no—
219C22×C4C22⋊D6111yescharacteristic
220C22×C4C22⋊D6111yescharacteristic
221C22×C4C22⋊D6111yescharacteristic
222C22×C4C22×D6111yescharacteristic
223C22×C4C22×D6111yescharacteristic
224C22×C4C22×D6111yescharacteristic
225SD16—2442no—
226D8—2442no—
227C2×C8—612no—
228C2×C8—612no—
229C2×C8—2442no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—612no—
233C4⋊C4—1221no—
234C4⋊C4C22×D6111yescharacteristic
235C4⋊C4C22×D6111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—1222no—
242C22⋊C4—1222no—
243C42—21no—
244C23—22no—
245C23—22no—
246C23—21no—
247C23—41no—
248C23—1222no—
249C23—2442no—
250C23—2442no—
251C23—2442no—
252C23C2×C22⋊D6111yescharacteristic
253C23C2×C22⋊D6111yescharacteristic
254C23C2×C22⋊D6111yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—1222no—
261D4—1222no—
262D4—2442no—
263D4—2444no—
264D4—2444no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—1222no—
276C2×C4—2442no—
277C2×C4C2×C22⋊D6111yescharacteristic
278C2×C4C2×C22⋊D6111yescharacteristic
279C2×C4C2×C22⋊D6111yescharacteristic
280C2×C4C23×D6111yescharacteristic
281C8—1222no—
282C8—1222no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—4884no—
295C22—2442no—
296C22—2442no—
297C22—2442no—
298C22#1451979712yes—
299C22#1451980212yes—
300C22C22×C22⋊D6111yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—2442no—
308C4#1451982212yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—81no—
313C2—4882no—
314C2#1684032111yescharacteristic
315C2C2×#1451979711yescharacteristic
316C2C2×#1451980211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#525C2
socleC22×C61C22×D4
hypercenter#525D61
hypocenterC61#3188
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. #16840095C2semidirect
3. #16840086C2semidirect
4. #16840078C2semidirect
5. #16839996C2semidirect
6. #16839993C2semidirect
7. #16839912C2semidirect
8. #16839907C2semidirect
9. #16839895C2semidirect
10. C2×C22⋊#92418C2semidirect
11. C61×#525C2semidirect
14. C2×#11758201C22semidirect
15. C2×#11758199C22semidirect
16. C22×#92418C22semidirect
23. #14519710C22semidirect
24. #14519708C22semidirect
25. #14519701C22semidirect
26. #14519698C22semidirect
27. #14519697C22semidirect
28. #14519697C22semidirect
31. C22⋊#92418C22semidirect
32. C2×#41×C61C22semidirect
36. C22⋊Q8×C61C22semidirect
38. #121×C61C22semidirect
42. #117×C61C22semidirect
159. #525D61semidirect
170. C61#3188semidirect
171. C2×#41C2×D61semidirect
180. C22⋊Q8C2×D61semidirect
186. #121C2×D61semidirect
190. #117C2×D61semidirect