Finite Group Databasebeta

← #21456172

Subgroups — #21456172

Order 7808.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840392C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic
3#16840128C211yesmaximal, characteristic, complemented
4#16840125C211yesmaximal, characteristic, complemented
5#16840123C211yesmaximal, characteristic, complemented
6#16840121C211yesmaximal, characteristic, complemented
7#16840118C211yesmaximal, characteristic, complemented
8#16840109C211yesmaximal, characteristic, complemented
9#16840107C211yesmaximal, characteristic, complemented
10#16839765C211yesmaximal, characteristic, complemented
11#16839762C211yesmaximal, characteristic, complemented
12#16839757C211yesmaximal, characteristic, complemented
13#102×D61C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519777C2211yescharacteristic, complemented
21#14519776—21no—
22#14519776C2211yescharacteristic, complemented
23#14519774C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519768C2211yescharacteristic, complemented
26#14519767—21no—
27#14519766C2211yescharacteristic
28#14519757—21no—
29#14519755—21no—
30#14519750—21no—
31#14519750—21no—
32#14519747—21no—
33#14519747—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37#14519701C2211yescharacteristic, complemented
38#14519701C2211yescharacteristic, complemented
39#14519699C2211yescharacteristic
40#14519699C2211yescharacteristic
41#14519699C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519688C2211yescharacteristic, complemented
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic, complemented
55#103×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65#11758226—22no—
66#11758226—22no—
67D4×D61—22no—
68D4×D61—22no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61C2311yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198D411yescharacteristic
92#11758198D411yescharacteristic
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—42no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—81no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—42no—
138D244—81no—
139D244—81no—
140C4×D61—42no—
141C4×D61—81no—
142C4×D61#4112yes—
143C4×D61#4112yes—
144Dic122—81no—
145Dic122—81no—
146C8×C61—21no—
147C8×C61—21no—
148#92418—21no—
149#92418—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—84no—
163C2×D61#12412yes—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61C2×#4111yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61#12412yes—
176#3136—611nomaximal, Sylow
177C2×C61—81no—
178C2×C61C2×#12411yescharacteristic
179C2×C61#57611yescharacteristic
180C2×C61#57711yescharacteristic
181D61—22no—
182D61—81no—
183D61—81no—
184#544—611no—
185#535—611no—
186#490—611no—
187#490—611no—
188#489—611no—
189#489—611no—
190#488—611no—
191#488D6111yescharacteristic, complemented
192#486—611no—
193#486—611no—
194#418—611no—
195#417—611no—
196#416—611no—
197C2×#102—611no—
198#405—611no—
199C61#313611yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C22×D4—611no—
202C2×M16—611no—
203C22×C8—611no—
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206C4⋊Q8—1221no—
207#127—611no—
208#127—611no—
209#125—611no—
210#125—1221no—
211#125C2×D6111yescharacteristic, complemented
212#124—611no—
213#124C2×D6111yescharacteristic
214C22⋊Q8—1221no—
215C22⋊Q8—1221no—
216#121—1221no—
217#121—1221no—
218#120—1221no—
219#120—1221no—
220#117—611no—
221#117—611no—
222C2×C4⋊C4—611no—
223#103—611no—
224#103—611no—
225#103C2×D6111yescharacteristic, complemented
226#103C2×D6111yescharacteristic, complemented
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237#102C2×D6111yescharacteristic
238#102C2×D6111yescharacteristic
239#97—611no—
240#97—611no—
241C4×C8—611no—
242C4×C8C2×D6111yescharacteristic, complemented
243C24—1221no—
244#41—1222no—
245#41—1222no—
246C2×Q8—1221no—
247C2×Q8—1221no—
248C2×Q8C22×D6111yescharacteristic
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1222no—
253C2×D4—1222no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263M16—1222no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—1222no—
267C2×C8C22×D6111yescharacteristic
268C2×C8C22×D6111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22×D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—611no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—21no—
293C23—611no—
294C23—1221no—
295C23—1221no—
296C23—4881no—
297C23—4881no—
298C23—2442no—
299Q8—21no—
300Q8—21no—
301Q8—4881no—
302Q8—4881no—
303D4—21no—
304D4—21no—
305D4—1221no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4—4881no—
310D4—4881no—
311D4—4881no—
312D4—4881no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—611no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—2442no—
327C2×C4D4×D6111yescharacteristic
328C2×C4D4×D6111yescharacteristic
329C2×C4C23×D6111yescharacteristic
330C8—21no—
331C8—21no—
332C8—1221no—
333C8—1221no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—612no—
338C22—1221no—
339C22—1221no—
340C22—4884no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—612no—
354C4—1221no—
355C4—1221no—
356C4—2441no—
357C4—2441no—
358C4#41×D6111yescharacteristic
359C4#41×D6111yescharacteristic
360C2—81no—
361C2—1222no—
362C2—4881no—
363C2—4881no—
364C2#124×D6111yescharacteristic
365C2#1684056411yescharacteristic
366C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3136
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840392C2semidirect
3. #16840128C2semidirect
4. #16840125C2semidirect
5. #16840123C2semidirect
6. #16840121C2semidirect
7. #16840118C2semidirect
8. #16840109C2semidirect
9. #16840107C2semidirect
10. #16839765C2semidirect
11. #16839762C2semidirect
12. #16839757C2semidirect
13. #102×D61C2semidirect
14. #16839716C2semidirect
15. C61×#488C2semidirect
20. #14519777C22semidirect
22. #14519776C22semidirect
25. #14519768C22semidirect
37. #14519701C22semidirect
38. #14519701C22semidirect
41. #14519699C22semidirect
42. #14519699C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. #14519688C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
52. #125×C61C22semidirect
54. #103×C61C22semidirect
55. #103×C61C22semidirect
58. C4×C8×C61C22semidirect
191. #488D61semidirect
199. C61#3136semidirect
211. #125C2×D61semidirect
225. #103C2×D61semidirect
226. #103C2×D61semidirect
242. C4×C8C2×D61semidirect