Finite Group Databasebeta

← #21457657

Subgroups — #21457657

Order 7808.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840451C211yesmaximal, characteristic, complemented
2#16840409C211yesmaximal, characteristic
3#16840115C211yesmaximal, characteristic, complemented
4#16840094C211yesmaximal, characteristic, complemented
5#16840065C211yesmaximal, characteristic, complemented
6#16840004C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839983C211yesmaximal, characteristic, complemented
9#16839926C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839756C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C22×#92418C2211yescharacteristic, complemented
22C2×C8×D61C2211yescharacteristic
23#14519770—21no—
24#14519769—21no—
25#14519768C2211yescharacteristic, complemented
26#14519764C2211yescharacteristic
27#14519759—21no—
28#14519759—21no—
29#14519757C2211yescharacteristic
30#14519757C2211yescharacteristic
31#14519756C2211yescharacteristic, complemented
32#14519748—21no—
33#14519745—21no—
34#14519742C2211yescharacteristic, complemented
35#14519739C2211yescharacteristic
36C4×C22⋊D61C2211yescharacteristic
37#14519734—21no—
38C4⋊C4×D61C2211yescharacteristic
39C22⋊C4×D61—21no—
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66D4×D61—22no—
67D4×D61—41no—
68#11758222—22no—
69#11758222—41no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758200—41no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108Dic244—41no—
109#11758190—22no—
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—81no—
117C22×D61C2×D411yescharacteristic
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—22no—
129C22⋊D61—42no—
130C22⋊D61—42no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244#4112yes—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—81no—
144Dic122—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—22no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—84no—
165C2×D61#13512yes—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3296—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61—81no—
181C2×C61#54611yescharacteristic
182C2×C61C2×#13511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—22no—
185D61—42no—
186#552—611no—
187#546—611no—
188#488—611no—
189#483—611no—
190#482D6111yescharacteristic, complemented
191#478—611no—
192#467—611no—
193#465—611no—
194#464—611no—
195#452—611no—
196#450—611no—
197C4×SD16—611no—
198C8×D4—611no—
199#416—611no—
200C2×#102—611no—
201C61#329611yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C22×C8—611no—
208C22×C8—611no—
209#126—1221no—
210#125—611no—
211#125—1221no—
212#124—611no—
213#123—1221no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8—611no—
218#121—1221no—
219#121C2×D6111yescharacteristic
220#120—1221no—
221C4×Q8—611no—
222C4×D4—611no—
223C4×D4—611no—
224#117—1221no—
225#117C2×D6111yescharacteristic, complemented
226C2×C4⋊C4—611no—
227C2×C22⋊C4—1221no—
228#107C2×D6111yescharacteristic, complemented
229#106—611no—
230#106C2×D6111yescharacteristic, complemented
231C4⋊C8—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241#102C2×D6111yescharacteristic
242C22⋊C8—611no—
243C22⋊C8C2×D6111yescharacteristic, complemented
244C4×C8—611no—
245C24—1221no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8—611no—
250C2×D4—21no—
251C2×D4—611no—
252C2×D4—611no—
253C2×D4—1221no—
254C2×D4—1222no—
255C2×D4—1221no—
256C2×D4—2441no—
257C2×D4C22×D6111yescharacteristic
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263Q16—2441no—
264SD16—1222no—
265SD16—2441no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—611no—
287C22⋊C4—611no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—21no—
295C42—611no—
296C42—1221no—
297C23—21no—
298C23—611no—
299C23—1221no—
300C23—4881no—
301C23—2442no—
302C23—2442no—
303C23D4×D6111yescharacteristic
304Q8—1221no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—612no—
312D4—1222no—
313D4—1221no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—612no—
345C22—1221no—
346C22—1221no—
347C22—1222no—
348C22—4884no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1221no—
357C4—1221no—
358C4—1221no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4#41×D6111yescharacteristic
363C4#1451982311yescharacteristic
364C2—41no—
365C2—81no—
366C2—1222no—
367C2—2442no—
368C2#1684040411yescharacteristic
369C2#135×D6111yescharacteristic
370C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3296
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840451C2semidirect
3. #16840115C2semidirect
4. #16840094C2semidirect
5. #16840065C2semidirect
6. #16840004C2semidirect
7. #16839989C2semidirect
8. #16839983C2semidirect
9. #16839926C2semidirect
10. #16839914C2semidirect
11. #16839849C2semidirect
12. #16839825C2semidirect
13. #16839756C2semidirect
14. #102×D61C2semidirect
15. C61×#482C2semidirect
18. C2×Dic244C22semidirect
21. C22×#92418C22semidirect
25. #14519768C22semidirect
31. #14519756C22semidirect
34. #14519742C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519702C22semidirect
43. #14519700C22semidirect
44. #14519700C22semidirect
45. #14519700C22semidirect
51. C8×Dic61C22semidirect
53. #117×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
58. C22⋊C8×C61C22semidirect
190. #482D61semidirect
201. C61#3296semidirect
225. #117C2×D61semidirect
228. #107C2×D61semidirect
230. #106C2×D61semidirect
243. C22⋊C8C2×D61semidirect