Finite Group Databasebeta

← #21457778

Subgroups — #21457778

Order 7808.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840413C211yesmaximal, characteristic, complemented
2#16840403C211yesmaximal, characteristic, complemented
3#16840123C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839910C211yesmaximal, characteristic, complemented
10#16839898C211yesmaximal, characteristic, complemented
11#16839873C211yesmaximal, characteristic, complemented
12#16839830C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14C2×#14519697C211yesmaximal, characteristic, complemented
15C61×#483C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222—21no—
18C22×D244C2211yescharacteristic
19C2×#11758201C2211yescharacteristic, complemented
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758189C2211yescharacteristic, complemented
23C22×#92418C2211yescharacteristic
24#14519776C2211yescharacteristic, complemented
25#14519766C2211yescharacteristic
26#14519762—21no—
27#14519762—21no—
28#14519760—21no—
29#14519755—21no—
30#14519752—21no—
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic, complemented
33#14519751C2211yescharacteristic
34#14519747—21no—
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic, complemented
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic, complemented
39C22⋊C4×D61—21no—
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C22⋊Q8×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61D411yescharacteristic
65#11758226—22no—
66#11758226—41no—
67#11758222—44no—
68C2×D244—22no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊Dic61D411yescharacteristic
92#11758201—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—22no—
110D488—41no—
111#11758189—41no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—81no—
119C22×D61C2×D411yescharacteristic
120Q8×C61—21no—
121Q8×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—22no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—42no—
143D244—42no—
144D244—42no—
145D244—81no—
146D244#4112yescomplemented
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—81no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61AGL(1,ℤ/8)12yes—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—22no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—84no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C2×#4111yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186#3306—611nomaximal, Sylow
187C2×C61—22no—
188C2×C61#54611yescharacteristic
189C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C61#57711yescharacteristic
191D61—41no—
192D61—42no—
193D61—81no—
194D61—81no—
195#547—611no—
196#546—611no—
197#489—611no—
198#483D6111yescharacteristic, complemented
199#481—611no—
200#476—611no—
201#469—611no—
202#465—611no—
203#463—611no—
204#449—611no—
205#447—611no—
206#442—611no—
207#435—611no—
208#417—611no—
209C2×#102—611no—
210C61#330611yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—1221no—
213C22×D4—611no—
214C2×SD16—611no—
215C2×D8—611no—
216C2×D8—611no—
217C2×M16—611no—
218C22×C8—611no—
219C4⋊Q8—611no—
220#124—611no—
221#123—1221no—
222#123—1221no—
223#123—1221no—
224C22⋊Q8—1221no—
225C22⋊Q8C2×D6111yescharacteristic
226#121—611no—
227#121—611no—
228#121—611no—
229#121—1221no—
230#120—1221no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C2×D6111yescharacteristic
236C2×C22⋊C4—1221no—
237#106—611no—
238#106C2×D6111yescharacteristic, complemented
239#106C2×D6111yescharacteristic, complemented
240C4⋊C8—611no—
241#103—611no—
242#103C2×D6111yescharacteristic, complemented
243#103C2×D6111yescharacteristic, complemented
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251C22⋊C8—611no—
252C22⋊C8C2×D6111yescharacteristic
253#97—611no—
254C24—1221no—
255#41—1222no—
256#41—2444no—
257#41—2441no—
258C2×Q8—1221no—
259C2×Q8C22×D6111yescharacteristic
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—1222no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278SD16—2441no—
279D8—1222no—
280D8—2441no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—2441no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4C22×D6111yescharacteristic
294C4⋊C4C22×D6111yescharacteristic
295C4⋊C4C22×D6111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C42—611no—
307C23—611no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—4881no—
312C23—2442no—
313C23—2442no—
314C23D4×D6111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—2442no—
318D4—612no—
319D4—1222no—
320D4—1221no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4—4881no—
326D4—2442no—
327D4—2442no—
328D4—2442no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4D4×D6111yescharacteristic
348C2×C4C23×D6111yescharacteristic
349C8—21no—
350C8—21no—
351C8—1221no—
352C8—1221no—
353C22—21no—
354C22—21no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1222no—
359C22—4884no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1451980412yes—
369C22C2×D4×D6111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—1221no—
376C4—1221no—
377C4—1221no—
378C4—2441no—
379C4#41×D6111yescharacteristic
380C4#1451982311yescharacteristic
381C2—22no—
382C2—4881no—
383C2—4881no—
384C2—2441no—
385C2—2442no—
386C2#1684040411yescharacteristic
387C2C2×#1451980411yescharacteristic
388C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #16840413C2semidirect
2. #16840403C2semidirect
3. #16840123C2semidirect
4. #16840082C2semidirect
5. #16840051C2semidirect
6. #16840016C2semidirect
7. #16839993C2semidirect
8. #16839980C2semidirect
9. #16839910C2semidirect
10. #16839898C2semidirect
11. #16839873C2semidirect
12. #16839830C2semidirect
13. #16839762C2semidirect
14. C2×#14519697C2semidirect
15. C61×#483C2semidirect
19. C2×#11758201C22semidirect
22. C2×#11758189C22semidirect
24. #14519776C22semidirect
32. #14519752C22semidirect
36. #14519739C22semidirect
38. C4⋊C4×D61C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519701C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. #14519687C22semidirect
54. #106×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
146. D244#41semidirect
198. #483D61semidirect
210. C61#3306semidirect
238. #106C2×D61semidirect
239. #106C2×D61semidirect
242. #103C2×D61semidirect
243. #103C2×D61semidirect