Finite Group Databasebeta

← #21457636

Subgroups — #21457636

Order 7808.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2D4×C22⋊D61C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840081C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13C2×#14519698C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×#11758201C2211yescharacteristic, complemented
19C22×#92418C2211yescharacteristic, complemented
20C2×C8×D61C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519773C2211yescharacteristic
23#14519767—21no—
24#14519757—21no—
25#14519754—21no—
26#14519753C2211yescharacteristic, complemented
27#14519751C2211yescharacteristic
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519746—21no—
31#14519745—21no—
32Q8×Dic61C2211yescharacteristic, complemented
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519737—21no—
36C2×C4⋊Dic61C2211yescharacteristic, complemented
37C4⋊C4×D61C2211yescharacteristic, complemented
38#14519709C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C22⋊Q8×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C24×C61—21no—
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—22no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—44no—
74C2×C22⋊D61D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77D4×D61—22no—
78D4×D61—41no—
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83SD16×C61—22no—
84SD16×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61D411yescharacteristic
93#11758201—41no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418—41no—
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C8×D61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—42no—
115C23×C61—42no—
116C23×C61—81no—
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129D4×C61#4112yes—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—81no—
141C22⋊D61SD1614yescomplemented
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61—81no—
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150D244—21no—
151D244—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—81no—
155Dic122—81no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—84no—
169C22×C61C2×SD1612yes—
170C22×C61C22×D411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—84no—
177C2×D61C2×SD1612yes—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61C2×#4111yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61C2×SD1612yes—
189#3295—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—42no—
192C2×C61—81no—
193C2×C61#54611yescharacteristic
194C2×C61C22×SD1611yescharacteristic
195C2×C61#57611yescharacteristic
196D61—22no—
197D61—81no—
198#554—611no—
199D42—611no—
200#486—611no—
201#481—611no—
202#481—611no—
203#476—611no—
204#465—611no—
205#465—611no—
206#460—611no—
207#450—611no—
208#450D6111yescharacteristic, complemented
209C4×SD16—611no—
210C8×D4—611no—
211C2×#102—611no—
212C2×#102—611no—
213C61#329511yescharacteristic, complemented, Sylow
214C22×D4—611no—
215C22×D4—1221no—
216C22×D4C2×D6111yescharacteristic
217C2×SD16—611no—
218C2×SD16C2×D6111yescharacteristic
219C2×SD16C2×D6111yescharacteristic, complemented
220C22×C8—611no—
221C22×C8—611no—
222C4⋊Q8—611no—
223#127—611no—
224#125—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—1221no—
227C22⋊Q8—1221no—
228C22⋊Q8C2×D6111yescharacteristic, complemented
229#121—611no—
230#121—611no—
231#121—1221no—
232#120—1221no—
233#120—1221no—
234C4×Q8—611no—
235C4×D4—611no—
236C4×D4—611no—
237C4×D4—1221no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240#106—611no—
241#106—611no—
242#106—611no—
243C4⋊C8—611no—
244#103—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102C2×D6111yescharacteristic
253#102C2×D6111yescharacteristic, complemented
254C22⋊C8—611no—
255C22⋊C8C2×D6111yescharacteristic, complemented
256C4×C8—611no—
257C24—21no—
258C24—1221no—
259C2×Q8—1221no—
260C2×Q8C22×D6111yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1222no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—2441no—
273C2×D4—2444no—
274C2×D4C22×D6111yescharacteristic
275C2×D4C22×D6111yescharacteristic
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4C22×D6111yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—2441no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—611no—
294C4⋊C4—611no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4C22×D6111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—611no—
316C23—1221no—
317C23—4881no—
318C23—2442no—
319C23—2442no—
320C23D4×D6111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—614no—
329D4—1221no—
330D4—1221no—
331D4—4881no—
332D4—2442no—
333D4—2442no—
334D4—2442no—
335D4—2442no—
336D4#1175822412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4D4×D6111yescharacteristic
353C2×C4C23×D6111yescharacteristic
354C8—21no—
355C8—21no—
356C8—1221no—
357C8—1221no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—612no—
368C22—1221no—
369C22—1221no—
370C22—4884no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22SD16×D6112yes—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—612no—
380C4—1221no—
381C4—1221no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4C2×#1175822411yescharacteristic
386C4#1451982211yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—1222no—
391C2—4881no—
392C2#1684039911yescharacteristic
393C2C2×SD16×D6111yescharacteristic
394C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3295
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840107C2semidirect
4. #16840081C2semidirect
5. #16840079C2semidirect
6. #16840050C2semidirect
7. #16839993C2semidirect
8. #16839988C2semidirect
9. #16839960C2semidirect
10. #16839911C2semidirect
11. SD16×Dic61C2semidirect
12. #16839825C2semidirect
13. C2×#14519698C2semidirect
14. #102×D61C2semidirect
15. C61×#450C2semidirect
18. C2×#11758201C22semidirect
19. C22×#92418C22semidirect
20. C2×C8×D61C22semidirect
21. #14519776C22semidirect
26. #14519753C22semidirect
32. Q8×Dic61C22semidirect
36. C2×C4⋊Dic61C22semidirect
37. C4⋊C4×D61C22semidirect
38. #14519709C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519701C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
47. #14519698C22semidirect
48. #14519698C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
54. C2×SD16×C61C22semidirect
55. C22⋊Q8×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
141. C22⋊D61SD16semidirect
208. #450D61semidirect
213. C61#3295semidirect
219. C2×SD16C2×D61semidirect
228. C22⋊Q8C2×D61semidirect
253. #102C2×D61semidirect
255. C22⋊C8C2×D61semidirect