Finite Group Databasebeta

← #21457638

Subgroups — #21457638

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
2#16840396C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840078C211yesmaximal, characteristic, complemented
6#16840051C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839912C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11#16839847C211yesmaximal, characteristic, complemented
12C8×C22⋊D61C211yesmaximal, characteristic, complemented
13C2×#14519699C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic, complemented
22#14519776C2211yescharacteristic, complemented
23#14519773C2211yescharacteristic
24#14519767—21no—
25#14519757—21no—
26#14519754—21no—
27#14519753C2211yescharacteristic, complemented
28#14519752C2211yescharacteristic
29#14519750—21no—
30#14519747—21no—
31#14519745—21no—
32Q8×Dic61C2211yescharacteristic, complemented
33#14519739C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519737—21no—
36C2×C4⋊Dic61C2211yescharacteristic, complemented
37C4⋊C4×D61C2211yescharacteristic, complemented
38#14519708C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519706C2211yescharacteristic, complemented
41#14519699C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic, complemented
54C22⋊Q8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69C22×Dic61—21no—
70D4×D61—22no—
71D4×D61—41no—
72D4×D61—44no—
73C2×D244—22no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—41no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83SD16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊Dic61D411yescharacteristic
93#11758201—22no—
94#11758201—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C8×D61—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C22⋊D61SD1614yescomplemented
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—81no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—42no—
149D244—42no—
150D244#4112yes—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—42no—
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—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61C2×SD1612yes—
166C22×C61C22×D411yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—22no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—84no—
176C2×D61—84no—
177C2×D61C2×SD1612yes—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61C2×#4111yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61C2×SD1612yes—
189#3295—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—81no—
192C2×C61#54611yescharacteristic
193C2×C61C22×SD1611yescharacteristic
194C2×C61#57611yescharacteristic
195D61—22no—
196D61—42no—
197D61—81no—
198#554—611no—
199D42—611no—
200#486—611no—
201#481—611no—
202#481—611no—
203#476—611no—
204#465—611no—
205#465D6111yescharacteristic, complemented
206#460—611no—
207#450—611no—
208#450—611no—
209C4×SD16—611no—
210C8×D4—611no—
211C2×#102—611no—
212C2×#102—611no—
213C61#329511yescharacteristic, complemented, Sylow
214C22×D4—611no—
215C22×D4—611no—
216C22×D4—1221no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16C2×D6111yescharacteristic, complemented
220C22×C8—611no—
221C22×C8C2×D6111yescharacteristic, complemented
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—1221no—
231#121C2×D6111yescharacteristic
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#106C2×D6111yescharacteristic, complemented
243C4⋊C8—611no—
244#103C2×D6111yescharacteristic, complemented
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102—611no—
253#102C2×D6111yescharacteristic, complemented
254C22⋊C8—611no—
255C22⋊C8—611no—
256C4×C8—611no—
257C24—1221no—
258C24—1221no—
259C2×Q8—1221no—
260C2×Q8C22×D6111yescharacteristic
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1222no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1222no—
271C2×D4—1221no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2444no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4C22×D6111yescharacteristic
281SD16—41no—
282SD16—1222no—
283SD16—2441no—
284C2×C8—41no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—2441no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—611no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4C22×D6111yescharacteristic
300C4⋊C4C22×D6111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C23—21no—
311C23—611no—
312C23—1221no—
313C23—1221no—
314C23—4881no—
315C23—4881no—
316C23—2442no—
317C23—2442no—
318C23—2442no—
319C23—2442no—
320C23D4×D6111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—614no—
328D4—612no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—4881no—
333D4—2442no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
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—41no—
361C22—41no—
362C22—41no—
363C22—612no—
364C22—1221no—
365C22—1221no—
366C22—1222no—
367C22—4884no—
368C22—4884no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22SD16×D6112yes—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—612no—
381C4—1221no—
382C4—1221no—
383C4—2441no—
384C4—2441no—
385C4#41×D6111yescharacteristic
386C4#1451982211yescharacteristic
387C2—22no—
388C2—81no—
389C2—1222no—
390C2—4881no—
391C2—2442no—
392C2#1684040111yescharacteristic
393C2C2×SD16×D6111yescharacteristic
394C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3295
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840107C2semidirect
4. #16840082C2semidirect
5. #16840078C2semidirect
6. #16840051C2semidirect
7. #16839994C2semidirect
8. #16839960C2semidirect
9. #16839912C2semidirect
10. #16839911C2semidirect
11. #16839847C2semidirect
12. C8×C22⋊D61C2semidirect
13. C2×#14519699C2semidirect
14. #102×D61C2semidirect
15. C61×#465C2semidirect
20. C2×#11758201C22semidirect
21. C2×C8×D61C22semidirect
22. #14519776C22semidirect
27. #14519753C22semidirect
32. Q8×Dic61C22semidirect
36. C2×C4⋊Dic61C22semidirect
37. C4⋊C4×D61C22semidirect
38. #14519708C22semidirect
39. #14519708C22semidirect
40. #14519706C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
45. #14519698C22semidirect
46. #14519698C22semidirect
48. #14519697C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
52. C2×SD16×C61C22semidirect
53. C22×C8×C61C22semidirect
54. C22⋊Q8×C61C22semidirect
56. #106×C61C22semidirect
57. #103×C61C22semidirect
58. #102×C61C22semidirect
138. C22⋊D61SD16semidirect
205. #465D61semidirect
213. C61#3295semidirect
219. C2×SD16C2×D61semidirect
221. C22×C8C2×D61semidirect
228. C22⋊Q8C2×D61semidirect
242. #106C2×D61semidirect
244. #103C2×D61semidirect
253. #102C2×D61semidirect