Finite Group Databasebeta

← #21457850

Subgroups — #21457850

Order 7808.

402 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#16840483C211yesmaximal, characteristic, complemented
2#16840403C211yesmaximal, characteristic
3#16840123C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840088C211yesmaximal, characteristic, complemented
6#16840051C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839986C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839865C211yesmaximal, characteristic, complemented
12#16839831C211yesmaximal, characteristic, complemented
13#16839768C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#470C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519772—21no—
23#14519770—21no—
24#14519766C2211yescharacteristic
25#14519763—21no—
26#14519762—21no—
27#14519753C2211yescharacteristic, complemented
28#14519752—21no—
29#14519752C2211yescharacteristic
30#14519747—21no—
31Q8×Dic61C2211yescharacteristic, complemented
32#14519742—21no—
33#14519739C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519736C2211yescharacteristic
36#14519735C2211yescharacteristic, complemented
37C22⋊C4×D61—21no—
38#14519710C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519706C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#103×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61D411yescharacteristic
64#11758226—22no—
65#11758226—41no—
66C2×D244—22no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77Q16×C61—41no—
78M16×C61—41no—
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—
87C22⋊Dic61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758201—22no—
90#11758201—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C8×D61—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—81no—
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
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×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—21no—
137D244—21no—
138D244—21no—
139D244—42no—
140D244—42no—
141D244—81no—
142D244#4112yes—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—42no—
146C4×D61—81no—
147Dic122—42no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—22no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61H(5,𝔽2)11yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178#3311—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61#54611yescharacteristic
181C2×C61#57511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—41no—
184D61—42no—
185D61—81no—
186#556—611no—
187#546—611no—
188#489—611no—
189#485—611no—
190#482—611no—
191#476—611no—
192#470D6111yescharacteristic, complemented
193#465—611no—
194#464—611no—
195#452—611no—
196#450—611no—
197#440—611no—
198#435—611no—
199#418—611no—
200#416—611no—
201C61#331111yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4—611no—
204C2×Q16C2×D6111yescharacteristic, complemented
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16C2×D6111yescharacteristic
208C22×C8—611no—
209C4⋊Q8—611no—
210#126—1221no—
211#126—1221no—
212#124—611no—
213#124—1221no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8C2×D6111yescharacteristic
217C22⋊Q8C2×D6111yescharacteristic
218#121—611no—
219#121—1221no—
220#120—1221no—
221C4×Q8—611no—
222C4×Q8—1221no—
223C4×D4—611no—
224C4×D4—611no—
225#117—611no—
226#117—611no—
227C2×C22⋊C4—1221no—
228#107—611no—
229#106—611no—
230#106C2×D6111yescharacteristic, complemented
231C4⋊C8—611no—
232#103—611no—
233#103—611no—
234#103C2×D6111yescharacteristic, complemented
235#103C2×D6111yescharacteristic, complemented
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244#97—611no—
245C24—1221no—
246#41—1222no—
247#41—2441no—
248C2×Q8—1221no—
249C2×Q8C22×D6111yescharacteristic
250C2×Q8C22×D6111yescharacteristic
251C2×D4—611no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1222no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—2441no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263Q16—41no—
264SD16—1222no—
265SD16—2441no—
266M16—41no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—2441no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
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—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—611no—
294C42—1221no—
295C42—1221no—
296C42—1221no—
297C23—611no—
298C23—1221no—
299C23—1221no—
300C23—4881no—
301C23—2442no—
302C23—2442no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—2442no—
309D4—612no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316D4—2441no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—1221no—
342C22—1221no—
343C22—1221no—
344C22—1222no—
345C22—4884no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1221no—
358C4—1221no—
359C4—1221no—
360C4—2441no—
361C4—2441no—
362C4#41×D6111yescharacteristic
363C4#1451982211yescharacteristic
364C2—41no—
365C2—4881no—
366C2—2441no—
367C2—2442no—
368C2#1684040111yescharacteristic
369C2#1684056111yescharacteristic
370C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3311
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #16840483C2semidirect
3. #16840123C2semidirect
4. #16840100C2semidirect
5. #16840088C2semidirect
6. #16840051C2semidirect
7. #16839994C2semidirect
8. #16839986C2semidirect
9. #16839923C2semidirect
10. #16839912C2semidirect
11. #16839865C2semidirect
12. #16839831C2semidirect
13. #16839768C2semidirect
14. #16839757C2semidirect
15. C61×#470C2semidirect
20. C2×C8×D61C22semidirect
21. #14519776C22semidirect
27. #14519753C22semidirect
31. Q8×Dic61C22semidirect
36. #14519735C22semidirect
38. #14519710C22semidirect
39. #14519708C22semidirect
40. #14519706C22semidirect
41. #14519701C22semidirect
42. #14519701C22semidirect
50. #14519689C22semidirect
51. #14519687C22semidirect
52. C2×Q16×C61C22semidirect
56. #106×C61C22semidirect
57. #103×C61C22semidirect
58. #103×C61C22semidirect
192. #470D61semidirect
201. C61#3311semidirect
204. C2×Q16C2×D61semidirect
230. #106C2×D61semidirect
234. #103C2×D61semidirect
235. #103C2×D61semidirect