Finite Group Databasebeta

← #21455770

Subgroups — #21455770

Order 7808.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840328C211yesmaximal, characteristic
2#16840243C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840084C211yesmaximal, characteristic, complemented
6#16840083C211yesmaximal, characteristic, complemented
7#16840080C211yesmaximal, characteristic, complemented
8#16840079C211yesmaximal, characteristic, complemented
9#16840077C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839799C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#102×D61C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#480C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519773—21no—
21#14519763—21no—
22#14519752C2211yescharacteristic
23#14519751C2211yescharacteristic
24#14519748C2211yescharacteristic
25#14519747—21no—
26#14519745—21no—
27#14519742—21no—
28#14519739—21no—
29C4×C22⋊D61—21no—
30C4×C22⋊D61—21no—
31#14519736C2211yescharacteristic, complemented
32#14519735C2211yescharacteristic
33#14519735C2211yescharacteristic
34#14519735C2211yescharacteristic, complemented
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic, complemented
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#107×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61D411yescharacteristic
68C2×C22⋊D61D411yescharacteristic
69D4×D61—22no—
70D4×D61—22no—
71#11758222—22no—
72#11758222—22no—
73C2×D244—21no—
74C2×D244D411yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122D411yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—42no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—81no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—22no—
128C22⋊D61—22no—
129C22⋊D61—42no—
130C22⋊D61—81no—
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—22no—
138D244—21no—
139D244—21no—
140D244—81no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—81no—
144C4×D61—81no—
145C4×D61#4112yes—
146C4×D61#4112yes—
147Dic122—22no—
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—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C2×D61#12312yes—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61C2×#4111yescharacteristic
174C4×C61C2×#4111yescharacteristic
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61#12312yes—
180#3096—611nomaximal, Sylow
181C2×C61—41no—
182C2×C61—81no—
183C2×C61C2×#12311yescharacteristic
184C2×C61#57611yescharacteristic
185C2×C61#57711yescharacteristic
186D61—22no—
187D61—41no—
188D61—81no—
189#535—611no—
190#520—611no—
191#482—611no—
192#482—611no—
193#482—611no—
194#482—611no—
195#481—611no—
196#481—611no—
197#480—611no—
198#480D6111yescharacteristic, complemented
199#428—611no—
200#427—611no—
201#418—611no—
202C2×#102—611no—
203#408—611no—
204C61#309611yescharacteristic, complemented, Sylow
205C2×#41—611no—
206C22×D4—611no—
207C2×M16—611no—
208C22×C8—611no—
209#127—1221no—
210#124—1221no—
211#121—611no—
212#121—611no—
213#121—611no—
214#121C2×D6111yescharacteristic
215#120—1221no—
216#120—1221no—
217C4×Q8—1221no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—611no—
222#117—611no—
223#117—611no—
224#117—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4C2×D6111yescharacteristic, complemented
228#107—611no—
229#107—611no—
230#107C2×D6111yescharacteristic, complemented
231#107C2×D6111yescharacteristic, complemented
232#106—611no—
233#106—611no—
234#106—611no—
235#106—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8—611no—
246C22⋊C8—611no—
247C22⋊C8C2×D6111yescharacteristic, complemented
248C24—1221no—
249#41—1222no—
250#41—1222no—
251C2×Q8—611no—
252C2×D4—21no—
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—1221no—
258C2×D4—1222no—
259C2×D4—1222no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4C22×D6111yescharacteristic
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270M16—1222no—
271C2×C8—611no—
272C2×C8—611no—
273C2×C8—1222no—
274C2×C8C22×D6111yescharacteristic
275C2×C8C22×D6111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22×D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C4⋊C4C22×D6111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—1221no—
294C42—1221no—
295C42—1221no—
296C42—1221no—
297C23—21no—
298C23—611no—
299C23—611no—
300C23—1221no—
301C23—4881no—
302C23—4881no—
303C23—2442no—
304C23D4×D6111yescharacteristic
305Q8—1222no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—1222no—
310D4—1222no—
311D4—1222no—
312D4—1221no—
313D4—1221no—
314D4—4881no—
315D4—4881no—
316D4—4881no—
317D4—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—611no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4D4×D6111yescharacteristic
336C2×C4C23×D6111yescharacteristic
337C8—21no—
338C8—21no—
339C8—1221no—
340C8—1221no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—612no—
348C22—1221no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—4884no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22C2×D4×D6111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—612no—
363C4—1221no—
364C4—2441no—
365C4—2441no—
366C4—2441no—
367C4#41×D6111yescharacteristic
368C4#41×D6111yescharacteristic
369C2—41no—
370C2—81no—
371C2—1222no—
372C2—4881no—
373C2—2441no—
374C2#123×D6111yescharacteristic
375C2#1684056311yescharacteristic
376C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3096
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #16840243C2semidirect
3. #16840089C2semidirect
4. #16840087C2semidirect
5. #16840084C2semidirect
6. #16840083C2semidirect
7. #16840080C2semidirect
8. #16840079C2semidirect
9. #16840077C2semidirect
10. #16839803C2semidirect
11. #16839799C2semidirect
12. #16839765C2semidirect
13. #102×D61C2semidirect
14. #16839727C2semidirect
15. C61×#480C2semidirect
31. #14519736C22semidirect
34. #14519735C22semidirect
36. C4⋊C4×D61C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
53. C2×C4⋊C4×C61C22semidirect
54. #107×C61C22semidirect
55. #107×C61C22semidirect
58. C22⋊C8×C61C22semidirect
198. #480D61semidirect
204. C61#3096semidirect
227. C2×C4⋊C4C2×D61semidirect
230. #107C2×D61semidirect
231. #107C2×D61semidirect
247. C22⋊C8C2×D61semidirect