Finite Group Databasebeta

← #21455871

Subgroups — #21455871

Order 7808.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840297C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic, complemented
3#16840099C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16839978C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839914C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic
10#16839853C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839844C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839814C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C22×C4×D61—21no—
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519772—21no—
23#14519765C2211yescharacteristic, complemented
24#14519762—21no—
25#14519757C2211yescharacteristic
26#14519752C2211yescharacteristic
27#14519742C2211yescharacteristic, complemented
28C4×D244C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30#14519739—21no—
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic, complemented
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735—21no—
36C4⋊C4×D61C2211yescharacteristic
37C22⋊C4×D61—21no—
38C42×D61C2211yescharacteristic
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50C8×Dic61C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64D4×D61—22no—
65D4×D61—22no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—44no—
74C2×C4×D61D411yescharacteristic
75C2×C4×D61D411yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88#11758200—22no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61D411yescharacteristic
103C4×Dic61D411yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108#11758190—22no—
109C23×C61—21no—
110C22×D61—24no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61#4112yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—42no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—24no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—21no—
135D244—42no—
136D244#4112yes—
137C4×D61—22no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—22no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—42no—
145Dic122—21no—
146Dic122—21no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—22no—
158C2×D61—48no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61#13512yes—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61C2×#4111yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61AGL(1,ℤ/8)12yes—
177#3105—611nomaximal, Sylow
178C2×C61—42no—
179C2×C61#52511yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
182D61—22no—
183D61—42no—
184D61—81no—
185#529—611no—
186C2×C4×D4—611no—
187#484—611no—
188#481—611no—
189#478—611no—
190#478D6111yescharacteristic, complemented
191#463—611no—
192#463—611no—
193#450—611no—
194#447—611no—
195C4×SD16—611no—
196C4×SD16—611no—
197C4×D8—611no—
198C4×D8—611no—
199#431—611no—
200C61#310511yescharacteristic, complemented, Sylow
201C22×D4—611no—
202C23×C4—1221no—
203C2×SD16—611no—
204C2×SD16—611no—
205C2×D8—611no—
206C2×D8—611no—
207#126—1221no—
208#125C2×D6111yescharacteristic, complemented
209#124—611no—
210#123—1221no—
211C22⋊Q8—611no—
212#121—611no—
213C4×Q8—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221C4×D4C2×D6111yescharacteristic
222#117—1221no—
223C2×C4⋊C4—611no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226#107—611no—
227#107C2×D6111yescharacteristic, complemented
228#106—611no—
229#106C2×D6111yescharacteristic, complemented
230C4⋊C8—611no—
231C4⋊C8C2×D6111yescharacteristic, complemented
232#103—611no—
233#103—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238#102C2×D6111yescharacteristic
239#102C2×D6111yescharacteristic
240C22⋊C8—611no—
241C22⋊C8—611no—
242C4×C8—611no—
243C4×C8—611no—
244C24—1221no—
245C2×Q8—611no—
246C2×D4—611no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1222no—
251C2×D4—1222no—
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—2444no—
263SD16—1222no—
264SD16—1222no—
265D8—1222no—
266D8—1222no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—611no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—611no—
290C42—611no—
291C42—611no—
292C42—1221no—
293C42C22×D6111yescharacteristic
294C23—21no—
295C23—611no—
296C23—1224no—
297C23—1221no—
298C23—1221no—
299C23—2442no—
300C23—2442no—
301Q8—1221no—
302Q8—1221no—
303D4—21no—
304D4—612no—
305D4—1224no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4—2442no—
310D4#1175822612yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4D4×D6111yescharacteristic
330C2×C4D4×D6111yescharacteristic
331C2×C4C23×D6111yescharacteristic
332C8—21no—
333C8—21no—
334C8—1221no—
335C8—1221no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—612no—
340C22—1221no—
341C22—1221no—
342C22—1222no—
343C22—2448no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—612no—
356C4—1221no—
357C4—1221no—
358C4—2441no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4C2×#1175822611yescharacteristic
362C2—42no—
363C2—1222no—
364C2—4881no—
365C2—2442no—
366C2#1684027511yescharacteristic
367C2#135×D6111yescharacteristic
368C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840297C2semidirect
2. C4×D4×D61C2semidirect
3. #16840099C2semidirect
4. #16840082C2semidirect
5. #16840059C2semidirect
6. #16839978C2semidirect
7. #16839977C2semidirect
8. #16839914C2semidirect
10. #16839853C2semidirect
11. #16839849C2semidirect
12. #16839844C2semidirect
13. #16839842C2semidirect
14. #16839814C2semidirect
15. C61×#478C2semidirect
23. #14519765C22semidirect
27. #14519742C22semidirect
32. #14519739C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519700C22semidirect
44. #14519699C22semidirect
47. #14519697C22semidirect
50. C8×Dic61C22semidirect
51. C8×Dic61C22semidirect
52. #125×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. C4⋊C8×C61C22semidirect
190. #478D61semidirect
200. C61#3105semidirect
208. #125C2×D61semidirect
227. #107C2×D61semidirect
229. #106C2×D61semidirect
231. C4⋊C8C2×D61semidirect