Finite Group Databasebeta

← #21456785

Subgroups — #21456785

Order 7808.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840297C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic, complemented
3#16840146C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839987C211yesmaximal, characteristic, complemented
7#16839983C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839914C211yesmaximal, characteristic, complemented
12#16839902C211yesmaximal, characteristic, complemented
13#16839897C211yesmaximal, characteristic
14#16839813C211yesmaximal, characteristic, complemented
15C61×#488C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758202C2211yescharacteristic, complemented
20C2×#11758190C2211yescharacteristic
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758200C2211yescharacteristic
23C2×#11758201C2211yescharacteristic, complemented
24C2×D488C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26#14519772—21no—
27#14519766C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519765C2211yescharacteristic, complemented
30#14519764C2211yescharacteristic
31#14519763—21no—
32#14519763—21no—
33#14519762—21no—
34#14519757C2211yescharacteristic
35#14519752C2211yescharacteristic
36#14519742C2211yescharacteristic, complemented
37#14519739—21no—
38#14519739C2211yescharacteristic, complemented
39#14519735—21no—
40C22⋊C4×D61—21no—
41C22⋊C4×D61—21no—
42C42×D61C2211yescharacteristic
43#14519706C2211yescharacteristic, complemented
44#14519706C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519700C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic, complemented
55#103×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63Q8×D61—41no—
64Q8×D61—41no—
65D4×D61—41no—
66D4×D61—41no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61D411yescharacteristic
73C2×C4×D61D411yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758202—41no—
90#11758201—41no—
91#11758200—41no—
92#11758199—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61D411yescharacteristic
106C4×Dic61D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—41no—
111D488—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—42no—
142C4×D61—22no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—41no—
146C4×D61—42no—
147C4×D61—42no—
148Dic122—21no—
149Dic122—21no—
150Dic122—21no—
151Dic122—21no—
152Dic122—42no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—84no—
170C2×D61#13512yes—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61H(5,𝔽2)11yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183#3211—611nomaximal, Sylow
184C2×C61—81no—
185C2×C61#53511yescharacteristic
186C2×C61C2×#13511yescharacteristic
187C2×C61#57511yescharacteristic
188D61—22no—
189D61—81no—
190D61—81no—
191#529—611no—
192C2×#124—611no—
193#495—611no—
194#495—611no—
195#488—611no—
196#488D6111yescharacteristic, complemented
197#464—611no—
198#464—611no—
199#463—611no—
200#463—611no—
201#451—611no—
202#450—611no—
203#448—611no—
204#447—611no—
205#431—611no—
206C61#321111yescharacteristic, complemented, Sylow
207C22×Q8—611no—
208C22×D4—611no—
209C2×Q16—611no—
210C2×Q16—611no—
211C2×SD16—611no—
212C2×SD16—611no—
213C2×SD16—611no—
214C2×SD16—611no—
215C2×D8—611no—
216C2×D8—611no—
217#126—1221no—
218#125C2×D6111yescharacteristic, complemented
219#124—611no—
220#124—611no—
221#124—611no—
222#124—611no—
223#124—1221no—
224#124—1221no—
225#124C2×D6111yescharacteristic
226#123—1221no—
227C22⋊Q8—611no—
228#121—611no—
229C4×Q8—611no—
230C4×D4—611no—
231C4×D4—1221no—
232#117—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C42—611no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103C2×D6111yescharacteristic, complemented
241#103C2×D6111yescharacteristic, complemented
242#102—611no—
243#102—611no—
244#102C2×D6111yescharacteristic
245#102C2×D6111yescharacteristic
246C22⋊C8—611no—
247C22⋊C8—611no—
248C4×C8—611no—
249C4×C8C2×D6111yescharacteristic, complemented
250C24—1221no—
251C2×Q8—611no—
252C2×Q8—611no—
253C2×Q8—1221no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8C22×D6111yescharacteristic
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269Q16—2441no—
270Q16—2441no—
271SD16—2441no—
272SD16—2441no—
273SD16—2441no—
274SD16—2441no—
275D8—2441no—
276D8—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4C22×D6111yescharacteristic
286C4⋊C4C22×D6111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—1221no—
304C42C22×D6111yescharacteristic
305C23—21no—
306C23—611no—
307C23—1221no—
308C23—1221no—
309C23—2442no—
310C23—2442no—
311C23—2442no—
312Q8—21no—
313Q8—21no—
314Q8—1221no—
315Q8—1221no—
316Q8—1221no—
317Q8—1221no—
318Q8—2442no—
319D4—21no—
320D4—21no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—2441no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4D4×D6111yescharacteristic
343C2×C4C23×D6111yescharacteristic
344C8—21no—
345C8—21no—
346C8—1221no—
347C8—1221no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—612no—
352C22—1221no—
353C22—1221no—
354C22—4884no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4—2441no—
372C4#1451982311yescharacteristic
373C4#1451982311yescharacteristic
374C2—81no—
375C2—1222no—
376C2—4881no—
377C2—4881no—
378C2#1684033011yescharacteristic
379C2#135×D6111yescharacteristic
380C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840297C2semidirect
2. #124×D61C2semidirect
3. #16840146C2semidirect
4. #16840144C2semidirect
5. #16840119C2semidirect
6. #16839987C2semidirect
7. #16839983C2semidirect
8. #16839980C2semidirect
9. #16839976C2semidirect
10. #16839919C2semidirect
11. #16839914C2semidirect
12. #16839902C2semidirect
14. #16839813C2semidirect
15. C61×#488C2semidirect
18. C2×Dic244C22semidirect
19. C2×#11758202C22semidirect
21. C2×#11758190C22semidirect
23. C2×#11758201C22semidirect
29. #14519765C22semidirect
36. #14519742C22semidirect
38. #14519739C22semidirect
43. #14519706C22semidirect
44. #14519706C22semidirect
45. #14519700C22semidirect
46. #14519700C22semidirect
51. C4×#92418C22semidirect
52. #125×C61C22semidirect
54. #103×C61C22semidirect
55. #103×C61C22semidirect
58. C4×C8×C61C22semidirect
196. #488D61semidirect
206. C61#3211semidirect
218. #125C2×D61semidirect
240. #103C2×D61semidirect
241. #103C2×D61semidirect
249. C4×C8C2×D61semidirect