Finite Group Databasebeta

← #21456659

Subgroups — #21456659

Order 7808.

418 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#16840274C211yesmaximal, characteristic, complemented
2#16840272C211yesmaximal, characteristic, complemented
3#16840105C211yesmaximal, characteristic, complemented
4#16840103C211yesmaximal, characteristic, complemented
5#16840088C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16840009C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839925C211yesmaximal, characteristic, complemented
12#16839908C211yesmaximal, characteristic, complemented
13#16839905C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic, complemented
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758199C2211yescharacteristic, complemented
23C2×#11758189C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519761—21no—
26#14519759—21no—
27#14519757C2211yescharacteristic
28#14519757C2211yescharacteristic
29#14519757C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic
33#14519748C2211yescharacteristic
34#14519747—21no—
35#14519745—21no—
36C4×D244—21no—
37C4×D244—21no—
38D4×Dic61—21no—
39#14519737—21no—
40#14519735C2211yescharacteristic
41#14519710C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519700C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61D411yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61D411yescharacteristic
68#11758224—41no—
69#11758224—41no—
70#11758222—41no—
71#11758222—41no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61D411yescharacteristic
79C2×C4×D61D411yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83C2×Dic122C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758200—41no—
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107C4×Dic61—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—41no—
111#11758190—41no—
112#11758189—41no—
113#11758189—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61C2×D411yescharacteristic
121C22×D61C2×D411yescharacteristic
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—42no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—42no—
145D244—42no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—42no—
153Dic122—21no—
154Dic122—21no—
155Dic122—21no—
156Dic122—21no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—44no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#3197—611nomaximal, Sylow
190C2×C61—41no—
191C2×C61—81no—
192C2×C61#53411yescharacteristic
193C2×C61#57511yescharacteristic
194C2×C61#57511yescharacteristic
195D61—41no—
196D61—41no—
197D61—81no—
198#525—611no—
199#525—611no—
200#485—611no—
201#485—611no—
202#482—611no—
203#482D6111yescharacteristic, complemented
204#470—611no—
205#469—611no—
206#468—611no—
207#468—611no—
208#452—611no—
209#452—611no—
210#449—611no—
211#449—611no—
212#407—611no—
213C61#319711yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41—611no—
216C23×C4—611no—
217C2×Q16—611no—
218C2×SD16—611no—
219C2×SD16—611no—
220C2×D8—611no—
221C2×M16—611no—
222C2×M16—611no—
223#123—1221no—
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227C22⋊Q8—611no—
228C22⋊Q8—611no—
229#121—611no—
230#121—611no—
231#121—611no—
232#121C2×D6111yescharacteristic
233#120—1221no—
234#120—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239#117—611no—
240#117C2×D6111yescharacteristic
241#107—611no—
242#107C2×D6111yescharacteristic, complemented
243#106—611no—
244#106C2×D6111yescharacteristic, complemented
245#103—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#102—611no—
250#102—611no—
251#102C2×D6111yescharacteristic, complemented
252#102C2×D6111yescharacteristic, complemented
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8—611no—
256C22⋊C8C2×D6111yescharacteristic
257C24—611no—
258#41—2441no—
259#41—2441no—
260#41—2441no—
261#41—2441no—
262C2×Q8—611no—
263C2×Q8—611no—
264C2×D4—21no—
265C2×D4—611no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4C22×D6111yescharacteristic
282Q16—2441no—
283SD16—2441no—
284SD16—2441no—
285D8—2441no—
286M16—2441no—
287M16—2441no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8C22×D6111yescharacteristic
291C2×C8C22×D6111yescharacteristic
292C4⋊C4—611no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4C22×D6111yescharacteristic
298C4⋊C4C22×D6111yescharacteristic
299C4⋊C4C22×D6111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—21no—
311C42—1221no—
312C23—21no—
313C23—611no—
314C23—611no—
315C23—1221no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23D4×D6111yescharacteristic
320Q8—1221no—
321Q8—1221no—
322Q8—1221no—
323Q8—1221no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1221no—
328D4—1221no—
329D4—2442no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2442no—
353C2×C4D4×D6111yescharacteristic
354C2×C4C23×D6111yescharacteristic
355C8—21no—
356C8—21no—
357C8—1221no—
358C8—1221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—2444no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1221no—
381C4—1221no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4#1451982311yescharacteristic
386C4#1451982311yescharacteristic
387C2—41no—
388C2—81no—
389C2—4881no—
390C2—2441no—
391C2—2441no—
392C2#1684032311yescharacteristic
393C2#1684055811yescharacteristic
394C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840274C2semidirect
2. #16840272C2semidirect
3. #16840105C2semidirect
4. #16840103C2semidirect
5. #16840088C2semidirect
6. #16840021C2semidirect
7. #16840014C2semidirect
8. #16840009C2semidirect
9. #16840007C2semidirect
10. #16839926C2semidirect
11. #16839925C2semidirect
12. #16839908C2semidirect
13. #16839905C2semidirect
14. #16839724C2semidirect
15. C61×#482C2semidirect
19. C2×Dic244C22semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758199C22semidirect
41. #14519710C22semidirect
42. #14519708C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
45. #14519700C22semidirect
46. #14519700C22semidirect
47. #14519699C22semidirect
48. #14519697C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
203. #482D61semidirect
213. C61#3197semidirect
242. #107C2×D61semidirect
244. #106C2×D61semidirect
251. #102C2×D61semidirect
252. #102C2×D61semidirect