Finite Group Databasebeta

← #21456677

Subgroups — #21456677

Order 7808.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840342C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840077C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839994C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839898C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×#11758222C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×D488C2211yescharacteristic
23C2×#11758189C2211yescharacteristic, complemented
24C2×C8×D61C2211yescharacteristic, complemented
25#14519774—21no—
26#14519765—21no—
27#14519755—21no—
28#14519753C2211yescharacteristic, complemented
29#14519752—21no—
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic
33#14519752C2211yescharacteristic
34#14519752C2211yescharacteristic, complemented
35#14519751C2211yescharacteristic
36#14519750—21no—
37#14519750—21no—
38#14519747—21no—
39#14519747—21no—
40C4⋊C4×D61C2211yescharacteristic, complemented
41#14519710C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64C2×C22⋊D61D411yescharacteristic
65#11758226—41no—
66#11758226—41no—
67#11758222—41no—
68#11758222—41no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244D411yescharacteristic
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122D411yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C42×C61—21no—
96#11758201—41no—
97#11758201—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111D488—41no—
112#11758189—41no—
113C8×D61—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61C2×D411yescharacteristic
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—41no—
134C22⋊D61—41no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—41no—
146D244—42no—
147D244—42no—
148D244—81no—
149D244—81no—
150D244—81no—
151D244—81no—
152D244—81no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—42no—
158C4×D61—81no—
159Dic122—41no—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61H(5,𝔽2)11yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194#3198—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61#53411yescharacteristic
197C2×C61#57611yescharacteristic
198C2×C61#57711yescharacteristic
199D61—41no—
200D61—41no—
201D61—81no—
202D61—81no—
203D61—81no—
204#537—611no—
205#535—611no—
206#485D6111yescharacteristic, complemented
207#482—611no—
208#481—611no—
209#480—611no—
210#469—611no—
211#468—611no—
212#466—611no—
213#465—611no—
214#450—611no—
215#449—611no—
216#449—611no—
217#447—611no—
218#408—611no—
219C61#319811yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41—611no—
222C22×D4—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×M16—611no—
228C22×C8—611no—
229#127—1221no—
230#124—1221no—
231C22⋊Q8—611no—
232C22⋊Q8—1221no—
233C22⋊Q8C2×D6111yescharacteristic
234#121—611no—
235#121—611no—
236#121—611no—
237#121—611no—
238#121—611no—
239#121—611no—
240#121—1221no—
241#121—1221no—
242#121—1221no—
243#120—1221no—
244#120—1221no—
245#117C2×D6111yescharacteristic
246C2×C4⋊C4—611no—
247#107—611no—
248#107C2×D6111yescharacteristic, complemented
249#106—611no—
250#106C2×D6111yescharacteristic, complemented
251#103C2×D6111yescharacteristic, complemented
252#103C2×D6111yescharacteristic, complemented
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258#102—611no—
259C22⋊C8—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262C22⋊C8C2×D6111yescharacteristic
263C24—1221no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—611no—
269C2×Q8C22×D6111yescharacteristic
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—611no—
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—2441no—
285C2×D4—2441no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4C22×D6111yescharacteristic
291SD16—2441no—
292SD16—2441no—
293D8—2441no—
294D8—2441no—
295M16—2441no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—2441no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4C22×D6111yescharacteristic
306C4⋊C4C22×D6111yescharacteristic
307C4⋊C4C22×D6111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—21no—
318C23—611no—
319C23—611no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—4881no—
324C23—4881no—
325C23—2442no—
326C23D4×D6111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2441no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—4881no—
337D4—4881no—
338D4—4881no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—2441no—
343D4—2442no—
344D4—2442no—
345D4—2441no—
346D4—2441no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—4881no—
361C2×C4—2442no—
362C2×C4D4×D6111yescharacteristic
363C2×C4C23×D6111yescharacteristic
364C8—21no—
365C8—21no—
366C8—1221no—
367C8—1221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—4884no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C2×D4×D6111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—1221no—
394C4—1221no—
395C4—2441no—
396C4#1451982311yescharacteristic
397C4#1451982311yescharacteristic
398C2—41no—
399C2—4881no—
400C2—4881no—
401C2—4881no—
402C2—2441no—
403C2—2441no—
404C2#1684032311yescharacteristic
405C2#1684056411yescharacteristic
406C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840342C2semidirect
2. #16840331C2semidirect
3. #16840086C2semidirect
4. #16840082C2semidirect
5. #16840077C2semidirect
6. #16840016C2semidirect
7. #16840011C2semidirect
8. #16839999C2semidirect
9. #16839994C2semidirect
10. #16839912C2semidirect
11. #16839910C2semidirect
12. #16839910C2semidirect
13. #16839898C2semidirect
14. #16839727C2semidirect
15. C61×#485C2semidirect
16. C2×#11758226C22semidirect
23. C2×#11758189C22semidirect
24. C2×C8×D61C22semidirect
28. #14519753C22semidirect
34. #14519752C22semidirect
40. C4⋊C4×D61C22semidirect
41. #14519710C22semidirect
42. #14519708C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
206. #485D61semidirect
219. C61#3198semidirect
248. #107C2×D61semidirect
250. #106C2×D61semidirect
251. #103C2×D61semidirect
252. #103C2×D61semidirect