Finite Group Databasebeta

← #21455494

Subgroups — #21455494

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×#14519785C211yesmaximal, characteristic, complemented
3#16840342C211yesmaximal, characteristic, complemented
4#16840328C211yesmaximal, characteristic, complemented
5#16840015C211yesmaximal, characteristic, complemented
6#16840014C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839996C211yesmaximal, characteristic, complemented
10#16839993C211yesmaximal, characteristic, complemented
11#16839988C211yesmaximal, characteristic, complemented
12#16839803C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519804—24no—
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519785—24no—
24C2×#11758189C2211yescharacteristic
25C2×#11758189C2211yescharacteristic, complemented
26C22×#92418C2211yescharacteristic, complemented
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic, complemented
29#14519773—21no—
30#14519763—21no—
31#14519755—21no—
32#14519753C2211yescharacteristic, complemented
33#14519752—21no—
34#14519752C2211yescharacteristic
35#14519752C2211yescharacteristic, complemented
36#14519751C2211yescharacteristic
37#14519751C2211yescharacteristic, complemented
38#14519750—21no—
39#14519750—21no—
40#14519748C2211yescharacteristic
41#14519747—21no—
42#14519745—21no—
43#14519735C2211yescharacteristic
44C4⋊C4×D61C2211yescharacteristic
45#14519710C2211yescharacteristic, complemented
46#14519709C2211yescharacteristic, complemented
47#14519708C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic
52#14519697C2211yescharacteristic
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C2×M16×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C2×C22⋊D61D411yescharacteristic
72#11758226—22no—
73#11758226—22no—
74D4×D61—22no—
75D4×D61—22no—
76#11758222—22no—
77#11758222—22no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244D411yescharacteristic
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87C2×C4×D61C2311yescharacteristic
88C2×Dic122D411yescharacteristic
89SD16×C61—22no—
90M16×C61—22no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C4⋊C4×C61C2311yescharacteristic
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊Dic61—21no—
99#11758201—22no—
100#11758199—22no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112C2×#92418—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115D488—22no—
116#11758189—22no—
117#11758189D414yescomplemented
118C8×D61—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61C2×D411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61C2×D411yescharacteristic
128C22×D61C2×D411yescharacteristic
129Q8×C61—21no—
130Q8×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—22no—
143C22⋊D61—42no—
144C22⋊D61—81no—
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151D244—22no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—42no—
157D244—81no—
158D244—81no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—42no—
162C4×D61—81no—
163C4×D61C2×D412yes—
164C4×D61#4112yes—
165Dic122—22no—
166C8×C61—21no—
167C8×C61C2×D412yes—
168#92418—21no—
169#92418C2×D412yes—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61C22×D411yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C2×D61#12112yes—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61C22×D411yescharacteristic
195C4×C61C2×#4111yescharacteristic
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199Dic61#12112yes—
200#3062—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—81no—
203C2×C61C2×#12111yescharacteristic
204C2×C61#57611yescharacteristic
205C2×C61#57711yescharacteristic
206D61—22no—
207D61—41no—
208D61—81no—
209D61—81no—
210C2×AGL(1,ℤ/8)—611no—
211C2×#131—611no—
212#537—611no—
213#535—611no—
214#469—611no—
215#469—611no—
216#468—611no—
217#468D6111yescharacteristic, complemented
218#466—611no—
219#466—611no—
220#465—611no—
221#465—611no—
222#428—611no—
223#416—611no—
224C2×#102—611no—
225C61#306211yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C2×#41—611no—
228C22×D4—611no—
229AGL(1,ℤ/8)—1224no—
230C2×SD16—611no—
231C2×SD16C2×D6111yescharacteristic
232C2×D8—611no—
233C2×D8—611no—
234#131—1224no—
235C2×M16—611no—
236C2×M16—611no—
237C2×M16C2×D6111yescharacteristic, complemented
238C22×C8—611no—
239C22×C8—611no—
240C22×C8—611no—
241#127—1221no—
242#124—1221no—
243C22⋊Q8—611no—
244C22⋊Q8—1221no—
245C22⋊Q8C2×D6111yescharacteristic, complemented
246#121—611no—
247#121—611no—
248#121—611no—
249#121—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#121—1221no—
254#121C2×D6111yescharacteristic
255#120—1221no—
256#120—1221no—
257#117—611no—
258C2×C4⋊C4—611no—
259#107—611no—
260#107C2×D6111yescharacteristic, complemented
261#106—611no—
262#106—611no—
263#103—611no—
264#103C2×D6111yescharacteristic, complemented
265#102—611no—
266#102—611no—
267#102—611no—
268#102—611no—
269#102—611no—
270#102C2×D6111yescharacteristic
271C24—1221no—
272#41—1222no—
273#41—1222no—
274#41—1222no—
275#41—1222no—
276C2×Q8—611no—
277C2×Q8C22×D6111yescharacteristic
278C2×D4—21no—
279C2×D4—611no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4C22×D6111yescharacteristic
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22×D6111yescharacteristic
299SD16—22no—
300SD16—1222no—
301D8—1222no—
302D8—1222no—
303M16—22no—
304M16—614no—
305M16—1222no—
306C2×C8—611no—
307C2×C8—611no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4C22×D6111yescharacteristic
319C4⋊C4C22×D6111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C42—1221no—
330C23—21no—
331C23—611no—
332C23—611no—
333C23—1221no—
334C23—1221no—
335C23—4881no—
336C23—4881no—
337C23—2442no—
338C23D4×D6111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—1222no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—1222no—
346D4—1222no—
347D4—1222no—
348D4—1221no—
349D4—1221no—
350D4—1221no—
351D4—1221no—
352D4—4881no—
353D4—4881no—
354D4—4881no—
355D4—4881no—
356D4—4881no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—611no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—611no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—2442no—
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—612no—
378C8—1221no—
379C8D4×D6112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—612no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22—4884no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22C2×D4×D6111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—612no—
405C4—1221no—
406C4—2441no—
407C4—2441no—
408C4C2×D4×D6111yescharacteristic
409C4#41×D6111yescharacteristic
410C2—41no—
411C2—81no—
412C2—1222no—
413C2—4881no—
414C2—4881no—
415C2—2441no—
416C2#121×D6111yescharacteristic
417C2#1684056611yescharacteristic
418C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3062
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519785C2semidirect
3. #16840342C2semidirect
4. #16840328C2semidirect
5. #16840015C2semidirect
6. #16840014C2semidirect
7. #16840011C2semidirect
8. #16839999C2semidirect
9. #16839996C2semidirect
10. #16839993C2semidirect
11. #16839988C2semidirect
12. #16839803C2semidirect
13. #16839757C2semidirect
14. #102×D61C2semidirect
15. C61×#468C2semidirect
25. C2×#11758189C22semidirect
26. C22×#92418C22semidirect
28. C2×C8×D61C22semidirect
32. #14519753C22semidirect
35. #14519752C22semidirect
37. #14519751C22semidirect
45. #14519710C22semidirect
46. #14519709C22semidirect
47. #14519708C22semidirect
48. #14519701C22semidirect
50. #14519699C22semidirect
53. #14519697C22semidirect
55. C2×M16×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #107×C61C22semidirect
59. #103×C61C22semidirect
117. #11758189D4semidirect
217. #468D61semidirect
225. C61#3062semidirect
237. C2×M16C2×D61semidirect
245. C22⋊Q8C2×D61semidirect
260. #107C2×D61semidirect
264. #103C2×D61semidirect