Finite Group Databasebeta

← #21457954

Subgroups — #21457954

Order 7808.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D244C211yesmaximal, characteristic, complemented
2#16840128C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839957C211yesmaximal, characteristic, complemented
9#16839895C211yesmaximal, characteristic, complemented
10#16839895C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839766C211yesmaximal, characteristic, complemented
14C2×#14519697C211yesmaximal, characteristic, complemented
15C61×#553C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic, complemented
22C2×#11758194C2211yescharacteristic, complemented
23C22×#92418C2211yescharacteristic, complemented
24#14519774C2211yescharacteristic
25#14519752—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519747—21no—
29#14519747—21no—
30C4×D244C2211yescharacteristic
31#14519710C2211yescharacteristic, complemented
32#14519708C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519698C2211yescharacteristic, complemented
36#14519697C2211yescharacteristic
37#14519697C2211yescharacteristic
38#14519697C2211yescharacteristic
39#14519697C2211yescharacteristic, complemented
40#14519697C2211yescharacteristic, complemented
41#14519697C2211yescharacteristic, complemented
42#14519697C2211yescharacteristic, complemented
43#14519697C2211yescharacteristic, complemented
44#14519697C2211yescharacteristic, complemented
45C22⋊#92418C2211yescharacteristic, complemented
46C22⋊#92418C2211yescharacteristic, complemented
47#14519688C2211yescharacteristic, complemented
48#126×C61—21no—
49#125×C61C2211yescharacteristic, complemented
50#123×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic, complemented
53#121×C61C2211yescharacteristic, complemented
54C4×D4×C61—21no—
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic, complemented
57#117×C61C2211yescharacteristic, complemented
58C2×C4⋊C4×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61D411yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71D4×D61—44no—
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61D411yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61D411yescharacteristic
96C22⋊C4×C61D411yescharacteristic
97C42×C61—21no—
98C42×C61C2311yescharacteristic
99#11758199—22no—
100#11758199—41no—
101#11758199—41no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124D4×C61—22no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—42no—
128D4×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2411yescharacteristic
143C22⋊D61—42no—
144C22⋊D61—42no—
145C2×Dic61—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244—42no—
152D244—42no—
153D244—42no—
154D244—81no—
155D244#4112yes—
156C4×D61—42no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61AGL(1,ℤ/8)12yes—
170C22×C61C22×D411yescharacteristic
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—84no—
181C2×D61—84no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61C2×#4111yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—41no—
192#3318—611nomaximal, Sylow
193C2×C61—22no—
194C2×C61—41no—
195C2×C61—81no—
196C2×C61#54611yescharacteristic
197C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C61#57611yescharacteristic
199D61—42no—
200D61—81no—
201D61—81no—
202#553D6111yescharacteristic, complemented
203D42—611no—
204#490—611no—
205#482—611no—
206#481—611no—
207#478—611no—
208#469—611no—
209#466—611no—
210#459—611no—
211#447—611no—
212#447—611no—
213#442—611no—
214#435—611no—
215#418—611no—
216C2×#102—611no—
217C61#331811yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—611no—
220C22×D4—1221no—
221C2×D8—611no—
222C2×D8—611no—
223C2×D8—611no—
224C2×M16—611no—
225C22×C8—611no—
226#127—611no—
227#126—21no—
228#125C2×D6111yescharacteristic, complemented
229#123—21no—
230#121—21no—
231#121—611no—
232#121—611no—
233#121—1221no—
234#121C2×D6111yescharacteristic, complemented
235#121C2×D6111yescharacteristic, complemented
236#120—1221no—
237#120—1221no—
238C4×D4—21no—
239C4×D4—611no—
240C4×D4C2×D6111yescharacteristic
241C4×D4C2×D6111yescharacteristic, complemented
242#117C2×D6111yescharacteristic, complemented
243C2×C4⋊C4C2×D6111yescharacteristic, complemented
244#107—611no—
245#106—611no—
246#106—611no—
247C4⋊C8—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97—611no—
261C24—1221no—
262C24—1221no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2444no—
279C2×D4C22⋊D6111yescharacteristic
280C2×D4C22×D6111yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285C22×C4C22×D6111yescharacteristic
286D8—1222no—
287D8—2441no—
288D8—2441no—
289M16—2441no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8—2441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—611no—
299C4⋊C4C22⋊D6111yescharacteristic
300C4⋊C4C22×D6111yescharacteristic
301C4⋊C4C22×D6111yescharacteristic
302C4⋊C4C22×D6111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4C22⋊D6111yescharacteristic
311C22⋊C4C22⋊D6111yescharacteristic
312C42—21no—
313C42C22×D6111yescharacteristic
314C23—21no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—4881no—
319C23—4881no—
320C23—2442no—
321C23—2442no—
322C23—2442no—
323C23—2442no—
324C23C2×C22⋊D6111yescharacteristic
325C23C2×C22⋊D6111yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—81no—
331D4—612no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—4881no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4C2×C22⋊D6111yescharacteristic
355C2×C4C2×C22⋊D6111yescharacteristic
356C2×C4C2×C22⋊D6111yescharacteristic
357C2×C4C2×C22⋊D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—1221no—
360C8—1221no—
361C8—1221no—
362C8—1221no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1222no—
372C22—4884no—
373C22—4884no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22#1451980212yes—
383C22C22×C22⋊D6111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—2441no—
392C4#41×D6111yescharacteristic
393C4#1451982311yescharacteristic
394C2—22no—
395C2—41no—
396C2—81no—
397C2—4881no—
398C2—4881no—
399C2—2442no—
400C2#1684040011yescharacteristic
401C2C2×#1451980211yescharacteristic
402C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#553C2
socleC22×C61C22×D4
hypercenter#553D61
hypocenterC61#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×D244C2semidirect
2. #16840128C2semidirect
3. #16840086C2semidirect
4. #16840080C2semidirect
5. #16840059C2semidirect
6. #16840013C2semidirect
7. #16839996C2semidirect
8. #16839957C2semidirect
9. #16839895C2semidirect
10. #16839895C2semidirect
11. #16839872C2semidirect
12. #16839834C2semidirect
13. #16839766C2semidirect
14. C2×#14519697C2semidirect
15. C61×#553C2semidirect
20. C2×#11758199C22semidirect
21. C2×#11758199C22semidirect
22. C2×#11758194C22semidirect
23. C22×#92418C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519698C22semidirect
39. #14519697C22semidirect
40. #14519697C22semidirect
41. #14519697C22semidirect
42. #14519697C22semidirect
43. #14519697C22semidirect
44. #14519697C22semidirect
45. C22⋊#92418C22semidirect
46. C22⋊#92418C22semidirect
47. #14519688C22semidirect
49. #125×C61C22semidirect
52. #121×C61C22semidirect
53. #121×C61C22semidirect
56. C4×D4×C61C22semidirect
57. #117×C61C22semidirect
58. C2×C4⋊C4×C61C22semidirect
202. #553D61semidirect
217. C61#3318semidirect
228. #125C2×D61semidirect
234. #121C2×D61semidirect
235. #121C2×D61semidirect
241. C4×D4C2×D61semidirect
242. #117C2×D61semidirect
243. C2×C4⋊C4C2×D61semidirect