Finite Group Databasebeta

← #21457840

Subgroups — #21457840

Order 7808.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840452C211yesmaximal, characteristic, complemented
2#16840126C211yesmaximal, characteristic, complemented
3#16840083C211yesmaximal, characteristic, complemented
4#16840073C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16840006C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839913C211yesmaximal, characteristic, complemented
10#16839913C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839767C211yesmaximal, characteristic, complemented
14C2×#14519698C211yesmaximal, characteristic, complemented
15D42×C61C211yesmaximal, characteristic
16C2×#11758200C2211yescharacteristic
17C2×#11758200C2211yescharacteristic, complemented
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758194C2211yescharacteristic, complemented
20C22×#92418C2211yescharacteristic, complemented
21#14519770—21no—
22#14519769C2211yescharacteristic, complemented
23#14519767—21no—
24#14519758—21no—
25#14519756C2211yescharacteristic, complemented
26#14519756C2211yescharacteristic, complemented
27C4×Dic122C2211yescharacteristic, complemented
28#14519736C2211yescharacteristic, complemented
29#14519733—21no—
30C2×C4⋊Dic61C2211yescharacteristic, complemented
31#14519710C2211yescharacteristic, complemented
32#14519710C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519700C2211yescharacteristic, complemented
36#14519698C2211yescharacteristic
37#14519698C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic, complemented
40#14519698C2211yescharacteristic, complemented
41#14519698C2211yescharacteristic, complemented
42#14519698C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic, complemented
45C22⋊#92418C2211yescharacteristic, complemented
46C22⋊#92418C2211yescharacteristic, complemented
47#14519688C2211yescharacteristic, complemented
48C22×D4×C61—21no—
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51#127×C61C2211yescharacteristic
52#121×C61—21no—
53#121×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55#120×C61—21no—
56#120×C61—21no—
57C4×D4×C61C2211yescharacteristic
58C4×D4×C61C2211yescharacteristic
59C24×C61—21no—
60C24×C61—21no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—44no—
72C2×D4×C61D411yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C2×D4×C61C2311yescharacteristic
75C2×D4×C61C2311yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61C2311yescharacteristic
78C22×C4×C61C2311yescharacteristic
79C22×Dic61—21no—
80C2×Dic122C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758200—22no—
93#11758200—41no—
94#11758200—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—42no—
116C23×C61—42no—
117C23×C61—42no—
118C23×C61—42no—
119C23×C61—81no—
120C23×C61—81no—
121C23×C61C2×D411yescharacteristic
122C23×C61C2×D411yescharacteristic
123D4×C61—22no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—42no—
130D4×C61—42no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—81no—
135D4×C61#4112yes—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152Dic122—21no—
153Dic122—21no—
154#92418—21no—
155#92418—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—84no—
173C22×C61—84no—
174C22×C61AGL(1,ℤ/8)12yes—
175C22×C61C22×D411yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61C2×#4111yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187#3310—611nomaximal, Sylow
188C2×C61—22no—
189C2×C61—41no—
190C2×C61—42no—
191C2×C61—81no—
192C2×C61—81no—
193C2×C61#54611yescharacteristic
194C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C61#57711yescharacteristic
196#552—611no—
197D42D6111yescharacteristic
198#490—611no—
199#482—611no—
200#480—611no—
201#478—611no—
202#468—611no—
203#465—611no—
204#460—611no—
205#450—611no—
206#450—611no—
207#440—611no—
208#435—611no—
209#418—611no—
210C2×#102—611no—
211C61#331011yescharacteristic, complemented, Sylow
212C22×D4—21no—
213C22×D4C2×D6111yescharacteristic
214C22×D4C2×D6111yescharacteristic
215C2×SD16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×M16—611no—
219C22×C8—611no—
220#127C2×D6111yescharacteristic
221#126—1221no—
222#125—611no—
223#125—1221no—
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227#121—21no—
228#121C2×D6111yescharacteristic
229#121C2×D6111yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—611no—
233C4×D4C2×D6111yescharacteristic
234C4×D4C2×D6111yescharacteristic
235#117—611no—
236#117—1221no—
237C2×C4⋊C4—611no—
238#107—611no—
239#107—611no—
240#106—611no—
241C4⋊C8—611no—
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97—611no—
255C24—21no—
256C24—21no—
257C2×Q8—611no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D6111yescharacteristic
270C2×D4C22×D6111yescharacteristic
271C2×D4C22×D6111yescharacteristic
272C2×D4C22×D6111yescharacteristic
273C22×C4—21no—
274C22×C4—1221no—
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277SD16—1222no—
278SD16—2441no—
279SD16—2441no—
280M16—2441no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—2441no—
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22⋊D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4C22⋊D6111yescharacteristic
304C22⋊C4C22⋊D6111yescharacteristic
305C42—1221no—
306C42—1221no—
307C42C22×D6111yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D6111yescharacteristic
318C23C2×C22⋊D6111yescharacteristic
319Q8—1221no—
320Q8—1221no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1175822412yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—2442no—
345C2×C4C2×C22⋊D6111yescharacteristic
346C2×C4C2×C22⋊D6111yescharacteristic
347C2×C4C2×C22⋊D6111yescharacteristic
348C2×C4C2×C22⋊D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—1221no—
351C8—1221no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1451980312yes—
371C22C22×C22⋊D6111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—2441no—
378C4—2441no—
379C4—2441no—
380C4—2441no—
381C4C2×#1175822411yescharacteristic
382C4#1451982211yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1684040611yescharacteristic
389C2C2×#1451980311yescharacteristic
390C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3310
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
2. #16840126C2semidirect
3. #16840083C2semidirect
4. #16840073C2semidirect
5. #16840062C2semidirect
6. #16840006C2semidirect
7. #16839989C2semidirect
8. #16839959C2semidirect
9. #16839913C2semidirect
10. #16839913C2semidirect
11. #16839862C2semidirect
12. #16839834C2semidirect
13. #16839767C2semidirect
14. C2×#14519698C2semidirect
17. C2×#11758200C22semidirect
18. C2×#11758200C22semidirect
19. C2×#11758194C22semidirect
20. C22×#92418C22semidirect
22. #14519769C22semidirect
25. #14519756C22semidirect
26. #14519756C22semidirect
27. C4×Dic122C22semidirect
28. #14519736C22semidirect
30. C2×C4⋊Dic61C22semidirect
31. #14519710C22semidirect
32. #14519710C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519700C22semidirect
39. #14519698C22semidirect
40. #14519698C22semidirect
41. #14519698C22semidirect
42. #14519698C22semidirect
43. #14519698C22semidirect
44. #14519698C22semidirect
45. C22⋊#92418C22semidirect
46. C22⋊#92418C22semidirect
47. #14519688C22semidirect
211. C61#3310semidirect