Finite Group Databasebeta

← #20253400

Subgroups — #20253400

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625350C211yesmaximal, characteristic, complemented
2#15689461C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689427C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689283C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic
10C4×#10625337C211yesmaximal, characteristic, complemented
11C4×#10625336C211yesmaximal, characteristic, complemented
12C4×#10625335C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689176C211yesmaximal, characteristic, complemented
15C47×#529C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×C22⋊D47—21no—
26C4×C22⋊D47—21no—
27#13093983C2211yescharacteristic
28#13093981—21no—
29C42×D47—21no—
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C4×C47⋊C8C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#126×C47—21no—
49#125×C47C2211yescharacteristic
50#124×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47C2211yescharacteristic
57#117×C47—21no—
58C2×C42×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47D411yescharacteristic
64C22×C4×C47D411yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67#10625350—22no—
68#10625350—22no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×Dic94C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47D411yescharacteristic
87C42×C47D411yescharacteristic
88C42×C47C2311yescharacteristic
89C42×C47C2311yescharacteristic
90C22⋊Dic47—21no—
91#10625337—22no—
92#10625336—22no—
93#10625335—22no—
94#10625334—22no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—42no—
116C2×C4×C47—22no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—41no—
123C2×C4×C47—42no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—24no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134D188—21no—
135D188#4112yes—
136C4×D47—24no—
137C4×D47—42no—
138C4×D47—42no—
139Dic94—21no—
140Dic94#4112yes—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47#13512yes—
163C4×C47C2×#4111yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—22no—
166Dic47—41no—
167Dic47—41no—
168#3102—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47—81no—
171C2×C47#52511yescharacteristic
172C2×C47C2×#13511yescharacteristic
173C2×C47#57511yescharacteristic
174D47—42no—
175#529D4711yescharacteristic, complemented
176C4×#41—471no—
177#485—471no—
178#482—471no—
179#479—471no—
180#478—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185C4×Q16—471no—
186C4×SD16—471no—
187C4×SD16—471no—
188C4×D8—471no—
189#431—471no—
190C47#310211yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196#126—21no—
197#125C2×D4711yescharacteristic
198#124C2×D4711yescharacteristic
199#123—21no—
200C22⋊Q8C2×D4711yescharacteristic
201#121C2×D4711yescharacteristic
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—21no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4C2×D4711yescharacteristic
211#117—21no—
212#117—471no—
213#117—941no—
214C2×C42—941no—
215C2×C42C2×D4711yescharacteristic
216#107—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8—471no—
232C4×C8—471no—
233C4×C8—471no—
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—21no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C22×C4—21no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4C22⋊D4711yescharacteristic
247C22×C4C22⋊D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—471no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—21no—
276C42—941no—
277C42—941no—
278C42—941no—
279C42C22⋊D4711yescharacteristic
280C42C22⋊D4711yescharacteristic
281C42C22×D4711yescharacteristic
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—941no—
285C23C2×C22⋊D4711yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—472no—
289Q8—941no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—472no—
294D4—944no—
295D4—941no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—944no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4C2×C22⋊D4711yescharacteristic
311C2×C4C2×C22⋊D4711yescharacteristic
312C2×C4C2×C22⋊D4711yescharacteristic
313C2×C4C2×C22⋊D4711yescharacteristic
314C2×C4C2×C22⋊D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—941no—
317C8—941no—
318C8—941no—
319C8—941no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—942no—
327C22—1881no—
328C22—1881no—
329C22C22×C22⋊D4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—942no—
338C4—1881no—
339C4—1881no—
340C4#1309404412yes—
341C4#41×D4711yescharacteristic
342C4#41×D4711yescharacteristic
343C2—41no—
344C2—81no—
345C2—1882no—
346C2#1568963011yescharacteristic
347C2C2×#1309404411yescharacteristic
348C2#1568992111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#529C2
socleC22×C47C22×D4
hypercenter#529D47
hypocenterC47#3102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#10625350C2semidirect
2. #15689461C2semidirect
3. #15689444C2semidirect
4. #15689427C2semidirect
5. #15689420C2semidirect
6. #15689342C2semidirect
7. #15689335C2semidirect
8. #15689283C2semidirect
10. C4×#10625337C2semidirect
11. C4×#10625336C2semidirect
12. C4×#10625335C2semidirect
13. C4×#10625334C2semidirect
14. #15689176C2semidirect
15. C47×#529C2semidirect
175. #529D47semidirect
190. C47#3102semidirect