Finite Group Databasebeta

← #20255364

Subgroups — #20255364

Order 6016.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic, complemented
2#15689491C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689451C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689325C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#15689119C211yesmaximal, characteristic, complemented
15C47×#547C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094019—21no—
22#13094016C2211yescharacteristic
23#13094006—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26#13093996—21no—
27C4×D188C2211yescharacteristic
28(C22⋊D47)⋊C4—21no—
29#13093983C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C2×#41×C47C2211yescharacteristic
50C4⋊Q8×C47C2211yescharacteristic
51#123×C47—21no—
52#123×C47—21no—
53C22⋊Q8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58C2×C4⋊C4×C47—21no—
59#41×C47—22no—
60#41×C47—22no—
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47D411yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C22×Dic47—21no—
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47D411yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47D411yescharacteristic
89C22⋊C4×C47D411yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625336—41no—
93#10625336—41no—
94#10625334—22no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119D4×C47—21no—
120D4×C47—41no—
121D4×C47—42no—
122D4×C47—42no—
123D4×C47#4112yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2411yescharacteristic
139C22⋊D47—42no—
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—81no—
145D188—21no—
146D188—21no—
147C4×D47—81no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—22no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177#3307—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—41no—
180C2×C47—42no—
181C2×C47#54611yescharacteristic
182C2×C47#57511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—81no—
185#553—471no—
186#547D4711yescharacteristic, complemented
187#491—471no—
188#485—471no—
189#483—471no—
190#478—471no—
191#468—471no—
192#465—471no—
193#461—471no—
194#449—471no—
195#449—471no—
196#442—471no—
197#435—471no—
198#417—471no—
199#416—471no—
200C47#330711yescharacteristic, complemented, Sylow
201C2×#41C2×D4711yescharacteristic
202C2×#41C2×D4711yescharacteristic
203C2×SD16—471no—
204C2×SD16—471no—
205C2×D8—471no—
206C2×M16—471no—
207C22×C8—471no—
208C4⋊Q8C2×D4711yescharacteristic
209#126—941no—
210#125—471no—
211#123—21no—
212#123—21no—
213#123—941no—
214C22⋊Q8C2×D4711yescharacteristic
215C22⋊Q8C2×D4711yescharacteristic
216#121—21no—
217#121—471no—
218#121—471no—
219#121—941no—
220C4×D4—471no—
221C4×D4—941no—
222C4×D4C2×D4711yescharacteristic
223C4×D4C2×D4711yescharacteristic
224#117—471no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—471no—
227#107—471no—
228#106—471no—
229#106—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241C22⋊C8—471no—
242C22⋊C8—471no—
243#97—471no—
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8C22×D4711yescharacteristic
249C2×Q8C22×D4711yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4C22⋊D4711yescharacteristic
256C2×D4C22×D4711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264SD16—1881no—
265SD16—1881no—
266D8—942no—
267M16—1881no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—471no—
271C2×C8—471no—
272C2×C8—1881no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4C22⋊D4711yescharacteristic
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4C22⋊D4711yescharacteristic
293C22⋊C4C22⋊D4711yescharacteristic
294C42—941no—
295C42C22×D4711yescharacteristic
296C23—21no—
297C23—941no—
298C23C2×C22⋊D4711yescharacteristic
299C23C2×C22⋊D4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—21no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—941no—
309D4—941no—
310D4—3761no—
311D4—1882no—
312D4#1062535212yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4C2×C22⋊D4711yescharacteristic
329C2×C4C2×C22⋊D4711yescharacteristic
330C2×C4C2×C22⋊D4711yescharacteristic
331C2×C4C2×C22⋊D4711yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—941no—
334C8—941no—
335C8—941no—
336C8—941no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C22×C22⋊D4711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4C2×#1062535211yescharacteristic
361C4#1309406911yescharacteristic
362C2—41no—
363C2—41no—
364C2—42no—
365C2—3761no—
366C2#1568976711yescharacteristic
367C2#1568992111yescharacteristic
368C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#547C2
socleC22×C47C22×D4
hypercenter#547D47
hypocenterC47#3307
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689491C2semidirect
3. #15689461C2semidirect
4. #15689451C2semidirect
5. #15689423C2semidirect
6. #15689371C2semidirect
7. #15689354C2semidirect
8. #15689325C2semidirect
9. #15689268C2semidirect
10. #15689268C2semidirect
11. #15689233C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. #15689119C2semidirect
15. C47×#547C2semidirect
186. #547D47semidirect
200. C47#3307semidirect