Finite Group Databasebeta

← #20255719

Subgroups — #20255719

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689831C211yesmaximal, characteristic, complemented
2#15689792C211yesmaximal, characteristic
3#15689468C211yesmaximal, characteristic, complemented
4#15689437C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689321C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11Q16×Dic47C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#15689123C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094020—21no—
22#13094020C2211yescharacteristic
23#13094014—21no—
24#13094004—21no—
25#13094001—21no—
26#13094000C2211yescharacteristic
27#13093998—21no—
28#13093998C2211yescharacteristic
29#13093995—21no—
30#13093995C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72C22×Dic47—21no—
73#10625354—22no—
74#10625354—41no—
75C2×D188—21no—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×Dic94—21no—
81Q16×C47—22no—
82SD16×C47—41no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47D411yescharacteristic
90#10625336—41no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107#10625329—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47#4112yes—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—42no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—42no—
132C22⋊D47—81no—
133C22⋊D47—81no—
134C22⋊D47—81no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—81no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142D188—21no—
143D188—21no—
144D188—42no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—42no—
148C4×D47—81no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C4×C47—22no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178Dic47#13712yes—
179#3333—471nomaximal, Sylow
180C2×C47—41no—
181C2×C47—81no—
182C2×C47#54611yescharacteristic
183C2×C47C2×#13711yescharacteristic
184C2×C47#57611yescharacteristic
185D47—41no—
186D47—81no—
187#554—471no—
188#550—471no—
189#486—471no—
190#480—471no—
191#480—471no—
192#477—471no—
193#468—471no—
194#468—471no—
195#460—471no—
196#452—471no—
197#452D4711yescharacteristic, complemented
198C4×Q16—471no—
199#436—471no—
200#417—471no—
201#417—471no—
202C47#333311yescharacteristic, complemented, Sylow
203C2×#41—471no—
204C2×#41C2×D4711yescharacteristic
205C2×Q16C2×D4711yescharacteristic
206C2×SD16—471no—
207C2×SD16C2×D4711yescharacteristic
208C2×M16—471no—
209C2×M16—471no—
210C4⋊Q8—471no—
211#127—471no—
212#127—941no—
213#125—941no—
214C22⋊Q8—471no—
215C22⋊Q8—941no—
216C22⋊Q8—941no—
217C22⋊Q8C2×D4711yescharacteristic
218#121—471no—
219#121—471no—
220#121—941no—
221#121—941no—
222C4×Q8—471no—
223C4×Q8—471no—
224C4×D4—471no—
225C4×D4—941no—
226C4×D4—941no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229#107—471no—
230#107—471no—
231#107—471no—
232C4⋊C8—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103C2×D4711yescharacteristic
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102C2×D4711yescharacteristic
243C22⋊C8—471no—
244C22⋊C8C2×D4711yescharacteristic
245C4×C8—471no—
246#41—22no—
247#41—41no—
248#41—942no—
249#41—1881no—
250C2×Q8—941no—
251C2×Q8C22×D4711yescharacteristic
252C2×Q8C22×D4711yescharacteristic
253C2×D4—21no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4C22×D4711yescharacteristic
262C22×C4—21no—
263C22×C4—471no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4C22×D4711yescharacteristic
268Q16—22no—
269SD16—41no—
270SD16—1881no—
271M16—1881no—
272M16—1881no—
273C2×C8—471no—
274C2×C8—471no—
275C2×C8C22×D4711yescharacteristic
276C2×C8C22×D4711yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—471no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4C22×D4711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C42—471no—
296C42—941no—
297C42—941no—
298C23—21no—
299C23—471no—
300C23—941no—
301C23D4×D4711yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—3761no—
306Q8#1062535212yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—942no—
311D4—941no—
312D4—941no—
313D4—3761no—
314D4—3761no—
315D4—3761no—
316D4—1882no—
317D4—1882no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—1882no—
335C2×C4D4×D4711yescharacteristic
336C2×C4C23×D4711yescharacteristic
337C8—21no—
338C8—21no—
339C8—941no—
340C8—941no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—941no—
348C22—941no—
349C22—941no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22C2×D4×D4711yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—472no—
359C4—941no—
360C4—941no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4C2×#1062535211yescharacteristic
365C4#1309406911yescharacteristic
366C2—41no—
367C2—81no—
368C2—3761no—
369C2—1881no—
370C2#1568976011yescharacteristic
371C2#137×D4711yescharacteristic
372C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3333
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689468C2semidirect
4. #15689437C2semidirect
5. #15689435C2semidirect
6. #15689416C2semidirect
7. #15689371C2semidirect
8. #15689366C2semidirect
9. #15689321C2semidirect
10. #15689284C2semidirect
11. Q16×Dic47C2semidirect
12. #15689198C2semidirect
13. #15689124C2semidirect
14. #15689123C2semidirect
15. C47×#452C2semidirect
197. #452D47semidirect
202. C47#3333semidirect