Finite Group Databasebeta

← #20255499

Subgroups — #20255499

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689830C211yesmaximal, characteristic, complemented
2#15689482C211yesmaximal, characteristic, complemented
3#15689451C211yesmaximal, characteristic, complemented
4#15689439C211yesmaximal, characteristic, complemented
5#15689408C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14C2×#13093948C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094015—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25#13094001—21no—
26#13094001—21no—
27C4×Dic94C2211yescharacteristic
28D4×Dic47—21no—
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47C2211yescharacteristic
54#121×C47—21no—
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47—21no—
89C42×C47C2311yescharacteristic
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92#10625337—22no—
93#10625337—41no—
94#10625335—41no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
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
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—42no—
118Q8×C47#4112yes—
119D4×C47—22no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123D4×C47—42no—
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×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—81no—
143C2×Dic47—81no—
144Dic94—21no—
145Dic94—21no—
146Dic94—81no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47#13712yes—
160C22×C47C22×D411yescharacteristic
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—22no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C2×#4111yescharacteristic
169C4×C47H(5,𝔽2)11yescharacteristic
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3316—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—41no—
177C2×C47—81no—
178C2×C47#54611yescharacteristic
179C2×C47C2×#13711yescharacteristic
180C2×C47#57711yescharacteristic
181#554—471no—
182#548D4711yescharacteristic
183#489—471no—
184#483—471no—
185#481—471no—
186#475—471no—
187#470—471no—
188#465—471no—
189#464—471no—
190#452—471no—
191#451—471no—
192#441—471no—
193#435—471no—
194#417—471no—
195C2×#103—471no—
196C47#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D4711yescharacteristic
198C22×Q8C2×D4711yescharacteristic
199C2×Q16—471no—
200C2×Q16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—471no—
205#125—941no—
206#124—21no—
207#124C2×D4711yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212C22⋊Q8—941no—
213C22⋊Q8C2×D4711yescharacteristic
214#121—21no—
215#121C2×D4711yescharacteristic
216C4×Q8—471no—
217C4×Q8C2×D4711yescharacteristic
218C4×D4—21no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—471no—
246C2×Q8—941no—
247C2×Q8C22×D4711yescharacteristic
248C2×Q8C22×D4711yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D4711yescharacteristic
252C2×D4C22×D4711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259Q16—942no—
260Q16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8—471no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—471no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22⋊D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4C22⋊D4711yescharacteristic
288C22⋊C4C22⋊D4711yescharacteristic
289C42—21no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—21no—
293C23C2×C22⋊D4711yescharacteristic
294C23C2×C22⋊D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—941no—
300Q8—941no—
301Q8—3761no—
302Q8#1062535212yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C2×C22⋊D4711yescharacteristic
326C2×C4C2×C22⋊D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—941no—
329C8—941no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1309405412yes—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4C2×#1062535211yescharacteristic
354C4#1309406911yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1568976711yescharacteristic
359C2C2×#1309405411yescharacteristic
360C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#548C2
socleC22×C47C22×D4
hypercenter#548D47
hypocenterC47#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689830C2semidirect
2. #15689482C2semidirect
3. #15689451C2semidirect
4. #15689439C2semidirect
5. #15689408C2semidirect
6. #15689379C2semidirect
7. #15689350C2semidirect
8. #15689342C2semidirect
9. #15689285C2semidirect
10. #15689279C2semidirect
11. #15689228C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. C2×#13093948C2semidirect
196. C47#3316semidirect