Finite Group Databasebeta

← #20254082

Subgroups — #20254082

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689670C211yesmaximal, characteristic, complemented
2#15689660C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689509C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689484C211yesmaximal, characteristic, complemented
7#15689360C211yesmaximal, characteristic, complemented
8#15689358C211yesmaximal, characteristic, complemented
9#15689355C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#97×D47C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625336C2211yescharacteristic
18C2×D376C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094020C2211yescharacteristic
24#13094019—21no—
25#13094015C2211yescharacteristic
26#13094013C2211yescharacteristic
27#13094010—21no—
28#13094009—21no—
29#13094000C2211yescharacteristic
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093997—21no—
33#13093995C2211yescharacteristic
34C4×D188—21no—
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic
37C4×C22⋊D47—21no—
38#13093981—21no—
39C42×D47C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65#10625350—44no—
66C2×D188—21no—
67C2×D188—21no—
68C2×D188C2311yescharacteristic
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47D411yescharacteristic
73C2×C4×D47D411yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76SD16×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86#10625336—22no—
87#10625334—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106D376—22no—
107C8×D47—22no—
108C8×D47—22no—
109C23×C47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—42no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—42no—
125C22⋊D47—42no—
126C22⋊D47—42no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—21no—
133D188—21no—
134D188—21no—
135D188—21no—
136D188—42no—
137D188—42no—
138C4×D47—22no—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—41no—
142C4×D47—42no—
143C4×D47—42no—
144Dic94—42no—
145C8×C47—21no—
146C8×C47#4112yescomplemented
147C47⋊C8—21no—
148C47⋊C8#4112yescomplemented
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47C22×D411yescharacteristic
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47AGL(1,ℤ/8)12yes—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47C2×#4111yescharacteristic
168C4×C47C2×#4111yescharacteristic
169Dic47—21no—
170Dic47—21no—
171Dic47—21no—
172Dic47—41no—
173Dic47—41no—
174#3180—471nomaximal, Sylow
175C2×C47—81no—
176C2×C47#53211yescharacteristic
177C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C47#57511yescharacteristic
179D47—22no—
180D47—81no—
181D47—81no—
182#532—471no—
183#529—471no—
184#501—471no—
185#496—471no—
186#490—471no—
187#489—471no—
188#466—471no—
189#466—471no—
190#465—471no—
191#465—471no—
192#442—471no—
193#442—471no—
194#440—471no—
195#440D4711yescharacteristic, complemented
196C2×#97—471no—
197C47#318011yescharacteristic, complemented, Sylow
198C2×#41—941no—
199C2×SD16—471no—
200C2×SD16C2×D4711yescharacteristic
201C2×D8—471no—
202C2×D8—471no—
203C22×C8—471no—
204C22×C8—471no—
205C4⋊Q8—471no—
206#127—471no—
207#126—941no—
208#125—471no—
209#124—471no—
210#124—941no—
211#123—941no—
212C22⋊Q8—471no—
213#121—471no—
214#121—471no—
215#121—471no—
216#121—941no—
217C4×Q8C2×D4711yescharacteristic
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—941no—
221C4×D4—941no—
222C4×D4C2×D4711yescharacteristic
223#117—941no—
224C2×C42—471no—
225#107—471no—
226#107C2×D4711yescharacteristic
227#106—471no—
228#106—471no—
229#103—471no—
230#103C2×D4711yescharacteristic
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237#97—471no—
238#97—471no—
239#97—471no—
240#97C2×D4711yescharacteristic
241#41—1884no—
242C2×Q8—941no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258SD16—22no—
259SD16—942no—
260D8—942no—
261D8—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8—942no—
265C2×C8—942no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—21no—
287C42—471no—
288C42—471no—
289C42—471no—
290C42C22×D4711yescharacteristic
291C23—21no—
292C23—471no—
293C23—941no—
294C23—941no—
295Q8—21no—
296Q8—21no—
297Q8—1882no—
298D4—21no—
299D4—21no—
300D4—941no—
301D4—941no—
302D4—941no—
303D4—941no—
304D4—1882no—
305D4—1882no—
306D4—1882no—
307D4—1882no—
308D4—1882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—942no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1881no—
322C2×C4—1882no—
323C2×C4—1882no—
324C2×C4D4×D4711yescharacteristic
325C2×C4D4×D4711yescharacteristic
326C2×C4C23×D4711yescharacteristic
327C8—21no—
328C8—472no—
329C8—941no—
330C8#1062535012yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—472no—
335C22—941no—
336C22—941no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—941no—
350C4—941no—
351C4—941no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4C2×#1062535011yescharacteristic
356C2—81no—
357C2—942no—
358C2—3761no—
359C2—3761no—
360C2#1568967011yescharacteristic
361C2AGL(1,ℤ/8)×D4711yescharacteristic
362C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3180
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689670C2semidirect
2. #15689660C2semidirect
3. #15689531C2semidirect
4. #15689509C2semidirect
5. #15689486C2semidirect
6. #15689484C2semidirect
7. #15689360C2semidirect
8. #15689358C2semidirect
9. #15689355C2semidirect
10. #15689349C2semidirect
11. #15689236C2semidirect
12. #15689233C2semidirect
13. #15689221C2semidirect
14. #97×D47C2semidirect
15. C47×#440C2semidirect
146. C8×C47#41semidirect
148. C47⋊C8#41semidirect
195. #440D47semidirect
197. C47#3180semidirect
330. C8#10625350semidirect