Finite Group Databasebeta

← #20256114

Subgroups — #20256114

Order 6016.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689850C211yesmaximal, characteristic, complemented
2#15689793C211yesmaximal, characteristic
3#15689486C211yesmaximal, characteristic, complemented
4#15689468C211yesmaximal, characteristic, complemented
5#15689421C211yesmaximal, characteristic, complemented
6#15689420C211yesmaximal, characteristic, complemented
7#15689401C211yesmaximal, characteristic, complemented
8#15689322C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689320C211yesmaximal, characteristic, complemented
11#15689251C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689214C211yesmaximal, characteristic, complemented
15C47×#490C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20#13094023—21no—
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094020C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094014—21no—
27#13093996—21no—
28#13093996—21no—
29#13093995—21no—
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32#13093989—21no—
33#13093989C2211yescharacteristic
34#13093989C2211yescharacteristic
35C4×D188C2211yescharacteristic
36D4×Dic47C2211yescharacteristic
37D4×Dic47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#127×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#102×C47C2211yescharacteristic
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625352—44no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×Dic94—21no—
73C2×Dic94D411yescharacteristic
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84#10625335—22no—
85#10625335—22no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625325—22no—
106C23×C47—21no—
107C23×C47—21no—
108C22×D47—21no—
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C22⋊D47—42no—
122C22⋊D47—81no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47—42no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188—21no—
135C4×D47—42no—
136Dic94—21no—
137Dic94—22no—
138Dic94—42no—
139Dic94#4112yescomplemented
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—22no—
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47AGL(1,ℤ/8)12yes—
167#3368—471nomaximal, Sylow
168C2×C47—81no—
169C2×C47—81no—
170C2×C47#54811yescharacteristic
171C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C47#57711yescharacteristic
173D47—81no—
174#557—471no—
175#550—471no—
176#490—471no—
177#490D4711yescharacteristic, complemented
178#486—471no—
179#478—471no—
180#478—471no—
181#474—471no—
182#460—471no—
183#460—471no—
184#460—471no—
185#446—471no—
186#440—471no—
187#440—471no—
188C4×SD16—471no—
189C47#336811yescharacteristic, complemented, Sylow
190C2×#41—941no—
191C2×SD16—471no—
192C2×SD16—471no—
193C2×SD16—471no—
194C4⋊Q8—471no—
195C4⋊Q8—941no—
196#127—471no—
197#127—471no—
198#127C2×D4711yescharacteristic
199#125—471no—
200#125—941no—
201#125—941no—
202#125C2×D4711yescharacteristic
203#121—941no—
204#121—941no—
205#121—941no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8—941no—
211C4×D4—471no—
212C4×D4—471no—
213C4×D4—471no—
214#107—471no—
215#107—471no—
216#106—471no—
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226#102C2×D4711yescharacteristic
227#102C2×D4711yescharacteristic
228#102C2×D4711yescharacteristic
229#102C2×D4711yescharacteristic
230#97—471no—
231#97C2×D4711yescharacteristic
232C4×C8—471no—
233#41—1884no—
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8—941no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4C22×D4711yescharacteristic
245C2×D4C22×D4711yescharacteristic
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249SD16—942no—
250SD16—942no—
251SD16—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C42—471no—
275C42—471no—
276C42—941no—
277C42—941no—
278C42—941no—
279C42C22×D4711yescharacteristic
280C23—21no—
281C23—21no—
282C23—941no—
283Q8—472no—
284Q8—942no—
285Q8—941no—
286Q8—1882no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—941no—
294D4—941no—
295D4—3761no—
296D4—3761no—
297D4—1882no—
298D4—1882no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4D4×D4711yescharacteristic
312C2×C4D4×D4711yescharacteristic
313C2×C4C23×D4711yescharacteristic
314C8—21no—
315C8—21no—
316C8—941no—
317C8—941no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—472no—
333C4—942no—
334C4—941no—
335C4—941no—
336C4—941no—
337C4—1881no—
338C4—1881no—
339C4#41×D4711yescharacteristic
340C4#1309407111yescharacteristic
341C2—81no—
342C2—81no—
343C2—3761no—
344C2#1568978111yescharacteristic
345C2AGL(1,ℤ/8)×D4711yescharacteristic
346C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#490C2
socleC22×C47C22×D4
hypercenter#490D47
hypocenterC47#3368
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #15689850C2semidirect
3. #15689486C2semidirect
4. #15689468C2semidirect
5. #15689421C2semidirect
6. #15689420C2semidirect
7. #15689401C2semidirect
8. #15689322C2semidirect
9. #15689322C2semidirect
10. #15689320C2semidirect
11. #15689251C2semidirect
12. #15689225C2semidirect
13. #15689220C2semidirect
14. #15689214C2semidirect
15. C47×#490C2semidirect
139. Dic94#41semidirect
177. #490D47semidirect
189. C47#3368semidirect