Finite Group Databasebeta

← #20256341

Subgroups — #20256341

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689834C211yesmaximal, characteristic, complemented
2#15689832C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689529C211yesmaximal, characteristic, complemented
5#15689524C211yesmaximal, characteristic, complemented
6#15689426C211yesmaximal, characteristic, complemented
7#15689425C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689421C211yesmaximal, characteristic, complemented
10#15689402C211yesmaximal, characteristic, complemented
11#15689252C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic
13#15689232C211yesmaximal, characteristic
14#15689203C211yesmaximal, characteristic
15C47×#474C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094016C2211yescharacteristic
19#13094015C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094004—21no—
23#13094003—21no—
24#13094001—21no—
25#13094001—21no—
26#13094000—21no—
27#13094000—21no—
28C4×Dic94C2211yescharacteristic
29C4×D188C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34C2×Dic47⋊C4—21no—
35C4⋊C4×D47—21no—
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×Dic94—21no—
69C2×Dic94D411yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80#10625334Q814yescomplemented
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C23×C47—21no—
104C22×D47—21no—
105Q8×C47—81no—
106D4×C47—21no—
107D4×C47C2×Q812yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—81no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—42no—
119C2×Dic47—81no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188C2×Q812yes—
126C4×D47—42no—
127C4×D47—81no—
128C4×D47—81no—
129Dic94—41no—
130Dic94—81no—
131C8×C47—21no—
132C8×C47—21no—
133C47⋊C8—21no—
134C47⋊C8C2×Q812yes—
135C22×C47—22no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47C22×D411yescharacteristic
139C2×D47—22no—
140C2×D47—41no—
141C2×D47—41no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47C22×Q811yescharacteristic
148C4×C472−1+411yescharacteristic
149Dic47—21no—
150Dic47—21no—
151Dic47—21no—
152Dic47—21no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3389—471nomaximal, Sylow
157C2×C47—42no—
158C2×C47D4×Q811yescharacteristic
159C2×C47#57511yescharacteristic
160C2×C47#57611yescharacteristic
161D47—42no—
162#554—471no—
163#554—471no—
164#501—471no—
165#501—471no—
166#499—471no—
167#478—471no—
168#478—471no—
169#478—471no—
170#478—471no—
171#474—471no—
172#474D4711yescharacteristic, complemented
173#446—471no—
174#442—471no—
175#442—471no—
176C4×D8—471no—
177C47#338911yescharacteristic, complemented, Sylow
178C2×D8—471no—
179C4⋊Q8—471no—
180C4⋊Q8C2×D4711yescharacteristic
181#125—471no—
182#125—471no—
183#125—471no—
184#125—471no—
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187C22⋊Q8—941no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C4×Q8—471no—
192C4×D4—471no—
193C4×D4—471no—
194C4×D4—471no—
195C4×D4—471no—
196C4×D4—471no—
197C4×D4C2×D4711yescharacteristic
198C2×C4⋊C4—941no—
199C2×C4⋊C4—941no—
200#107—471no—
201#107—471no—
202#107—471no—
203#107C2×D4711yescharacteristic
204#107C2×D4711yescharacteristic
205#106—471no—
206#106—471no—
207#106—471no—
208#106—471no—
209C4⋊C8—471no—
210C4⋊C8—471no—
211C4⋊C8C2×D4711yescharacteristic
212#102—471no—
213#102—471no—
214#102—471no—
215#102—471no—
216#102C2×D4711yescharacteristic
217#102C2×D4711yescharacteristic
218#97—471no—
219#97—471no—
220C4×C8—471no—
221C2×Q8—21no—
222C2×Q8—471no—
223C2×Q8—941no—
224C2×D4—471no—
225C2×D4C22×D4711yescharacteristic
226C22×C4—21no—
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4—941no—
232D8—474no—
233C2×C8—471no—
234C2×C8—471no—
235C2×C8C22×D4711yescharacteristic
236C2×C8C22×D4711yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4C22×D4711yescharacteristic
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C42—471no—
263C42—471no—
264C42C22×D4711yescharacteristic
265C23—21no—
266C23—941no—
267Q8—81no—
268Q8—3761no—
269Q8—1881no—
270D4—21no—
271D4—472no—
272D4—941no—
273D4Q8×D4712yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—471no—
279C2×C4—471no—
280C2×C4—471no—
281C2×C4—471no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—3761no—
286C2×C4—3761no—
287C2×C4—3761no—
288C2×C4—1882no—
289C2×C4—1882no—
290C2×C4D4×D4711yescharacteristic
291C2×C4D4×D4711yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—21no—
294C8—21no—
295C8—472no—
296C8—941no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—942no—
301C22—1881no—
302C22—1881no—
303C22C2×D4×D4711yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—941no—
310C4—941no—
311C4—941no—
312C4—941no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4C2×Q8×D4711yescharacteristic
317C4#1309407111yescharacteristic
318C2—42no—
319C2—1882no—
320C2#1568978611yescharacteristic
321C2#1568992211yescharacteristic
322C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3389
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
2. #15689832C2semidirect
3. #15689531C2semidirect
4. #15689529C2semidirect
5. #15689524C2semidirect
6. #15689426C2semidirect
7. #15689425C2semidirect
8. #15689424C2semidirect
9. #15689421C2semidirect
10. #15689402C2semidirect
11. #15689252C2semidirect
15. C47×#474C2semidirect
80. #10625334Q8semidirect
172. #474D47semidirect
177. C47#3389semidirect