Finite Group Databasebeta

← #20255828

Subgroups — #20255828

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689777C211yesmaximal, characteristic
2#15689533C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689451C211yesmaximal, characteristic, complemented
5#15689447C211yesmaximal, characteristic, complemented
6#15689436C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic, complemented
8#15689418C211yesmaximal, characteristic, complemented
9#15689371C211yesmaximal, characteristic, complemented
10#15689354C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689166C211yesmaximal, characteristic, complemented
14C2×#13093957C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625336C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094008—21no—
22#13094008—21no—
23#13094004—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093957C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47—21no—
50#125×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47D411yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—44no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47D411yescharacteristic
86C22⋊C4×C47D411yescharacteristic
87C42×C47—21no—
88C42×C47—21no—
89C42×C47C2311yescharacteristic
90#10625336—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100#10625329—22no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47C2×D411yescharacteristic
107C23×C47C2×D411yescharacteristic
108C22×D47—21no—
109Q8×C47—21no—
110Q8×C47—21no—
111D4×C47—22no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×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×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—42no—
127C22⋊D47—42no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133D188—21no—
134D188—21no—
135C4×D47—42no—
136Dic94—42no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C47⋊C8#4112yescomplemented
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47AGL(1,ℤ/8)12yes—
147C22×C47C22×D411yescharacteristic
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C472−1+411yescharacteristic
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3343—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—41no—
167C2×C47#54711yescharacteristic
168C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C47#57811yescharacteristic
170D47—81no—
171#552D4711yescharacteristic, complemented
172#547—471no—
173#501—471no—
174#484—471no—
175#483—471no—
176#482—471no—
177#480—471no—
178#478—471no—
179#477—471no—
180#468—471no—
181#465—471no—
182#440—471no—
183#435—471no—
184#428—471no—
185C2×#107—471no—
186C47#334311yescharacteristic, complemented, Sylow
187C2×#41—941no—
188C2×SD16—471no—
189C2×M16—471no—
190C22×C8—471no—
191C4⋊Q8—471no—
192#126—21no—
193#125—21no—
194#125C2×D4711yescharacteristic
195#123—21no—
196#123—941no—
197#123—941no—
198C22⋊Q8—941no—
199C22⋊Q8C2×D4711yescharacteristic
200C22⋊Q8C2×D4711yescharacteristic
201#121—471no—
202#121—471no—
203C4×Q8C2×D4711yescharacteristic
204C4×D4—471no—
205C4×D4C2×D4711yescharacteristic
206#117—21no—
207#117C2×D4711yescharacteristic
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4C2×D4711yescharacteristic
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227C22⋊C8—471no—
228C22⋊C8—471no—
229#97—471no—
230#41—1884no—
231C2×Q8—941no—
232C2×Q8C22×D4711yescharacteristic
233C2×D4—471no—
234C2×D4—941no—
235C2×D4—941no—
236C2×D4C22⋊D4711yescharacteristic
237C22×C4—21no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4C22×D4711yescharacteristic
242C22×C4C22×D4711yescharacteristic
243SD16—942no—
244M16—942no—
245C2×C8—471no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—942no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22⋊D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4C22⋊D4711yescharacteristic
273C22⋊C4C22⋊D4711yescharacteristic
274C42—21no—
275C42—21no—
276C42C22×D4711yescharacteristic
277C23—941no—
278C23C2×C22⋊D4711yescharacteristic
279C23C2×C22⋊D4711yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—1882no—
283D4—22no—
284D4—941no—
285D4—941no—
286D4—1882no—
287D4—1882no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4—1882no—
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C2×C22⋊D4711yescharacteristic
306C2×C4C2×C22⋊D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—472no—
309C8—941no—
310C8—941no—
311C8—941no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—1881no—
318C22—1881no—
319C22—1881no—
320C22#1309404912yes—
321C22C22×C22⋊D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407111yescharacteristic
335C2—22no—
336C2—41no—
337C2—3761no—
338C2#1568977211yescharacteristic
339C2C2×#1309404911yescharacteristic
340C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689456C2semidirect
4. #15689451C2semidirect
5. #15689447C2semidirect
6. #15689436C2semidirect
7. #15689420C2semidirect
8. #15689418C2semidirect
9. #15689371C2semidirect
10. #15689354C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689166C2semidirect
14. C2×#13093957C2semidirect
15. C47×#552C2semidirect
140. C47⋊C8#41semidirect
171. #552D47semidirect
186. C47#3343semidirect