Finite Group Databasebeta

← #20255860

Subgroups — #20255860

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic, complemented
2#15689777C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689442C211yesmaximal, characteristic, complemented
7#15689437C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689414C211yesmaximal, characteristic, complemented
10#15689376C211yesmaximal, characteristic, complemented
11#15689359C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14C2×#13093956C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×D376C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094019—21no—
20#13094016C2211yescharacteristic
21#13094008—21no—
22#13094008—21no—
23#13094006—21no—
24#13094004—21no—
25#13093998C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093996—21no—
30C4×D188C2211yescharacteristic
31C4×D188C2211yescharacteristic
32(C22⋊D47)⋊C4—21no—
33#13093983C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093956C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625352—44no—
70C2×D188C2311yescharacteristic
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×Dic94—21no—
75M16×C47—22no—
76C2×C8×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105D376—22no—
106C23×C47C2×D411yescharacteristic
107C23×C47C2×D411yescharacteristic
108C22×D47—21no—
109C22×D47—21no—
110D4×C47—22no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C22⋊D47—42no—
122C22⋊D47—42no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131C2×Dic47—42no—
132C2×Dic47—81no—
133D188—21no—
134D188—21no—
135D188—21no—
136D188—21no—
137C4×D47—42no—
138C4×D47—81no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47—21no—
142C8×C47—21no—
143C8×C47#4112yescomplemented
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47AGL(1,ℤ/8)12yes—
150C22×C47C22×D411yescharacteristic
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47C2×#4111yescharacteristic
162C4×C472−1+411yescharacteristic
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3345—471nomaximal, Sylow
170C2×C47—22no—
171C2×C47—41no—
172C2×C47#54711yescharacteristic
173C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C47#57711yescharacteristic
175D47—81no—
176D47—81no—
177#553—471no—
178#547—471no—
179#501—471no—
180#482—471no—
181#481—471no—
182#481—471no—
183#480—471no—
184#478—471no—
185#476—471no—
186#469—471no—
187#466—471no—
188#442—471no—
189#435D4711yescharacteristic, complemented
190#428—471no—
191C2×#106—471no—
192C47#334511yescharacteristic, complemented, Sylow
193C2×#41—941no—
194C2×D8—471no—
195C2×M16C2×D4711yescharacteristic
196C22×C8C2×D4711yescharacteristic
197C4⋊Q8—471no—
198#126—941no—
199#125—471no—
200#123—941no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204#121—471no—
205#121—471no—
206#121—471no—
207#121—471no—
208#121—941no—
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—941no—
212C4×D4C2×D4711yescharacteristic
213#117—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217#107—471no—
218#107—471no—
219#107—471no—
220#106—471no—
221#106—471no—
222#106—471no—
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8C2×D4711yescharacteristic
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233C22⋊C8C2×D4711yescharacteristic
234C22⋊C8C2×D4711yescharacteristic
235#97C2×D4711yescharacteristic
236#41—1884no—
237C2×Q8—941no—
238C2×D4—471no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4D18811yescharacteristic
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252D8—942no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4D18811yescharacteristic
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4D18811yescharacteristic
280C22⋊C4D18811yescharacteristic
281C42—941no—
282C42C22×D4711yescharacteristic
283C23—941no—
284C23—941no—
285C23C2×D18811yescharacteristic
286C23C2×D18811yescharacteristic
287Q8—1882no—
288D4—22no—
289D4—941no—
290D4—941no—
291D4—941no—
292D4—941no—
293D4—3761no—
294D4—1882no—
295D4—1882no—
296D4—1882no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4—3761no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4C2×D18811yescharacteristic
313C2×C4C2×D18811yescharacteristic
314C2×C4C2×D18811yescharacteristic
315C2×C4C2×D18811yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1062535212yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22#1309405212yes—
333C22C22×D18811yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4—1881no—
344C4C2×#1062535211yescharacteristic
345C4#1309407111yescharacteristic
346C2—22no—
347C2—41no—
348C2—3761no—
349C2—3761no—
350C2#1568977711yescharacteristic
351C2C2×#1309405211yescharacteristic
352C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3345
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689777C2semidirect
3. #15689532C2semidirect
4. #15689448C2semidirect
5. #15689442C2semidirect
6. #15689442C2semidirect
7. #15689437C2semidirect
8. #15689424C2semidirect
9. #15689414C2semidirect
10. #15689376C2semidirect
11. #15689359C2semidirect
12. #15689236C2semidirect
13. #15689165C2semidirect
14. C2×#13093956C2semidirect
15. C47×#435C2semidirect
143. C8×C47#41semidirect
189. #435D47semidirect
192. C47#3345semidirect
320. C8#10625352semidirect