Finite Group Databasebeta

← #20256096

Subgroups — #20256096

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689832C211yesmaximal, characteristic, complemented
2#15689794C211yesmaximal, characteristic, complemented
3#15689488C211yesmaximal, characteristic, complemented
4#15689486C211yesmaximal, characteristic, complemented
5#15689468C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689422C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic, complemented
11#15689316C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689232C211yesmaximal, characteristic, complemented
14#15689203C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094021C2211yescharacteristic
21#13094020C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094016C2211yescharacteristic
24#13094015C2211yescharacteristic
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28#13093998—21no—
29#13093997—21no—
30#13093997—21no—
31C4×Dic94C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic
36C2×Dic47⋊C4—21no—
37#13093957C2211yescharacteristic
38#13093955C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625350—44no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94—21no—
77C2×Dic94D411yescharacteristic
78D8×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88#10625334—22no—
89#10625334—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C23×C47—21no—
108C22×D47—21no—
109C22×D47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47#4112yescomplemented
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47—81no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—42no—
122C22⋊D47—42no—
123C22⋊D47—81no—
124C22⋊D47—81no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47—81no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188—21no—
135D188—21no—
136D188—21no—
137D188—42no—
138D188—81no—
139C4×D47—42no—
140C4×D47—42no—
141Dic94—22no—
142Dic94—81no—
143C8×C47—21no—
144C8×C47—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C22×C47—22no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C22×D411yescharacteristic
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C472−1+411yescharacteristic
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47AGL(1,ℤ/8)12yes—
172#3366—471nomaximal, Sylow
173C2×C47—42no—
174C2×C47—81no—
175C2×C47#54811yescharacteristic
176C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C47#57611yescharacteristic
178D47—81no—
179D47—81no—
180#554—471no—
181#550—471no—
182#490—471no—
183#490—471no—
184#486—471no—
185#478—471no—
186#478—471no—
187#476—471no—
188#459—471no—
189#459—471no—
190#459—471no—
191#446—471no—
192#442—471no—
193#442D4711yescharacteristic, complemented
194C4×D8—471no—
195C47#336611yescharacteristic, complemented, Sylow
196C2×#41—941no—
197C2×D8—471no—
198C2×D8—471no—
199C2×D8C2×D4711yescharacteristic
200C4⋊Q8—471no—
201#127—471no—
202#127—471no—
203#127—471no—
204#125—471no—
205#125—471no—
206C22⋊Q8—941no—
207C22⋊Q8—941no—
208C22⋊Q8—941no—
209#121—941no—
210#121—941no—
211#121—941no—
212C4×Q8—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4C2×D4711yescharacteristic
218C4×D4C2×D4711yescharacteristic
219C2×C4⋊C4—941no—
220#107—471no—
221#106—471no—
222#106C2×D4711yescharacteristic
223C4⋊C8—471no—
224C4⋊C8—471no—
225C4⋊C8—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102C2×D4711yescharacteristic
235#102C2×D4711yescharacteristic
236#97—471no—
237#97C2×D4711yescharacteristic
238C4×C8—471no—
239#41—1884no—
240C2×Q8—471no—
241C2×Q8—941no—
242C2×D4—471no—
243C2×D4—471no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4C22×D4711yescharacteristic
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258D8—22no—
259D8—942no—
260D8—942no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C42—471no—
284C42—471no—
285C42C22×D4711yescharacteristic
286C23—21no—
287C23—21no—
288C23—941no—
289C23—941no—
290Q8—942no—
291Q8—3761no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—941no—
296D4—941no—
297D4—941no—
298D4—941no—
299D4—3761no—
300D4—3761no—
301D4—3761no—
302D4—1882no—
303D4—1882no—
304D4—1882no—
305D4#1062535012yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4—1882no—
320C2×C4D4×D4711yescharacteristic
321C2×C4D4×D4711yescharacteristic
322C2×C4C23×D4711yescharacteristic
323C8—21no—
324C8—21no—
325C8—941no—
326C8—941no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22C2×D4×D4711yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—472no—
345C4—941no—
346C4—941no—
347C4—941no—
348C4—1881no—
349C4—1881no—
350C4C2×#1062535011yescharacteristic
351C4#1309407111yescharacteristic
352C2—42no—
353C2—81no—
354C2—3761no—
355C2—3761no—
356C2#1568978211yescharacteristic
357C2AGL(1,ℤ/8)×D4711yescharacteristic
358C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3366
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689832C2semidirect
2. #15689794C2semidirect
3. #15689488C2semidirect
4. #15689486C2semidirect
5. #15689468C2semidirect
6. #15689423C2semidirect
7. #15689422C2semidirect
8. #15689412C2semidirect
9. #15689318C2semidirect
10. #15689316C2semidirect
11. #15689316C2semidirect
12. #15689251C2semidirect
13. #15689232C2semidirect
14. #15689203C2semidirect
15. C47×#442C2semidirect
113. D4×C47#41semidirect
193. #442D47semidirect
195. C47#3366semidirect
305. D4#10625350semidirect