Finite Group Databasebeta

← #20253107

Subgroups — #20253107

Order 6016.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689923C211yesmaximal, characteristic, complemented
2#15689921C211yesmaximal, characteristic, complemented
3C2×#13094044C211yesmaximal, characteristic, complemented
4C2×#13094032C211yesmaximal, characteristic, complemented
5#15689397C212yesmaximal, complemented
6#15689392C212yesmaximal, complemented
7#15689389C212yesmaximal, complemented
8#15689385C212yesmaximal, complemented
9C2×#13093959C211yesmaximal, characteristic, complemented
10#15689105C211yesmaximal, characteristic, complemented
11C47×#413C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14#13094057—21no—
15#13094057C2212yes—
16#13094055C2212yes—
17#13094054—21no—
18#13094052—21no—
19#13094052C2212yes—
20#13094050C2212yes—
21#13094049—21no—
22#13094046—22no—
23#13094044—22no—
24#13094044—21no—
25#13094044—21no—
26#13094044—21no—
27#13094044—21no—
28C2×#10625337C2211yescharacteristic, complemented
29C2×#10625335C2211yescharacteristic, complemented
30C2×#10625336C2211yescharacteristic, complemented
31C2×#10625334C2211yescharacteristic, complemented
32#13094032—21no—
33#13094032—21no—
34#13094032C2212yes—
35#13094032C2212yes—
36C2×#10625329C2211yescharacteristic
37C2×#10625324—21no—
38C22×C47⋊C8C2211yescharacteristic
39C2×C8×D47—21no—
40#13093959C2212yescomplemented
41#13093959C2212yescomplemented
42#13093942C2212yescomplemented
43#13093940C2212yescomplemented
44C2×#41×C47C2211yescharacteristic
45C2×M16×C47C2211yescharacteristic
46C2×M16×C47C2211yescharacteristic
47#101×C47C2212yescomplemented
48#100×C47C2212yescomplemented
49#41×C47—21no—
50#41×C47—21no—
51#41×C47—21no—
52#41×C47—21no—
53C2×Q8×C47C2311yescharacteristic
54C2×D4×C47—21no—
55C2×D4×C47C2311yescharacteristic
56C22×C4×C47—21no—
57C22×C4×C47C2311yescharacteristic
58C2×C22⋊D47—21no—
59C2×C22⋊D47—21no—
60#10625350—21no—
61#10625350—21no—
62#10625350—21no—
63#10625350—21no—
64#10625350—21no—
65#10625350—21no—
66#10625350D412yes—
67#10625350C2312yes—
68C2×D188D411yescharacteristic
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×Dic94D411yescharacteristic
73C2×Dic94C2311yescharacteristic
74M16×C47—21no—
75M16×C47—21no—
76M16×C47C2312yes—
77M16×C47C2312yes—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80#10625337—22no—
81#10625337—21no—
82#10625337—21no—
83#10625336—22no—
84#10625336—21no—
85#10625336—21no—
86#10625335—22no—
87#10625335—21no—
88#10625335—21no—
89#10625334—22no—
90#10625334—21no—
91#10625334—21no—
92#10625329—21no—
93#10625329C2312yes—
94C2×C47⋊C8—21no—
95C2×C47⋊C8D411yescharacteristic
96C2×C47⋊C8D411yescharacteristic
97C2×C47⋊C8D411yescharacteristic
98C2×C47⋊C8D411yescharacteristic
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101Dic188—22no—
102D376—22no—
103#10625325—22no—
104#10625325—22no—
105#10625324—22no—
106#10625324—22no—
107C8×D47—22no—
108C8×D47—22no—
109C23×C47—21no—
110C23×C47#4111yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—41no—
118D4×C47—41no—
119C2×C4×C47—21no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47#4111yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—22no—
129C22⋊D47—22no—
130C22⋊D47—41no—
131C22⋊D47—41no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134D188—21no—
135D188—21no—
136D188—21no—
137D188C2×D412yes—
138C4×D47—22no—
139C4×D47—22no—
140C4×D47—41no—
141C4×D47—41no—
142Dic94—21no—
143Dic94—21no—
144Dic94—21no—
145Dic94C2×D412yes—
146C8×C47—22no—
147C8×C47—22no—
148C47⋊C8—22no—
149C47⋊C8C2×D411yescharacteristic
150C47⋊C8C2×D411yescharacteristic
151C47⋊C8C2×D411yescharacteristic
152C47⋊C8C2×D411yescharacteristic
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—81no—
156C22×C47#12111yescharacteristic
157C22×C47#12111yescharacteristic
158C22×C47C2×#4111yescharacteristic
159C2×D47—22no—
160C2×D47—42no—
161C2×D47—41no—
162C2×D47—81no—
163C4×C47—41no—
164C4×C47#12111yescharacteristic
165C4×C47#12111yescharacteristic
166C4×C47C22×D411yescharacteristic
167C4×C47C22×D411yescharacteristic
168Dic47—22no—
169Dic47—41no—
170#3067—471nomaximal, Sylow
171C2×C47—21no—
172C2×C47—21no—
173C2×C47—21no—
174C2×C47—81no—
175C2×C47C2×#12111yescharacteristic
176D47—42no—
177D47—81no—
178#575—471no—
179#575—471no—
180C2×#135—471no—
181C2×#131—471no—
182#473—472no—
183#472—472no—
184#471—472no—
185#471—472no—
186C2×#108—471no—
187#413—471no—
188#413D4711yescharacteristic, complemented
189C47#306711yescharacteristic, complemented, Sylow
190C2×#41—471no—
191C2×#41—471no—
192C2×#41C2×D4711yescharacteristic
193#137—472no—
194#137—472no—
195#137—941no—
196#137—941no—
197AGL(1,ℤ/8)—472no—
198AGL(1,ℤ/8)—472no—
199AGL(1,ℤ/8)—941no—
200AGL(1,ℤ/8)—941no—
201#135—942no—
202#135—941no—
203#135—941no—
204#135—941no—
205#135—941no—
206#135—942no—
207C2×Q16—471no—
208C2×SD16—471no—
209C2×SD16—471no—
210C2×D8—471no—
211#131—472no—
212#131—472no—
213#131—941no—
214#131—941no—
215C2×M16—471no—
216C2×M16—941no—
217C2×M16C2×D4711yescharacteristic
218C2×M16C2×D4711yescharacteristic
219C22×C8—471no—
220C22×C8—941no—
221#108—472no—
222#108—472no—
223#101—472no—
224#101C2×D4712yescomplemented
225#100—472no—
226#100C2×D4712yescomplemented
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—472no—
232#41—472no—
233#41—941no—
234#41—941no—
235#41—941no—
236#41—941no—
237#41—941no—
238#41—941no—
239C2×Q8—471no—
240C2×Q8—471no—
241C2×Q8C22×D4711yescharacteristic
242C2×D4—21no—
243C2×D4—471no—
244C2×D4—471no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252Q16—942no—
253Q16—941no—
254Q16—941no—
255Q16—942no—
256SD16—942no—
257SD16—942no—
258SD16—941no—
259SD16—941no—
260SD16—941no—
261SD16—941no—
262SD16—942no—
263SD16—942no—
264D8—942no—
265D8—941no—
266D8—941no—
267D8—942no—
268M16—21no—
269M16—21no—
270M16—472no—
271M16—942no—
272M16—942no—
273M16—941no—
274M16C22×D4712yes—
275M16C22×D4712yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—471no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—942no—
285C2×C8—942no—
286C2×C8—941no—
287C23—21no—
288C23—941no—
289C23—941no—
290C23#1062535011yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—472no—
294Q8—941no—
295Q8—941no—
296Q8—941no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—472no—
302D4—942no—
303D4—942no—
304D4—941no—
305D4—941no—
306D4—941no—
307D4—1881no—
308D4—1881no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—941no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—941no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4#1062535011yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4D4×D4711yescharacteristic
321C2×C4D4×D4711yescharacteristic
322C2×C4D4×D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C8—22no—
325C8—22no—
326C8—471no—
327C8—471no—
328C8—471no—
329C8—471no—
330C8—942no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—942no—
335C22—3761no—
336C22—1882no—
337C22—1881no—
338C22#1309399711yescharacteristic
339C22#1309399711yescharacteristic
340C22C2×#1062535011yescharacteristic
341C4—41no—
342C4—942no—
343C4—1881no—
344C4#1309399711yescharacteristic
345C4#1309399711yescharacteristic
346C4C2×D4×D4711yescharacteristic
347C4C2×D4×D4711yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—3761no—
353C2—1882no—
354C2C2×#1309399711yescharacteristic
subgroupG/H
centerC4#13093997
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#413C2
socleC2×C47C2×#121
hypercenter#413D47
hypocenterC47#3067
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #15689923C2semidirect
2. #15689921C2semidirect
3. C2×#13094044C2semidirect
4. C2×#13094032C2semidirect
5. #15689397C2semidirect
6. #15689392C2semidirect
7. #15689389C2semidirect
8. #15689385C2semidirect
9. C2×#13093959C2semidirect
10. #15689105C2semidirect
11. C47×#413C2semidirect
28. C2×#10625337C22semidirect
29. C2×#10625335C22semidirect
30. C2×#10625336C22semidirect
31. C2×#10625334C22semidirect
40. #13093959C22semidirect
41. #13093959C22semidirect
42. #13093942C22semidirect
43. #13093940C22semidirect
47. #101×C47C22semidirect
48. #100×C47C22semidirect
188. #413D47semidirect
189. C47#3067semidirect
224. #101C2×D47semidirect
226. #100C2×D47semidirect