Finite Group Databasebeta

← #26371077

Subgroups — #26371077

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252969C211yesmaximal, characteristic
2#20245596C212yesmaximal, complemented
3#20245590C211yesmaximal, characteristic, complemented
4#20245585C211yesmaximal, characteristic, complemented
5#20245579C212yesmaximal, complemented
6#20245573C211yesmaximal, characteristic, complemented
7#20245568C211yesmaximal, characteristic, complemented
8#20245170C212yesmaximal, complemented
9#20245093C212yesmaximal, complemented
10C2×C22⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
11C2×C47×#427C211yesmaximal, characteristic, complemented
12C2×#13094046C2211yescharacteristic
13#15689634—21no—
14C22×C47⋊C16C2212yes—
15#15689364C2211yescharacteristic
16#15689364C2211yescharacteristic
17#15689359C2211yescharacteristic
18#15689359C2211yescharacteristic
19#15689352—21no—
20#15689352—21no—
21#15689161C2211yescharacteristic
22#15689120—21no—
23#15688950C2212yescomplemented
24#15688950C2212yescomplemented
25#15688948C2212yescomplemented
26#15688948C2212yescomplemented
27#15688926C2212yescomplemented
28#15688926C2212yescomplemented
29#15688923C2212yescomplemented
30#15688923C2212yescomplemented
31C22⋊(C47⋊C16)C2211yescharacteristic
32C22⋊(C47⋊C16)C2211yescharacteristic
33C22⋊(C47⋊C16)C2212yes—
34C23×C8×C47C2211yescharacteristic
35C2×#117×C47—21no—
36C47×#427—21no—
37C47×#427—21no—
38C47×#427C2212yes—
39C47×#427C2212yes—
40C2×#107×C47C2211yescharacteristic
41C2×#107×C47C2211yescharacteristic
42C2×#106×C47—21no—
43C2×#10625350—21no—
44#13094046—24no—
45C2×Dic188C2311yescharacteristic
46C2×#10625325—21no—
47C2×D376C2311yescharacteristic
48#13094007—41no—
49#13094003—21no—
50#13094003—21no—
51#13093998—21no—
52#13093998—21no—
53#13093993—41no—
54C4×C22⋊D47—41no—
55C4×C22⋊D47—41no—
56#13093983—21no—
57C2×C47⋊C16—24no—
58C2×C47⋊C16C2312yes—
59C2×C47⋊C16C2312yes—
60#13093958C2311yescharacteristic
61#13093958C2311yescharacteristic
62#13093956—21no—
63#13093949—21no—
64#13093949—21no—
65#13093946—21no—
66#13093946—21no—
67C23×C4×C47D411yescharacteristic
68C22×C8×C47—24no—
69C22×C8×C47D411yescharacteristic
70C22×C8×C47D411yescharacteristic
71C22×C8×C47D411yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75#117×C47—22no—
76#117×C47—22no—
77#117×C47—41no—
78#117×C47—41no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C22⋊C4×C47—41no—
82C2×C42×C47—41no—
83#107×C47—21no—
84#107×C47—21no—
85#107×C47C2312yes—
86#107×C47C2312yes—
87#106×C47—22no—
88#106×C47—22no—
89C24×C47D811yescharacteristic
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47D811yescharacteristic
95C22×C4×C47D811yescharacteristic
96C22×C4×C47D811yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C2×C22⋊D47—41no—
101C2×C22⋊D47—41no—
102C2×C22⋊D47—41no—
103#10625350—42no—
104#10625350—42no—
105C2×D188—21no—
106C2×C4×D47—41no—
107C2×Dic94—21no—
108C2×C8×C47—22no—
109C2×C8×C47—22no—
110C2×C8×C47—22no—
111C2×C8×C47—22no—
112C2×C8×C47—22no—
113C2×C8×C47C2×D411yescharacteristic
114C2×C8×C47C2×D411yescharacteristic
115C2×C8×C47C2×D411yescharacteristic
116C2×C8×C47#4114yes—
117C2×C8×C47C2411yescharacteristic
118C4⋊C4×C47—22no—
119C4⋊C4×C47—22no—
120C4⋊C4×C47—41no—
121C4⋊C4×C47—41no—
122C22⋊C4×C47—42no—
123C22⋊C4×C47—42no—
124C42×C47—42no—
125C42×C47—42no—
126C22⋊Dic47—41no—
127C22⋊Dic47—41no—
128C22⋊Dic47—41no—
129(C2×D47)⋊C4—41no—
130(C2×D47)⋊C4—41no—
131C4⋊Dic47—21no—
132C4⋊Dic47—21no—
133Dic47⋊C4—41no—
134Dic47⋊C4—41no—
135C4×Dic47—41no—
136Dic188—22no—
137D376—22no—
138#10625325—42no—
139C47⋊C16—22no—
140C47⋊C16—22no—
141C23×C47—22no—
142C23×C47—22no—
143C23×C47—41no—
144C23×C47C2×D811yescharacteristic
145C23×C47C2×D811yescharacteristic
146C23×C47C2×D811yescharacteristic
147C22×D47—41no—
148C2×C4×C47—22no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—22no—
154C2×C4×C47—22no—
155C2×C4×C47—42no—
156C2×C4×C47—42no—
157C2×C4×C47—82no—
158C2×C4×C47—82no—
159C2×C4×C47#12312yes—
160C2×C4×C47C2×D811yescharacteristic
161C2×C4×C47C2×D811yescharacteristic
162C2×C4×C47C2×D811yescharacteristic
163C2×C4×C47#13712yes—
164C2×C4×C47C22×D411yescharacteristic
165C22⋊D47—82no—
166C22⋊D47—82no—
167C22⋊D47—82no—
168C2×Dic47—41no—
169C2×Dic47—41no—
170C2×Dic47—41no—
171D188—41no—
172D188—41no—
173C4×D47—82no—
174Dic94—41no—
175Dic94—41no—
176C8×C47—21no—
177C8×C47—21no—
178C8×C47#12312yes—
179C8×C47C2×#4112yes—
180#33645—471nomaximal, Sylow
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—44no—
189C22×C47#48012yes—
190C22×C47#50812yes—
191C22×C47C22×D811yescharacteristic
192C2×D47—81no—
193C2×D47—81no—
194C2×D47—81no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—82no—
198C4×C47—82no—
199C4×C47#48012yes—
200C4×C47C2×#12311yescharacteristic
201C4×C47C2×#13711yescharacteristic
202Dic47—81no—
203Dic47—81no—
204Dic47—81no—
205#3050—471no—
206C2×#427D4711yescharacteristic, complemented
207#2237—472no—
208#2236—471no—
209#2235—471no—
210#2234—472no—
211#2233—471no—
212#2232—471no—
213#2158—472no—
214#2138—472no—
215C2×C22⋊C16—471no—
216C2×C47—22no—
217C2×C47—22no—
218C2×C47—41no—
219C2×C47C2×#48011yescharacteristic
220C2×C47C2×#50811yescharacteristic
221C2×C47#341411yescharacteristic
222D47—161no—
223C2×#135—471no—
224C23×C8C2×D4711yescharacteristic
225#525—941no—
226C2×#117—21no—
227C22×C16—472no—
228#467—471no—
229#467—471no—
230#466—471no—
231#466—471no—
232#465—941no—
233#465—941no—
234#427—21no—
235#427—21no—
236#427—471no—
237#427C2×D4712yes—
238#427C2×D4712yes—
239C2×#107C2×D4711yescharacteristic
240C2×#107C2×D4711yescharacteristic
241C2×#106—21no—
242#416—941no—
243#367—472no—
244#367—472no—
245#366—472no—
246#366—472no—
247#358—472no—
248#358—472no—
249#357—472no—
250#357—472no—
251C22⋊C16—471no—
252C22⋊C16—471no—
253C22⋊C16—472no—
254C47#3364511yescharacteristic, complemented, Sylow
255C2×#41—941no—
256C23×C4C22⋊D4711yescharacteristic
257#135—944no—
258C2×Q16—471no—
259C2×SD16—941no—
260C2×D8—471no—
261C22×C8—24no—
262C22×C8C22⋊D4711yescharacteristic
263C22×C8C22⋊D4711yescharacteristic
264C22×C8C22⋊D4711yescharacteristic
265C22×C8C22×D4711yescharacteristic
266C22×C8C22×D4711yescharacteristic
267C22×C8C22×D4711yescharacteristic
268#123—1881no—
269C22⋊Q8—941no—
270C22⋊Q8—941no—
271#121—941no—
272#121—941no—
273#120—1881no—
274C4×D4—1881no—
275C4×D4—1881no—
276#117—22no—
277#117—22no—
278#117—41no—
279#117—41no—
280#117—941no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C22⋊C4—41no—
284C2×C42—41no—
285C2×C16—472no—
286C2×C16—472no—
287C2×C16—944no—
288#107—21no—
289#107—21no—
290#107—471no—
291#107—471no—
292#107C22×D4712yes—
293#107C22×D4712yes—
294#106—22no—
295#106—22no—
296#106—941no—
297#103—941no—
298#103—941no—
299#102—941no—
300#102—941no—
301C24#1062533411yescharacteristic
302#41—1882no—
303#41—1882no—
304C2×Q8—941no—
305C2×D4—941no—
306C2×D4—1881no—
307C2×D4—1881no—
308C2×D4—1881no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—1881no—
314C22×C4#1062533411yescharacteristic
315C22×C4#1062533411yescharacteristic
316C22×C4#1062533411yescharacteristic
317C22×C4C2×C22⋊D4711yescharacteristic
318C22×C4C2×C22⋊D4711yescharacteristic
319C22×C4C2×C22⋊D4711yescharacteristic
320Q16—942no—
321SD16—1882no—
322D8—942no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8#1062535014yes—
329C2×C8C2×C22⋊D4711yescharacteristic
330C2×C8C2×C22⋊D4711yescharacteristic
331C2×C8C2×C22⋊D4711yescharacteristic
332C2×C8C23×D4711yescharacteristic
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—941no—
338C4⋊C4—941no—
339C4⋊C4—1881no—
340C4⋊C4—1881no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—1881no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C42—42no—
349C42—42no—
350C42—1881no—
351C16—942no—
352C16—942no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—1881no—
357C23C2×#1062533411yescharacteristic
358C23C2×#1062533411yescharacteristic
359C23C2×#1062533411yescharacteristic
360Q8—1881no—
361Q8—1881no—
362D4—3762no—
363D4—3762no—
364D4—3762no—
365D4—1881no—
366D4—1881no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—3762no—
379C2×C4—1881no—
380C2×C4—1881no—
381C2×C4—1881no—
382C2×C4#1309400712yes—
383C2×C4C2×#1062533411yescharacteristic
384C2×C4C2×#1062533411yescharacteristic
385C2×C4C2×#1062533411yescharacteristic
386C2×C4#1309405512yes—
387C2×C4C22×C22⋊D4711yescharacteristic
388C8—21no—
389C8—21no—
390C8#1309400712yes—
391C8C2×#1062535012yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—3761no—
401C22—3761no—
402C22—3761no—
403C22#1568943612yes—
404C22#1568955312yes—
405C22C22×#1062533411yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—82no—
410C4—3761no—
411C4—3761no—
412C4—3761no—
413C4#1568943612yes—
414C4C2×#1309400711yescharacteristic
415C4C2×#1309405511yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—7521no—
420C2C2×#1568943611yescharacteristic
421C2C2×#1568955311yescharacteristic
422C2#2025652211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#427C2
socleC22×C47C22×D8
prime radical#20252969C2
hypercenterC2×#427D47
hypocenterC47#33645
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #20245596C2semidirect
3. #20245590C2semidirect
4. #20245585C2semidirect
5. #20245579C2semidirect
6. #20245573C2semidirect
7. #20245568C2semidirect
8. #20245170C2semidirect
9. #20245093C2semidirect
10. C2×C22⋊(C47⋊C16)C2semidirect
11. C2×C47×#427C2semidirect
23. #15688950C22semidirect
24. #15688950C22semidirect
25. #15688948C22semidirect
26. #15688948C22semidirect
27. #15688926C22semidirect
28. #15688926C22semidirect
29. #15688923C22semidirect
30. #15688923C22semidirect
206. C2×#427D47semidirect
254. C47#33645semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202529692
#202455962
#202455902
#202455852
#202455792
#202455732
#202455682
#202451702
#202450932
C2×C22⋊(C47⋊C16)2
C2×C47×#4272
#3364547