Finite Group Databasebeta

← #26199897

Subgroups — #26199897

Order 12032.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254730C211yesmaximal, characteristic, complemented
2#20254331C211yesmaximal, characteristic
3#20253764C211yesmaximal, characteristic
4#20252331C211yesmaximal, characteristic, complemented
5#20242959C212yesmaximal, complemented
6#20242931C212yesmaximal, complemented
7#20242835C212yesmaximal, complemented
8#20242807C212yesmaximal, complemented
9#20242141C211yesmaximal, characteristic, complemented
10C2×#15688866C211yesmaximal, characteristic
11C47×#1542C211yesmaximal, characteristic, complemented
12#15689680C2211yescharacteristic
13C2×#13094021C2211yescharacteristic
14#15689496—21no—
15#15689489—22no—
16#15689471C2212yes—
17#15689471C2212yes—
18#15689470—21no—
19#15689418—21no—
20#15689415C2212yescomplemented
21#15689362—22no—
22#15689333—21no—
23#15689330C2212yescomplemented
24#15689324C2212yes—
25#15689324C2212yes—
26#15689276—22no—
27#15689252—22no—
28#15689250C2212yescomplemented
29#15689247C2212yescomplemented
30#15689149—21no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32#15689127—21no—
33#15689127—21no—
34#15689078—21no—
35C4×#10625329C2211yescharacteristic
36#15688875C2212yescomplemented
37#15688873C2212yescomplemented
38#15688866C2212yes—
39#15688866C2212yes—
40C47×#533C2211yescharacteristic
41C47×#431C2211yescharacteristic
42C2×C4⋊C8×C47C2211yescharacteristic
43C47×#333C2211yescharacteristic, complemented
44C47×#333C2211yescharacteristic, complemented
45C47×#332C2211yescharacteristic, complemented
46C47×#332C2211yescharacteristic, complemented
47C22×D188—21no—
48C22×D188—21no—
49C22×D188—21no—
50C2×#10625337—22no—
51C2×#10625325—22no—
52C2×#10625325—22no—
53C2×#10625329D411yescharacteristic
54C2×#10625329D411yescharacteristic
55C22×C47⋊C8—21no—
56#13094024D411yescharacteristic
57#13094024D411yescharacteristic
58#13094021—21no—
59#13094021—21no—
60#13094021—21no—
61#13094021C2312yes—
62#13094016—21no—
63#13094003—21no—
64#13094003D412yes—
65C4×Dic94—21no—
66C4×Dic94C2312yes—
67#13093983—21no—
68#13093957—22no—
69C4⋊(C47⋊C8)—21no—
70C4⋊(C47⋊C8)C2312yes—
71Dic47⋊C8—22no—
72Dic47⋊C8—22no—
73#13093948—22no—
74#13093947—22no—
75#13093946—22no—
76#13093946—22no—
77#13093944—22no—
78#13093944—22no—
79#13093944—22no—
80#13093944—22no—
81#13093935D412yes—
82#13093934—22no—
83C4×C47⋊C8C2312yes—
84C8×Dic47—22no—
85C22×C8×C47—21no—
86C4⋊Q8×C47C2311yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88#125×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93#117×C47—21no—
94C2×C42×C47C2311yescharacteristic
95C4⋊C8×C47—21no—
96C4⋊C8×C47C2311yescharacteristic
97C4⋊C8×C47C2311yescharacteristic
98C4⋊C8×C47C2311yescharacteristic
99C4⋊C8×C47C2311yescharacteristic
100C22⋊C8×C47—21no—
101C4×C8×C47—21no—
102C23×D47—41no—
103C2×Q8×C47—21no—
104C2×Q8×C47—21no—
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C2×D188—22no—
109C2×D188—22no—
110C2×D188—22no—
111C2×D188—42no—
112C2×D188—42no—
113C2×D188—41no—
114C2×D188—41no—
115C2×D188—41no—
116C2×D188—81no—
117C2×D188—81no—
118C2×D188—82no—
119C2×Dic94—21no—
120C2×Dic94C2×D412yes—
121C2×C8×C47—21no—
122C2×C8×C47—21no—
123C2×C8×C47—21no—
124C2×C8×C47—21no—
125C2×C8×C47—42no—
126C4⋊C4×C47—21no—
127C4⋊C4×C47—21no—
128C4⋊C4×C47—21no—
129C4⋊C4×C47—21no—
130C4⋊C4×C47—41no—
131C4⋊C4×C47—41no—
132C22⋊C4×C47—41no—
133C42×C47—41no—
134C42×C47C2×D411yescharacteristic
135C42×C47C2×D411yescharacteristic
136C42×C47#4111yescharacteristic
137C42×C47C2411yescharacteristic
138C22⋊Dic47—22no—
139#10625337—82no—
140C4⋊Dic47—21no—
141C4⋊Dic47—21no—
142C4⋊Dic47—21no—
143C4⋊Dic47C2×D412yes—
144Dic47⋊C4—22no—
145Dic47⋊C4—22no—
146C4×Dic47—22no—
147#10625329—22no—
148#10625329—22no—
149C2×C47⋊C8—22no—
150C2×C47⋊C8—81no—
151C2×C47⋊C8C2×D412yes—
152C2×C47⋊C8C2×D412yes—
153#10625325—82no—
154#10625325—82no—
155C23×C47#12111yescharacteristic
156C22×D47—42no—
157C22×D47—82no—
158C22×D47—82no—
159C22×D47—82no—
160Q8×C47—41no—
161Q8×C47—41no—
162Q8×C47—81no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47#12111yescharacteristic
169C2×C4×C47#12111yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47#13512yes—
172C2×C4×C47#13712yes—
173C2×C4×C47C22×D411yescharacteristic
174C2×C4×C47C22×D411yescharacteristic
175C2×C4×C47C2×#4111yescharacteristic
176C2×Dic47—22no—
177C2×Dic47—22no—
178D188—42no—
179D188—42no—
180D188—42no—
181D188—42no—
182D188—82no—
183D188—82no—
184D188—82no—
185D188—82no—
186Dic94—22no—
187Dic94—22no—
188Dic94—81no—
189C8×C47—41no—
190C8×C47—41no—
191C8×C47—41no—
192C8×C47—41no—
193C47⋊C8—22no—
194C47⋊C8—22no—
195C47⋊C8—42no—
196#19242—471nomaximal, Sylow
197C22×C47—21no—
198C22×C47—21no—
199C22×C47#46412yes—
200C22×C47C2×#12111yescharacteristic
201C2×D47—82no—
202C2×D47—82no—
203C2×D47—82no—
204C2×D47—164no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—81no—
209C4×C47—81no—
210C4×C47#46412yes—
211C4×C47C2×#13511yescharacteristic
212C4×C47C2×#13711yescharacteristic
213C4×C47#57611yescharacteristic
214C4×C47#57711yescharacteristic
215Dic47—42no—
216Dic47—42no—
217#3249—471no—
218#3208—471no—
219#3138—471no—
220#2962—471no—
221#1702—472no—
222#1698—472no—
223#1682—472no—
224#1678—472no—
225#1565—471no—
226#1542D4711yescharacteristic, complemented
227C2×#331—471no—
228C2×C47—22no—
229C2×C47C2×#46411yescharacteristic
230C2×C47#306211yescharacteristic
231C2×C47#306811yescharacteristic
232D47—162no—
233#533—471no—
234#533C2×D4711yescharacteristic
235C2×#127—471no—
236#492—941no—
237#490—942no—
238#486—472no—
239#486—472no—
240#486—941no—
241#477—472no—
242#477—941no—
243#467—942no—
244#462—472no—
245#462—941no—
246#460—472no—
247#460—472no—
248#450—942no—
249#446—472no—
250#446—942no—
251C8×Q8—472no—
252#431C2×D4711yescharacteristic
253#424—941no—
254C2×C4⋊C8—471no—
255C2×C4⋊C8C2×D4711yescharacteristic
256#418—941no—
257#418—941no—
258#405—941no—
259C4×M16—471no—
260#335—472no—
261#334—472no—
262#333C2×D4711yescharacteristic, complemented
263#333C2×D4711yescharacteristic, complemented
264#332C2×D4711yescharacteristic, complemented
265#332C2×D4711yescharacteristic, complemented
266#331—472no—
267#331—472no—
268C47#1924211yescharacteristic, complemented, Sylow
269C22×D4—941no—
270C22×D4—941no—
271C22×D4—941no—
272C2×Q16—942no—
273C2×SD16—942no—
274C2×SD16—942no—
275C2×M16—471no—
276C2×M16—471no—
277C22×C8—21no—
278C22×C8—941no—
279C4⋊Q8—471no—
280C4⋊Q8—471no—
281C4⋊Q8C22×D4711yescharacteristic
282C4⋊Q8C22×D4711yescharacteristic
283#127—472no—
284#127—941no—
285#127—941no—
286#127—941no—
287#125—21no—
288#125—941no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—472no—
292C22⋊Q8—941no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—472no—
296C4×Q8—941no—
297#117—21no—
298#117—941no—
299C2×C42C22×D4711yescharacteristic
300#107—942no—
301C4⋊C8—21no—
302C4⋊C8—472no—
303C4⋊C8—942no—
304C4⋊C8—942no—
305C4⋊C8—941no—
306C4⋊C8C22×D4711yescharacteristic
307C4⋊C8C22×D4711yescharacteristic
308C4⋊C8C22×D4711yescharacteristic
309C4⋊C8C22×D4711yescharacteristic
310#103—942no—
311#103—942no—
312#102—942no—
313#102—942no—
314#102—942no—
315#102—942no—
316#102—942no—
317#102—942no—
318C22⋊C8—21no—
319#97—472no—
320#97—942no—
321C4×C8—21no—
322C4×C8—472no—
323C4×C8—942no—
324C24—1881no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—472no—
328C2×Q8—941no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—3761no—
333C2×D4—3761no—
334C2×D4—3762no—
335C2×D4—1881no—
336C2×D4—1881no—
337C2×D4—1881no—
338C2×D4—1882no—
339C2×D4—1882no—
340C22×C4#1062535011yescharacteristic
341C22×C4D4×D4711yescharacteristic
342C22×C4D4×D4711yescharacteristic
343Q16—3762no—
344SD16—3762no—
345SD16—3762no—
346M16—942no—
347M16—942no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—42no—
353C2×C8—472no—
354C2×C8—472no—
355C2×C8—942no—
356C2×C8—3761no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—472no—
364C4⋊C4—942no—
365C4⋊C4—941no—
366C4⋊C4—941no—
367C4⋊C4—941no—
368C4⋊C4—942no—
369C22⋊C4—41no—
370C22⋊C4—942no—
371C42—41no—
372C42—942no—
373C42#1062535011yescharacteristic
374C42D4×D4711yescharacteristic
375C42D4×D4711yescharacteristic
376C42C23×D4711yescharacteristic
377C23—3762no—
378C23—3762no—
379C23—3762no—
380C23—1882no—
381C23#1309399711yescharacteristic
382Q8—41no—
383Q8—41no—
384Q8—81no—
385Q8—942no—
386Q8—942no—
387Q8—3761no—
388D4—3762no—
389D4—3762no—
390D4—3762no—
391D4—3762no—
392D4—1882no—
393D4—1882no—
394D4—1882no—
395D4—1882no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—942no—
402C2×C4—942no—
403C2×C4#1309399711yescharacteristic
404C2×C4#1309399711yescharacteristic
405C2×C4#1309399711yescharacteristic
406C2×C4#1309404512yes—
407C2×C4#1309405612yes—
408C2×C4C2×D4×D4711yescharacteristic
409C2×C4C2×D4×D4711yescharacteristic
410C2×C4C2×#1062535011yescharacteristic
411C8—41no—
412C8—41no—
413C8—41no—
414C8—41no—
415C8—942no—
416C8—942no—
417C8—1882no—
418C22—21no—
419C22—21no—
420C22—3762no—
421C22—3762no—
422C22—3762no—
423C22—7524no—
424C22#1568934812yes—
425C22C2×#1309399711yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—81no—
430C4—81no—
431C4—1882no—
432C4—1882no—
433C4#1568934812yes—
434C4C2×#1309404511yescharacteristic
435C4C2×#1309405611yescharacteristic
436C4#1568992511yescharacteristic
437C4#1568993011yescharacteristic
438C2—22no—
439C2—7522no—
440C2C2×#1568934811yescharacteristic
441C2#2025307111yescharacteristic
442C2#2025311911yescharacteristic
subgroupG/H
centerC22C2×#13093997
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1542C2
socleC22×C47C2×#121
prime radicalC2×#13094021C22
hypercenter#1542D47
hypocenterC47#19242
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #20254730C2semidirect
4. #20252331C2semidirect
5. #20242959C2semidirect
6. #20242931C2semidirect
7. #20242835C2semidirect
8. #20242807C2semidirect
9. #20242141C2semidirect
11. C47×#1542C2semidirect
20. #15689415C22semidirect
23. #15689330C22semidirect
28. #15689250C22semidirect
29. #15689247C22semidirect
36. #15688875C22semidirect
37. #15688873C22semidirect
43. C47×#333C22semidirect
44. C47×#333C22semidirect
45. C47×#332C22semidirect
46. C47×#332C22semidirect
226. #1542D47semidirect
262. #333C2×D47semidirect
263. #333C2×D47semidirect
264. #332C2×D47semidirect
265. #332C2×D47semidirect
268. C47#19242semidirect

Maximal subgroups

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

subgroupindex
#202547302
#202543312
#202537642
#202523312
#202429592
#202429312
#202428352
#202428072
#202421412
C2×#156888662
C47×#15422
#1924247