Finite Group Databasebeta

← #26199888

Subgroups — #26199888

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#20254329C211yesmaximal, characteristic
3#20252335C211yesmaximal, characteristic, complemented
4#20242953C212yesmaximal, complemented
5#20242925C212yesmaximal, complemented
6#20242829C212yesmaximal, complemented
7#20242801C212yesmaximal, complemented
8#20242140C211yesmaximal, characteristic, complemented
9#20242045C211yesmaximal, characteristic, complemented
10C2×#15688867C211yesmaximal, characteristic
11C47×#3138C211yesmaximal, characteristic
12#15689680C2211yescharacteristic
13#15689495—21no—
14#15689469—21no—
15#15689418—21no—
16#15689415C2212yescomplemented
17#15689362—22no—
18#15689333—21no—
19#15689330C2212yescomplemented
20#15689320C2212yes—
21#15689320C2212yes—
22#15689274—22no—
23#15689253C2212yescomplemented
24#15689251—22no—
25C8×Dic94C2212yescomplemented
26#15689176C2211yescharacteristic
27#15689151—21no—
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30#15689081—21no—
31#15688876C2212yescomplemented
32#15688874C2212yescomplemented
33#15688872C2211yescharacteristic, complemented
34#15688872C2211yescharacteristic, complemented
35#15688869C2211yescharacteristic, complemented
36#15688869C2211yescharacteristic, complemented
37#15688867C2212yes—
38#15688867C2212yes—
39C47×#533C2211yescharacteristic
40C2×#127×C47C2211yescharacteristic
41C47×#490—22no—
42C47×#486C2212yes—
43C47×#486C2212yes—
44C47×#418—21no—
45C47×#418—21no—
46C4×M16×C47C2211yescharacteristic
47C2×#10625337—22no—
48C2×#10625335—22no—
49C2×#10625335—22no—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52#13094024D411yescharacteristic
53#13094024D411yescharacteristic
54#13094016—21no—
55#13094003—21no—
56#13094003D412yes—
57C4×Dic94—21no—
58C4×Dic94C2312yes—
59#13093983—21no—
60#13093957—22no—
61C4⋊(C47⋊C8)—21no—
62C4⋊(C47⋊C8)—21no—
63C4⋊(C47⋊C8)C2311yescharacteristic
64C4⋊(C47⋊C8)C2311yescharacteristic
65C4⋊(C47⋊C8)C2311yescharacteristic
66C4⋊(C47⋊C8)C2311yescharacteristic
67C4⋊(C47⋊C8)C2312yes—
68Dic47⋊C8—22no—
69Dic47⋊C8—22no—
70#13093948—22no—
71#13093947—22no—
72#13093945—22no—
73#13093945—22no—
74C22⋊(C47⋊C8)—21no—
75#13093934—22no—
76C4×C47⋊C8—21no—
77C8×Dic47—22no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C2×M16×C47D411yescharacteristic
82C2×M16×C47D411yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85#127×C47—21no—
86#127×C47—21no—
87#127×C47—21no—
88#127×C47C2312yes—
89#125×C47—21no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94#117×C47—21no—
95C2×C42×C47C2311yescharacteristic
96#102×C47—22no—
97#102×C47—22no—
98#102×C47—22no—
99#102×C47—22no—
100#97×C47D412yes—
101C4×C8×C47C2312yes—
102C24×C47—41no—
103C2×Q8×C47—21no—
104C2×Q8×C47—21no—
105C2×D4×C47—22no—
106C2×D4×C47—22no—
107C2×D4×C47—22no—
108C2×D4×C47—41no—
109C2×D4×C47—41no—
110C2×D4×C47—41no—
111C2×D4×C47—42no—
112C2×D4×C47—42no—
113C2×D4×C47—81no—
114C2×D4×C47—81no—
115C2×D4×C47—82no—
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C2×Dic94—21no—
120C2×Dic94C2×D412yes—
121M16×C47—22no—
122M16×C47—22no—
123C2×C8×C47C2×D412yes—
124C2×C8×C47C2×D412yes—
125C4⋊C4×C47—21no—
126C4⋊C4×C47—21no—
127C4⋊C4×C47—21no—
128C4⋊C4×C47—21no—
129C4⋊C4×C47—41no—
130C4⋊C4×C47—41no—
131C22⋊C4×C47—41no—
132C42×C47—41no—
133C42×C47C2×D411yescharacteristic
134C42×C47C2×D411yescharacteristic
135C42×C47#4111yescharacteristic
136C42×C47C2411yescharacteristic
137C22⋊Dic47—22no—
138#10625337—82no—
139#10625335—82no—
140#10625335—82no—
141C4⋊Dic47—21no—
142C4⋊Dic47—21no—
143C4⋊Dic47—21no—
144C4⋊Dic47C2×D412yes—
145Dic47⋊C4—22no—
146Dic47⋊C4—22no—
147C4×Dic47—22no—
148C2×C47⋊C8—21no—
149C2×C47⋊C8—21no—
150C2×C47⋊C8—21no—
151C2×C47⋊C8—21no—
152C2×C47⋊C8—22no—
153C2×C47⋊C8—42no—
154C2×C47⋊C8—81no—
155C23×C47—42no—
156C23×C47—82no—
157C23×C47—82no—
158C23×C47—82no—
159C23×C47#12111yescharacteristic
160Q8×C47—41no—
161Q8×C47—41no—
162Q8×C47—81no—
163D4×C47—42no—
164D4×C47—42no—
165D4×C47—42no—
166D4×C47—42no—
167D4×C47—82no—
168D4×C47—82no—
169D4×C47—82no—
170D4×C47—82no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47#12111yescharacteristic
178C2×C4×C47#12111yescharacteristic
179C2×C4×C47#13512yes—
180C2×C4×C47#13712yes—
181C2×C4×C47C22×D411yescharacteristic
182C2×C4×C47C22×D411yescharacteristic
183C2×C4×C47C2×#4111yescharacteristic
184C2×Dic47—22no—
185C2×Dic47—22no—
186Dic94—22no—
187Dic94—22no—
188Dic94—81no—
189C8×C47—22no—
190C8×C47—22no—
191C47⋊C8—41no—
192C47⋊C8—41no—
193C47⋊C8—42no—
194C47⋊C8—41no—
195C47⋊C8—41no—
196#19242—471nomaximal, Sylow
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—82no—
200C22×C47—82no—
201C22×C47—82no—
202C22×C47—164no—
203C22×C47#46412yes—
204C22×C47C2×#12111yescharacteristic
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#3138D4711yescharacteristic
220#2962—471no—
221#1702—472no—
222#1698—472no—
223#1682—472no—
224#1678—472no—
225#1565—471no—
226#1542—471no—
227C2×#331—471no—
228C2×C47—22no—
229C2×C47—162no—
230C2×C47C2×#46411yescharacteristic
231C2×C47#306211yescharacteristic
232C2×C47#306811yescharacteristic
233#533—471no—
234#533C2×D4711yescharacteristic
235C2×#127C2×D4711yescharacteristic
236#492—941no—
237#490—22no—
238#486—941no—
239#486C2×D4712yes—
240#486C2×D4712yes—
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#431—471no—
253#424—941no—
254C2×C4⋊C8—471no—
255C2×C4⋊C8—471no—
256#418—21no—
257#418—21no—
258#405—941no—
259C4×M16C2×D4711yescharacteristic
260#335—472no—
261#334—472no—
262#333—471no—
263#333—471no—
264#332—471no—
265#332—471no—
266#331—472no—
267#331—472no—
268C47#1924211yescharacteristic, complemented, Sylow
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C2×Q16—942no—
273C2×SD16—942no—
274C2×SD16—942no—
275C2×M16C22⋊D4711yescharacteristic
276C2×M16C22⋊D4711yescharacteristic
277C22×C8—941no—
278C22×C8—941no—
279C4⋊Q8—471no—
280C4⋊Q8—471no—
281C4⋊Q8C22×D4711yescharacteristic
282C4⋊Q8C22×D4711yescharacteristic
283#127—21no—
284#127—21no—
285#127—21no—
286#127C22×D4712yes—
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—471no—
302C4⋊C8—471no—
303C4⋊C8—472no—
304C4⋊C8—471no—
305C4⋊C8—471no—
306C4⋊C8—942no—
307C4⋊C8—942no—
308C4⋊C8—941no—
309C4⋊C8—941no—
310#103—942no—
311#103—942no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316#102—942no—
317#102—942no—
318C22⋊C8—941no—
319#97—942no—
320#97C22⋊D4712yes—
321C4×C8—942no—
322C4×C8—941no—
323C4×C8C22×D4712yes—
324C24—41no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—472no—
328C2×Q8—941no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—82no—
340C22×C4D4×D4711yescharacteristic
341C22×C4#1062535211yescharacteristic
342C22×C4C2×C22⋊D4711yescharacteristic
343Q16—3762no—
344SD16—3762no—
345SD16—3762no—
346M16—22no—
347M16—22no—
348C2×C8—941no—
349C2×C8—941no—
350C2×C8—942no—
351C2×C8—941no—
352C2×C8—941no—
353C2×C8—3761no—
354C2×C8—1882no—
355C2×C8C2×C22⋊D4712yes—
356C2×C8C2×C22⋊D4712yes—
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—
373C42D4×D4711yescharacteristic
374C42#1062535211yescharacteristic
375C42C2×C22⋊D4711yescharacteristic
376C42C23×D4711yescharacteristic
377C23—42no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#1309399511yescharacteristic
382Q8—41no—
383Q8—41no—
384Q8—81no—
385Q8—942no—
386Q8—942no—
387Q8—3761no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4—82no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—942no—
402C2×C4—942no—
403C2×C4#1309399511yescharacteristic
404C2×C4#1309399511yescharacteristic
405C2×C4#1309399511yescharacteristic
406C2×C4#1309404412yes—
407C2×C4#1309405412yes—
408C2×C4C2×D4×D4711yescharacteristic
409C2×C4C22×C22⋊D4711yescharacteristic
410C2×C4C2×#1062535211yescharacteristic
411C8—22no—
412C8—22no—
413C8—1881no—
414C8—1881no—
415C8—1882no—
416C8—1881no—
417C8—1881no—
418C22—21no—
419C22—21no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—164no—
424C22#1568934212yes—
425C22C2×#1309399511yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—81no—
430C4—81no—
431C4—1882no—
432C4—1882no—
433C4#1568934212yes—
434C4C2×#1309404411yescharacteristic
435C4C2×#1309405411yescharacteristic
436C4#1568992711yescharacteristic
437C4#1568993311yescharacteristic
438C2—22no—
439C2—162no—
440C2C2×#1568934211yescharacteristic
441C2#2025306211yescharacteristic
442C2#2025311211yescharacteristic
subgroupG/H
centerC22C2×#13093995
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#3138C2
socleC22×C47C2×#121
prime radicalC2×#127×C47C22
hypercenter#3138D47
hypocenterC47#19242
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #20254730C2semidirect
3. #20252335C2semidirect
4. #20242953C2semidirect
5. #20242925C2semidirect
6. #20242829C2semidirect
7. #20242801C2semidirect
8. #20242140C2semidirect
9. #20242045C2semidirect
16. #15689415C22semidirect
19. #15689330C22semidirect
23. #15689253C22semidirect
25. C8×Dic94C22semidirect
31. #15688876C22semidirect
32. #15688874C22semidirect
33. #15688872C22semidirect
34. #15688872C22semidirect
35. #15688869C22semidirect
36. #15688869C22semidirect
268. C47#19242semidirect

Maximal subgroups

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

subgroupindex
#202547302
#202543292
#202523352
#202429532
#202429252
#202428292
#202428012
#202421402
#202420452
C2×#156888672
C47×#31382
#1924247