Finite Group Databasebeta

← #26112543

Subgroups — #26112543

Order 12032.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253388C211yesmaximal, characteristic
2#20244216C211yesmaximal, characteristic, complemented
3#20241882C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic, complemented
5#20241291C211yesmaximal, characteristic, complemented
6#20241221C211yesmaximal, characteristic, complemented
7C42×D4×C47C211yesmaximal, characteristic, complemented
8#15689673C2211yescharacteristic
9#15689436—21no—
10#15689403C412yescomplemented
11#15689318C412yescomplemented
12#15689257—21no—
13C4×#10625334—22no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16#15689147C2211yescharacteristic
17C2×#13093952—21no—
18C2×#13093952—21no—
19#15688856—22no—
20D4⋊(C47⋊C8)—22no—
21C2×C4×D4×C47—21no—
22C2×C4×D4×C47C2211yescharacteristic
23C22×C42×C47—21no—
24C4×C4⋊C4×C47—21no—
25C4×C4⋊C4×C47C2211yescharacteristic
26C4×C22⋊C4×C47—22no—
27C4×C22⋊C4×C47—21no—
28C43×C47C2211yescharacteristic
29C2×#10625350—21no—
30C2×#10625334—22no—
31C2×#10625329—21no—
32#13094024C2×C411yescharacteristic, complemented
33#13094021C2×C411yescharacteristic, complemented
34#13094012—21no—
35#13093998—21no—
36#13093998—21no—
37C4×D188—21no—
38C4×D188—21no—
39#13093957—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C412yescomplemented
44#13093952—42no—
45#13093952—42no—
46#13093945—22no—
47#13093944—22no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×D4×C47D411yescharacteristic
53C23×C4×C47—22no—
54C23×C4×C47—21no—
55C4×D4×C47—28no—
56C4×D4×C47—21no—
57C4×D4×C47—21no—
58C4×D4×C47C2×C412yes—
59C4×D4×C47D412yes—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47D411yescharacteristic
62C2×C22⋊C4×C47—22no—
63C2×C22⋊C4×C47—21no—
64C2×C42×C47—21no—
65C2×C42×C47—22no—
66C2×C42×C47—21no—
67C2×C42×C47—21no—
68C2×C42×C47—42no—
69C2×C42×C47—42no—
70C2×C42×C47D411yescharacteristic
71C2×C42×C47D411yescharacteristic
72C2×C42×C47C2311yescharacteristic
73#95×C47—22no—
74#95×C47D412yes—
75C24×C47—21no—
76C2×D4×C47—24no—
77C2×D4×C47—21no—
78C2×D4×C47C22⋊C412yes—
79C22×C4×C47—21no—
80C22×C4×C47—28no—
81C22×C4×C47—21no—
82C22×C4×C47—22no—
83C22×C4×C47—21no—
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—44no—
87C22×C4×C47—44no—
88C22×C4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47C2×D411yescharacteristic
95C2×C22⋊D47—41no—
96#10625350—41no—
97#10625350—41no—
98#10625350—41no—
99#10625350—41no—
100C2×D188—21no—
101C2×D188—21no—
102C2×D188—21no—
103C2×C4×D47—41no—
104C2×Dic94—21no—
105C4⋊C4×C47—24no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47C22⋊C412yes—
108C22⋊C4×C47—28no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C42×C47—24no—
112C42×C47—21no—
113C42×C47—21no—
114C42×C47—21no—
115C42×C47—42no—
116C42×C47—44no—
117C42×C47—41no—
118C42×C47—41no—
119C42×C47D812yescomplemented
120C42×C47C22×C411yescharacteristic
121C42×C47C2×D411yescharacteristic
122C42×C47#4111yescharacteristic
123C42×C47#4111yescharacteristic
124#10625334—44no—
125(C2×D47)⋊C4—41no—
126(C2×D47)⋊C4—41no—
127C4⋊Dic47—21no—
128C4⋊Dic47—21no—
129#10625329—41no—
130#10625329—41no—
131C2×C47⋊C8—22no—
132C2×C47⋊C8—41no—
133C2×C47⋊C8—41no—
134C23×C47—24no—
135C23×C47—22no—
136C23×C47—42no—
137C23×C47—41no—
138C23×C47—41no—
139C23×C47#12011yescharacteristic
140C22×D47—41no—
141D4×C47—24no—
142D4×C47—22no—
143D4×C47#10414yescomplemented
144C2×C4×C47—22no—
145C2×C4×C47—22no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—22no—
149C2×C4×C47—24no—
150C2×C4×C47—22no—
151C2×C4×C47—41no—
152C2×C4×C47—416no—
153C2×C4×C47—41no—
154C2×C4×C47—42no—
155C2×C4×C47—42no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—42no—
163C2×C4×C47C2×C22⋊C411yescharacteristic
164C2×C4×C47C4×D411yescharacteristic
165C2×C4×C47C4×D411yescharacteristic
166C2×C4×C47#12111yescharacteristic
167C2×C4×C47#12111yescharacteristic
168C2×C4×C47#12311yescharacteristic
169C2×C4×C47C2×D811yescharacteristic
170C2×C4×C47#13511yescharacteristic
171C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
173C22⋊D47—81no—
174C22⋊D47—81no—
175C2×Dic47—41no—
176D188—42no—
177D188—41no—
178D188—41no—
179D188—81no—
180C4×D47—81no—
181C4×D47—81no—
182Dic94—41no—
183Dic94—41no—
184C47⋊C8—42no—
185C47⋊C8—81no—
186C47⋊C8—81no—
187#9233—471nomaximal, Sylow
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—24no—
191C22×C47—44no—
192C22×C47—44no—
193C22×C47—42no—
194C22×C47—42no—
195C22×C47#38611yescharacteristic
196C22×C47#44711yescharacteristic
197C22×C47#44911yescharacteristic
198C2×D47—81no—
199C2×D47—81no—
200C2×D47—81no—
201C4×C47—24no—
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—21no—
205C4×C47—42no—
206C4×C47—44no—
207C4×C47—42no—
208C4×C47C2×#10412yes—
209C4×C47C4×D811yescharacteristic
210C4×C47#44211yescharacteristic
211C4×C47#45911yescharacteristic
212C4×C47#46311yescharacteristic
213Dic47—81no—
214#3100—471no—
215C42×D4D4711yescharacteristic, complemented
216#1962—471no—
217#1502—471no—
218#1486—471no—
219#1303—471no—
220#1276—471no—
221C2×C47—21no—
222C2×C47—21no—
223C2×C47—44no—
224C2×C47#187911yescharacteristic
225C2×C47#189611yescharacteristic
226C2×C47#190611yescharacteristic
227D47—161no—
228#532—471no—
229C2×C4×D4—21no—
230C2×C4×D4C2×D4711yescharacteristic
231C22×C42—21no—
232#480—941no—
233#474—472no—
234#459—472no—
235#447—941no—
236C4×D8—942no—
237#431—471no—
238#431—471no—
239#423—471no—
240C2×#104—941no—
241C2×#104—941no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4C2×D4711yescharacteristic
244C4×C22⋊C4—21no—
245C4×C22⋊C4—22no—
246C43C2×D4711yescharacteristic
247#327—942no—
248D4⋊C8—942no—
249C47#923311yescharacteristic, complemented, Sylow
250C2×#41—941no—
251C22×D4C22⋊D4711yescharacteristic
252C23×C4—22no—
253C23×C4—21no—
254C2×D8—942no—
255C2×M16—941no—
256C4⋊Q8—471no—
257#127—471no—
258#124—941no—
259#121—941no—
260#121—941no—
261C4×D4—28no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—941no—
265C4×D4—941no—
266C4×D4C4×D4712yes—
267C4×D4D18812yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C22⋊D4711yescharacteristic
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—42no—
277C2×C42—42no—
278C2×C42C22⋊D4711yescharacteristic
279C2×C42C22⋊D4711yescharacteristic
280C2×C42C22×D4711yescharacteristic
281#107—942no—
282C4⋊C8—472no—
283C4⋊C8—941no—
284C4⋊C8—941no—
285C4⋊C8—941no—
286#104—1882no—
287#104—1882no—
288#102—942no—
289#102—942no—
290C22⋊C8—941no—
291C22⋊C8—941no—
292C4×C8—941no—
293C4×C8—941no—
294#95—22no—
295#95C22⋊D4712yes—
296C24—21no—
297#41—1881no—
298#41—1881no—
299#41—1881no—
300#41—1881no—
301C2×Q8—941no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—941no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—1881no—
308C2×D4(C2×D47)⋊C412yes—
309C22×C4—21no—
310C22×C4—28no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—1881no—
323C22×C4C2×C22⋊D4711yescharacteristic
324C22×C4C2×C22⋊D4711yescharacteristic
325C22×C4C2×C22⋊D4711yescharacteristic
326D8—1884no—
327M16—1881no—
328M16—1881no—
329C2×C8—942no—
330C2×C8—1881no—
331C2×C8—1881no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—941no—
335C4⋊C4—941no—
336C4⋊C4(C2×D47)⋊C412yes—
337C22⋊C4—28no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—1881no—
341C22⋊C4—1881no—
342C42—24no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—42no—
347C42—44no—
348C42—41no—
349C42—41no—
350C42#1062533412yescomplemented
351C42C2×C4×D4711yescharacteristic
352C42C2×D18811yescharacteristic
353C42#1062535011yescharacteristic
354C42#1062535011yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—1881no—
361C23#1309399311yescharacteristic
362Q8—1881no—
363Q8—1881no—
364D4—24no—
365D4—22no—
366D4—3761no—
367D4—3761no—
368D4—3761no—
369D4—1881no—
370D4—1882no—
371D4—1881no—
372D4#1309395214yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—416no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—3761no—
393C2×C4—3761no—
394C2×C4—1881no—
395C2×C4C2×(C2×D47)⋊C411yescharacteristic
396C2×C4C4×C22⋊D4711yescharacteristic
397C2×C4C4×C22⋊D4711yescharacteristic
398C2×C4#1309399811yescharacteristic
399C2×C4#1309399811yescharacteristic
400C2×C4#1309400711yescharacteristic
401C2×C4C2×#1062533411yescharacteristic
402C2×C4#1309404411yescharacteristic
403C2×C4#1309404911yescharacteristic
404C2×C4#1309405011yescharacteristic
405C8—3761no—
406C8—3761no—
407C8—1882no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—3761no—
416C22—3761no—
417C22—3761no—
418C22#1568900211yescharacteristic
419C22#1568925711yescharacteristic
420C22#1568926811yescharacteristic
421C4—24no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—44no—
426C4—42no—
427C4—42no—
428C4—3761no—
429C4C2×#1309395212yes—
430C4C4×#1062533411yescharacteristic
431C4#1568923311yescharacteristic
432C4#1568931811yescharacteristic
433C4#1568933811yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—7521no—
438C2#2024373611yescharacteristic
439C2#2024383111yescharacteristic
440C2#2024388911yescharacteristic
subgroupG/H
centerC2×C4#13093998
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC42×D4×C47C2
socleC22×C47#386
prime radical#20253388C2
cosocleC2×C42×C47C23
hypercenterC42×D4D47
hypocenterC47#9233
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #20244216C2semidirect
3. #20241882C2semidirect
4. #20241813C2semidirect
5. #20241291C2semidirect
6. #20241221C2semidirect
7. C42×D4×C47C2semidirect
10. #15689403C4semidirect
11. #15689318C4semidirect
32. #13094024C2×C4semidirect
33. #13094021C2×C4semidirect
43. C4⋊(C47⋊C8)C2×C4semidirect
119. C42×C47D8semidirect
143. D4×C47#104semidirect
215. C42×D4D47semidirect
249. C47#9233semidirect
350. C42#10625334semidirect
372. D4#13093952semidirect

Maximal subgroups

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

subgroupindex
#202533882
#202442162
#202418822
#202418132
#202412912
#202412212
C42×D4×C472
#923347