Finite Group Databasebeta

← #26111039

Subgroups — #26111039

Order 12032.

764 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689318C211yesmaximal, characteristic
2#20244315C211yesmaximal, characteristic, complemented
3#20244193C211yesmaximal, characteristic, complemented
4C2×D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#20241271C211yesmaximal, characteristic, complemented
6#20241229C211yesmaximal, characteristic, complemented
7D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
8C22×#10625334—21no—
9C2×#13094021C2211yescharacteristic
10#15689318—22no—
11#15689318C414yescomplemented
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093944—21no—
15C2×#13093944—21no—
16C2×#13093944—21no—
17C2×#13093944—22no—
18C2×C4×C47⋊C8C2211yescharacteristic
19D4⋊(C47⋊C8)—22no—
20C2×C4×D4×C47—21no—
21C2×C4×D4×C47C2211yescharacteristic
22C22×C4⋊C4×C47—21no—
23C47×#389—21no—
24C47×#385—22no—
25C47×#384C2211yescharacteristic
26C47×#380—21no—
27C4×C4⋊C4×C47C2211yescharacteristic
28C22×D188—21no—
29C22×D188—21no—
30C22×D188—21no—
31C2×#10625334—24no—
32C2×#10625334—42no—
33C2×#10625334—42no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37#13094021—21no—
38#13094021—21no—
39#13094021—21no—
40#13094021C2×C412yescomplemented
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)C2×C412yescomplemented
45#13093944—24no—
46#13093944—44no—
47#13093944—42no—
48#13093944—42no—
49C4×C47⋊C8—21no—
50C4×C47⋊C8—21no—
51C22×D4×C47D411yescharacteristic
52C23×C4×C47—21no—
53C23×C4×C47—22no—
54C4×D4×C47—21no—
55C4×D4×C47—21no—
56C4×D4×C47—42no—
57C4×D4×C47—42no—
58C4×D4×C47C2×C412yes—
59C4×D4×C47D412yes—
60C2×C4⋊C4×C47—22no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—42no—
64C2×C4⋊C4×C47—42no—
65C2×C4⋊C4×C47D411yescharacteristic
66C2×C4⋊C4×C47D411yescharacteristic
67C2×C4⋊C4×C47D411yescharacteristic
68C2×C4⋊C4×C47D412yes—
69C2×C22⋊C4×C47—21no—
70C2×C22⋊C4×C47—22no—
71C2×C42×C47—21no—
72C2×C42×C47C2311yescharacteristic
73#95×C47—22no—
74#95×C47—21no—
75C24×C47—21no—
76C23×D47—41no—
77C2×D4×C47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47C22⋊C412yes—
81C2×D4×C47D812yes—
82C2×D4×C47SD1612yes—
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—21no—
88C22×C4×C47—22no—
89C22×C4×C47—44no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—44no—
95C22×C4×C47—82no—
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C2×D188—22no—
100C2×D188—22no—
101C2×D188—22no—
102C2×D188—42no—
103C2×D188—42no—
104C2×D188—41no—
105C2×D188—41no—
106C2×D188—41no—
107C2×D188—41no—
108C2×D188—41no—
109C2×D188—41no—
110C2×D188—41no—
111C2×D188—41no—
112C2×D188—41no—
113C2×D188—41no—
114C2×D188—41no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47—21no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—44no—
120C4⋊C4×C47—42no—
121C4⋊C4×C47—41no—
122C4⋊C4×C47—41no—
123C4⋊C4×C47—41no—
124C4⋊C4×C47—41no—
125C4⋊C4×C47C22⋊C412yes—
126C4⋊C4×C47D812yescomplemented
127C22⋊C4×C47—22no—
128C22⋊C4×C47—22no—
129C22⋊C4×C47—44no—
130C42×C47—41no—
131C42×C47—41no—
132C42×C47C22×C411yescharacteristic
133C42×C47C2×D411yescharacteristic
134C42×C47#4111yescharacteristic
135C42×C47#4111yescharacteristic
136#10625334—48no—
137C2×C47⋊C8—22no—
138C2×C47⋊C8—22no—
139C2×C47⋊C8—41no—
140C2×C47⋊C8—41no—
141C2×C47⋊C8—41no—
142C2×C47⋊C8—41no—
143C2×C47⋊C8—41no—
144C2×C47⋊C8—41no—
145C2×C47⋊C8—41no—
146C23×C47—22no—
147C23×C47—22no—
148C23×C47—22no—
149C23×C47—41no—
150C23×C47—41no—
151C23×C47—41no—
152C23×C47—41no—
153C23×C47#12011yescharacteristic
154C22×D47—42no—
155C22×D47—81no—
156C22×D47—81no—
157C22×D47—81no—
158C22×D47—81no—
159C22×D47—81no—
160C22×D47—81no—
161D4×C47—22no—
162D4×C47—22no—
163D4×C47—22no—
164D4×C47#10214yescomplemented
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—22no—
168C2×C4×C47—22no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—42no—
174C2×C4×C47—42no—
175C2×C4×C47—42no—
176C2×C4×C47—42no—
177C2×C4×C47—41no—
178C2×C4×C47—42no—
179C2×C4×C47—42no—
180C2×C4×C47—41no—
181C2×C4×C47—42no—
182C2×C4×C47—41no—
183C2×C4×C47—88no—
184C2×C4×C47C2×C22⋊C411yescharacteristic
185C2×C4×C47C4×D411yescharacteristic
186C2×C4×C47C4×D411yescharacteristic
187C2×C4×C47#12111yescharacteristic
188C2×C4×C47#12111yescharacteristic
189C2×C4×C47#12311yescharacteristic
190C2×C4×C47C2×D811yescharacteristic
191C2×C4×C47C2×D811yescharacteristic
192C2×C4×C47C2×SD1611yescharacteristic
193C2×C4×C47#13511yescharacteristic
194C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C47#13711yescharacteristic
198D188—44no—
199D188—42no—
200D188—42no—
201D188—42no—
202D188—42no—
203D188—82no—
204D188—81no—
205D188—81no—
206D188—81no—
207D188—81no—
208C47⋊C8—42no—
209C47⋊C8—42no—
210C47⋊C8—81no—
211#8977—471nomaximal, Sylow
212C22×C47—24no—
213C22×C47—42no—
214C22×C47—42no—
215C22×C47—42no—
216C22×C47—42no—
217C22×C47—42no—
218C22×C47—42no—
219C22×C47#38611yescharacteristic
220C22×C47#44711yescharacteristic
221C22×C47#44711yescharacteristic
222C22×C47#44811yescharacteristic
223C22×C47#44911yescharacteristic
224C22×C47#45311yescharacteristic
225C22×C47#45411yescharacteristic
226C2×D47—82no—
227C2×D47—82no—
228C2×D47—82no—
229C2×D47—161no—
230C2×D47—161no—
231C2×D47—161no—
232C2×D47—161no—
233C4×C47—21no—
234C4×C47—21no—
235C4×C47—42no—
236C4×C47—42no—
237C4×C47—82no—
238C4×C47—81no—
239C4×C47C2×#10211yescharacteristic
240C4×C47#41711yescharacteristic
241C4×C47C4×D811yescharacteristic
242C4×C47#44211yescharacteristic
243C4×C47#45911yescharacteristic
244C4×C47#46311yescharacteristic
245C4×C47#48011yescharacteristic
246C4×C47#48111yescharacteristic
247C2×#459—471no—
248D4×C4⋊C4D4711yescharacteristic, complemented
249#1982—471no—
250#1957—471no—
251C2×D4⋊C8—471no—
252#1296—471no—
253#1279—471no—
254C2×C47—44no—
255C2×C47#161911yescharacteristic
256C2×C47#162211yescharacteristic
257C2×C47#162511yescharacteristic
258C2×C47#162711yescharacteristic
259C2×C47#187411yescharacteristic
260C2×C47#187911yescharacteristic
261C2×C47#188311yescharacteristic
262D47—162no—
263C22×D8—941no—
264C2×#127—471no—
265C2×C4×D4—21no—
266C2×C4×D4C2×D4711yescharacteristic
267C22×C4⋊C4—21no—
268#459—474no—
269#459—942no—
270C2×C4⋊C8—471no—
271C2×C4⋊C8—471no—
272C2×#102—941no—
273C2×#102—942no—
274C2×#102—941no—
275C2×#102—941no—
276C2×C4×C8—471no—
277#389—21no—
278#385—22no—
279#384C2×D4711yescharacteristic
280#380—21no—
281C4×C4⋊C4C2×D4711yescharacteristic
282D4⋊C8—942no—
283C47#897711yescharacteristic, complemented, Sylow
284C22×D4—941no—
285C22×D4—941no—
286C22×D4—941no—
287C22×D4C22⋊D4711yescharacteristic
288C23×C4—21no—
289C23×C4—22no—
290C2×D8—944no—
291C2×D8—1882no—
292C2×D8—1882no—
293C22×C8—941no—
294C22×C8—941no—
295C22×C8—941no—
296#127—472no—
297#127—941no—
298#127—941no—
299#127—941no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4C4×D4712yes—
305C4×D4D18812yes—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4C22⋊D4711yescharacteristic
312C2×C4⋊C4C22⋊D4711yescharacteristic
313C2×C4⋊C4C22⋊D4711yescharacteristic
314C2×C4⋊C4C22⋊D4712yes—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C42—21no—
318C2×C42C22×D4711yescharacteristic
319C4⋊C8—472no—
320C4⋊C8—941no—
321C4⋊C8—941no—
322C4⋊C8—941no—
323#102—944no—
324#102—1882no—
325#102—1884no—
326#102—1882no—
327C4×C8—941no—
328C4×C8—941no—
329#95—22no—
330#95—21no—
331C24—21no—
332C24—1881no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—942no—
337C2×D4—942no—
338C2×D4—942no—
339C2×D4—1882no—
340C2×D4—1882no—
341C2×D4—1881no—
342C2×D4—1881no—
343C2×D4—1881no—
344C2×D4—1881no—
345C2×D4—1881no—
346C2×D4—1881no—
347C2×D4—1881no—
348C2×D4—1881no—
349C2×D4—1881no—
350C2×D4—1881no—
351C2×D4—1881no—
352C2×D4(C2×D47)⋊C412yes—
353C2×D4#1062533412yes—
354C2×D4#1062533612yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—44no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4C2×C22⋊D4711yescharacteristic
369C22×C4C2×C22⋊D4711yescharacteristic
370C22×C4C2×C22⋊D4711yescharacteristic
371D8—1888no—
372C2×C8—942no—
373C2×C8—942no—
374C2×C8—1881no—
375C2×C8—1881no—
376C2×C8—1881no—
377C2×C8—1881no—
378C2×C8—1881no—
379C2×C8—1881no—
380C2×C8—1881no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—42no—
386C4⋊C4—44no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4(C2×D47)⋊C412yes—
392C4⋊C4#1062533412yescomplemented
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—44no—
396C42—41no—
397C42—41no—
398C42C2×C4×D4711yescharacteristic
399C42C2×D18811yescharacteristic
400C42#1062535011yescharacteristic
401C42#1062535011yescharacteristic
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—3761no—
410C23—3761no—
411C23—3761no—
412C23—3761no—
413C23—3761no—
414C23—3761no—
415C23—1882no—
416C23#1309399311yescharacteristic
417D4—22no—
418D4—22no—
419D4—22no—
420D4—3762no—
421D4—3761no—
422D4—3761no—
423D4—3761no—
424D4—3761no—
425D4—1884no—
426D4—1882no—
427D4—1882no—
428D4—1882no—
429D4—1882no—
430D4#1309394414yescomplemented
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—88no—
450C2×C4C2×(C2×D47)⋊C411yescharacteristic
451C2×C4C4×C22⋊D4711yescharacteristic
452C2×C4C4×C22⋊D4711yescharacteristic
453C2×C4#1309399811yescharacteristic
454C2×C4#1309399811yescharacteristic
455C2×C4#1309400711yescharacteristic
456C2×C4C2×#1062533411yescharacteristic
457C2×C4C2×#1062533411yescharacteristic
458C2×C4C2×#1062533611yescharacteristic
459C2×C4#1309404411yescharacteristic
460C2×C4#1309404911yescharacteristic
461C2×C4#1309405011yescharacteristic
462C2×C4#1309405011yescharacteristic
463C2×C4#1309405511yescharacteristic
464C8—3761no—
465C8—1882no—
466C8—1882no—
467C22—24no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—3762no—
475C22—3762no—
476C22—3762no—
477C22—7521no—
478C22—7521no—
479C22—7521no—
480C22—7521no—
481C22#1568900211yescharacteristic
482C22#1568925711yescharacteristic
483C22#1568925711yescharacteristic
484C22#1568926211yescharacteristic
485C22#1568926811yescharacteristic
486C22#1568929111yescharacteristic
487C22#1568929611yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—82no—
493C4—81no—
494C4C2×#1309394411yescharacteristic
495C4#1568912211yescharacteristic
496C4C4×#1062533411yescharacteristic
497C4#1568923311yescharacteristic
498C4#1568931811yescharacteristic
499C4#1568933811yescharacteristic
500C4#1568943611yescharacteristic
501C4#1568944111yescharacteristic
502C2—44no—
503C2—7522no—
504C2#2024244211yescharacteristic
505C2#2024246011yescharacteristic
506C2#2024247711yescharacteristic
507C2#2024249111yescharacteristic
508C2#2024370511yescharacteristic
509C2#2024373611yescharacteristic
510C2#2024376411yescharacteristic
subgroupG/H
centerC23#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingD4×C4⋊C4×C47C2
socleC23×C47#120
prime radicalC2×#15689318C2
cosocleC2×C42×C47C23
hypercenterD4×C4⋊C4D47
hypocenterC47#8977
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20244315C2semidirect
3. #20244193C2semidirect
4. C2×D4⋊(C47⋊C8)C2semidirect
5. #20241271C2semidirect
6. #20241229C2semidirect
7. D4×C4⋊C4×C47C2semidirect
11. #15689318C4semidirect
40. #13094021C2×C4semidirect
44. C4⋊(C47⋊C8)C2×C4semidirect
126. C4⋊C4×C47D8semidirect
164. D4×C47#102semidirect
248. D4×C4⋊C4D47semidirect
283. C47#8977semidirect
392. C4⋊C4#10625334semidirect
430. D4#13093944semidirect

Maximal subgroups

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

subgroupindex
C2×#156893182
#202443152
#202441932
C2×D4⋊(C47⋊C8)2
#202412712
#202412292
D4×C4⋊C4×C472
#897747