Finite Group Databasebeta

← #26109032

Subgroups — #26109032

Order 12032.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13093998C211yesmaximal, characteristic
2C2×#15688858C212yesmaximal
3#20241618C211yesmaximal, characteristic, complemented
4#20241268C212yesmaximal, complemented
5C47×#1797C211yesmaximal, characteristic, complemented
6C2×#13093998C2211yescharacteristic
7C2×C4×D188C411yescharacteristic, complemented
8C2×C4×C22⋊D47—21no—
9C22×C4⋊Dic47—21no—
10#15689025C411yescharacteristic, complemented
11#15689021C411yescharacteristic, complemented
12#15689014—21no—
13#15689002—21no—
14#15688983C2211yescharacteristic
15C4×C4⋊Dic47C411yescharacteristic, complemented
16C4×(C2×D47)⋊C4—21no—
17C2×C47⋊#95—21no—
18C2×C47⋊#95C2212yes—
19#15688858—24no—
20C22×C42×C47C2211yescharacteristic
21C2×C4⋊C8×C47—21no—
22C2×C22⋊C8×C47C2212yes—
23C47×#336—21no—
24C22×D188C2×C411yescharacteristic
25C22×C22⋊D47—21no—
26C23×Dic47—22no—
27C22×C4×D47—21no—
28#13093998—21no—
29#13093998—21no—
30#13093998D412yes—
31#13093998Q812yes—
32C4×D188—42no—
33C4×C22⋊D47—42no—
34C4×C22⋊D47—42no—
35C2×C4⋊Dic47—24no—
36C2×C4⋊Dic47—42no—
37C2×C4⋊Dic47—42no—
38C2×C4⋊Dic47C2×C411yescharacteristic
39C2×C4⋊Dic47C2×C411yescharacteristic
40C2×C4⋊Dic47C2×C411yescharacteristic
41C2×Dic47⋊C4—21no—
42C2×C22⋊Dic47—21no—
43C2×(C2×D47)⋊C4—21no—
44C2×(C2×D47)⋊C4—21no—
45C2×(C2×D47)⋊C4—21no—
46C2×(C2×D47)⋊C4—21no—
47C2×C4×Dic47—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—22no—
52C47⋊#95—22no—
53C47⋊#95—42no—
54C23×C4×C47D411yescharacteristic
55C23×C4×C47D411yescharacteristic
56C23×C4×C47C2311yescharacteristic
57C22×C8×C47—22no—
58C2×C42×C47—42no—
59C2×C42×C47C2×C411yescharacteristic
60C2×C42×C47C2×C411yescharacteristic
61C2×C42×C47D411yescharacteristic
62C2×C42×C47D411yescharacteristic
63C4⋊C8×C47—42no—
64C22⋊C8×C47—22no—
65C22⋊C8×C47—22no—
66C24×C47C2×D411yescharacteristic
67C23×D47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C22⋊C411yescharacteristic
78C22×C4×C47C22⋊C411yescharacteristic
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47D812yes—
81C22×C4×C47SD1612yes—
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×Q811yescharacteristic
86C22×C4×C47#4111yescharacteristic
87C22×C4×C47#4111yescharacteristic
88C2×C22⋊D47—22no—
89C2×C22⋊D47—22no—
90C2×C22⋊D47—41no—
91C2×C22⋊D47—41no—
92C2×C22⋊D47—41no—
93C2×C22⋊D47—41no—
94C22×Dic47—21no—
95C22×Dic47—24no—
96C22×Dic47—21no—
97C22×Dic47—21no—
98C22×Dic47—42no—
99C22×Dic47—42no—
100C22×Dic47—42no—
101C22×Dic47—42no—
102C22×Dic47—42no—
103C22×Dic47—42no—
104C2×D188—21no—
105C2×D188—41no—
106C2×D188—41no—
107C2×D188C4⋊C412yescomplemented
108C2×C4×D47—42no—
109C2×C4×D47—42no—
110C2×C4×D47—42no—
111C2×C8×C47—42no—
112C2×C8×C47—42no—
113C2×C8×C47—42no—
114C42×C47—22no—
115C42×C47—22no—
116C42×C47—41no—
117C42×C47—41no—
118C22⋊Dic47—41no—
119C22⋊Dic47—41no—
120(C2×D47)⋊C4—22no—
121(C2×D47)⋊C4—22no—
122(C2×D47)⋊C4—42no—
123(C2×D47)⋊C4—42no—
124(C2×D47)⋊C4—42no—
125C4⋊Dic47—21no—
126C4⋊Dic47—48no—
127C4⋊Dic47—41no—
128C4⋊Dic47—41no—
129C4⋊Dic47C4⋊C412yescomplemented
130Dic47⋊C4—42no—
131C4×Dic47—42no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47C2×C22⋊C411yescharacteristic
137C23×C47#12111yescharacteristic
138C23×C47C22⋊Q811yescharacteristic
139C23×C47C2×D811yescharacteristic
140C23×C47C2×SD1611yescharacteristic
141C23×C47AGL(1,ℤ/8)11yescharacteristic
142C23×C47#13711yescharacteristic
143C22×D47—22no—
144C22×D47—41no—
145C22×D47—41no—
146C22×D47—41no—
147C22×D47—41no—
148C22×D47—41no—
149C22×D47—41no—
150C2×C4×C47—24no—
151C2×C4×C47—24no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—42no—
165C2×C4×C47—42no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47#9912yes—
171C2×C4×C47#10212yes—
172C2×C4×C47#10212yes—
173C2×C4×C47#10412yes—
174C2×C4×C47C2×C4⋊C411yescharacteristic
175C2×C4×C47#11711yescharacteristic
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47C22⋊Q811yescharacteristic
178C22⋊D47—42no—
179C22⋊D47—42no—
180C22⋊D47—42no—
181C22⋊D47—42no—
182C2×Dic47—22no—
183C2×Dic47—41no—
184C2×Dic47—41no—
185C2×Dic47—44no—
186C2×Dic47—44no—
187C2×Dic47—44no—
188C2×Dic47—41no—
189C2×Dic47—41no—
190C2×Dic47—41no—
191C2×Dic47—41no—
192C2×Dic47—41no—
193C2×Dic47—41no—
194C2×Dic47—82no—
195C2×Dic47—82no—
196C2×Dic47—82no—
197C2×Dic47—82no—
198D188—42no—
199D188—42no—
200C4×D47—84no—
201C8×C47—82no—
202#8577—471nomaximal, Sylow
203C22×C47—21no—
204C22×C47—21no—
205C22×C47—21no—
206C22×C47—21no—
207C22×C47—21no—
208C22×C47—21no—
209C22×C47—21no—
210C22×C47—21no—
211C22×C47—21no—
212C22×C47—21no—
213C22×C47—21no—
214C22×C47—21no—
215C22×C47#38011yescharacteristic
216C22×C47C2×#9911yescharacteristic
217C22×C47#41011yescharacteristic
218C22×C47C2×#10211yescharacteristic
219C22×C47#41711yescharacteristic
220C22×C47C2×#10411yescharacteristic
221C22×C47#42111yescharacteristic
222C22×C47#45911yescharacteristic
223C22×C47#46111yescharacteristic
224C22×C47#47411yescharacteristic
225C22×C47#47611yescharacteristic
226C2×D47—42no—
227C2×D47—42no—
228C2×D47—42no—
229C2×D47—81no—
230C2×D47—81no—
231C2×D47—81no—
232C2×D47—81no—
233C4×C47—21no—
234C4×C47—21no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—22no—
238C4×C47—22no—
239C4×C47—22no—
240C4×C47—22no—
241Dic47—42no—
242Dic47—84no—
243Dic47—81no—
244Dic47—81no—
245C4×#121—471no—
246#1797D4711yescharacteristic, complemented
247C2×#327—472no—
248C4⋊#95—471no—
249#1294—472no—
250C2×C47—21no—
251C2×C47—21no—
252C2×C47—21no—
253C2×C47—21no—
254C2×C47#150211yescharacteristic
255C2×C47#150411yescharacteristic
256C2×C47#151211yescharacteristic
257C2×C47#151911yescharacteristic
258C2×C47#179911yescharacteristic
259C2×C47#180211yescharacteristic
260C2×C47#180611yescharacteristic
261D47—82no—
262C2×#121—471no—
263C2×C4×D4—471no—
264C2×C4×D4—941no—
265C22×C4⋊C4—941no—
266C22×C42C2×D4711yescharacteristic
267C2×C4⋊C8—21no—
268C2×C22⋊C8C2×D4712yes—
269#390—471no—
270#389—471no—
271#388—941no—
272#386—941no—
273#380—471no—
274C4×C4⋊C4—471no—
275C4×C22⋊C4—941no—
276C2×#95—472no—
277C2×#95—941no—
278#336—21no—
279#327—944no—
280C47#857711yescharacteristic, complemented, Sylow
281C22×D4—471no—
282C22×D4—941no—
283C23×C4—942no—
284C23×C4—941no—
285C23×C4D18811yescharacteristic
286C23×C4D18811yescharacteristic
287C23×C4C22×D4711yescharacteristic
288C22×C8—22no—
289#121—472no—
290#121—472no—
291#121—941no—
292#121—941no—
293C4×D4—1882no—
294C4×D4—1882no—
295C4×D4—1882no—
296C2×C4⋊C4—471no—
297C2×C4⋊C4—471no—
298C2×C4⋊C4—471no—
299C2×C4⋊C4—944no—
300C2×C4⋊C4—941no—
301C2×C4⋊C4—1882no—
302C2×C4⋊C4—1882no—
303C2×C22⋊C4—941no—
304C2×C22⋊C4—941no—
305C2×C22⋊C4—941no—
306C2×C22⋊C4—941no—
307C2×C22⋊C4—941no—
308C2×C42—42no—
309C2×C42—941no—
310C2×C42C4×D4711yescharacteristic
311C2×C42C4×D4711yescharacteristic
312C2×C42C22⋊D4711yescharacteristic
313C2×C42C22⋊D4711yescharacteristic
314C4⋊C8—42no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317#95—941no—
318#95—941no—
319#95—941no—
320#95—942no—
321#95—942no—
322#95—1882no—
323C24—941no—
324C24C2×D18811yescharacteristic
325C2×D4—472no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—941no—
329C2×D4—1881no—
330C2×D4—1881no—
331C2×D4—1881no—
332C2×D4—1881no—
333C2×D4—1881no—
334C2×D4—1881no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—941no—
344C22×C4—944no—
345C22×C4—941no—
346C22×C4—941no—
347C22×C4—1882no—
348C22×C4—1882no—
349C22×C4—1882no—
350C22×C4—1882no—
351C22×C4—1882no—
352C22×C4—1882no—
353C22×C4—1882no—
354C22×C4—1882no—
355C22×C4—1882no—
356C22×C4#1062532512yes—
357C22×C4D37612yes—
358C22×C4(C2×D47)⋊C411yescharacteristic
359C22×C4(C2×D47)⋊C411yescharacteristic
360C22×C4(C2×D47)⋊C411yescharacteristic
361C22×C4(C2×D47)⋊C411yescharacteristic
362C22×C4C2×C4×D4711yescharacteristic
363C22×C4D4×D4711yescharacteristic
364C22×C4#1062535211yescharacteristic
365C22×C4Q8×D4711yescharacteristic
366C22×C4#1062535411yescharacteristic
367C22×C4C2×C22⋊D4711yescharacteristic
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—472no—
372C4⋊C4—941no—
373C4⋊C4—1881no—
374C4⋊C4—1881no—
375C4⋊C4—1888no—
376C4⋊C4—1882no—
377C22⋊C4—942no—
378C22⋊C4—942no—
379C22⋊C4—1881no—
380C22⋊C4—1881no—
381C22⋊C4—1882no—
382C22⋊C4—1882no—
383C22⋊C4—1882no—
384C42—22no—
385C42—22no—
386C42—41no—
387C42—41no—
388C42—1882no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—942no—
394C23—1881no—
395C23—1881no—
396C23—1881no—
397C23—1881no—
398C23—1881no—
399C23—1881no—
400C23C2×(C2×D47)⋊C411yescharacteristic
401C23#1309399911yescharacteristic
402C23#1309400411yescharacteristic
403C23C2×D37611yescharacteristic
404C23C2×#1062532511yescharacteristic
405C23#1309405211yescharacteristic
406C23#1309405711yescharacteristic
407D4—1882no—
408D4—1882no—
409D4—1882no—
410D4—1882no—
411D4—1882no—
412D4—1882no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—942no—
434C2×C4—3764no—
435C2×C4—3762no—
436C2×C4—3762no—
437C2×C4—3762no—
438C2×C4—3762no—
439C2×C4—1884no—
440C2×C4—1884no—
441C2×C4—1884no—
442C2×C4—1881no—
443C2×C4—1881no—
444C2×C4—1881no—
445C2×C4—1881no—
446C2×C4—1881no—
447C2×C4—1881no—
448C2×C4—1881no—
449C2×C4—1881no—
450C2×C4#1309393812yes—
451C2×C4#1309394612yes—
452C2×C4#1309394612yes—
453C2×C4#1309395012yes—
454C2×C4C4⋊C4×D4711yescharacteristic
455C2×C4#1309398211yescharacteristic
456C2×C4#1309399511yescharacteristic
457C2×C4#1309400011yescharacteristic
458C8—82no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—3761no—
472C22—3761no—
473C22—3761no—
474C22—3761no—
475C22—1882no—
476C22—1882no—
477C22—1882no—
478C22#1568898011yescharacteristic
479C22C2×#1309393811yescharacteristic
480C22#1568909611yescharacteristic
481C22C2×#1309394611yescharacteristic
482C22#1568912511yescharacteristic
483C22C2×#1309395011yescharacteristic
484C22#1568913911yescharacteristic
485C22#1568931911yescharacteristic
486C22#1568932911yescharacteristic
487C22#1568940411yescharacteristic
488C22#1568941411yescharacteristic
489C4—22no—
490C4—22no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—22no—
496C4—22no—
497C4—3764no—
498C4—3761no—
499C4—3761no—
500C4—1882no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—3762no—
506C2#2024188411yescharacteristic
507C2#2024189311yescharacteristic
508C2#2024192711yescharacteristic
509C2#2024195711yescharacteristic
510C2#2024337311yescharacteristic
511C2#2024338911yescharacteristic
512C2#2024340511yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1797C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenter#1797D47
hypocenterC47#8577
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #20241618C2semidirect
4. #20241268C2semidirect
5. C47×#1797C2semidirect
7. C2×C4×D188C4semidirect
10. #15689025C4semidirect
11. #15689021C4semidirect
15. C4×C4⋊Dic47C4semidirect
107. C2×D188C4⋊C4semidirect
129. C4⋊Dic47C4⋊C4semidirect
246. #1797D47semidirect
280. C47#8577semidirect

Maximal subgroups

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

subgroupindex
C4×#130939982
C2×#156888582
#202416182
#202412682
C47×#17972
#857747