Finite Group Databasebeta

← #26111616

Subgroups — #26111616

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689174C211yesmaximal, characteristic
2C4×#13094000C211yesmaximal, characteristic
3#20243365C211yesmaximal, characteristic
4C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#20241228C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13094000C411yescharacteristic
9C2×C42×D47C2211yescharacteristic
10#15689174—22no—
11#15689174—22no—
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×Dic47⋊C8—21no—
14C2×(C2×D47)⋊C8—21no—
15C2×(C2×D47)⋊C8—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17#15689030C411yescharacteristic
18#15689019C411yescharacteristic
19#15689004—21no—
20#15688994—21no—
21#15688980C411yescharacteristic
22C4×Dic47⋊C4—21no—
23C4×C4⋊Dic47C2211yescharacteristic
24C4×(C2×D47)⋊C4—21no—
25#15688877—21no—
26Q8⋊(C47⋊C8)—22no—
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×Q8⋊C8—22no—
31C22×C4×D47C2×C411yescharacteristic
32C22×C4×D47D411yescharacteristic
33C22×C4×D47D411yescharacteristic
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36#13094000—22no—
37#13094000C814yescomplemented
38C2×C4⋊Dic47C2×C411yescharacteristic
39C2×C4⋊Dic47C2×C411yescharacteristic
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—21no—
42C2×(C2×D47)⋊C4—21no—
43C2×(C2×D47)⋊C4—21no—
44C2×C4×Dic47—21no—
45C2×C4×Dic47C2×C411yescharacteristic
46C2×C4×Dic47D411yescharacteristic
47C2×C4×Dic47D411yescharacteristic
48C42×D47—21no—
49C42×D47—21no—
50C42×D47—21no—
51C42×D47—21no—
52C4⋊(C47⋊C8)—21no—
53C4⋊(C47⋊C8)—21no—
54Dic47⋊C8—24no—
55(C2×D47)⋊C8—24no—
56(C2×D47)⋊C8—42no—
57C4×C47⋊C8—21no—
58C4×C47⋊C8D412yes—
59C47⋊#95—21no—
60C47⋊#95—21no—
61C47⋊#95—21no—
62C47⋊#95—21no—
63C47⋊#95—21no—
64C22×Q8×C47C2×C411yescharacteristic
65C22×C8×C47—21no—
66C22×C8×C47—21no—
67C4×Q8×C47—21no—
68C4×Q8×C47—21no—
69C4×Q8×C47—21no—
70C4×Q8×C47—21no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47C2×C411yescharacteristic
73C2×C42×C47—21no—
74C2×C42×C47C2311yescharacteristic
75C4⋊C8×C47—21no—
76C4⋊C8×C47—21no—
77C4×C8×C47—21no—
78C4×C8×C47D412yes—
79C23×D47C22⋊C411yescharacteristic
80C2×Q8×C47—21no—
81C2×Q8×C47—21no—
82C2×Q8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×Q8×C47C2×C812yes—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×Dic47—21no—
92C22×Dic47—21no—
93C22×Dic47C22⋊C411yescharacteristic
94C22×Dic47C22⋊C411yescharacteristic
95C22×Dic47C22⋊C411yescharacteristic
96C2×C4×D47—21no—
97C2×C4×D47—21no—
98C2×C4×D47—21no—
99C2×C4×D47—21no—
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47—21no—
103C2×C4×D47—21no—
104C2×C4×D47—21no—
105C2×C4×D47—21no—
106C2×C4×D47—21no—
107C2×C4×D47—21no—
108C2×C4×D47—41no—
109C2×C4×D47—41no—
110C2×C4×D47C2×C812yes—
111C2×C4×D47M1612yes—
112C2×C8×C47—22no—
113C2×C8×C47—41no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C2×C8×C47—41no—
117C2×C8×C47—41no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—21no—
120C4⋊C4×C47—41no—
121C4⋊C4×C47—41no—
122C42×C47—41no—
123C42×C47—41no—
124C42×C47C2×D411yescharacteristic
125C42×C47C2×D411yescharacteristic
126C42×C47#4111yescharacteristic
127C42×C47#4111yescharacteristic
128(C2×D47)⋊C4—24no—
129(C2×D47)⋊C4—42no—
130C4⋊Dic47—21no—
131C4⋊Dic47—21no—
132C4⋊Dic47—21no—
133C4⋊Dic47C2×C812yes—
134Dic47⋊C4—24no—
135Dic47⋊C4—42no—
136C4×Dic47—21no—
137C4×Dic47—21no—
138C4×Dic47—21no—
139C4×Dic47—21no—
140C4×Dic47—21no—
141C4×Dic47—21no—
142C4×Dic47—41no—
143C4×Dic47—41no—
144C2×C47⋊C8—22no—
145C2×C47⋊C8—41no—
146C2×C47⋊C8—41no—
147C2×C47⋊C8—41no—
148C2×C47⋊C8—41no—
149C2×C47⋊C8—41no—
150C23×C47C2×C22⋊C411yescharacteristic
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—21no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47C22⋊C812yes—
158Q8×C47—22no—
159Q8×C47—22no—
160Q8×C47—41no—
161Q8×C47—41no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—22no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47C4×D411yescharacteristic
171C2×C4×C47C4×D411yescharacteristic
172C2×C4×C47#12011yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C2×C4×C47#12111yescharacteristic
175C2×C4×C47#12311yescharacteristic
176C2×C4×C47C22×C811yescharacteristic
177C2×C4×C47C2×M1611yescharacteristic
178C2×C4×C47#13111yescharacteristic
179C2×C4×C47#13111yescharacteristic
180C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C47#13711yescharacteristic
182C2×C4×C47#13711yescharacteristic
183C2×C4×C47#13711yescharacteristic
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—22no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—21no—
193C2×Dic47—41no—
194C2×Dic47—41no—
195C2×Dic47—41no—
196C2×Dic47—41no—
197C2×Dic47—41no—
198C2×Dic47C22⋊C812yes—
199C4×D47—22no—
200C4×D47—22no—
201C4×D47—22no—
202C4×D47—22no—
203C4×D47—42no—
204C4×D47—42no—
205C4×D47—41no—
206C4×D47—41no—
207C4×D47—41no—
208C4×D47—41no—
209C8×C47—42no—
210C8×C47—81no—
211C47⋊C8—42no—
212C47⋊C8—81no—
213#9073—471nomaximal, Sylow
214C22×C47#38611yescharacteristic
215C22×C47C2×C22⋊C811yescharacteristic
216C22×C47#40811yescharacteristic
217C22×C47#41711yescharacteristic
218C22×C47#41911yescharacteristic
219C22×C47#42111yescharacteristic
220C22×C47#42111yescharacteristic
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C4×C47—21no—
229C4×C47—21no—
230C4×C47—42no—
231C4×C47—81no—
232C4×C47C8×D411yescharacteristic
233C4×C47C8×D411yescharacteristic
234C4×C47#43511yescharacteristic
235C4×C47#43511yescharacteristic
236C4×C47#46811yescharacteristic
237C4×C47#46811yescharacteristic
238C4×C47#47011yescharacteristic
239C4×C47#47011yescharacteristic
240Dic47—22no—
241Dic47—41no—
242Dic47—41no—
243Dic47—42no—
244Dic47—81no—
245C2×#431—471no—
246C4×C22⋊Q8—471no—
247#1797—471no—
248C2×Q8⋊C8—471no—
249C2×Q8⋊C8D4711yescharacteristic, complemented
250#1279—471no—
251#1279—471no—
252C2×C47#147711yescharacteristic
253C2×C47#147911yescharacteristic
254C2×C47#149511yescharacteristic
255C2×C47#149711yescharacteristic
256C2×C47#186911yescharacteristic
257C2×C47#189411yescharacteristic
258C2×C47#189711yescharacteristic
259D47—42no—
260C2×C22⋊Q8—471no—
261C2×C4×Q8C2×D4711yescharacteristic
262C22×C42—471no—
263#431—942no—
264#431—942no—
265C2×C4⋊C8—471no—
266C2×C4⋊C8—941no—
267C2×C4⋊C8C2×D4711yescharacteristic
268C2×C22⋊C8—941no—
269C2×C22⋊C8—941no—
270C2×C4×C8—471no—
271C2×C4×C8C2×D4711yescharacteristic
272#391—471no—
273#389—471no—
274#387—941no—
275#385—941no—
276#380—471no—
277C4×C4⋊C4—471no—
278C4×C4⋊C4—941no—
279C4×C22⋊C4—941no—
280#336—941no—
281Q8⋊C8—22no—
282Q8⋊C8—942no—
283C47#907311yescharacteristic, complemented, Sylow
284C22×Q8C4×D4711yescharacteristic
285C23×C4—471no—
286C23×C4—471no—
287C23×C4—471no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—941no—
291C22×C8—941no—
292C22⋊Q8—474no—
293C22⋊Q8—942no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—471no—
300C2×C4⋊C4—471no—
301C2×C4⋊C4—941no—
302C2×C4⋊C4—941no—
303C2×C4⋊C4C4×D4711yescharacteristic
304C2×C22⋊C4—941no—
305C2×C22⋊C4—941no—
306C2×C42—21no—
307C2×C42—471no—
308C2×C42—471no—
309C2×C42—471no—
310C2×C42—941no—
311C2×C42—941no—
312C2×C42—941no—
313C2×C42—941no—
314C2×C42—941no—
315C2×C42C22×D4711yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—944no—
319C4⋊C8—941no—
320C4⋊C8—941no—
321C22⋊C8—944no—
322C22⋊C8—1882no—
323C4×C8—21no—
324C4×C8—472no—
325C4×C8—941no—
326C4×C8C22⋊D4712yes—
327#95—941no—
328#95—941no—
329#95—941no—
330#95—941no—
331#95—941no—
332C24—471no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8C8×D4712yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—471no—
342C22×C4—472no—
343C22×C4—472no—
344C22×C4—471no—
345C22×C4—471no—
346C22×C4—941no—
347C22×C4—941no—
348C22×C4—941no—
349C22×C4—941no—
350C22×C4—941no—
351C22×C4—941no—
352C22×C4—941no—
353C22×C4—941no—
354C22×C4—941no—
355C22×C4—941no—
356C22×C4—941no—
357C22×C4—941no—
358C22×C4—941no—
359C22×C4—941no—
360C22×C4—1881no—
361C22×C4—1881no—
362C22×C4C2×C4×D4711yescharacteristic
363C22×C4D4×D4711yescharacteristic
364C22×C4D4×D4711yescharacteristic
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—942no—
372C2×C8—1881no—
373C2×C8—1881no—
374C2×C8—1881no—
375C2×C8—1881no—
376C2×C8—1881no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—472no—
382C4⋊C4—944no—
383C4⋊C4—941no—
384C4⋊C4—941no—
385C4⋊C4—941no—
386C4⋊C4—1882no—
387C22⋊C4—944no—
388C22⋊C4—1882no—
389C42—41no—
390C42—41no—
391C42—941no—
392C42—941no—
393C42—941no—
394C42—941no—
395C42—941no—
396C42—941no—
397C42—1881no—
398C42—1881no—
399C42#1062535011yescharacteristic
400C42D4×D4711yescharacteristic
401C42#1062535211yescharacteristic
402C42C2×C22⋊D4711yescharacteristic
403C23—472no—
404C23—941no—
405C23—941no—
406C23—941no—
407C23—941no—
408C23—941no—
409C23—941no—
410C23C22⋊C4×D4711yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—41no—
414Q8—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—472no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—942no—
427C2×C4—942no—
428C2×C4—942no—
429C2×C4—942no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—942no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—1882no—
438C2×C4—1882no—
439C2×C4—1881no—
440C2×C4—1881no—
441C2×C4—1881no—
442C2×C4—1881no—
443C2×C4—1881no—
444C2×C4—1881no—
445C2×C4—1881no—
446C2×C4—1881no—
447C2×C4—1881no—
448C2×C4(C22⋊D47)⋊C411yescharacteristic
449C2×C4C4×C22⋊D4711yescharacteristic
450C2×C4#1309399211yescharacteristic
451C2×C4#1309399511yescharacteristic
452C2×C4#1309399711yescharacteristic
453C2×C4#1309400611yescharacteristic
454C2×C4C2×C8×D4711yescharacteristic
455C2×C4M16×D4711yescharacteristic
456C2×C4#1309403011yescharacteristic
457C2×C4#1309403211yescharacteristic
458C2×C4#1309405111yescharacteristic
459C2×C4#1309405311yescharacteristic
460C2×C4#1309405611yescharacteristic
461C2×C4#1309405611yescharacteristic
462C8—42no—
463C8—81no—
464C8—3761no—
465C8—1882no—
466C22—942no—
467C22—942no—
468C22—942no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22#1568899911yescharacteristic
474C22C22⋊C8×D4711yescharacteristic
475C22#1568908811yescharacteristic
476C22#1568912311yescharacteristic
477C22#1568913011yescharacteristic
478C22#1568913811yescharacteristic
479C22#1568913811yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—942no—
485C4—3761no—
486C4—1881no—
487C4—1882no—
488C4—1881no—
489C4(C22⋊D47)⋊C811yescharacteristic
490C4C8×C22⋊D4711yescharacteristic
491C4#1568919211yescharacteristic
492C4#1568919711yescharacteristic
493C4#1568936611yescharacteristic
494C4#1568937211yescharacteristic
495C4#1568937811yescharacteristic
496C4#1568938011yescharacteristic
497C2—1882no—
498C2#2024177411yescharacteristic
499C2#2024178111yescharacteristic
500C2#2024185211yescharacteristic
501C2#2024185911yescharacteristic
502C2#2024367711yescharacteristic
503C2#2024381811yescharacteristic
504C2#2024383311yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#9073
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C47⋊C8)C2semidirect
5. #20241228C2semidirect
6. #20241227C2semidirect
7. C2×C47×Q8⋊C8C2semidirect
37. #13094000C8semidirect
249. C2×Q8⋊C8D47semidirect
283. C47#9073semidirect

Maximal subgroups

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

subgroupindex
C2×#156891742
C4×#130940002
#202433652
C2×Q8⋊(C47⋊C8)2
#202412282
#202412272
C2×C47×Q8⋊C82
#907347