Finite Group Databasebeta

← #26228293

Subgroups — #26228293

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689254C211yesmaximal, characteristic, complemented
2C2×#15689178C211yesmaximal, characteristic
3C4×#13094000C211yesmaximal, characteristic
4#20244111C211yesmaximal, characteristic, complemented
5#20244110C211yesmaximal, characteristic, complemented
6#20244105C211yesmaximal, characteristic, complemented
7#20244002C211yesmaximal, characteristic
8#20243999C211yesmaximal, characteristic
9#20243995C211yesmaximal, characteristic
10#20243992C211yesmaximal, characteristic
11#20243950C211yesmaximal, characteristic, complemented
12#20243943C211yesmaximal, characteristic, complemented
13#20243365C211yesmaximal, characteristic
14#20243265C211yesmaximal, characteristic, complemented
15C47×#1985C211yesmaximal, characteristic, complemented
16C2×#13094000C411yescharacteristic
17C2×C42×D47C2211yescharacteristic
18#15689254—24no—
19#15689178—24no—
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×#13093934C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35C2×C8×Dic47C2211yescharacteristic
36#15689030C411yescharacteristic
37#15689019C411yescharacteristic
38#15689004C411yescharacteristic
39#15689004C411yescharacteristic
40#15688994C411yescharacteristic
41#15688994C411yescharacteristic
42#15688980C411yescharacteristic
43C4×Dic47⋊C4C2211yescharacteristic
44C4×Dic47⋊C4C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46C4×(C2×D47)⋊C4C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×C4×Q8×C47C2211yescharacteristic
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C4×D47C2×C411yescharacteristic
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094000—24no—
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×C4⋊Dic47C2×C411yescharacteristic
71C2×Dic47⋊C4C2×C411yescharacteristic
72C2×Dic47⋊C4C2×C411yescharacteristic
73C2×Dic47⋊C4C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×(C2×D47)⋊C4C2×C411yescharacteristic
76C2×(C2×D47)⋊C4C2×C411yescharacteristic
77C2×(C2×D47)⋊C4C2×C411yescharacteristic
78C2×(C2×D47)⋊C4C2×C411yescharacteristic
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47C2×C411yescharacteristic
81C2×C4×Dic47C2311yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83C2×C4×Dic47C2311yescharacteristic
84C42×D47—22no—
85C42×D47—22no—
86C4⋊(C47⋊C8)—22no—
87C4⋊(C47⋊C8)—22no—
88C4⋊(C47⋊C8)—22no—
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91Dic47⋊C8—41no—
92Dic47⋊C8—41no—
93(C2×D47)⋊C8—22no—
94(C2×D47)⋊C8—22no—
95(C2×D47)⋊C8—41no—
96(C2×D47)⋊C8—41no—
97#13093935—22no—
98#13093935D414yes—
99#13093934—41no—
100C4×C47⋊C8—22no—
101C8×Dic47—41no—
102C47⋊#95C2×C411yescharacteristic
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C22×Q8×C47C2×C411yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C4×Q8×C47—22no—
118C4×Q8×C47—22no—
119C2×C4⋊C4×C47C2×C411yescharacteristic
120C2×C4⋊C4×C47C2×C411yescharacteristic
121C2×C4⋊C4×C47C2×C411yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125C4⋊C8×C47—22no—
126#97×C47—22no—
127C23×D47C22×C411yescharacteristic
128C2×Q8×C47—22no—
129C2×Q8×C47—22no—
130C2×Q8×C47—41no—
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47C22×C411yescharacteristic
139C22×Dic47C22×C411yescharacteristic
140C22×Dic47C22×C411yescharacteristic
141C22×Dic47C22×C411yescharacteristic
142C22×Dic47C22×C411yescharacteristic
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—22no—
155C2×C4×D47—41no—
156C2×C4×D47—41no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—22no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47C2×D412yes—
177C42×C47#4112yes—
178(C2×D47)⋊C4—22no—
179(C2×D47)⋊C4—41no—
180(C2×D47)⋊C4—41no—
181(C2×D47)⋊C4M1614yes—
182C4⋊Dic47—22no—
183C4⋊Dic47—41no—
184Dic47⋊C4—22no—
185Dic47⋊C4—22no—
186Dic47⋊C4—22no—
187Dic47⋊C4—22no—
188C4×Dic47—22no—
189C4×Dic47—22no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8C2×D412yes—
207C2×C47⋊C8C2×D412yes—
208C23×C47C23×C411yescharacteristic
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47—21no—
213C22×D47—21no—
214C22×D47—21no—
215C22×D47C2×M1612yes—
216Q8×C47—44no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47C4×D412yes—
233C2×C4×C47C4×D412yes—
234C2×C4×C47C2×M1612yes—
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47H(5,𝔽2)11yescharacteristic
238C2×C4×C472−1+411yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47C2×M1612yes—
261C2×Dic47#13112yes—
262C4×D47—44no—
263C4×D47—44no—
264C4×D47—41no—
265C4×D47—41no—
266C4×D47—41no—
267C4×D47—41no—
268C8×C47—41no—
269C8×C47—41no—
270C8×C47—41no—
271C8×C47—41no—
272C47⋊C8—22no—
273C47⋊C8—22no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276#22108—471nomaximal, Sylow
277C22×C47C2×C4×D411yescharacteristic
278C22×C47#51911yescharacteristic
279C22×C47#52011yescharacteristic
280C22×C47C22×M1611yescharacteristic
281C22×C47C2×#13111yescharacteristic
282C22×C47#56811yescharacteristic
283C22×C47#56811yescharacteristic
284C2×D47—22no—
285C2×D47—22no—
286C2×D47—22no—
287C2×D47—41no—
288C2×D47—41no—
289C2×D47—41no—
290C2×D47—41no—
291C4×C47—22no—
292C4×C47—22no—
293C4×C47—22no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47#53611yescharacteristic
298C4×C47#53711yescharacteristic
299C4×C47#54111yescharacteristic
300C4×C47#54211yescharacteristic
301Dic47—22no—
302Dic47—22no—
303Dic47—41no—
304Dic47—41no—
305Dic47—41no—
306Dic47—41no—
307Dic47—41no—
308C2×#446—471no—
309C2×#432—471no—
310C4×C22⋊Q8—471no—
311#1985D4711yescharacteristic, complemented
312#1940—471no—
313#1940—471no—
314#1939—471no—
315#1924—471no—
316#1924—471no—
317#1923—471no—
318#1923—471no—
319#1917—471no—
320#1916—471no—
321#1797—471no—
322#1771—471no—
323C2×C47#232311yescharacteristic
324C2×C47#293311yescharacteristic
325C2×C47D4×M1611yescharacteristic
326C2×C47#298311yescharacteristic
327C2×C47#298511yescharacteristic
328C2×C47#299011yescharacteristic
329C2×C47#299511yescharacteristic
330D47—42no—
331C2×C22⋊Q8—471no—
332C2×C4×Q8C2×D4711yescharacteristic
333C22×C42—471no—
334#446—944no—
335#432—944no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×C4⋊C8—471no—
339C2×C4⋊C8—471no—
340C2×C4⋊C8—471no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8—471no—
343C2×C4⋊C8C2×D4711yescharacteristic
344C2×C22⋊C8—471no—
345C2×C22⋊C8—471no—
346C2×C22⋊C8—471no—
347C2×C22⋊C8—471no—
348C2×#97—471no—
349C2×#97—471no—
350C2×#97—471no—
351C2×#97C2×D4711yescharacteristic
352C2×C4×C8—471no—
353C2×C4×C8—471no—
354#391—471no—
355#389—471no—
356#387—471no—
357#387—471no—
358#385—471no—
359#385—471no—
360#380—471no—
361C4×C4⋊C4—471no—
362C4×C4⋊C4—471no—
363C4×C4⋊C4—471no—
364C4×C22⋊C4—471no—
365C4×C22⋊C4—471no—
366#336—471no—
367#336—471no—
368#336—471no—
369#336—471no—
370#336—471no—
371#336—471no—
372#336C2×D4711yescharacteristic
373#336C2×D4711yescharacteristic
374#336C2×D4711yescharacteristic
375#336C2×D4711yescharacteristic
376C47#2210811yescharacteristic, complemented, Sylow
377C22×Q8C4×D4711yescharacteristic
378C23×C4—471no—
379C23×C4—471no—
380C23×C4—471no—
381C22×C8—471no—
382C22×C8—471no—
383C22×C8—471no—
384C22×C8—471no—
385C22×C8C22×D4711yescharacteristic
386C22×C8C22×D4711yescharacteristic
387C22×C8C22×D4711yescharacteristic
388C22×C8C22×D4711yescharacteristic
389C22⋊Q8—944no—
390C4×Q8—22no—
391C4×Q8—22no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4C4×D4711yescharacteristic
399C2×C4⋊C4C4×D4711yescharacteristic
400C2×C4⋊C4C4×D4711yescharacteristic
401C2×C22⋊C4—471no—
402C2×C22⋊C4—471no—
403C2×C22⋊C4—471no—
404C2×C22⋊C4—471no—
405C2×C42—471no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—471no—
409C2×C42—471no—
410C2×C42—942no—
411C2×C42—942no—
412C2×C42C22×D4711yescharacteristic
413C2×C42C22×D4711yescharacteristic
414C2×C42C22×D4711yescharacteristic
415C4⋊C8—22no—
416C4⋊C8—942no—
417C4⋊C8—942no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421C4⋊C8—1881no—
422C4⋊C8—1881no—
423C22⋊C8—942no—
424C22⋊C8—942no—
425C22⋊C8—1881no—
426C22⋊C8—1881no—
427#97—22no—
428#97—474no—
429#97—942no—
430#97—1881no—
431C4×C8—942no—
432C4×C8—1881no—
433#95—471no—
434#95—471no—
435#95—471no—
436#95—471no—
437#95—471no—
438#95—471no—
439#95—471no—
440#95—471no—
441#95—471no—
442#95—471no—
443C24—471no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—41no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—471no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—1881no—
465C22×C4—1881no—
466C22×C4C2×C4×D4711yescharacteristic
467C22×C4C2×C4×D4711yescharacteristic
468C22×C4C2×C4×D4711yescharacteristic
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4C23×D4711yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—472no—
486C2×C8—472no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—942no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—1881no—
506C22⋊C4—474no—
507C22⋊C4—942no—
508C22⋊C4—1881no—
509C22⋊C4—1881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—942no—
515C42—942no—
516C42—941no—
517C42—941no—
518C42—941no—
519C42—941no—
520C42—941no—
521C42—941no—
522C42D4×D4712yes—
523C42#1062535212yes—
524C23—472no—
525C23—941no—
526C23—941no—
527C23—941no—
528C23—941no—
529C23—941no—
530C23—941no—
531C23C22×C4×D4711yescharacteristic
532Q8—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—1884no—
570C2×C4—1884no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4—1881no—
575C2×C4(C22⋊D47)⋊C412yes—
576C2×C4(C22⋊D47)⋊C412yes—
577C2×C4M16×D4712yes—
578C2×C4C2×D4×D4711yescharacteristic
579C2×C4C2×#1062535211yescharacteristic
580C2×C4#1309407011yescharacteristic
581C2×C4#1309407111yescharacteristic
582C2×C4#1309407211yescharacteristic
583C2×C4#1309407211yescharacteristic
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—942no—
589C8—942no—
590C8—1881no—
591C8—1881no—
592C22—942no—
593C22—942no—
594C22—942no—
595C22—1881no—
596C22—1881no—
597C22—1881no—
598C22—1881no—
599C22C2×(C22⋊D47)⋊C411yescharacteristic
600C22#1568959911yescharacteristic
601C22#1568960511yescharacteristic
602C22C2×M16×D4711yescharacteristic
603C22#131×D4711yescharacteristic
604C22#1568988811yescharacteristic
605C22#1568988911yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—942no—
613C4—942no—
614C4—1881no—
615C4—1881no—
616C4—1881no—
617C4—1881no—
618C4—1881no—
619C4#1568969611yescharacteristic
620C4#1568970311yescharacteristic
621C4#1568973411yescharacteristic
622C4#1568974211yescharacteristic
623C2—1882no—
624C2#2024607311yescharacteristic
625C2#2025211811yescharacteristic
626C2#2025212011yescharacteristic
627C2#2025247011yescharacteristic
628C2#2025248111yescharacteristic
629C2#2025251211yescharacteristic
630C2#2025255711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1985C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1985D47
hypocenterC47#22108
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
1. C2×#15689254C2semidirect
4. #20244111C2semidirect
5. #20244110C2semidirect
6. #20244105C2semidirect
11. #20243950C2semidirect
12. #20243943C2semidirect
14. #20243265C2semidirect
15. C47×#1985C2semidirect
311. #1985D47semidirect
376. C47#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#156892542
C2×#156891782
C4×#130940002
#202441112
#202441102
#202441052
#202440022
#202439992
#202439952
#202439922
#202439502
#202439432
#202433652
#202432652
C47×#19852
#2210847