Finite Group Databasebeta

← #26242816

Subgroups — #26242816

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246675C211yesmaximal, characteristic
2#20244328C211yesmaximal, characteristic, complemented
3#20244326C211yesmaximal, characteristic, complemented
4#20244001C211yesmaximal, characteristic, complemented
5#20244000C211yesmaximal, characteristic, complemented
6#20243998C211yesmaximal, characteristic, complemented
7#20243683C211yesmaximal, characteristic
8#20243677C211yesmaximal, characteristic
9#20243573C211yesmaximal, characteristic, complemented
10#20243570C211yesmaximal, characteristic, complemented
11#20243567C211yesmaximal, characteristic, complemented
12#20243567C211yesmaximal, characteristic, complemented
13#20243507C211yesmaximal, characteristic, complemented
14#20243506C211yesmaximal, characteristic, complemented
15C47×#1924C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×#13093934C2211yescharacteristic
30#15689065C411yescharacteristic
31#15689064C411yescharacteristic
32#15689052C411yescharacteristic
33#15689051C411yescharacteristic
34#15689039C411yescharacteristic
35#15689038C411yescharacteristic
36#15689036C411yescharacteristic
37#15689035C411yescharacteristic
38C4×(C2×D47)⋊C4C2211yescharacteristic
39C4×(C2×D47)⋊C4C2211yescharacteristic
40C4×C22⋊Dic47C2211yescharacteristic
41#15688969C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688877C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Dic94C2×C411yescharacteristic
60C22×C22⋊D47C2×C411yescharacteristic
61C22×C4×D47C2311yescharacteristic
62C2×#10625329—41no—
63C2×#10625329—41no—
64C2×#10625329—41no—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C2×C8×D47—41no—
70C2×C8×D47—41no—
71C2×C8×D47—41no—
72C4×Dic94—41no—
73C4×Dic94—41no—
74C4×C22⋊D47—41no—
75C4×C22⋊D47—41no—
76C2×C4⋊Dic47C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×(C2×D47)⋊C4C2×C411yescharacteristic
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C4⋊(C47⋊C8)—41no—
92C4⋊(C47⋊C8)—41no—
93Dic47⋊C8—41no—
94Dic47⋊C8—41no—
95Dic47⋊C8—41no—
96C22⋊(C47⋊C8)—41no—
97(C2×D47)⋊C8—41no—
98(C2×D47)⋊C8—41no—
99(C2×D47)⋊C8—41no—
100#13093934—41no—
101C47⋊#95C2×C411yescharacteristic
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
111C23×C4×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C22⋊C4×C47C2×C411yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—41no—
121C22⋊C8×C47—41no—
122C22⋊C8×C47—41no—
123#97×C47—41no—
124#95×C47C2×C411yescharacteristic
125#95×C47C2×C411yescharacteristic
126C24×C47C22×C411yescharacteristic
127C23×D47C22×C411yescharacteristic
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C2411yescharacteristic
140C2×C22⋊D47—22no—
141C2×C22⋊D47—41no—
142C2×C22⋊D47—41no—
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C22×Dic47C22×C411yescharacteristic
146C22×Dic47C22×C411yescharacteristic
147C22×Dic47C22×C411yescharacteristic
148C22×Dic47C22×C411yescharacteristic
149C22×Dic47C22×C411yescharacteristic
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×Dic94—41no—
157C2×Dic94—41no—
158C2×Dic94—41no—
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—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C22⋊Dic47—41no—
178C22⋊Dic47—41no—
179C22⋊Dic47—41no—
180(C2×D47)⋊C4—22no—
181(C2×D47)⋊C4—22no—
182(C2×D47)⋊C4—41no—
183(C2×D47)⋊C4—41no—
184(C2×D47)⋊C4—41no—
185C4⋊Dic47—41no—
186Dic47⋊C4—41no—
187Dic47⋊C4—41no—
188Dic47⋊C4—41no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195#10625329—44no—
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⋊C8—21no—
207C2×C47⋊C8—21no—
208C8×D47—44no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47C23×C411yescharacteristic
217C22×D47—21no—
218C22×D47—21no—
219C22×D47—21no—
220C22×D47—21no—
221C22×D47—21no—
222C22×D47—21no—
223C22×D47#13112yes—
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×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47H(5,𝔽2)11yescharacteristic
244C2×C4×C47H(5,𝔽2)11yescharacteristic
245C2×C4×C47H(5,𝔽2)11yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C2×C4×C472−1+411yescharacteristic
249C22⋊D47—44no—
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×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
270C2×Dic47—21no—
271C4×D47—41no—
272C4×D47—41no—
273C4×D47—41no—
274C4×D47—41no—
275Dic94—44no—
276C8×C47—41no—
277C8×C47—41no—
278C8×C47—41no—
279C8×C47—41no—
280C47⋊C8—41no—
281C47⋊C8—41no—
282C47⋊C8—41no—
283C47⋊C8—41no—
284#23354—471nomaximal, Sylow
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47#51811yescharacteristic
293C22×C47#52011yescharacteristic
294C22×C47#52011yescharacteristic
295C22×C47C2×#13111yescharacteristic
296C22×C47#56811yescharacteristic
297C22×C47#56811yescharacteristic
298C22×C47#56811yescharacteristic
299C2×D47—22no—
300C2×D47—22no—
301C2×D47—22no—
302C2×D47—41no—
303C2×D47—41no—
304C2×D47—41no—
305C2×D47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—41no—
309C4×C47—41no—
310C4×C47—41no—
311C4×C47H(3,𝔽4)11yescharacteristic
312C4×C47#56211yescharacteristic
313C4×C47#56211yescharacteristic
314C4×C47#56311yescharacteristic
315Dic47—41no—
316Dic47—41no—
317Dic47—41no—
318Dic47—41no—
319Dic47—41no—
320Dic47—41no—
321Dic47—41no—
322#2398—471no—
323#1985—471no—
324#1985—471no—
325#1924—471no—
326#1924—471no—
327#1924—471no—
328#1924D4711yescharacteristic, complemented
329#1870—471no—
330#1869—471no—
331#1851—471no—
332#1851—471no—
333#1850—471no—
334#1850—471no—
335#1832—471no—
336#1832—471no—
337C2×C47—81no—
338C2×C47#237911yescharacteristic
339C2×C47#297611yescharacteristic
340C2×C47#297811yescharacteristic
341C2×C47#299211yescharacteristic
342C2×C47#299211yescharacteristic
343C2×C47#299511yescharacteristic
344C2×C47#299511yescharacteristic
345D47—42no—
346C22×M16—471no—
347C23×C8—471no—
348C2×C4×Q8—471no—
349C2×C4×D4—471no—
350C2×C4⋊C8—471no—
351C2×C4⋊C8—471no—
352C2×C4⋊C8—471no—
353C2×C4⋊C8—471no—
354C2×C4⋊C8—471no—
355C2×C4⋊C8C2×D4711yescharacteristic
356C2×C22⋊C8—471no—
357C2×C22⋊C8—471no—
358C2×C22⋊C8—471no—
359C2×C22⋊C8—471no—
360C2×C22⋊C8C2×D4711yescharacteristic
361C2×C22⋊C8C2×D4711yescharacteristic
362C2×#97—471no—
363C2×#97C2×D4711yescharacteristic
364#400—471no—
365#400—471no—
366#397—471no—
367#397—471no—
368#394—471no—
369#394—471no—
370#393—471no—
371#393—471no—
372C4×C22⋊C4—471no—
373C4×C22⋊C4—471no—
374C4×C22⋊C4—471no—
375C4×C22⋊C4C2×D4711yescharacteristic
376#376—471no—
377#336—471no—
378#336—471no—
379#336—471no—
380#336—471no—
381#336—471no—
382#336—471no—
383#336—471no—
384#336—471no—
385#336—471no—
386#336—471no—
387#336C2×D4711yescharacteristic
388#336C2×D4711yescharacteristic
389C47#2335411yescharacteristic, complemented, Sylow
390C22×Q8—471no—
391C22×D4—471no—
392C23×C4—471no—
393C23×C4C22×D4711yescharacteristic
394C2×M16—1881no—
395C2×M16—1881no—
396C2×M16—1881no—
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—471no—
400C22×C8—471no—
401C22×C8—1881no—
402C22×C8—1881no—
403C22×C8—1881no—
404C22×C8C22×D4711yescharacteristic
405C22×C8C22×D4711yescharacteristic
406C22×C8C22×D4711yescharacteristic
407C22×C8C22×D4711yescharacteristic
408C4×Q8—1881no—
409C4×Q8—1881no—
410C4×D4—1881no—
411C4×D4—1881no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C4⋊C4—471no—
415C2×C4⋊C4—471no—
416C2×C22⋊C4—471no—
417C2×C22⋊C4—471no—
418C2×C22⋊C4—471no—
419C2×C22⋊C4—471no—
420C2×C22⋊C4—471no—
421C2×C22⋊C4—471no—
422C2×C22⋊C4—471no—
423C2×C22⋊C4—471no—
424C2×C22⋊C4C4×D4711yescharacteristic
425C2×C22⋊C4C4×D4711yescharacteristic
426C2×C42—471no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42C22×D4711yescharacteristic
430C2×C42C22×D4711yescharacteristic
431C4⋊C8—41no—
432C4⋊C8—1881no—
433C4⋊C8—1881no—
434C4⋊C8—1881no—
435C4⋊C8—1881no—
436C4⋊C8—1881no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—1881no—
440C22⋊C8—1881no—
441C22⋊C8—1881no—
442C22⋊C8—1881no—
443#97—41no—
444#97—1881no—
445#95—471no—
446#95—471no—
447#95—471no—
448#95—471no—
449#95—471no—
450#95—471no—
451#95—471no—
452#95—471no—
453#95—471no—
454#95—471no—
455#95C4×D4711yescharacteristic
456#95C4×D4711yescharacteristic
457C24—471no—
458C24C2×C4×D4711yescharacteristic
459C2×Q8—1881no—
460C2×Q8—1881no—
461C2×Q8—1881no—
462C2×D4—942no—
463C2×D4—1881no—
464C2×D4—1881no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4C2×C4×D4711yescharacteristic
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4C2×C4×D4711yescharacteristic
487C22×C4C2×C4×D4711yescharacteristic
488C22×C4C2×C4×D4711yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—1884no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—1884no—
516C4⋊C4—1881no—
517C4⋊C4—1881no—
518C4⋊C4—1881no—
519C4⋊C4—1881no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—942no—
523C22⋊C4—942no—
524C22⋊C4—1881no—
525C22⋊C4—1881no—
526C22⋊C4—1881no—
527C22⋊C4—1881no—
528C22⋊C4—1881no—
529C22⋊C4—1881no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—941no—
535C42—941no—
536C42—941no—
537C42—941no—
538C42—941no—
539C42—941no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—472no—
548C23—941no—
549C23—941no—
550C23—941no—
551C23—941no—
552C23—941no—
553C23—941no—
554C23C22×C4×D4711yescharacteristic
555Q8—1884no—
556D4—1884no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—941no—
583C2×C4—941no—
584C2×C4—941no—
585C2×C4—941no—
586C2×C4—941no—
587C2×C4—941no—
588C2×C4—941no—
589C2×C4—941no—
590C2×C4—941no—
591C2×C4—941no—
592C2×C4—941no—
593C2×C4—941no—
594C2×C4—941no—
595C2×C4—941no—
596C2×C4—941no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4#1309406911yescharacteristic
602C2×C4#1309406911yescharacteristic
603C2×C4#1309407011yescharacteristic
604C2×C4#1309407011yescharacteristic
605C2×C4#1309407111yescharacteristic
606C2×C4#1309407111yescharacteristic
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—1881no—
612C8—1881no—
613C8—1881no—
614C8—1881no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—942no—
623C22—942no—
624C22—942no—
625C22—1881no—
626C22—1881no—
627C22—1881no—
628C22—1881no—
629C22#1568959511yescharacteristic
630C22#1568960211yescharacteristic
631C22#1568960311yescharacteristic
632C22#131×D4711yescharacteristic
633C22#1568988811yescharacteristic
634C22#1568988911yescharacteristic
635C22#1568988911yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—1881no—
642C4—1881no—
643C4—1881no—
644C4—1881no—
645C4—1881no—
646C4—1881no—
647C4—1881no—
648C4#1568986511yescharacteristic
649C4#1568986811yescharacteristic
650C4#1568987011yescharacteristic
651C4#1568987511yescharacteristic
652C2—81no—
653C2—1882no—
654C2#2024655711yescharacteristic
655C2#2025243211yescharacteristic
656C2#2025244711yescharacteristic
657C2#2025252211yescharacteristic
658C2#2025252311yescharacteristic
659C2#2025255911yescharacteristic
660C2#2025256011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1924C2
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1924D47
hypocenterC47#23354
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. #20244328C2semidirect
3. #20244326C2semidirect
4. #20244001C2semidirect
5. #20244000C2semidirect
6. #20243998C2semidirect
9. #20243573C2semidirect
10. #20243570C2semidirect
11. #20243567C2semidirect
12. #20243567C2semidirect
13. #20243507C2semidirect
14. #20243506C2semidirect
15. C47×#1924C2semidirect
328. #1924D47semidirect
389. C47#23354semidirect

Maximal subgroups

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

subgroupindex
#202466752
#202443282
#202443262
#202440012
#202440002
#202439982
#202436832
#202436772
#202435732
#202435702
#202435672
#202435072
#202435062
C47×#19242
#2335447