Finite Group Databasebeta

← #26224547

Subgroups — #26224547

Order 12032.

682 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244003C211yesmaximal, characteristic
2#20243996C211yesmaximal, characteristic
3#20243996C211yesmaximal, characteristic
4#20243954C211yesmaximal, characteristic, complemented
5#20243947C211yesmaximal, characteristic, complemented
6#20243947C211yesmaximal, characteristic, complemented
7#20243533C211yesmaximal, characteristic, complemented
8#20243263C211yesmaximal, characteristic, complemented
9#20243263C211yesmaximal, characteristic, complemented
10#20243257C211yesmaximal, characteristic, complemented
11#20243166C211yesmaximal, characteristic
12#20243166C211yesmaximal, characteristic
13C22⋊C4×C47⋊C8C211yesmaximal, characteristic
14#20243075C211yesmaximal, characteristic, complemented
15C47×#2401C211yesmaximal, characteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×C22⋊(C47⋊C8)C2211yescharacteristic
21C2×C22⋊(C47⋊C8)C2211yescharacteristic
22C2×C22⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093935C2211yescharacteristic
24C2×#13093935C2211yescharacteristic
25C2×#13093935C2211yescharacteristic
26C2×#13093935C2211yescharacteristic
27C2×#13093935C2211yescharacteristic
28C2×C4×C47⋊C8C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32#15688878C2211yescharacteristic
33#15688878C2211yescharacteristic
34#15688878C2211yescharacteristic
35#15688878C2211yescharacteristic
36#15688878C2211yescharacteristic
37#15688878C2211yescharacteristic
38#15688878C2211yescharacteristic
39#15688878C2211yescharacteristic
40#15688878C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44C47×#401C411yescharacteristic
45C47×#400C411yescharacteristic
46C47×#400C411yescharacteristic
47C47×#400C411yescharacteristic
48C47×#397C411yescharacteristic
49C47×#397C411yescharacteristic
50C47×#397C411yescharacteristic
51C47×#396C411yescharacteristic
52C4×C4⋊C4×C47C2211yescharacteristic
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C4×C22⋊C4×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47C2211yescharacteristic
58C47×#376C2211yescharacteristic
59C22×C47⋊C8—22no—
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C4⋊(C47⋊C8)—22no—
71C4⋊(C47⋊C8)—22no—
72C4⋊(C47⋊C8)—22no—
73C22⋊(C47⋊C8)—22no—
74C22⋊(C47⋊C8)—22no—
75C22⋊(C47⋊C8)—22no—
76#13093935—22no—
77#13093935—22no—
78#13093935—22no—
79#13093935—22no—
80#13093935—22no—
81C4×C47⋊C8—22no—
82C4×C47⋊C8—22no—
83C4×C47⋊C8—22no—
84C4×C47⋊C8—22no—
85C23×C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2×C411yescharacteristic
87C2×C4⋊C4×C47C2×C411yescharacteristic
88C2×C4⋊C4×C47C2×C411yescharacteristic
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C22⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C22⋊C4×C47C2×C411yescharacteristic
96C2×C22⋊C4×C47C2×C411yescharacteristic
97C2×C22⋊C4×C47C2×C411yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#95×C47C2×C411yescharacteristic
105#95×C47C2×C411yescharacteristic
106#95×C47C2×C411yescharacteristic
107#95×C47C2×C411yescharacteristic
108#95×C47C2×C411yescharacteristic
109#95×C47C2×C411yescharacteristic
110#95×C47C2×C411yescharacteristic
111#95×C47C2×C411yescharacteristic
112#95×C47C2×C411yescharacteristic
113#95×C47C2×C411yescharacteristic
114#95×C47C2×C411yescharacteristic
115#95×C47C2×C411yescharacteristic
116#95×C47C2×C411yescharacteristic
117#95×C47C2×C411yescharacteristic
118#95×C47C2×C411yescharacteristic
119#95×C47C2×C411yescharacteristic
120C24×C47C22×C411yescharacteristic
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
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×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C2411yescharacteristic
141C4⋊C4×C47—22no—
142C4⋊C4×C47—22no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47—41no—
146C4⋊C4×C47—41no—
147C22⋊C4×C47—22no—
148C22⋊C4×C47—22no—
149C22⋊C4×C47—22no—
150C22⋊C4×C47—22no—
151C22⋊C4×C47—41no—
152C22⋊C4×C47—41no—
153C42×C47—21no—
154C42×C47—21no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—21no—
164C42×C47—21no—
165C2×C47⋊C8—21no—
166C2×C47⋊C8—21no—
167C2×C47⋊C8—21no—
168C2×C47⋊C8—21no—
169C2×C47⋊C8—21no—
170C2×C47⋊C8—21no—
171C2×C47⋊C8—21no—
172C2×C47⋊C8—21no—
173C2×C47⋊C8—21no—
174C2×C47⋊C8—21no—
175C2×C47⋊C8—21no—
176C2×C47⋊C8—21no—
177C2×C47⋊C8—21no—
178C2×C47⋊C8—21no—
179C2×C47⋊C8—21no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—44no—
184C2×C47⋊C8#4112yes—
185C2×C47⋊C8#4112yes—
186C2×C47⋊C8#4112yes—
187C2×C47⋊C8#4112yes—
188C2×C47⋊C8#4112yes—
189C2×C47⋊C8#4112yes—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47#13112yes—
197C23×C47C23×C411yescharacteristic
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
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×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47#13112yes—
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C47⋊C8—22no—
248C47⋊C8—22no—
249C47⋊C8—22no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8#12614yes—
255#21669—471nomaximal, Sylow
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47C4×#4111yescharacteristic
264C22×C47C4×#4111yescharacteristic
265C22×C47C4×#4111yescharacteristic
266C22×C47C2×#13111yescharacteristic
267C22×C47C2×#13111yescharacteristic
268C22×C47#56811yescharacteristic
269C22×C47#56811yescharacteristic
270C4×C47—22no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47C2×#12611yescharacteristic
284C4×C47#52911yescharacteristic
285C4×C47#52911yescharacteristic
286C4×C47#52911yescharacteristic
287#2401D4711yescharacteristic
288#1924—471no—
289#1923—471no—
290#1923—471no—
291#1917—471no—
292#1916—471no—
293#1916—471no—
294#1840—471no—
295#1771—471no—
296#1771—471no—
297#1770—471no—
298#1752—471no—
299#1752—471no—
300C8×C22⋊C4—471no—
301#1726—471no—
302C2×C47—42no—
303C2×C47C4×#12611yescharacteristic
304C2×C47#296611yescharacteristic
305C2×C47#296711yescharacteristic
306C2×C47#296811yescharacteristic
307C2×C47#296811yescharacteristic
308C2×C47#296811yescharacteristic
309C2×C47#296911yescharacteristic
310C23×C8—471no—
311C2×C4⋊C8—471no—
312C2×C4⋊C8—471no—
313C2×C4⋊C8—471no—
314C2×C22⋊C8—471no—
315C2×C22⋊C8—471no—
316C2×C22⋊C8—471no—
317C2×#97—471no—
318C2×#97—471no—
319C2×#97—471no—
320C2×#97—471no—
321C2×#97—471no—
322C2×C4×C8—471no—
323C2×C4×C8—471no—
324C2×C4×C8—471no—
325C2×C4×C8—471no—
326#401Dic4711yescharacteristic
327#400Dic4711yescharacteristic
328#400Dic4711yescharacteristic
329#400Dic4711yescharacteristic
330#397Dic4711yescharacteristic
331#397Dic4711yescharacteristic
332#397Dic4711yescharacteristic
333#396Dic4711yescharacteristic
334C4×C4⋊C4C2×D4711yescharacteristic
335C4×C4⋊C4C2×D4711yescharacteristic
336C4×C4⋊C4C2×D4711yescharacteristic
337C4×C22⋊C4C2×D4711yescharacteristic
338C4×C22⋊C4C2×D4711yescharacteristic
339C4×C22⋊C4C2×D4711yescharacteristic
340#376C2×D4711yescharacteristic
341#336—471no—
342#336—471no—
343#336—471no—
344#336—471no—
345#336—471no—
346#336—471no—
347#336—471no—
348#336—471no—
349#336—471no—
350#336—471no—
351#336—471no—
352#336—471no—
353C47#2166911yescharacteristic, complemented, Sylow
354C23×C4C22×D4711yescharacteristic
355C22×C8—471no—
356C22×C8—471no—
357C22×C8—471no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C22×C8—471no—
362C22×C8—471no—
363C22×C8—942no—
364C22×C8—942no—
365C22×C8—942no—
366C2×C4⋊C4C2×Dic4711yescharacteristic
367C2×C4⋊C4C2×Dic4711yescharacteristic
368C2×C4⋊C4C2×Dic4711yescharacteristic
369C2×C4⋊C4C2×Dic4711yescharacteristic
370C2×C4⋊C4C2×Dic4711yescharacteristic
371C2×C4⋊C4C2×Dic4711yescharacteristic
372C2×C22⋊C4C2×Dic4711yescharacteristic
373C2×C22⋊C4C2×Dic4711yescharacteristic
374C2×C22⋊C4C2×Dic4711yescharacteristic
375C2×C22⋊C4C2×Dic4711yescharacteristic
376C2×C22⋊C4C2×Dic4711yescharacteristic
377C2×C22⋊C4C2×Dic4711yescharacteristic
378C2×C42C22×D4711yescharacteristic
379C2×C42C22×D4711yescharacteristic
380C2×C42C22×D4711yescharacteristic
381C2×C42C22×D4711yescharacteristic
382C2×C42C22×D4711yescharacteristic
383C2×C42C22×D4711yescharacteristic
384C4⋊C8—942no—
385C4⋊C8—942no—
386C4⋊C8—942no—
387C22⋊C8—942no—
388C22⋊C8—942no—
389C22⋊C8—942no—
390#97—942no—
391#97—942no—
392#97—942no—
393#97—942no—
394#97—942no—
395C4×C8—942no—
396C4×C8—942no—
397C4×C8—942no—
398C4×C8—942no—
399#95C2×Dic4711yescharacteristic
400#95C2×Dic4711yescharacteristic
401#95C2×Dic4711yescharacteristic
402#95C2×Dic4711yescharacteristic
403#95C2×Dic4711yescharacteristic
404#95C2×Dic4711yescharacteristic
405#95C2×Dic4711yescharacteristic
406#95C2×Dic4711yescharacteristic
407#95C2×Dic4711yescharacteristic
408#95C2×Dic4711yescharacteristic
409#95C2×Dic4711yescharacteristic
410#95C2×Dic4711yescharacteristic
411#95C2×Dic4711yescharacteristic
412#95C2×Dic4711yescharacteristic
413#95C2×Dic4711yescharacteristic
414#95C2×Dic4711yescharacteristic
415C24C22×Dic4711yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4C22×Dic4711yescharacteristic
423C22×C4C22×Dic4711yescharacteristic
424C22×C4C22×Dic4711yescharacteristic
425C22×C4C22×Dic4711yescharacteristic
426C22×C4C22×Dic4711yescharacteristic
427C22×C4C22×Dic4711yescharacteristic
428C22×C4C22×Dic4711yescharacteristic
429C22×C4C22×Dic4711yescharacteristic
430C22×C4C22×Dic4711yescharacteristic
431C22×C4C22×Dic4711yescharacteristic
432C22×C4C22×Dic4711yescharacteristic
433C22×C4C22×Dic4711yescharacteristic
434C22×C4C22×Dic4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436C2×C8—472no—
437C2×C8—472no—
438C2×C8—472no—
439C2×C8—472no—
440C2×C8—472no—
441C2×C8—472no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—1884no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23#1309403112yes—
492C23C23×Dic4711yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4#1309403112yes—
536C2×C4#41×D4711yescharacteristic
537C2×C4#41×D4711yescharacteristic
538C2×C4#41×D4711yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C2×C4#41×D4711yescharacteristic
541C2×C4#41×D4711yescharacteristic
542C8—474no—
543C8—942no—
544C8—942no—
545C8—942no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22#41×Dic4711yescharacteristic
558C22#41×Dic4711yescharacteristic
559C22#41×Dic4711yescharacteristic
560C22C2×#1309403111yescharacteristic
561C22C2×#1309403111yescharacteristic
562C22#1568989011yescharacteristic
563C22#1568989011yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4#126×D4711yescharacteristic
578C4#1568965611yescharacteristic
579C4#1568965611yescharacteristic
580C4#1568965611yescharacteristic
581C2—42no—
582C2#126×Dic4711yescharacteristic
583C2#2025236411yescharacteristic
584C2#2025237511yescharacteristic
585C2#2025238411yescharacteristic
586C2#2025238411yescharacteristic
587C2#2025238411yescharacteristic
588C2#2025239311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#2401C2
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenter#2401D47
hypocenterC47#21669
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
4. #20243954C2semidirect
5. #20243947C2semidirect
6. #20243947C2semidirect
7. #20243533C2semidirect
8. #20243263C2semidirect
9. #20243263C2semidirect
10. #20243257C2semidirect
14. #20243075C2semidirect
353. C47#21669semidirect

Maximal subgroups

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

subgroupindex
#202440032
#202439962
#202439542
#202439472
#202435332
#202432632
#202432572
#202431662
C22⋊C4×C47⋊C82
#202430752
C47×#24012
#2166947