Finite Group Databasebeta

← #26243056

Subgroups — #26243056

Order 12032.

606 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#20246689C211yesmaximal, characteristic
2#20244111C211yesmaximal, characteristic, complemented
3#20244110C211yesmaximal, characteristic, complemented
4#20244107C211yesmaximal, characteristic, complemented
5#20244002C211yesmaximal, characteristic
6#20244001C211yesmaximal, characteristic
7#20243992C211yesmaximal, characteristic
8#20243951C211yesmaximal, characteristic, complemented
9#20243943C211yesmaximal, characteristic, complemented
10#20243572C211yesmaximal, characteristic
11#20243572C211yesmaximal, characteristic
12#20243569C211yesmaximal, characteristic
13#20243541C211yesmaximal, characteristic, complemented
14#20243532C211yesmaximal, characteristic, complemented
15C47×#1917C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×Dic47⋊C8C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×(C2×D47)⋊C8C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×#13093934C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30C47⋊#401C411yescharacteristic
31#15689065C411yescharacteristic
32#15689062C411yescharacteristic
33#15689061C411yescharacteristic
34#15689052C411yescharacteristic
35#15689050C411yescharacteristic
36#15689049C411yescharacteristic
37#15689045C411yescharacteristic
38C4×Dic47⋊C4C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×(C2×D47)⋊C4C2211yescharacteristic
41C4×(C2×D47)⋊C4C2211yescharacteristic
42C4×(C2×D47)⋊C4C2211yescharacteristic
43#15688969C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×C4×D47C2311yescharacteristic
60C2×#10625324—41no—
61C2×#10625324—41no—
62C2×#10625324—41no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C2×C4⋊Dic47C2×C411yescharacteristic
68C2×C4⋊Dic47C2×C411yescharacteristic
69C2×Dic47⋊C4C2×C411yescharacteristic
70C2×Dic47⋊C4C2×C411yescharacteristic
71C2×(C2×D47)⋊C4C2×C411yescharacteristic
72C2×(C2×D47)⋊C4C2×C411yescharacteristic
73C2×(C2×D47)⋊C4C2×C411yescharacteristic
74C2×(C2×D47)⋊C4C2×C411yescharacteristic
75C2×(C2×D47)⋊C4C2×C411yescharacteristic
76C2×(C2×D47)⋊C4C2×C411yescharacteristic
77C2×C4×Dic47C2311yescharacteristic
78C2×C4×Dic47C2311yescharacteristic
79C2×C4×Dic47C2311yescharacteristic
80C4⋊(C47⋊C8)—41no—
81C4⋊(C47⋊C8)—41no—
82C4⋊(C47⋊C8)—41no—
83Dic47⋊C8—41no—
84Dic47⋊C8—41no—
85Dic47⋊C8—41no—
86Dic47⋊C8—41no—
87Dic47⋊C8—41no—
88(C2×D47)⋊C8—41no—
89(C2×D47)⋊C8—41no—
90(C2×D47)⋊C8—41no—
91#13093934—41no—
92C4×C47⋊C8—41no—
93C47⋊#95C2×C411yescharacteristic
94C47⋊#95C2×C411yescharacteristic
95C47⋊#95C2×C411yescharacteristic
96C47⋊#95C2×C411yescharacteristic
97C47⋊#95C2×C411yescharacteristic
98C47⋊#95C2×C411yescharacteristic
99C47⋊#95C2×C411yescharacteristic
100C47⋊#95C2×C411yescharacteristic
101C47⋊#95C2×C411yescharacteristic
102C47⋊#95C2×C411yescharacteristic
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2×C411yescharacteristic
112C2×C4⋊C4×C47C2×C411yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C4⋊C8×C47—41no—
117#97×C47—41no—
118#95×C47C2×C411yescharacteristic
119#95×C47C2×C411yescharacteristic
120C23×D47C22×C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C2411yescharacteristic
128C22×Dic47C22×C411yescharacteristic
129C22×Dic47C22×C411yescharacteristic
130C22×Dic47C22×C411yescharacteristic
131C22×Dic47C22×C411yescharacteristic
132C22×Dic47C22×C411yescharacteristic
133C22×Dic47C22×C411yescharacteristic
134C22×Dic47C22×C411yescharacteristic
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—21no—
141C2×C8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—41no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161(C2×D47)⋊C4—22no—
162(C2×D47)⋊C4—41no—
163(C2×D47)⋊C4—41no—
164(C2×D47)⋊C4—41no—
165(C2×D47)⋊C4—41no—
166(C2×D47)⋊C4—41no—
167C4⋊Dic47—41no—
168C4⋊Dic47—41no—
169Dic47⋊C4—22no—
170Dic47⋊C4—41no—
171C4×Dic47—21no—
172C4×Dic47—21no—
173C4×Dic47—21no—
174C4×Dic47—21no—
175C4×Dic47—21no—
176C4×Dic47—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—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189#10625324—44no—
190C23×C47C23×C411yescharacteristic
191C22×D47—21no—
192C22×D47—21no—
193C22×D47—21no—
194C22×D47—21no—
195C22×D47—21no—
196C22×D47—21no—
197C22×D47—21no—
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#13112yes—
216C2×C4×C47H(5,𝔽2)11yescharacteristic
217C2×C4×C47H(5,𝔽2)11yescharacteristic
218C2×C4×C47H(5,𝔽2)11yescharacteristic
219C2×C4×C472−1+411yescharacteristic
220C2×C4×C472−1+411yescharacteristic
221C2×C4×C472−1+411yescharacteristic
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C4×D47—41no—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#23382—471nomaximal, Sylow
256C22×C47#52011yescharacteristic
257C22×C47#52011yescharacteristic
258C22×C47#52011yescharacteristic
259C22×C47C2×#13111yescharacteristic
260C22×C47#56811yescharacteristic
261C22×C47#56811yescharacteristic
262C22×C47#56811yescharacteristic
263C2×D47—41no—
264C2×D47—41no—
265C2×D47—41no—
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C2×D47—41no—
270C4×C47—22no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47#56011yescharacteristic
277C4×C47#56311yescharacteristic
278C4×C47#56311yescharacteristic
279C4×C47#56311yescharacteristic
280Dic47—41no—
281Dic47—41no—
282Dic47—41no—
283Dic47—41no—
284Dic47—41no—
285Dic47—41no—
286Dic47—41no—
287#2401—471no—
288#1940—471no—
289#1940—471no—
290#1939—471no—
291#1924—471no—
292#1924—471no—
293#1923—471no—
294#1917—471no—
295#1917D4711yescharacteristic, complemented
296#1916—471no—
297#1851—471no—
298#1851—471no—
299#1851—471no—
300#1843—471no—
301#1840—471no—
302C2×C47#238311yescharacteristic
303C2×C47#299211yescharacteristic
304C2×C47#299311yescharacteristic
305C2×C47#299311yescharacteristic
306C2×C47#299511yescharacteristic
307C2×C47#299511yescharacteristic
308C2×C47#299511yescharacteristic
309D47—81no—
310C22×M16—471no—
311C2×C4⋊C8—471no—
312C2×C4⋊C8—471no—
313C2×C4⋊C8—471no—
314C2×C4⋊C8—471no—
315C2×C4⋊C8—471no—
316C2×C4⋊C8—471no—
317C2×C4⋊C8—471no—
318C2×C4⋊C8—471no—
319C2×C4⋊C8C2×D4711yescharacteristic
320C2×C22⋊C8—471no—
321C2×C22⋊C8—471no—
322C2×C22⋊C8—471no—
323C2×#97—471no—
324C2×#97C2×D4711yescharacteristic
325C2×C4×C8—471no—
326#401—471no—
327#400—471no—
328#400—471no—
329#400—471no—
330#397—471no—
331#397—471no—
332#397—471no—
333#396—471no—
334C4×C4⋊C4—471no—
335C4×C4⋊C4—471no—
336C4×C4⋊C4C2×D4711yescharacteristic
337C4×C22⋊C4—471no—
338C4×C22⋊C4—471no—
339C4×C22⋊C4—471no—
340#376—471no—
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#336C2×D4711yescharacteristic
350#336C2×D4711yescharacteristic
351#336C2×D4711yescharacteristic
352#336C2×D4711yescharacteristic
353C47#2338211yescharacteristic, complemented, Sylow
354C23×C4—471no—
355C2×M16—1881no—
356C2×M16—1881no—
357C2×M16—1881no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C22×C8—471no—
362C22×C8C22×D4711yescharacteristic
363C22×C8C22×D4711yescharacteristic
364C22×C8C22×D4711yescharacteristic
365C22×C8C22×D4711yescharacteristic
366C2×C4⋊C4—471no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4C4×D4711yescharacteristic
371C2×C4⋊C4C4×D4711yescharacteristic
372C2×C22⋊C4—471no—
373C2×C22⋊C4—471no—
374C2×C22⋊C4—471no—
375C2×C22⋊C4—471no—
376C2×C22⋊C4—471no—
377C2×C22⋊C4—471no—
378C2×C42—471no—
379C2×C42—471no—
380C2×C42—471no—
381C2×C42C22×D4711yescharacteristic
382C2×C42C22×D4711yescharacteristic
383C2×C42C22×D4711yescharacteristic
384C4⋊C8—41no—
385C4⋊C8—1881no—
386C4⋊C8—1881no—
387C4⋊C8—1881no—
388C4⋊C8—1881no—
389C4⋊C8—1881no—
390C4⋊C8—1881no—
391C4⋊C8—1881no—
392C4⋊C8—1881no—
393C22⋊C8—1881no—
394C22⋊C8—1881no—
395C22⋊C8—1881no—
396#97—41no—
397#97—1881no—
398C4×C8—1881no—
399#95—471no—
400#95—471no—
401#95—471no—
402#95—471no—
403#95—471no—
404#95—471no—
405#95—471no—
406#95—471no—
407#95—471no—
408#95—471no—
409#95—471no—
410#95—471no—
411#95—471no—
412#95—471no—
413#95C4×D4711yescharacteristic
414#95C4×D4711yescharacteristic
415C24—471no—
416C22×C4—471no—
417C22×C4—471no—
418C22×C4—471no—
419C22×C4—471no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—471no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4C2×C4×D4711yescharacteristic
430C22×C4C2×C4×D4711yescharacteristic
431C22×C4C2×C4×D4711yescharacteristic
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4C2×C4×D4711yescharacteristic
434C22×C4C2×C4×D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436M16—1884no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
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—941no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—942no—
464C4⋊C4—1881no—
465C4⋊C4—1881no—
466C4⋊C4—1881no—
467C22⋊C4—942no—
468C22⋊C4—1881no—
469C22⋊C4—1881no—
470C22⋊C4—1881no—
471C22⋊C4—1881no—
472C22⋊C4—1881no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—941no—
480C42—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42—941no—
485C23—941no—
486C23—941no—
487C23—941no—
488C23—941no—
489C23—941no—
490C23—941no—
491C23—941no—
492C23C22×C4×D4711yescharacteristic
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—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—941no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4#1309403212yes—
536C2×C4#1309406911yescharacteristic
537C2×C4#1309407011yescharacteristic
538C2×C4#1309407011yescharacteristic
539C2×C4#1309407111yescharacteristic
540C2×C4#1309407111yescharacteristic
541C2×C4#1309407211yescharacteristic
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C22—1881no—
551C22—1881no—
552C22—1881no—
553C22—1881no—
554C22—1881no—
555C22—1881no—
556C22—1881no—
557C22#1568960211yescharacteristic
558C22#1568960311yescharacteristic
559C22#1568960511yescharacteristic
560C22C2×#1309403211yescharacteristic
561C22#1568988811yescharacteristic
562C22#1568988811yescharacteristic
563C22#1568988911yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—1881no—
571C4—1881no—
572C4—1881no—
573C4—1881no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4#1568986311yescharacteristic
578C4#1568987411yescharacteristic
579C4#1568987511yescharacteristic
580C4#1568987711yescharacteristic
581C2—3761no—
582C2#2024657811yescharacteristic
583C2#2025252911yescharacteristic
584C2#2025253211yescharacteristic
585C2#2025254011yescharacteristic
586C2#2025255311yescharacteristic
587C2#2025255711yescharacteristic
588C2#2025255911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1917C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1917D47
hypocenterC47#23382
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #20244111C2semidirect
3. #20244110C2semidirect
4. #20244107C2semidirect
8. #20243951C2semidirect
9. #20243943C2semidirect
13. #20243541C2semidirect
14. #20243532C2semidirect
15. C47×#1917C2semidirect
295. #1917D47semidirect
353. C47#23382semidirect

Maximal subgroups

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

subgroupindex
#202466892
#202441112
#202441102
#202441072
#202440022
#202440012
#202439922
#202439512
#202439432
#202435722
#202435692
#202435412
#202435322
C47×#19172
#2338247