Finite Group Databasebeta

← #26288931

Subgroups — #26288931

Order 12032.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246402C211yesmaximal, characteristic
2#20244792C211yesmaximal, characteristic, complemented
3#20244773C211yesmaximal, characteristic, complemented
4#20244570C211yesmaximal, characteristic
5#20244570C211yesmaximal, characteristic
6#20244144C211yesmaximal, characteristic, complemented
7#20244118C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic, complemented
9#20243959C211yesmaximal, characteristic, complemented
10#20243956C211yesmaximal, characteristic, complemented
11#20243634C211yesmaximal, characteristic, complemented
12#20243575C211yesmaximal, characteristic, complemented
13#20243472C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C47×#2496C211yesmaximal, characteristic, complemented
16C2×#13093998C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×(C22⋊D47)⋊C4—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32#15689025C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689015—21no—
35#15689000—21no—
36#15688997—21no—
37C4×C4⋊Dic47C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#126×C47—21no—
49C47×#400—21no—
50C47×#397—21no—
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#387—21no—
54C47×#384C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C22⋊D47—21no—
61C23×Dic47—21no—
62C22×C4×D47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13093998—22no—
68#13093998—22no—
69C4×D188—22no—
70C4×D188—41no—
71(C22⋊D47)⋊C4—44no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—41no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×C4×Dic47—21no—
84#13093957—22no—
85#13093957—22no—
86#13093957—22no—
87#13093957—41no—
88C4⋊(C47⋊C8)—22no—
89#13093944—22no—
90#13093944—22no—
91#13093944—22no—
92#13093944—41no—
93C22⋊(C47⋊C8)—22no—
94C22⋊(C47⋊C8)—41no—
95C4×C47⋊C8—41no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C23×C4×C47C2311yescharacteristic
99#126×C47—44no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47D411yescharacteristic
111C2×C22⋊C4×C47D411yescharacteristic
112C2×C42×C47—21no—
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47D411yescharacteristic
121#95×C47D411yescharacteristic
122C24×C47C2×D411yescharacteristic
123C23×D47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
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×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2411yescharacteristic
140C2×C22⋊D47—24no—
141C2×C22⋊D47—42no—
142C2×C22⋊D47—42no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—81no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188#4112yes—
155C2×C4×D47—42no—
156C2×C4×D47—42no—
157C2×C4×D47—81no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—42no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C22⋊C4×C47—41no—
171C22⋊C4×C47—42no—
172C22⋊C4×C47—42no—
173C22⋊C4×C47D814yes—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C42×C47—21no—
178C42×C47—42no—
179(C2×D47)⋊C4—24no—
180(C2×D47)⋊C4—42no—
181(C2×D47)⋊C4—42no—
182(C2×D47)⋊C4—81no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—42no—
188C4⋊Dic47#4112yes—
189C4⋊Dic47#4112yes—
190Dic47⋊C4—42no—
191C4×Dic47—42no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—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#4112yes—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47C2×D812yes—
211C23×C47C22×D411yescharacteristic
212C22×D47—22no—
213C22×D47—41no—
214C22×D47—41no—
215C22×D47—41no—
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—41no—
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—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47C2×D812yes—
249C2×C4×C47C2×D812yes—
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47H(5,𝔽2)11yescharacteristic
255C2×C4×C472−1+411yescharacteristic
256C22⋊D47—48no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—84no—
267D188—22no—
268D188—22no—
269D188—41no—
270D188—41no—
271C4×D47—84no—
272C47⋊C8—22no—
273C47⋊C8—41no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276#27030—471nomaximal, Sylow
277C22×C47—22no—
278C22×C47—22no—
279C22×C47—22no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47#52511yescharacteristic
285C22×C47#54611yescharacteristic
286C22×C47#54711yescharacteristic
287C22×C47C22×D811yescharacteristic
288C22×C47#57511yescharacteristic
289C22×C47#57711yescharacteristic
290C22×C47#57811yescharacteristic
291C2×D47—42no—
292C2×D47—42no—
293C2×D47—42no—
294C2×D47—81no—
295C2×D47—81no—
296C2×D47—81no—
297C2×D47—81no—
298C4×C47—22no—
299C4×C47—22no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—81no—
304C4×C47—81no—
305C4×C47—81no—
306C4×C47—81no—
307C4×C47#52911yescharacteristic
308C4×C47#53911yescharacteristic
309C4×C47#55311yescharacteristic
310C4×C47#55611yescharacteristic
311Dic47—42no—
312Dic47—42no—
313Dic47—81no—
314#2496D4711yescharacteristic, complemented
315#2361—471no—
316#2071—471no—
317#2067—471no—
318#2033—471no—
319#2033—471no—
320#1947—471no—
321#1942—471no—
322#1923—471no—
323#1918—471no—
324#1918—471no—
325#1862—471no—
326#1852—471no—
327#1823—471no—
328C4×#102—471no—
329C2×C47—42no—
330C2×C47#246611yescharacteristic
331C2×C47#310011yescharacteristic
332C2×C47#312011yescharacteristic
333C2×C47#329411yescharacteristic
334C2×C47#331311yescharacteristic
335C2×C47#333411yescharacteristic
336C2×C47#335111yescharacteristic
337D47—82no—
338C2×#126—21no—
339C2×#121—471no—
340C2×C4×D4—471no—
341C2×C4×D4—941no—
342C22×C4⋊C4—471no—
343C2×#107—471no—
344C2×#107—471no—
345C2×#107—471no—
346C2×#107—471no—
347C2×C4⋊C8—471no—
348C2×#102—471no—
349C2×#102—471no—
350C2×#102—471no—
351C2×#102—471no—
352C2×C22⋊C8—471no—
353C2×C22⋊C8—471no—
354C2×C4×C8—471no—
355#400—21no—
356#397—21no—
357#390—471no—
358#389—471no—
359#389C2×D4711yescharacteristic
360#389C2×D4711yescharacteristic
361#388—941no—
362#387—21no—
363#386—941no—
364#385—941no—
365#384C2×D4711yescharacteristic
366#380C2×D4711yescharacteristic
367#380C2×D4711yescharacteristic
368C4×C4⋊C4—471no—
369C4×C4⋊C4C2×D4711yescharacteristic
370C4×C22⋊C4C2×D4711yescharacteristic
371#340—471no—
372#340—471no—
373#340—471no—
374#340—471no—
375#340—471no—
376#340—471no—
377#340—471no—
378#340—471no—
379#336—471no—
380#336—471no—
381C47#2703011yescharacteristic, complemented, Sylow
382C22×D4—471no—
383C22×D4—941no—
384C23×C4—941no—
385C23×C4—941no—
386C23×C4C22×D4711yescharacteristic
387C22×C8—471no—
388C22×C8—471no—
389C22×C8—471no—
390C22×C8—471no—
391#126—44no—
392#121—942no—
393#121—942no—
394C4×D4—942no—
395C4×D4—1881no—
396C4×D4—1884no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—471no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—941no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—1881no—
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C4⋊C4C22×D4711yescharacteristic
411C2×C4⋊C4C22×D4711yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—941no—
415C2×C22⋊C4—941no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4C22⋊D4711yescharacteristic
419C2×C22⋊C4C22⋊D4711yescharacteristic
420C2×C42—21no—
421C2×C42—941no—
422C2×C42C22×D4711yescharacteristic
423C2×C42C22×D4711yescharacteristic
424#107—942no—
425#107—942no—
426#107—942no—
427#107—1881no—
428C4⋊C8—942no—
429#102—942no—
430#102—942no—
431#102—942no—
432#102—1881no—
433C22⋊C8—942no—
434C22⋊C8—1881no—
435C4×C8—1881no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—941no—
442#95—941no—
443#95C22⋊D4711yescharacteristic
444#95C22⋊D4711yescharacteristic
445C24—941no—
446C24C2×C22⋊D4711yescharacteristic
447C2×D4—472no—
448C2×D4—944no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—1882no—
455C2×D4—1882no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—941no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—3761no—
470C22×C4—3761no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4—1882no—
474C22×C4—1882no—
475C22×C4C2×C22⋊D4711yescharacteristic
476C22×C4C2×C22⋊D4711yescharacteristic
477C22×C4C2×C22⋊D4711yescharacteristic
478C22×C4C2×C22⋊D4711yescharacteristic
479C22×C4C2×C22⋊D4711yescharacteristic
480C22×C4C23×D4711yescharacteristic
481C2×C8—472no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—472no—
506C4⋊C4—472no—
507C4⋊C4—941no—
508C4⋊C4—941no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—1882no—
512C4⋊C4—1882no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—944no—
517C22⋊C4—3761no—
518C22⋊C4—1882no—
519C22⋊C4—1882no—
520C22⋊C4#1062533414yes—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—1882no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—942no—
534C23—1881no—
535C23—1881no—
536C23—1881no—
537C23—1881no—
538C23—1881no—
539C23—1881no—
540C23C2×#1062533412yes—
541C23C22×C22⋊D4711yescharacteristic
542D4—942no—
543D4—942no—
544D4—1888no—
545D4—1881no—
546D4—1881no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—3764no—
579C2×C4—3764no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4C2×#1062533412yes—
588C2×C4C2×#1062533412yes—
589C2×C4#41×D4711yescharacteristic
590C2×C4#41×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4#1309407011yescharacteristic
594C2×C4#1309407111yescharacteristic
595C8—942no—
596C8—1881no—
597C8—1881no—
598C8—1881no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—3761no—
607C22—3761no—
608C22—3761no—
609C22—3761no—
610C22—1882no—
611C22—1882no—
612C22—1882no—
613C22#1568963011yescharacteristic
614C22#1568976111yescharacteristic
615C22#1568977211yescharacteristic
616C22C22×#1062533411yescharacteristic
617C22#1568992111yescharacteristic
618C22#1568993111yescharacteristic
619C22#1568993811yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—3761no—
630C4—1882no—
631C4—1882no—
632C4#1568965611yescharacteristic
633C4#1568971411yescharacteristic
634C4#1568982411yescharacteristic
635C4#1568984011yescharacteristic
636C2—42no—
637C2—3762no—
638C2#2024742011yescharacteristic
639C2#2025338411yescharacteristic
640C2#2025359611yescharacteristic
641C2#2025519511yescharacteristic
642C2#2025544811yescharacteristic
643C2#2025573111yescharacteristic
644C2#2025594811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2496C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenter#2496D47
hypocenterC47#27030
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #20244792C2semidirect
3. #20244773C2semidirect
6. #20244144C2semidirect
7. #20244118C2semidirect
8. #20243996C2semidirect
9. #20243959C2semidirect
10. #20243956C2semidirect
11. #20243634C2semidirect
12. #20243575C2semidirect
13. #20243472C2semidirect
14. C4×#13093944C2semidirect
15. C47×#2496C2semidirect
314. #2496D47semidirect
381. C47#27030semidirect

Maximal subgroups

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

subgroupindex
#202464022
#202447922
#202447732
#202445702
#202441442
#202441182
#202439962
#202439592
#202439562
#202436342
#202435752
#202434722
C4×#130939442
C47×#24962
#2703047