Finite Group Databasebeta

← #26228355

Subgroups — #26228355

Order 12032.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689420C211yesmaximal, characteristic
2#20245852C211yesmaximal, characteristic
3#20244346C211yesmaximal, characteristic, complemented
4#20244154C211yesmaximal, characteristic, complemented
5#20244118C211yesmaximal, characteristic, complemented
6#20244113C211yesmaximal, characteristic, complemented
7#20244070C211yesmaximal, characteristic
8#20244070C211yesmaximal, characteristic
9#20244015C211yesmaximal, characteristic
10#20244008C211yesmaximal, characteristic
11#20243980C211yesmaximal, characteristic, complemented
12#20243973C211yesmaximal, characteristic, complemented
13#20243395C211yesmaximal, characteristic
14C4×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C4×#125×C47C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17C2×#13093981—21no—
18#15689420C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689025C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689014—21no—
36#15689014—21no—
37C4×C4⋊Dic47C2211yescharacteristic
38C4×(C2×D47)⋊C4—21no—
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×#125×C47C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#387—21no—
53C47×#387—21no—
54C47×#382C2211yescharacteristic
55C4×C4⋊C4×C47—21no—
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C43×C47C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C4×D188—22no—
67C4×D188C2×C414yes—
68#13093981—44no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×C4×Dic47—21no—
80#13093957—41no—
81#13093957C2×C414yes—
82#13093955—41no—
83#13093955C2×C414yes—
84C4⋊(C47⋊C8)—22no—
85C4⋊(C47⋊C8)C2×C414yes—
86#13093944—41no—
87#13093944—41no—
88#13093944C2×C414yes—
89#13093944C2×C414yes—
90C4×C47⋊C8—41no—
91C4×C47⋊C8—41no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95#125×C47—22no—
96#125×C47C2×C414yes—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C42×C47—21no—
106C2×C42×C47—21no—
107C2×C42×C47D411yescharacteristic
108C2×C42×C47D411yescharacteristic
109C2×C42×C47D411yescharacteristic
110C2×C42×C47D411yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120C23×D47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2411yescharacteristic
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188C22×C412yes—
141C2×C4×D47—24no—
142C2×C4×D47—42no—
143C2×C4×D47—42no—
144C4⋊C4×C47—24no—
145C4⋊C4×C47—24no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—42no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47C22×C412yes—
155C4⋊C4×C47C22×C412yes—
156C42×C47—22no—
157C42×C47—22no—
158C42×C47—22no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—41no—
164C42×C47—42no—
165C42×C47—42no—
166C42×C47C22×C412yes—
167C42×C47#4112yes—
168(C2×D47)⋊C4—24no—
169(C2×D47)⋊C4—42no—
170(C2×D47)⋊C4—42no—
171(C2×D47)⋊C4—42no—
172(C2×D47)⋊C4—42no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47C22×C412yes—
179Dic47⋊C4—42no—
180Dic47⋊C4—42no—
181C4×Dic47—42no—
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—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8C22×C412yes—
193C2×C47⋊C8C22×C412yes—
194C23×C47C22×D411yescharacteristic
195C22×D47—22no—
196C22×D47—41no—
197C22×D47—41no—
198C22×D47—41no—
199C22×D47—41no—
200C22×D47—41no—
201C22×D47—41no—
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—22no—
213C2×C4×C47—22no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C4×D412yes—
228C2×C4×C47C4×D412yes—
229C2×C4×C47#13512yes—
230C2×C4×C47#13512yes—
231C2×C4×C47AGL(1,ℤ/8)12yes—
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47H(5,𝔽2)11yescharacteristic
235C2×C4×C472−1+411yescharacteristic
236C2×C4×C472−1+411yescharacteristic
237C2×C4×C472−1+411yescharacteristic
238C2×Dic47—22no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247D188—22no—
248D188—22no—
249D188—41no—
250D188—41no—
251C4×D47—48no—
252C47⋊C8—22no—
253C47⋊C8—22no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256#22114—471nomaximal, Sylow
257C22×C47C2×C4×D411yescharacteristic
258C22×C47#53611yescharacteristic
259C22×C47#53711yescharacteristic
260C22×C47C2×#13511yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C47#57511yescharacteristic
264C2×D47—42no—
265C2×D47—42no—
266C2×D47—42no—
267C2×D47—81no—
268C2×D47—81no—
269C2×D47—81no—
270C2×D47—81no—
271C4×C47—22no—
272C4×C47—22no—
273C4×C47—22no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—42no—
277C4×C47—42no—
278C4×C47—41no—
279C4×C47—81no—
280C4×C47—81no—
281C4×C47#51911yescharacteristic
282C4×C47#52011yescharacteristic
283C4×C47#54111yescharacteristic
284C4×C47#54211yescharacteristic
285Dic47—42no—
286Dic47—81no—
287Dic47—81no—
288C2×#478—471no—
289C4×#125D4711yescharacteristic, complemented
290#2293—471no—
291#1989—471no—
292#1949—471no—
293#1942—471no—
294#1941—471no—
295#1934—471no—
296#1934—471no—
297#1926—471no—
298#1925—471no—
299#1921—471no—
300#1920—471no—
301#1804—471no—
302C4×C4⋊C8—471no—
303C2×C47#232311yescharacteristic
304C2×C47C4×#13511yescharacteristic
305C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
306C2×C47#322811yescharacteristic
307C2×C47#323211yescharacteristic
308C2×C47#324711yescharacteristic
309C2×C47#325011yescharacteristic
310D47—82no—
311C2×#125C2×D4711yescharacteristic
312C2×C4×D4—471no—
313C2×#117—941no—
314#478—478no—
315C2×#107—471no—
316C2×#107—471no—
317C2×#106—471no—
318C2×#106—471no—
319C2×C4⋊C8—471no—
320C2×C4⋊C8—471no—
321C2×#102—471no—
322C2×#102—471no—
323C2×#102—471no—
324C2×#102—471no—
325C2×C4×C8—471no—
326C2×C4×C8—471no—
327#390—471no—
328#390—471no—
329#389—471no—
330#389—471no—
331#389C2×D4711yescharacteristic
332#389C2×D4711yescharacteristic
333#388—941no—
334#388—941no—
335#387—21no—
336#387—21no—
337#382C2×D4711yescharacteristic
338C4×C4⋊C4—21no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4C2×D4711yescharacteristic
342C4×C4⋊C4C2×D4711yescharacteristic
343C4×C22⋊C4—941no—
344C43C2×D4711yescharacteristic
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#340—471no—
351#340—471no—
352#340—471no—
353#336—471no—
354#336—471no—
355C47#2211411yescharacteristic, complemented, Sylow
356C22×D4—471no—
357C23×C4—941no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C22×C8—471no—
362#125—22no—
363#125C4×D4714yes—
364C4×D4—474no—
365C4×D4—942no—
366#117—1884no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4C22×D4711yescharacteristic
377C2×C4⋊C4C22×D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C22⋊C4—941no—
381C2×C22⋊C4—941no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—941no—
388C2×C42C22⋊D4711yescharacteristic
389C2×C42C22⋊D4711yescharacteristic
390C2×C42C22⋊D4711yescharacteristic
391C2×C42C22⋊D4711yescharacteristic
392C2×C42C22×D4711yescharacteristic
393C2×C42C22×D4711yescharacteristic
394C2×C42C22×D4711yescharacteristic
395#107—474no—
396#107—1881no—
397#106—474no—
398#106—1881no—
399C4⋊C8—474no—
400C4⋊C8—942no—
401#102—474no—
402#102—474no—
403#102—1881no—
404#102—1881no—
405C4×C8—1881no—
406C4×C8—1881no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—941no—
414#95—941no—
415#95—941no—
416C24—941no—
417C2×D4—472no—
418C2×D4—941no—
419C2×D4—941no—
420C2×D4—941no—
421C2×D4—941no—
422C2×D4—941no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—941no—
428C22×C4—944no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—1882no—
432C22×C4—1882no—
433C22×C4C2×C22⋊D4711yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435C22×C4C2×C22⋊D4711yescharacteristic
436C22×C4C2×C22⋊D4711yescharacteristic
437C22×C4C2×C22⋊D4711yescharacteristic
438C22×C4C2×C22⋊D4711yescharacteristic
439C22×C4C23×D4711yescharacteristic
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—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—472no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4C2×C4×D4712yes—
471C4⋊C4C2×C4×D4712yes—
472C22⋊C4—944no—
473C22⋊C4—1882no—
474C22⋊C4—1882no—
475C22⋊C4—1882no—
476C22⋊C4—1882no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—42no—
486C42—42no—
487C42—1882no—
488C42C2×C4×D4712yes—
489C42#1062535012yes—
490C23—942no—
491C23—1881no—
492C23—1881no—
493C23—1881no—
494C23—1881no—
495C23—1881no—
496C23—1881no—
497C23C22×C22⋊D4711yescharacteristic
498D4—942no—
499D4—942no—
500D4—1881no—
501D4—1881no—
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—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—942no—
528C2×C4—1888no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4C4×C22⋊D4712yes—
538C2×C4C4×C22⋊D4712yes—
539C2×C4#1309404412yes—
540C2×C4#1309404412yes—
541C2×C4#1309404912yes—
542C2×C4C22×C4×D4711yescharacteristic
543C2×C4C2×#1062535011yescharacteristic
544C2×C4#1309407011yescharacteristic
545C2×C4#1309407111yescharacteristic
546C2×C4#1309407211yescharacteristic
547C2×C4#1309407211yescharacteristic
548C8—942no—
549C8—942no—
550C8—1881no—
551C8—1881no—
552C22—3761no—
553C22—3761no—
554C22—3761no—
555C22—3761no—
556C22—1882no—
557C22—1882no—
558C22—1882no—
559C22C2×C4×C22⋊D4711yescharacteristic
560C22#1568969711yescharacteristic
561C22#1568970111yescharacteristic
562C22C2×#1309404411yescharacteristic
563C22C2×#1309404411yescharacteristic
564C22C2×#1309404911yescharacteristic
565C22#1568992111yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—3761no—
577C4—3761no—
578C4—1882no—
579C4#1568959911yescharacteristic
580C4#1568960511yescharacteristic
581C4#1568973111yescharacteristic
582C4#1568974511yescharacteristic
583C2—3762no—
584C2#2024606411yescharacteristic
585C2C4×#1309404411yescharacteristic
586C2C4×#1309404911yescharacteristic
587C2#2025452411yescharacteristic
588C2#2025455611yescharacteristic
589C2#2025471411yescharacteristic
590C2#2025473511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#125×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenterC4×#125D47
hypocenterC47#22114
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
3. #20244346C2semidirect
4. #20244154C2semidirect
5. #20244118C2semidirect
6. #20244113C2semidirect
11. #20243980C2semidirect
12. #20243973C2semidirect
14. C4×C4⋊(C47⋊C8)C2semidirect
15. C4×#125×C47C2semidirect
18. #15689420C4semidirect
289. C4×#125D47semidirect
355. C47#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#156894202
#202458522
#202443462
#202441542
#202441182
#202441132
#202440702
#202440152
#202440082
#202439802
#202439732
#202433952
C4×C4⋊(C47⋊C8)2
C4×#125×C472
#2211447