Finite Group Databasebeta

← #26244969

Subgroups — #26244969

Order 12032.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689163C211yesmaximal, characteristic, complemented
2C2×#15689147C211yesmaximal, characteristic, complemented
3C2×#15689122C211yesmaximal, characteristic
4C2×#15689122C211yesmaximal, characteristic
5#20245878C211yesmaximal, characteristic
6#20244780C212yesmaximal, complemented
7#20244773C212yesmaximal, complemented
8#20244766C212yesmaximal, complemented
9#20244759C212yesmaximal, complemented
10#20243107C211yesmaximal, characteristic, complemented
11C2×C47×#389C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14C22×#10625329C2211yescharacteristic
15C2×#13093983C2211yescharacteristic
16#15689163—24no—
17C2×#13093957C2212yes—
18C2×#13093955C2212yes—
19#15689147—24no—
20C2×C4⋊(C47⋊C8)C2212yes—
21C2×C4⋊(C47⋊C8)C2212yes—
22#15689122—24no—
23#15689122—24no—
24C2×#13093947C2212yes—
25C2×#13093947C2212yes—
26C2×#13093944C2212yes—
27C2×#13093944C2212yes—
28#15689029C2211yescharacteristic
29#15689029C2211yescharacteristic
30#15689025C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689002—21no—
33#15689002—21no—
34C4×(C2×D47)⋊C4—21no—
35C4×(C2×D47)⋊C4—21no—
36#15688885C2212yes—
37#15688885C2212yes—
38C22×C4⋊C4×C47—21no—
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C4⋊C4×C47C2211yescharacteristic
41C22×C42×C47C2211yescharacteristic
42C47×#389—21no—
43C47×#389—21no—
44C47×#389C2212yes—
45C47×#389C2212yes—
46C2×#95×C47—21no—
47C2×#10625350—22no—
48C2×#10625350—22no—
49C2×#10625350—22no—
50C2×#10625350—22no—
51C2×#10625350—22no—
52C2×#10625350Q814yes—
53C22×Dic94C2311yescharacteristic
54C22×D188C2311yescharacteristic
55C22×C22⋊D47—21no—
56C22×C4×D47—21no—
57C2×#10625329—22no—
58C2×#10625329—22no—
59C2×#10625329—22no—
60C2×#10625329—22no—
61C2×#10625329—22no—
62C2×#10625329D414yes—
63C22×C47⋊C8C2312yes—
64C22×C47⋊C8C2312yes—
65#13093983—22no—
66#13093983—22no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C22⋊Dic47—21no—
70C2×(C2×D47)⋊C4—21no—
71C2×(C2×D47)⋊C4—21no—
72C2×(C2×D47)⋊C4—21no—
73C2×(C2×D47)⋊C4—21no—
74C2×C4×Dic47—21no—
75#13093957—24no—
76#13093955—24no—
77C4⋊(C47⋊C8)—24no—
78C4⋊(C47⋊C8)—24no—
79#13093947—24no—
80#13093947—24no—
81#13093944—24no—
82#13093944—24no—
83C47⋊#95—21no—
84C47⋊#95—21no—
85C47⋊#95—21no—
86C47⋊#95—21no—
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47D411yescharacteristic
90C23×C4×C47D411yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—44no—
100C2×C4⋊C4×C47D414yes—
101C2×C4⋊C4×C47C2312yes—
102C2×C4⋊C4×C47C2312yes—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47D411yescharacteristic
106C2×C42×C47D411yescharacteristic
107C2×C42×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109#95×C47—22no—
110#95×C47—22no—
111C24×C47C2×D411yescharacteristic
112C23×D47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—24no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—42no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47—42no—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×Q812yes—
135C22×C4×C47#4112yes—
136C22×C4×C47#4112yes—
137C22×C4×C47#4112yes—
138C22×C4×C47C2411yescharacteristic
139C2×C22⋊D47—24no—
140C2×C22⋊D47—42no—
141C2×C22⋊D47—42no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145#10625350—28no—
146#10625350—28no—
147#10625350—44no—
148#10625350—44no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C2×Q812yes—
155C2×C4×D47—24no—
156C2×C4×D47—42no—
157C2×C4×D47—42no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94C2×Q812yes—
164C4⋊C4×C47—24no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—44no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47—44no—
171C4⋊C4×C47C2×D414yes—
172C42×C47—22no—
173C42×C47—22no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C42×C47—21no—
178C22⋊Dic47—42no—
179(C2×D47)⋊C4—42no—
180(C2×D47)⋊C4—42no—
181(C2×D47)⋊C4—42no—
182(C2×D47)⋊C4—42no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4×Dic47—42no—
188#10625329—28no—
189#10625329—44no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8C2×D414yes—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47#12112yes—
201C23×C47#12112yes—
202C23×C47C22⋊Q812yes—
203C23×C47C22×D411yescharacteristic
204C22×D47—22no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
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—24no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—44no—
223C2×C4×C47—44no—
224C2×C4×C47—48no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—84no—
231C2×C4×C47#12112yes—
232C2×C4×C47#12112yes—
233C2×C4×C47#12114yes—
234C2×C4×C47C22⋊Q812yes—
235C2×C4×C47C22⋊Q814yes—
236C2×C4×C47C22⋊Q814yes—
237C2×C4×C47#12614yes—
238C2×C4×C47AGL(1,ℤ/8)12yes—
239C2×C4×C47#13712yes—
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×Q811yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C22⋊D47—48no—
247C2×Dic47—22no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256D188—22no—
257D188—22no—
258D188—41no—
259D188—41no—
260C4×D47—48no—
261Dic94—22no—
262Dic94—22no—
263Dic94—41no—
264Dic94—41no—
265C47⋊C8—24no—
266C47⋊C8—42no—
267#23617—471nomaximal, Sylow
268C22×C47—22no—
269C22×C47—22no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47#39614yes—
275C22×C47C2×#12111yescharacteristic
276C22×C47C2×#12111yescharacteristic
277C22×C47C2×C22⋊Q811yescharacteristic
278C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C47C2×#13711yescharacteristic
280C22×C47#57511yescharacteristic
281C22×C47#57511yescharacteristic
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—42no—
285C2×D47—81no—
286C2×D47—81no—
287C2×D47—81no—
288C2×D47—81no—
289C4×C47—22no—
290C4×C47—22no—
291C4×C47—44no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—82no—
295C4×C47#39614yes—
296C4×C47C2×#12111yescharacteristic
297C4×C47C2×C22⋊Q811yescharacteristic
298C4×C47C2×C22⋊Q811yescharacteristic
299C4×C47C2×#12611yescharacteristic
300Dic47—42no—
301Dic47—81no—
302Dic47—81no—
303C2×#428—471no—
304C2×#423—471no—
305C2×#417—471no—
306C2×#417—471no—
307#2297—471no—
308C2×#389D4711yescharacteristic, complemented
309#2068—472no—
310#2067—472no—
311#2066—472no—
312#2065—472no—
313#1736—471no—
314C2×C47—24no—
315C2×C47C2×#39611yescharacteristic
316C2×C47#303611yescharacteristic
317C2×C47#303711yescharacteristic
318C2×C47#305511yescharacteristic
319C2×C47#305611yescharacteristic
320C2×C47#307911yescharacteristic
321C2×C47#308011yescharacteristic
322D47—82no—
323C22×#41—471no—
324C22×M16—471no—
325C22×M16—471no—
326C2×#117—471no—
327C22×C4⋊C4—21no—
328C22×C4⋊C4C2×D4711yescharacteristic
329C22×C4⋊C4C2×D4711yescharacteristic
330C22×C42C2×D4711yescharacteristic
331#428—944no—
332C2×#107—472no—
333C2×#106—472no—
334#423—944no—
335C2×C4⋊C8—472no—
336C2×C4⋊C8—472no—
337#417—944no—
338#417—944no—
339C2×#103—472no—
340C2×#103—472no—
341C2×#102—472no—
342C2×#102—472no—
343#391—471no—
344#391—471no—
345#390—471no—
346#390—471no—
347#389—21no—
348#389—21no—
349#389C2×D4712yes—
350#389C2×D4712yes—
351#386—941no—
352#386—941no—
353C4×C22⋊C4—941no—
354C4×C22⋊C4—941no—
355C2×#95—21no—
356#340—472no—
357#340—472no—
358C47#2361711yescharacteristic, complemented, Sylow
359C2×#41—474no—
360C2×#41—942no—
361C2×#41—942no—
362C2×#41—942no—
363C2×#41—942no—
364C2×#41—942no—
365C22×Q8—471no—
366C22×D4—471no—
367C22×D4—941no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—941no—
371C23×C4C22⋊D4711yescharacteristic
372C23×C4C22⋊D4711yescharacteristic
373C23×C4C22×D4711yescharacteristic
374C2×M16—474no—
375C2×M16—942no—
376C2×M16—942no—
377C2×M16—942no—
378C2×M16—942no—
379C2×M16—942no—
380C22×C8—472no—
381C22×C8—472no—
382#117—942no—
383#117—942no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4D18814yes—
395C2×C4⋊C4C22×D4712yes—
396C2×C4⋊C4C22×D4712yes—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—941no—
405C2×C42C22⋊D4711yescharacteristic
406C2×C42C22⋊D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#107—944no—
410#106—944no—
411C4⋊C8—944no—
412C4⋊C8—944no—
413#103—944no—
414#103—944no—
415#102—944no—
416#102—944no—
417#95—22no—
418#95—22no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423C24—941no—
424C24C2×C22⋊D4711yescharacteristic
425#41—948no—
426#41—948no—
427#41—1884no—
428#41—1884no—
429C2×Q8—472no—
430C2×Q8—941no—
431C2×Q8—941no—
432C2×Q8—941no—
433C2×Q8—941no—
434C2×Q8—941no—
435C2×D4—472no—
436C2×D4—944no—
437C2×D4—941no—
438C2×D4—941no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—1882no—
443C2×D4—1882no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—941no—
459C22×C4—944no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4C2×D18812yes—
465C22×C4#1062535012yes—
466C22×C4D4×D4712yes—
467C22×C4#1062535212yes—
468C22×C4Q8×D4712yes—
469C22×C4#1062535412yes—
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C2×C22⋊D4711yescharacteristic
472C22×C4C2×C22⋊D4711yescharacteristic
473C22×C4C2×C22⋊D4711yescharacteristic
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C23×D4711yescharacteristic
476M16—948no—
477M16—1884no—
478C2×C8—474no—
479C2×C8—942no—
480C2×C8—942no—
481C2×C8—942no—
482C2×C8—942no—
483C2×C8—942no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—44no—
489C4⋊C4—42no—
490C4⋊C4—44no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4C2×D18814yes—
496C22⋊C4—1882no—
497C22⋊C4—1882no—
498C22⋊C4—1882no—
499C22⋊C4—1882no—
500C22⋊C4—1882no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—1882no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—942no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23—1881no—
518C23—1881no—
519C23#1309399612yes—
520C23#1309399812yes—
521C23#1309400012yes—
522C23C22×C22⋊D4711yescharacteristic
523Q8—942no—
524Q8—942no—
525Q8—1881no—
526Q8—1881no—
527D4—942no—
528D4—942no—
529D4—1888no—
530D4—1881no—
531D4—1881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—942no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1888no—
562C2×C4#1309399612yes—
563C2×C4#1309399812yes—
564C2×C4#1309399914yes—
565C2×C4#1309400012yes—
566C2×C4#1309400214yes—
567C2×C4#1309400414yes—
568C2×C4#1309401914yes—
569C2×C4#1309405012yes—
570C2×C4#1309405512yes—
571C2×C4C2×D4×D4711yescharacteristic
572C2×C4C22×D18811yescharacteristic
573C2×C4C2×Q8×D4711yescharacteristic
574C2×C4C2×#1062535211yescharacteristic
575C2×C4C2×#1062535011yescharacteristic
576C2×C4C2×#1062535411yescharacteristic
577C8—944no—
578C8—1882no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—3761no—
586C22—3761no—
587C22—3761no—
588C22—3761no—
589C22—1882no—
590C22—1882no—
591C22—1882no—
592C22#1568904514yes—
593C22C2×#1309399611yescharacteristic
594C22C2×#1309399811yescharacteristic
595C22C2×#1309400011yescharacteristic
596C22C2×#1309405011yescharacteristic
597C22C2×#1309405511yescharacteristic
598C22#1568992111yescharacteristic
599C22#1568992111yescharacteristic
600C4—22no—
601C4—22no—
602C4—41no—
603C4—41no—
604C4—44no—
605C4—82no—
606C4—3761no—
607C4—3761no—
608C4—1882no—
609C4#1568904514yes—
610C4C2×#1309399911yescharacteristic
611C4C2×#1309400211yescharacteristic
612C4C2×#1309400411yescharacteristic
613C4C2×#1309401911yescharacteristic
614C2—24no—
615C2—3762no—
616C2C2×#1568904511yescharacteristic
617C2#2025285211yescharacteristic
618C2#2025286011yescharacteristic
619C2#2025300311yescharacteristic
620C2#2025301411yescharacteristic
621C2#2025319711yescharacteristic
622C2#2025320611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#389C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#389D47
hypocenterC47#23617
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#15689163C2semidirect
2. C2×#15689147C2semidirect
6. #20244780C2semidirect
7. #20244773C2semidirect
8. #20244766C2semidirect
9. #20244759C2semidirect
10. #20243107C2semidirect
11. C2×C47×#389C2semidirect
308. C2×#389D47semidirect
358. C47#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#156891632
C2×#156891472
C2×#156891222
#202458782
#202447802
#202447732
#202447662
#202447592
#202431072
C2×C47×#3892
#2361747