Finite Group Databasebeta

← #26238348

Subgroups — #26238348

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253174C211yesmaximal, characteristic
2#20252332C211yesmaximal, characteristic, complemented
3#20251955C211yesmaximal, characteristic
4#20244363C211yesmaximal, characteristic, complemented
5#20244162C211yesmaximal, characteristic, complemented
6#20244137C211yesmaximal, characteristic, complemented
7#20244133C211yesmaximal, characteristic, complemented
8#20243990C211yesmaximal, characteristic, complemented
9#20243666C211yesmaximal, characteristic
10#20243664C211yesmaximal, characteristic
11#20243236C211yesmaximal, characteristic, complemented
12#20243227C211yesmaximal, characteristic
13#20243224C211yesmaximal, characteristic
14#20243192C211yesmaximal, characteristic
15C47×#1922C211yesmaximal, characteristic, complemented
16C2×#13094032C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18#15689676C2211yescharacteristic
19#15689591C2211yescharacteristic
20#15689433C411yescharacteristic, complemented
21#15689429C411yescharacteristic, complemented
22#15689426C411yescharacteristic, complemented
23#15689422C411yescharacteristic, complemented
24#15689417C411yescharacteristic, complemented
25#15689412C411yescharacteristic, complemented
26#15689407C411yescharacteristic, complemented
27#15689402C411yescharacteristic, complemented
28#15689253—21no—
29#15689251—21no—
30#15689251—21no—
31C8×Dic94—21no—
32C2×#13093960C2211yescharacteristic
33C2×#13093959C2211yescharacteristic
34#15689159C2211yescharacteristic
35#15689150C2211yescharacteristic
36#15689150C2211yescharacteristic
37#15689149C2211yescharacteristic
38#15689148—21no—
39#15689148—21no—
40#15689146C2211yescharacteristic
41#15689145—21no—
42C2×Dic47⋊C8C2211yescharacteristic
43C2×Dic47⋊C8C2211yescharacteristic
44C4⋊C8×D47—21no—
45C2×#13093952C2211yescharacteristic
46C2×#13093950C2211yescharacteristic
47#15689120C2211yescharacteristic
48#15689117C2211yescharacteristic
49#15689081C2211yescharacteristic
50M16×Dic47C2211yescharacteristic
51C2×C8×Dic47C2211yescharacteristic
52C2×C8×Dic47C2211yescharacteristic
53C42×Dic47C2211yescharacteristic
54#15688887C2211yescharacteristic
55#15688884C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688882C2211yescharacteristic
58#15688882C2211yescharacteristic
59#15688878C2211yescharacteristic
60C47×#427C2211yescharacteristic
61C47×#424C2211yescharacteristic
62C47×#405C2211yescharacteristic
63C47×#341C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094032—22no—
69#13094032—41no—
70#13094030—22no—
71#13094030—41no—
72C2×#10625329C2311yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80#13094023C2×C411yescharacteristic
81#13094023C2×C411yescharacteristic
82#13094015C2×C411yescharacteristic
83#13094015C2×C411yescharacteristic
84#13094001—21no—
85#13094001—21no—
86C4×Dic94—21no—
87C4×Dic94—21no—
88#13093989C2×C411yescharacteristic
89#13093989C2×C411yescharacteristic
90#13093986C2×C411yescharacteristic
91#13093986C2×C411yescharacteristic
92(C22⋊D47)⋊C4—21no—
93(C22⋊D47)⋊C4—21no—
94#13093983C2311yescharacteristic
95#13093981—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47C2311yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C42×D47—21no—
101#13093960—41no—
102#13093959—41no—
103#13093957C2×C411yescharacteristic
104#13093957C2×C411yescharacteristic
105#13093955C2×C411yescharacteristic
106#13093955C2×C411yescharacteristic
107C4⋊(C47⋊C8)—21no—
108C4⋊(C47⋊C8)—21no—
109C4⋊(C47⋊C8)—21no—
110C4⋊(C47⋊C8)—21no—
111Dic47⋊C8—21no—
112Dic47⋊C8—21no—
113Dic47⋊C8—21no—
114Dic47⋊C8—21no—
115Dic47⋊C8C2×C411yescharacteristic
116Dic47⋊C8C2×C411yescharacteristic
117Dic47⋊C8C2×C411yescharacteristic
118Dic47⋊C8C2×C411yescharacteristic
119Dic47⋊C8D411yescharacteristic
120Dic47⋊C8D411yescharacteristic
121Dic47⋊C8D411yescharacteristic
122Dic47⋊C8D411yescharacteristic
123#13093952—22no—
124#13093950Q814yescomplemented
125#13093949C2×C411yescharacteristic
126#13093949C2×C411yescharacteristic
127#13093947C2×C411yescharacteristic
128#13093947C2×C411yescharacteristic
129#13093946C2×C411yescharacteristic
130#13093946C2×C411yescharacteristic
131#13093944C2×C411yescharacteristic
132#13093944C2×C411yescharacteristic
133#13093934—21no—
134#13093934—21no—
135C8×Dic47—21no—
136C8×Dic47—21no—
137C8×Dic47—41no—
138C8×Dic47—41no—
139C2×M16×C47C2311yescharacteristic
140C2×M16×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143#117×C47C2311yescharacteristic
144#117×C47C2311yescharacteristic
145C2×C42×C47C2311yescharacteristic
146#107×C47C2×C411yescharacteristic
147#107×C47C2×C411yescharacteristic
148#106×C47C2×C411yescharacteristic
149#106×C47C2×C411yescharacteristic
150C4⋊C8×C47—21no—
151C4⋊C8×C47—21no—
152#97×C47—21no—
153C4×C8×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C2411yescharacteristic
156C2×C22⋊D47—21no—
157C22×Dic47—21no—
158C22×Dic47#4111yescharacteristic
159C22×Dic47#4111yescharacteristic
160#10625350—21no—
161#10625350—21no—
162#10625350C2×Q812yes—
163#10625350#4112yes—
164C2×D188C22×C411yescharacteristic
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94C22×C411yescharacteristic
171M16×C47—21no—
172M16×C47—21no—
173M16×C47—21no—
174M16×C47C2×Q812yes—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47C22×C411yescharacteristic
182C2×C8×C47C22×C411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
185C4⋊C4×C47C22×C411yescharacteristic
186C4⋊C4×C47C22×C411yescharacteristic
187C4⋊C4×C47C22×C411yescharacteristic
188C4⋊C4×C47C22×C411yescharacteristic
189C22⋊C4×C47—21no—
190C22⋊C4×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C22⋊Dic47—21no—
196(C2×D47)⋊C4—21no—
197(C2×D47)⋊C4—21no—
198C4⋊Dic47—21no—
199C4⋊Dic47—21no—
200C4⋊Dic47C22×C411yescharacteristic
201C4⋊Dic47C22×C411yescharacteristic
202Dic47⋊C4—21no—
203Dic47⋊C4—21no—
204Dic47⋊C4—21no—
205Dic47⋊C4—21no—
206Dic47⋊C4—21no—
207Dic47⋊C4—21no—
208C4×Dic47—24no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—42no—
214C4×Dic47C22×C411yescharacteristic
215C4×Dic47C22×C411yescharacteristic
216C4×Dic47C2×D411yescharacteristic
217C4×Dic47C2×D411yescharacteristic
218C4×Dic47C2×Q812yes—
219#10625329—21no—
220#10625329—21no—
221#10625329—21no—
222#10625329—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8C22×C411yescharacteristic
230C2×C47⋊C8C22×C411yescharacteristic
231C2×C47⋊C8C2×D411yescharacteristic
232C2×C47⋊C8C2×D411yescharacteristic
233#10625324—42no—
234#10625324—42no—
235C8×D47—42no—
236C8×D47—42no—
237C23×C47C2×#4111yescharacteristic
238C22×D47—21no—
239C2×C4×C47—22no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C23×C411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C22×Q811yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47H(5,𝔽2)11yescharacteristic
251C2×C4×C472−1+411yescharacteristic
252C22⋊D47—22no—
253C22⋊D47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—21no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—41no—
262C2×Dic47C4×D411yescharacteristic
263C2×Dic47C4×D411yescharacteristic
264C2×Dic47C4×D411yescharacteristic
265C2×Dic47C4×D411yescharacteristic
266D188—21no—
267D188C4×Q812yes—
268C4×D47—22no—
269C4×D47—22no—
270C4×D47—42no—
271C4×D47—81no—
272Dic94—21no—
273Dic94—42no—
274Dic94—81no—
275Dic94C4×Q812yes—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C8×C47—21no—
280C8×C47—22no—
281C8×C47—41no—
282C47⋊C8—21no—
283C47⋊C8—21no—
284C47⋊C8—21no—
285C47⋊C8—21no—
286C47⋊C8—41no—
287C47⋊C8—41no—
288#22982—471nomaximal, Sylow
289C22×C47—21no—
290C22×C47—21no—
291C22×C47C2×C4×D411yescharacteristic
292C22×C47#55211yescharacteristic
293C22×C47#55411yescharacteristic
294C2×D47—22no—
295C2×D47—41no—
296C2×D47—41no—
297C4×C47—42no—
298C4×C47—41no—
299C4×C47—41no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47C2×C4×Q811yescharacteristic
303C4×C47#52011yescharacteristic
304C4×C47#54611yescharacteristic
305C4×C47D4×Q811yescharacteristic
306Dic47—24no—
307Dic47—22no—
308Dic47—21no—
309Dic47—21no—
310Dic47—21no—
311Dic47—41no—
312Dic47—41no—
313Dic47#44312yes—
314#3076—471no—
315#2962—471no—
316#2906—471no—
317#1994—471no—
318#1950—471no—
319#1945—471no—
320#1945—471no—
321#1922—471no—
322#1922D4711yescharacteristic, complemented
323#1866—471no—
324#1866—471no—
325C4×C4⋊C8—471no—
326#1764—471no—
327#1764—471no—
328C4×#104—471no—
329C2×C47—21no—
330C2×C47—21no—
331C2×C47#236011yescharacteristic
332C2×C47C2×#44311yescharacteristic
333C2×C47#295611yescharacteristic
334D47—42no—
335C2×#131—471no—
336C2×#131—471no—
337#533—471no—
338C4×#41—471no—
339#479—471no—
340#479—471no—
341#478—471no—
342#478—471no—
343#477—471no—
344#476—471no—
345#475—471no—
346#474—471no—
347#446—941no—
348#446—941no—
349#446—941no—
350C8×Q8—941no—
351C2×#108—471no—
352C2×#108—471no—
353#427—471no—
354#427C2×D4711yescharacteristic
355#424—471no—
356#424—471no—
357#424—471no—
358#424—941no—
359#424—941no—
360#424C2×D4711yescharacteristic
361#423—471no—
362#423—941no—
363C2×C4⋊C8—471no—
364C2×C4⋊C8—471no—
365C2×C4⋊C8—941no—
366C2×#104—471no—
367C2×#104—471no—
368#416—471no—
369#416—471no—
370#405—471no—
371#405C2×D4711yescharacteristic
372C4×M16—471no—
373C2×C4×C8—471no—
374C2×C4×C8—471no—
375C43—471no—
376#341—471no—
377#341C2×D4711yescharacteristic
378#339—471no—
379#339—471no—
380#339—471no—
381#339—471no—
382#339C2×D4711yescharacteristic
383#339C2×D4711yescharacteristic
384#336—471no—
385#336C2×D4711yescharacteristic
386C47#2298211yescharacteristic, complemented, Sylow
387C2×#41—471no—
388#131—942no—
389#131—942no—
390#131—1881no—
391#131—1881no—
392C2×M16—471no—
393C2×M16—471no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16C22×D4711yescharacteristic
397C2×M16C22×D4711yescharacteristic
398C22×C8—471no—
399C22×C8—471no—
400C22×C8—941no—
401C22×C8—941no—
402C22×C8C22×D4711yescharacteristic
403C22×C8C22×D4711yescharacteristic
404C4⋊Q8—471no—
405C4⋊Q8—471no—
406#125—471no—
407#125—471no—
408C22⋊Q8—941no—
409C22⋊Q8—941no—
410C4×Q8—471no—
411C4×Q8—471no—
412C4×Q8—941no—
413C4×Q8—941no—
414C4×D4—471no—
415C4×D4—471no—
416C4×D4—941no—
417C4×D4—941no—
418#117—471no—
419#117—941no—
420#117C22×D4711yescharacteristic
421#117C22×D4711yescharacteristic
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—941no—
425C2×C42—941no—
426C2×C42—941no—
427C2×C42C22×D4711yescharacteristic
428#108—1881no—
429#108—1881no—
430#107—471no—
431#107—471no—
432#107C4×D4711yescharacteristic
433#107C4×D4711yescharacteristic
434#106—471no—
435#106—471no—
436#106C4×D4711yescharacteristic
437#106C4×D4711yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—471no—
441C4⋊C8—471no—
442C4⋊C8—471no—
443C4⋊C8—471no—
444C4⋊C8—471no—
445C4⋊C8—471no—
446C4⋊C8—471no—
447C4⋊C8—471no—
448C4⋊C8—941no—
449C4⋊C8—941no—
450C4⋊C8—941no—
451C4⋊C8—941no—
452C4⋊C8—941no—
453C4⋊C8—941no—
454C4⋊C8—941no—
455C4⋊C8—941no—
456#104—474no—
457#104—942no—
458#103—471no—
459#103—471no—
460#103—471no—
461#103—471no—
462#102—471no—
463#102—471no—
464#102—471no—
465#102—471no—
466#97—21no—
467#97—941no—
468#97—941no—
469C4×C8—21no—
470C4×C8—941no—
471C4×C8—941no—
472C4×C8—1881no—
473C4×C8—1881no—
474#41—472no—
475#41—472no—
476#41—941no—
477#41—941no—
478C2×Q8—471no—
479C2×Q8—941no—
480C2×Q8—941no—
481C2×D4—471no—
482C2×D4—941no—
483C22×C4—21no—
484C22×C4—471no—
485C22×C4—471no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4C23×D4711yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—941no—
495M16—941no—
496M16—941no—
497M16—941no—
498M16—1882no—
499M16—1882no—
500M16Q8×D4712yes—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—1882no—
518C2×C8—1882no—
519C2×C8C2×C4×D4711yescharacteristic
520C2×C8C2×C4×D4711yescharacteristic
521C2×C8D4×D4711yescharacteristic
522C2×C8D4×D4711yescharacteristic
523C4⋊C4—471no—
524C4⋊C4—471no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—941no—
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C4⋊C4C2×C4×D4711yescharacteristic
536C4⋊C4C2×C4×D4711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—471no—
547C42—471no—
548C42—471no—
549C42—471no—
550C42—472no—
551C42—941no—
552C42—941no—
553C42—944no—
554C42—941no—
555C42—941no—
556C42—1882no—
557C23—941no—
558C23#41×D4711yescharacteristic
559Q8—472no—
560Q8—941no—
561Q8—3761no—
562Q8—1882no—
563D4—472no—
564D4—942no—
565D4—942no—
566D4—941no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—471no—
575C2×C4—471no—
576C2×C4—471no—
577C2×C4—471no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—941no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—941no—
586C2×C4—941no—
587C2×C4—3761no—
588C2×C4—1882no—
589C2×C4—1881no—
590C2×C4C22×C4×D4711yescharacteristic
591C2×C4C2×D4×D4711yescharacteristic
592C2×C4C2×Q8×D4711yescharacteristic
593C2×C4#41×D4711yescharacteristic
594C2×C4#1309407011yescharacteristic
595C2×C4#1309407111yescharacteristic
596C8—21no—
597C8—21no—
598C8—22no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—941no—
603C8—941no—
604C8—941no—
605C8—941no—
606C8—1881no—
607C8—1881no—
608C22—21no—
609C22—21no—
610C22—942no—
611C22—1881no—
612C22—1881no—
613C22C4×D4×D4711yescharacteristic
614C22#1568980911yescharacteristic
615C22#1568982911yescharacteristic
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—472no—
622C4—944no—
623C4—941no—
624C4—942no—
625C4—941no—
626C4—941no—
627C4—1881no—
628C4—1881no—
629C4C4×Q8×D4711yescharacteristic
630C4#1568960311yescharacteristic
631C4#1568976511yescharacteristic
632C4#1568978611yescharacteristic
633C2—21no—
634C2—21no—
635C2—1882no—
636C2#2024639611yescharacteristic
637C2#443×D4711yescharacteristic
638C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1922C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#1922D47
hypocenterC47#22982
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #20252332C2semidirect
4. #20244363C2semidirect
5. #20244162C2semidirect
6. #20244137C2semidirect
7. #20244133C2semidirect
8. #20243990C2semidirect
11. #20243236C2semidirect
15. C47×#1922C2semidirect
20. #15689433C4semidirect
21. #15689429C4semidirect
22. #15689426C4semidirect
23. #15689422C4semidirect
24. #15689417C4semidirect
25. #15689412C4semidirect
26. #15689407C4semidirect
27. #15689402C4semidirect
124. #13093950Q8semidirect
322. #1922D47semidirect
386. C47#22982semidirect

Maximal subgroups

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

subgroupindex
#202531742
#202523322
#202519552
#202443632
#202441622
#202441372
#202441332
#202439902
#202436662
#202436642
#202432362
#202432272
#202432242
#202431922
C47×#19222
#2298247