Finite Group Databasebeta

← #26238370

Subgroups — #26238370

Order 12032.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253172C211yesmaximal, characteristic
2#20252332C211yesmaximal, characteristic, complemented
3#20251954C211yesmaximal, characteristic
4#20244367C211yesmaximal, characteristic, complemented
5#20244162C211yesmaximal, characteristic, complemented
6#20244140C211yesmaximal, characteristic, complemented
7#20244136C211yesmaximal, characteristic, complemented
8#20243987C211yesmaximal, characteristic, complemented
9#20243986C211yesmaximal, characteristic, complemented
10#20243665C211yesmaximal, characteristic
11#20243663C211yesmaximal, characteristic
12#20243246C211yesmaximal, characteristic, complemented
13#20243233C211yesmaximal, characteristic
14#20243200C211yesmaximal, characteristic
15C47×#1764C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17#15689676C2211yescharacteristic
18#41×Dic47C2211yescharacteristic
19#15689432C411yescharacteristic, complemented
20#15689428C411yescharacteristic, complemented
21#15689425C411yescharacteristic, complemented
22#15689421C411yescharacteristic, complemented
23#15689416C411yescharacteristic, complemented
24#15689411C411yescharacteristic, complemented
25#15689406C411yescharacteristic, complemented
26#15689401C411yescharacteristic, complemented
27#15689253—21no—
28#15689251—21no—
29#15689251—21no—
30C8×Dic94—21no—
31C2×#13093960C2211yescharacteristic
32C2×#13093959C2211yescharacteristic
33#15689161C2211yescharacteristic
34#15689159C2211yescharacteristic
35#15689151—21no—
36#15689151C2211yescharacteristic
37#15689150C2211yescharacteristic
38#15689149—21no—
39#15689149C2211yescharacteristic
40#15689149C2211yescharacteristic
41#15689146—21no—
42#15689146C2211yescharacteristic
43C2×Dic47⋊C8—21no—
44C2×Dic47⋊C8C2211yescharacteristic
45C2×Dic47⋊C8C2211yescharacteristic
46C2×#13093951C2211yescharacteristic
47#15689119C2211yescharacteristic
48#15689081C2211yescharacteristic
49M16×Dic47C2211yescharacteristic
50C2×#13093935C2211yescharacteristic
51#15688969C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688884C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688882C2211yescharacteristic
58#15688877C2211yescharacteristic
59#15688877C2211yescharacteristic
60C2×#131×C47C2211yescharacteristic
61C2×#104×C47C2211yescharacteristic
62C47×#416C2211yescharacteristic
63C47×#405C2211yescharacteristic
64C2×C4×C8×C47C2211yescharacteristic
65C47×#341C2211yescharacteristic
66C47×#339C2211yescharacteristic
67#13094031—22no—
68#13094031—41no—
69C2×#10625329—21no—
70C2×#10625329C2311yescharacteristic
71C2×#10625329C2311yescharacteristic
72C22×C47⋊C8—21no—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094023C2×C411yescharacteristic
76#13094023C2×C411yescharacteristic
77#13094015C2×C411yescharacteristic
78#13094015C2×C411yescharacteristic
79#13094001—21no—
80#13094001—21no—
81Q8×Dic47C2×C411yescharacteristic
82Q8×Dic47C2×C411yescharacteristic
83C4×Dic94—21no—
84C4×Dic94—21no—
85D4×Dic47—21no—
86D4×Dic47—21no—
87D4×Dic47C2×C411yescharacteristic
88D4×Dic47C2×C411yescharacteristic
89#13093983—21no—
90#13093983C2311yescharacteristic
91#13093983C2311yescharacteristic
92C2×C4×Dic47—21no—
93C2×C4×Dic47C2311yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95#13093960—41no—
96#13093959—41no—
97#13093958C2×C411yescharacteristic
98#13093958C2×C411yescharacteristic
99#13093957C2×C411yescharacteristic
100#13093957C2×C411yescharacteristic
101#13093956C2×C411yescharacteristic
102#13093956C2×C411yescharacteristic
103#13093955C2×C411yescharacteristic
104#13093955C2×C411yescharacteristic
105C4⋊(C47⋊C8)—21no—
106C4⋊(C47⋊C8)—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109Dic47⋊C8—21no—
110Dic47⋊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#13093951—22no—
124#13093948C2×C411yescharacteristic
125#13093948C2×C411yescharacteristic
126#13093945C2×C411yescharacteristic
127#13093945C2×C411yescharacteristic
128#13093935—41no—
129#13093934—21no—
130#13093934—21no—
131C8×Dic47—21no—
132C8×Dic47—21no—
133C47⋊#95—21no—
134C47⋊#95—21no—
135C2×#41×C47C2311yescharacteristic
136#131×C47—22no—
137#131×C47—41no—
138C2×M16×C47—21no—
139C2×M16×C47C2311yescharacteristic
140C2×M16×C47C2311yescharacteristic
141C22×C8×C47—21no—
142C22×C8×C47C2311yescharacteristic
143C22×C8×C47C2311yescharacteristic
144#117×C47C2311yescharacteristic
145C2×C42×C47C2311yescharacteristic
146#104×C47Q814yescomplemented
147#103×C47C2×C411yescharacteristic
148#103×C47C2×C411yescharacteristic
149#102×C47C2×C411yescharacteristic
150#102×C47C2×C411yescharacteristic
151#97×C47—21no—
152C4×C8×C47—21no—
153C4×C8×C47—41no—
154#41×C47—21no—
155#41×C47—21no—
156#41×C47C2×Q812yes—
157#41×C47#4112yes—
158C2×Q8×C47C22×C411yescharacteristic
159C2×D4×C47—21no—
160C2×D4×C47C22×C411yescharacteristic
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47C2411yescharacteristic
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47#4111yescharacteristic
168C22×Dic47#4111yescharacteristic
169C2×Dic94—21no—
170C2×Dic94—21no—
171M16×C47—21no—
172M16×C47—21no—
173M16×C47—21no—
174M16×C47—42no—
175M16×C47C2×Q812yes—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—42no—
183C2×C8×C47C22×C411yescharacteristic
184C2×C8×C47C22×C411yescharacteristic
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C4⋊C4×C47C22×C411yescharacteristic
188C4⋊C4×C47C22×C411yescharacteristic
189C22⋊C4×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47C2×Q812yes—
193C22⋊Dic47—21no—
194C22⋊Dic47—21no—
195C22⋊Dic47—21no—
196C22⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—21no—
199C4⋊Dic47—21no—
200C4⋊Dic47—21no—
201C4⋊Dic47C22×C411yescharacteristic
202C4⋊Dic47C22×C411yescharacteristic
203C4⋊Dic47C22×C411yescharacteristic
204C4⋊Dic47C22×C411yescharacteristic
205Dic47⋊C4—21no—
206Dic47⋊C4—21no—
207Dic47⋊C4—21no—
208Dic47⋊C4—21no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
214C4×Dic47—21no—
215C4×Dic47C22×C411yescharacteristic
216C4×Dic47C22×C411yescharacteristic
217C4×Dic47C2×D411yescharacteristic
218C4×Dic47C2×D411yescharacteristic
219#10625329—21no—
220#10625329—21no—
221#10625329—21no—
222#10625329—21no—
223#10625329—42no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—42no—
231C2×C47⋊C8C22×C411yescharacteristic
232C2×C47⋊C8C22×C411yescharacteristic
233C2×C47⋊C8C2×D411yescharacteristic
234C2×C47⋊C8C2×D411yescharacteristic
235C23×C47—21no—
236C23×C47C2×#4111yescharacteristic
237Q8×C47—21no—
238Q8×C47C4×Q812yes—
239D4×C47—22no—
240D4×C47—22no—
241D4×C47—21no—
242D4×C47C4×Q812yes—
243C2×C4×C47—21no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—22no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47C23×C411yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×Q811yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47H(5,𝔽2)11yescharacteristic
256C2×C4×C472−1+411yescharacteristic
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—42no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—81no—
268C2×Dic47C4×D411yescharacteristic
269C2×Dic47C4×D411yescharacteristic
270C2×Dic47C4×D411yescharacteristic
271C2×Dic47C4×D411yescharacteristic
272Dic94—42no—
273Dic94—81no—
274C8×C47—21no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—22no—
279C8×C47—41no—
280C47⋊C8—21no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—21no—
284C47⋊C8—41no—
285C47⋊C8—41no—
286#22984—471nomaximal, Sylow
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—22no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47C2×C4×D411yescharacteristic
293C22×C47#55211yescharacteristic
294C22×C47#55411yescharacteristic
295C4×C47—22no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47C2×C4×Q811yescharacteristic
300C4×C47#52011yescharacteristic
301C4×C47#54611yescharacteristic
302C4×C47D4×Q811yescharacteristic
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—21no—
307Dic47—41no—
308Dic47—41no—
309Dic47—41no—
310Dic47—41no—
311Dic47—81no—
312#3076—471no—
313#2962—471no—
314#2906—471no—
315#1995—471no—
316#1950—471no—
317#1946—471no—
318#1945—471no—
319#1922—471no—
320#1922—471no—
321#1866—471no—
322#1866—471no—
323#1768—471no—
324#1765—471no—
325#1764D4711yescharacteristic
326#1759—471no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47—42no—
330C2×C47#236011yescharacteristic
331C2×C47#295511yescharacteristic
332C2×C47#295711yescharacteristic
333C2×#131—471no—
334C2×#131C2×D4711yescharacteristic
335#533—471no—
336C4×#41—471no—
337#479—471no—
338#479—471no—
339#478—471no—
340#478—471no—
341#477—471no—
342#476—471no—
343#475—471no—
344#474—471no—
345#446—941no—
346#446—941no—
347#446—941no—
348C8×Q8—941no—
349C2×#108—471no—
350C2×#108—471no—
351#427—471no—
352#427—471no—
353#424—471no—
354#424—471no—
355#424—471no—
356#424—471no—
357#424—941no—
358#424—941no—
359#423—471no—
360#423—941no—
361C2×C4⋊C8—471no—
362C2×C4⋊C8—471no—
363C2×C4⋊C8—941no—
364C2×#104—471no—
365C2×#104C2×D4711yescharacteristic
366#416—471no—
367#416C2×D4711yescharacteristic
368#405—471no—
369#405C2×D4711yescharacteristic
370C4×M16—471no—
371C2×#97—471no—
372C2×C4×C8C2×D4711yescharacteristic
373#376—471no—
374#341—471no—
375#341C2×D4711yescharacteristic
376#339—471no—
377#339—471no—
378#339—471no—
379#339—471no—
380#339—471no—
381#339C2×D4711yescharacteristic
382#336—471no—
383#336—471no—
384C47#2298411yescharacteristic, complemented, Sylow
385C2×#41C22×D4711yescharacteristic
386#131—22no—
387#131—41no—
388#131—942no—
389#131—1881no—
390C2×M16—21no—
391C2×M16—471no—
392C2×M16—471no—
393C2×M16—941no—
394C2×M16C22×D4711yescharacteristic
395C2×M16C22×D4711yescharacteristic
396C22×C8—21no—
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—941no—
400C22×C8C22×D4711yescharacteristic
401C22×C8C22×D4711yescharacteristic
402C4⋊Q8—471no—
403C4⋊Q8—471no—
404#125—471no—
405#125—471no—
406C22⋊Q8—941no—
407C22⋊Q8—941no—
408C4×Q8—471no—
409C4×Q8—471no—
410C4×Q8—941no—
411C4×Q8—941no—
412C4×D4—471no—
413C4×D4—471no—
414C4×D4—941no—
415C4×D4—941no—
416#117—471no—
417#117—471no—
418#117—941no—
419#117C22×D4711yescharacteristic
420C2×C42—471no—
421C2×C42—471no—
422C2×C42—941no—
423C2×C42C22×D4711yescharacteristic
424#108—1881no—
425#108—1881no—
426#107—471no—
427#107—471no—
428#107—471no—
429#107—471no—
430#106—471no—
431#106—471no—
432#106—471no—
433#106—471no—
434C4⋊C8—471no—
435C4⋊C8—471no—
436C4⋊C8—471no—
437C4⋊C8—471no—
438C4⋊C8—471no—
439C4⋊C8—471no—
440C4⋊C8—471no—
441C4⋊C8—471no—
442C4⋊C8—941no—
443C4⋊C8—941no—
444C4⋊C8—941no—
445C4⋊C8—941no—
446C4⋊C8—941no—
447C4⋊C8—941no—
448C4⋊C8—941no—
449C4⋊C8—941no—
450C4⋊C8—941no—
451C4⋊C8—941no—
452#104—942no—
453#104Dic9414yescomplemented
454#103—471no—
455#103—471no—
456#103C4×D4711yescharacteristic
457#103C4×D4711yescharacteristic
458#102—471no—
459#102—471no—
460#102C4×D4711yescharacteristic
461#102C4×D4711yescharacteristic
462#97—21no—
463#97—941no—
464#97—941no—
465#97—1881no—
466C4×C8—21no—
467C4×C8—41no—
468C4×C8—941no—
469C4×C8—941no—
470#95—941no—
471#95—941no—
472#41—21no—
473#41—21no—
474#41C2×Dic9412yes—
475#41#1062535012yes—
476C2×Q8—941no—
477C2×Q8—941no—
478C2×Q8C2×C4×D4711yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D4711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—471no—
484C22×C4—471no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4C23×D4711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—42no—
493M16—941no—
494M16—941no—
495M16—941no—
496M16—941no—
497M16—1882no—
498M16C2×Dic9412yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—471no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—1882no—
517C2×C8C2×C4×D4711yescharacteristic
518C2×C8C2×C4×D4711yescharacteristic
519C2×C8D4×D4711yescharacteristic
520C2×C8D4×D4711yescharacteristic
521C4⋊C4—471no—
522C4⋊C4—471no—
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
535C22⋊C4—21no—
536C22⋊C4—941no—
537C22⋊C4—941no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C42—21no—
541C42—21no—
542C42—471no—
543C42—471no—
544C42—471no—
545C42—471no—
546C42—941no—
547C42—941no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42—941no—
552C42C2×Dic9412yes—
553C23—21no—
554C23#41×D4711yescharacteristic
555Q8—21no—
556Q8—3761no—
557Q8—1882no—
558Q8C4×Dic9412yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4C4×Dic9412yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—471no—
572C2×C4—471no—
573C2×C4—471no—
574C2×C4—471no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—3761no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1882no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4C22×C4×D4711yescharacteristic
587C2×C4C2×D4×D4711yescharacteristic
588C2×C4C22×Dic9411yescharacteristic
589C2×C4C2×#1062535011yescharacteristic
590C2×C4#1309406911yescharacteristic
591C2×C4#1309407111yescharacteristic
592C8—21no—
593C8—21no—
594C8—22no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—941no—
599C8—941no—
600C8—941no—
601C8—941no—
602C8—1881no—
603C8—1881no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C4×D4×D4711yescharacteristic
610C22#1568980611yescharacteristic
611C22#1568983211yescharacteristic
612C4—22no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—941no—
617C4—941no—
618C4—941no—
619C4—941no—
620C4—3761no—
621C4—1881no—
622C4—1881no—
623C4—1881no—
624C4—1881no—
625C4C2×C4×Dic9411yescharacteristic
626C4#1568960211yescharacteristic
627C4#1568976311yescharacteristic
628C4D4×Dic9411yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#2024639411yescharacteristic
633C2#2025228611yescharacteristic
634C2#2025230011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1764C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C23
cosocleC22×C4×C47C24
hypercenter#1764D47
hypocenterC47#22984
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #20252332C2semidirect
4. #20244367C2semidirect
5. #20244162C2semidirect
6. #20244140C2semidirect
7. #20244136C2semidirect
8. #20243987C2semidirect
9. #20243986C2semidirect
12. #20243246C2semidirect
19. #15689432C4semidirect
20. #15689428C4semidirect
21. #15689425C4semidirect
22. #15689421C4semidirect
23. #15689416C4semidirect
24. #15689411C4semidirect
25. #15689406C4semidirect
26. #15689401C4semidirect
146. #104×C47Q8semidirect
384. C47#22984semidirect
453. #104Dic94semidirect

Maximal subgroups

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

subgroupindex
#202531722
#202523322
#202519542
#202443672
#202441622
#202441402
#202441362
#202439872
#202439862
#202436652
#202436632
#202432462
#202432332
#202432002
C47×#17642
#2298447