Finite Group Databasebeta

← #26234786

Subgroups — #26234786

Order 12032.

850 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252272C211yesmaximal, characteristic
2#20252264C211yesmaximal, characteristic
3#20251988C211yesmaximal, characteristic, complemented
4#20251983C211yesmaximal, characteristic, complemented
5#20244174C211yesmaximal, characteristic, complemented
6#20244169C211yesmaximal, characteristic, complemented
7#20243623C211yesmaximal, characteristic, complemented
8#20243623C211yesmaximal, characteristic, complemented
9#20243616C211yesmaximal, characteristic, complemented
10#20243616C211yesmaximal, characteristic, complemented
11#20243556C211yesmaximal, characteristic, complemented
12#20243452C211yesmaximal, characteristic, complemented
13#20243447C211yesmaximal, characteristic, complemented
14#20243272C211yesmaximal, characteristic, complemented
15C2×C47×#444C211yesmaximal, characteristic
16#15689606C2211yescharacteristic
17#15689606C2211yescharacteristic
18#15689606C2211yescharacteristic
19#15689606C2211yescharacteristic
20#15689235—21no—
21#15689230—21no—
22#15689224—21no—
23#15689224—21no—
24Q16×Dic47—21no—
25SD16×Dic47—21no—
26SD16×Dic47—21no—
27D8×Dic47—21no—
28C2×#13093960C2211yescharacteristic
29#15689165—21no—
30#15689165—21no—
31#15689165—21no—
32#15689165—21no—
33#15689165C2211yescharacteristic
34#15689165C2211yescharacteristic
35#15689165C2211yescharacteristic
36#15689165C2211yescharacteristic
37#15689161—21no—
38#15689161—21no—
39#15689161C2211yescharacteristic
40C2×#13093958—21no—
41C2×#13093958C2211yescharacteristic
42C2×#13093958C2211yescharacteristic
43C2×#13093956—21no—
44C2×#13093956C2211yescharacteristic
45C2×#13093956C2211yescharacteristic
46#15689124C2211yescharacteristic
47#15689124C2211yescharacteristic
48#15689124C2211yescharacteristic
49#15689124C2211yescharacteristic
50#15689078C2211yescharacteristic
51#15689078C2211yescharacteristic
52#15688993C2211yescharacteristic
53#15688989C2211yescharacteristic
54#15688891C2211yescharacteristic
55#15688891C2211yescharacteristic
56#15688891C2211yescharacteristic
57#15688891C2211yescharacteristic
58#15688883C2211yescharacteristic
59#15688883C2211yescharacteristic
60C2×#135×C47C2211yescharacteristic
61C2×#131×C47C2211yescharacteristic
62C2×#131×C47C2211yescharacteristic
63C47×#444C418yescomplemented
64C2×#108×C47C2211yescharacteristic
65C2×#104×C47C2211yescharacteristic
66C2×#104×C47C2211yescharacteristic
67C2×#97×C47C2211yescharacteristic
68C2×#10625329C2311yescharacteristic
69C2×#10625329C2311yescharacteristic
70Q8×Dic47—21no—
71Q8×Dic47—21no—
72Q8×Dic47—21no—
73Q8×Dic47—21no—
74D4×Dic47—21no—
75D4×Dic47—21no—
76D4×Dic47—21no—
77D4×Dic47—21no—
78D4×Dic47—41no—
79D4×Dic47—41no—
80D4×Dic47—41no—
81D4×Dic47—41no—
82#13093983—21no—
83#13093983—21no—
84#13093983—21no—
85#13093983—21no—
86#13093983C2311yescharacteristic
87#13093983C2311yescharacteristic
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—41no—
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97#13093960—22no—
98#13093958—21no—
99#13093958—21no—
100#13093958—21no—
101#13093958—21no—
102#13093958—21no—
103#13093958—21no—
104#13093958—21no—
105#13093958—21no—
106#13093958D411yescharacteristic
107#13093958D411yescharacteristic
108#13093956—21no—
109#13093956—21no—
110#13093956—21no—
111#13093956—21no—
112#13093956—21no—
113#13093956—21no—
114#13093956—21no—
115#13093956—21no—
116#13093956D411yescharacteristic
117#13093956D411yescharacteristic
118#13093948—21no—
119#13093948—21no—
120#13093948—21no—
121#13093948—21no—
122#13093945—21no—
123#13093945—21no—
124#13093945—21no—
125#13093945—21no—
126#13093934—21no—
127#13093934—21no—
128C8×Dic47—21no—
129C8×Dic47—21no—
130C47⋊#95—41no—
131C2×#41×C47C2311yescharacteristic
132C2×#41×C47C2311yescharacteristic
133#135×C47C2×C414yes—
134#135×C47Q814yes—
135C2×Q16×C47D411yescharacteristic
136C2×SD16×C47D411yescharacteristic
137C2×SD16×C47D411yescharacteristic
138C2×D8×C47D411yescharacteristic
139#131×C47—22no—
140#131×C47—22no—
141#131×C47C2×C414yescomplemented
142#131×C47C2×C414yescomplemented
143C2×M16×C47—21no—
144C2×M16×C47—21no—
145C2×M16×C47C2311yescharacteristic
146C2×M16×C47C2311yescharacteristic
147C22×C8×C47—21no—
148C22×C8×C47—21no—
149C22×C8×C47C2311yescharacteristic
150C22×C8×C47C2311yescharacteristic
151C2×C42×C47C2311yescharacteristic
152#108×C47C2×C414yescomplemented
153#104×C47C2×C414yescomplemented
154#104×C47C2×C414yescomplemented
155#97×C47C2×C414yescomplemented
156#41×C47—21no—
157#41×C47—21no—
158#41×C47—21no—
159#41×C47—21no—
160#41×C47C22×C412yes—
161#41×C47C22×C412yes—
162#41×C47C2×Q812yes—
163#41×C47C2×Q812yes—
164C2×Q8×C47C2×D411yescharacteristic
165C2×Q8×C47C2×D411yescharacteristic
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47C2×D411yescharacteristic
169C2×D4×C47C2×D411yescharacteristic
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47C2411yescharacteristic
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—41no—
179C22×Dic47—41no—
180C22×Dic47—41no—
181C22×Dic47—41no—
182Q16×C47C4⋊C414yescomplemented
183SD16×C47C4⋊C414yescomplemented
184SD16×C47C4⋊C414yescomplemented
185D8×C47C4⋊C414yescomplemented
186M16×C47—21no—
187M16×C47—21no—
188M16×C47—24no—
189M16×C47—24no—
190M16×C47C22×C412yes—
191M16×C47C22×C412yes—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—24no—
195C2×C8×C47—24no—
196C2×C8×C47C22×C412yes—
197C2×C8×C47C22×C412yes—
198C2×C8×C47C2×D411yescharacteristic
199C2×C8×C47C2×D411yescharacteristic
200C2×C8×C47C2×D411yescharacteristic
201C2×C8×C47C2×D411yescharacteristic
202C2×C8×C47C2×Q812yes—
203C2×C8×C47#4112yes—
204C42×C47—21no—
205C42×C47C22×C412yes—
206C22⋊Dic47—21no—
207C22⋊Dic47—21no—
208C22⋊Dic47—41no—
209C22⋊Dic47—41no—
210C22⋊Dic47—41no—
211C22⋊Dic47—41no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—41no—
221C4⋊Dic47—41no—
222C4⋊Dic47—41no—
223C4⋊Dic47—41no—
224C4⋊Dic47—82no—
225C4⋊Dic47C2×D411yescharacteristic
226C4⋊Dic47C2×D411yescharacteristic
227C4⋊Dic47C2×D411yescharacteristic
228C4⋊Dic47C2×D411yescharacteristic
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—41no—
232C4×Dic47—41no—
233C4×Dic47—41no—
234C4×Dic47—41no—
235#10625329—21no—
236#10625329—21no—
237#10625329—21no—
238#10625329—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47H(5,𝔽2)11yescharacteristic
244Q8×C47—21no—
245Q8×C47—21no—
246Q8×C47C2×C4⋊C412yes—
247Q8×C47C2×C4⋊C412yes—
248D4×C47—22no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47—22no—
252D4×C47—21no—
253D4×C47—21no—
254D4×C47C2×C4⋊C412yes—
255D4×C47C2×C4⋊C412yes—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47C23×C411yescharacteristic
266C2×C4×C47C22×D411yescharacteristic
267C2×C4×C47C22×D411yescharacteristic
268C2×C4×C47C22×Q811yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C472−1+411yescharacteristic
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—81no—
280C2×Dic47—81no—
281C2×Dic47—81no—
282C2×Dic47—81no—
283C2×Dic47—161no—
284C2×Dic47—161no—
285C2×Dic47—161no—
286C2×Dic47—161no—
287C8×C47—22no—
288C8×C47—22no—
289C8×C47C2×C4⋊C412yes—
290C8×C47C2×C4⋊C412yes—
291C8×C47C4×D412yes—
292C8×C47C4×D412yes—
293C47⋊C8—41no—
294C47⋊C8—41no—
295#22693—471nomaximal, Sylow
296C22×C47—21no—
297C22×C47—21no—
298C22×C47—22no—
299C22×C47—22no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47—41no—
304C22×C47#52011yescharacteristic
305C22×C47D4211yescharacteristic
306C22×C47#55411yescharacteristic
307C4×C47—22no—
308C4×C47—22no—
309C4×C47—42no—
310C4×C47C22×C4⋊C411yescharacteristic
311C4×C47C2×C4×D411yescharacteristic
312C4×C47#54711yescharacteristic
313C4×C47D4×Q811yescharacteristic
314Dic47—41no—
315Dic47—41no—
316Dic47—41no—
317Dic47—41no—
318Dic47—81no—
319Dic47—81no—
320Dic47—81no—
321Dic47—81no—
322C2×#444D4711yescharacteristic
323#2952—471no—
324#2951—471no—
325#2913—471no—
326#2912—471no—
327#1952—471no—
328#1951—471no—
329#1860—471no—
330#1860—471no—
331#1859—471no—
332#1859—471no—
333#1847—471no—
334#1816—471no—
335#1815—471no—
336#1773—471no—
337C2×C47—21no—
338C2×C47—21no—
339C2×C47—42no—
340C2×C47—42no—
341C2×C47D4×C4⋊C411yescharacteristic
342C2×C47#328811yescharacteristic
343C2×C47#328911yescharacteristic
344C2×#135C2×D4711yescharacteristic
345C2×#131C2×D4711yescharacteristic
346C2×#131C2×D4711yescharacteristic
347#520—471no—
348#520—471no—
349#520—471no—
350#520—471no—
351#444Dic4718yescomplemented
352#442—941no—
353#441—941no—
354#440—941no—
355#440—941no—
356C4×Q16—941no—
357C4×SD16—941no—
358C4×SD16—941no—
359C4×D8—941no—
360C2×#108—471no—
361C2×#108C2×D4711yescharacteristic
362#428—471no—
363#428—471no—
364#428—471no—
365#428—471no—
366#428—941no—
367#428—941no—
368#428—941no—
369#428—941no—
370#427—471no—
371#427—941no—
372#427—941no—
373C2×#107—471no—
374C2×#107—471no—
375C2×#107—941no—
376C2×#106—471no—
377C2×#106—471no—
378C2×#106—941no—
379C2×#104C2×D4711yescharacteristic
380C2×#104C2×D4711yescharacteristic
381#417—471no—
382#417—471no—
383#417—471no—
384#417—471no—
385#405—471no—
386#405—471no—
387C2×#97C2×D4711yescharacteristic
388#384—471no—
389#382—471no—
390#343—471no—
391#343—471no—
392#343—471no—
393#343—471no—
394#339—471no—
395#339—471no—
396C47#2269311yescharacteristic, complemented, Sylow
397C2×#41C22×D4711yescharacteristic
398C2×#41C22×D4711yescharacteristic
399#135Dic9414yes—
400#135C2×Dic4714yes—
401C2×Q16D18811yescharacteristic
402C2×SD16D18811yescharacteristic
403C2×SD16D18811yescharacteristic
404C2×D8D18811yescharacteristic
405#131—22no—
406#131—22no—
407#131C2×Dic4714yescomplemented
408#131C2×Dic4714yescomplemented
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—471no—
412C2×M16—471no—
413C2×M16C22×D4711yescharacteristic
414C2×M16C22×D4711yescharacteristic
415C22×C8—21no—
416C22×C8—21no—
417C22×C8C22×D4711yescharacteristic
418C22×C8C22×D4711yescharacteristic
419C4×Q8—941no—
420C4×Q8—941no—
421C4×Q8—941no—
422C4×Q8—941no—
423C4×D4—941no—
424C4×D4—941no—
425C4×D4—941no—
426C4×D4—941no—
427C4×D4—1881no—
428C4×D4—1881no—
429C4×D4—1881no—
430C4×D4—1881no—
431#117—471no—
432#117—471no—
433#117—941no—
434#117—941no—
435#117—941no—
436#117—941no—
437C2×C4⋊C4—471no—
438C2×C4⋊C4—471no—
439C2×C4⋊C4—471no—
440C2×C4⋊C4—471no—
441C2×C4⋊C4—941no—
442C2×C4⋊C4—941no—
443C2×C4⋊C4—941no—
444C2×C4⋊C4—941no—
445C2×C4⋊C4—1881no—
446C2×C42C22×D4711yescharacteristic
447#108—942no—
448#108C2×Dic4714yescomplemented
449#107—471no—
450#107—471no—
451#107—941no—
452#107—941no—
453#107—941no—
454#107—941no—
455#107—941no—
456#107—941no—
457#107—941no—
458#107—941no—
459#106—471no—
460#106—471no—
461#106—941no—
462#106—941no—
463#106—941no—
464#106—941no—
465#106—941no—
466#106—941no—
467#106—941no—
468#106—941no—
469#104C2×Dic4714yescomplemented
470#104C2×Dic4714yescomplemented
471#103—941no—
472#103—941no—
473#103—941no—
474#103—941no—
475#102—941no—
476#102—941no—
477#102—941no—
478#102—941no—
479#97—941no—
480#97—941no—
481#97C2×Dic4714yescomplemented
482C4×C8—941no—
483C4×C8—941no—
484#95—1881no—
485#41—21no—
486#41—21no—
487#41—21no—
488#41—21no—
489#41C2×Dic9412yes—
490#41C2×Dic9412yes—
491#41C22×Dic4712yes—
492#41C22×Dic4712yes—
493C2×Q8C2×D18811yescharacteristic
494C2×Q8C2×D18811yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4C2×D18811yescharacteristic
498C2×D4C2×D18811yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—1881no—
507C22×C4—1881no—
508C22×C4—1881no—
509C22×C4—1881no—
510C22×C4C23×D4711yescharacteristic
511Q16C4⋊Dic4714yescomplemented
512SD16C4⋊Dic4714yescomplemented
513SD16C4⋊Dic4714yescomplemented
514D8C4⋊Dic4714yescomplemented
515M16—21no—
516M16—21no—
517M16—24no—
518M16—24no—
519M16—941no—
520M16—941no—
521M16—941no—
522M16—941no—
523M16C22×Dic4712yes—
524M16C22×Dic4712yes—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—941no—
530C2×C8—941no—
531C2×C8C2×Dic9412yes—
532C2×C8C2×D18811yescharacteristic
533C2×C8C2×D18811yescharacteristic
534C2×C8D4×D4711yescharacteristic
535C2×C8D4×D4711yescharacteristic
536C2×C8#1062535212yes—
537C2×C8C22×Dic4712yes—
538C2×C8C22×Dic4712yes—
539C4⋊C4—471no—
540C4⋊C4—471no—
541C4⋊C4—471no—
542C4⋊C4—471no—
543C4⋊C4—941no—
544C4⋊C4—941no—
545C4⋊C4—941no—
546C4⋊C4—941no—
547C4⋊C4—941no—
548C4⋊C4—941no—
549C4⋊C4—941no—
550C4⋊C4—941no—
551C4⋊C4—3762no—
552C4⋊C4—1881no—
553C4⋊C4—1881no—
554C4⋊C4—1881no—
555C4⋊C4—1881no—
556C22⋊C4—941no—
557C22⋊C4—941no—
558C22⋊C4—1881no—
559C22⋊C4—1881no—
560C22⋊C4—1881no—
561C22⋊C4—1881no—
562C42—21no—
563C42—941no—
564C42—941no—
565C42—1881no—
566C42—1881no—
567C42—1881no—
568C42—1881no—
569C42C22×Dic4712yes—
570C23—21no—
571C23—21no—
572C23#1309407011yescharacteristic
573Q8—21no—
574Q8—21no—
575Q8C2×C4⋊Dic4712yes—
576Q8C2×C4⋊Dic4712yes—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4—21no—
582D4—21no—
583D4C2×C4⋊Dic4712yes—
584D4C2×C4⋊Dic4712yes—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—941no—
595C2×C4—941no—
596C2×C4—941no—
597C2×C4—941no—
598C2×C4—3761no—
599C2×C4—3761no—
600C2×C4—3761no—
601C2×C4—3761no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4—7521no—
607C2×C4—7521no—
608C2×C4—7521no—
609C2×C4—7521no—
610C2×C4C23×Dic4711yescharacteristic
611C2×C4C2×D4×D4711yescharacteristic
612C2×C4C22×D18811yescharacteristic
613C2×C4C22×Dic9411yescharacteristic
614C2×C4C2×#1062535211yescharacteristic
615C2×C4#1309407111yescharacteristic
616C8—22no—
617C8—22no—
618C8—1881no—
619C8—1881no—
620C8C2×C4⋊Dic4712yes—
621C8C2×C4⋊Dic4712yes—
622C8D4×Dic4712yes—
623C8D4×Dic4712yes—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22#1568960611yescharacteristic
633C22D4×D18811yescharacteristic
634C22#1568983011yescharacteristic
635C4—22no—
636C4—22no—
637C4—42no—
638C4—3761no—
639C4—3761no—
640C4—3761no—
641C4—3761no—
642C4—1881no—
643C4—1881no—
644C4—1881no—
645C4—1881no—
646C4C22×C4⋊Dic4711yescharacteristic
647C4C2×D4×Dic4711yescharacteristic
648C4#1568977711yescharacteristic
649C4D4×Dic9411yescharacteristic
650C2—21no—
651C2—21no—
652C2—42no—
653C2—42no—
654C2D4×C4⋊Dic4711yescharacteristic
655C2#2025515511yescharacteristic
656C2#2025516411yescharacteristic
subgroupG/H
centerC22D4×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#444C2
socleC22×C47D42
prime radicalC2×#135×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#444D47
hypocenterC47#22693
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
3. #20251988C2semidirect
4. #20251983C2semidirect
5. #20244174C2semidirect
6. #20244169C2semidirect
7. #20243623C2semidirect
8. #20243623C2semidirect
9. #20243616C2semidirect
10. #20243616C2semidirect
11. #20243556C2semidirect
12. #20243452C2semidirect
13. #20243447C2semidirect
14. #20243272C2semidirect
63. C47×#444C4semidirect
141. #131×C47C2×C4semidirect
142. #131×C47C2×C4semidirect
152. #108×C47C2×C4semidirect
153. #104×C47C2×C4semidirect
154. #104×C47C2×C4semidirect
155. #97×C47C2×C4semidirect
182. Q16×C47C4⋊C4semidirect
183. SD16×C47C4⋊C4semidirect
184. SD16×C47C4⋊C4semidirect
185. D8×C47C4⋊C4semidirect
351. #444Dic47semidirect
396. C47#22693semidirect
407. #131C2×Dic47semidirect
408. #131C2×Dic47semidirect
448. #108C2×Dic47semidirect
469. #104C2×Dic47semidirect
470. #104C2×Dic47semidirect
481. #97C2×Dic47semidirect
511. Q16C4⋊Dic47semidirect
512. SD16C4⋊Dic47semidirect
513. SD16C4⋊Dic47semidirect
514. D8C4⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
#202522722
#202522642
#202519882
#202519832
#202441742
#202441692
#202436232
#202436162
#202435562
#202434522
#202434472
#202432722
C2×C47×#4442
#2269347