Finite Group Databasebeta

← #25157078

Subgroups — #25157078

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144564C211yesmaximal, characteristic, complemented
2#19144143C211yesmaximal, characteristic
3#19143188C211yesmaximal, characteristic, complemented
4#19136140C211yesmaximal, characteristic, complemented
5#19136101C211yesmaximal, characteristic, complemented
6#19136043C211yesmaximal, characteristic, complemented
7#19135810C211yesmaximal, characteristic, complemented
8#19135250C211yesmaximal, characteristic, complemented
9#19135194C211yesmaximal, characteristic, complemented
10#19135108C211yesmaximal, characteristic, complemented
11#19134964C211yesmaximal, characteristic, complemented
12#19134924C211yesmaximal, characteristic
13#19134828C211yesmaximal, characteristic, complemented
14#19134826C211yesmaximal, characteristic, complemented
15C43×#2951C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583470C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583240—21no—
21#14583240—21no—
22#14583234—21no—
23#14583229—21no—
24#14583119—21no—
25#14583112—21no—
26#14583107—21no—
27#14583102—21no—
28#14582942—21no—
29#14582942C2211yescharacteristic
30#14582939—21no—
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582935—21no—
34#14582935C2211yescharacteristic
35C2×#13063256—21no—
36C2×#13063256C2211yescharacteristic
37#14582925C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40#14582907C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#135×C43C2211yescharacteristic
57C43×#520C2211yescharacteristic
58C43×#520C2211yescharacteristic
59C43×#440—21no—
60C43×#440—21no—
61C4×Q16×C43—21no—
62C4×D8×C43—21no—
63C2×#107×C43C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72#13063332—22no—
73#13063332—22no—
74C2×#10621877—21no—
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C22×C43⋊C8—21no—
79C22×C43⋊C8C2311yescharacteristic
80#13063323—21no—
81#13063312—21no—
82#13063306—41no—
83#13063304—21no—
84#13063304—21no—
85Q8×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—41no—
88#13063284—21no—
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258D411yescharacteristic
97#13063258D411yescharacteristic
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256D411yescharacteristic
104#13063256D411yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063252—22no—
108#13063252—22no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063246—21no—
117#13063243—22no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)—21no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C2×#41×C43C2311yescharacteristic
123C2×#41×C43C2311yescharacteristic
124#135×C43—22no—
125#135×C43—22no—
126C2×Q16×C43D411yescharacteristic
127C2×SD16×C43D411yescharacteristic
128C2×SD16×C43D411yescharacteristic
129C2×D8×C43D411yescharacteristic
130C2×M16×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—41no—
137C4×D4×C43—41no—
138#117×C43—21no—
139#117×C43—21no—
140#117×C43C2311yescharacteristic
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145#107×C43—21no—
146#107×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#102×C43—21no—
150#102×C43—21no—
151#97×C43—21no—
152C4×C8×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43#4112yes—
160#41×C43#4112yes—
161C2×Q8×C43C2×D411yescharacteristic
162C2×Q8×C43C2×D411yescharacteristic
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—41no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184Q16×C43—22no—
185SD16×C43—22no—
186SD16×C43—22no—
187D8×C43—22no—
188M16×C43—21no—
189M16×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C22⋊C4×C43—21no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C22⋊Dic43—21no—
210C22⋊Dic43—41no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213#10621885—42no—
214#10621883—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—41no—
218C4⋊Dic43C2×D411yescharacteristic
219C4⋊Dic43C2×D411yescharacteristic
220Dic43⋊C4—41no—
221Dic43⋊C4—41no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—41no—
226#10621877—24no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877#4112yes—
233C2×C43⋊C8—24no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8C2×D411yescharacteristic
241C23×C43—21no—
242C23×C43—21no—
243C23×C43H(5,𝔽2)11yescharacteristic
244Q8×C43—21no—
245Q8×C43—21no—
246Q8×C43—21no—
247Q8×C43#12312yes—
248D4×C43—22no—
249D4×C43—22no—
250D4×C43—21no—
251D4×C43—21no—
252D4×C43—21no—
253D4×C43—41no—
254D4×C43—41no—
255D4×C43#12312yes—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—81no—
267C2×C4×C43—81no—
268C2×C4×C43—161no—
269C2×C4×C43—161no—
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C432−1+411yescharacteristic
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—81no—
286C2×Dic43—161no—
287Dic86—41no—
288Dic86—41no—
289Dic86—41no—
290Dic86—41no—
291C8×C43—21no—
292C8×C43—21no—
293C8×C43—41no—
294C43⋊C8—21no—
295C43⋊C8—22no—
296C43⋊C8—21no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299#26192—431nomaximal, Sylow
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—22no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43#53911yescharacteristic
309C22×C43D4211yescharacteristic
310C22×C43#55311yescharacteristic
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43C2×#12311yescharacteristic
318C4×C43#52511yescharacteristic
319C4×C43#54711yescharacteristic
320C4×C43#54811yescharacteristic
321Dic43—41no—
322Dic43—41no—
323Dic43—81no—
324Dic43—81no—
325Dic43—81no—
326#3097—431no—
327#3046—431no—
328#2951D4311yescharacteristic
329#2912—431no—
330#2097—431no—
331#2089—431no—
332#2079—431no—
333#2038—431no—
334#1930—431no—
335#1922—431no—
336#1908—431no—
337#1882—431no—
338#1876—431no—
339#1860—431no—
340#1860—431no—
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—42no—
344C2×C43—81no—
345C2×C43#244311yescharacteristic
346C2×C43#328911yescharacteristic
347C2×C43#329011yescharacteristic
348C2×#137—431no—
349C2×#135C2×D4311yescharacteristic
350C2×#131—431no—
351#536—431no—
352#520—431no—
353#520C2×D4311yescharacteristic
354#520C2×D4311yescharacteristic
355#485—861no—
356#485—861no—
357#484—861no—
358#483—861no—
359#464—861no—
360#463—861no—
361#462—861no—
362#461—861no—
363#440—21no—
364#440—21no—
365C4×Q16—21no—
366C4×D8—21no—
367#428—431no—
368#428—431no—
369#428—431no—
370#428—861no—
371#428—861no—
372#427—431no—
373#427—861no—
374C2×#107C2×D4311yescharacteristic
375C2×#106—431no—
376C2×#106—861no—
377#424—431no—
378C2×#104—431no—
379C2×#104—431no—
380#419—431no—
381#417—431no—
382#417C2×D4311yescharacteristic
383#417C2×D4311yescharacteristic
384C2×#103—431no—
385C2×#103—431no—
386C2×#101—431no—
387#408—431no—
388#405C2×D4311yescharacteristic
389#391—431no—
390#382—431no—
391#343—431no—
392#343—431no—
393#343—431no—
394#341—431no—
395#341—431no—
396#339—431no—
397#339—431no—
398#336—431no—
399C43#2619211yescharacteristic, complemented, Sylow
400C2×#41C22×D4311yescharacteristic
401C2×#41C22×D4311yescharacteristic
402C22×Q8—431no—
403#137—862no—
404#137—862no—
405#135—22no—
406#135—22no—
407C2×Q16—861no—
408C2×Q16C22⋊D4311yescharacteristic
409C2×SD16—861no—
410C2×SD16C22⋊D4311yescharacteristic
411C2×SD16C22⋊D4311yescharacteristic
412C2×D8C22⋊D4311yescharacteristic
413#131—862no—
414#131—862no—
415C2×M16—431no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—861no—
419C2×M16C22×D4311yescharacteristic
420C22×C8—431no—
421C22×C8—861no—
422C22×C8C22×D4311yescharacteristic
423C4⋊Q8—861no—
424#124—861no—
425#123—1721no—
426C22⋊Q8—861no—
427C22⋊Q8—861no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—861no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—41no—
434C4×D4—41no—
435C4×D4—861no—
436C4×D4—1721no—
437#117—21no—
438#117—21no—
439#117—431no—
440#117—861no—
441#117C22×D4311yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C42—431no—
449#107—21no—
450#107—21no—
451#107—431no—
452#107—431no—
453#107—861no—
454#107—861no—
455#107—861no—
456#106—431no—
457#106—431no—
458#106—861no—
459#106—861no—
460#106—861no—
461#106—861no—
462#106—861no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465#104—862no—
466#104—862no—
467#103—21no—
468#103—21no—
469#103—861no—
470#103—861no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#102—21no—
477#102—21no—
478#102—861no—
479#101—862no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482#97—21no—
483C4×C8—21no—
484#95—1721no—
485#95—1721no—
486#41—21no—
487#41—21no—
488#41—21no—
489#41—21no—
490#41—21no—
491#41—21no—
492#41#1062189812yes—
493#41#1062189812yes—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8C2×C22⋊D4311yescharacteristic
501C2×Q8C2×C22⋊D4311yescharacteristic
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×C22⋊D4311yescharacteristic
505C2×D4C2×C22⋊D4311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—1721no—
516C22×C4C23×D4311yescharacteristic
517Q16—22no—
518Q16—1722no—
519SD16—22no—
520SD16—22no—
521SD16—1722no—
522D8—22no—
523M16—21no—
524M16—21no—
525M16—432no—
526M16—864no—
527M16—861no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—431no—
536C2×C8—431no—
537C2×C8—864no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8C2×C22⋊D4311yescharacteristic
544C2×C8C2×C22⋊D4311yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—431no—
552C4⋊C4—431no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—1721no—
556C4⋊C4—1721no—
557C4⋊C4—1721no—
558C4⋊C4D4×D4311yescharacteristic
559C4⋊C4D4×D4311yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—861no—
564C22⋊C4—1721no—
565C22⋊C4—1721no—
566C22⋊C4—1721no—
567C42—21no—
568C42—41no—
569C42—41no—
570C42—861no—
571C42—861no—
572C42—861no—
573C42—1721no—
574C23—21no—
575C23—21no—
576C23#1306337011yescharacteristic
577Q8—21no—
578Q8—21no—
579Q8—21no—
580Q8—1721no—
581Q8—1721no—
582Q8—1721no—
583Q8—1721no—
584Q8#1306330812yes—
585D4—22no—
586D4—22no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—41no—
591D4—41no—
592D4#1306330812yes—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—161no—
606C2×C4—161no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—3441no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—6881no—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C22×C22⋊D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4#1306337211yescharacteristic
624C8—21no—
625C8—21no—
626C8—41no—
627C8—861no—
628C8—861no—
629C8—862no—
630C8—1721no—
631C8—1721no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22#1458349111yescharacteristic
641C22D4×C22⋊D4311yescharacteristic
642C22#1458359811yescharacteristic
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—3441no—
650C4—3441no—
651C4—3441no—
652C4—1721no—
653C4—1721no—
654C4C2×#1306330811yescharacteristic
655C4#1458340811yescharacteristic
656C4#1458354811yescharacteristic
657C4#1458355811yescharacteristic
658C2—21no—
659C2—21no—
660C2—42no—
661C2—81no—
662C2#1913832411yescharacteristic
663C2#1914636611yescharacteristic
664C2#1914637711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2951C2
socleC22×C43D42
prime radicalC2×#135×C43C22
hypercenter#2951D43
hypocenterC43#26192
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #19144564C2semidirect
3. #19143188C2semidirect
4. #19136140C2semidirect
5. #19136101C2semidirect
6. #19136043C2semidirect
7. #19135810C2semidirect
8. #19135250C2semidirect
9. #19135194C2semidirect
10. #19135108C2semidirect
11. #19134964C2semidirect
13. #19134828C2semidirect
14. #19134826C2semidirect
399. C43#26192semidirect

Maximal subgroups

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

subgroupindex
#191445642
#191441432
#191431882
#191361402
#191361012
#191360432
#191358102
#191352502
#191351942
#191351082
#191349642
#191349242
#191348282
#191348262
C43×#29512
#2619243