Finite Group Databasebeta

← #25157080

Subgroups — #25157080

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#19144558C211yesmaximal, characteristic, complemented
2#19143471C211yesmaximal, characteristic
3#19143188C211yesmaximal, characteristic, complemented
4#19136141C211yesmaximal, characteristic, complemented
5#19136100C211yesmaximal, characteristic, complemented
6#19136043C211yesmaximal, characteristic, complemented
7#19135809C211yesmaximal, characteristic, complemented
8#19135247C211yesmaximal, characteristic, complemented
9#19135191C211yesmaximal, characteristic, complemented
10#19135112C211yesmaximal, characteristic, complemented
11#19134966C211yesmaximal, characteristic, complemented
12#19134924C211yesmaximal, characteristic
13#19134828C211yesmaximal, characteristic, complemented
14#19134826C211yesmaximal, characteristic, complemented
15C43×#3046C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583382C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583237—21no—
20#14583237—21no—
21#14583232—21no—
22#14583227—21no—
23#14583000—21no—
24#14583000—21no—
25Q16×Dic43—21no—
26D8×Dic43—21no—
27#14582942—21no—
28#14582942C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582939—21no—
31#14582939C2211yescharacteristic
32#14582935—21no—
33#14582935C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35C2×#13063256—21no—
36C2×#13063256C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39#14582908C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582854C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#137×C43C2211yescharacteristic
57C2×#135×C43C2211yescharacteristic
58C43×#536C2211yescharacteristic
59C43×#520C2211yescharacteristic
60C43×#464—21no—
61C43×#463—21no—
62C43×#462—21no—
63C43×#461—21no—
64C43×#424C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C2×#103×C43C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8—21no—
74C22×C43⋊C8C2311yescharacteristic
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77D4×Dic43—21no—
78D4×Dic43—21no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81#13063284—21no—
82#13063284—21no—
83#13063284C2311yescharacteristic
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—21no—
90#13063259—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258D411yescharacteristic
95#13063258D411yescharacteristic
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256D411yescharacteristic
102#13063256D411yescharacteristic
103#13063252—22no—
104#13063252—22no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063246—21no—
112#13063246—21no—
113#13063244—22no—
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)—21no—
116#13063235—21no—
117C8×Dic43—21no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C2×#41×C43C2311yescharacteristic
121C2×#41×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123#137×C43—22no—
124#137×C43—22no—
125#135×C43—22no—
126#135×C43—22no—
127C2×Q16×C43—21no—
128C2×Q16×C43D411yescharacteristic
129C2×SD16×C43—21no—
130C2×SD16×C43D411yescharacteristic
131C2×SD16×C43D411yescharacteristic
132C2×D8×C43D411yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4⋊Q8×C43—21no—
136#124×C43—21no—
137#123×C43—41no—
138C22⋊Q8×C43—21no—
139C22⋊Q8×C43—21no—
140C4×Q8×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—41no—
143#117×C43—21no—
144#117×C43C2311yescharacteristic
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149#103×C43—21no—
150#103×C43—21no—
151#103×C43—21no—
152#102×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×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C2×D411yescharacteristic
168C2×Q8×C43C2×D411yescharacteristic
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43C2×D411yescharacteristic
172C2×D4×C43C2×D411yescharacteristic
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—41no—
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—41no—
183C22×Dic43—41no—
184Q16×C43—22no—
185Q16×C43—42no—
186SD16×C43—22no—
187SD16×C43—22no—
188SD16×C43—42no—
189D8×C43—22no—
190M16×C43—21no—
191M16×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C42×C43—21no—
209C42×C43—41no—
210C22⋊Dic43—21no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—41no—
218C4⋊Dic43—41no—
219C4⋊Dic43C2×D411yescharacteristic
220C4⋊Dic43C2×D411yescharacteristic
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—41no—
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—41no—
248Q8×C43—41no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43#12312yes—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43—21no—
255D4×C43—21no—
256D4×C43—21no—
257D4×C43—41no—
258D4×C43—41no—
259D4×C43#12312yes—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—81no—
273C2×C4×C43—161no—
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C432−1+411yescharacteristic
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—81no—
288C2×Dic43—81no—
289C2×Dic43—161no—
290C2×Dic43—161no—
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#3046D4311yescharacteristic
328#2951—431no—
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×#137C2×D4311yescharacteristic
349C2×#135C2×D4311yescharacteristic
350C2×#131—431no—
351#536C2×D4311yescharacteristic
352#520—431no—
353#520—431no—
354#520C2×D4311yescharacteristic
355#485—861no—
356#485—861no—
357#484—861no—
358#483—861no—
359#464—21no—
360#463—21no—
361#462—21no—
362#461—21no—
363#440—861no—
364#440—861no—
365C4×Q16—861no—
366C4×D8—861no—
367#428—431no—
368#428—431no—
369#428—431no—
370#428—861no—
371#428—861no—
372#427—431no—
373#427—861no—
374C2×#107—431no—
375C2×#106—431no—
376C2×#106—861no—
377#424C2×D4311yescharacteristic
378C2×#104—431no—
379C2×#104—431no—
380#419—431no—
381#417—431no—
382#417—431no—
383#417C2×D4311yescharacteristic
384C2×#103—431no—
385C2×#103C2×D4311yescharacteristic
386C2×#101—431no—
387#408—431no—
388#405—431no—
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×Q8C22×D4311yescharacteristic
403#137—22no—
404#137—22no—
405#135—22no—
406#135—22no—
407C2×Q16—21no—
408C2×Q16C22⋊D4311yescharacteristic
409C2×SD16—21no—
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—21no—
424#124—21no—
425#123—41no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C4×Q8—21no—
429C4×Q8—861no—
430C4×Q8—861no—
431C4×D4—21no—
432C4×D4—41no—
433C4×D4—861no—
434C4×D4—861no—
435C4×D4—1721no—
436C4×D4—1721no—
437#117—21no—
438#117—431no—
439#117—861no—
440#117—861no—
441#117C22×D4311yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C42—431no—
449#107—431no—
450#107—431no—
451#107—861no—
452#107—861no—
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—21no—
464C4⋊C8—21no—
465#104—862no—
466#104—862no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—861no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#102—21no—
477#102—861no—
478#102—861no—
479#101—862no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482#97—861no—
483C4×C8—861no—
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#1062190012yes—
493#41#1062190012yes—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
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—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—1721no—
515C22×C4—1721no—
516C22×C4C23×D4311yescharacteristic
517Q16—22no—
518Q16—42no—
519SD16—22no—
520SD16—22no—
521SD16—42no—
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—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—431no—
551C4⋊C4—431no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—1721no—
557C4⋊C4—1721no—
558C4⋊C4D4×D4311yescharacteristic
559C4⋊C4D4×D4311yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—861no—
565C22⋊C4—1721no—
566C22⋊C4—1721no—
567C42—21no—
568C42—41no—
569C42—861no—
570C42—861no—
571C42—861no—
572C42—1721no—
573C42—1721no—
574C23—21no—
575C23—21no—
576C23#1306337011yescharacteristic
577Q8—21no—
578Q8—21no—
579Q8—21no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8#1306330612yes—
585D4—22no—
586D4—22no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—41no—
591D4—41no—
592D4#1306330612yes—
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—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—161no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—3441no—
610C2×C4—3441no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—6881no—
617C2×C4—6881no—
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C22×C22⋊D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4C2×#1062190011yescharacteristic
622C2×C4C2×#1062190011yescharacteristic
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#1458349411yescharacteristic
641C22D4×C22⋊D4311yescharacteristic
642C22#1458359211yescharacteristic
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—3441no—
650C4—3441no—
651C4—3441no—
652C4—1721no—
653C4—1721no—
654C4C2×#1306330611yescharacteristic
655C4#1458340911yescharacteristic
656C4#1458354811yescharacteristic
657C4#1458355511yescharacteristic
658C2—21no—
659C2—21no—
660C2—42no—
661C2—81no—
662C2#1913832611yescharacteristic
663C2#1914636811yescharacteristic
664C2#1914638111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3046C2
socleC22×C43D42
prime radicalC2×#135×C43C22
hypercenter#3046D43
hypocenterC43#26192
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3046

Complements

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

NH ≅ G/Ntype
1. #19144558C2semidirect
3. #19143188C2semidirect
4. #19136141C2semidirect
5. #19136100C2semidirect
6. #19136043C2semidirect
7. #19135809C2semidirect
8. #19135247C2semidirect
9. #19135191C2semidirect
10. #19135112C2semidirect
11. #19134966C2semidirect
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
#191445582
#191434712
#191431882
#191361412
#191361002
#191360432
#191358092
#191352472
#191351912
#191351122
#191349662
#191349242
#191348282
#191348262
C43×#30462
#2619243