Finite Group Databasebeta

← #25125505

Subgroups — #25125505

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582940C211yesmaximal, characteristic, complemented
2#19143111C211yesmaximal, characteristic
3#417×D43C211yesmaximal, characteristic
4#19143037C211yesmaximal, characteristic
5#19136044C211yesmaximal, characteristic, complemented
6#19136043C211yesmaximal, characteristic, complemented
7#19136042C211yesmaximal, characteristic, complemented
8#19136040C211yesmaximal, characteristic, complemented
9#19136039C211yesmaximal, characteristic, complemented
10#19136038C211yesmaximal, characteristic, complemented
11#19136036C211yesmaximal, characteristic, complemented
12#19134332C211yesmaximal, characteristic, complemented
13#343×D43C211yesmaximal, characteristic, complemented
14#19134320C211yesmaximal, characteristic, complemented
15C43×#2078C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582940—22no—
24#14582940—22no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#14582906—21no—
29#14582902—21no—
30#14582901C2211yescharacteristic
31#14582901C2211yescharacteristic
32#14582900C2211yescharacteristic
33#14582900C2211yescharacteristic
34#14582899—21no—
35#14582898C2211yescharacteristic
36#14582898C2211yescharacteristic
37#14582897—21no—
38#14582894—21no—
39#14582892—21no—
40#103×D43—21no—
41#102×D43—21no—
42#14582867C2211yescharacteristic
43#14582866C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582864—22no—
46#14582861—22no—
47#14582668C2211yescharacteristic, complemented
48#14582668C2211yescharacteristic, complemented
49#14582667C2211yescharacteristic, complemented
50#14582667C2211yescharacteristic, complemented
51#14582667C2211yescharacteristic, complemented
52#14582667C2211yescharacteristic, complemented
53#14582664C2211yescharacteristic, complemented
54#14582663C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56C2×#107×C43C2211yescharacteristic, complemented
57C43×#417C2211yescharacteristic
58C43×#417C2211yescharacteristic
59C43×#408C2211yescharacteristic
60C43×#343C2211yescharacteristic, complemented
61C43×#343C2211yescharacteristic, complemented
62C43×#341C2211yescharacteristic, complemented
63C2×#10621902D411yescharacteristic
64C2×#10621898—21no—
65C2×#10621898C2311yescharacteristic
66C2×#10621900—21no—
67C2×#10621900D411yescharacteristic
68#41×D43—22no—
69#41×D43—22no—
70#41×D43—22no—
71#41×D43—22no—
72C2×Q8×D43D411yescharacteristic
73C2×D4×D43—21no—
74C2×D4×D43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621872—22no—
82C2×#10621872—22no—
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×#10621872D412yes—
87C2×#10621872D412yes—
88M16×D43—22no—
89M16×D43—22no—
90M16×D43—22no—
91M16×D43—22no—
92M16×D43—22no—
93M16×D43—22no—
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—21no—
96C2×C8×D43—21no—
97C2×C8×D43—21no—
98#13063283—21no—
99#13063283—21no—
100#13063283—21no—
101#13063283—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C4⋊C4×D43—21no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×C4×Dic43—21no—
111#13063258—22no—
112#13063257—22no—
113#13063256—22no—
114#13063250—21no—
115#13063250—21no—
116#13063249—21no—
117#13063249—21no—
118#13063248—21no—
119#13063248—21no—
120#13063247—21no—
121#13063247—21no—
122#13063246—21no—
123#13063246—21no—
124#13063245—21no—
125#13063245—21no—
126C22⋊(C43⋊C8)—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—22no—
129C2×#41×C43C2311yescharacteristic
130C2×M16×C43C2311yescharacteristic
131C2×M16×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136#107×C43—22no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141C22⋊C8×C43—22no—
142C23×D43—21no—
143C23×D43#4111yescharacteristic
144#41×C43—21no—
145#41×C43—21no—
146#41×C43—21no—
147#41×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—21no—
156C2×C22⋊D43—21no—
157C2×C22⋊D43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43#4111yescharacteristic
162#10621902—22no—
163#10621902—22no—
164Q8×D43—22no—
165Q8×D43—22no—
166#10621900—22no—
167#10621900—22no—
168#10621900—42no—
169#10621900—42no—
170D4×D43—22no—
171D4×D43—22no—
172D4×D43—42no—
173D4×D43—42no—
174#10621898—21no—
175#10621898—21no—
176#10621898—21no—
177#10621898—21no—
178#10621898—42no—
179#10621898—42no—
180C2×D172—21no—
181C2×D172C2×D411yescharacteristic
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—82no—
190C2×C4×D43C2×D411yescharacteristic
191C2×C4×D43C2×D411yescharacteristic
192C2×C4×D43C2×D411yescharacteristic
193C2×C4×D43C2×D411yescharacteristic
194C2×C4×D43#4112yes—
195C2×C4×D43#4112yes—
196C2×C4×D43#4112yes—
197C2×C4×D43#4112yes—
198C2×Dic86—21no—
199C2×Dic86C2×D411yescharacteristic
200M16×C43—21no—
201M16×C43—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—21no—
205M16×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C2×D412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216(C2×D43)⋊C4—41no—
217(C2×D43)⋊C4—41no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222Dic43⋊C4—41no—
223Dic43⋊C4—41no—
224C4×Dic43—41no—
225C4×Dic43—41no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C2×D412yes—
238#10621872—24no—
239#10621872—24no—
240#10621872—42no—
241#10621872—42no—
242#10621872—42no—
243C8×D43—42no—
244C8×D43—42no—
245C8×D43—42no—
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—42no—
252C22×D43—81no—
253C22×D43—81no—
254C22×D43#12111yescharacteristic
255C22×D43#12111yescharacteristic
256C22×D43#12612yes—
257C22×D43#12612yes—
258Q8×C43—21no—
259Q8×C43—21no—
260D4×C43—21no—
261D4×C43—21no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—81no—
270C2×C4×C43—81no—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C22⋊D43—41no—
278C22⋊D43—41no—
279C22⋊D43—42no—
280C22⋊D43—42no—
281C2×Dic43—21no—
282C2×Dic43—42no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—81no—
286C2×Dic43—81no—
287C2×Dic43#12111yescharacteristic
288C2×Dic43#12111yescharacteristic
289C2×Dic43#12612yes—
290C2×Dic43#12612yes—
291D172—21no—
292D172—21no—
293D172—42no—
294C4×D43—42no—
295C4×D43—41no—
296C4×D43—41no—
297C4×D43—42no—
298C4×D43—82no—
299C4×D43—82no—
300C4×D43#12312yes—
301C4×D43#12312yes—
302C4×D43#12312yes—
303C4×D43#12312yes—
304C4×D43#12312yes—
305C4×D43#12312yes—
306C4×D43#12412yes—
307C4×D43#12412yes—
308Dic86—21no—
309Dic86—21no—
310Dic86—42no—
311C8×C43—22no—
312C8×C43—41no—
313C8×C43—41no—
314C8×C43—41no—
315C43⋊C8—22no—
316C43⋊C8—41no—
317C43⋊C8—41no—
318C43⋊C8—41no—
319#23647—431nomaximal, Sylow
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43C2×#12111yescharacteristic
326C22×C43C2×#12611yescharacteristic
327C22×C43C2×#12611yescharacteristic
328C2×D43—21no—
329C2×D43—21no—
330C2×D43—21no—
331C2×D43—21no—
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—41no—
335C2×D43—41no—
336C2×D43—41no—
337C2×D43—84no—
338C2×D43#39712yes—
339C2×D43#39712yes—
340C4×C43—41no—
341C4×C43—81no—
342C4×C43—81no—
343C4×C43C2×#12311yescharacteristic
344C4×C43C2×#12311yescharacteristic
345C4×C43C2×#12311yescharacteristic
346C4×C43C2×#12411yescharacteristic
347Dic43—41no—
348Dic43—81no—
349Dic43—81no—
350Dic43#39712yes—
351Dic43#39712yes—
352C2×#428—431no—
353#2896—431no—
354C2×#417—431no—
355#2879—431no—
356#2079—431no—
357#2079—431no—
358#2079—431no—
359#2079—431no—
360#2078—431no—
361#2078—431no—
362#2078—431no—
363#2078D4311yescharacteristic, complemented
364#1742—431no—
365C2×#343—431no—
366#1738—431no—
367C2×C43—21no—
368C2×C43—21no—
369C2×C43—81no—
370C2×C43C2×#39711yescharacteristic
371C2×C43#306811yescharacteristic
372C2×C43#306911yescharacteristic
373D43—22no—
374D43—22no—
375D43—81no—
376C22×#41—431no—
377C22×M16—431no—
378C22×M16—431no—
379C22×M16—431no—
380C22×M16—431no—
381C2×#117—431no—
382C22×C4⋊C4—431no—
383#428—862no—
384#428—862no—
385C2×#107—431no—
386C2×#107C2×D4311yescharacteristic, complemented
387C2×#106—431no—
388C2×#106—431no—
389#419—861no—
390#418—861no—
391#417—431no—
392#417—431no—
393#417—431no—
394#417—431no—
395#417—431no—
396#417—431no—
397#417—861no—
398#417—861no—
399#417C2×D4311yescharacteristic
400#417C2×D4311yescharacteristic
401#416—861no—
402#416—861no—
403C2×#103—861no—
404C2×#102—861no—
405#408—431no—
406#408—431no—
407#408—431no—
408#408—862no—
409#408C2×D4311yescharacteristic
410#407—862no—
411#343—431no—
412#343—431no—
413#343—431no—
414#343—431no—
415#343—431no—
416#343—431no—
417#343C2×D4311yescharacteristic, complemented
418#343C2×D4311yescharacteristic, complemented
419#341—431no—
420#341—431no—
421#341—431no—
422#341C2×D4311yescharacteristic, complemented
423C43#2364711yescharacteristic, complemented, Sylow
424C2×#41—431no—
425C2×#41—431no—
426C2×#41—431no—
427C2×#41—861no—
428C2×#41—861no—
429C2×#41—862no—
430C2×#41—862no—
431C2×#41—862no—
432C2×#41—862no—
433C2×#41C22×D4311yescharacteristic
434C22×Q8—431no—
435C22×D4—431no—
436C22×D4—861no—
437C23×C4—431no—
438C23×C4—861no—
439C23×C4—861no—
440C2×M16—432no—
441C2×M16—432no—
442C2×M16—431no—
443C2×M16—431no—
444C2×M16—431no—
445C2×M16—862no—
446C2×M16—862no—
447C2×M16—861no—
448C2×M16—861no—
449C2×M16—861no—
450C2×M16—862no—
451C2×M16—862no—
452C2×M16—862no—
453C2×M16—862no—
454C2×M16—862no—
455C2×M16—862no—
456C2×M16C22×D4311yescharacteristic
457C2×M16C22×D4311yescharacteristic
458C2×M16C22×D4311yescharacteristic
459C22×C8—431no—
460C22×C8—861no—
461C22×C8—861no—
462C22×C8—861no—
463C22×C8C22×D4311yescharacteristic
464#117—861no—
465#117—861no—
466#117—861no—
467#117—861no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C22⋊C4—861no—
478C2×C42—861no—
479#107—22no—
480#107—862no—
481#106—862no—
482#106—862no—
483#103—21no—
484#103—21no—
485#103—861no—
486#103—861no—
487#103—861no—
488#103—861no—
489#103—861no—
490#103—861no—
491#102—21no—
492#102—21no—
493#102—861no—
494#102—861no—
495#102—861no—
496#102—861no—
497#102—861no—
498#102—861no—
499C22⋊C8—22no—
500C22⋊C8—862no—
501C22⋊C8—862no—
502C22⋊C8—862no—
503C24—431no—
504C24—861no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—862no—
510#41—862no—
511#41—862no—
512#41—862no—
513#41—861no—
514#41—861no—
515#41—861no—
516#41—861no—
517#41—1722no—
518#41—1722no—
519#41—1722no—
520#41—1722no—
521C2×Q8—431no—
522C2×Q8—861no—
523C2×Q8—862no—
524C2×Q8—862no—
525C2×Q8D4×D4311yescharacteristic
526C2×D4—21no—
527C2×D4—431no—
528C2×D4—861no—
529C2×D4—862no—
530C2×D4—862no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—1722no—
535C2×D4—1722no—
536C2×D4D4×D4311yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—431no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—3442no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4C23×D4311yescharacteristic
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16—21no—
566M16—21no—
567M16—864no—
568M16—864no—
569M16—861no—
570M16—861no—
571M16—861no—
572M16—861no—
573M16—861no—
574M16—861no—
575M16—1722no—
576M16—1722no—
577M16—1722no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—432no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—1722no—
590C2×C8—1722no—
591C2×C8—1722no—
592C2×C8D4×D4312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—1721no—
602C4⋊C4—1721no—
603C22⋊C4—1721no—
604C22⋊C4—1721no—
605C42—1721no—
606C42—1721no—
607C23—21no—
608C23—431no—
609C23—431no—
610C23—432no—
611C23—432no—
612C23—861no—
613C23—3441no—
614C23—3441no—
615C23—1721no—
616C23—1721no—
617C23—1722no—
618C23#41×D4311yescharacteristic
619Q8—21no—
620Q8—21no—
621Q8—861no—
622Q8—861no—
623Q8—1722no—
624D4—21no—
625D4—21no—
626D4—41no—
627D4—41no—
628D4—861no—
629D4—861no—
630D4—1722no—
631D4—1722no—
632D4—1722no—
633D4—1721no—
634D4—1721no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—431no—
643C2×C4—431no—
644C2×C4—432no—
645C2×C4—432no—
646C2×C4—432no—
647C2×C4—432no—
648C2×C4—432no—
649C2×C4—432no—
650C2×C4—432no—
651C2×C4—432no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—861no—
655C2×C4—3442no—
656C2×C4—3442no—
657C2×C4—3441no—
658C2×C4—3441no—
659C2×C4—1722no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4C2×D4×D4311yescharacteristic
668C2×C4#41×D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C2×C4#41×D4311yescharacteristic
671C2×C4#41×D4311yescharacteristic
672C8—22no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—862no—
677C8—1721no—
678C8—1721no—
679C8—1721no—
680C22—21no—
681C22—21no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—432no—
686C22—432no—
687C22—861no—
688C22—861no—
689C22—861no—
690C22—861no—
691C22—3444no—
692C22—1722no—
693C22—1722no—
694C22—1721no—
695C22—1721no—
696C22—1721no—
697C22#121×D4311yescharacteristic
698C22#126×D4311yescharacteristic
699C22#126×D4311yescharacteristic
700C4—41no—
701C4—81no—
702C4—81no—
703C4—432no—
704C4—432no—
705C4—3441no—
706C4—3441no—
707C4—1721no—
708C4#123×D4311yescharacteristic
709C4#123×D4311yescharacteristic
710C4#123×D4311yescharacteristic
711C4#124×D4311yescharacteristic
712C2—21no—
713C2—21no—
714C2—81no—
715C2—862no—
716C2—862no—
717C2—3441no—
718C2#397×D4311yescharacteristic
719C2#1914432111yescharacteristic
720C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2078C2
socleC22×C43C2×#121
prime radicalC2×#41×D43C22
hypercenter#2078D43
hypocenterC43#23647
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. C2×#14582940C2semidirect
5. #19136044C2semidirect
6. #19136043C2semidirect
7. #19136042C2semidirect
8. #19136040C2semidirect
9. #19136039C2semidirect
10. #19136038C2semidirect
11. #19136036C2semidirect
12. #19134332C2semidirect
13. #343×D43C2semidirect
14. #19134320C2semidirect
15. C43×#2078C2semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×#13063256C22semidirect
47. #14582668C22semidirect
48. #14582668C22semidirect
49. #14582667C22semidirect
50. #14582667C22semidirect
51. #14582667C22semidirect
52. #14582667C22semidirect
53. #14582664C22semidirect
54. #14582663C22semidirect
55. #14582663C22semidirect
56. C2×#107×C43C22semidirect
60. C43×#343C22semidirect
61. C43×#343C22semidirect
62. C43×#341C22semidirect
363. #2078D43semidirect
386. C2×#107C2×D43semidirect
417. #343C2×D43semidirect
418. #343C2×D43semidirect
422. #341C2×D43semidirect
423. C43#23647semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
#191431112
#417×D432
#191430372
#191360442
#191360432
#191360422
#191360402
#191360392
#191360382
#191360362
#191343322
#343×D432
#191343202
C43×#20782
#2364743