Finite Group Databasebeta

← #25099100

Subgroups — #25099100

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582946C211yesmaximal, characteristic, complemented
2C2×#14582914C211yesmaximal, characteristic
3#19143110C211yesmaximal, characteristic
4#408×D43C211yesmaximal, characteristic
5#405×D43C211yesmaximal, characteristic, complemented
6#19135246C211yesmaximal, characteristic, complemented
7#19135245C211yesmaximal, characteristic, complemented
8#19135244C211yesmaximal, characteristic, complemented
9#19135243C211yesmaximal, characteristic, complemented
10#19135242C211yesmaximal, characteristic, complemented
11#19135241C211yesmaximal, characteristic, complemented
12#19135240C211yesmaximal, characteristic, complemented
13#19134303C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#117×D43C2211yescharacteristic
23#14582946—24no—
24C2×#13063261C2211yescharacteristic, complemented
25C2×#13063260C2211yescharacteristic, complemented
26C2×#13063260C2211yescharacteristic, complemented
27#14582914—24no—
28C2×#13063253C2211yescharacteristic
29C2×#13063252C2211yescharacteristic
30C2×#13063251C2211yescharacteristic
31#14582906C411yescharacteristic, complemented
32#14582906C411yescharacteristic, complemented
33#14582902C411yescharacteristic, complemented
34#14582902C411yescharacteristic, complemented
35#14582899C411yescharacteristic, complemented
36#14582899C411yescharacteristic, complemented
37#14582897C411yescharacteristic, complemented
38#14582897C411yescharacteristic, complemented
39#14582896C2211yescharacteristic
40#14582895C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582867C2211yescharacteristic
43#14582866C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582864—21no—
46#14582864—21no—
47C22⋊C8×D43—21no—
48C22⋊C8×D43—21no—
49#14582857C2211yescharacteristic, complemented
50#14582856—21no—
51#14582855C2211yescharacteristic, complemented
52#14582854C2211yescharacteristic, complemented
53#14582853—21no—
54#97×D43—21no—
55C4×C8×D43—21no—
56#14582660C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582658C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C2×#108×C43C2211yescharacteristic, complemented
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C43×#405C2211yescharacteristic, complemented
67C43×#339C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621900—21no—
73C2×#10621900C2×C411yescharacteristic
74#41×D43—22no—
75#41×D43—22no—
76#41×D43—22no—
77#41×D43—22no—
78C2×Q8×D43C2×C411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872—21no—
89C2×#10621872C2×C411yescharacteristic
90C2×#10621872C2×C411yescharacteristic
91C2×#10621872C2×C411yescharacteristic
92C2×#10621872C2×C411yescharacteristic
93M16×D43—22no—
94M16×D43—22no—
95M16×D43—22no—
96M16×D43D414yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—21no—
100C2×C8×D43—22no—
101C2×C8×D43—22no—
102C2×C8×D43—21no—
103C2×C8×D43D411yescharacteristic
104C2×C8×D43D411yescharacteristic
105C2×C8×D43D411yescharacteristic
106C2×C8×D43D411yescharacteristic
107#13063284C2311yescharacteristic
108#13063283C2×C411yescharacteristic
109#13063283C2×C411yescharacteristic
110#13063282—21no—
111#13063282—22no—
112#13063282—22no—
113#13063281—21no—
114C2×Dic43⋊C4—21no—
115C4⋊C4×D43C2×C411yescharacteristic
116C4⋊C4×D43C2×C411yescharacteristic
117C2×(C2×D43)⋊C4—21no—
118C22⋊C4×D43—21no—
119C2×C4×Dic43C2311yescharacteristic
120C42×D43—21no—
121#13063261—22no—
122#13063260—22no—
123#13063260—22no—
124#13063253—22no—
125#13063252—22no—
126#13063251—22no—
127#13063250C2×C411yescharacteristic
128#13063250C2×C411yescharacteristic
129#13063249C2×C411yescharacteristic
130#13063249C2×C411yescharacteristic
131#13063248C2×C411yescharacteristic
132#13063248C2×C411yescharacteristic
133#13063247C2×C411yescharacteristic
134#13063247C2×C411yescharacteristic
135#13063246C2×C411yescharacteristic
136#13063246C2×C411yescharacteristic
137#13063245C2×C411yescharacteristic
138#13063245C2×C411yescharacteristic
139C22⋊(C43⋊C8)—21no—
140C22⋊(C43⋊C8)—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145#13063236—21no—
146#13063235—21no—
147#13063235—21no—
148C4×C43⋊C8—21no—
149C8×Dic43—21no—
150C8×Dic43—21no—
151C2×#41×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#117×C43C2311yescharacteristic
157C2×C42×C43C2311yescharacteristic
158#108×C43—22no—
159#104×C43—22no—
160#103×C43C2×C411yescharacteristic
161#103×C43C2×C411yescharacteristic
162#102×C43C2×C411yescharacteristic
163#102×C43C2×C411yescharacteristic
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166#97×C43—21no—
167C4×C8×C43—21no—
168C23×D43—21no—
169C23×D43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174C2×Q8×C43C22×C411yescharacteristic
175C2×D4×C43—21no—
176C2×D4×C43C22×C411yescharacteristic
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43#4111yescharacteristic
186#10621902—22no—
187#10621902—22no—
188Q8×D43—22no—
189Q8×D43—22no—
190#10621900—22no—
191#10621900—22no—
192#10621900—42no—
193#10621900—42no—
194D4×D43—22no—
195D4×D43—22no—
196D4×D43—42no—
197D4×D43—42no—
198#10621898—21no—
199#10621898—21no—
200#10621898—21no—
201#10621898—21no—
202#10621898—42no—
203#10621898—42no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43C22×C411yescharacteristic
214C2×C4×D43C22×C411yescharacteristic
215C2×C4×D43C2×D411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D412yes—
218C2×C4×D43#4112yes—
219C2×C4×D43#4112yes—
220C2×C4×D43#4112yes—
221C2×Dic86—21no—
222C2×Dic86C22×C411yescharacteristic
223M16×C43—21no—
224M16×C43—21no—
225M16×C43—21no—
226M16×C43C2×D412yes—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43C22×C411yescharacteristic
234C2×C8×C43C22×C411yescharacteristic
235C2×C8×C43C2×D411yescharacteristic
236C2×C8×C43C2×D411yescharacteristic
237C4⋊C4×C43C22×C411yescharacteristic
238C4⋊C4×C43C22×C411yescharacteristic
239C22⋊C4×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C22⋊Dic43—21no—
244(C2×D43)⋊C4—21no—
245(C2×D43)⋊C4—21no—
246(C2×D43)⋊C4—42no—
247C4⋊Dic43C22×C411yescharacteristic
248C4⋊Dic43C22×C411yescharacteristic
249Dic43⋊C4—21no—
250Dic43⋊C4—21no—
251Dic43⋊C4—42no—
252C4×Dic43—21no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256C4×Dic43—21no—
257#10621877—21no—
258#10621877—21no—
259#10621877—21no—
260#10621877C2×D412yes—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C411yescharacteristic
268C2×C43⋊C8C22×C411yescharacteristic
269C2×C43⋊C8C2×D411yescharacteristic
270C2×C43⋊C8C2×D411yescharacteristic
271#10621872—22no—
272#10621872—22no—
273#10621872—22no—
274#10621872—22no—
275#10621872—24no—
276#10621872—42no—
277C8×D43—24no—
278C8×D43—22no—
279C8×D43—22no—
280C8×D43—22no—
281C8×D43—22no—
282C8×D43—42no—
283C23×C43—21no—
284C23×C43C2×#4111yescharacteristic
285C22×D43—21no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43C4×D411yescharacteristic
292C22×D43C4×D411yescharacteristic
293C22×D43#12412yes—
294C22×D43#12612yes—
295Q8×C43—21no—
296Q8×C43—21no—
297D4×C43—21no—
298D4×C43—21no—
299D4×C43—41no—
300D4×C43—41no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43C23×C411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C22⋊D43—41no—
316C22⋊D43—41no—
317C22⋊D43—42no—
318C22⋊D43—42no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—42no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43C4×D411yescharacteristic
327C2×Dic43C4×D411yescharacteristic
328C2×Dic43#12412yes—
329C2×Dic43#12612yes—
330D172—21no—
331D172—21no—
332D172—42no—
333C4×D43—42no—
334C4×D43—42no—
335C4×D43—42no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—42no—
339C4×D43#11712yes—
340C4×D43#11712yes—
341C4×D43C4×D412yes—
342C4×D43C4×D412yes—
343C4×D43#12112yes—
344C4×D43#12112yes—
345C4×D43#12312yes—
346C4×D43#12312yes—
347Dic86—21no—
348Dic86—21no—
349Dic86—42no—
350C8×C43—21no—
351C8×C43—21no—
352C8×C43—22no—
353C8×C43—21no—
354C8×C43—21no—
355C8×C43—41no—
356C43⋊C8—21no—
357C43⋊C8—21no—
358C43⋊C8—22no—
359C43⋊C8—21no—
360C43⋊C8—21no—
361C43⋊C8—41no—
362#21070—431nomaximal, Sylow
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43C2×C4×D411yescharacteristic
369C22×C43C2×#12411yescharacteristic
370C22×C43C2×#12611yescharacteristic
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—84no—
381C2×D43#38812yes—
382C2×D43#38812yes—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—81no—
387C4×C43C2×#11711yescharacteristic
388C4×C43C2×C4×D411yescharacteristic
389C4×C43C2×#12111yescharacteristic
390C4×C43C2×#12311yescharacteristic
391Dic43—41no—
392Dic43—41no—
393Dic43—41no—
394Dic43—81no—
395Dic43#38812yes—
396Dic43#38812yes—
397C2×#430—431no—
398C2×#421—431no—
399#2896—431no—
400C2×#408—431no—
401C2×#405—431no—
402#1929—431no—
403#1929—431no—
404#1929—431no—
405#1929—431no—
406#1929—431no—
407#1929—431no—
408#1929—431no—
409#1929D4311yescharacteristic, complemented
410#1733—431no—
411#1729—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—81no—
415C2×C43C2×#38811yescharacteristic
416C2×C43#295511yescharacteristic
417C2×C43#295511yescharacteristic
418D43—22no—
419D43—22no—
420D43—81no—
421C22×#41—431no—
422C22×M16—431no—
423C22×M16—431no—
424C22×M16—431no—
425C23×C8—431no—
426C2×#117—431no—
427C2×#117—431no—
428#430—864no—
429C2×#108—431no—
430C2×#108—431no—
431C2×#108—431no—
432C2×#108C2×D4311yescharacteristic, complemented
433#421—864no—
434C2×#104—431no—
435C2×#104—431no—
436C2×#104—431no—
437C2×#104C2×D4311yescharacteristic
438#419—431no—
439#419—431no—
440#418—431no—
441#418—431no—
442#417—431no—
443#417—431no—
444#417—431no—
445#417—431no—
446#416—431no—
447#416—431no—
448#416—431no—
449#416C2×D4311yescharacteristic
450#408—431no—
451#408—431no—
452#408—431no—
453#408—861no—
454#408—861no—
455#408C2×D4311yescharacteristic
456C2×C22⋊C8—861no—
457C2×C22⋊C8—861no—
458#405—431no—
459#405—431no—
460#405—431no—
461#405—861no—
462#405—861no—
463#405C2×D4311yescharacteristic, complemented
464C2×#97—861no—
465C2×C4×C8—861no—
466#339—431no—
467#339—431no—
468#339—431no—
469#339C2×D4311yescharacteristic, complemented
470#336—431no—
471#336—431no—
472#336—431no—
473#336C2×D4311yescharacteristic, complemented
474C43#2107011yescharacteristic, complemented, Sylow
475C2×#41—431no—
476C2×#41—431no—
477C2×#41—431no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—862no—
481C2×#41—862no—
482C2×#41—862no—
483C2×#41—862no—
484C2×#41C22×D4311yescharacteristic
485C22×Q8—431no—
486C22×D4—431no—
487C22×D4—861no—
488C23×C4—431no—
489C23×C4—861no—
490C2×M16—431no—
491C2×M16—431no—
492C2×M16—431no—
493C2×M16—431no—
494C2×M16—431no—
495C2×M16—434no—
496C2×M16—431no—
497C2×M16—861no—
498C2×M16—862no—
499C2×M16—862no—
500C2×M16—861no—
501C2×M16—862no—
502C2×M16—862no—
503C2×M16—862no—
504C2×M16C22×D4311yescharacteristic
505C2×M16C22×D4311yescharacteristic
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—431no—
509C22×C8—431no—
510C22×C8—431no—
511C22×C8—431no—
512C22×C8—862no—
513C22×C8—862no—
514C22×C8—861no—
515C22×C8—861no—
516C22×C8C22×D4311yescharacteristic
517C22×C8C22×D4311yescharacteristic
518#117—431no—
519#117—431no—
520#117—431no—
521#117—861no—
522#117—862no—
523#117—862no—
524#117—861no—
525#117C22×D4311yescharacteristic
526C2×C4⋊C4—431no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C42—431no—
532C2×C42—861no—
533C2×C42C22×D4311yescharacteristic
534#108—22no—
535#108—862no—
536#108—862no—
537#108—862no—
538#104—22no—
539#104—862no—
540#104—862no—
541#104—862no—
542#103—431no—
543#103—431no—
544#103—431no—
545#103—431no—
546#103—431no—
547#103—431no—
548#103C4×D4311yescharacteristic
549#103C4×D4311yescharacteristic
550#102—431no—
551#102—431no—
552#102—431no—
553#102—431no—
554#102—431no—
555#102—431no—
556#102C4×D4311yescharacteristic
557#102C4×D4311yescharacteristic
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—861no—
561C22⋊C8—861no—
562C22⋊C8—861no—
563C22⋊C8—861no—
564C22⋊C8—861no—
565C22⋊C8—861no—
566#97—21no—
567#97—861no—
568#97—861no—
569#97—861no—
570C4×C8—21no—
571C4×C8—861no—
572C4×C8—861no—
573C4×C8—861no—
574C24—431no—
575C24—861no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—861no—
585#41—861no—
586#41—861no—
587#41—861no—
588#41—1722no—
589#41—1722no—
590#41—1722no—
591#41—1722no—
592C2×Q8—431no—
593C2×Q8—861no—
594C2×Q8—862no—
595C2×Q8—862no—
596C2×Q8C2×C4×D4311yescharacteristic
597C2×D4—21no—
598C2×D4—431no—
599C2×D4—861no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—1722no—
606C2×D4—1722no—
607C2×D4C2×C4×D4311yescharacteristic
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—432no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—432no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4C23×D4311yescharacteristic
629M16—21no—
630M16—21no—
631M16—21no—
632M16—432no—
633M16—862no—
634M16—862no—
635M16—862no—
636M16—862no—
637M16—864no—
638M16—861no—
639M16—861no—
640M16—861no—
641M16—1722no—
642M16D4×D4312yes—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—431no—
650C2×C8—431no—
651C2×C8—431no—
652C2×C8—431no—
653C2×C8—862no—
654C2×C8—862no—
655C2×C8—862no—
656C2×C8—862no—
657C2×C8—864no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—1722no—
665C2×C8C2×C4×D4311yescharacteristic
666C2×C8C2×C4×D4311yescharacteristic
667C2×C8D4×D4311yescharacteristic
668C2×C8D4×D4311yescharacteristic
669C4⋊C4—431no—
670C4⋊C4—431no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—1722no—
674C4⋊C4C2×C4×D4311yescharacteristic
675C4⋊C4C2×C4×D4311yescharacteristic
676C22⋊C4—21no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—1722no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—861no—
685C42—861no—
686C42—861no—
687C42—861no—
688C42—861no—
689C23—21no—
690C23—431no—
691C23—431no—
692C23—432no—
693C23—432no—
694C23—861no—
695C23—1721no—
696C23—1721no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23#41×D4311yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—861no—
704Q8—861no—
705Q8—1722no—
706D4—21no—
707D4—21no—
708D4—41no—
709D4—41no—
710D4—861no—
711D4—861no—
712D4—1722no—
713D4—1722no—
714D4—1722no—
715D4—1721no—
716D4—1721no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4C22×C4×D4311yescharacteristic
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4#41×D4311yescharacteristic
754C2×C4#41×D4311yescharacteristic
755C2×C4#41×D4311yescharacteristic
756C8—21no—
757C8—21no—
758C8—22no—
759C8—21no—
760C8—21no—
761C8—41no—
762C8—861no—
763C8—861no—
764C8—862no—
765C8—861no—
766C8—861no—
767C8—1721no—
768C22—21no—
769C22—21no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—432no—
774C22—432no—
775C22—861no—
776C22—861no—
777C22—861no—
778C22—861no—
779C22—3444no—
780C22—1722no—
781C22—1722no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22C4×D4×D4311yescharacteristic
786C22#124×D4311yescharacteristic
787C22#126×D4311yescharacteristic
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—432no—
793C4—432no—
794C4—3441no—
795C4—1721no—
796C4—1721no—
797C4—1721no—
798C4#117×D4311yescharacteristic
799C4C4×D4×D4311yescharacteristic
800C4#121×D4311yescharacteristic
801C4#123×D4311yescharacteristic
802C2—21no—
803C2—21no—
804C2—81no—
805C2—862no—
806C2—862no—
807C2—3441no—
808C2#388×D4311yescharacteristic
809C2#1914349311yescharacteristic
810C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1929C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1929D43
hypocenterC43#21070
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#14582946C2semidirect
5. #405×D43C2semidirect
6. #19135246C2semidirect
7. #19135245C2semidirect
8. #19135244C2semidirect
9. #19135243C2semidirect
10. #19135242C2semidirect
11. #19135241C2semidirect
12. #19135240C2semidirect
13. #19134303C2semidirect
14. #19134290C2semidirect
15. C43×#1929C2semidirect
24. C2×#13063261C22semidirect
25. C2×#13063260C22semidirect
26. C2×#13063260C22semidirect
31. #14582906C4semidirect
32. #14582906C4semidirect
33. #14582902C4semidirect
34. #14582902C4semidirect
35. #14582899C4semidirect
36. #14582899C4semidirect
37. #14582897C4semidirect
38. #14582897C4semidirect
49. #14582857C22semidirect
51. #14582855C22semidirect
52. #14582854C22semidirect
56. #14582660C22semidirect
57. #14582659C22semidirect
58. #14582658C22semidirect
59. #14582654C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
62. C2×#108×C43C22semidirect
66. C43×#405C22semidirect
67. C43×#339C22semidirect
68. C43×#336C22semidirect
409. #1929D43semidirect
432. C2×#108C2×D43semidirect
463. #405C2×D43semidirect
469. #339C2×D43semidirect
473. #336C2×D43semidirect
474. C43#21070semidirect

Maximal subgroups

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

subgroupindex
C2×#145829462
C2×#145829142
#191431102
#408×D432
#405×D432
#191352462
#191352452
#191352442
#191352432
#191352422
#191352412
#191352402
#191343032
#191342902
C43×#19292
#2107043