Finite Group Databasebeta

← #25096288

Subgroups — #25096288

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583664C211yesmaximal, characteristic
2C2×#14582946C211yesmaximal, characteristic, complemented
3C2×#14582940C211yesmaximal, characteristic, complemented
4#19143111C211yesmaximal, characteristic
5#417×D43C211yesmaximal, characteristic
6#19134660C211yesmaximal, characteristic, complemented
7#19134658C211yesmaximal, characteristic, complemented
8#19134657C211yesmaximal, characteristic, complemented
9#19134654C211yesmaximal, characteristic, complemented
10#19134653C211yesmaximal, characteristic, complemented
11#19134652C211yesmaximal, characteristic, complemented
12#19134651C211yesmaximal, characteristic, complemented
13#19134332C211yesmaximal, characteristic, complemented
14#343×D43C211yesmaximal, characteristic, complemented
15C43×#1816C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583664—24no—
18#14583664C418yescomplemented
19C2×#13063333—21no—
20C2×#13063333C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22C2×#13063331—21no—
23C2×#13063331C2211yescharacteristic
24C22×#10621872—21no—
25C22×#10621872C2211yescharacteristic
26C2×M16×D43—21no—
27C2×M16×D43C2211yescharacteristic
28C2×M16×D43C2211yescharacteristic
29C2×M16×D43C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582946—24no—
33C2×#13063261C2211yescharacteristic, complemented
34C2×#13063260C2211yescharacteristic, complemented
35C2×#13063260C2211yescharacteristic, complemented
36#14582940—21no—
37#14582940—21no—
38#14582940—21no—
39#14582940—21no—
40C2×#13063258C2211yescharacteristic, complemented
41C2×#13063257C2211yescharacteristic, complemented
42C2×#13063256C2211yescharacteristic, complemented
43#14582906—21no—
44#14582902—21no—
45#14582901C2211yescharacteristic
46#14582901C2211yescharacteristic
47#14582900C2211yescharacteristic
48#14582900C2211yescharacteristic
49#14582899—21no—
50#14582898C2211yescharacteristic
51#14582898C2211yescharacteristic
52#14582897—21no—
53#14582894—21no—
54#14582892—21no—
55#103×D43—21no—
56#102×D43—21no—
57#14582668C2211yescharacteristic, complemented
58#14582668C2211yescharacteristic, complemented
59#14582667C2211yescharacteristic, complemented
60#14582667C2211yescharacteristic, complemented
61#14582667C2211yescharacteristic, complemented
62#14582667C2211yescharacteristic, complemented
63C2×#131×C43C2211yescharacteristic
64C2×#108×C43C2211yescharacteristic, complemented
65C2×#107×C43C2211yescharacteristic, complemented
66C43×#417C2211yescharacteristic
67C43×#417C2211yescharacteristic
68C43×#343C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C2×#10621902D411yescharacteristic
71C2×#10621898—21no—
72C2×#10621898C2311yescharacteristic
73C2×#10621900—21no—
74C2×#10621900D411yescharacteristic
75#41×D43—22no—
76#41×D43—22no—
77#41×D43C2×C414yes—
78#41×D43Q814yes—
79C2×Q8×D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43D411yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063333—22no—
86#13063333—28no—
87#13063333C2×C414yescomplemented
88#13063332—22no—
89#13063332C2×C414yescomplemented
90#13063331—22no—
91#13063331—28no—
92#13063331C2×C414yescomplemented
93C2×#10621877—21no—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621877C2311yescharacteristic
97C2×#10621872—21no—
98C2×#10621872—21no—
99C2×#10621872—21no—
100C2×#10621872—28no—
101C2×#10621872—21no—
102C2×#10621872—21no—
103C2×#10621872C2×C414yes—
104C2×#10621872D411yescharacteristic
105C2×#10621872D411yescharacteristic
106C2×#10621872D411yescharacteristic
107C2×#10621872D411yescharacteristic
108C2×#10621872D414yes—
109M16×D43—22no—
110M16×D43—28no—
111M16×D43—22no—
112M16×D43—22no—
113M16×D43—22no—
114M16×D43—22no—
115M16×D43C2×C414yes—
116C22×C43⋊C8—21no—
117C22×C43⋊C8C2311yescharacteristic
118C2×C8×D43—21no—
119C2×C8×D43—21no—
120C2×C8×D43—21no—
121C2×C8×D43—21no—
122C2×C8×D43—21no—
123#13063283—21no—
124#13063283—21no—
125#13063283—21no—
126#13063283—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C4⋊C4×D43—21no—
131C4⋊C4×D43—21no—
132C4⋊C4×D43—21no—
133C4⋊C4×D43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×C4×Dic43—21no—
136#13063261—22no—
137#13063260—22no—
138#13063260—22no—
139#13063258—21no—
140#13063258—21no—
141#13063257—21no—
142#13063257—21no—
143#13063256—21no—
144#13063256—21no—
145#13063250—21no—
146#13063250—21no—
147#13063249—21no—
148#13063249—21no—
149#13063248—21no—
150#13063248—21no—
151#13063247—21no—
152#13063247—21no—
153#13063246—21no—
154#13063246—21no—
155#13063245—21no—
156#13063245—21no—
157C2×#41×C43C2311yescharacteristic
158#131×C43—22no—
159#131×C43C2×C414yescomplemented
160C2×M16×C43—21no—
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C2×M16×C43C2311yescharacteristic
164C22×C8×C43—21no—
165C22×C8×C43C2311yescharacteristic
166C2×C4⋊C4×C43C2311yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168#108×C43—22no—
169#107×C43—21no—
170#107×C43—21no—
171#103×C43—21no—
172#103×C43—21no—
173#102×C43—21no—
174#102×C43—21no—
175C23×D43—21no—
176C23×D43#4111yescharacteristic
177#41×C43—21no—
178#41×C43—21no—
179#41×C43C22×C412yes—
180#41×C43C2×Q812yes—
181C2×Q8×C43C2×D411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C2×D411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43#4111yescharacteristic
195#10621902—22no—
196#10621902C4⋊C414yes—
197Q8×D43—22no—
198Q8×D43C4⋊C414yes—
199#10621900—24no—
200#10621900—24no—
201#10621900—22no—
202#10621900C4⋊C414yes—
203D4×D43—22no—
204D4×D43—24no—
205D4×D43—24no—
206D4×D43C4⋊C414yes—
207#10621898—21no—
208#10621898—21no—
209#10621898—24no—
210#10621898—24no—
211#10621898C22×C412yes—
212#10621898C2×Q812yes—
213C2×D172—21no—
214C2×D172C2×D411yescharacteristic
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—21no—
220C2×C4×D43—41no—
221C2×C4×D43—41no—
222C2×C4×D43—82no—
223C2×C4×D43C22×C412yes—
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D412yes—
229C2×C4×D43C2×Q812yes—
230C2×C4×D43#4112yes—
231C2×Dic86—21no—
232C2×Dic86C2×D411yescharacteristic
233M16×C43—21no—
234M16×C43—24no—
235M16×C43—21no—
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239M16×C43C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—24no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43C22×C412yes—
245C2×C8×C43C2×D411yescharacteristic
246C2×C8×C43C2×D411yescharacteristic
247C2×C8×C43C2×D412yes—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252(C2×D43)⋊C4—41no—
253(C2×D43)⋊C4—41no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258Dic43⋊C4—41no—
259Dic43⋊C4—41no—
260C4×Dic43—41no—
261C4×Dic43—41no—
262#10621877—21no—
263#10621877—24no—
264#10621877—21no—
265#10621877—21no—
266#10621877—21no—
267#10621877—21no—
268#10621877C22×C412yes—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—24no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8C22×C412yes—
274C2×C43⋊C8C2×D411yescharacteristic
275C2×C43⋊C8C2×D411yescharacteristic
276C2×C43⋊C8C2×D412yes—
277#10621872—24no—
278#10621872—24no—
279#10621872—24no—
280#10621872—42no—
281#10621872—42no—
282#10621872C22⋊C414yes—
283#10621872C22⋊C414yes—
284#10621872C22⋊C414yes—
285#10621872C22⋊C414yes—
286C8×D43—24no—
287C8×D43—24no—
288C8×D43—24no—
289C8×D43—42no—
290C8×D43—42no—
291C23×C43—21no—
292C23×C43C2×#4111yescharacteristic
293C22×D43—21no—
294C22×D43—24no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—81no—
298C22×D43—81no—
299C22×D43#11712yes—
300C22×D43#12111yescharacteristic
301C22×D43#12111yescharacteristic
302C22×D43C22⋊Q812yes—
303Q8×C43—21no—
304Q8×C43C2×C4⋊C412yes—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—21no—
308D4×C43C2×C4⋊C412yes—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—81no—
315C2×C4×C43—81no—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×Q811yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C22⋊D43—22no—
323C22⋊D43—22no—
324C22⋊D43—24no—
325C22⋊D43—24no—
326C2×Dic43—21no—
327C2×Dic43—24no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—81no—
331C2×Dic43—81no—
332C2×Dic43#11712yes—
333C2×Dic43#12111yescharacteristic
334C2×Dic43#12111yescharacteristic
335C2×Dic43C22⋊Q812yes—
336D172—24no—
337D172—21no—
338D172C2×C4⋊C412yes—
339C4×D43—24no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—24no—
343C4×D43—82no—
344C4×D43—82no—
345C4×D43C2×C22⋊C412yes—
346C4×D43C2×C22⋊C412yes—
347C4×D43C2×C4⋊C412yes—
348C4×D43C2×C4⋊C412yes—
349C4×D43#12112yes—
350C4×D43#12112yes—
351C4×D43C22⋊Q812yes—
352C4×D43C22⋊Q812yes—
353Dic86—21no—
354Dic86—24no—
355Dic86C2×C4⋊C412yes—
356C8×C43—22no—
357C8×C43—41no—
358C8×C43—41no—
359C8×C43C2×C22⋊C412yes—
360C8×C43C2×C22⋊C412yes—
361C43⋊C8—22no—
362C43⋊C8—41no—
363C43⋊C8—41no—
364C43⋊C8C2×C22⋊C412yes—
365C43⋊C8C2×C22⋊C412yes—
366#20679—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—22no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43C2×#11711yescharacteristic
373C22×C43C2×#12111yescharacteristic
374C22×C43C2×C22⋊Q811yescharacteristic
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—22no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—84no—
385C2×D43#38012yes—
386C2×D43#38012yes—
387C4×C43—22no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43C22×C22⋊C411yescharacteristic
391C4×C43C22×C4⋊C411yescharacteristic
392C4×C43C2×#12111yescharacteristic
393C4×C43C2×C22⋊Q811yescharacteristic
394Dic43—22no—
395Dic43—81no—
396Dic43—81no—
397Dic43#38012yes—
398Dic43#38012yes—
399C2×#568—431no—
400C2×#430—431no—
401C2×#428—431no—
402#2896—431no—
403C2×#417—431no—
404#1816—431no—
405#1816—431no—
406#1816—431no—
407#1816D4311yescharacteristic, complemented
408#1815—431no—
409#1815—431no—
410#1815—431no—
411#1815—431no—
412#1742—431no—
413C2×#343—431no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—42no—
417C2×C43C2×#38011yescharacteristic
418C2×C43#306811yescharacteristic
419C2×C43#306911yescharacteristic
420D43—22no—
421D43—22no—
422D43—42no—
423C22×#41—431no—
424#568—438no—
425#568—864no—
426C2×#131—431no—
427C2×#131—431no—
428C2×#131—431no—
429C2×#131—861no—
430C2×#131—861no—
431C2×#131C2×D4311yescharacteristic
432C22×M16—431no—
433C22×M16—431no—
434C22×M16—431no—
435C22×M16—431no—
436C22×M16—861no—
437C22×M16—861no—
438C2×#117—431no—
439C22×C4⋊C4—431no—
440#430—864no—
441C2×#108—431no—
442C2×#108—431no—
443C2×#108—431no—
444C2×#108C2×D4311yescharacteristic, complemented
445#428—861no—
446#428—861no—
447#428—861no—
448#428—861no—
449C2×#107—431no—
450C2×#107C2×D4311yescharacteristic, complemented
451C2×#106—431no—
452C2×#106—431no—
453#419—861no—
454#418—861no—
455#417—431no—
456#417—431no—
457#417—431no—
458#417—431no—
459#417—431no—
460#417—431no—
461#417—861no—
462#417—861no—
463#417C2×D4311yescharacteristic
464#417C2×D4311yescharacteristic
465#416—861no—
466#416—861no—
467C2×#103—861no—
468C2×#102—861no—
469#343—431no—
470#343—431no—
471#343—431no—
472#343—431no—
473#343—431no—
474#343—431no—
475#343C2×D4311yescharacteristic, complemented
476#343C2×D4311yescharacteristic, complemented
477C43#2067911yescharacteristic, complemented, Sylow
478C2×#41—434no—
479C2×#41—434no—
480C2×#41—431no—
481C2×#41—431no—
482C2×#41—431no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41C22×D4311yescharacteristic
488C22×Q8—431no—
489C22×D4—431no—
490C22×D4—861no—
491C23×C4—431no—
492C23×C4—861no—
493C23×C4—861no—
494#131—22no—
495#131—434no—
496#131—434no—
497#131—434no—
498#131—868no—
499#131—862no—
500#131—862no—
501#131—868no—
502#131—862no—
503#131C4×D4314yescomplemented
504C2×M16—21no—
505C2×M16—434no—
506C2×M16—431no—
507C2×M16—431no—
508C2×M16—431no—
509C2×M16—431no—
510C2×M16—434no—
511C2×M16—431no—
512C2×M16—434no—
513C2×M16—431no—
514C2×M16—431no—
515C2×M16—861no—
516C2×M16—868no—
517C2×M16—861no—
518C2×M16—861no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—868no—
522C2×M16—862no—
523C2×M16—861no—
524C2×M16—862no—
525C2×M16—862no—
526C2×M16—862no—
527C2×M16—862no—
528C2×M16C22×D4311yescharacteristic
529C2×M16C22×D4311yescharacteristic
530C2×M16C22×D4311yescharacteristic
531C22×C8—21no—
532C22×C8—431no—
533C22×C8—861no—
534C22×C8—861no—
535C22×C8—861no—
536C22×C8—861no—
537C22×C8—861no—
538C22×C8—861no—
539C22×C8C22×D4311yescharacteristic
540#117—861no—
541#117—861no—
542#117—861no—
543#117—861no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4C22×D4311yescharacteristic
552C2×C4⋊C4C22×D4311yescharacteristic
553C2×C22⋊C4—861no—
554C2×C42—861no—
555#108—22no—
556#108—862no—
557#108—862no—
558#108—862no—
559#107—21no—
560#107—21no—
561#107—861no—
562#107—861no—
563#106—861no—
564#106—861no—
565#106—861no—
566#106—861no—
567#103—21no—
568#103—21no—
569#103—861no—
570#103—861no—
571#103—861no—
572#103—861no—
573#103—861no—
574#103—861no—
575#102—21no—
576#102—21no—
577#102—861no—
578#102—861no—
579#102—861no—
580#102—861no—
581#102—861no—
582#102—861no—
583C24—431no—
584C24—861no—
585#41—21no—
586#41—21no—
587#41—434no—
588#41—434no—
589#41—432no—
590#41—432no—
591#41—864no—
592#41—864no—
593#41—864no—
594#41—864no—
595#41—862no—
596#41—862no—
597#41—861no—
598#41—861no—
599#41C2×C4×D4312yes—
600#41Q8×D4312yes—
601C2×Q8—434no—
602C2×Q8—431no—
603C2×Q8—861no—
604C2×Q8—862no—
605C2×Q8D4×D4311yescharacteristic
606C2×D4—21no—
607C2×D4—434no—
608C2×D4—431no—
609C2×D4—861no—
610C2×D4—862no—
611C2×D4—861no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4D4×D4311yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—431no—
621C22×C4—432no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—432no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—3442no—
638C22×C4—1721no—
639C22×C4—1721no—
640C22×C4C23×D4311yescharacteristic
641M16—21no—
642M16—24no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—434no—
648M16—434no—
649M16—434no—
650M16—434no—
651M16—432no—
652M16—864no—
653M16—864no—
654M16—864no—
655M16—861no—
656M16—864no—
657M16—861no—
658M16—861no—
659M16—861no—
660M16—861no—
661M16—1722no—
662M16—1722no—
663M16C2×C4×D4312yes—
664C2×C8—21no—
665C2×C8—24no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—432no—
669C2×C8—431no—
670C2×C8—431no—
671C2×C8—432no—
672C2×C8—864no—
673C2×C8—864no—
674C2×C8—864no—
675C2×C8—861no—
676C2×C8—864no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—1722no—
680C2×C8—1722no—
681C2×C8C2×C4×D4312yes—
682C2×C8D4×D4311yescharacteristic
683C2×C8D4×D4311yescharacteristic
684C2×C8D4×D4312yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—1721no—
694C4⋊C4—1721no—
695C22⋊C4—1721no—
696C22⋊C4—1721no—
697C42—1721no—
698C42—1721no—
699C23—21no—
700C23—431no—
701C23—431no—
702C23—432no—
703C23—432no—
704C23—864no—
705C23—861no—
706C23—3441no—
707C23—3441no—
708C23—1721no—
709C23—1721no—
710C23#41×D4311yescharacteristic
711Q8—21no—
712Q8—432no—
713Q8—864no—
714Q8—861no—
715Q8C4⋊C4×D4312yes—
716D4—22no—
717D4—22no—
718D4—21no—
719D4—432no—
720D4—864no—
721D4—864no—
722D4—864no—
723D4—862no—
724D4—862no—
725D4—861no—
726D4C4⋊C4×D4312yes—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—432no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—432no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—861no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—3442no—
753C2×C4—3442no—
754C2×C4—3441no—
755C2×C4—3441no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4C22×C4×D4311yescharacteristic
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C2×D4×D4311yescharacteristic
762C2×C4C2×Q8×D4311yescharacteristic
763C2×C4#41×D4311yescharacteristic
764C8—22no—
765C8—41no—
766C8—41no—
767C8—432no—
768C8—432no—
769C8—862no—
770C8—1721no—
771C8—1721no—
772C8C22⋊C4×D4312yes—
773C8C22⋊C4×D4312yes—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—432no—
780C22—432no—
781C22—861no—
782C22—861no—
783C22—861no—
784C22—861no—
785C22—862no—
786C22—3444no—
787C22—1722no—
788C22—1722no—
789C22—1721no—
790C22—1721no—
791C22#117×D4311yescharacteristic
792C22#121×D4311yescharacteristic
793C22C22⋊Q8×D4311yescharacteristic
794C4—22no—
795C4—81no—
796C4—81no—
797C4—432no—
798C4—432no—
799C4—862no—
800C4—3441no—
801C4—3441no—
802C4C2×C22⋊C4×D4311yescharacteristic
803C4C2×C4⋊C4×D4311yescharacteristic
804C4#121×D4311yescharacteristic
805C4C22⋊Q8×D4311yescharacteristic
806C2—21no—
807C2—21no—
808C2—42no—
809C2—862no—
810C2—862no—
811C2—1722no—
812C2#380×D4311yescharacteristic
813C2#1914432111yescharacteristic
814C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1816C2
socleC22×C43C2×#121
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1816D43
hypocenterC43#20679
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1816

Complements

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

NH ≅ G/Ntype
2. C2×#14582946C2semidirect
3. C2×#14582940C2semidirect
6. #19134660C2semidirect
7. #19134658C2semidirect
8. #19134657C2semidirect
9. #19134654C2semidirect
10. #19134653C2semidirect
11. #19134652C2semidirect
12. #19134651C2semidirect
13. #19134332C2semidirect
14. #343×D43C2semidirect
15. C43×#1816C2semidirect
18. #14583664C4semidirect
33. C2×#13063261C22semidirect
34. C2×#13063260C22semidirect
35. C2×#13063260C22semidirect
40. C2×#13063258C22semidirect
41. C2×#13063257C22semidirect
42. C2×#13063256C22semidirect
57. #14582668C22semidirect
58. #14582668C22semidirect
59. #14582667C22semidirect
60. #14582667C22semidirect
61. #14582667C22semidirect
62. #14582667C22semidirect
64. C2×#108×C43C22semidirect
65. C2×#107×C43C22semidirect
68. C43×#343C22semidirect
69. C43×#343C22semidirect
87. #13063333C2×C4semidirect
89. #13063332C2×C4semidirect
92. #13063331C2×C4semidirect
159. #131×C43C2×C4semidirect
407. #1816D43semidirect
444. C2×#108C2×D43semidirect
450. C2×#107C2×D43semidirect
475. #343C2×D43semidirect
476. #343C2×D43semidirect
477. C43#20679semidirect
503. #131C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
C2×#145829462
C2×#145829402
#191431112
#417×D432
#191346602
#191346582
#191346572
#191346542
#191346532
#191346522
#191346512
#191343322
#343×D432
C43×#18162
#2067943