Finite Group Databasebeta

← #25129506

Subgroups — #25129506

Order 11008.

1280 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144515C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3#19139074C211yesmaximal, characteristic, complemented
4#19135816C212yesmaximal, complemented
5#19135809C212yesmaximal, complemented
6#19135064C211yesmaximal, characteristic, complemented
7#19134898C211yesmaximal, characteristic, complemented
8#19134821C212yesmaximal, complemented
9#19134554C212yesmaximal, complemented
10#19134539C211yesmaximal, characteristic, complemented
11C43×#3489C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14#14583232—21no—
15#14583227—21no—
16#14583215—21no—
17#14583210—21no—
18#14582942C2212yescomplemented
19C2×#13063252C2212yes—
20C2×#13063252C2212yes—
21C2×#13063252C2212yescomplemented
22#14582900—21no—
23#14582900—21no—
24#14582900C2212yes—
25#14582900C2212yes—
26#14582900C2212yescomplemented
27C2×#13063249—21no—
28C2×#13063246—21no—
29C2×#13063244C2212yescomplemented
30#14582863C2211yescharacteristic
31#14582829—22no—
32#14582806C2212yescomplemented
33#14582771—22no—
34#14582768C2212yescomplemented
35C4×C22⋊Dic43C2211yescharacteristic
36#14582668C2212yescomplemented
37#14582658C2212yescomplemented
38C2×2−1+4×C43C2211yescharacteristic
39C22×#41×C43C2211yescharacteristic
40D4×Q8×C43—21no—
41C43×#548—21no—
42C43×#547—21no—
43C43×#547—22no—
44C43×#546—21no—
45C43×#546—22no—
46C43×#537—21no—
47C43×#537C2211yescharacteristic
48C43×#536—21no—
49C43×#536C2211yescharacteristic
50C43×#525—21no—
51C43×#525C2211yescharacteristic
52C2×C22⋊Q8×C43—21no—
53C2×C22⋊Q8×C43C2211yescharacteristic
54C43×#520C2211yescharacteristic
55C23×Dic43—21no—
56C2×#10621877—21no—
57C2×#10621877—42no—
58C2×#10621877C2312yes—
59C2×#10621877C2312yes—
60C22×C43⋊C8—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2312yes—
67C2×Dic43⋊C4—24no—
68C2×C22⋊Dic43—21no—
69C2×C4×Dic43C2312yes—
70#13063258—22no—
71#13063256—22no—
72#13063252—24no—
73#13063252—42no—
74#13063252—42no—
75#13063249—22no—
76#13063249—22no—
77#13063249—22no—
78#13063246—22no—
79#13063246—22no—
80#13063246—22no—
81#13063244—42no—
82C22⋊(C43⋊C8)—21no—
83C22⋊(C43⋊C8)—21no—
84C43⋊#95—24no—
85C43⋊#95—21no—
862−1+4×C43—24no—
872−1+4×C43—42no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—22no—
92C2×#41×C43—21no—
93C2×#41×C43—24no—
94C2×#41×C43—42no—
95C2×#41×C43D411yescharacteristic
96C2×#41×C43D411yescharacteristic
97C2×#41×C43C2311yescharacteristic
98C2×#41×C43C2311yescharacteristic
99C2×#41×C43C2311yescharacteristic
100C22×Q8×C43—21no—
101C22×Q8×C43—21no—
102C22×Q8×C43D411yescharacteristic
103C22×Q8×C43C2311yescharacteristic
104C22×D4×C43—21no—
105C22×D4×C43D411yescharacteristic
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C4⋊Q8×C43—22no—
109C4⋊Q8×C43—21no—
110#124×C43—22no—
111#124×C43—21no—
112#123×C43—22no—
113#123×C43—22no—
114#123×C43—22no—
115#123×C43—21no—
116#123×C43—22no—
117C22⋊Q8×C43—22no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43D411yescharacteristic
129C22⋊Q8×C43D411yescharacteristic
130#121×C43—22no—
131#121×C43—22no—
132#121×C43—22no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—22no—
136#121×C43D411yescharacteristic
137#121×C43D411yescharacteristic
138#120×C43—22no—
139#120×C43—21no—
140C4×Q8×C43—21no—
141C4×D4×C43—22no—
142C4×D4×C43—22no—
143C4×D4×C43—21no—
144C4×D4×C43—22no—
145C4×D4×C43—21no—
146C4×D4×C43—21no—
147#117×C43—21no—
148#117×C43C2311yescharacteristic
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43D412yes—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43D412yes—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157#41×C43—22no—
158#41×C43—22no—
159#41×C43—22no—
160#41×C43—22no—
161#41×C43—22no—
162#41×C43—22no—
163#41×C43—22no—
164#41×C43—44no—
165#41×C43—41no—
166#41×C43—41no—
167#41×C43—44no—
168#41×C43—44no—
169#41×C43—48no—
170#41×C43—42no—
171#41×C43—42no—
172#41×C43#4114yes—
173C2×Q8×C43—22no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—22no—
178C2×Q8×C43—22no—
179C2×Q8×C43—22no—
180C2×Q8×C43—41no—
181C2×Q8×C43—44no—
182C2×Q8×C43—42no—
183C2×Q8×C43—42no—
184C2×Q8×C43C2×D411yescharacteristic
185C2×Q8×C43C2×D411yescharacteristic
186C2×Q8×C43C2×D411yescharacteristic
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—44no—
199C2×D4×C43—41no—
200C2×D4×C43C2×D411yescharacteristic
201C2×D4×C43C2×D411yescharacteristic
202C2×D4×C43C2×D411yescharacteristic
203C22×C4×C43—21no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—44no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2411yescharacteristic
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—41no—
226C22×Dic43—41no—
227C22×Dic43—82no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—22no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—22no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2×D411yescharacteristic
239C4⋊C4×C43C2×D411yescharacteristic
240C22⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C42×C43—22no—
253C42×C43—21no—
254C22⋊Dic43—24no—
255C4⋊Dic43—22no—
256C4⋊Dic43—22no—
257C4⋊Dic43—41no—
258C4⋊Dic43—41no—
259Dic43⋊C4—84no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262#10621877—22no—
263#10621877—22no—
264#10621877—22no—
265#10621877—22no—
266#10621877—42no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—42no—
270C23×C43—21no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—41no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43—81no—
279C23×C43#12011yescharacteristic
280C23×C43#12011yescharacteristic
281C23×C43C22×D411yescharacteristic
282Q8×C43—21no—
283Q8×C43—21no—
284Q8×C43—21no—
285Q8×C43—22no—
286Q8×C43—42no—
287Q8×C43—44no—
288Q8×C43—41no—
289Q8×C43—41no—
290Q8×C43—42no—
291Q8×C43#12312yes—
292D4×C43—24no—
293D4×C43—21no—
294D4×C43—21no—
295D4×C43—21no—
296D4×C43—22no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—44no—
301D4×C43—42no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—81no—
305D4×C43—82no—
306D4×C43#12312yes—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—24no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—24no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—44no—
327C2×C4×C43—44no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—82no—
333C2×C4×C43#12011yescharacteristic
334C2×C4×C43#12011yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4112yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×Dic43—24no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—44no—
343C2×Dic43—42no—
344C2×Dic43—82no—
345C2×Dic43—82no—
346C43⋊C8—42no—
347C43⋊C8—42no—
348#24030—431nomaximal, Sylow
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—22no—
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—44no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—84no—
367C22×C43#45612yes—
368C22×C43C2×#12011yescharacteristic
369C22×C43#54612yes—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—42no—
378C4×C43—41no—
379C4×C43C2×#12311yescharacteristic
380C4×C43#53411yescharacteristic
381C4×C43#54612yes—
382Dic43—44no—
383Dic43—82no—
384#3489D4311yescharacteristic
385#3092—431no—
386C2×#417—431no—
387#2502—431no—
388#2039—432no—
389#2038—432no—
390#1901—431no—
391#1871—431no—
392#1859—432no—
393#1793—432no—
394#1789—431no—
395C2×C43—22no—
396C2×C43—22no—
397C2×C43—41no—
398C2×C43—42no—
399C2×C43—81no—
400C2×C43—81no—
401C2×C43#240511yescharacteristic
402C2×C43C2×#45611yescharacteristic
403C2×C43#302111yescharacteristic
404C2×2−1+4C2×D4311yescharacteristic
405C22×#41C2×D4311yescharacteristic
406C22×M16—431no—
407D4×Q8—21no—
408#548—21no—
409#547—21no—
410#547—22no—
411#546—21no—
412#546—22no—
413#537—21no—
414#537C2×D4311yescharacteristic
415#536—21no—
416#536C2×D4311yescharacteristic
417#525—21no—
418#525C2×D4311yescharacteristic
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8C2×D4311yescharacteristic
421#520C2×D4311yescharacteristic
422C22×C4⋊C4—431no—
423#484—861no—
424#483—861no—
425#481—861no—
426#480—861no—
427#428—432no—
428C2×#104—432no—
429C2×#104—432no—
430C2×#104—432no—
431#417—432no—
432#417—432no—
433#417—432no—
434#417—861no—
435#417—861no—
436C2×#103—861no—
437C2×#102—861no—
438C2×#101—432no—
439#407—431no—
440#398—862no—
441#391—432no—
442#385—862no—
443#384—432no—
444C4×C22⋊C4—431no—
445#343—432no—
446#339—432no—
447C43#2403011yescharacteristic, complemented, Sylow
4482−1+4—24no—
4492−1+4—42no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—24no—
456C2×#41—42no—
457C2×#41C22⋊D4311yescharacteristic
458C2×#41C22⋊D4311yescharacteristic
459C2×#41C22×D4311yescharacteristic
460C2×#41C22×D4311yescharacteristic
461C2×#41C22×D4311yescharacteristic
462C22×Q8—21no—
463C22×Q8—21no—
464C22×Q8C22⋊D4311yescharacteristic
465C22×Q8C22×D4311yescharacteristic
466C22×D4—21no—
467C22×D4C22⋊D4311yescharacteristic
468C23×C4—21no—
469C23×C4—861no—
470C23×C4C22×D4311yescharacteristic
471C2×M16—432no—
472C2×M16—432no—
473C2×M16—861no—
474C2×M16—1722no—
475C22×C8—861no—
476C4⋊Q8—22no—
477C4⋊Q8—21no—
478#124—22no—
479#124—21no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—21no—
484#123—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8C22⋊D4311yescharacteristic
497C22⋊Q8C22⋊D4311yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—22no—
504#121C22⋊D4311yescharacteristic
505#121C22⋊D4311yescharacteristic
506#120—22no—
507#120—21no—
508C4×Q8—21no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515#117—21no—
516#117C22×D4311yescharacteristic
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—432no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22⋊D4312yes—
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4C22⋊D4312yes—
531C2×C42—432no—
532#107—862no—
533#106—862no—
534#104—864no—
535#104—1722no—
536#104—1722no—
537#103—862no—
538#103—862no—
539#103—862no—
540#102—862no—
541#102—862no—
542#102—862no—
543#101—1722no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546#95—861no—
547#95—864no—
548C24—21no—
549C24C2×C22⋊D4311yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—44no—
558#41—41no—
559#41—41no—
560#41—44no—
561#41—44no—
562#41—48no—
563#41—42no—
564#41—42no—
565#41#1062190014yes—
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—41no—
574C2×Q8—44no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8C2×C22⋊D4311yescharacteristic
578C2×Q8C2×C22⋊D4311yescharacteristic
579C2×Q8C2×C22⋊D4311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—44no—
593C2×D4C2×C22⋊D4311yescharacteristic
594C2×D4C2×C22⋊D4311yescharacteristic
595C2×D4C2×C22⋊D4311yescharacteristic
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—3442no—
611C22×C4—1721no—
612C22×C4—1721no—
613C22×C4C2×C22⋊D4312yes—
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4312yes—
620C22×C4C23×D4311yescharacteristic
621M16—862no—
622M16—862no—
623M16—862no—
624M16—862no—
625M16—1722no—
626C2×C8—862no—
627C2×C8—862no—
628C2×C8—1722no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—862no—
640C4⋊C4—862no—
641C4⋊C4—3444no—
642C4⋊C4—1721no—
643C4⋊C4—1721no—
644C4⋊C4C2×C22⋊D4311yescharacteristic
645C4⋊C4C2×C22⋊D4311yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—864no—
659C42—22no—
660C42—21no—
661C42—862no—
662C42—862no—
663C23—22no—
664C23—21no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23#1306329411yescharacteristic
673C23#1306329411yescharacteristic
674C23C22×C22⋊D4311yescharacteristic
675Q8—21no—
676Q8—21no—
677Q8—21no—
678Q8—22no—
679Q8—42no—
680Q8—44no—
681Q8—41no—
682Q8—41no—
683Q8—42no—
684Q8#1306330612yes—
685D4—24no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—22no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—81no—
698D4—82no—
699D4#1306330612yes—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
726C2×C4—864no—
727C2×C4—3442no—
728C2×C4—3442no—
729C2×C4—1724no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4#1306329411yescharacteristic
734C2×C4#1306329411yescharacteristic
735C2×C4C22×C22⋊D4311yescharacteristic
736C2×C4C22×C22⋊D4311yescharacteristic
737C2×C4C2×#1062190012yes—
738C2×C4#1306337012yes—
739C8—1722no—
740C8—1722no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—44no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—84no—
759C22#1458308212yes—
760C22C2×#1306329411yescharacteristic
761C22#1458354312yes—
762C4—21no—
763C4—21no—
764C4—22no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—3442no—
772C4—1724no—
773C4C2×#1306330611yescharacteristic
774C4#1458345811yescharacteristic
775C4#1458354312yes—
776C2—22no—
777C2—22no—
778C2—41no—
779C2—42no—
780C2—81no—
781C2—81no—
782C2#1913791811yescharacteristic
783C2C2×#1458308211yescharacteristic
784C2#1914396711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3489C2
socleC22×C43C2×#120
hypercenter#3489D43
hypocenterC43#24030
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #19144515C2semidirect
2. C2×#14582900C2semidirect
3. #19139074C2semidirect
4. #19135816C2semidirect
5. #19135809C2semidirect
6. #19135064C2semidirect
7. #19134898C2semidirect
8. #19134821C2semidirect
9. #19134554C2semidirect
10. #19134539C2semidirect
18. #14582942C22semidirect
21. C2×#13063252C22semidirect
26. #14582900C22semidirect
29. C2×#13063244C22semidirect
32. #14582806C22semidirect
34. #14582768C22semidirect
36. #14582668C22semidirect
37. #14582658C22semidirect
447. C43#24030semidirect

Maximal subgroups

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

subgroupindex
#191445152
C2×#145829002
#191390742
#191358162
#191358092
#191350642
#191348982
#191348212
#191345542
#191345392
C43×#34892
#2403043