Finite Group Databasebeta

← #25974932

Subgroups — #25974932

Order 11008.

2082 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148444C211yesmaximal, characteristic, complemented
2#19148361C211yesmaximal, characteristic, complemented
3#19146783C214yesmaximal, complemented
4#19146768C214yesmaximal, complemented
5#19146603C214yesmaximal, complemented
6#19146588C214yesmaximal, complemented
7#19144941C211yesmaximal, characteristic, complemented
8#19144575C212yesmaximal, complemented
9#19144402C211yesmaximal, characteristic, complemented
10#19144275C212yesmaximal, complemented
11#19144061C211yesmaximal, characteristic, complemented
12#19143883C212yesmaximal, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14#19143129C212yesmaximal, complemented
15C43×#2932C211yesmaximal, characteristic, complemented
16C2×#13063372C2212yes—
17C2×#13063353C2212yes—
18C22×#10621873C2211yescharacteristic
19#14583631—22no—
20#14583623—21no—
21#14583614C2212yes—
22#14583595C2214yes—
23#14583570C2212yescomplemented
24#14583569—21no—
25#14583569—21no—
26D4×Dic86C2212yescomplemented
27#14583564—21no—
28#14583558C2214yescomplemented
29#14583557—22no—
30#14583553C2212yes—
31#14583486—22no—
32#14583477C2212yes—
33#14583476—22no—
34#14583463C2212yes—
35#14583456C2211yescharacteristic
36#14583449C2211yescharacteristic
37#14583444—22no—
38#14583409—22no—
39#14583382C2212yes—
40C2×C4×Dic86C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic
42#14583268C2212yescomplemented
43#14583264C2212yescomplemented
44#14583259C2212yescomplemented
45#14583259C2212yescomplemented
46#14583241C2214yescomplemented
47#14583235C2214yescomplemented
48#14583224C2214yescomplemented
49#14583213C2214yescomplemented
50#14583207C2214yescomplemented
51#14583195C2212yescomplemented
52#14583185C2212yescomplemented
53#14583152C2214yes—
54#14583145C2214yes—
55#14583135C2214yes—
56#14583128C2214yes—
57#14583115C2214yes—
58#14583105C2212yes—
59#14583095C2212yes—
60#14583046C2214yes—
61#14583046C2214yes—
62#14583040C2214yes—
63#14583040C2214yes—
64#14583001C2214yes—
65#14583001C2214yes—
66#14582941C2212yes—
67C2×#13063259C2211yescharacteristic
68#14582909C2212yes—
69#14582909C2214yescomplemented
70#14582901C2212yes—
71#14582901C2214yescomplemented
72#14582896C2212yes—
73#14582896C2212yes—
74#14582896C2214yescomplemented
75C2×#13063250C2211yescharacteristic
76C2×#13063250C2214yescomplemented
77C2×#13063247C2211yescharacteristic
78C2×#131×C43C2212yes—
79C43×#532C2211yescharacteristic
80C43×#435C2214yescomplemented
81C43×#435C2214yescomplemented
82C43×#423C2211yescharacteristic
83C43×#408C2212yes—
84C2×#97×C43C2211yescharacteristic
85#13063372—28no—
86#13063372—44no—
87C2×#10621898C2312yes—
88C2×#10621898C2314yes—
89C2×#10621900—22no—
90C2×#10621900—24no—
91C2×#10621900—22no—
92C22×Dic86C2314yes—
93C22×Dic86C2311yescharacteristic
94C2×Q8×D43—22no—
95C22×D172C2311yescharacteristic
96C22×C4×D43—21no—
97#13063353—44no—
98C2×#10621873—24no—
99C2×#10621873C2314yes—
100C2×#10621873C2314yes—
101C2×D344C2314yes—
102#13063325C2311yescharacteristic
103#13063325C2311yescharacteristic
104#13063325C2311yescharacteristic
105#13063324—22no—
106#13063322C2311yescharacteristic
107#13063321—22no—
108#13063321—22no—
109#13063320—24no—
110#13063317C2312yes—
111#13063314—22no—
112#13063313C2312yes—
113#13063311—24no—
114#13063311—24no—
115#13063309—24no—
116#13063307—24no—
117#13063305—22no—
118#13063304—21no—
119#13063304—21no—
120#13063304C2314yes—
121#13063303—24no—
122#13063302—24no—
123#13063301—22no—
124#13063299—21no—
125#13063299—21no—
126#13063299C2314yes—
127#13063299C2314yes—
128#13063299C2314yes—
129#13063298—24no—
130#13063297—24no—
131#13063297—24no—
132#13063297—24no—
133#13063296—22no—
134#13063296—22no—
135#13063293—24no—
136Q8×Dic43—22no—
137C4×Dic86—21no—
138C4×Dic86—21no—
139C4×Dic86—21no—
140C4×Dic86—21no—
141C4×Dic86C2312yes—
142C4×Dic86C2312yes—
143C4×D172—21no—
144C4×D172—21no—
145C4×D172—21no—
146C4×D172—21no—
147C4×D172C2312yes—
148C4×D172C2312yes—
149D4×Dic43—22no—
150D4×Dic43—22no—
151D4×Dic43—24no—
152#13063287—22no—
153(C22⋊D43)⋊C4—24no—
154(C22⋊D43)⋊C4—24no—
155#13063284C2314yes—
156#13063284C2312yes—
157#13063283—22no—
158C2×C4⋊Dic43C2314yes—
159C2×C4⋊Dic43C2311yescharacteristic
160C2×C4⋊Dic43C2311yescharacteristic
161C2×Dic43⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×C4×Dic43—21no—
164#13063259C2314yes—
165#13063259C2314yes—
166#13063257C2314yes—
167#13063250C2312yes—
168#13063250C2312yes—
169#13063250C2314yes—
170#13063250C2314yes—
171#13063250C2314yes—
172#13063250C2312yes—
173#13063250C2312yes—
174#13063250C2314yes—
175#13063247C2312yes—
176#13063247C2312yes—
177#13063247C2314yes—
178#13063247C2314yes—
179#13063247C2312yes—
180#13063247C2312yes—
181C2×#41×C43C2312yes—
182#131×C43—44no—
183C2×M16×C43C2312yes—
184C2×M16×C43C2314yes—
185C22×C8×C43C2311yescharacteristic
186C22×C8×C43C2311yescharacteristic
187C22×C8×C43C2314yes—
188C4⋊Q8×C43D411yescharacteristic
189#127×C43D411yescharacteristic
190#124×C43D412yes—
191#121×C43D412yes—
192#121×C43D412yes—
193C4×D4×C43C2312yes—
194C4×D4×C43C2312yes—
195C2×C42×C43C2311yescharacteristic
196C4⋊C8×C43C2312yes—
197C4⋊C8×C43C2312yes—
198C22⋊C8×C43C2314yes—
199C22⋊C8×C43C2314yes—
200#97×C43C2312yes—
201#97×C43C2312yes—
202C23×D43—21no—
203#41×C43—24no—
204#41×C43—24no—
205C2×Q8×C43C2×D412yes—
206C2×D4×C43C2×D414yes—
207C2×D4×C43C2×D412yes—
208C2×D4×C43C2×D412yes—
209C2×D4×C43C2×D412yes—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2414yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—22no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C22×Dic43—21no—
220C22×Dic43—24no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—24no—
224Q8×D43—48no—
225#10621900—48no—
226#10621900—416no—
227#10621900—84no—
228#10621898—24no—
229#10621898—24no—
230#10621898—28no—
231#10621898—44no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172C2412yes—
238C2×D172C2412yes—
239C2×C4×D43—22no—
240C2×C4×D43—24no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—82no—
244C2×Dic86—21no—
245C2×Dic86—22no—
246C2×Dic86—28no—
247C2×Dic86—21no—
248C2×Dic86—24no—
249C2×Dic86—21no—
250C2×Dic86—44no—
251C2×Dic86#4114yescomplemented
252C2×Dic86C2412yes—
253C2×Dic86C2412yes—
254M16×C43—24no—
255M16×C43—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—44no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C2×C8×C43C2414yes—
262C4⋊C4×C43C2×D412yes—
263C4⋊C4×C43C2×D412yes—
264C22⋊C4×C43C2×D414yes—
265C22⋊C4×C43C2×D414yes—
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2411yescharacteristic
269C42×C43C2411yescharacteristic
270C22⋊Dic43—22no—
271C22⋊Dic43—24no—
272C22⋊Dic43—24no—
273(C2×D43)⋊C4—22no—
274(C2×D43)⋊C4—22no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—22no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—22no—
280C4⋊Dic43—21no—
281C4⋊Dic43—24no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43C2412yes—
288C4⋊Dic43C2412yes—
289C4⋊Dic43C2412yes—
290C4⋊Dic43C2412yes—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—24no—
295Dic43⋊C4—22no—
296C4×Dic43—22no—
297C4×Dic43—22no—
298C4×Dic43—24no—
299C4×Dic43—22no—
300D344—44no—
301#10621873—28no—
302#10621873—44no—
303C23×C43C22×D414yes—
304C23×C43C22×D411yescharacteristic
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—42no—
308C22×D43—81no—
309C22×D43—81no—
310Q8×C43—24no—
311D4×C43—28no—
312D4×C43—24no—
313D4×C43—42no—
314D4×C43—42no—
315C2×C4×C43—24no—
316C2×C4×C43—24no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D414yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43H(5,𝔽2)12yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—48no—
329C22⋊D43—44no—
330C22⋊D43—84no—
331C22⋊D43—84no—
332C22⋊D43—84no—
333C2×Dic43—24no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—48no—
341C2×Dic43—81no—
342C2×Dic43—84no—
343C2×Dic43—81no—
344D172—22no—
345D172—22no—
346D172—22no—
347D172—22no—
348D172—42no—
349D172—42no—
350D172—81no—
351C4×D43—48no—
352C4×D43—44no—
353C4×D43—44no—
354C4×D43—82no—
355Dic86—24no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—48no—
360Dic86—42no—
361Dic86—81no—
362Dic86C2×#4114yes—
363C8×C43—22no—
364C8×C43—24no—
365C8×C43—22no—
366#61220—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—24no—
370C22×C43—24no—
371C22×C43—24no—
372C22×C43#54612yes—
373C22×C43C23×D411yescharacteristic
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—84no—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—24no—
386C4×C43#54612yes—
387C4×C43C22×#4111yescharacteristic
388C4×C43C2×H(5,𝔽2)11yescharacteristic
389Dic43—24no—
390Dic43—42no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394Dic43—42no—
395#3506—431no—
396#3497—431no—
397#3321—434no—
398#3320—434no—
399#3309—434no—
400#3308—434no—
401#3135—431no—
402#3098—432no—
403#3078—431no—
404#3062—432no—
405#3036—431no—
406#3010—432no—
407C2×#440—431no—
408#2932D4311yescharacteristic, complemented
409#2898—432no—
410C2×C43—22no—
411C2×C43—44no—
412C2×C43C2×#54611yescharacteristic
413C2×C43#358511yescharacteristic
414C2×C43#358611yescharacteristic
415D43—82no—
416D43—82no—
417C2×2−1+4—432no—
418C2×AGL(1,ℤ/8)—432no—
419C22×SD16—431no—
420C2×#131C2×D4312yes—
421#559—862no—
422#556—861no—
423#555—432no—
424#553—434no—
425#550—432no—
426#550—861no—
427#550—861no—
428D4×Q8—432no—
429D4×Q8—861no—
430#548—434no—
431#548—862no—
432#547—432no—
433#538—862no—
434#537—432no—
435#537—862no—
436#535—432no—
437#533—431no—
438#532—431no—
439#532—862no—
440#532C2×D4311yescharacteristic
441#525—862no—
442#520—432no—
443C2×C4×Q8—431no—
444C2×C4×D4—431no—
445#491—432no—
446#490—432no—
447#489—432no—
448#489—432no—
449#485—434no—
450#484—434no—
451#482—434no—
452#480—434no—
453#479—434no—
454#477—432no—
455#475—432no—
456#469—434no—
457#468—434no—
458#466—434no—
459#465—434no—
460#463—434no—
461#461—432no—
462#459—432no—
463#449—434no—
464#449—434no—
465#448—434no—
466#448—434no—
467#440—434no—
468#440—434no—
469#435C2×D4314yescomplemented
470#435C2×D4314yescomplemented
471#428—432no—
472C2×#107—431no—
473#423C2×D4311yescharacteristic
474#419—432no—
475#419—434no—
476#417—432no—
477#417—434no—
478#416—432no—
479#416—432no—
480#416—434no—
481C2×#103—431no—
482C2×#103—434no—
483C2×#102—431no—
484#408C2×D4312yes—
485C2×#97C2×D4311yescharacteristic
486C43#6122011yescharacteristic, complemented, Sylow
4872−1+4—868no—
4882−1+4—1724no—
489C2×#41—432no—
490C2×#41—434no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—862no—
494C2×#41C22×D4312yes—
495C22×Q8—431no—
496C22×Q8—434no—
497C22×Q8—862no—
498C22×D4—431no—
499C23×C4—861no—
500AGL(1,ℤ/8)—1724no—
501C2×SD16—434no—
502C2×SD16—434no—
503C2×SD16—864no—
504C2×D8—434no—
505#131—44no—
506C2×M16C22×D4312yes—
507C2×M16C22×D4314yes—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510C22×C8C22×D4314yes—
511C4⋊Q8—431no—
512C4⋊Q8—431no—
513C4⋊Q8—431no—
514C4⋊Q8—862no—
515C4⋊Q8D17211yescharacteristic
516#127—431no—
517#127—862no—
518#127—862no—
519#127D17211yescharacteristic
520#126—864no—
521#125—432no—
522#124—432no—
523#124—862no—
524#124—864no—
525#124—864no—
526#124D17212yes—
527#123—864no—
528#123—864no—
529C22⋊Q8—434no—
530C22⋊Q8—862no—
531C22⋊Q8—861no—
532C22⋊Q8—861no—
533C22⋊Q8—862no—
534C22⋊Q8—864no—
535C22⋊Q8—864no—
536#121—434no—
537#121—434no—
538#121—434no—
539#121—862no—
540#121—864no—
541#121—862no—
542#121—864no—
543#121—864no—
544#121—861no—
545#121—861no—
546#121—864no—
547#121D17212yes—
548#121D17212yes—
549#120—864no—
550C4×Q8—432no—
551C4×Q8—432no—
552C4×Q8—862no—
553C4×Q8—861no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×D4—432no—
558C4×D4—432no—
559C4×D4—864no—
560C4×D4—862no—
561C4×D4—862no—
562C4×D4—862no—
563C4×D4—864no—
564C4×D4—864no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569C4×D4C22×D4312yes—
570C4×D4C22×D4312yes—
571#117—432no—
572#117—434no—
573#117—862no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—434no—
577C2×C4⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582#107—434no—
583#106—434no—
584C4⋊C8C22×D4312yes—
585C4⋊C8C22×D4312yes—
586#103—434no—
587#103—432no—
588#103—434no—
589#103—434no—
590#103—434no—
591#103—432no—
592#103—432no—
593#103—432no—
594#102—434no—
595#102—432no—
596#102—434no—
597#102—432no—
598#102—432no—
599#102—432no—
600C22⋊C8C22×D4314yes—
601C22⋊C8C22×D4314yes—
602#97C22×D4312yes—
603#97C22×D4312yes—
604C24—861no—
605#41—24no—
606#41—24no—
607#41—868no—
608#41—864no—
609#41—864no—
610#41—3444no—
611#41—1724no—
612#41—17216no—
613#41—1728no—
614C2×Q8—434no—
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—868no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—864no—
622C2×Q8—862no—
623C2×Q8—1724no—
624C2×Q8—1728no—
625C2×Q8C2×D17212yes—
626C2×D4—432no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—862no—
632C2×D4—864no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4C2×D17214yes—
639C2×D4C2×D17212yes—
640C2×D4C2×D17212yes—
641C2×D4C2×D17212yes—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—864no—
646C22×C4—864no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—864no—
650C22×C4—862no—
651C22×C4—3442no—
652C22×C4C2×D17211yescharacteristic
653C22×C4C2×D17211yescharacteristic
654C22×C4C23×D4314yes—
655C22×C4C23×D4311yescharacteristic
656SD16—868no—
657SD16—1724no—
658D8—1724no—
659M16—24no—
660M16—44no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8C23×D4312yes—
665C2×C8C23×D4312yes—
666C2×C8C23×D4314yes—
667C4⋊C4—432no—
668C4⋊C4—432no—
669C4⋊C4—432no—
670C4⋊C4—432no—
671C4⋊C4—861no—
672C4⋊C4—864no—
673C4⋊C4—861no—
674C4⋊C4—862no—
675C4⋊C4—862no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—862no—
679C4⋊C4—864no—
680C4⋊C4—861no—
681C4⋊C4—862no—
682C4⋊C4—861no—
683C4⋊C4C2×D17212yes—
684C4⋊C4C2×D17212yes—
685C22⋊C4—862no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—862no—
689C22⋊C4—862no—
690C22⋊C4—864no—
691C22⋊C4—862no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—862no—
695C22⋊C4C2×D17214yes—
696C22⋊C4C2×D17214yes—
697C42—862no—
698C42—862no—
699C42—864no—
700C42—862no—
701C42C2×D17211yescharacteristic
702C42C2×D17211yescharacteristic
703C42C23×D4311yescharacteristic
704C42C23×D4311yescharacteristic
705C23—862no—
706C23—862no—
707C23—3441no—
708C23—3441no—
709C23—1722no—
710C23C22×D17214yes—
711C23C22×D17211yescharacteristic
712Q8—24no—
713Q8—434no—
714Q8—862no—
715Q8—864no—
716Q8—862no—
717Q8—862no—
718Q8—3441no—
719Q8—1728no—
720Q8—1722no—
721D4—28no—
722D4—24no—
723D4—42no—
724D4—42no—
725D4—862no—
726D4—862no—
727D4—862no—
728D4—862no—
729D4—3441no—
730D4—3444no—
731D4—3444no—
732D4—3444no—
733D4—1722no—
734D4—1728no—
735D4—1724no—
736D4—1722no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—862no—
742C2×C4—864no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—3442no—
749C2×C4—3441no—
750C2×C4—3444no—
751C2×C4—3441no—
752C2×C4—1728no—
753C2×C4—1724no—
754C2×C4—1728no—
755C2×C4—1724no—
756C2×C4C22×D17211yescharacteristic
757C2×C4C22×D17211yescharacteristic
758C2×C4C22×D17214yes—
759C2×C4C22×D17211yescharacteristic
760C2×C4C22×D17211yescharacteristic
761C2×C4C22×D17211yescharacteristic
762C2×C4#41×D4312yes—
763C2×C4#1306337012yes—
764C2×C4C24×D4311yescharacteristic
765C8—22no—
766C8—22no—
767C8—24no—
768C22—21no—
769C22—21no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—3444no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22#1458354412yes—
781C22C23×D17211yescharacteristic
782C4—24no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—864no—
788C4—1722no—
789C4—1722no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C4#1458354412yes—
794C4C2×#41×D4311yescharacteristic
795C4C2×#1306337011yescharacteristic
796C2—22no—
797C2—44no—
798C2—3442no—
799C2—3442no—
800C2C2×#1458354411yescharacteristic
801C2#1914937611yescharacteristic
802C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2932C2
socleC22×C43C23×D4
hypercenter#2932D43
hypocenterC43#61220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #532 ◁ #2932

Complements

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

NH ≅ G/Ntype
1. #19148444C2semidirect
2. #19148361C2semidirect
3. #19146783C2semidirect
4. #19146768C2semidirect
5. #19146603C2semidirect
6. #19146588C2semidirect
7. #19144941C2semidirect
8. #19144575C2semidirect
9. #19144402C2semidirect
10. #19144275C2semidirect
11. #19144061C2semidirect
12. #19143883C2semidirect
13. C2×#14583001C2semidirect
14. #19143129C2semidirect
15. C43×#2932C2semidirect
23. #14583570C22semidirect
26. D4×Dic86C22semidirect
28. #14583558C22semidirect
42. #14583268C22semidirect
43. #14583264C22semidirect
44. #14583259C22semidirect
45. #14583259C22semidirect
46. #14583241C22semidirect
47. #14583235C22semidirect
48. #14583224C22semidirect
49. #14583213C22semidirect
50. #14583207C22semidirect
51. #14583195C22semidirect
52. #14583185C22semidirect
69. #14582909C22semidirect
71. #14582901C22semidirect
74. #14582896C22semidirect
76. C2×#13063250C22semidirect
80. C43×#435C22semidirect
81. C43×#435C22semidirect
251. C2×Dic86#41semidirect
408. #2932D43semidirect
469. #435C2×D43semidirect
470. #435C2×D43semidirect
486. C43#61220semidirect

Maximal subgroups

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

subgroupindex
#191484442
#191483612
#191467832
#191467682
#191466032
#191465882
#191449412
#191445752
#191444022
#191442752
#191440612
#191438832
C2×#145830012
#191431292
C43×#29322
#6122043