Finite Group Databasebeta

← #10577742

Subgroups — #10577742

Order 512.

6590 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62880C212yesmaximal, complemented
2#62292C218yesmaximal, complemented
3#62290C218yesmaximal, complemented
4#62276C214yesmaximal, complemented
5#62270C214yesmaximal, complemented
6#62266C218yesmaximal, complemented
7#61289C212yesmaximal, complemented
8#61284C212yesmaximal, complemented
9#61223C214yesmaximal, complemented
10#61218C214yesmaximal, complemented
11#61089C212yesmaximal, complemented
12#61084C212yesmaximal, complemented
13#60920C212yesmaximal, complemented
14#60771C214yesmaximal, complemented
15#60682C211yesmaximal, characteristic, complemented
16C2×#3176C211yesmaximal, characteristic, complemented
17#60458C214yesmaximal, complemented
18#60140C211yesmaximal, characteristic, complemented
19C2×#576C2214yescomplemented
20C22×#131C2212yescomplemented
21#3562—28no—
22#3543—28no—
23#3542C22116yescomplemented
24#3539C2218yescomplemented
25#3537—28no—
26#3537C2218yescomplemented
27#3534—28no—
28#3512C2214yescomplemented
29#3506C2214yescomplemented
30#3498C2214yescomplemented
31#3496C2214yescomplemented
32#3488C2218yescomplemented
33#3455C2212yescomplemented
34C2×#540C2212yescomplemented
35#3449C2211yescharacteristic
36#3355C2218yescomplemented
37#3354C2218yescomplemented
38#3351C22116yescomplemented
39#3341C2214yescomplemented
40#3339C2218yescomplemented
41#3339C2218yescomplemented
42#3336C2218yescomplemented
43#3334C2214yescomplemented
44#3319C22116yescomplemented
45#3318C22116yescomplemented
46#3318C22116yescomplemented
47#3317C22116yescomplemented
48#3310C22116yescomplemented
49#3309C22116yescomplemented
50#3307C22116yescomplemented
51#3306C22116yescomplemented
52#3287C2218yescomplemented
53#3283C2214yescomplemented
54#3280C2218yescomplemented
55D4×D8C2218yescomplemented
56D4×D8C2214yescomplemented
57#3274C22116yescomplemented
58#3273C2218yescomplemented
59#3272C2218yescomplemented
60#3260C2218yescomplemented
61#3259C2218yescomplemented
62#3257C22116yescomplemented
63#3204C2218yescomplemented
64#3199C2218yescomplemented
65#3198C22116yescomplemented
66#3197C2218yescomplemented
67#3194C22116yescomplemented
68#3192C2218yescomplemented
69#3177C2212yescomplemented
70#3176C2214yescomplemented
71#3176C2214yescomplemented
72#3176C2214yescomplemented
73#3176C2214yescomplemented
74#3176C2212yescomplemented
75#3175C2214yescomplemented
76#3174C2214yescomplemented
77#3173C2214yescomplemented
78#3160C2211yescharacteristic, complemented
79C2×#499C2211yescharacteristic, complemented
80#3147C2211yescharacteristic, complemented
81C2×#493C2211yescharacteristic, complemented
82#3135C2212yescomplemented
83C2×#490C2212yescomplemented
84#3099C2218yescomplemented
85#3096C2218yescomplemented
86#3080C2214yescomplemented
87#3077C2214yescomplemented
88#3062C2218yescomplemented
89#3062C22116yescomplemented
90#3061C2218yescomplemented
91#3061C2214yescomplemented
92#3058C2218yescomplemented
93#3058C2214yescomplemented
94#3055C22116yescomplemented
95#3055C2218yescomplemented
96#3054C2212yescomplemented
97C2×#469C2212yescomplemented
98#3050C2212yescomplemented
99#3050C2218yescomplemented
100C2×#466C2212yescomplemented
101C2×#466C2218yescomplemented
102#3038C2214yescomplemented
103#3036C2214yescomplemented
104#3012C2218yescomplemented
105#3008C2218yescomplemented
106#2943C2212yescomplemented
107C2×#442C2212yescomplemented
108C4×#135C2212yescomplemented
109C2×C4×D8C2212yescomplemented
110#2932C2212yescomplemented
111#2932C2212yescomplemented
112#2931C2212yescomplemented
113#2931C2212yescomplemented
114#2930C2214yescomplemented
115#2930C2214yescomplemented
116#2929C2214yescomplemented
117#2929C2214yescomplemented
118#2913C2214yescomplemented
119#2905C2211yescharacteristic, complemented
120#2897C2218yescomplemented
121#2879C2212yescomplemented
122C2×#405C2211yescharacteristic, complemented
123C2×H(5,𝔽2)C2318yes—
124C22×#41C2312yes—
125#576—416no—
126C2×AGL(1,ℤ/8)C2318yes—
127C2×AGL(1,ℤ/8)C23116yes—
128C2×#135C2312yes—
129C2×#135C2312yes—
130C2×#135C2318yes—
131C22×D8C2312yes—
132C22×D8C2312yes—
133C22×D8C2318yes—
134C2×#131—48no—
135C2×#131C2314yes—
136C2×#131C2314yes—
137C2×#131C2314yes—
138C2×#131C2314yes—
139C22×M16C2311yescharacteristic
140C22×M16C2312yes—
141C22×M16C2314yes—
142C23×C8C2311yescharacteristic
143C23×C8C2314yes—
144#562—216no—
145#560—216no—
146#560—216no—
147#560—216no—
148#559—28no—
149#556—24no—
150#555C2318yes—
151#553—216no—
152#553—216no—
153#553C23116yes—
154#553C23116yes—
155#552C23116yes—
156#551—216no—
157#550—28no—
158#550—24no—
159#550C23116yes—
160#548—28no—
161#547—24no—
162#547C2318yes—
163#547C2318yes—
164#546—216no—
165#546—28no—
166#546—28no—
167#546—216no—
168#546C23116yes—
169D42—216no—
170D42—28no—
171D42—24no—
172D42—216no—
173D42—216no—
174D42C2318yes—
175D42C23116yes—
176#542C2318yes—
177#541—24no—
178#541C2314yes—
179#540—24no—
180#540—216no—
181#540—216no—
182#540—28no—
183#540C2314yes—
184#540C2318yes—
185#540C2318yes—
186#539—216no—
187#539—24no—
188#538—216no—
189#538—216no—
190#538—28no—
191#538—24no—
192#537D414yes—
193#537C2318yes—
194#537C23116yes—
195#536D414yes—
196#535—28no—
197#535—216no—
198#535D414yes—
199#535C2318yes—
200#535C23116yes—
201#534—28no—
202#534—216no—
203#534—216no—
204#534D414yes—
205#533C2312yes—
206#532—24no—
207#532C2312yes—
208#532C2312yes—
209#532C2312yes—
210C2×#127—24no—
211C2×#127C2312yes—
212#529—28no—
213#529—28no—
214C2×#125C2312yes—
215#525—28no—
216#525C23116yes—
217#525C2314yes—
218#525C2314yes—
219#525C2314yes—
220C2×#123—24no—
221C2×#121—28no—
222C2×#121—24no—
223C2×#121C23116yes—
224C2×#121C2314yes—
225#520C2318yes—
226C4×#41C2314yes—
227C2×C4×D4C2314yes—
228C2×#117C2311yescharacteristic
229#500C2312yes—
230#499C2314yes—
231#499C2312yes—
232#499C2314yes—
233#499C2312yes—
234#498C2312yes—
235#495C2312yes—
236#495C2312yes—
237#494C2311yescharacteristic
238#493C2314yes—
239#493C2314yes—
240#493C2311yescharacteristic
241#492C2312yes—
242#491C2314yes—
243#490C2318yes—
244#490C2318yes—
245#490C2314yes—
246#489C2318yes—
247#485C23116yes—
248#483C23116yes—
249#482C23116yes—
250#482C23116yes—
251#482C23116yes—
252#481C23116yes—
253#481C23116yes—
254#480C23116yes—
255#479C23116yes—
256#478C23116yes—
257#478C23116yes—
258#476C2318yes—
259#474C2318yes—
260#470C2314yes—
261#469C23116yes—
262#469C2314yes—
263#469C2318yes—
264#469C2318yes—
265#469C23116yes—
266#469C23116yes—
267#468C23116yes—
268#468C2318yes—
269#468C23116yes—
270#468C23116yes—
271#467C2318yes—
272#467C2314yes—
273#466C2318yes—
274#466C2318yes—
275#466C2318yes—
276#466C2314yes—
277#466C2318yes—
278#466C2318yes—
279#466C23116yes—
280#466C23116yes—
281#465C2318yes—
282#465C23116yes—
283#465C23116yes—
284#463C23116yes—
285#461C2318yes—
286#460C23116yes—
287#459C23116yes—
288#459C2318yes—
289#452C23116yes—
290#450C23116yes—
291#449C23116yes—
292#449C23116yes—
293#449C23116yes—
294#447C23116yes—
295#447C23116yes—
296#447C23116yes—
297#442C2314yes—
298#442C2318yes—
299#442C2318yes—
300#441C2314yes—
301#440C2318yes—
302C4×Q16C2314yes—
303C4×SD16C2318yes—
304C4×D8C2314yes—
305C4×D8C2314yes—
306C4×D8C2314yes—
307C4×D8C2314yes—
308C4×D8C2314yes—
309#436C2318yes—
310#436C2314yes—
311#436C2314yes—
312#435C2318yes—
313#435C2318yes—
314#435C2318yes—
315#435C2318yes—
316C8×D4C2314yes—
317C8×D4C2318yes—
318C8×D4C2314yes—
319#428C2318yes—
320#428C23116yes—
321#427C2318yes—
322#427C2312yes—
323#427C2312yes—
324C2×#107C2318yes—
325C2×#107C2312yes—
326C2×#106C2312yes—
327#424C2314yes—
328#424C2314yes—
329#423C2312yes—
330#423C2312yes—
331#418C2318yes—
332#418C23116yes—
333#417C2318yes—
334#417C23116yes—
335#416C2314yes—
336#416C2314yes—
337#416C23116yes—
338C2×#102C2314yes—
339C2×#102C2314yes—
340C2×#102C23116yes—
341#408C2314yes—
342#408C2314yes—
343#408C2314yes—
344#408C2314yes—
345#407C2314yes—
346#407C2314yes—
347#405C2312yes—
348#405C2312yes—
349#405C2312yes—
350#405C2312yes—
351C2×#97C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355H(5,𝔽2)—416no—
356H(5,𝔽2)—416no—
357C2×#41—28no—
358C2×#41—28no—
359C2×#41—44no—
360C2×#41—44no—
361C2×#41C2×D414yes—
362C2×#41C2×D414yes—
363C2×#41C2414yes—
364C2×#41C24116yes—
365C2×#41C2414yes—
366C2×#41C2414yes—
367C22×Q8C2×D412yes—
368C22×D4—24no—
369C22×D4—216no—
370C22×D4—216no—
371C22×D4—28no—
372C22×D4—28no—
373C22×D4—216no—
374C22×D4—24no—
375C22×D4C2×D414yes—
376C22×D4C2×D412yes—
377C22×D4C2414yes—
378C22×D4C24116yes—
379C23×C4—24no—
380C23×C4C2411yescharacteristic
381C23×C4C2414yes—
382AGL(1,ℤ/8)—432no—
383AGL(1,ℤ/8)—416no—
384#135—28no—
385#135—416no—
386#135—44no—
387C2×Q16C2412yes—
388C2×Q16C2412yes—
389C2×SD16C2414yes—
390C2×SD16C24116yes—
391C2×SD16C2414yes—
392C2×D8—28no—
393C2×D8—416no—
394C2×D8—44no—
395C2×D8C2412yes—
396C2×D8C2414yes—
397C2×D8C2414yes—
398C2×D8C24116yes—
399C2×D8C2418yes—
400C2×D8C2412yes—
401#131—216no—
402#131—48no—
403#131—48no—
404#131—48no—
405C2×M16—42no—
406C2×M16—48no—
407C2×M16—44no—
408C2×M16C2414yes—
409C2×M16C2418yes—
410C2×M16C2414yes—
411C2×M16C2418yes—
412C2×M16C2412yes—
413C2×M16C2412yes—
414C22×C8—24no—
415C22×C8—48no—
416C22×C8C2412yes—
417C22×C8C2412yes—
418C22×C8C2411yescharacteristic
419C22×C8C2418yes—
420C22×C8C2411yescharacteristic
421C22×C8C2411yescharacteristic
422C22×C8C2414yes—
423C22×C8C2418yes—
424C22×C8C2411yescharacteristic
425C4⋊Q8C2×D412yes—
426C4⋊Q8C2×D412yes—
427C4⋊Q8C2412yes—
428C4⋊Q8C2414yes—
429#127—28no—
430#127—216no—
431#127—216no—
432#127—24no—
433#127C2×D412yes—
434#127C2×D412yes—
435#127C2418yes—
436#127C2412yes—
437#126—28no—
438#126—216no—
439#126—216no—
440#126—216no—
441#126—28no—
442#125—28no—
443#125—216no—
444#125—24no—
445#125C2418yes—
446#125C2414yes—
447#124—28no—
448#124—216no—
449#124—28no—
450#124—216no—
451#124C2×D414yes—
452#124C2×D414yes—
453#124C2414yes—
454#123—216no—
455#123—24no—
456#123—216no—
457#123—216no—
458#123—216no—
459#123—28no—
460#123—216no—
461#123—216no—
462#123—28no—
463#123—216no—
464#123—216no—
465#123—216no—
466#123C2×D418yes—
467#123C2×D418yes—
468C22⋊Q8—28no—
469C22⋊Q8—216no—
470C22⋊Q8—24no—
471C22⋊Q8—28no—
472C22⋊Q8—28no—
473C22⋊Q8C2×D418yes—
474C22⋊Q8C2×D418yes—
475C22⋊Q8C2418yes—
476C22⋊Q8C24116yes—
477#121—216no—
478#121—28no—
479#121—28no—
480#121—28no—
481#121—216no—
482#121—216no—
483#121—216no—
484#121—216no—
485#121—216no—
486#121—24no—
487#121—216no—
488#121—216no—
489#121—28no—
490#121—28no—
491#121—216no—
492#121—216no—
493#121—216no—
494#121—216no—
495#121—28no—
496#121—216no—
497#121—216no—
498#121C2×D414yes—
499#121C2×D414yes—
500#121C2×D418yes—
501#121C2×D418yes—
502#121C2×D418yes—
503#121C2418yes—
504#121C24116yes—
505#121C24116yes—
506#121C24116yes—
507#121C24116yes—
508#120—216no—
509#120—24no—
510#120—216no—
511#120—216no—
512#120—216no—
513#120—216no—
514#120—216no—
515#120—216no—
516#120—216no—
517#120C2×D418yes—
518#120C2×D418yes—
519C4×Q8—28no—
520C4×Q8—24no—
521C4×Q8C2418yes—
522C4×D4—216no—
523C4×D4—28no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—216no—
527C4×D4—216no—
528C4×D4—216no—
529C4×D4—216no—
530C4×D4—216no—
531C4×D4—24no—
532C4×D4—24no—
533C4×D4—24no—
534C4×D4C2418yes—
535C4×D4C2418yes—
536C4×D4C2418yes—
537C4×D4C2414yes—
538C4×D4C2418yes—
539C4×D4C2414yes—
540#117—28no—
541#117—216no—
542#117—24no—
543#117C2×D414yes—
544#117C2414yes—
545#117C24116yes—
546#117C2412yes—
547#117C2412yes—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—28no—
550C2×C4⋊C4C2×D412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C24116yes—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—216no—
556C2×C22⋊C4—216no—
557C2×C22⋊C4C2×D412yes—
558C2×C42—24no—
559C2×C42C2411yescharacteristic
560C2×C42C2411yescharacteristic
561#107C2414yes—
562#107C2414yes—
563#107C2414yes—
564#107C24116yes—
565#107C2414yes—
566#106C2418yes—
567#106C2414yes—
568#106C24116yes—
569#106C2414yes—
570C4⋊C8C2418yes—
571C4⋊C8C2414yes—
572C4⋊C8C2414yes—
573#103C2418yes—
574#103C24116yes—
575#103C2418yes—
576#102C24116yes—
577#102C2418yes—
578#102C24116yes—
579#102C24116yes—
580#102C2418yes—
581#102C2418yes—
582#102C24116yes—
583#102C2418yes—
584C22⋊C8C2418yes—
585C22⋊C8C2418yes—
586C22⋊C8C2418yes—
587C22⋊C8C2418yes—
588#97C2412yes—
589#97C2412yes—
590#97C2412yes—
591#97C2412yes—
592C4×C8C2411yescharacteristic
593C4×C8C2411yescharacteristic
594C4×C8C2412yes—
595C4×C8C2411yescharacteristic
596C4×C8C2411yescharacteristic
597C4×C8C2412yes—
598C24—24no—
599C24—216no—
600C24C22×D411yescharacteristic
601C24C22×D414yes—
602#41—28no—
603#41—28no—
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—48no—
609#41—48no—
610#41—416no—
611#41—416no—
612#41—816no—
613#41—168no—
614C2×Q8—24no—
615C2×Q8—44no—
616C2×Q8C22×D414yes—
617C2×Q8C22×D414yes—
618C2×Q8C2514yes—
619C2×D4—24no—
620C2×D4—216no—
621C2×D4—216no—
622C2×D4—28no—
623C2×D4—216no—
624C2×D4—216no—
625C2×D4—216no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—216no—
629C2×D4—216no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—416no—
634C2×D4—416no—
635C2×D4—48no—
636C2×D4—816no—
637C2×D4—832no—
638C2×D4—164no—
639C2×D4—168no—
640C2×D4—1616no—
641C2×D4—164no—
642C2×D4—1616no—
643C2×D4C22×D418yes—
644C2×D4C22×D414yes—
645C2×D4C22×D414yes—
646C2×D4C22×D414yes—
647C2×D4C22×D418yes—
648C2×D4C22×D414yes—
649C2×D4C22×D418yes—
650C2×D4C2514yes—
651C2×D4C2518yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—216no—
656C22×C4—24no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—216no—
660C22×C4—28no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—164no—
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D412yes—
666C22×C4C22×D412yes—
667C22×C4C22×D412yes—
668C22×C4C22×D418yes—
669C22×C4C22×D414yes—
670C22×C4C2518yes—
671C22×C4C2512yes—
672C22×C4C2511yescharacteristic
673Q16—24no—
674Q16—42no—
675SD16—28no—
676SD16—44no—
677SD16—416no—
678D8—28no—
679D8—28no—
680D8—24no—
681D8—48no—
682D8—416no—
683D8—42no—
684M16—28no—
685M16—216no—
686M16—42no—
687M16—42no—
688M16—48no—
689M16—44no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—24no—
694C2×C8—24no—
695C2×C8—216no—
696C2×C8—44no—
697C2×C8—48no—
698C2×C8H(5,𝔽2)14yes—
699C2×C8C2511yescharacteristic
700C2×C8C2511yescharacteristic
701C2×C8C2512yes—
702C2×C8C2512yes—
703C2×C8C2518yes—
704C2×C8C2511yescharacteristic
705C2×C8C2511yescharacteristic
706C4⋊C4—24no—
707C4⋊C4—216no—
708C4⋊C4—216no—
709C4⋊C4—24no—
710C4⋊C4—216no—
711C4⋊C4—24no—
712C4⋊C4—28no—
713C4⋊C4—28no—
714C4⋊C4—28no—
715C4⋊C4C22×D414yes—
716C4⋊C4C22×D414yes—
717C4⋊C4C22×D414yes—
718C4⋊C4C22×D414yes—
719C4⋊C4C22×D418yes—
720C4⋊C4C2518yes—
721C4⋊C4C2518yes—
722C22⋊C4—216no—
723C22⋊C4—24no—
724C22⋊C4—216no—
725C22⋊C4—28no—
726C22⋊C4—216no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—216no—
730C22⋊C4—216no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—216no—
735C22⋊C4C22×D418yes—
736C22⋊C4C22×D414yes—
737C22⋊C4C22×D414yes—
738C22⋊C4C22×D418yes—
739C22⋊C4C22×D418yes—
740C22⋊C4C22×D418yes—
741C42—28no—
742C42—24no—
743C42—216no—
744C42C22×D412yes—
745C42C22×D412yes—
746C42C2511yescharacteristic
747C42C2511yescharacteristic
748C42C2512yes—
749C23—22no—
750C23—24no—
751C23—28no—
752C23—44no—
753C23—42no—
754C23—48no—
755C23—48no—
756C23—84no—
757C23—84no—
758C23—816no—
759C23—816no—
760C23—816no—
761C23C23×D418yes—
762C23C23×D412yes—
763C23C23×D411yescharacteristic
764Q8—28no—
765Q8—24no—
766Q8—24no—
767Q8—44no—
768Q8—84no—
769D4—216no—
770D4—28no—
771D4—24no—
772D4—28no—
773D4—24no—
774D4—28no—
775D4—44no—
776D4—48no—
777D4—44no—
778D4—48no—
779D4—44no—
780D4—48no—
781D4—48no—
782D4—816no—
783D4—84no—
784D4—816no—
785D4—816no—
786D4—816no—
787D4—816no—
788D4—816no—
789D4—88no—
790D4—816no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—44no—
801C2×C4—48no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—48no—
805C2×C4—88no—
806C2×C4—88no—
807C2×C4—816no—
808C2×C4—88no—
809C2×C4—84no—
810C2×C4—816no—
811C2×C4C23×D414yes—
812C2×C4C23×D418yes—
813C2×C4C23×D412yes—
814C2×C4C23×D412yes—
815C2×C4C23×D412yes—
816C2×C4C23×D411yescharacteristic
817C2×C4C2×H(5,𝔽2)12yes—
818C2×C4#58512yes—
819C2×C4C2611yescharacteristic
820C8—22no—
821C8—28no—
822C8—22no—
823C8—21no—
824C8—21no—
825C8C2×H(5,𝔽2)12yes—
826C8C2×H(5,𝔽2)12yes—
827C22—22no—
828C22—22no—
829C22—28no—
830C22—28no—
831C22—28no—
832C22—24no—
833C22—44no—
834C22—48no—
835C22—48no—
836C22—48no—
837C22—48no—
838C22—82no—
839C22—88no—
840C22—168no—
841C22—3216no—
842C22#349612yes—
843C22C24×D411yescharacteristic
844C4—22no—
845C4—28no—
846C4—22no—
847C4—22no—
848C4—24no—
849C4—44no—
850C4—48no—
851C4—48no—
852C4#349612yes—
853C4C22×H(5,𝔽2)11yescharacteristic
854C4C2×#58511yescharacteristic
855C2—22no—
856C2—42no—
857C2—48no—
858C2—88no—
859C2—84no—
860C2C2×#349611yescharacteristic
861C2#6309112yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3449 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62880C2semidirect
2. #62292C2semidirect
3. #62290C2semidirect
4. #62276C2semidirect
5. #62270C2semidirect
6. #62266C2semidirect
7. #61289C2semidirect
8. #61284C2semidirect
9. #61223C2semidirect
10. #61218C2semidirect
11. #61089C2semidirect
12. #61084C2semidirect
13. #60920C2semidirect
14. #60771C2semidirect
15. #60682C2semidirect
16. C2×#3176C2semidirect
17. #60458C2semidirect
18. #60140C2semidirect
19. C2×#576C22semidirect
20. C22×#131C22semidirect
23. #3542C22semidirect
24. #3539C22semidirect
26. #3537C22semidirect
28. #3512C22semidirect
29. #3506C22semidirect
30. #3498C22semidirect
31. #3496C22semidirect
32. #3488C22semidirect
33. #3455C22semidirect
34. C2×#540C22semidirect
36. #3355C22semidirect
37. #3354C22semidirect
38. #3351C22semidirect
39. #3341C22semidirect
40. #3339C22semidirect
41. #3339C22semidirect
42. #3336C22semidirect
43. #3334C22semidirect
44. #3319C22semidirect
45. #3318C22semidirect
46. #3318C22semidirect
47. #3317C22semidirect
48. #3310C22semidirect
49. #3309C22semidirect
50. #3307C22semidirect
51. #3306C22semidirect
52. #3287C22semidirect
53. #3283C22semidirect
54. #3280C22semidirect
55. D4×D8C22semidirect
56. D4×D8C22semidirect
57. #3274C22semidirect
58. #3273C22semidirect
59. #3272C22semidirect
60. #3260C22semidirect
61. #3259C22semidirect
62. #3257C22semidirect
63. #3204C22semidirect
64. #3199C22semidirect
65. #3198C22semidirect
66. #3197C22semidirect
67. #3194C22semidirect
68. #3192C22semidirect
69. #3177C22semidirect
70. #3176C22semidirect
71. #3176C22semidirect
72. #3176C22semidirect
73. #3176C22semidirect
74. #3176C22semidirect
75. #3175C22semidirect
76. #3174C22semidirect
77. #3173C22semidirect
78. #3160C22semidirect
79. C2×#499C22semidirect
80. #3147C22semidirect
81. C2×#493C22semidirect
82. #3135C22semidirect
83. C2×#490C22semidirect
84. #3099C22semidirect
85. #3096C22semidirect
86. #3080C22semidirect
87. #3077C22semidirect
88. #3062C22semidirect
89. #3062C22semidirect
90. #3061C22semidirect
91. #3061C22semidirect
92. #3058C22semidirect
93. #3058C22semidirect
94. #3055C22semidirect
95. #3055C22semidirect
96. #3054C22semidirect
97. C2×#469C22semidirect
98. #3050C22semidirect
99. #3050C22semidirect
100. C2×#466C22semidirect
101. C2×#466C22semidirect
102. #3038C22semidirect
103. #3036C22semidirect
104. #3012C22semidirect
105. #3008C22semidirect
106. #2943C22semidirect
107. C2×#442C22semidirect
108. C4×#135C22semidirect
109. C2×C4×D8C22semidirect
110. #2932C22semidirect
111. #2932C22semidirect
112. #2931C22semidirect
113. #2931C22semidirect
114. #2930C22semidirect
115. #2930C22semidirect
116. #2929C22semidirect
117. #2929C22semidirect
118. #2913C22semidirect
119. #2905C22semidirect
120. #2897C22semidirect
121. #2879C22semidirect
122. C2×#405C22semidirect

Maximal subgroups

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

subgroupindex
#628802
#622922
#622902
#622762
#622702
#622662
#612892
#612842
#612232
#612182
#610892
#610842
#609202
#607712
#606822
C2×#31762
#604582
#601402