Finite Group Databasebeta

← #10581397

Subgroups — #10581397

Order 512.

6326 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62835C211yesmaximal, characteristic, complemented
2C2×#3548C211yesmaximal, characteristic, complemented
3#62356C218yesmaximal, complemented
4#62343C214yesmaximal, complemented
5#62331C214yesmaximal, complemented
6#61809C214yesmaximal, complemented
7#61792C214yesmaximal, complemented
8#61735C214yesmaximal, complemented
9#61717C212yesmaximal, complemented
10#61695C212yesmaximal, complemented
11#61686C214yesmaximal, complemented
12#61667C214yesmaximal, complemented
13#61596C214yesmaximal, complemented
14#61586C212yesmaximal, complemented
15#61565C212yesmaximal, complemented
16#60971C211yesmaximal, characteristic, complemented
17#60951C211yesmaximal, characteristic, complemented
18#60947C211yesmaximal, characteristic, complemented
19#60941C211yesmaximal, characteristic, complemented
20#60763C218yesmaximal, complemented
21#60236C211yesmaximal, characteristic, complemented
22#3561—22no—
23#3559—22no—
24#3554—22no—
25#3550C2212yescomplemented
26#3548—22no—
27#3548—22no—
28#3548—22no—
29#3548—22no—
30#3548C2214yes—
31#3548C2214yes—
32#3548C2214yes—
33#3548C2214yes—
34#3548C2212yescomplemented
35#3547C2214yescomplemented
36#3536—22no—
37C2×#562—22no—
38#3522—22no—
39#3520C2214yes—
40#3511—22no—
41#3511C2212yescomplemented
42#3508—21no—
43#3507C2212yescomplemented
44#3506C2212yes—
45#3503—21no—
46#3501C2212yes—
47#3499C2212yescomplemented
48#3497C2212yescomplemented
49#3494—22no—
50#3489C2214yes—
51C2×#554—21no—
52C2×#554C2212yes—
53C2×#550—21no—
54C2×#550C2212yes—
55C2×#547C2212yes—
56C2×#547C2212yes—
57C2×#540—22no—
58C2×#537—22no—
59C2×#537C2214yes—
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic
65#3356C2218yescomplemented
66#3354C2218yescomplemented
67#3353C2218yescomplemented
68#3344C22116yescomplemented
69#3335C2218yescomplemented
70#3335C2218yescomplemented
71#3335C2218yescomplemented
72#3332C2218yescomplemented
73#3332C2218yescomplemented
74#3331C2218yescomplemented
75#3331C2218yescomplemented
76#3331C2218yescomplemented
77#3330C2218yescomplemented
78#3317C22116yescomplemented
79#3316C22116yescomplemented
80#3304C2218yescomplemented
81#3303C2218yescomplemented
82#3302C2218yescomplemented
83#3299C2218yescomplemented
84#3298C2218yescomplemented
85#3298C2218yescomplemented
86#3284C2218yescomplemented
87#3284C2218yescomplemented
88#3283C2218yescomplemented
89#3278C2218yescomplemented
90#3276C2218yescomplemented
91#3276C2218yescomplemented
92#3271C22116yescomplemented
93#3255C2214yescomplemented
94#3254C2212yescomplemented
95#3253C2212yescomplemented
96#3248C2214yescomplemented
97#3246C2214yescomplemented
98#3238C2212yes—
99#3235C2212yescomplemented
100#3231C2212yescomplemented
101#3229C2212yes—
102#3229C2211yescharacteristic
103#3229C2212yes—
104#3229C2212yescomplemented
105#3227C2212yescomplemented
106#3226C2211yescharacteristic
107#3217C2212yes—
108#3214C2212yescomplemented
109#3210C2212yescomplemented
110#3209C2211yescharacteristic
111#3209C2212yes—
112#3209C2212yescomplemented
113#3208C2212yes—
114#3206C2211yescharacteristic
115#3206C2212yescomplemented
116#3204C22116yescomplemented
117#3204C22116yescomplemented
118#3201C22116yescomplemented
119#3201C22116yescomplemented
120#3195C2218yes—
121#3195C2214yes—
122#3194C2218yes—
123#3194C2214yes—
124#3190C2214yes—
125#3190C2218yes—
126#3187C2214yes—
127#3187C2218yes—
128#3185C2214yescomplemented
129#3171C2214yescomplemented
130#3170C2212yescomplemented
131#3167C2214yescomplemented
132#3167C2212yescomplemented
133#3113C2214yes—
134#3113C2214yescomplemented
135#3108C2214yes—
136#3107C2214yescomplemented
137#3106C2214yescomplemented
138#3103C2214yescomplemented
139#3101C2212yes—
140#3101C2212yes—
141#3101C2212yes—
142#3100C2212yes—
143#3099C22116yescomplemented
144#3092C2218yes—
145C2×#483C2218yes—
146#3063C22116yescomplemented
147#3060C22116yescomplemented
148#3013C22116yescomplemented
149#3007C2218yes—
150#3002C2218yes—
151#2981C2214yescomplemented
152#2979C2214yescomplemented
153#2975C2212yes—
154#2974C2214yes—
155#2972C2212yes—
156#2935C2214yescomplemented
157#2931C2214yescomplemented
158#2920C2211yescharacteristic
159C2×#431C2211yescharacteristic
160#2880C2214yes—
161C2×2−1+4C2314yes—
162C22×#41—22no—
163C22×#41—21no—
164C22×#41C2314yes—
165C22×#41C2312yes—
166C2×#137C23116yes—
167C2×#135C23116yes—
168C2×#131C2318yes—
169#563—24no—
170#562—28no—
171#562—28no—
172#562—28no—
173#562—28no—
174#562—24no—
175#562—28no—
176#559—22no—
177#559—22no—
178#559—24no—
179Q82—22no—
180#557—22no—
181#556—24no—
182#556C2314yes—
183#556C2314yes—
184#555—24no—
185#555C2314yes—
186#554—24no—
187#554—24no—
188#554—24no—
189#554—24no—
190#554—22no—
191#554—24no—
192#554—24no—
193#554—24no—
194#554—24no—
195#554—24no—
196#554C2314yes—
197#554C2314yes—
198#554C2318yes—
199#554C2318yes—
200#553—24no—
201#553—24no—
202#553—24no—
203#552C2318yes—
204#551—28no—
205#550—24no—
206#550—24no—
207#550—24no—
208#550—24no—
209#550—22no—
210#550—22no—
211#550—24no—
212#550—24no—
213#550C2314yes—
214#550C2318yes—
215#550C2318yes—
216D4×Q8—24no—
217D4×Q8—22no—
218D4×Q8C2314yes—
219D4×Q8C2314yes—
220D4×Q8C2314yes—
221#548—24no—
222#548—24no—
223#548—24no—
224#548C2318yes—
225#547—24no—
226#547—28no—
227#547—24no—
228#547—24no—
229#547—24no—
230#547—24no—
231#547—24no—
232#547—24no—
233#547C2314yes—
234#547C2314yes—
235#547C2318yes—
236#547C2318yes—
237#547C2318yes—
238#547C2314yes—
239#547C2318yes—
240#546—28no—
241#546—24no—
242#546—24no—
243#544—24no—
244#544—22no—
245#543—24no—
246#542—24no—
247#542—28no—
248#542—24no—
249#542—24no—
250#542—24no—
251#540—24no—
252#540—28no—
253#540—28no—
254#540—28no—
255#540—28no—
256#540—24no—
257#539—24no—
258#539—28no—
259#538—24no—
260#537—28no—
261#537—28no—
262#537—28no—
263#537—28no—
264#537—28no—
265#537—28no—
266#537—24no—
267#537—24no—
268#537C23116yes—
269#537C23116yes—
270#537C2314yes—
271#537C2318yes—
272#536—24no—
273#536C2314yes—
274#536C2318yes—
275#535—22no—
276#533—22no—
277#533—21no—
278#533—21no—
279#533—21no—
280#533—21no—
281#533—21no—
282#533—21no—
283#533—21no—
284#533—21no—
285#533C2312yes—
286#533C2311yescharacteristic
287#533C2312yes—
288#533C2312yes—
289#533C2312yes—
290#533C2312yes—
291#533C2312yes—
292#533C2311yescharacteristic
293#533C2312yes—
294#533C2312yes—
295#533C2311yescharacteristic
296#532—22no—
297#532—22no—
298#532—24no—
299#532—21no—
300#532—21no—
301#532—21no—
302#532—21no—
303#532D412yes—
304#532D412yes—
305#532D412yes—
306#532D412yes—
307#532C2311yescharacteristic
308#532C2311yescharacteristic
309#532C2312yes—
310#532C2312yes—
311#532C2312yes—
312#532C2311yescharacteristic
313#532C2312yes—
314#532C2312yes—
315#532C2312yes—
316#532C2312yes—
317#532C2312yes—
318C2×C4⋊Q8—22no—
319C2×C4⋊Q8D411yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2311yescharacteristic
324C2×C4⋊Q8C2311yescharacteristic
325C2×#127—22no—
326C2×#127D411yescharacteristic
327C2×#127C2311yescharacteristic
328#529—24no—
329#529—21no—
330#529—21no—
331#529—21no—
332#529—21no—
333#529C2312yes—
334#529C2312yes—
335C2×#125—22no—
336C2×#125—21no—
337C2×#125—21no—
338C2×#124—21no—
339C2×#124D412yes—
340#525—21no—
341#525—21no—
342#525C2318yes—
343#525C2312yes—
344C2×#123—24no—
345C2×#123—24no—
346C2×C22⋊Q8—24no—
347C2×C22⋊Q8—21no—
348C2×C22⋊Q8—21no—
349C2×C22⋊Q8—22no—
350C2×C22⋊Q8—24no—
351C2×C22⋊Q8C2318yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×#121—24no—
356C2×#121—24no—
357C2×#121—22no—
358C2×#121—24no—
359C2×#121—21no—
360C2×#121—24no—
361C2×#121D412yes—
362C2×#121D412yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365#520—24no—
366#520—22no—
367#520C2314yes—
368#518—22no—
369C4×#41—21no—
370C4×#41—21no—
371C4×#41C2312yes—
372C2×C4×Q8—21no—
373C2×C4×Q8—21no—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×D4—22no—
377C2×C4×D4—22no—
378C2×C4×D4—21no—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×#117—21no—
383C2×#117—21no—
384C22×C4⋊C4—22no—
385C22×C4⋊C4C2314yes—
386C22×C42C2311yescharacteristic
387#501C2314yes—
388#500C2312yes—
389#498C2312yes—
390#498C2314yes—
391#498C2314yes—
392#496C2314yes—
393#494C2312yes—
394#494C2314yes—
395#492C2312yes—
396#492C2314yes—
397#490C2314yes—
398#489C2314yes—
399#487C2314yes—
400#487C2312yes—
401#487C2314yes—
402#487C2314yes—
403#487C2312yes—
404#487C2312yes—
405#486C2312yes—
406#486C2314yes—
407#485C23116yes—
408#485C2318yes—
409#484C23116yes—
410#483C23116yes—
411#483C23116yes—
412#483C23116yes—
413#483C2314yes—
414#483C2314yes—
415#483C2314yes—
416#483C2318yes—
417#483C2314yes—
418#483C2318yes—
419#482C23116yes—
420#482C2318yes—
421#481C23116yes—
422#481C23116yes—
423#481C2318yes—
424#480C2314yes—
425#480C2314yes—
426#479C2318yes—
427#477C2314yes—
428#476C2314yes—
429#476C2314yes—
430#476C2314yes—
431#476C2314yes—
432#475C2318yes—
433#475C2318yes—
434#475C2314yes—
435#475C2318yes—
436#474C2314yes—
437#474C2314yes—
438#470C23116yes—
439#470C23116yes—
440#470C23116yes—
441#469C23116yes—
442#469C2318yes—
443#468C23116yes—
444#468C2318yes—
445#467C23116yes—
446#467C2318yes—
447#465C23116yes—
448#465C23116yes—
449#465C23116yes—
450#465C2318yes—
451#465C2318yes—
452#465C2318yes—
453#464C2318yes—
454#462C2314yes—
455#462C2318yes—
456#462C2318yes—
457#461C2314yes—
458#461C2314yes—
459#461C2314yes—
460#461C2314yes—
461#460C2318yes—
462#460C2314yes—
463#459C2314yes—
464#459C2314yes—
465#452C23116yes—
466#452C23116yes—
467#452C23116yes—
468#452C2318yes—
469#452C23116yes—
470#451C2314yes—
471#451C2318yes—
472#451C2318yes—
473#451C23116yes—
474#450C2314yes—
475#450C2314yes—
476#450C2314yes—
477#449C23116yes—
478#449C23116yes—
479#449C2318yes—
480#448C2318yes—
481#448C2314yes—
482#448C23116yes—
483#447C2314yes—
484#441C23116yes—
485C4×Q16C2318yes—
486C4×SD16C2318yes—
487C4×SD16C2318yes—
488C4×SD16C2318yes—
489C4×SD16C2318yes—
490C4×D8C2318yes—
491#436C2318yes—
492#436C2318yes—
493#436C2318yes—
494#435C23116yes—
495C8×D4C2318yes—
496C8×D4C2318yes—
497C8×D4C2318yes—
498#432C2312yes—
499#432C2312yes—
500#431C2312yes—
501#431C2311yescharacteristic
502#431C2311yescharacteristic
503#431C2312yes—
504#431C2312yes—
505#431C2312yes—
506#431C2312yes—
507#428C23116yes—
508C2×#106C23116yes—
509#423C2312yes—
510C2×C4⋊C8C2312yes—
511#417C23116yes—
512#417C23116yes—
513#416C23116yes—
514C2×#103C23116yes—
515#408C23116yes—
516#408C2318yes—
517#407C2318yes—
518#407C2312yes—
519C2×C22⋊C8C2318yes—
520C2×C22⋊C8C2312yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
5232−1+4—88no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—28no—
536C2×#41—84no—
537C2×#41—84no—
538C2×#41—88no—
539C2×#41—88no—
540C2×#41C2×D414yes—
541C2×#41C2×D414yes—
542C2×#41C2412yes—
543C2×#41C2418yes—
544C2×#41C24116yes—
545C2×#41C2414yes—
546C2×#41C2414yes—
547C22×Q8—24no—
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8—21no—
551C22×Q8C2×D412yes—
552C22×Q8C2412yes—
553C22×Q8C2412yes—
554C22×Q8C2418yes—
555C22×D4—22no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4C2×D412yes—
561C22×D4C2×D412yes—
562C22×D4C2×D414yes—
563C22×D4C2×D412yes—
564C22×D4C2412yes—
565C23×C4—24no—
566C23×C4—22no—
567C23×C4—24no—
568C23×C4C2×D411yescharacteristic
569C23×C4C2×D411yescharacteristic
570C23×C4C2414yes—
571C23×C4C2411yescharacteristic
572#137—816no—
573#135—816no—
574C2×Q16C24116yes—
575C2×Q16C2418yes—
576C2×SD16C2418yes—
577C2×SD16C2418yes—
578C2×SD16C2418yes—
579C2×SD16C2418yes—
580C2×D8C2418yes—
581#131—88no—
582C2×M16C2414yes—
583C2×M16C24116yes—
584C22×C8C2414yes—
585C22×C8C24116yes—
586C4⋊Q8—24no—
587C4⋊Q8—28no—
588C4⋊Q8—24no—
589C4⋊Q8—24no—
590C4⋊Q8—24no—
591C4⋊Q8—21no—
592C4⋊Q8—21no—
593C4⋊Q8—21no—
594C4⋊Q8—21no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597C4⋊Q8—21no—
598C4⋊Q8—21no—
599C4⋊Q8—21no—
600C4⋊Q8—21no—
601C4⋊Q8C2×D412yes—
602C4⋊Q8C2×D412yes—
603C4⋊Q8C2×D412yes—
604C4⋊Q8C2×D412yes—
605C4⋊Q8C2412yes—
606C4⋊Q8C2412yes—
607C4⋊Q8C2412yes—
608C4⋊Q8C2412yes—
609C4⋊Q8C2411yescharacteristic
610C4⋊Q8C2412yes—
611C4⋊Q8C2412yes—
612C4⋊Q8C2412yes—
613C4⋊Q8C2412yes—
614C4⋊Q8C2412yes—
615C4⋊Q8C2412yes—
616C4⋊Q8C2411yescharacteristic
617C4⋊Q8C2411yescharacteristic
618#127—28no—
619#127—28no—
620#127—24no—
621#127—21no—
622#127—21no—
623#127C2×D412yes—
624#127C2×D412yes—
625#127C2×D412yes—
626#127C2×D412yes—
627#127C2412yes—
628#127C2412yes—
629#127C2411yescharacteristic
630#126—28no—
631#126—28no—
632#126—28no—
633#126—22no—
634#126—22no—
635#125—28no—
636#125—28no—
637#125—24no—
638#125—24no—
639#125—28no—
640#125—22no—
641#125—22no—
642#125—22no—
643#125—22no—
644#125—22no—
645#125—22no—
646#125—22no—
647#125—22no—
648#125—21no—
649#125—21no—
650#125C2412yes—
651#124—24no—
652#124—24no—
653#124—24no—
654#124—28no—
655#124—28no—
656#124—28no—
657#124—22no—
658#124—22no—
659#124—22no—
660#124—22no—
661#124—21no—
662#124—21no—
663#124C2×D414yes—
664#124C2×D414yes—
665#124C2×D414yes—
666#124C2×D414yes—
667#124C2412yes—
668#123—28no—
669#123—28no—
670#123—28no—
671#123—28no—
672#123—22no—
673#123—22no—
674#123—22no—
675#123—28no—
676#123—216no—
677#123—216no—
678#123—216no—
679#123—216no—
680#123—28no—
681#123—28no—
682#123—28no—
683C22⋊Q8—216no—
684C22⋊Q8—216no—
685C22⋊Q8—24no—
686C22⋊Q8—28no—
687C22⋊Q8—22no—
688C22⋊Q8—22no—
689C22⋊Q8—22no—
690C22⋊Q8—22no—
691C22⋊Q8—22no—
692C22⋊Q8—22no—
693C22⋊Q8—22no—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8—22no—
697C22⋊Q8—22no—
698C22⋊Q8—22no—
699C22⋊Q8—28no—
700C22⋊Q8—28no—
701C22⋊Q8—28no—
702C22⋊Q8—21no—
703C22⋊Q8—21no—
704C22⋊Q8—21no—
705C22⋊Q8—21no—
706C22⋊Q8—28no—
707C22⋊Q8—28no—
708C22⋊Q8—24no—
709C22⋊Q8—28no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8C2412yes—
718C22⋊Q8C2414yes—
719C22⋊Q8C2414yes—
720C22⋊Q8C2414yes—
721C22⋊Q8C2414yes—
722C22⋊Q8C2418yes—
723C22⋊Q8C2418yes—
724C22⋊Q8C24116yes—
725C22⋊Q8C2412yes—
726C22⋊Q8C2418yes—
727#121—216no—
728#121—216no—
729#121—216no—
730#121—216no—
731#121—28no—
732#121—28no—
733#121—216no—
734#121—216no—
735#121—24no—
736#121—24no—
737#121—28no—
738#121—24no—
739#121—24no—
740#121—28no—
741#121—28no—
742#121—28no—
743#121—28no—
744#121—22no—
745#121—22no—
746#121—22no—
747#121—22no—
748#121—22no—
749#121—22no—
750#121—28no—
751#121—21no—
752#121—21no—
753#121—21no—
754#121—21no—
755#121—216no—
756#121—216no—
757#121—28no—
758#121C2×D414yes—
759#121C2×D414yes—
760#121C2×D414yes—
761#121C2×D414yes—
762#121C2×D414yes—
763#121C2×D414yes—
764#121C2×D414yes—
765#121C2×D414yes—
766#121C2414yes—
767#121C2414yes—
768#121C24116yes—
769#121C2412yes—
770#121C2412yes—
771#121C2418yes—
772#120—22no—
773#120—28no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—22no—
778C4×Q8—22no—
779C4×Q8—22no—
780C4×Q8—22no—
781C4×Q8—22no—
782C4×Q8—22no—
783C4×Q8—22no—
784C4×Q8—22no—
785C4×Q8—22no—
786C4×Q8—22no—
787C4×Q8—22no—
788C4×Q8—22no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8C2414yes—
794C4×Q8C2414yes—
795C4×Q8C2414yes—
796C4×Q8C2414yes—
797C4×Q8C2412yes—
798C4×Q8C2412yes—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—24no—
802C4×D4—24no—
803C4×D4—24no—
804C4×D4—24no—
805C4×D4—24no—
806C4×D4—28no—
807C4×D4—24no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—22no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—24no—
819C4×D4—28no—
820C4×D4—22no—
821C4×D4—22no—
822C4×D4—22no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4C2×D414yes—
831C4×D4C2×D414yes—
832C4×D4C2×D414yes—
833C4×D4C2×D414yes—
834C4×D4C2414yes—
835C4×D4C2414yes—
836C4×D4C2412yes—
837C4×D4C2412yes—
838C4×D4C2414yes—
839C4×D4C2414yes—
840C4×D4C2414yes—
841C4×D4C2414yes—
842#117—22no—
843#117—22no—
844#117—22no—
845#117—22no—
846#117—22no—
847#117—22no—
848#117—22no—
849#117—22no—
850#117—21no—
851#117—21no—
852#117—24no—
853#117—28no—
854#117—22no—
855#117—22no—
856#117—22no—
857#117C2412yes—
858#117C2418yes—
859C2×C4⋊C4—21no—
860C2×C4⋊C4—24no—
861C2×C4⋊C4—24no—
862C2×C4⋊C4—28no—
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—21no—
868C2×C4⋊C4—22no—
869C2×C4⋊C4—21no—
870C2×C4⋊C4—22no—
871C2×C4⋊C4—22no—
872C2×C4⋊C4—22no—
873C2×C4⋊C4—28no—
874C2×C4⋊C4—28no—
875C2×C4⋊C4—28no—
876C2×C4⋊C4—24no—
877C2×C4⋊C4—24no—
878C2×C4⋊C4C2×D412yes—
879C2×C4⋊C4C2×D412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C24116yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2418yes—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—24no—
888C2×C22⋊C4—28no—
889C2×C22⋊C4—24no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—22no—
892C2×C22⋊C4C2×D414yes—
893C2×C22⋊C4C2×D414yes—
894C2×C42—22no—
895C2×C42—22no—
896C2×C42—22no—
897C2×C42C2×D411yescharacteristic
898C2×C42C2×D411yescharacteristic
899C2×C42C2×D411yescharacteristic
900C2×C42C2×D411yescharacteristic
901C2×C42C2×D411yescharacteristic
902C2×C42C2×D411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909#107C2418yes—
910#107C2418yes—
911#106C2418yes—
912#106C2418yes—
913#106C2418yes—
914#106C24116yes—
915#106C2418yes—
916C4⋊C8C2412yes—
917C4⋊C8C2414yes—
918C4⋊C8C2412yes—
919C4⋊C8C2414yes—
920C4⋊C8C2414yes—
921#103C2418yes—
922#103C2418yes—
923#103C2418yes—
924#103C24116yes—
925#103C2418yes—
926#103C24116yes—
927#103C2418yes—
928#103C2418yes—
929#102C2418yes—
930#102C2418yes—
931#102C2418yes—
932#102C2418yes—
933#102C2418yes—
934#102C2418yes—
935C22⋊C8C2412yes—
936C22⋊C8C2414yes—
937C22⋊C8C2412yes—
938C22⋊C8C2414yes—
939C22⋊C8C24116yes—
940C22⋊C8C2414yes—
941C22⋊C8C24116yes—
942#97C2414yes—
943C4×C8C2412yes—
944C4×C8C2414yes—
945C4×C8C2412yes—
946C4×C8C2414yes—
947C24—22no—
948C24C22×D411yescharacteristic
949C24C22×D414yes—
950#41—48no—
951#41—48no—
952#41—44no—
953#41—416no—
954#41—416no—
955#41—416no—
956#41—44no—
957#41—82no—
958#41—84no—
959#41—84no—
960#41—84no—
961#41—84no—
962#41—84no—
963#41—84no—
964#41—88no—
965#41—816no—
966#41—816no—
967#41—816no—
968#41—816no—
969#41—88no—
970C2×Q8—21no—
971C2×Q8—22no—
972C2×Q8—22no—
973C2×Q8—22no—
974C2×Q8—22no—
975C2×Q8—22no—
976C2×Q8—21no—
977C2×Q8—22no—
978C2×Q8—22no—
979C2×Q8—22no—
980C2×Q8—28no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—416no—
984C2×Q8—44no—
985C2×Q8—82no—
986C2×Q8—82no—
987C2×Q8—82no—
988C2×Q8—88no—
989C2×Q8C22×D414yes—
990C2×Q8C22×D414yes—
991C2×Q8C2512yes—
992C2×Q8C2514yes—
993C2×Q8C2514yes—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—216no—
1002C2×D4—216no—
1003C2×D4—28no—
1004C2×D4—21no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—22no—
1008C2×D4—21no—
1009C2×D4—22no—
1010C2×D4—22no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—82no—
1015C2×D4—84no—
1016C2×D4—82no—
1017C2×D4—84no—
1018C2×D4—88no—
1019C2×D4—88no—
1020C2×D4C22×D414yes—
1021C2×D4C22×D414yes—
1022C2×D4C22×D414yes—
1023C2×D4C22×D414yes—
1024C2×D4C22×D418yes—
1025C2×D4C22×D414yes—
1026C2×D4C22×D418yes—
1027C2×D4C22×D414yes—
1028C2×D4C2512yes—
1029C2×D4C2514yes—
1030C22×C4—24no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—216no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—28no—
1045C22×C4—216no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—48no—
1049C22×C4—48no—
1050C22×C4—88no—
1051C22×C4—88no—
1052C22×C4C22×D411yescharacteristic
1053C22×C4C22×D411yescharacteristic
1054C22×C4C22×D411yescharacteristic
1055C22×C4C22×D411yescharacteristic
1056C22×C4C22×D411yescharacteristic
1057C22×C4C22×D411yescharacteristic
1058C22×C4C22×D411yescharacteristic
1059C22×C4C22×D411yescharacteristic
1060C22×C4C22×D411yescharacteristic
1061C22×C4C22×D411yescharacteristic
1062C22×C4C22×D411yescharacteristic
1063C22×C4C22×D411yescharacteristic
1064C22×C4C22×D411yescharacteristic
1065C22×C4C22×D411yescharacteristic
1066C22×C4C22×D414yes—
1067C22×C4C22×D418yes—
1068C22×C4C22×D411yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2518yes—
1072C22×C4C2511yescharacteristic
1073Q16—416no—
1074Q16—48no—
1075SD16—48no—
1076SD16—48no—
1077SD16—48no—
1078SD16—48no—
1079D8—48no—
1080M16—44no—
1081M16—416no—
1082C2×C8—44no—
1083C2×C8—416no—
1084C2×C8C2514yes—
1085C2×C8C2514yes—
1086C2×C8C2518yes—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—216no—
1096C4⋊C4—216no—
1097C4⋊C4—28no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—28no—
1119C4⋊C4—22no—
1120C4⋊C4—21no—
1121C4⋊C4—21no—
1122C4⋊C4—21no—
1123C4⋊C4—21no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4C22×D414yes—
1129C4⋊C4C22×D414yes—
1130C4⋊C4C22×D414yes—
1131C4⋊C4C22×D414yes—
1132C4⋊C4C2512yes—
1133C4⋊C4C2514yes—
1134C4⋊C4C2512yes—
1135C4⋊C4C2514yes—
1136C4⋊C4C2514yes—
1137C22⋊C4—22no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—216no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—22no—
1147C22⋊C4—22no—
1148C22⋊C4—28no—
1149C22⋊C4—216no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—22no—
1157C22⋊C4—22no—
1158C22⋊C4—28no—
1159C22⋊C4—22no—
1160C22⋊C4—22no—
1161C22⋊C4C22×D418yes—
1162C22⋊C4C22×D418yes—
1163C22⋊C4C22×D418yes—
1164C22⋊C4C22×D418yes—
1165C42—24no—
1166C42—22no—
1167C42—22no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—22no—
1172C42—28no—
1173C42C22×D411yescharacteristic
1174C42C22×D411yescharacteristic
1175C42C22×D411yescharacteristic
1176C42C22×D411yescharacteristic
1177C42C22×D411yescharacteristic
1178C42C22×D411yescharacteristic
1179C42C22×D411yescharacteristic
1180C42C22×D411yescharacteristic
1181C42C22×D411yescharacteristic
1182C42C22×D411yescharacteristic
1183C42C22×D411yescharacteristic
1184C42C22×D411yescharacteristic
1185C42C2511yescharacteristic
1186C42C2511yescharacteristic
1187C42C2511yescharacteristic
1188C42C2511yescharacteristic
1189C23—22no—
1190C23—28no—
1191C23—22no—
1192C23—24no—
1193C23—41no—
1194C23—44no—
1195C23—41no—
1196C23—44no—
1197C23—44no—
1198C23—44no—
1199C23—44no—
1200C23C23×D411yescharacteristic
1201C23C23×D418yes—
1202C23C23×D411yescharacteristic
1203C23C23×D411yescharacteristic
1204Q8—24no—
1205Q8—28no—
1206Q8—28no—
1207Q8—44no—
1208Q8—44no—
1209Q8—44no—
1210Q8—44no—
1211Q8—44no—
1212Q8—44no—
1213Q8—44no—
1214Q8—42no—
1215Q8—88no—
1216Q8—82no—
1217Q8—82no—
1218Q8—82no—
1219Q8—81no—
1220D4—28no—
1221D4—24no—
1222D4—24no—
1223D4—24no—
1224D4—28no—
1225D4—28no—
1226D4—44no—
1227D4—48no—
1228D4—44no—
1229D4—44no—
1230D4—48no—
1231D4—44no—
1232D4—44no—
1233D4—44no—
1234D4—44no—
1235D4—44no—
1236D4—42no—
1237D4—82no—
1238D4—82no—
1239D4—81no—
1240D4—816no—
1241D4—84no—
1242D4—84no—
1243D4—816no—
1244D4—88no—
1245D4—82no—
1246D4—88no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—216no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—44no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—48no—
1274C2×C4—41no—
1275C2×C4—44no—
1276C2×C4—44no—
1277C2×C4—44no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—44no—
1281C2×C4—48no—
1282C2×C4—48no—
1283C2×C4—44no—
1284C2×C4—816no—
1285C2×C4—88no—
1286C2×C4—816no—
1287C2×C4—88no—
1288C2×C4—82no—
1289C2×C4—88no—
1290C2×C4#57714yes—
1291C2×C4C23×D411yescharacteristic
1292C2×C4C23×D411yescharacteristic
1293C2×C4C23×D411yescharacteristic
1294C2×C4C23×D418yes—
1295C2×C4C23×D411yescharacteristic
1296C2×C4C23×D411yescharacteristic
1297C2×C4C23×D411yescharacteristic
1298C2×C4C23×D411yescharacteristic
1299C2×C4C23×D411yescharacteristic
1300C2×C4C23×D411yescharacteristic
1301C2×C4C23×D411yescharacteristic
1302C2×C4C23×D411yescharacteristic
1303C2×C4C2611yescharacteristic
1304C8—24no—
1305C8—28no—
1306C8—24no—
1307C22—21no—
1308C22—21no—
1309C22—21no—
1310C22—21no—
1311C22—28no—
1312C22—21no—
1313C22—21no—
1314C22—28no—
1315C22—21no—
1316C22—28no—
1317C22—21no—
1318C22—44no—
1319C22—42no—
1320C22—42no—
1321C22—44no—
1322C22—42no—
1323C22—44no—
1324C22—82no—
1325C22—88no—
1326C22—88no—
1327C22C2×#57712yes—
1328C22C24×D411yescharacteristic
1329C4—21no—
1330C4—21no—
1331C4—21no—
1332C4—21no—
1333C4—21no—
1334C4—21no—
1335C4—21no—
1336C4—28no—
1337C4—21no—
1338C4—44no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4C2×#57712yes—
1347C4C2×#57712yes—
1348C4#358612yes—
1349C4H(7,𝔽2)12yes—
1350C2—22no—
1351C2—41no—
1352C2—41no—
1353C2—48no—
1354C2—82no—
1355C2—84no—
1356C2#6284211yescharacteristic
1357C2C22×#57711yescharacteristic
1358C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62835C2semidirect
2. C2×#3548C2semidirect
3. #62356C2semidirect
4. #62343C2semidirect
5. #62331C2semidirect
6. #61809C2semidirect
7. #61792C2semidirect
8. #61735C2semidirect
9. #61717C2semidirect
10. #61695C2semidirect
11. #61686C2semidirect
12. #61667C2semidirect
13. #61596C2semidirect
14. #61586C2semidirect
15. #61565C2semidirect
16. #60971C2semidirect
17. #60951C2semidirect
18. #60947C2semidirect
19. #60941C2semidirect
20. #60763C2semidirect
21. #60236C2semidirect
25. #3550C22semidirect
34. #3548C22semidirect
35. #3547C22semidirect
41. #3511C22semidirect
43. #3507C22semidirect
47. #3499C22semidirect
48. #3497C22semidirect
65. #3356C22semidirect
66. #3354C22semidirect
67. #3353C22semidirect
68. #3344C22semidirect
69. #3335C22semidirect
70. #3335C22semidirect
71. #3335C22semidirect
72. #3332C22semidirect
73. #3332C22semidirect
74. #3331C22semidirect
75. #3331C22semidirect
76. #3331C22semidirect
77. #3330C22semidirect
78. #3317C22semidirect
79. #3316C22semidirect
80. #3304C22semidirect
81. #3303C22semidirect
82. #3302C22semidirect
83. #3299C22semidirect
84. #3298C22semidirect
85. #3298C22semidirect
86. #3284C22semidirect
87. #3284C22semidirect
88. #3283C22semidirect
89. #3278C22semidirect
90. #3276C22semidirect
91. #3276C22semidirect
92. #3271C22semidirect
93. #3255C22semidirect
94. #3254C22semidirect
95. #3253C22semidirect
96. #3248C22semidirect
97. #3246C22semidirect
99. #3235C22semidirect
100. #3231C22semidirect
104. #3229C22semidirect
105. #3227C22semidirect
108. #3214C22semidirect
109. #3210C22semidirect
112. #3209C22semidirect
115. #3206C22semidirect
116. #3204C22semidirect
117. #3204C22semidirect
118. #3201C22semidirect
119. #3201C22semidirect
128. #3185C22semidirect
129. #3171C22semidirect
130. #3170C22semidirect
131. #3167C22semidirect
132. #3167C22semidirect
134. #3113C22semidirect
136. #3107C22semidirect
137. #3106C22semidirect
138. #3103C22semidirect
143. #3099C22semidirect
146. #3063C22semidirect
147. #3060C22semidirect
148. #3013C22semidirect
151. #2981C22semidirect
152. #2979C22semidirect
156. #2935C22semidirect
157. #2931C22semidirect

Maximal subgroups

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

subgroupindex
#628352
C2×#35482
#623562
#623432
#623312
#618092
#617922
#617352
#617172
#616952
#616862
#616672
#615962
#615862
#615652
#609712
#609512
#609472
#609412
#607632
#602362