Finite Group Databasebeta

← #10578511

Subgroups — #10578511

Order 512.

5846 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62932C212yesmaximal, complemented
2#62412C218yesmaximal, complemented
3#62407C214yesmaximal, complemented
4#62399C214yesmaximal, complemented
5#62380C212yesmaximal, complemented
6#62380C214yesmaximal, complemented
7#62377C214yesmaximal, complemented
8#62375C212yesmaximal, complemented
9#62364C212yesmaximal, complemented
10#62361C212yesmaximal, complemented
11#61413C212yesmaximal, complemented
12#61411C211yesmaximal, characteristic, complemented
13C2×#3393C211yesmaximal, characteristic, complemented
14#61372C212yesmaximal, complemented
15#61370C211yesmaximal, characteristic, complemented
16Q8×#135C211yesmaximal, characteristic, complemented
17#61344C214yesmaximal, complemented
18#61340C212yesmaximal, complemented
19#61323C212yesmaximal, complemented
20#60927C214yesmaximal, complemented
21#60923C212yesmaximal, complemented
22#60715C211yesmaximal, characteristic, complemented
23#60713C212yesmaximal, complemented
24#60696C212yesmaximal, complemented
25#60695C211yesmaximal, characteristic
26Q8×#131C211yesmaximal, characteristic, complemented
27#3564—28no—
28#3557—24no—
29#3557C2218yescomplemented
30#3555—22no—
31#3555—24no—
32#3555C2214yescomplemented
33#3555C2218yescomplemented
34#3550—22no—
35#3550C2214yescomplemented
36#3538—24no—
37#3523—22no—
38#3523C2214yescomplemented
39#3510C2214yes—
40#3510C2214yes—
41#3509C2212yes—
42#3509C2212yes—
43#3507—22no—
44#3507C2214yescomplemented
45#3502C2214yes—
46#3501C2212yes—
47#3495—24no—
48Q8×#41C2212yes—
49Q8×#41C2211yescharacteristic
50C2×#556C2212yes—
51#3461C2214yes—
52#3460C2212yes—
53#3401C2218yes—
54#3401C2218yes—
55#3398C2214yescomplemented
56#3398C2214yescomplemented
57#3396C2214yes—
58#3396C2214yes—
59#3395C2212yescomplemented
60#3395C2212yescomplemented
61#3393C2212yes—
62#3393C2214yes—
63#3393C2212yes—
64#3393C2214yes—
65#3393C2214yes—
66#3393C2212yes—
67#3393C2212yes—
68#3393C2214yes—
69#3393C2212yescomplemented
70#3393C2212yescomplemented
71#3390C2218yescomplemented
72#3389C2214yes—
73#3387C2218yescomplemented
74#3384C2214yes—
75#3383C2214yescomplemented
76#3383C2211yescharacteristic, complemented
77#3383C2214yescomplemented
78#3383C2214yescomplemented
79#3383C2212yescomplemented
80Q8×Q16C2214yescomplemented
81Q8×Q16C2211yescharacteristic, complemented
82#3381C2212yescomplemented
83#3381C2214yescomplemented
84#3380C2212yes—
85#3380C2214yes—
86#3380C2211yescharacteristic, complemented
87#3380C2212yescomplemented
88Q8×SD16C2212yescomplemented
89Q8×D8C2212yes—
90Q8×D8C2211yescharacteristic, complemented
91#3377C2218yescomplemented
92#3377C2218yescomplemented
93#3377C2218yescomplemented
94#3376C2218yescomplemented
95#3376C2218yescomplemented
96#3375C2218yescomplemented
97#3372C2214yescomplemented
98#3372C2218yescomplemented
99#3371C2218yescomplemented
100#3371C2218yescomplemented
101#3369C2214yescomplemented
102#3369C2218yescomplemented
103#3367C2214yescomplemented
104#3367C2214yescomplemented
105#3365C2218yescomplemented
106#3364C2214yescomplemented
107#3364C2218yescomplemented
108#3360C2214yescomplemented
109#3360C2214yescomplemented
110#3359C2214yescomplemented
111#3263C2218yescomplemented
112#3262C2218yescomplemented
113#3260C2218yescomplemented
114#3258C2218yescomplemented
115#3258C2218yescomplemented
116#3258C2218yescomplemented
117#3256C2218yescomplemented
118#3254C2214yescomplemented
119#3252C2214yescomplemented
120#3252C2218yescomplemented
121#3250C2218yescomplemented
122#3248C2214yescomplemented
123#3248C2218yescomplemented
124#3246C2214yescomplemented
125#3185C2214yescomplemented
126#3183C2218yes—
127#3179C2214yes—
128#3178C2218yescomplemented
129#3177C2214yescomplemented
130#3177C2214yescomplemented
131#3177C2214yescomplemented
132#3176C2212yes—
133#3175C2212yes—
134#3175C2214yes—
135#3175C2214yes—
136#3175C2214yescomplemented
137#3173C2218yes—
138#3172C2218yescomplemented
139#3171C2214yes—
140#3170C2214yescomplemented
141#3170C2212yescomplemented
142#3170C2212yescomplemented
143#3169C2212yes—
144#3168C2212yes—
145#3168C2214yes—
146#3168C2214yes—
147#3168C2214yescomplemented
148#3164C2211yescharacteristic
149#3164C2212yes—
150#3160C2212yes—
151#3160C2211yescharacteristic
152#3156C2212yes—
153#3155C2211yescharacteristic
154C2×#495C2212yes—
155C2×#494C2211yescharacteristic
156#3140C2214yes—
157#3139C2212yes—
158#3137C2214yes—
159#3136C2212yes—
160#3082C2214yes—
161#3082C2214yes—
162#3081C2214yes—
163#3078C2214yes—
164#3077C2212yes—
165#3076C2212yes—
166#3076C2214yes—
167#3063C2214yes—
168#3062C2212yes—
169#3061C2211yescharacteristic
170#3059C2212yes—
171#3059C2212yes—
172#3058C2211yescharacteristic
173#3057C2214yes—
174#3044C2214yes—
175#3043C2214yes—
176#3042C2214yes—
177#3040C2214yes—
178#3039C2212yes—
179C2×#464C2214yes—
180C2×#461C2212yes—
181Q8×M16C2211yescharacteristic
182Q8×M16C2212yescomplemented
183#2962C2211yescharacteristic
184#2962C2212yes—
185#2962C2212yescomplemented
186#2962C2214yescomplemented
187#2960C2211yescharacteristic
188#2960C2212yes—
189#2960C2212yescomplemented
190#2960C2214yescomplemented
191C2×C8×Q8C2211yescharacteristic
192C2×C8×Q8C2212yescomplemented
193#2950C2212yes—
194#2950C2212yes—
195#2950C2212yes—
196#2949C2214yes—
197#2948C2212yes—
198C4×#137C2214yes—
199C4×AGL(1,ℤ/8)C2212yes—
200C4×#135C2211yescharacteristic
201C4×#135C2212yes—
202C2×C4×Q16C2212yes—
203C2×C4×D8C2211yescharacteristic
204#2906C2211yescharacteristic
205#2906C2212yes—
206C4×#131C2211yescharacteristic
207C4×#131C2212yes—
208C2×#137C2314yes—
209C2×AGL(1,ℤ/8)C2312yes—
210C2×#135C2311yescharacteristic
211C22×Q16C2312yes—
212C22×Q16C2312yes—
213C22×SD16C2314yes—
214C22×D8C2311yescharacteristic
215C2×#131C2311yescharacteristic
216C2×#131C2312yes—
217C2×#131C2311yescharacteristic
218#563—28no—
219#563—28no—
220#563—28no—
221#563—28no—
222#563—28no—
223#563—28no—
224#559—24no—
225#559—24no—
226#559C2318yes—
227#559C2318yes—
228Q82—24no—
229Q82D411yescharacteristic
230Q82C2312yes—
231Q82C2318yes—
232#557—24no—
233#557—24no—
234#557—24no—
235#557—22no—
236#557—22no—
237#557D411yescharacteristic
238#557D412yes—
239#557C2314yes—
240#557C2314yes—
241#557C2312yes—
242#557C2318yes—
243#557C2318yes—
244#557C2318yes—
245#557C2314yes—
246#556—24no—
247#556—24no—
248#556—28no—
249#556—22no—
250#556—22no—
251#556—24no—
252#556—28no—
253#556—24no—
254#556—24no—
255#556—22no—
256#556—22no—
257#556C2314yes—
258#556C2314yes—
259#556C2318yes—
260#556C2314yes—
261#556C2318yes—
262#556C2314yes—
263#556C2318yes—
264#554—22no—
265#554—24no—
266#554—22no—
267#554—24no—
268#554D412yes—
269#554D411yescharacteristic
270#554D412yes—
271#554D414yes—
272#554C2312yes—
273#554C2314yes—
274#554C2318yes—
275#554C2314yes—
276#552—28no—
277#552—28no—
278#552—24no—
279#552—28no—
280#552—24no—
281#552—24no—
282#552—24no—
283#552—24no—
284#552—24no—
285#552—24no—
286#552—24no—
287#552—28no—
288#551—28no—
289#551—28no—
290#551—28no—
291#551—28no—
292D4×Q8—22no—
293D4×Q8—24no—
294D4×Q8—22no—
295D4×Q8—24no—
296D4×Q8D412yes—
297D4×Q8D411yescharacteristic
298D4×Q8C2314yes—
299D4×Q8C2312yes—
300#544—24no—
301#544—28no—
302#544—28no—
303#544C2314yes—
304#544C2312yes—
305#543—24no—
306#542—24no—
307#542—24no—
308#542—28no—
309#542—28no—
310#542—28no—
311#542—22no—
312#542—24no—
313#542C2318yes—
314#542C2318yes—
315#542C2314yes—
316#542C2318yes—
317#541—24no—
318#541—28no—
319#541—28no—
320#541—24no—
321#541—28no—
322#541—28no—
323#541—24no—
324#541—24no—
325#541—28no—
326#541C2318yes—
327#541C2318yes—
328#540—22no—
329#540C2314yes—
330#539—28no—
331#539—28no—
332#539—28no—
333#539—28no—
334#538—24no—
335#537C2312yes—
336#536—24no—
337#536—24no—
338#536—24no—
339#536C2314yes—
340#536C2314yes—
341#535C2312yes—
342#535C2312yes—
343#533—22no—
344#533—22no—
345#533—28no—
346#533—24no—
347#533—22no—
348#533—24no—
349#533C2318yes—
350#533C2314yes—
351#533C2314yes—
352#533C2312yes—
353#533C2314yes—
354#533C2311yescharacteristic
355#533C2312yes—
356#533C2312yes—
357#533C2314yes—
358#532—22no—
359#532C2314yes—
360C2×C4⋊Q8C2312yes—
361#529—24no—
362#529—24no—
363#529—22no—
364#529—28no—
365#529—24no—
366#529C2314yes—
367#529C2318yes—
368#529C2318yes—
369#529C2318yes—
370C2×#126—24no—
371C2×#124C2314yes—
372#525—24no—
373C2×C22⋊Q8—22no—
374C2×C22⋊Q8—24no—
375#520—24no—
376#519—24no—
377#519C2314yes—
378#519C2314yes—
379#518C2314yes—
380C4×#41C2312yes—
381C4×#41C2314yes—
382C4×#41C2311yescharacteristic
383C4×#41C2312yes—
384C2×C4×Q8—22no—
385C2×C4×Q8C2314yes—
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2312yes—
388C2×C4×D4C2312yes—
389C2×#117—22no—
390#501C2318yes—
391#501C2314yes—
392#500C2311yescharacteristic
393#500C2314yes—
394#500C2312yes—
395#500C2311yescharacteristic
396#500C2312yes—
397#500C2312yes—
398#499C2312yes—
399#499C2314yes—
400#499C2312yes—
401#499C2312yes—
402#499C2312yes—
403#499C2314yes—
404#499C2312yes—
405#498C2312yes—
406#498C2314yes—
407#497C2318yes—
408#496C2314yes—
409#495C2312yes—
410#495C2314yes—
411#495C2314yes—
412#495C2314yes—
413#495C2314yes—
414#495C2314yes—
415#494C2312yes—
416#494C2312yes—
417#494C2314yes—
418#494C2312yes—
419#494C2312yes—
420#493C2312yes—
421#491C2318yes—
422#491C2318yes—
423#490C2314yes—
424#489C2318yes—
425#489C2318yes—
426#489C2314yes—
427#489C2318yes—
428#488C2318yes—
429#488C2318yes—
430#488C2318yes—
431#488C2314yes—
432#487C2314yes—
433#487C2318yes—
434#487C2314yes—
435#486C2314yes—
436#479C2314yes—
437#479C2314yes—
438#479C2314yes—
439#479C2318yes—
440#479C2318yes—
441#479C2318yes—
442#479C2318yes—
443#479C2318yes—
444#479C2318yes—
445#478C2314yes—
446#478C2314yes—
447#478C2314yes—
448#478C2318yes—
449#478C2318yes—
450#478C2318yes—
451#477C2312yes—
452#477C2314yes—
453#477C2318yes—
454#477C2318yes—
455#477C2318yes—
456#476C2312yes—
457#476C2314yes—
458#476C2314yes—
459#476C2318yes—
460#475C2312yes—
461#475C2314yes—
462#475C2318yes—
463#475C2318yes—
464#475C2318yes—
465#474C2312yes—
466#474C2314yes—
467#474C2314yes—
468#474C2318yes—
469#470C2318yes—
470#470C2318yes—
471#470C2318yes—
472#469C2314yes—
473#469C2314yes—
474#468C2314yes—
475#468C2314yes—
476#468C2318yes—
477#468C2318yes—
478#468C2318yes—
479#467C2314yes—
480#467C2314yes—
481#467C2312yes—
482#467C2314yes—
483#467C2314yes—
484#467C2318yes—
485#466C2312yes—
486#466C2312yes—
487#466C2312yes—
488#466C2314yes—
489#465C2318yes—
490#465C2318yes—
491#465C2314yes—
492#465C2318yes—
493#464C2318yes—
494#464C2318yes—
495#464C2318yes—
496#464C2318yes—
497#464C2318yes—
498#464C2318yes—
499#464C2318yes—
500#464C2318yes—
501#464C2318yes—
502#464C2318yes—
503#463C2318yes—
504#463C2318yes—
505#463C2318yes—
506#463C2318yes—
507#462C2314yes—
508#462C2318yes—
509#462C2318yes—
510#462C2314yes—
511#461C2314yes—
512#461C2318yes—
513#461C2314yes—
514#461C2314yes—
515#461C2318yes—
516#461C2318yes—
517#461C2314yes—
518#460C2318yes—
519#460C2318yes—
520#446C2312yes—
521#446C2312yes—
522#446C2314yes—
523#446C2314yes—
524#446C2314yes—
525#446C2314yes—
526#446C2314yes—
527#446C2312yes—
528#446C2314yes—
529#446C2312yes—
530#446C2314yes—
531C8×Q8C2312yes—
532C8×Q8C2312yes—
533C8×Q8C2314yes—
534C8×Q8C2312yes—
535C8×Q8C2311yescharacteristic
536C8×Q8C2311yescharacteristic
537C8×Q8C2312yes—
538C8×Q8C2311yescharacteristic
539C8×Q8C2312yes—
540C8×Q8C2312yes—
541C8×Q8C2311yescharacteristic
542C8×Q8C2314yes—
543C8×Q8C2314yes—
544#442C2314yes—
545#442C2318yes—
546#441C2318yes—
547#441C2318yes—
548#441C2318yes—
549#441C2318yes—
550#440C2318yes—
551#440C2318yes—
552#440C2318yes—
553#440C2314yes—
554C4×Q16C2314yes—
555C4×Q16C2318yes—
556C4×Q16C2314yes—
557C4×Q16C2314yes—
558C4×Q16C2312yes—
559C4×Q16C2314yes—
560C4×Q16C2314yes—
561C4×Q16C2311yescharacteristic
562C4×Q16C2314yes—
563C4×Q16C2312yes—
564C4×Q16C2314yes—
565C4×Q16C2314yes—
566C4×Q16C2311yescharacteristic
567C4×Q16C2314yes—
568C4×Q16C2314yes—
569C4×SD16C2314yes—
570C4×SD16C2318yes—
571C4×SD16C2318yes—
572C4×SD16C2318yes—
573C4×SD16C2312yes—
574C4×SD16C2314yes—
575C4×SD16C2312yes—
576C4×SD16C2314yes—
577C4×D8C2314yes—
578C4×D8C2312yes—
579C4×D8C2314yes—
580C4×D8C2311yescharacteristic
581C4×D8C2312yes—
582C4×D8C2312yes—
583C4×D8C2314yes—
584C4×D8C2311yescharacteristic
585C4×D8C2312yes—
586C4×D8C2312yes—
587C4×D8C2312yes—
588#428C2314yes—
589#428C2312yes—
590#427C2312yes—
591#427C2314yes—
592#427C2312yes—
593#427C2311yescharacteristic
594C2×#107C2311yescharacteristic
595#424C2312yes—
596#424C2312yes—
597#424C2312yes—
598#424C2314yes—
599#424C2314yes—
600#424C2314yes—
601#423C2311yescharacteristic
602#423C2312yes—
603#423C2312yes—
604#423C2314yes—
605C2×C4⋊C8C2311yescharacteristic
606C2×C4⋊C8C2312yes—
607C2×C4⋊C8C2312yes—
608C2×C4⋊C8C2314yes—
609#419C2314yes—
610#419C2314yes—
611#419C2314yes—
612#418C2314yes—
613#418C2312yes—
614#417C2312yes—
615#416C2312yes—
616#416C2314yes—
617C2×#103C2314yes—
618C2×#102C2312yes—
619#405C2311yescharacteristic
620#405C2312yes—
621#405C2311yescharacteristic
622#405C2312yes—
623#405C2314yes—
624#405C2314yes—
625#405C2312yes—
626#405C2312yes—
627C4×M16C2311yescharacteristic
628C4×M16C2312yes—
629C4×M16C2312yes—
630C4×M16C2314yes—
631C2×C4×C8C2311yescharacteristic
632C2×C4×C8C2312yes—
633C2×C4×C8C2314yes—
634C2×C4×C8C2312yes—
635C2×#41—24no—
636C2×#41C2412yes—
637C2×#41C2411yescharacteristic
638C22×Q8—22no—
639C22×Q8—24no—
640C22×Q8C2×D411yescharacteristic
641C22×Q8C2×D412yes—
642C22×Q8C2414yes—
643C22×D4C2412yes—
644C23×C4—22no—
645#137—48no—
646AGL(1,ℤ/8)—44no—
647#135—24no—
648C2×Q16—28no—
649C2×Q16—44no—
650C2×Q16C2414yes—
651C2×Q16C2414yes—
652C2×Q16C2411yescharacteristic
653C2×Q16C2414yes—
654C2×Q16C2414yes—
655C2×Q16C2418yes—
656C2×SD16—48no—
657C2×SD16C2412yes—
658C2×SD16C2418yes—
659C2×SD16C2418yes—
660C2×SD16C2414yes—
661C2×SD16C2418yes—
662C2×D8—24no—
663C2×D8C2412yes—
664C2×D8C2412yes—
665C2×D8C2411yescharacteristic
666C2×D8C2414yes—
667#131—24no—
668#131—44no—
669#131—42no—
670C2×M16C2411yescharacteristic
671C2×M16C2412yes—
672C2×M16C2411yescharacteristic
673C2×M16C2412yes—
674C2×M16C2414yes—
675C2×M16C2412yes—
676C22×C8C2412yes—
677C22×C8C2411yescharacteristic
678C22×C8C2412yes—
679C22×C8C2414yes—
680C22×C8C2412yes—
681C22×C8C2411yescharacteristic
682C4⋊Q8—24no—
683C4⋊Q8—22no—
684C4⋊Q8—28no—
685C4⋊Q8—24no—
686C4⋊Q8—28no—
687C4⋊Q8—28no—
688C4⋊Q8—22no—
689C4⋊Q8—28no—
690C4⋊Q8—24no—
691C4⋊Q8—24no—
692C4⋊Q8—22no—
693C4⋊Q8—28no—
694C4⋊Q8—28no—
695C4⋊Q8—22no—
696C4⋊Q8—22no—
697C4⋊Q8C2×D411yescharacteristic
698C4⋊Q8C2×D411yescharacteristic
699C4⋊Q8C2×D412yes—
700C4⋊Q8C2×D414yes—
701C4⋊Q8C2×D412yes—
702C4⋊Q8C2×D412yes—
703C4⋊Q8C2×D414yes—
704C4⋊Q8C2×D412yes—
705C4⋊Q8C2414yes—
706C4⋊Q8C2414yes—
707C4⋊Q8C2418yes—
708C4⋊Q8C2414yes—
709C4⋊Q8C2412yes—
710C4⋊Q8C2412yes—
711C4⋊Q8C2414yes—
712C4⋊Q8C2414yes—
713C4⋊Q8C2418yes—
714#127—22no—
715#127C2414yes—
716#126—28no—
717#126—28no—
718#126—28no—
719#126—28no—
720#126—24no—
721#126—28no—
722#126—28no—
723#126—28no—
724#126—28no—
725#126—28no—
726#126—28no—
727#126—28no—
728#126—28no—
729#126—28no—
730#126—28no—
731#126—28no—
732#126—28no—
733#126—28no—
734#126—24no—
735#126—28no—
736#126—28no—
737#126—28no—
738#125—22no—
739#125—28no—
740#125—24no—
741#125—28no—
742#125—28no—
743#125—28no—
744#125—24no—
745#125—24no—
746#125—24no—
747#125—24no—
748#125—24no—
749#125—28no—
750#125—28no—
751#125—28no—
752#125—28no—
753#125—28no—
754#125—28no—
755#125—28no—
756#125—28no—
757#125—28no—
758#125—24no—
759#125—24no—
760#125C2×D412yes—
761#125C2×D412yes—
762#125C2×D414yes—
763#125C2×D414yes—
764#125C2×D412yes—
765#125C2×D414yes—
766#125C2414yes—
767#125C2414yes—
768#125C2414yes—
769#125C2418yes—
770#125C2414yes—
771#124—22no—
772#124—28no—
773#124—28no—
774#124—24no—
775#124—28no—
776#124—24no—
777#124—28no—
778#124—28no—
779#124—24no—
780#124—24no—
781#124—24no—
782#124C2418yes—
783#124C2418yes—
784#124C2414yes—
785#124C2418yes—
786#123—28no—
787#123—28no—
788#123—28no—
789#123—24no—
790#123—28no—
791#123—24no—
792#123—28no—
793#123—24no—
794#123—28no—
795#123—28no—
796#123—28no—
797#123—24no—
798#123—28no—
799#123—28no—
800#123—28no—
801#123—28no—
802C22⋊Q8—24no—
803C22⋊Q8—24no—
804C22⋊Q8—24no—
805C22⋊Q8—28no—
806C22⋊Q8—22no—
807C22⋊Q8—22no—
808C22⋊Q8—24no—
809C22⋊Q8—24no—
810C22⋊Q8—24no—
811C22⋊Q8—28no—
812C22⋊Q8—28no—
813C22⋊Q8—28no—
814C22⋊Q8—22no—
815C22⋊Q8—24no—
816C22⋊Q8—24no—
817C22⋊Q8—24no—
818C22⋊Q8—28no—
819C22⋊Q8—22no—
820C22⋊Q8—24no—
821C22⋊Q8—24no—
822C22⋊Q8—28no—
823C22⋊Q8—24no—
824C22⋊Q8—24no—
825C22⋊Q8—24no—
826C22⋊Q8—22no—
827C22⋊Q8—24no—
828C22⋊Q8—28no—
829C22⋊Q8—24no—
830C22⋊Q8—24no—
831C22⋊Q8—24no—
832C22⋊Q8—28no—
833C22⋊Q8—28no—
834C22⋊Q8—28no—
835C22⋊Q8—28no—
836C22⋊Q8—28no—
837C22⋊Q8—28no—
838C22⋊Q8—24no—
839C22⋊Q8C2×D412yes—
840C22⋊Q8C2×D414yes—
841C22⋊Q8C2×D412yes—
842C22⋊Q8C2×D412yes—
843C22⋊Q8C2×D414yes—
844C22⋊Q8C2×D414yes—
845C22⋊Q8C2×D414yes—
846C22⋊Q8C2×D414yes—
847C22⋊Q8C2×D414yes—
848C22⋊Q8C2×D412yes—
849C22⋊Q8C2×D414yes—
850C22⋊Q8C2418yes—
851C22⋊Q8C2418yes—
852C22⋊Q8C2414yes—
853#121—24no—
854#121—22no—
855#121—24no—
856#121—22no—
857#121—22no—
858#121—24no—
859#121—24no—
860#121C2414yes—
861#121C2414yes—
862#121C2414yes—
863#120—24no—
864#120—24no—
865C4×Q8—22no—
866C4×Q8—24no—
867C4×Q8—24no—
868C4×Q8—28no—
869C4×Q8—22no—
870C4×Q8—24no—
871C4×Q8—28no—
872C4×Q8—24no—
873C4×Q8—24no—
874C4×Q8—24no—
875C4×Q8—24no—
876C4×Q8—28no—
877C4×Q8—28no—
878C4×Q8—22no—
879C4×Q8—24no—
880C4×Q8—24no—
881C4×Q8—24no—
882C4×Q8—28no—
883C4×Q8—24no—
884C4×Q8—22no—
885C4×Q8—24no—
886C4×Q8—24no—
887C4×Q8C2×D411yescharacteristic
888C4×Q8C2×D412yes—
889C4×Q8C2×D411yescharacteristic
890C4×Q8C2×D412yes—
891C4×Q8C2×D412yes—
892C4×Q8C2×D414yes—
893C4×Q8C2×D411yescharacteristic
894C4×Q8C2×D412yes—
895C4×Q8C2×D412yes—
896C4×Q8C2×D411yescharacteristic
897C4×Q8C2418yes—
898C4×Q8C2418yes—
899C4×Q8C2412yes—
900C4×Q8C2414yes—
901C4×Q8C2414yes—
902C4×Q8C2412yes—
903C4×Q8C2418yes—
904C4×Q8C2418yes—
905C4×Q8C2418yes—
906C4×Q8C2418yes—
907C4×Q8C2411yescharacteristic
908C4×Q8C2412yes—
909C4×Q8C2411yescharacteristic
910C4×Q8C2412yes—
911C4×Q8C2414yes—
912C4×Q8C2412yes—
913C4×Q8C2414yes—
914C4×D4—22no—
915C4×D4—24no—
916C4×D4—22no—
917C4×D4—24no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—24no—
921C4×D4—28no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—28no—
925C4×D4—28no—
926C4×D4—22no—
927C4×D4—22no—
928C4×D4—24no—
929C4×D4C2×D412yes—
930C4×D4C2×D414yes—
931C4×D4C2×D412yes—
932C4×D4C2×D411yescharacteristic
933C4×D4C2×D412yes—
934C4×D4C2×D414yes—
935C4×D4C2×D411yescharacteristic
936C4×D4C2×D412yes—
937C4×D4C2414yes—
938C4×D4C2414yes—
939C4×D4C2414yes—
940C4×D4C2412yes—
941C4×D4C2412yes—
942C4×D4C2414yes—
943C4×D4C2418yes—
944C4×D4C2418yes—
945#117—24no—
946#117—28no—
947#117—24no—
948#117—24no—
949#117—24no—
950#117—28no—
951#117—28no—
952#117—24no—
953#117—28no—
954#117—24no—
955#117—28no—
956#117—28no—
957#117—22no—
958#117—24no—
959#117—24no—
960#117—28no—
961#117—28no—
962#117—28no—
963#117C2414yes—
964#117C2412yes—
965#117C2412yes—
966#117C2411yescharacteristic
967#117C2412yes—
968#117C2414yes—
969C2×C4⋊C4—22no—
970C2×C4⋊C4—24no—
971C2×C4⋊C4—22no—
972C2×C4⋊C4—22no—
973C2×C4⋊C4—24no—
974C2×C4⋊C4—24no—
975C2×C4⋊C4—28no—
976C2×C4⋊C4C2×D411yescharacteristic
977C2×C4⋊C4C2×D412yes—
978C2×C4⋊C4C2×D412yes—
979C2×C4⋊C4C2×D414yes—
980C2×C4⋊C4C2412yes—
981C2×C22⋊C4—24no—
982C2×C22⋊C4—22no—
983C2×C22⋊C4—24no—
984C2×C22⋊C4—28no—
985C2×C42—24no—
986C2×C42—24no—
987C2×C42—22no—
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2414yes—
991C2×C42C2412yes—
992#107C2412yes—
993#107C2412yes—
994#107C2412yes—
995#107C2412yes—
996#107C2411yescharacteristic
997#107C2411yescharacteristic
998#107C2412yes—
999#107C2412yes—
1000#107C2414yes—
1001#107C2414yes—
1002#107C2414yes—
1003#107C2418yes—
1004#106C2412yes—
1005#106C2414yes—
1006#106C2414yes—
1007#106C2414yes—
1008#106C2414yes—
1009#106C2418yes—
1010#106C2414yes—
1011C4⋊C8C2411yescharacteristic
1012C4⋊C8C2412yes—
1013C4⋊C8C2411yescharacteristic
1014C4⋊C8C2412yes—
1015C4⋊C8C2414yes—
1016C4⋊C8C2412yes—
1017C4⋊C8C2414yes—
1018C4⋊C8C2412yes—
1019C4⋊C8C2414yes—
1020C4⋊C8C2414yes—
1021C4⋊C8C2412yes—
1022C4⋊C8C2412yes—
1023C4⋊C8C2414yes—
1024C4⋊C8C2412yes—
1025C4⋊C8C2414yes—
1026C4⋊C8C2414yes—
1027C4⋊C8C2414yes—
1028#103C2418yes—
1029#103C2418yes—
1030#103C2414yes—
1031#103C2414yes—
1032#103C2412yes—
1033#103C2412yes—
1034#103C2414yes—
1035#103C2418yes—
1036#103C2418yes—
1037#103C2418yes—
1038#103C2418yes—
1039#103C2418yes—
1040#103C2418yes—
1041#102C2414yes—
1042#102C2414yes—
1043#102C2414yes—
1044#102C2414yes—
1045#102C2412yes—
1046#102C2412yes—
1047#102C2414yes—
1048#102C2414yes—
1049#102C2418yes—
1050#102C2418yes—
1051#102C2414yes—
1052#97C2414yes—
1053#97C2414yes—
1054#97C2412yes—
1055#97C2412yes—
1056#97C2412yes—
1057#97C2414yes—
1058C4×C8C2411yescharacteristic
1059C4×C8C2412yes—
1060C4×C8C2412yes—
1061C4×C8C2411yescharacteristic
1062C4×C8C2414yes—
1063C4×C8C2412yes—
1064C4×C8C2411yescharacteristic
1065C4×C8C2411yescharacteristic
1066C4×C8C2414yes—
1067C4×C8C2412yes—
1068C4×C8C2414yes—
1069C4×C8C2412yes—
1070C4×C8C2412yes—
1071C4×C8C2412yes—
1072C24—22no—
1073#41—22no—
1074#41—22no—
1075#41—24no—
1076#41—24no—
1077#41—88no—
1078C2×Q8—24no—
1079C2×Q8—22no—
1080C2×Q8—22no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—24no—
1084C2×Q8—24no—
1085C2×Q8—28no—
1086C2×Q8—28no—
1087C2×Q8—42no—
1088C2×Q8—44no—
1089C2×Q8—88no—
1090C2×Q8—84no—
1091C2×Q8C22×D411yescharacteristic
1092C2×Q8C22×D412yes—
1093C2×Q8C22×D411yescharacteristic
1094C2×Q8C22×D411yescharacteristic
1095C2×Q8C22×D412yes—
1096C2×Q8C22×D414yes—
1097C2×Q8C22×D412yes—
1098C2×Q8C22×D414yes—
1099C2×Q8C2518yes—
1100C2×Q8C2512yes—
1101C2×D4—22no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—22no—
1106C2×D4—24no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4C22×D412yes—
1111C2×D4C22×D411yescharacteristic
1112C2×D4C2514yes—
1113C2×D4C2512yes—
1114C22×C4—24no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—22no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—22no—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—28no—
1124C22×C4—24no—
1125C22×C4—84no—
1126C22×C4C22×D411yescharacteristic
1127C22×C4C22×D412yes—
1128C22×C4C22×D412yes—
1129C22×C4C22×D411yescharacteristic
1130C22×C4C22×D412yes—
1131C22×C4C22×D414yes—
1132C22×C4C22×D412yes—
1133C22×C4C22×D414yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136Q16—28no—
1137Q16—28no—
1138Q16—22no—
1139Q16—44no—
1140Q16—44no—
1141Q16—48no—
1142SD16—24no—
1143SD16—48no—
1144SD16—48no—
1145SD16—44no—
1146SD16—48no—
1147D8—24no—
1148D8—24no—
1149D8—22no—
1150D8—44no—
1151M16—22no—
1152M16—22no—
1153M16—24no—
1154M16—24no—
1155M16—44no—
1156M16—42no—
1157C2×C8—24no—
1158C2×C8—22no—
1159C2×C8—24no—
1160C2×C8—44no—
1161C2×C8—42no—
1162C2×C82−1+414yes—
1163C2×C8C2512yes—
1164C2×C8C2511yescharacteristic
1165C2×C8C2512yes—
1166C2×C8C2511yescharacteristic
1167C2×C8C2514yes—
1168C2×C8C2512yes—
1169C2×C8C2512yes—
1170C2×C8C2511yescharacteristic
1171C2×C8C2511yescharacteristic
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—22no—
1188C4⋊C4—22no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4C22×D411yescharacteristic
1209C4⋊C4C22×D412yes—
1210C4⋊C4C22×D412yes—
1211C4⋊C4C22×D414yes—
1212C4⋊C4C22×D412yes—
1213C4⋊C4C22×D412yes—
1214C4⋊C4C22×D411yescharacteristic
1215C4⋊C4C22×D414yes—
1216C4⋊C4C22×D414yes—
1217C4⋊C4C22×D414yes—
1218C4⋊C4C22×D412yes—
1219C4⋊C4C22×D412yes—
1220C4⋊C4C22×D414yes—
1221C4⋊C4C22×D412yes—
1222C4⋊C4C22×D414yes—
1223C4⋊C4C22×D412yes—
1224C4⋊C4C22×D412yes—
1225C4⋊C4C22×D411yescharacteristic
1226C4⋊C4C22×D411yescharacteristic
1227C4⋊C4C22×D414yes—
1228C4⋊C4C22×D412yes—
1229C4⋊C4C22×D414yes—
1230C4⋊C4C22×D412yes—
1231C4⋊C4C22×D414yes—
1232C4⋊C4C22×D414yes—
1233C4⋊C4C2514yes—
1234C4⋊C4C2512yes—
1235C4⋊C4C2514yes—
1236C4⋊C4C2514yes—
1237C4⋊C4C2512yes—
1238C22⋊C4—24no—
1239C22⋊C4—22no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—28no—
1246C22⋊C4—28no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4C22×D414yes—
1263C22⋊C4C22×D412yes—
1264C22⋊C4C22×D412yes—
1265C22⋊C4C22×D412yes—
1266C22⋊C4C22×D414yes—
1267C22⋊C4C22×D414yes—
1268C42—28no—
1269C42—24no—
1270C42—22no—
1271C42—24no—
1272C42—28no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—28no—
1277C42—28no—
1278C42—28no—
1279C42—28no—
1280C42C22×D411yescharacteristic
1281C42C22×D412yes—
1282C42C22×D414yes—
1283C42C22×D412yes—
1284C42C22×D411yescharacteristic
1285C42C22×D412yes—
1286C42C22×D414yes—
1287C42C22×D412yes—
1288C42C2511yescharacteristic
1289C42C2512yes—
1290C42C2511yescharacteristic
1291C42C2514yes—
1292C42C2512yes—
1293C42C2512yes—
1294C23—24no—
1295C23—22no—
1296C23—44no—
1297C23—82no—
1298C23—82no—
1299C23C23×D412yes—
1300C23C23×D411yescharacteristic
1301Q8—22no—
1302Q8—22no—
1303Q8—24no—
1304Q8—22no—
1305Q8—22no—
1306Q8—28no—
1307Q8—28no—
1308Q8—22no—
1309Q8—42no—
1310Q8—44no—
1311Q8—42no—
1312Q8—44no—
1313Q8—44no—
1314Q8—48no—
1315Q8—82no—
1316Q8—84no—
1317Q8—88no—
1318Q8—84no—
1319Q8—84no—
1320D4—24no—
1321D4—24no—
1322D4—22no—
1323D4—22no—
1324D4—24no—
1325D4—22no—
1326D4—44no—
1327D4—44no—
1328D4—84no—
1329D4—84no—
1330D4—84no—
1331D4—84no—
1332D4—84no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—28no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—44no—
1345C2×C4—42no—
1346C2×C4—41no—
1347C2×C4—42no—
1348C2×C4—42no—
1349C2×C4—44no—
1350C2×C4—48no—
1351C2×C4—48no—
1352C2×C4—44no—
1353C2×C4—44no—
1354C2×C4—84no—
1355C2×C4—88no—
1356C2×C4—82no—
1357C2×C4—84no—
1358C2×C4—88no—
1359C2×C4—84no—
1360C2×C4—82no—
1361C2×C4C23×D412yes—
1362C2×C4C23×D412yes—
1363C2×C4C23×D412yes—
1364C2×C4C23×D412yes—
1365C2×C4C23×D411yescharacteristic
1366C2×C4C23×D414yes—
1367C2×C4C23×D412yes—
1368C2×C4C23×D414yes—
1369C2×C4C23×D412yes—
1370C2×C4C23×D412yes—
1371C2×C4C23×D411yescharacteristic
1372C2×C4C23×D411yescharacteristic
1373C2×C4C23×D411yescharacteristic
1374C2×C4C23×D411yescharacteristic
1375C2×C4C2×2−1+412yes—
1376C2×C4#58512yes—
1377C2×C4C2611yescharacteristic
1378C8—22no—
1379C8—22no—
1380C8—21no—
1381C8—22no—
1382C8—21no—
1383C8—22no—
1384C8—24no—
1385C8C2×2−1+412yes—
1386C8C2×2−1+412yes—
1387C22—21no—
1388C22—21no—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—42no—
1393C22—44no—
1394C22—44no—
1395C22—42no—
1396C22—42no—
1397C22—44no—
1398C22—164no—
1399C22#349712yes—
1400C22C24×D411yescharacteristic
1401C4—22no—
1402C4—21no—
1403C4—22no—
1404C4—22no—
1405C4—22no—
1406C4—24no—
1407C4—22no—
1408C4—21no—
1409C4—24no—
1410C4—21no—
1411C4—22no—
1412C4—22no—
1413C4—42no—
1414C4—48no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4#349712yes—
1421C4#358412yes—
1422C4C22×2−1+411yescharacteristic
1423C4C2×#58511yescharacteristic
1424C2—22no—
1425C2—42no—
1426C2—82no—
1427C2—84no—
1428C2C2×#349711yescharacteristic
1429C2C2×#358411yescharacteristic
1430C2#6309311yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#60695C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ Q8×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62932C2semidirect
2. #62412C2semidirect
3. #62407C2semidirect
4. #62399C2semidirect
5. #62380C2semidirect
6. #62380C2semidirect
7. #62377C2semidirect
8. #62375C2semidirect
9. #62364C2semidirect
10. #62361C2semidirect
11. #61413C2semidirect
12. #61411C2semidirect
13. C2×#3393C2semidirect
14. #61372C2semidirect
15. #61370C2semidirect
16. Q8×#135C2semidirect
17. #61344C2semidirect
18. #61340C2semidirect
19. #61323C2semidirect
20. #60927C2semidirect
21. #60923C2semidirect
22. #60715C2semidirect
23. #60713C2semidirect
24. #60696C2semidirect
26. Q8×#131C2semidirect
29. #3557C22semidirect
32. #3555C22semidirect
33. #3555C22semidirect
35. #3550C22semidirect
38. #3523C22semidirect
44. #3507C22semidirect
55. #3398C22semidirect
56. #3398C22semidirect
59. #3395C22semidirect
60. #3395C22semidirect
69. #3393C22semidirect
70. #3393C22semidirect
71. #3390C22semidirect
73. #3387C22semidirect
75. #3383C22semidirect
76. #3383C22semidirect
77. #3383C22semidirect
78. #3383C22semidirect
79. #3383C22semidirect
80. Q8×Q16C22semidirect
81. Q8×Q16C22semidirect
82. #3381C22semidirect
83. #3381C22semidirect
86. #3380C22semidirect
87. #3380C22semidirect
88. Q8×SD16C22semidirect
90. Q8×D8C22semidirect
91. #3377C22semidirect
92. #3377C22semidirect
93. #3377C22semidirect
94. #3376C22semidirect
95. #3376C22semidirect
96. #3375C22semidirect
97. #3372C22semidirect
98. #3372C22semidirect
99. #3371C22semidirect
100. #3371C22semidirect
101. #3369C22semidirect
102. #3369C22semidirect
103. #3367C22semidirect
104. #3367C22semidirect
105. #3365C22semidirect
106. #3364C22semidirect
107. #3364C22semidirect
108. #3360C22semidirect
109. #3360C22semidirect
110. #3359C22semidirect
111. #3263C22semidirect
112. #3262C22semidirect
113. #3260C22semidirect
114. #3258C22semidirect
115. #3258C22semidirect
116. #3258C22semidirect
117. #3256C22semidirect
118. #3254C22semidirect
119. #3252C22semidirect
120. #3252C22semidirect
121. #3250C22semidirect
122. #3248C22semidirect
123. #3248C22semidirect
124. #3246C22semidirect
125. #3185C22semidirect
128. #3178C22semidirect
129. #3177C22semidirect
130. #3177C22semidirect
131. #3177C22semidirect
136. #3175C22semidirect
138. #3172C22semidirect
140. #3170C22semidirect
141. #3170C22semidirect
142. #3170C22semidirect
147. #3168C22semidirect
182. Q8×M16C22semidirect
185. #2962C22semidirect
186. #2962C22semidirect
189. #2960C22semidirect
190. #2960C22semidirect
192. C2×C8×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#629322
#624122
#624072
#623992
#623802
#623772
#623752
#623642
#623612
#614132
#614112
C2×#33932
#613722
#613702
Q8×#1352
#613442
#613402
#613232
#609272
#609232
#607152
#607132
#606962
#606952
Q8×#1312