Finite Group Databasebeta

← #10575899

Subgroups — #10575899

Order 512.

6152 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic, complemented
2C2×#3512C211yesmaximal, characteristic, complemented
3#61021C218yesmaximal, complemented
4#61020C214yesmaximal, complemented
5#61019C214yesmaximal, complemented
6#61010C218yesmaximal, complemented
7#61009C218yesmaximal, complemented
8#60921C212yesmaximal, complemented
9#60920C212yesmaximal, complemented
10#60866C212yesmaximal, complemented
11#60861C212yesmaximal, complemented
12#60805C212yesmaximal, complemented
13#60802C212yesmaximal, complemented
14#60755C214yesmaximal, complemented
15#60702C214yesmaximal, complemented
16#60569C212yesmaximal, complemented
17#60568C212yesmaximal, complemented
18#60565C214yesmaximal, complemented
19#60123C211yesmaximal, characteristic, complemented
20#3512—24no—
21#3512—24no—
22#3512C2214yes—
23#3512C2214yes—
24#3512C2214yescomplemented
25#3512C2214yescomplemented
26#3512C2214yescomplemented
27#3511C2214yescomplemented
28#3510C2214yescomplemented
29#3509C2212yescomplemented
30#3508C2212yescomplemented
31#3507—22no—
32#3506—22no—
33#3505—22no—
34#3505—22no—
35#3480—24no—
36#3475—24no—
37C2×#553—22no—
38C2×#553—22no—
39C2×#553—22no—
40C2×#552—22no—
41#3455C2212yes—
42#3455C2212yes—
43C2×#541C2211yescharacteristic
44C2×#541C2211yescharacteristic, complemented
45C2×#540C2211yescharacteristic
46C2×#540C2211yescharacteristic, complemented
47#3449C2212yes—
48C2×#537C2212yes—
49#3444C2212yes—
50#3444C2212yes—
51C2×#533C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#532C2211yescharacteristic, complemented
54C2×#529C2212yes—
55C2×#529C2212yescomplemented
56C22×#125C2211yescharacteristic, complemented
57#3428C2212yes—
58C2×#520C2212yescomplemented
59C2×C4×#41C2211yescharacteristic
60#3261C2218yescomplemented
61#3260C2218yescomplemented
62#3260C2218yescomplemented
63#3259C2218yescomplemented
64#3258C22116yescomplemented
65#3257C22116yescomplemented
66#3240C2218yescomplemented
67#3239C2214yescomplemented
68#3238C2214yescomplemented
69#3236C2218yescomplemented
70#3234C2218yescomplemented
71#3233C2218yescomplemented
72#3232C2218yescomplemented
73#3232C22116yescomplemented
74#3219C2218yescomplemented
75#3218C2214yescomplemented
76#3217C2214yescomplemented
77#3216C2218yescomplemented
78#3214C2218yescomplemented
79#3212C2218yescomplemented
80#3212C22116yescomplemented
81#3211C2218yescomplemented
82#3204C22116yescomplemented
83#3203C22116yescomplemented
84#3201C22116yescomplemented
85#3198C22116yescomplemented
86#3183C22116yescomplemented
87#3181C2218yescomplemented
88#3180C2218yescomplemented
89#3172C2218yescomplemented
90#3171C2218yescomplemented
91#3168C22116yescomplemented
92#3166C2214yescomplemented
93#3153C2214yes—
94#3142C2214yes—
95#3140C2214yescomplemented
96#3127C2218yescomplemented
97#3126C2218yescomplemented
98#3125C22116yescomplemented
99#3124C22116yescomplemented
100#3123C2218yescomplemented
101#3122C2218yescomplemented
102#3120C22116yescomplemented
103#3120C22116yescomplemented
104#3119C22116yescomplemented
105#3119C22116yescomplemented
106#3095C2214yes—
107#3094C2214yes—
108#3092C2218yescomplemented
109#3080C2214yescomplemented
110#3080C2214yescomplemented
111#3078C2214yescomplemented
112#3077C2214yescomplemented
113#3056C2218yescomplemented
114#3055C2218yescomplemented
115#3039C2214yescomplemented
116#3038C2214yescomplemented
117#3037C2214yes—
118#3036C2214yes—
119#3007C2214yes—
120#3006C2214yes—
121#3005C2218yescomplemented
122C4×#137C2218yescomplemented
123C4×AGL(1,ℤ/8)C2218yescomplemented
124#2923C2214yescomplemented
125#2923C2214yescomplemented
126#2922C2214yescomplemented
127#2922C2214yescomplemented
128#2921C2212yes—
129#2921C2212yescomplemented
130#2920C2212yes—
131#2920C2212yescomplemented
132#2905C2212yescomplemented
133#2879C2212yes—
134C2×C4×M16C2212yescomplemented
135C22×#41C2312yes—
136C22×#41C2312yes—
137C22×#41C2311yescharacteristic
138C2×#137C2318yes—
139C2×AGL(1,ℤ/8)C2318yes—
140C22×M16C2314yes—
141#559—24no—
142#559—28no—
143#557—24no—
144#556—24no—
145#556—28no—
146#556—24no—
147#555—24no—
148#554—24no—
149#553—28no—
150#553—28no—
151#553—28no—
152#553—28no—
153#553—28no—
154#553—28no—
155#553—28no—
156#553—28no—
157#553—28no—
158#553—28no—
159#553—28no—
160#553—28no—
161#553—28no—
162#553—24no—
163#553—24no—
164#553—28no—
165#553—28no—
166#552—28no—
167#552—28no—
168#552—28no—
169#552—28no—
170#552—28no—
171#552—24no—
172#552—24no—
173#551—28no—
174#551—28no—
175#550—24no—
176#548—24no—
177#548—24no—
178#547—24no—
179#546—24no—
180#546—24no—
181#542C2318yes—
182#542C2318yes—
183#541—22no—
184#541—22no—
185#541—24no—
186#541C2314yes—
187#541C2314yes—
188#541C2314yes—
189#541C2314yes—
190#541C2314yes—
191#541C2314yes—
192#540—22no—
193#540—22no—
194#540—24no—
195#540C2314yes—
196#540C2314yes—
197#540C2314yes—
198#540C2314yes—
199#540C2314yes—
200#540C2314yes—
201#539—24no—
202#539—24no—
203#538—24no—
204#538—24no—
205#537—24no—
206#537—24no—
207#537C2318yes—
208#537C2318yes—
209#537C2318yes—
210#536—22no—
211#536C2314yes—
212#535—22no—
213#535C2314yes—
214#534—22no—
215#534—22no—
216#533—22no—
217#533—22no—
218#533C2314yes—
219#533C2314yes—
220#533C2312yes—
221#533C2312yes—
222#533C2312yes—
223#533C2312yes—
224#532—24no—
225#532—22no—
226#532—22no—
227#532—24no—
228#532C2312yes—
229#532C2312yes—
230#532C2312yes—
231#532C2312yes—
232#532C2314yes—
233#532C2314yes—
234#532C2314yes—
235#532C2314yes—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×#127C2311yescharacteristic
240C2×#127C2311yescharacteristic
241#529—28no—
242#529—28no—
243#529—22no—
244#529—22no—
245#529—22no—
246#529—22no—
247#529—24no—
248#529—24no—
249#529—24no—
250#529—24no—
251#529—24no—
252#529—24no—
253#529C2318yes—
254#529C2318yes—
255#529C2318yes—
256#529C2314yes—
257#529C2314yes—
258#529C2314yes—
259#529C2314yes—
260#529C2318yes—
261C2×#126—22no—
262C2×#126—22no—
263C2×#126—22no—
264C2×#126—22no—
265C2×#125—22no—
266C2×#125—22no—
267C2×#125—22no—
268C2×#125—24no—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277#525—24no—
278#525—24no—
279#525—24no—
280#525C2314yes—
281#525C2314yes—
282C2×#123—22no—
283C2×#123—22no—
284C2×#123—22no—
285C2×#123—22no—
286C2×C22⋊Q8—22no—
287C2×C22⋊Q8—22no—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×#121—22no—
291C2×#121—22no—
292C2×#121—22no—
293C2×#121—22no—
294C2×#121—22no—
295C2×#121—22no—
296C2×#121—22no—
297C2×#121C2312yes—
298C2×#121C2312yes—
299#520—24no—
300#520—24no—
301#520—24no—
302#520C2318yes—
303#520C2318yes—
304#520C2318yes—
305#519C2314yes—
306#518—24no—
307#518C2314yes—
308C4×#41—24no—
309C4×#41—24no—
310C4×#41—24no—
311C4×#41D414yes—
312C4×#41D414yes—
313C4×#41C2314yes—
314C4×#41C2314yes—
315C4×#41C2312yes—
316C4×#41C2312yes—
317C4×#41C2312yes—
318C4×#41C2312yes—
319C2×C4×Q8—22no—
320C2×C4×Q8D412yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4—22no—
324C2×C4×D4—22no—
325C2×C4×D4—22no—
326C2×C4×D4—22no—
327C2×C4×D4—22no—
328C2×C4×D4—22no—
329C2×C4×D4D412yes—
330C2×C4×D4D412yes—
331C2×C4×D4D412yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×#117—24no—
335C2×#117—22no—
336C2×#117—22no—
337C2×#117—22no—
338C2×#117C2312yes—
339C2×#117C2311yescharacteristic
340C2×#117C2311yescharacteristic
341C2×#117C2311yescharacteristic
342C22×C4⋊C4—22no—
343C22×C4⋊C4—22no—
344C22×C4⋊C4C2312yes—
345C22×C42C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348#501C2318yes—
349#501C2318yes—
350#499C23116yes—
351#497C2318yes—
352#496C2318yes—
353#495C23116yes—
354#491C2318yes—
355#490C2318yes—
356#489C2318yes—
357#489C2318yes—
358#488C23116yes—
359#488C23116yes—
360#485C23116yes—
361#484C23116yes—
362#484C2318yes—
363#483C23116yes—
364#483C2318yes—
365#482C23116yes—
366#481C23116yes—
367#481C2318yes—
368#480C23116yes—
369#480C2318yes—
370#479C23116yes—
371#479C23116yes—
372#479C23116yes—
373#478C23116yes—
374#478C23116yes—
375#478C23116yes—
376#477C2318yes—
377#476C2318yes—
378#475C2318yes—
379#474C2318yes—
380#470C23116yes—
381#469C23116yes—
382#468C23116yes—
383#468C23116yes—
384#467C23116yes—
385#466C23116yes—
386#465C23116yes—
387#465C23116yes—
388#464C23116yes—
389#463C23116yes—
390#462C2318yes—
391#462C23116yes—
392#461C2318yes—
393#461C23116yes—
394#460C2318yes—
395#460C23116yes—
396#459C2318yes—
397#459C23116yes—
398#452C23116yes—
399#452C23116yes—
400#452C23116yes—
401#451C2318yes—
402#450C2318yes—
403#449C23116yes—
404#449C23116yes—
405#449C23116yes—
406#448C2318yes—
407#447C2318yes—
408#442C23116yes—
409#441C23116yes—
410#440C23116yes—
411#440C23116yes—
412C4×Q16C23116yes—
413C4×SD16C23116yes—
414C4×SD16C23116yes—
415C4×D8C23116yes—
416#433C2318yes—
417#433C2318yes—
418#433C2318yes—
419#433C2318yes—
420#432C2314yes—
421#432C2314yes—
422#432C2318yes—
423#431C2314yes—
424#431C2314yes—
425#431C2318yes—
426#428C2318yes—
427#428C2318yes—
428#424C2318yes—
429#424C2318yes—
430#423C2314yes—
431#423C2314yes—
432#419C2318yes—
433#418C2318yes—
434#417C2318yes—
435#417C2318yes—
436#408C2318yes—
437#408C2318yes—
438#407C2314yes—
439#407C2314yes—
440C4×M16C2314yes—
441C4×M16C2314yes—
442C4×M16C2314yes—
443C4×M16C2314yes—
444C2×#97C2314yes—
445C2×C4×C8C2314yes—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—44no—
452C2×#41—48no—
453C2×#41—48no—
454C2×#41C2×D412yes—
455C2×#41C2×D412yes—
456C2×#41C2414yes—
457C2×#41C2418yes—
458C2×#41C2414yes—
459C2×#41C2412yes—
460C2×#41C2412yes—
461C22×Q8—22no—
462C22×Q8C2×D411yescharacteristic
463C22×Q8C2412yes—
464C22×Q8C2412yes—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4C2×D411yescharacteristic
472C22×D4C2×D411yescharacteristic
473C22×D4C2×D411yescharacteristic
474C22×D4C2412yes—
475C22×D4C2412yes—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4C2×D412yes—
482C23×C4C2×D412yes—
483C23×C4C2×D412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487#137—416no—
488AGL(1,ℤ/8)—416no—
489C2×Q16C24116yes—
490C2×SD16C24116yes—
491C2×SD16C24116yes—
492C2×D8C24116yes—
493C2×M16—48no—
494C2×M16C2418yes—
495C2×M16C2418yes—
496C22×C8C2418yes—
497C4⋊Q8—24no—
498C4⋊Q8—22no—
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8C2412yes—
503C4⋊Q8C2412yes—
504C4⋊Q8C2414yes—
505C4⋊Q8C2414yes—
506C4⋊Q8C2414yes—
507#127—24no—
508#127—22no—
509#127—22no—
510#127C2412yes—
511#127C2412yes—
512#127C2414yes—
513#126—28no—
514#126—28no—
515#126—28no—
516#126—28no—
517#126—28no—
518#126—28no—
519#126—28no—
520#126—28no—
521#126—28no—
522#126—24no—
523#126—24no—
524#126—28no—
525#126—24no—
526#126—24no—
527#126—28no—
528#126—28no—
529#125—28no—
530#125—28no—
531#125—28no—
532#125—28no—
533#125—28no—
534#125—28no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—22no—
539#125—28no—
540#125—28no—
541#125—24no—
542#125—24no—
543#125—24no—
544#125C2414yes—
545#125C2414yes—
546#125C2414yes—
547#125C2414yes—
548#125C2414yes—
549#125C2414yes—
550#124—24no—
551#124—24no—
552#124—28no—
553#124—28no—
554#124—22no—
555#124—22no—
556#124—24no—
557#124—24no—
558#124—24no—
559#124C2414yes—
560#124C2414yes—
561#124C2414yes—
562#124C2414yes—
563#123—24no—
564#123—24no—
565#123—24no—
566#123—24no—
567#123—24no—
568#123—24no—
569#123—28no—
570#123—28no—
571#123—28no—
572#123—28no—
573#123—24no—
574#123—24no—
575#123—28no—
576#123—28no—
577#123—28no—
578#123—28no—
579#123—28no—
580#123—28no—
581#123—28no—
582#123—28no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586C22⋊Q8—24no—
587C22⋊Q8—24no—
588C22⋊Q8—24no—
589C22⋊Q8—24no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—24no—
593C22⋊Q8—24no—
594C22⋊Q8—24no—
595C22⋊Q8—28no—
596C22⋊Q8—28no—
597C22⋊Q8C2414yes—
598C22⋊Q8C2414yes—
599C22⋊Q8C2418yes—
600C22⋊Q8C2418yes—
601C22⋊Q8C2418yes—
602#121—28no—
603#121—28no—
604#121—28no—
605#121—28no—
606#121—28no—
607#121—28no—
608#121—28no—
609#121—28no—
610#121—28no—
611#121—24no—
612#121—24no—
613#121—24no—
614#121—28no—
615#121—28no—
616#121—24no—
617#121—22no—
618#121—22no—
619#121—24no—
620#121—24no—
621#121—24no—
622#121—28no—
623#121—28no—
624#121—28no—
625#121—28no—
626#121—28no—
627#121—28no—
628#121C2414yes—
629#121C2414yes—
630#121C2418yes—
631#121C2418yes—
632#121C2418yes—
633#120—24no—
634#120—24no—
635#120—24no—
636#120—24no—
637C4×Q8—28no—
638C4×Q8—24no—
639C4×Q8—24no—
640C4×Q8—24no—
641C4×Q8—24no—
642C4×Q8—24no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8C2×D414yes—
648C4×Q8C2×D414yes—
649C4×Q8C2×D414yes—
650C4×Q8C2×D414yes—
651C4×Q8C2418yes—
652C4×Q8C2414yes—
653C4×Q8C2414yes—
654C4×Q8C2418yes—
655C4×Q8C2418yes—
656C4×D4—24no—
657C4×D4—24no—
658C4×D4—24no—
659C4×D4—24no—
660C4×D4—28no—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—28no—
664C4×D4—28no—
665C4×D4—28no—
666C4×D4—28no—
667C4×D4—28no—
668C4×D4—28no—
669C4×D4—28no—
670C4×D4—28no—
671C4×D4—28no—
672C4×D4—28no—
673C4×D4—28no—
674C4×D4—28no—
675C4×D4—24no—
676C4×D4—24no—
677C4×D4—24no—
678C4×D4—28no—
679C4×D4—24no—
680C4×D4—28no—
681C4×D4—24no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—24no—
685C4×D4—24no—
686C4×D4C2×D414yes—
687C4×D4C2×D414yes—
688C4×D4C2×D414yes—
689C4×D4C2×D414yes—
690C4×D4C2×D414yes—
691C4×D4C2×D414yes—
692C4×D4C2×D414yes—
693C4×D4C2×D414yes—
694C4×D4C2×D414yes—
695C4×D4C2×D414yes—
696C4×D4C2×D414yes—
697C4×D4C2×D414yes—
698C4×D4C2418yes—
699C4×D4C2414yes—
700C4×D4C2414yes—
701C4×D4C2418yes—
702C4×D4C2418yes—
703#117—22no—
704#117—22no—
705#117—24no—
706#117—24no—
707#117—28no—
708#117—28no—
709#117—28no—
710#117—28no—
711#117—24no—
712#117—24no—
713#117—28no—
714#117—24no—
715#117—24no—
716#117—28no—
717#117—24no—
718#117—24no—
719#117—28no—
720#117—28no—
721#117C2×D412yes—
722#117C2×D412yes—
723#117C2×D414yes—
724#117C2×D414yes—
725#117C2414yes—
726#117C2414yes—
727#117C2412yes—
728#117C2412yes—
729#117C2412yes—
730#117C2412yes—
731#117C2412yes—
732#117C2412yes—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—22no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—22no—
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—28no—
741C2×C4⋊C4—28no—
742C2×C4⋊C4—24no—
743C2×C4⋊C4—22no—
744C2×C4⋊C4—22no—
745C2×C4⋊C4—22no—
746C2×C4⋊C4—22no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—28no—
750C2×C4⋊C4—28no—
751C2×C4⋊C4—28no—
752C2×C4⋊C4C2×D412yes—
753C2×C4⋊C4C2×D412yes—
754C2×C4⋊C4C2×D412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—24no—
769C2×C22⋊C4—28no—
770C2×C22⋊C4C2×D412yes—
771C2×C22⋊C4C2×D412yes—
772C2×C22⋊C4C2×D412yes—
773C2×C42—22no—
774C2×C42—22no—
775C2×C42—22no—
776C2×C42—24no—
777C2×C42—24no—
778C2×C42C2×D412yes—
779C2×C42C2×D412yes—
780C2×C42C2×D412yes—
781C2×C42C2×D412yes—
782C2×C42C2×D412yes—
783C2×C42C2×D414yes—
784C2×C42C2×D414yes—
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2412yes—
790C2×C42C2411yescharacteristic
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797#107C24116yes—
798#107C24116yes—
799#106C24116yes—
800#106C24116yes—
801C4⋊C8C2418yes—
802C4⋊C8C24116yes—
803C4⋊C8C2418yes—
804#103C24116yes—
805#103C24116yes—
806#103C24116yes—
807#103C24116yes—
808#102C24116yes—
809#102C24116yes—
810#102C24116yes—
811#102C24116yes—
812C22⋊C8C2418yes—
813C22⋊C8C24116yes—
814C22⋊C8C2418yes—
815#97C2418yes—
816#97C2418yes—
817C4×C8C2418yes—
818C4×C8C2418yes—
819C24—22no—
820C24—22no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824#41—28no—
825#41—28no—
826#41—44no—
827#41—44no—
828#41—44no—
829#41—44no—
830#41—44no—
831#41—416no—
832#41—44no—
833#41—48no—
834#41—416no—
835#41—48no—
836#41—88no—
837#41—88no—
838C2×Q8—22no—
839C2×Q8—24no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8—28no—
843C2×Q8—42no—
844C2×Q8—44no—
845C2×Q8—84no—
846C2×Q8C22×D412yes—
847C2×Q8C22×D412yes—
848C2×Q8C2514yes—
849C2×Q8C2514yes—
850C2×D4—24no—
851C2×D4—28no—
852C2×D4—24no—
853C2×D4—28no—
854C2×D4—28no—
855C2×D4—24no—
856C2×D4—28no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—24no—
862C2×D4—28no—
863C2×D4—28no—
864C2×D4—44no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—48no—
869C2×D4—48no—
870C2×D4—84no—
871C2×D4—84no—
872C2×D4—84no—
873C2×D4—84no—
874C2×D4C22×D412yes—
875C2×D4C22×D412yes—
876C2×D4C22×D412yes—
877C2×D4C22×D412yes—
878C2×D4C22×D412yes—
879C2×D4C22×D412yes—
880C2×D4C2514yes—
881C2×D4C2514yes—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—24no—
890C22×C4—28no—
891C22×C4—24no—
892C22×C4—28no—
893C22×C4—24no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—82no—
902C22×C4—82no—
903C22×C4—82no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D412yes—
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D414yes—
920C22×C4C22×D412yes—
921C22×C4C22×D414yes—
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D414yes—
925C22×C4C22×D414yes—
926C22×C4C2512yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2512yes—
930C22×C4C2511yescharacteristic
931Q16—416no—
932SD16—416no—
933SD16—416no—
934D8—416no—
935M16—216no—
936M16—48no—
937C2×C8—48no—
938C2×C8C25116yes—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—28no—
961C4⋊C4—24no—
962C4⋊C4—28no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—28no—
966C4⋊C4C22×D414yes—
967C4⋊C4C22×D414yes—
968C4⋊C4C22×D414yes—
969C4⋊C4C22×D414yes—
970C4⋊C4C22×D414yes—
971C4⋊C4C22×D414yes—
972C4⋊C4C2514yes—
973C4⋊C4C2514yes—
974C4⋊C4C2518yes—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—28no—
979C22⋊C4—24no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—24no—
991C22⋊C4—28no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4C22×D414yes—
999C22⋊C4C22×D414yes—
1000C22⋊C4C22×D414yes—
1001C22⋊C4C22×D414yes—
1002C22⋊C4C22×D414yes—
1003C22⋊C4C22×D414yes—
1004C42—24no—
1005C42—28no—
1006C42—24no—
1007C42—24no—
1008C42—28no—
1009C42—28no—
1010C42—24no—
1011C42C22×D412yes—
1012C42C22×D412yes—
1013C42C22×D412yes—
1014C42C22×D414yes—
1015C42C22×D412yes—
1016C42C22×D414yes—
1017C42C22×D412yes—
1018C42C22×D414yes—
1019C42C22×D412yes—
1020C42C22×D412yes—
1021C42C22×D412yes—
1022C42C22×D414yes—
1023C42C2511yescharacteristic
1024C42C2512yes—
1025C42C2511yescharacteristic
1026C42C2511yescharacteristic
1027C42C2511yescharacteristic
1028C42C2512yes—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—24no—
1033C23—24no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—44no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—84no—
1042C23C23×D411yescharacteristic
1043C23C23×D412yes—
1044C23C23×D411yescharacteristic
1045C23C23×D412yes—
1046C23C23×D411yescharacteristic
1047Q8—24no—
1048Q8—28no—
1049Q8—24no—
1050Q8—42no—
1051Q8—42no—
1052Q8—44no—
1053Q8—48no—
1054Q8—44no—
1055Q8—84no—
1056D4—24no—
1057D4—28no—
1058D4—24no—
1059D4—42no—
1060D4—42no—
1061D4—42no—
1062D4—42no—
1063D4—42no—
1064D4—42no—
1065D4—44no—
1066D4—48no—
1067D4—416no—
1068D4—48no—
1069D4—48no—
1070D4—44no—
1071D4—88no—
1072D4—84no—
1073D4—84no—
1074D4—88no—
1075D4—84no—
1076D4—88no—
1077D4—88no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—28no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—44no—
1098C2×C4—42no—
1099C2×C4—44no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—416no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—48no—
1113C2×C4—88no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4—88no—
1117C2×C4—88no—
1118C2×C4—88no—
1119C2×C4—84no—
1120C2×C4C23×D411yescharacteristic
1121C2×C4C23×D414yes—
1122C2×C4C23×D412yes—
1123C2×C4C23×D412yes—
1124C2×C4C23×D414yes—
1125C2×C4C23×D412yes—
1126C2×C4C23×D412yes—
1127C2×C4C23×D412yes—
1128C2×C4C23×D411yescharacteristic
1129C2×C4C23×D412yes—
1130C2×C4C23×D411yescharacteristic
1131C2×C4#58514yes—
1132C2×C4C2611yescharacteristic
1133C8—216no—
1134C22—22no—
1135C22—24no—
1136C22—22no—
1137C22—24no—
1138C22—22no—
1139C22—21no—
1140C22—22no—
1141C22—21no—
1142C22—22no—
1143C22—44no—
1144C22—44no—
1145C22—48no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—82no—
1150C22—82no—
1151C22—88no—
1152C22—164no—
1153C22#344912yes—
1154C22C24×D411yescharacteristic
1155C4—22no—
1156C4—22no—
1157C4—24no—
1158C4—22no—
1159C4—24no—
1160C4—22no—
1161C4—22no—
1162C4—21no—
1163C4—21no—
1164C4—22no—
1165C4—44no—
1166C4—44no—
1167C4—48no—
1168C4—44no—
1169C4—44no—
1170C4#344912yes—
1171C4C2×#58512yes—
1172C2—22no—
1173C2—42no—
1174C2—41no—
1175C2—42no—
1176C2—41no—
1177C2—84no—
1178C2—84no—
1179C2C2×#344911yescharacteristic
1180C2#6309012yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62815C2semidirect
2. C2×#3512C2semidirect
3. #61021C2semidirect
4. #61020C2semidirect
5. #61019C2semidirect
6. #61010C2semidirect
7. #61009C2semidirect
8. #60921C2semidirect
9. #60920C2semidirect
10. #60866C2semidirect
11. #60861C2semidirect
12. #60805C2semidirect
13. #60802C2semidirect
14. #60755C2semidirect
15. #60702C2semidirect
16. #60569C2semidirect
17. #60568C2semidirect
18. #60565C2semidirect
19. #60123C2semidirect
24. #3512C22semidirect
25. #3512C22semidirect
26. #3512C22semidirect
27. #3511C22semidirect
28. #3510C22semidirect
29. #3509C22semidirect
30. #3508C22semidirect
44. C2×#541C22semidirect
46. C2×#540C22semidirect
53. C2×#532C22semidirect
55. C2×#529C22semidirect
56. C22×#125C22semidirect
58. C2×#520C22semidirect
60. #3261C22semidirect
61. #3260C22semidirect
62. #3260C22semidirect
63. #3259C22semidirect
64. #3258C22semidirect
65. #3257C22semidirect
66. #3240C22semidirect
67. #3239C22semidirect
68. #3238C22semidirect
69. #3236C22semidirect
70. #3234C22semidirect
71. #3233C22semidirect
72. #3232C22semidirect
73. #3232C22semidirect
74. #3219C22semidirect
75. #3218C22semidirect
76. #3217C22semidirect
77. #3216C22semidirect
78. #3214C22semidirect
79. #3212C22semidirect
80. #3212C22semidirect
81. #3211C22semidirect
82. #3204C22semidirect
83. #3203C22semidirect
84. #3201C22semidirect
85. #3198C22semidirect
86. #3183C22semidirect
87. #3181C22semidirect
88. #3180C22semidirect
89. #3172C22semidirect
90. #3171C22semidirect
91. #3168C22semidirect
92. #3166C22semidirect
95. #3140C22semidirect
96. #3127C22semidirect
97. #3126C22semidirect
98. #3125C22semidirect
99. #3124C22semidirect
100. #3123C22semidirect
101. #3122C22semidirect
102. #3120C22semidirect
103. #3120C22semidirect
104. #3119C22semidirect
105. #3119C22semidirect
108. #3092C22semidirect
109. #3080C22semidirect
110. #3080C22semidirect
111. #3078C22semidirect
112. #3077C22semidirect
113. #3056C22semidirect
114. #3055C22semidirect
115. #3039C22semidirect
116. #3038C22semidirect
121. #3005C22semidirect
122. C4×#137C22semidirect
123. C4×AGL(1,ℤ/8)C22semidirect
124. #2923C22semidirect
125. #2923C22semidirect
126. #2922C22semidirect
127. #2922C22semidirect
129. #2921C22semidirect
131. #2920C22semidirect
132. #2905C22semidirect
134. C2×C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#628152
C2×#35122
#610212
#610202
#610192
#610102
#610092
#609212
#609202
#608662
#608612
#608052
#608022
#607552
#607022
#605692
#605682
#605652
#601232