Finite Group Databasebeta

← #10576517

Subgroups — #10576517

Order 512.

6419 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62855C211yesmaximal, characteristic, complemented
2#62854C211yesmaximal, characteristic, complemented
3#61337C218yesmaximal, complemented
4#61336C218yesmaximal, complemented
5#61334C214yesmaximal, complemented
6#61332C214yesmaximal, complemented
7#61331C218yesmaximal, complemented
8#61329C218yesmaximal, complemented
9#61327C214yesmaximal, complemented
10#61325C214yesmaximal, complemented
11#60612C211yesmaximal, characteristic, complemented
12C2×#3136C212yesmaximal, complemented
13#60493C212yesmaximal, complemented
14#60490C211yesmaximal, characteristic, complemented
15#60426C212yesmaximal, complemented
16#60425C211yesmaximal, characteristic, complemented
17#60191C211yesmaximal, characteristic, complemented
18#60161C212yesmaximal, complemented
19C2×#2946C211yesmaximal, characteristic, complemented
20C2×#575C2212yes—
21C22×AGL(1,ℤ/8)C2211yescharacteristic
22#3510C2218yescomplemented
23#3508C2218yescomplemented
24#3506C2214yes—
25#3506C2214yes—
26#3504—24no—
27#3504C2218yescomplemented
28#3503—24no—
29#3503C2218yescomplemented
30#3502C2214yescomplemented
31#3501—24no—
32#3501C2214yescomplemented
33#3494—24no—
34#3494—24no—
35#3490—24no—
36#3460—22no—
37#3460—22no—
38#3458—22no—
39#3458C2211yescharacteristic
40#3458C2211yescharacteristic
41C2×#544—22no—
42C2×#544C2212yes—
43#3449C2211yescharacteristic
44C2×#535C2212yes—
45#3428C2212yes—
46#3428C2212yes—
47C2×#520C2211yescharacteristic
48C2×#518C2211yescharacteristic
49#3377C22116yescomplemented
50#3376C22116yescomplemented
51#3375C22116yescomplemented
52#3373C22116yescomplemented
53#3371C22116yescomplemented
54#3371C22116yescomplemented
55#3370C22116yescomplemented
56#3370C22116yescomplemented
57#3369C2218yescomplemented
58#3368C2218yescomplemented
59#3368C22116yescomplemented
60#3367C2218yescomplemented
61#3366C2218yescomplemented
62#3366C22116yescomplemented
63#3365C22116yescomplemented
64#3364C2218yescomplemented
65#3362C2218yescomplemented
66#3361C22116yescomplemented
67#3360C2218yescomplemented
68#3358C2218yescomplemented
69#3137C2214yescomplemented
70#3137C2214yescomplemented
71#3136C2218yescomplemented
72#3136C2218yescomplemented
73#3136C2218yescomplemented
74#3136C2218yescomplemented
75#3136C2214yescomplemented
76#3136C2214yescomplemented
77#3135C2214yescomplemented
78C2×#490C2214yescomplemented
79C2×#489C2214yescomplemented
80#3131C2214yescomplemented
81C2×#488C2214yescomplemented
82C2×#486C2214yescomplemented
83#3084C2218yescomplemented
84#3083C2218yescomplemented
85#3082C2218yescomplemented
86#3081C2218yescomplemented
87#3081C2218yescomplemented
88#3081C2218yescomplemented
89#3080C2218yescomplemented
90#3079C2218yescomplemented
91#3077C2214yescomplemented
92#3077C2214yescomplemented
93#3046C2218yescomplemented
94#3045C2218yes—
95#3045C2218yes—
96#3045C2218yescomplemented
97#3043C2218yescomplemented
98#3041C2218yescomplemented
99#3040C2218yescomplemented
100#3038C2218yescomplemented
101#3037C2214yescomplemented
102#3036C2214yescomplemented
103#2961C2214yescomplemented
104#2961C2218yescomplemented
105#2960C2214yescomplemented
106#2960C2218yescomplemented
107#2947C2214yescomplemented
108#2947C2214yescomplemented
109#2947C2214yescomplemented
110#2947C2214yescomplemented
111#2946C2218yescomplemented
112#2946C2218yescomplemented
113#2946C2214yescomplemented
114#2946C2214yescomplemented
115#2946C2214yescomplemented
116#2946C2214yescomplemented
117#2943C2218yescomplemented
118C2×#442C2212yescomplemented
119C2×#440C2212yescomplemented
120C4×#135C2218yescomplemented
121C2×C4×SD16C2212yescomplemented
122C2×C4×D8C2212yescomplemented
123#2911C2212yes—
124C2×#428C2211yescharacteristic
125#2905C2211yescharacteristic
126#2905C2212yes—
127#2896C2212yes—
128C2×#417C2212yes—
129C2×#418C2212yes—
130C2×#416C2211yescharacteristic
131C2×#416C2212yes—
132C22×#102C2211yescharacteristic
133C2×#405C2212yes—
134C2×#405C2211yescharacteristic
135C22×#41C2312yes—
136C22×#41C2311yescharacteristic
137C23×D4C2311yescharacteristic
138#575—216no—
139C2×#137C2314yes—
140C2×#137C2314yes—
141C2×AGL(1,ℤ/8)—28no—
142C2×AGL(1,ℤ/8)C2314yes—
143C2×AGL(1,ℤ/8)C2314yes—
144C2×AGL(1,ℤ/8)C2318yes—
145C2×#135C2318yes—
146C22×SD16C2312yes—
147C22×D8C2312yes—
148C22×M16C2312yes—
149C22×M16C2311yescharacteristic
150C23×C8C2311yescharacteristic
151#559C23116yes—
152#559C23116yes—
153Q82—24no—
154Q82C2318yescomplemented
155#557—24no—
156#557—28no—
157#557C2318yescomplemented
158#557C23116yescomplemented
159#556C2318yes—
160#556C2318yes—
161#555—24no—
162#555—24no—
163#554—24no—
164#554—28no—
165#554—216no—
166#554—216no—
167#554—216no—
168#554C2318yescomplemented
169#554C23116yescomplemented
170#553—28no—
171#553—28no—
172#551—216no—
173#551—216no—
174#550C2318yes—
175#550C2318yes—
176D4×Q8—24no—
177D4×Q8—216no—
178D4×Q8C2318yescomplemented
179#547—24no—
180#547—24no—
181#546—216no—
182#546—216no—
183#544—28no—
184#544—28no—
185#544—28no—
186#544—28no—
187#544—28no—
188#544—24no—
189#544—24no—
190#544—21no—
191#544—21no—
192#544D412yes—
193#544D412yes—
194#544D414yes—
195#544D414yes—
196#544C2314yes—
197#544C2314yes—
198#544C2318yes—
199#544C2318yes—
200#543—28no—
201#543—22no—
202#543D414yes—
203#542—28no—
204#542—28no—
205#540—28no—
206#540—28no—
207#538—28no—
208#538—28no—
209#537—21no—
210#537—21no—
211#536C2314yes—
212#535—24no—
213#535—24no—
214#535C2318yes—
215#535C2318yes—
216#535C2314yes—
217#534—22no—
218#533—28no—
219#533—28no—
220#533—28no—
221#533—24no—
222#533C2314yes—
223#533C2314yes—
224#533C2318yes—
225#532—28no—
226#532—28no—
227#532C2314yes—
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8—22no—
230C2×C4⋊Q8C2314yes—
231C2×#127C2314yes—
232#529—28no—
233#529—28no—
234C2×#125—28no—
235C2×#125—22no—
236C2×#125C2314yes—
237C2×#124C2314yes—
238#525—28no—
239#525—28no—
240#525—24no—
241C2×C22⋊Q8—28no—
242C2×C22⋊Q8—24no—
243C2×#121—22no—
244C2×#121—22no—
245C2×#120—24no—
246#520—24no—
247#520—22no—
248#520—22no—
249#520—22no—
250#520—22no—
251#520C2314yes—
252#520C2314yes—
253#520C2318yes—
254#520C2314yes—
255#520C2314yes—
256#519C2314yes—
257#519C2314yes—
258#518—24no—
259#518—24no—
260#518—24no—
261#518C2318yes—
262#518C2314yes—
263#518C2314yes—
264C4×#41—24no—
265C4×#41—24no—
266C4×#41C2318yes—
267C4×#41C2318yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4—21no—
270C2×C4×D4—21no—
271C2×C4×D4—22no—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×#117—24no—
276C2×#117—24no—
277C2×#117—21no—
278C2×#117C2312yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2312yes—
282C22×C4⋊C4—21no—
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4—22no—
285#491C2318yescomplemented
286#490C23116yes—
287#490C23116yes—
288#490C2318yescomplemented
289#489C23116yes—
290#489C23116yes—
291#489C2318yescomplemented
292#489C2318yescomplemented
293#488C23116yes—
294#488C23116yes—
295#488C2318yescomplemented
296#488C2318yescomplemented
297#487C2314yescomplemented
298#487C2314yescomplemented
299#486C23116yes—
300#486C23116yes—
301#486C2314yescomplemented
302#486C2314yescomplemented
303#479C23116yescomplemented
304#479C23116yescomplemented
305#478C23116yes—
306#478C23116yes—
307#478C23116yescomplemented
308#478C23116yescomplemented
309#477C23116yescomplemented
310#476C2318yes—
311#476C2318yes—
312#476C23116yescomplemented
313#475C23116yescomplemented
314#474C2318yes—
315#474C2318yes—
316#474C23116yescomplemented
317#464C23116yes—
318#464C23116yes—
319#464C23116yescomplemented
320#463C23116yes—
321#463C23116yes—
322#463C23116yescomplemented
323#462C2318yescomplemented
324#461C2318yescomplemented
325#460C23116yes—
326#460C23116yes—
327#460C2318yescomplemented
328#459C23116yes—
329#459C23116yes—
330#459C2318yescomplemented
331#446C2318yescomplemented
332#446C23116yescomplemented
333#446C2318yescomplemented
334#446C23116yescomplemented
335C8×Q8C2318yescomplemented
336C8×Q8C2318yescomplemented
337#442C23116yes—
338#442C2318yescomplemented
339#442C2318yescomplemented
340#441C2318yescomplemented
341#441C2318yescomplemented
342#440C23116yes—
343#440C2318yescomplemented
344#440C2318yescomplemented
345#440C2318yescomplemented
346#440C2318yescomplemented
347C4×Q16C2318yescomplemented
348C4×Q16C2318yescomplemented
349C4×SD16C2318yes—
350C4×SD16C2318yes—
351C4×SD16C2318yescomplemented
352C4×SD16C2318yescomplemented
353C4×SD16C2318yescomplemented
354C4×SD16C2318yescomplemented
355C4×D8C2318yes—
356C4×D8C2318yes—
357C4×D8C2318yescomplemented
358C4×D8C2318yescomplemented
359#428C2314yes—
360#428C2314yes—
361#428C2314yes—
362#428C2318yes—
363#428C2314yes—
364#427C2318yes—
365C2×#107C2312yes—
366C2×#106C2312yes—
367#424C2318yes—
368#424C2318yes—
369#424C2318yes—
370#423C2314yes—
371#423C2318yes—
372#419C2314yes—
373#418C2318yes—
374#418C2318yes—
375#418C2314yes—
376#417C2314yes—
377#417C2318yes—
378#417C2314yes—
379#417C2318yes—
380#416C2318yes—
381#416C2314yes—
382#416C2314yes—
383#416C2314yes—
384#416C2314yes—
385#416C2314yes—
386#416C2314yes—
387C2×#103C2314yes—
388C2×#103C2312yes—
389C2×#103C2312yes—
390C2×#103C2311yescharacteristic
391C2×#103C2311yescharacteristic
392C2×#102C2314yes—
393C2×#102C2314yes—
394C2×#102C2314yes—
395C2×#102C2312yes—
396C2×#102C2314yes—
397C2×#102C2314yes—
398C2×#102C2312yes—
399C2×#102C2312yes—
400C2×#102C2312yes—
401C2×#102C2311yescharacteristic
402C2×#102C2311yescharacteristic
403#405C2314yes—
404#405C2314yes—
405#405C2314yes—
406#405C2314yes—
407#405C2314yes—
408#405C2314yes—
409C2×#97C2314yes—
410C2×#97C2312yes—
411C2×C4×C8C2314yes—
412C2×C4×C8C2312yes—
413C25—21no—
414C2×#41—28no—
415C2×#41—28no—
416C2×#41—22no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—24no—
420C2×#41—28no—
421C2×#41—28no—
422C2×#41#4118yescomplemented
423C2×#41C2414yes—
424C2×#41C2414yes—
425C2×#41C2414yes—
426C22×Q8—28no—
427C22×Q8—24no—
428C22×Q8C2412yes—
429C22×Q8C2411yescharacteristic
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4—24no—
435C22×D4—24no—
436C22×D4—24no—
437C22×D4—24no—
438C22×D4C2412yes—
439C22×D4C2414yes—
440C22×D4C2412yes—
441C22×D4C2411yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4C2411yescharacteristic
449#137—216no—
450#137—216no—
451AGL(1,ℤ/8)—232no—
452AGL(1,ℤ/8)—216no—
453AGL(1,ℤ/8)—216no—
454#135—232no—
455C2×Q16C2418yes—
456C2×SD16—28no—
457C2×SD16C2418yes—
458C2×SD16C2418yes—
459C2×SD16C2418yes—
460C2×D8—28no—
461C2×D8C2418yes—
462C2×D8C2418yes—
463C2×M16—24no—
464C2×M16—28no—
465C2×M16C2414yes—
466C2×M16C2414yes—
467C2×M16C2414yes—
468C22×C8—24no—
469C22×C8C2412yes—
470C22×C8C2411yescharacteristic
471C22×C8C2412yes—
472C22×C8C2411yescharacteristic
473C22×C8C2412yes—
474C22×C8C2414yes—
475C4⋊Q8—216no—
476C4⋊Q8—28no—
477C4⋊Q8—28no—
478C4⋊Q8—24no—
479C4⋊Q8—216no—
480C4⋊Q8—28no—
481C4⋊Q8—24no—
482C4⋊Q8—28no—
483C4⋊Q8—28no—
484C4⋊Q8C2×D418yes—
485C4⋊Q8C2×D418yes—
486C4⋊Q8C2×D414yes—
487C4⋊Q8C2×D414yes—
488C4⋊Q8C2414yes—
489C4⋊Q8C24116yes—
490C4⋊Q8C2414yes—
491C4⋊Q8C2414yes—
492#127—28no—
493#127C24116yes—
494#127C2414yes—
495#126—216no—
496#126—216no—
497#125—28no—
498#125—24no—
499#125—216no—
500#125—216no—
501#125—28no—
502#125—24no—
503#125—216no—
504#125—28no—
505#125C2×D418yes—
506#125C2×D418yes—
507#125C2×D418yes—
508#125C24116yes—
509#125C2418yes—
510#124—216no—
511#124—216no—
512#124—28no—
513#124C24116yes—
514#124C2418yes—
515#123—216no—
516#123—216no—
517#123—216no—
518#123—216no—
519#123—28no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—216no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—216no—
527C22⋊Q8—28no—
528C22⋊Q8—24no—
529C22⋊Q8—24no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—216no—
535C22⋊Q8—28no—
536C22⋊Q8—28no—
537C22⋊Q8C2×D418yes—
538C22⋊Q8C2×D418yes—
539C22⋊Q8C2×D4116yes—
540C22⋊Q8C2×D4116yes—
541#121—24no—
542#121—24no—
543#121—28no—
544#121—28no—
545#121—28no—
546#121—28no—
547#121—24no—
548#121—24no—
549#121—28no—
550#121—28no—
551#121—216no—
552#121—216no—
553#120—216no—
554#120—216no—
555#120—28no—
556C4×Q8—28no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—216no—
562C4×Q8—28no—
563C4×Q8—24no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8C2418yes—
567C4×Q8C2418yes—
568C4×Q8C2418yes—
569C4×Q8C2418yes—
570C4×Q8C2418yes—
571C4×Q8C2418yes—
572C4×Q8C2418yes—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—216no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4C2418yes—
596C4×D4C2418yes—
597C4×D4C2418yes—
598C4×D4C2418yes—
599C4×D4C2418yes—
600C4×D4C2418yes—
601C4×D4C2418yes—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—28no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—28no—
611#117—28no—
612#117—28no—
613#117—28no—
614#117—28no—
615#117—28no—
616#117C2×D414yes—
617#117C2×D414yes—
618#117C2×D414yes—
619#117C2414yes—
620#117C2414yes—
621#117C2414yes—
622#117C2414yes—
623#117C2414yes—
624#117C2414yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—28no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—28no—
637C2×C4⋊C4—216no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D412yes—
641C2×C4⋊C4C2×D412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—216no—
656C2×C22⋊C4—28no—
657C2×C22⋊C4—28no—
658C2×C22⋊C4C2×D412yes—
659C2×C22⋊C4C2×D414yes—
660C2×C42—22no—
661C2×C42—21no—
662C2×C42—22no—
663C2×C42—28no—
664C2×C42—28no—
665C2×C42C2412yes—
666C2×C42C2414yes—
667#107C2418yes—
668#107C2418yes—
669#107C2418yes—
670#106C2418yes—
671#106C2418yes—
672#106C2418yes—
673C4⋊C8C24116yes—
674C4⋊C8C24116yes—
675C4⋊C8C2418yes—
676C4⋊C8C2418yes—
677#103C2412yes—
678#103C2412yes—
679#103C2414yes—
680#103C2414yes—
681#103C2414yes—
682#103C2414yes—
683#103C2414yes—
684#103C24116yes—
685#103C2418yes—
686#103C2418yes—
687#102C2414yes—
688#102C2414yes—
689#102C2418yes—
690#102C2412yes—
691#102C2412yes—
692#102C2414yes—
693#102C2414yes—
694#102C2414yes—
695#102C2414yes—
696#102C2414yes—
697#102C24116yes—
698#102C24116yes—
699#102C24116yes—
700#102C2418yes—
701#102C2418yes—
702#97C2418yes—
703#97C2418yes—
704#97C2418yes—
705C4×C8C2414yes—
706C4×C8C2414yes—
707C4×C8C2418yes—
708C4×C8C2418yes—
709C24—21no—
710C24—24no—
711C24—22no—
712C24—22no—
713C24—44no—
714C24—161no—
715C24—161no—
716C24C22×D411yescharacteristic
717#41—216no—
718#41—28no—
719#41—28no—
720#41—28no—
721#41—28no—
722#41—28no—
723#41—48no—
724#41—48no—
725#41—168no—
726#41—168no—
727#41C2×#41116yes—
728C2×Q8—21no—
729C2×Q8—22no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—216no—
733C2×Q8—22no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—164no—
737C2×Q8—168no—
738C2×Q8C22×D418yes—
739C2×Q8C22×D418yes—
740C2×Q8C2×#4114yes—
741C2×Q8C2514yes—
742C2×Q8C2512yes—
743C2×D4—28no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—21no—
748C2×D4—22no—
749C2×D4—24no—
750C2×D4—22no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—216no—
754C2×D4—216no—
755C2×D4—24no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—24no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—48no—
765C2×D4—164no—
766C2×D4—164no—
767C2×D4C2×#4114yes—
768C2×D4C2514yes—
769C2×D4C2514yes—
770C2×D4C2512yes—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—48no—
791C22×C4—162no—
792C22×C4—162no—
793C22×C4—162no—
794C22×C4—161no—
795C22×C4C22×D412yes—
796C22×C4C22×D414yes—
797C22×C4C22×D414yes—
798C22×C4C22×D412yes—
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D412yes—
801C22×C4C2×#4114yes—
802C22×C42−1+414yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805Q16—216no—
806SD16—216no—
807SD16—216no—
808SD16—216no—
809D8—216no—
810D8—216no—
811M16—28no—
812M16—28no—
813M16—28no—
814C2×C8—24no—
815C2×C8—28no—
816C2×C8—24no—
817C2×C8—22no—
818C2×C8—24no—
819C2×C8—22no—
820C2×C8C2511yescharacteristic
821C2×C8C2511yescharacteristic
822C2×C8C2512yes—
823C2×C8C2518yes—
824C2×C8C2514yes—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—216no—
834C4⋊C4—216no—
835C4⋊C4—28no—
836C4⋊C4—216no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4C22×D414yes—
846C4⋊C4C22×D414yes—
847C4⋊C4C22×D414yes—
848C4⋊C4C22×D414yes—
849C4⋊C4C22×D414yes—
850C4⋊C4C22×D418yes—
851C4⋊C4C22×D4116yes—
852C4⋊C4C22×D414yes—
853C4⋊C4C22×D418yes—
854C4⋊C4C22×D4116yes—
855C4⋊C4C2514yes—
856C4⋊C4C2514yes—
857C4⋊C4C2514yes—
858C4⋊C4C2512yes—
859C4⋊C4C2512yes—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—216no—
871C22⋊C4—216no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4C22×D418yes—
875C22⋊C4C22×D418yes—
876C22⋊C4C22×D418yes—
877C42—24no—
878C42—24no—
879C42—28no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—28no—
884C42—24no—
885C42C22×D418yes—
886C42C22×D414yes—
887C42C2514yes—
888C42C2518yes—
889C23—22no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—41no—
894C23—41no—
895C23—44no—
896C23—44no—
897C23—48no—
898C23—81no—
899C23—82no—
900C23—82no—
901C23—81no—
902C23—82no—
903C23—82no—
904C23—84no—
905C23—84no—
906C23—168no—
907C23#54814yes—
908C23C23×D411yescharacteristic
909C23C23×D412yes—
910Q8—22no—
911Q8—24no—
912Q8—24no—
913Q8—24no—
914Q8—48no—
915Q8—48no—
916Q8—44no—
917Q8—84no—
918Q8—84no—
919Q8—816no—
920Q8C22×#4114yes—
921D4—216no—
922D4—24no—
923D4—24no—
924D4—22no—
925D4—24no—
926D4—24no—
927D4—24no—
928D4—48no—
929D4—48no—
930D4—48no—
931D4—44no—
932D4—44no—
933D4—816no—
934D4—816no—
935D4—84no—
936D4—84no—
937D4C22×#4114yes—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—216no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4—88no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4—88no—
960C2×C4—88no—
961C2×C4—82no—
962C2×C4—81no—
963C2×C4—82no—
964C2×C4—81no—
965C2×C4—84no—
966C2×C4—82no—
967C2×C4#54814yes—
968C2×C4#54818yes—
969C2×C4C23×D414yes—
970C2×C4C23×D418yes—
971C2×C4C23×D418yes—
972C2×C4C23×D414yes—
973C2×C4C23×D412yes—
974C2×C4C23×D411yescharacteristic
975C2×C4C22×#4114yes—
976C2×C4C22×#4112yes—
977C2×C4C2×2−1+414yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2611yescharacteristic
980C8—24no—
981C8—28no—
982C8—21no—
983C8—21no—
984C8—22no—
985C22—21no—
986C22—22no—
987C22—21no—
988C22—22no—
989C22—24no—
990C22—44no—
991C22—42no—
992C22—42no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—84no—
1000C22—88no—
1001C22—164no—
1002C22—168no—
1003C22C2×#54812yes—
1004C22C2×#54814yes—
1005C22C24×D411yescharacteristic
1006C4—24no—
1007C4—28no—
1008C4—28no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—44no—
1017C4C2×#54814yes—
1018C4C2×#54812yes—
1019C4C23×#4111yescharacteristic
1020C4C22×2−1+411yescharacteristic
1021C2—22no—
1022C2—24no—
1023C2—44no—
1024C2—84no—
1025C2—84no—
1026C2C22×#54811yescharacteristic
1027C2#6309111yescharacteristic
1028C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3458 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62855C2semidirect
2. #62854C2semidirect
3. #61337C2semidirect
4. #61336C2semidirect
5. #61334C2semidirect
6. #61332C2semidirect
7. #61331C2semidirect
8. #61329C2semidirect
9. #61327C2semidirect
10. #61325C2semidirect
11. #60612C2semidirect
12. C2×#3136C2semidirect
13. #60493C2semidirect
14. #60490C2semidirect
15. #60426C2semidirect
16. #60425C2semidirect
17. #60191C2semidirect
18. #60161C2semidirect
19. C2×#2946C2semidirect
22. #3510C22semidirect
23. #3508C22semidirect
27. #3504C22semidirect
29. #3503C22semidirect
30. #3502C22semidirect
32. #3501C22semidirect
49. #3377C22semidirect
50. #3376C22semidirect
51. #3375C22semidirect
52. #3373C22semidirect
53. #3371C22semidirect
54. #3371C22semidirect
55. #3370C22semidirect
56. #3370C22semidirect
57. #3369C22semidirect
58. #3368C22semidirect
59. #3368C22semidirect
60. #3367C22semidirect
61. #3366C22semidirect
62. #3366C22semidirect
63. #3365C22semidirect
64. #3364C22semidirect
65. #3362C22semidirect
66. #3361C22semidirect
67. #3360C22semidirect
68. #3358C22semidirect
69. #3137C22semidirect
70. #3137C22semidirect
71. #3136C22semidirect
72. #3136C22semidirect
73. #3136C22semidirect
74. #3136C22semidirect
75. #3136C22semidirect
76. #3136C22semidirect
77. #3135C22semidirect
78. C2×#490C22semidirect
79. C2×#489C22semidirect
80. #3131C22semidirect
81. C2×#488C22semidirect
82. C2×#486C22semidirect
83. #3084C22semidirect
84. #3083C22semidirect
85. #3082C22semidirect
86. #3081C22semidirect
87. #3081C22semidirect
88. #3081C22semidirect
89. #3080C22semidirect
90. #3079C22semidirect
91. #3077C22semidirect
92. #3077C22semidirect
93. #3046C22semidirect
96. #3045C22semidirect
97. #3043C22semidirect
98. #3041C22semidirect
99. #3040C22semidirect
100. #3038C22semidirect
101. #3037C22semidirect
102. #3036C22semidirect
103. #2961C22semidirect
104. #2961C22semidirect
105. #2960C22semidirect
106. #2960C22semidirect
107. #2947C22semidirect
108. #2947C22semidirect
109. #2947C22semidirect
110. #2947C22semidirect
111. #2946C22semidirect
112. #2946C22semidirect
113. #2946C22semidirect
114. #2946C22semidirect
115. #2946C22semidirect
116. #2946C22semidirect
117. #2943C22semidirect
118. C2×#442C22semidirect
119. C2×#440C22semidirect
120. C4×#135C22semidirect
121. C2×C4×SD16C22semidirect
122. C2×C4×D8C22semidirect
154. Q82C23semidirect
157. #557C23semidirect
158. #557C23semidirect
168. #554C23semidirect
169. #554C23semidirect
178. D4×Q8C23semidirect
285. #491C23semidirect
288. #490C23semidirect
291. #489C23semidirect
292. #489C23semidirect
295. #488C23semidirect
296. #488C23semidirect
297. #487C23semidirect
298. #487C23semidirect
301. #486C23semidirect
302. #486C23semidirect
303. #479C23semidirect
304. #479C23semidirect
307. #478C23semidirect
308. #478C23semidirect
309. #477C23semidirect
312. #476C23semidirect
313. #475C23semidirect
316. #474C23semidirect
319. #464C23semidirect
322. #463C23semidirect
323. #462C23semidirect
324. #461C23semidirect
327. #460C23semidirect
330. #459C23semidirect
331. #446C23semidirect
332. #446C23semidirect
333. #446C23semidirect
334. #446C23semidirect
335. C8×Q8C23semidirect
336. C8×Q8C23semidirect
338. #442C23semidirect
339. #442C23semidirect
340. #441C23semidirect
341. #441C23semidirect
343. #440C23semidirect
344. #440C23semidirect
345. #440C23semidirect
346. #440C23semidirect
347. C4×Q16C23semidirect
348. C4×Q16C23semidirect
351. C4×SD16C23semidirect
352. C4×SD16C23semidirect
353. C4×SD16C23semidirect
354. C4×SD16C23semidirect
357. C4×D8C23semidirect
358. C4×D8C23semidirect
422. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
#628552
#628542
#613372
#613362
#613342
#613322
#613312
#613292
#613272
#613252
#606122
C2×#31362
#604932
#604902
#604262
#604252
#601912
#601612
C2×#29462