Finite Group Databasebeta

← #10581812

Subgroups — #10581812

Order 512.

6293 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62813C211yesmaximal, characteristic, complemented
2#62800C211yesmaximal, characteristic
3#62594C212yesmaximal, complemented
4#62582C216yesmaximal, complemented
5#62454C212yesmaximal, complemented
6#62448C216yesmaximal, complemented
7#61966C216yesmaximal, complemented
8#61965C216yesmaximal, complemented
9#61952C212yesmaximal, complemented
10#61951C212yesmaximal, complemented
11#61909C214yesmaximal, complemented
12#61607C2112yesmaximal, complemented
13#60963C213yesmaximal, complemented
14#60952C213yesmaximal, complemented
15#60804C213yesmaximal, complemented
16C2×#3216C213yesmaximal, complemented
17#60283C211yesmaximal, characteristic, complemented
18#3522—21no—
19#3519—23no—
20#3517C2212yes—
21#3514C2216yes—
22#3511C2213yes—
23#3508C2213yes—
24#3504—23no—
25#3504—21no—
26#3503C2211yescharacteristic
27#3503C2213yescomplemented
28#3503C2211yescharacteristic, complemented
29#3503C2213yescomplemented
30#3503C2211yescharacteristic, complemented
31#3502—21no—
32#3502C2212yescomplemented
33#3501—23no—
34#3501C2216yescomplemented
35#3498C2211yescharacteristic
36#3494—23no—
37#3488—21no—
38#3483—21no—
39#3481—23no—
40#3480C2212yes—
41Q8×#41—21no—
42Q8×#41—23no—
43Q8×#41C2212yes—
44Q8×#41C2216yescomplemented
45D4×#41C2216yes—
46#3460—23no—
47#3458—23no—
48#3444C2213yes—
49C2×#533C2213yescomplemented
50C2×#533C2213yescomplemented
51C2×#532C2213yes—
52C4×H(5,𝔽2)—21no—
53#3428—21no—
54C2×C4×#41C2211yescharacteristic
55#3400C22112yescomplemented
56#3398C22112yescomplemented
57#3395C2214yescomplemented
58#3392C2214yescomplemented
59#3375C22112yescomplemented
60#3369C22112yescomplemented
61#3363C2214yescomplemented
62#3362C2214yescomplemented
63#3333C22112yescomplemented
64#3331C22112yescomplemented
65#3316C22124yescomplemented
66#3314C22124yescomplemented
67#3299C22112yescomplemented
68#3295C22112yescomplemented
69D4×Q16C22112yescomplemented
70D4×SD16C22112yescomplemented
71#3278C22112yescomplemented
72#3276C22112yescomplemented
73#3270C22124yescomplemented
74#3266C22124yescomplemented
75#3255C2216yescomplemented
76#3254C2216yescomplemented
77#3249C2216yescomplemented
78#3246C2216yescomplemented
79#3239C2216yescomplemented
80#3238C2216yescomplemented
81#3237C2211yescharacteristic, complemented
82#3237C2213yescomplemented
83#3218C2216yescomplemented
84#3218C2216yescomplemented
85#3216C22112yescomplemented
86#3216C2213yescomplemented
87#3216C2213yescomplemented
88#3216C2216yescomplemented
89#3216C2216yescomplemented
90#3216C2216yescomplemented
91#3216C22112yescomplemented
92#3215C22112yescomplemented
93#3210C22112yescomplemented
94#3209C2216yescomplemented
95#3208C2216yescomplemented
96#3196C22112yescomplemented
97#3190C22112yescomplemented
98#3181C22112yescomplemented
99#3172C2216yescomplemented
100#3172C2216yescomplemented
101#3152C2216yescomplemented
102C2×#497C2216yescomplemented
103#3141C2216yescomplemented
104C2×#489C2216yescomplemented
105#3116C22112yescomplemented
106#3113C2216yescomplemented
107#3112C2216yescomplemented
108#3107C22112yescomplemented
109#3104C2216yescomplemented
110#3103C2216yescomplemented
111#3037C22112yescomplemented
112C2×#462C2216yescomplemented
113C2×#460C2216yescomplemented
114#3007C22112yescomplemented
115C2×#452C22112yescomplemented
116#2989C2216yescomplemented
117#2988C2212yes—
118#2984C2212yescomplemented
119#2974C2216yescomplemented
120#2971C2212yescomplemented
121#2970C2216yescomplemented
122#2920C2213yescomplemented
123C2×#432C2213yescomplemented
124C2×H(5,𝔽2)—21no—
125C22×#41D411yescharacteristic
126C22×#41C2316yes—
127C2×#137C23124yes—
128C22×Q16C23112yes—
129C22×SD16C23112yes—
130#559—23no—
131#559C2316yes—
132Q82—21no—
133Q82—23no—
134Q82—21no—
135Q82C2312yes—
136Q82C2316yes—
137#557—21no—
138#557—23no—
139#557—22no—
140#557—26no—
141#557—22no—
142#557—26no—
143#557C2312yes—
144#557C2312yes—
145#557C2316yes—
146#556C2316yes—
147#555—23no—
148#555—26no—
149#554—23no—
150#554—23no—
151#554—26no—
152#554—23no—
153#554—26no—
154#554—212no—
155#554—26no—
156#554—26no—
157#554—212no—
158#554—26no—
159#554—23no—
160#554C2316yes—
161#554C2316yes—
162#554C23112yes—
163#553—26no—
164#553—26no—
165#553—26no—
166#551—212no—
167#550—22no—
168#550—21no—
169#550—23no—
170#550C2316yes—
171#550C2312yes—
172D4×Q8—23no—
173D4×Q8—26no—
174D4×Q8—23no—
175D4×Q8C2316yes—
176D4×Q8C2316yes—
177D4×Q8C23112yes—
178D4×Q8C2316yes—
179#548—22no—
180#548C23112yes—
181#547—26no—
182#547C2316yes—
183#546—26no—
184#546—26no—
185#546—212no—
186#546C23112yes—
187D42—26no—
188D42—23no—
189D42C2316yes—
190#544—26no—
191#544—26no—
192#544—23no—
193#544—23no—
194#544—23no—
195#544—23no—
196#544—23no—
197#544—26no—
198#544—26no—
199#543—212no—
200#542—26no—
201#542—26no—
202#540—26no—
203#540—26no—
204#538—212no—
205#537—23no—
206#535—23no—
207#535—23no—
208#533—26no—
209#533—26no—
210#533—212no—
211#533—23no—
212#533—23no—
213#533—23no—
214#533—23no—
215#533—23no—
216#533—23no—
217#533—23no—
218#533—23no—
219#533C2313yes—
220#533C2316yes—
221#533C2313yes—
222#533C2316yes—
223#533C2313yes—
224#533C2313yes—
225#533C2316yes—
226#533C2311yescharacteristic
227#533C2313yes—
228#533C2316yes—
229#533C2316yes—
230#533C2311yescharacteristic
231#532—26no—
232#532—23no—
233#532—23no—
234#532—23no—
235#532—23no—
236#532C2316yes—
237#532C2313yes—
238#532C2316yes—
239#532C2316yes—
240#532C2313yes—
241#532C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#127C2313yes—
248#529—26no—
249#529—23no—
250#529—23no—
251#529—23no—
252#529—23no—
253#529C2316yes—
254#529C2316yes—
255C2×#125—23no—
256C2×#125—23no—
257C2×#124C2316yes—
258#525—23no—
259#525—23no—
260#525—212no—
261#525C2316yes—
262C2×C22⋊Q8—23no—
263C2×C22⋊Q8—23no—
264C2×C22⋊Q8C2316yes—
265C2×C22⋊Q8C2316yes—
266C2×#121—23no—
267C2×#121—23no—
268#520—23no—
269#520—21no—
270#520—23no—
271#520—21no—
272#520—21no—
273#520—22no—
274#520—23no—
275#519—22no—
276#518—26no—
277#518—26no—
278#518—23no—
279C4×#41—22no—
280C4×#41—26no—
281C4×#41—22no—
282C4×#41—23no—
283C4×#41—23no—
284C4×#41D411yescharacteristic
285C4×#41D413yes—
286C4×#41D413yes—
287C4×#41D411yescharacteristic
288C4×#41C2316yes—
289C4×#41C2311yescharacteristic
290C4×#41C2313yes—
291C4×#41C2313yes—
292C4×#41C2311yescharacteristic
293C2×C4×Q8—23no—
294C2×C4×Q8—23no—
295C2×C4×Q8D411yescharacteristic
296C2×C4×Q8C2316yes—
297C2×C4×Q8C2316yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4—26no—
300C2×C4×D4—23no—
301C2×C4×D4—23no—
302C2×C4×D4D413yes—
303C2×C4×D4C2313yes—
304C2×#117—23no—
305C2×#117—23no—
306C2×#117D413yes—
307C22×C42C2313yes—
308#501C2312yes—
309#501C2316yes—
310#497C23124yes—
311#497C2316yes—
312#497C23112yes—
313#497C2316yes—
314#494C23112yes—
315#492C23112yes—
316#491C2312yes—
317#491C2316yes—
318#489C23124yes—
319#489C2316yes—
320#489C23112yes—
321#489C2316yes—
322#487C23112yes—
323#486C23112yes—
324#485C2314yes—
325#485C23112yes—
326#484C23112yes—
327#483C23112yes—
328#481C23112yes—
329#480C23112yes—
330#477C23112yes—
331#477C2312yes—
332#477C2316yes—
333#476C23112yes—
334#475C2312yes—
335#475C2316yes—
336#475C23112yes—
337#474C23112yes—
338#470C23112yes—
339#470C23112yes—
340#468C23112yes—
341#468C23112yes—
342#467C23124yes—
343#465C23124yes—
344#464C23124yes—
345#464C23124yes—
346#462C23112yes—
347#462C2316yes—
348#462C2316yes—
349#462C23112yes—
350#462C23112yes—
351#462C23112yes—
352#462C23112yes—
353#461C23112yes—
354#461C23112yes—
355#460C23112yes—
356#460C2316yes—
357#460C2316yes—
358#460C23112yes—
359#460C23112yes—
360#452C23124yes—
361#452C23112yes—
362#452C23112yes—
363#452C23124yes—
364#452C23124yes—
365#451C23112yes—
366#451C23112yes—
367#451C23124yes—
368#450C23124yes—
369#448C23112yes—
370#448C23112yes—
371#446C23112yes—
372C8×Q8C2314yes—
373#441C23124yes—
374#440C23124yes—
375C4×Q16C23112yes—
376C4×Q16C23112yes—
377C4×SD16C23112yes—
378C4×SD16C23112yes—
379#436C23112yes—
380#435C23124yes—
381C8×D4C23112yes—
382#432C2316yes—
383#432C2316yes—
384#432C2313yes—
385#432C2316yes—
386#432C2311yescharacteristic
387#432C2316yes—
388#431C2316yes—
389#431C2316yes—
390#423C2316yes—
391C2×C4⋊C8C2316yes—
392#417C23124yes—
393C2×#103C23112yes—
394C2×#102C23112yes—
395#407C2316yes—
396C2×C22⋊C8C2316yes—
397C4×M16C2316yes—
398C2×#97C2316yes—
399H(5,𝔽2)—48no—
400C2×#41—28no—
401C2×#41—22no—
402C2×#41—23no—
403C2×#41—23no—
404C2×#41—26no—
405C2×#41—26no—
406C2×#41—812no—
407C2×#41C2×D413yes—
408C2×#41C2×D413yes—
409C2×#41C2×D411yescharacteristic
410C2×#41C2×D411yescharacteristic
411C2×#41C2416yes—
412C2×#41C24112yes—
413C22×Q8—23no—
414C22×Q8—23no—
415C22×Q8C2×D411yescharacteristic
416C22×Q8C2416yes—
417C22×Q8C2416yes—
418C22×Q8C2416yes—
419C22×D4—26no—
420C22×D4—26no—
421C22×D4—23no—
422C22×D4—23no—
423C22×D4C2×D413yes—
424C22×D4C2416yes—
425C23×C4—26no—
426C23×C4C2×D413yes—
427C23×C4C2×D413yes—
428C23×C4C2413yes—
429#137—824no—
430C2×Q16—812no—
431C2×Q16C24112yes—
432C2×Q16C24124yes—
433C2×Q16C24112yes—
434C2×SD16—812no—
435C2×SD16C24112yes—
436C2×SD16C24124yes—
437C2×SD16C24112yes—
438C2×M16C24112yes—
439C22×C8C24112yes—
440C4⋊Q8—26no—
441C4⋊Q8—26no—
442C4⋊Q8—26no—
443C4⋊Q8—212no—
444C4⋊Q8—26no—
445C4⋊Q8—26no—
446C4⋊Q8—212no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8—23no—
450C4⋊Q8—23no—
451C4⋊Q8—23no—
452C4⋊Q8—23no—
453C4⋊Q8—23no—
454C4⋊Q8—23no—
455C4⋊Q8—23no—
456C4⋊Q8—23no—
457C4⋊Q8C2411yescharacteristic
458C4⋊Q8C2413yes—
459C4⋊Q8C2413yes—
460C4⋊Q8C2416yes—
461C4⋊Q8C2416yes—
462C4⋊Q8C2416yes—
463C4⋊Q8C2411yescharacteristic
464C4⋊Q8C2413yes—
465C4⋊Q8C2416yes—
466C4⋊Q8C2416yes—
467C4⋊Q8C2411yescharacteristic
468C4⋊Q8C2411yescharacteristic
469#127—26no—
470#127—23no—
471#127—23no—
472#127C2413yes—
473#127C2416yes—
474#126—212no—
475#126—26no—
476#126—26no—
477#125—26no—
478#125—26no—
479#125—26no—
480#125—212no—
481#125—26no—
482#125—26no—
483#125—212no—
484#125—21no—
485#125—23no—
486#125—26no—
487#125—23no—
488#125—23no—
489#125—26no—
490#125—26no—
491#125—26no—
492#125—26no—
493#125—23no—
494#125—23no—
495#125C2412yes—
496#124—26no—
497#124—212no—
498#124—26no—
499#124—26no—
500#124—23no—
501#124—23no—
502#124C2416yes—
503#124C24112yes—
504#123—26no—
505#123—26no—
506#123—26no—
507#123—212no—
508#123—212no—
509#123—212no—
510C22⋊Q8—26no—
511C22⋊Q8—21no—
512C22⋊Q8—23no—
513C22⋊Q8—26no—
514C22⋊Q8—26no—
515C22⋊Q8—26no—
516C22⋊Q8—23no—
517C22⋊Q8—23no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—26no—
523C22⋊Q8—26no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—23no—
527C22⋊Q8—23no—
528C22⋊Q8—212no—
529C22⋊Q8—212no—
530C22⋊Q8—212no—
531C22⋊Q8—212no—
532C22⋊Q8—212no—
533C22⋊Q8—212no—
534C22⋊Q8—212no—
535C22⋊Q8—212no—
536C22⋊Q8—212no—
537C22⋊Q8—212no—
538C22⋊Q8C2416yes—
539C22⋊Q8C2412yes—
540C22⋊Q8C24112yes—
541C22⋊Q8C2416yes—
542C22⋊Q8C2416yes—
543C22⋊Q8C2416yes—
544C22⋊Q8C2416yes—
545#121—212no—
546#121—26no—
547#121—23no—
548#121—23no—
549#121—26no—
550#121—26no—
551#121—26no—
552#121—26no—
553#121—26no—
554#121—26no—
555#121—23no—
556#121—23no—
557#121—26no—
558#121—26no—
559#121—212no—
560#121—212no—
561#121C2416yes—
562#121C2416yes—
563#120—26no—
564#120—212no—
565#120—212no—
566C4×Q8—26no—
567C4×Q8—22no—
568C4×Q8—26no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—21no—
572C4×Q8—23no—
573C4×Q8—26no—
574C4×Q8—26no—
575C4×Q8—23no—
576C4×Q8—23no—
577C4×Q8—26no—
578C4×Q8—26no—
579C4×Q8—26no—
580C4×Q8—26no—
581C4×Q8—26no—
582C4×Q8—26no—
583C4×Q8—26no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8—23no—
587C4×Q8—23no—
588C4×Q8C2×D411yescharacteristic
589C4×Q8C2×D413yes—
590C4×Q8C2×D411yescharacteristic
591C4×Q8C2×D413yes—
592C4×Q8C2×D411yescharacteristic
593C4×Q8C2×D413yes—
594C4×Q8C2412yes—
595C4×Q8C2416yes—
596C4×Q8C2416yes—
597C4×Q8C2416yes—
598C4×Q8C24112yes—
599C4×Q8C2416yes—
600C4×Q8C2416yes—
601C4×Q8C2411yescharacteristic
602C4×Q8C2413yes—
603C4×D4—26no—
604C4×D4—212no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—212no—
608C4×D4—26no—
609C4×D4—26no—
610C4×D4—26no—
611C4×D4—26no—
612C4×D4—26no—
613C4×D4—26no—
614C4×D4—26no—
615C4×D4—26no—
616C4×D4—26no—
617C4×D4—26no—
618C4×D4—212no—
619C4×D4—26no—
620C4×D4—23no—
621C4×D4—23no—
622C4×D4—26no—
623C4×D4—26no—
624C4×D4—26no—
625C4×D4—26no—
626C4×D4—26no—
627C4×D4—23no—
628C4×D4—23no—
629C4×D4C2×D413yes—
630C4×D4C2×D413yes—
631C4×D4C2×D416yes—
632C4×D4C2×D413yes—
633C4×D4C2×D413yes—
634C4×D4C2×D416yes—
635C4×D4C2×D413yes—
636C4×D4C2×D416yes—
637C4×D4C2×D413yes—
638C4×D4C2416yes—
639C4×D4C2416yes—
640C4×D4C2413yes—
641C4×D4C2416yes—
642C4×D4C2413yes—
643#117—21no—
644#117—23no—
645#117—26no—
646#117—26no—
647#117—26no—
648#117—26no—
649#117—26no—
650#117—23no—
651#117—23no—
652#117—23no—
653#117—23no—
654#117—26no—
655#117—26no—
656#117—26no—
657#117—26no—
658#117C2×D413yes—
659#117C2×D413yes—
660#117C2×D416yes—
661#117C2×D416yes—
662#117C2×D413yes—
663#117C2×D413yes—
664#117C2412yes—
665C2×C4⋊C4—23no—
666C2×C4⋊C4—23no—
667C2×C4⋊C4—23no—
668C2×C4⋊C4—23no—
669C2×C4⋊C4—23no—
670C2×C4⋊C4—23no—
671C2×C4⋊C4—23no—
672C2×C4⋊C4—23no—
673C2×C4⋊C4—26no—
674C2×C4⋊C4—26no—
675C2×C4⋊C4—26no—
676C2×C4⋊C4—26no—
677C2×C4⋊C4—26no—
678C2×C4⋊C4C2×D413yes—
679C2×C4⋊C4C2×D413yes—
680C2×C4⋊C4C2416yes—
681C2×C4⋊C4C2416yes—
682C2×C22⋊C4—26no—
683C2×C22⋊C4—26no—
684C2×C22⋊C4—26no—
685C2×C22⋊C4—26no—
686C2×C22⋊C4—212no—
687C2×C22⋊C4C2×D416yes—
688C2×C42—26no—
689C2×C42—26no—
690C2×C42—26no—
691C2×C42C2×D413yes—
692C2×C42C2×D413yes—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2×D413yes—
697C2×C42C2413yes—
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702C2×C42C2411yescharacteristic
703#107C2414yes—
704#107C24112yes—
705#106C2414yes—
706#106C24112yes—
707C4⋊C8C2416yes—
708C4⋊C8C24112yes—
709C4⋊C8C2412yes—
710C4⋊C8C24112yes—
711#103C24112yes—
712#103C24124yes—
713#103C24112yes—
714#103C2414yes—
715#103C24112yes—
716#103C2414yes—
717#103C24112yes—
718#102C24112yes—
719#102C24124yes—
720#102C24112yes—
721C22⋊C8C2416yes—
722C22⋊C8C24112yes—
723C22⋊C8C2412yes—
724C22⋊C8C24112yes—
725#97C2416yes—
726#97C24112yes—
727#97C2412yes—
728C4×C8C24112yes—
729C24—26no—
730C24C22×D413yes—
731#41—24no—
732#41—212no—
733#41—212no—
734#41—412no—
735#41—424no—
736#41—48no—
737#41—412no—
738#41—812no—
739#41—812no—
740#41—86no—
741#41#13718yescomplemented
742C2×Q8—24no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—23no—
747C2×Q8—26no—
748C2×Q8—26no—
749C2×Q8—26no—
750C2×Q8—26no—
751C2×Q8—26no—
752C2×Q8—46no—
753C2×Q8—46no—
754C2×Q8—412no—
755C2×Q8—412no—
756C2×Q8—86no—
757C2×Q8—86no—
758C2×Q8C22×D413yes—
759C2×Q8C22×D411yescharacteristic
760C2×Q8C2516yes—
761C2×Q8C2512yes—
762C2×Q8C2516yes—
763C2×D4—212no—
764C2×D4—26no—
765C2×D4—26no—
766C2×D4—26no—
767C2×D4—212no—
768C2×D4—23no—
769C2×D4—23no—
770C2×D4—26no—
771C2×D4—26no—
772C2×D4—26no—
773C2×D4—412no—
774C2×D4—424no—
775C2×D4—412no—
776C2×D4—86no—
777C2×D4—812no—
778C2×D4C22×D416yes—
779C2×D4C22×D413yes—
780C2×D4C22×D413yes—
781C2×D4C2516yes—
782C22×C4—212no—
783C22×C4—26no—
784C22×C4—26no—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—212no—
792C22×C4—46no—
793C22×C4—83no—
794C22×C4—812no—
795C22×C4C22×D413yes—
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D413yes—
798C22×C4C22×D413yes—
799C22×C4C22×D413yes—
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D413yes—
802C22×C4C22×D413yes—
803C22×C4C22×D413yes—
804C22×C4C22×D413yes—
805C22×C4C22×D413yes—
806C22×C4C22×D413yes—
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D413yes—
810C22×C4C2511yescharacteristic
811C22×C4C2513yes—
812C22×C4C2513yes—
813Q16—412no—
814Q16—424no—
815Q16—412no—
816SD16—412no—
817SD16—424no—
818SD16—412no—
819M16—412no—
820C2×C8—412no—
821C2×C8C2514yes—
822C2×C8C25112yes—
823C4⋊C4—21no—
824C4⋊C4—23no—
825C4⋊C4—21no—
826C4⋊C4—23no—
827C4⋊C4—21no—
828C4⋊C4—23no—
829C4⋊C4—22no—
830C4⋊C4—26no—
831C4⋊C4—22no—
832C4⋊C4—26no—
833C4⋊C4—23no—
834C4⋊C4—23no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—26no—
846C4⋊C4—212no—
847C4⋊C4—212no—
848C4⋊C4—26no—
849C4⋊C4—26no—
850C4⋊C4—26no—
851C4⋊C4—26no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—26no—
857C4⋊C4—26no—
858C4⋊C4—26no—
859C4⋊C4C22×D413yes—
860C4⋊C4C22×D413yes—
861C4⋊C4C22×D413yes—
862C4⋊C4C22×D416yes—
863C4⋊C4C22×D413yes—
864C4⋊C4C22×D416yes—
865C4⋊C4C2512yes—
866C4⋊C4C2516yes—
867C4⋊C4C2512yes—
868C4⋊C4C2512yes—
869C22⋊C4—26no—
870C22⋊C4—22no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—212no—
875C22⋊C4—26no—
876C22⋊C4—22no—
877C22⋊C4—212no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—212no—
882C22⋊C4—26no—
883C22⋊C4—26no—
884C22⋊C4—26no—
885C22⋊C4C22×D416yes—
886C22⋊C4C22×D416yes—
887C22⋊C4C22×D416yes—
888C22⋊C4C22×D416yes—
889C42—26no—
890C42—22no—
891C42—22no—
892C42—26no—
893C42—26no—
894C42—212no—
895C42—26no—
896C42—26no—
897C42C22×D413yes—
898C42C22×D411yescharacteristic
899C42C22×D411yescharacteristic
900C42C22×D413yes—
901C42C22×D413yes—
902C42C22×D413yes—
903C42C22×D413yes—
904C42C22×D413yes—
905C42C22×D413yes—
906C42C22×D413yes—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C2513yes—
910C42C2511yescharacteristic
911C42C2513yes—
912C42C2511yescharacteristic
913C23—26no—
914C23—26no—
915C23—43no—
916C23—43no—
917C23—412no—
918C23—86no—
919C23—86no—
920C23C23×D411yescharacteristic
921C23C23×D413yes—
922C23C23×D413yes—
923Q8—26no—
924Q8—22no—
925Q8—26no—
926Q8—26no—
927Q8—22no—
928Q8—212no—
929Q8—42no—
930Q8—46no—
931Q8—42no—
932Q8—42no—
933Q8—86no—
934Q8—86no—
935Q8—86no—
936Q8—86no—
937Q8—86no—
938Q8C2×#13714yes—
939D4—212no—
940D4—212no—
941D4—26no—
942D4—46no—
943D4—412no—
944D4—412no—
945D4—46no—
946D4—412no—
947D4—86no—
948D4—86no—
949D4—812no—
950D4—86no—
951D4C2×#137112yes—
952C2×C4—26no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—22no—
966C2×C4—26no—
967C2×C4—43no—
968C2×C4—43no—
969C2×C4—43no—
970C2×C4—41no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—43no—
975C2×C4—43no—
976C2×C4—412no—
977C2×C4—412no—
978C2×C4—812no—
979C2×C4—86no—
980C2×C4—86no—
981C2×C4—86no—
982C2×C4—86no—
983C2×C4—86no—
984C2×C4—86no—
985C2×C4C2×#137112yes—
986C2×C4C23×D413yes—
987C2×C4C23×D411yescharacteristic
988C2×C4C23×D413yes—
989C2×C4C23×D411yescharacteristic
990C2×C4C23×D411yescharacteristic
991C2×C4C23×D411yescharacteristic
992C2×C4C23×D413yes—
993C2×C4C23×D413yes—
994C2×C4C23×D413yes—
995C2×C4C23×D411yescharacteristic
996C2×C4C23×D413yes—
997C2×C4C2611yescharacteristic
998C8—212no—
999C8—24no—
1000C22—23no—
1001C22—23no—
1002C22—21no—
1003C22—23no—
1004C22—21no—
1005C22—23no—
1006C22—21no—
1007C22—23no—
1008C22—46no—
1009C22—46no—
1010C22—46no—
1011C22—86no—
1012C22—1612no—
1013C22C22×#13716yes—
1014C22C24×D411yescharacteristic
1015C4—21no—
1016C4—23no—
1017C4—21no—
1018C4—21no—
1019C4—23no—
1020C4—23no—
1021C4—21no—
1022C4—23no—
1023C4—23no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—46no—
1028C4—46no—
1029C4—42no—
1030C4—46no—
1031C4C22×#13712yes—
1032C4C22×#13716yes—
1033C4H(7,𝔽2)12yes—
1034C2—26no—
1035C2—43no—
1036C2—41no—
1037C2—86no—
1038C2#6285211yescharacteristic
1039C2C23×#13711yescharacteristic
1040C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62800C2
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. #62813C2semidirect
3. #62594C2semidirect
4. #62582C2semidirect
5. #62454C2semidirect
6. #62448C2semidirect
7. #61966C2semidirect
8. #61965C2semidirect
9. #61952C2semidirect
10. #61951C2semidirect
11. #61909C2semidirect
12. #61607C2semidirect
13. #60963C2semidirect
14. #60952C2semidirect
15. #60804C2semidirect
16. C2×#3216C2semidirect
17. #60283C2semidirect
27. #3503C22semidirect
28. #3503C22semidirect
29. #3503C22semidirect
30. #3503C22semidirect
32. #3502C22semidirect
34. #3501C22semidirect
44. Q8×#41C22semidirect
49. C2×#533C22semidirect
50. C2×#533C22semidirect
55. #3400C22semidirect
56. #3398C22semidirect
57. #3395C22semidirect
58. #3392C22semidirect
59. #3375C22semidirect
60. #3369C22semidirect
61. #3363C22semidirect
62. #3362C22semidirect
63. #3333C22semidirect
64. #3331C22semidirect
65. #3316C22semidirect
66. #3314C22semidirect
67. #3299C22semidirect
68. #3295C22semidirect
69. D4×Q16C22semidirect
70. D4×SD16C22semidirect
71. #3278C22semidirect
72. #3276C22semidirect
73. #3270C22semidirect
74. #3266C22semidirect
75. #3255C22semidirect
76. #3254C22semidirect
77. #3249C22semidirect
78. #3246C22semidirect
79. #3239C22semidirect
80. #3238C22semidirect
81. #3237C22semidirect
82. #3237C22semidirect
83. #3218C22semidirect
84. #3218C22semidirect
85. #3216C22semidirect
86. #3216C22semidirect
87. #3216C22semidirect
88. #3216C22semidirect
89. #3216C22semidirect
90. #3216C22semidirect
91. #3216C22semidirect
92. #3215C22semidirect
93. #3210C22semidirect
94. #3209C22semidirect
95. #3208C22semidirect
96. #3196C22semidirect
97. #3190C22semidirect
98. #3181C22semidirect
99. #3172C22semidirect
100. #3172C22semidirect
101. #3152C22semidirect
102. C2×#497C22semidirect
103. #3141C22semidirect
104. C2×#489C22semidirect
105. #3116C22semidirect
106. #3113C22semidirect
107. #3112C22semidirect
108. #3107C22semidirect
109. #3104C22semidirect
110. #3103C22semidirect
111. #3037C22semidirect
112. C2×#462C22semidirect
113. C2×#460C22semidirect
114. #3007C22semidirect
115. C2×#452C22semidirect
116. #2989C22semidirect
118. #2984C22semidirect
119. #2974C22semidirect
120. #2971C22semidirect
121. #2970C22semidirect
122. #2920C22semidirect
123. C2×#432C22semidirect
741. #41#137semidirect

Maximal subgroups

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

subgroupindex
#628132
#628002
#625942
#625822
#624542
#624482
#619662
#619652
#619522
#619512
#619092
#616072
#609632
#609522
#608042
C2×#32162
#602832