Finite Group Databasebeta

← #10579503

Subgroups — #10579503

Order 512.

6240 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#62148C212yesmaximal, complemented
4#62147C212yesmaximal, complemented
5#62134C216yesmaximal, complemented
6#62133C216yesmaximal, complemented
7#62121C2112yesmaximal, complemented
8#62105C214yesmaximal, complemented
9Q8×AGL(1,ℤ/8)C212yesmaximal, complemented
10#61322C212yesmaximal, complemented
11#61257C216yesmaximal, complemented
12#61159C216yesmaximal, complemented
13#60918C213yesmaximal, complemented
14#60865C213yesmaximal, complemented
15#60559C213yesmaximal, complemented
16#60484C213yesmaximal, complemented
17#60263C211yesmaximal, characteristic, complemented
18#3523—21no—
19#3520—23no—
20#3518C2212yescomplemented
21#3515C2216yescomplemented
22#3511C2213yescomplemented
23#3509C2213yescomplemented
24#3503C2211yescharacteristic, complemented
25#3499C2211yescharacteristic, complemented
26#3495—23no—
27#3489—21no—
28#3482—21no—
29#3482—23no—
30#3482—21no—
31#3482—23no—
32#3482—21no—
33#3482—23no—
34#3482C2212yes—
35#3482C2216yes—
36#3482C2216yes—
37#3482C2212yes—
38Q8×#41C2212yes—
39C2×#557C2211yescharacteristic
40#3475C2216yes—
41C2×#556C2213yes—
42C2×#552—23no—
43C2×D4×Q8C2211yescharacteristic
44C2×#548—21no—
45C2×#547C2213yes—
46#3461—23no—
47#3444C2213yes—
48C2×#533C2213yes—
49C2×#533C2213yes—
50C2×#529—23no—
51C4×2−1+4—21no—
52C2×C4×#41C2213yes—
53C2×C4×#41C2211yescharacteristic
54C22×C4×Q8—21no—
55#3386C22112yescomplemented
56#3384C22112yescomplemented
57Q8×SD16C2214yescomplemented
58Q8×D8C2214yescomplemented
59#3374C22112yescomplemented
60#3372C22112yescomplemented
61#3363C2214yescomplemented
62#3359C2214yescomplemented
63#3356C22112yescomplemented
64#3353C22112yescomplemented
65#3350C22124yescomplemented
66#3349C22124yescomplemented
67#3342C22112yescomplemented
68#3340C22112yescomplemented
69#3331C22112yescomplemented
70#3330C22112yescomplemented
71#3315C22124yescomplemented
72#3307C22124yescomplemented
73#3303C22112yescomplemented
74#3302C22112yescomplemented
75#3255C2216yescomplemented
76#3254C2216yescomplemented
77#3252C22112yescomplemented
78#3249C2216yescomplemented
79#3248C22112yescomplemented
80#3246C2216yescomplemented
81#3237C22112yescomplemented
82#3236C22112yescomplemented
83#3231C22112yescomplemented
84#3230C2216yescomplemented
85#3229C2216yescomplemented
86#3165C2216yes—
87#3139C2216yes—
88#3116C2216yescomplemented
89#3115C2216yescomplemented
90#3111C22112yescomplemented
91#3107C2216yescomplemented
92#3106C2216yescomplemented
93#3102C22112yescomplemented
94#3095C22112yes—
95#3093C2216yes—
96#3080C22112yescomplemented
97#3079C2216yes—
98#3079C2216yescomplemented
99#3079C2216yescomplemented
100#3078C2216yes—
101#3078C2216yes—
102#3078C2213yes—
103#3077C2213yes—
104#3077C2216yes—
105#3076C22112yescomplemented
106#3076C22112yescomplemented
107#3056C22112yes—
108#3039C2216yes—
109#3037C2213yes—
110#3036C2211yescharacteristic
111#3005C2216yes—
112#2991C2212yescomplemented
113#2990C2216yescomplemented
114#2989C2216yescomplemented
115#2988C2212yescomplemented
116Q8×M16C2212yes—
117C4×#137C2216yes—
118C4×AGL(1,ℤ/8)C2216yes—
119D4×M16C2216yes—
120#2920C2213yes—
121#2911C2216yes—
122C2×#423C2213yes—
123#2896C2216yes—
124C2×2−1+4—21no—
125C22×#41D411yescharacteristic
126C22×#41C2313yes—
127C23×Q8—21no—
128C2×#137C2316yes—
129C2×AGL(1,ℤ/8)C2312yes—
130C22×M16C2316yes—
131Q82C2312yes—
132#557—21no—
133#557—23no—
134#557—21no—
135#557—23no—
136#557C2312yes—
137#557C2316yes—
138#557C2316yes—
139#556—23no—
140#556—23no—
141#556—26no—
142#556—23no—
143#556—23no—
144#556—26no—
145#556C2316yes—
146#556C2316yes—
147#556C23112yes—
148#556C2316yes—
149#555C2316yes—
150#554—26no—
151#554C2316yes—
152#554C2316yes—
153#553C23112yes—
154#552—26no—
155#552—26no—
156#552—26no—
157#552—212no—
158#552—26no—
159#552—212no—
160#552—26no—
161#552—212no—
162#552—26no—
163#552—26no—
164#552C23112yes—
165#551—212no—
166D4×Q8—22no—
167D4×Q8—21no—
168D4×Q8—23no—
169D4×Q8—21no—
170D4×Q8—23no—
171D4×Q8C2312yes—
172D4×Q8C2312yes—
173D4×Q8C2316yes—
174#548—22no—
175#548—22no—
176#548—26no—
177#548—26no—
178#548—22no—
179#548—26no—
180#547—26no—
181#547—23no—
182#547—23no—
183#547—26no—
184#547—23no—
185#547—23no—
186#547C2316yes—
187#547C2316yes—
188#547C23112yes—
189#547C2316yes—
190#546—26no—
191#544—23no—
192#542—26no—
193#542—26no—
194#541—26no—
195#541—26no—
196#539—212no—
197#537—23no—
198#536—23no—
199#536—23no—
200#533—26no—
201#533—23no—
202#533—23no—
203#533—23no—
204#533—23no—
205#533—23no—
206#533—23no—
207#533—23no—
208#533—23no—
209#533C2313yes—
210#533C2313yes—
211#533C2316yes—
212#533C2316yes—
213#533C2316yes—
214#533C2316yes—
215#533C2316yes—
216#533C2316yes—
217#533C2313yes—
218#533C2316yes—
219#532C2311yescharacteristic
220#532C2313yes—
221#532C2313yes—
222C2×C4⋊Q8C2313yes—
223C2×C4⋊Q8C2313yes—
224C2×C4⋊Q8C2313yes—
225C2×C4⋊Q8C2313yes—
226#529—26no—
227#529—212no—
228#529—26no—
229#529—26no—
230#529—26no—
231#529—212no—
232#529—212no—
233#529—26no—
234#529—23no—
235#529—23no—
236#529—23no—
237#529—23no—
238#529C2316yes—
239#529C2316yes—
240C2×#126—26no—
241C2×#125—23no—
242C2×#125—23no—
243C2×#125C2316yes—
244C2×#124—23no—
245#525—23no—
246#525—23no—
247#525C2316yes—
248C2×#123—26no—
249C2×C22⋊Q8—23no—
250C2×C22⋊Q8—23no—
251C2×C22⋊Q8—23no—
252C2×C22⋊Q8—23no—
253C2×C22⋊Q8C2316yes—
254C2×#121—23no—
255#520—21no—
256#520—26no—
257#520—23no—
258#519—22no—
259#519—23no—
260C4×#41—26no—
261C4×#41—23no—
262C4×#41—23no—
263C4×#41—23no—
264C4×#41—23no—
265C4×#41—23no—
266C4×#41—23no—
267C4×#41D411yescharacteristic
268C4×#41D413yes—
269C4×#41D413yes—
270C4×#41D411yescharacteristic
271C4×#41C2316yes—
272C4×#41C2316yes—
273C4×#41C2316yes—
274C4×#41C2316yes—
275C4×#41C2316yes—
276C4×#41C2311yescharacteristic
277C4×#41C2311yescharacteristic
278C4×#41C2313yes—
279C4×#41C2313yes—
280C2×C4×Q8—21no—
281C2×C4×Q8—22no—
282C2×C4×Q8—26no—
283C2×C4×Q8—22no—
284C2×C4×Q8—26no—
285C2×C4×Q8—22no—
286C2×C4×Q8—23no—
287C2×C4×Q8—23no—
288C2×C4×Q8—23no—
289C2×C4×Q8—23no—
290C2×C4×Q8D411yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4—23no—
295C2×C4×D4—23no—
296C2×C4×D4D413yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×#117—23no—
301C2×#117—23no—
302C2×#117D413yes—
303C2×#117C2313yes—
304C2×#117C2316yes—
305C22×C4⋊C4—23no—
306C22×C42—23no—
307C22×C42C2313yes—
308#501C23124yes—
309#500C23112yes—
310#498C23112yes—
311#491C23124yes—
312#487C23112yes—
313#487C23112yes—
314#485C23124yes—
315#485C23112yes—
316#485C23124yes—
317#485C23112yes—
318#484C23124yes—
319#483C23124yes—
320#482C23112yes—
321#482C23112yes—
322#479C23124yes—
323#479C23124yes—
324#479C23112yes—
325#478C23112yes—
326#478C23124yes—
327#477C23112yes—
328#477C23112yes—
329#477C2316yes—
330#477C23112yes—
331#476C23112yes—
332#476C2316yes—
333#476C23112yes—
334#475C23112yes—
335#475C23112yes—
336#475C2316yes—
337#475C23112yes—
338#474C23112yes—
339#474C2316yes—
340#474C23112yes—
341#470C23124yes—
342#468C23124yes—
343#467C23124yes—
344#465C23124yes—
345#464C23112yes—
346#463C2314yes—
347#462C23112yes—
348#462C2316yes—
349#462C23112yes—
350#461C23112yes—
351#461C2312yes—
352#461C23112yes—
353#460C2316yes—
354#459C2312yes—
355#452C23112yes—
356#452C23112yes—
357#449C23112yes—
358#449C23112yes—
359#446C23112yes—
360C8×Q8C2314yes—
361#442C23112yes—
362#441C23112yes—
363#440C23112yes—
364#440C23112yes—
365C4×Q16C23112yes—
366C4×SD16C23112yes—
367C4×SD16C23112yes—
368C4×D8C23112yes—
369#436C23112yes—
370#435C23124yes—
371C8×D4C23112yes—
372#432C2316yes—
373#432C2316yes—
374#431C2316yes—
375#431C2316yes—
376#428C2316yes—
377#428C23112yes—
378#428C2316yes—
379#428C23112yes—
380#428C23112yes—
381#427C23124yes—
382#423C2313yes—
383#423C2316yes—
384#423C2311yescharacteristic
385#423C2316yes—
386#423C2316yes—
387C2×C4⋊C8C2316yes—
388C2×C4⋊C8C2316yes—
389#419C23112yes—
390#419C2316yes—
391#418C2316yes—
392#417C23112yes—
393#417C23112yes—
394#417C2316yes—
395#417C2312yes—
396#416C23124yes—
397#407C2316yes—
398C4×M16C2316yes—
3992−1+4—48no—
400C2×#41—26no—
401C2×#41—23no—
402C2×#41—23no—
403C2×#41—23no—
404C2×#41—23no—
405C2×#41—212no—
406C2×#41—46no—
407C2×#41—44no—
408C2×#41C2×D411yescharacteristic
409C2×#41C2×D411yescharacteristic
410C2×#41C2×D413yes—
411C2×#41C2×D413yes—
412C2×#41C2412yes—
413C2×#41C2416yes—
414C2×#41C2416yes—
415C22×Q8—26no—
416C22×Q8—22no—
417C22×Q8—22no—
418C22×Q8—23no—
419C22×Q8—23no—
420C22×Q8—23no—
421C22×Q8—48no—
422C22×Q8C2×D411yescharacteristic
423C22×Q8C2413yes—
424C22×D4—23no—
425C22×D4C2×D413yes—
426C22×D4C2411yescharacteristic
427C23×C4—23no—
428C23×C4—23no—
429C23×C4—21no—
430C23×C4C2×D413yes—
431C23×C4C2×D413yes—
432C23×C4C2413yes—
433#137—412no—
434AGL(1,ℤ/8)—28no—
435C2×Q16C24112yes—
436C2×SD16C2414yes—
437C2×SD16C24112yes—
438C2×D8C2414yes—
439C2×M16—412no—
440C2×M16C2416yes—
441C2×M16C2412yes—
442C2×M16C24112yes—
443C22×C8C24112yes—
444C4⋊Q8—26no—
445C4⋊Q8—26no—
446C4⋊Q8—23no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8—23no—
450C4⋊Q8—23no—
451C4⋊Q8—23no—
452C4⋊Q8—23no—
453C4⋊Q8—23no—
454C4⋊Q8C2416yes—
455C4⋊Q8C2416yes—
456C4⋊Q8C2411yescharacteristic
457C4⋊Q8C2413yes—
458C4⋊Q8C2413yes—
459C4⋊Q8C2416yes—
460C4⋊Q8C2416yes—
461C4⋊Q8C2416yes—
462C4⋊Q8C2416yes—
463#127C2411yescharacteristic
464#126—212no—
465#126—212no—
466#126—212no—
467#126—212no—
468#126—212no—
469#126—212no—
470#126—212no—
471#126—26no—
472#126—26no—
473#125—26no—
474#125—212no—
475#125—26no—
476#125—212no—
477#125—26no—
478#125—212no—
479#125—26no—
480#125—26no—
481#125—26no—
482#125—26no—
483#125—26no—
484#125—26no—
485#125—23no—
486#125—23no—
487#125C2416yes—
488#125C24112yes—
489#124—26no—
490#124—26no—
491#124—212no—
492#124—26no—
493#124—212no—
494#124—23no—
495#124—23no—
496#124C2412yes—
497#123—212no—
498#123—26no—
499#123—26no—
500#123—26no—
501#123—212no—
502#123—212no—
503#123—212no—
504#123—212no—
505#123—212no—
506#123—212no—
507C22⋊Q8—26no—
508C22⋊Q8—23no—
509C22⋊Q8—23no—
510C22⋊Q8—26no—
511C22⋊Q8—26no—
512C22⋊Q8—26no—
513C22⋊Q8—26no—
514C22⋊Q8—26no—
515C22⋊Q8—26no—
516C22⋊Q8—26no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—23no—
523C22⋊Q8—23no—
524C22⋊Q8—26no—
525C22⋊Q8—212no—
526C22⋊Q8—26no—
527C22⋊Q8—26no—
528C22⋊Q8—26no—
529C22⋊Q8—212no—
530C22⋊Q8—212no—
531C22⋊Q8C24112yes—
532C22⋊Q8C24112yes—
533C22⋊Q8C2416yes—
534C22⋊Q8C2416yes—
535#121—26no—
536#121—26no—
537#121—212no—
538#121—212no—
539#121—26no—
540#121—21no—
541#121—21no—
542#121—23no—
543#121—23no—
544#121C2416yes—
545#121C2416yes—
546#120—26no—
547C4×Q8—26no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—26no—
551C4×Q8—26no—
552C4×Q8—212no—
553C4×Q8—26no—
554C4×Q8—26no—
555C4×Q8—26no—
556C4×Q8—26no—
557C4×Q8—26no—
558C4×Q8—26no—
559C4×Q8—26no—
560C4×Q8—23no—
561C4×Q8—23no—
562C4×Q8—26no—
563C4×Q8—26no—
564C4×Q8—26no—
565C4×Q8—26no—
566C4×Q8—26no—
567C4×Q8—23no—
568C4×Q8—23no—
569C4×Q8—23no—
570C4×Q8—23no—
571C4×Q8—23no—
572C4×Q8—23no—
573C4×Q8C2×D411yescharacteristic
574C4×Q8C2×D413yes—
575C4×Q8C2×D411yescharacteristic
576C4×Q8C2×D413yes—
577C4×Q8C2×D411yescharacteristic
578C4×Q8C2×D413yes—
579C4×Q8C2416yes—
580C4×Q8C2416yes—
581C4×Q8C2416yes—
582C4×Q8C2416yes—
583C4×Q8C2416yes—
584C4×Q8C2416yes—
585C4×Q8C2411yescharacteristic
586C4×Q8C2413yes—
587C4×D4—26no—
588C4×D4—26no—
589C4×D4—26no—
590C4×D4—26no—
591C4×D4—26no—
592C4×D4—26no—
593C4×D4—26no—
594C4×D4—26no—
595C4×D4—26no—
596C4×D4—26no—
597C4×D4—26no—
598C4×D4—26no—
599C4×D4—26no—
600C4×D4—26no—
601C4×D4—26no—
602C4×D4—212no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—23no—
606C4×D4—23no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—23no—
610C4×D4—23no—
611C4×D4C2×D413yes—
612C4×D4C2×D416yes—
613C4×D4C2×D413yes—
614C4×D4C2×D413yes—
615C4×D4C2×D413yes—
616C4×D4C2×D416yes—
617C4×D4C2×D413yes—
618C4×D4C2×D413yes—
619C4×D4C2×D416yes—
620C4×D4C2412yes—
621C4×D4C2412yes—
622C4×D4C2416yes—
623C4×D4C2416yes—
624C4×D4C2416yes—
625C4×D4C2416yes—
626C4×D4C2413yes—
627C4×D4C2416yes—
628C4×D4C2413yes—
629#117—26no—
630#117—26no—
631#117—26no—
632#117—26no—
633#117—23no—
634#117—23no—
635#117—26no—
636#117—26no—
637#117—23no—
638#117—23no—
639#117—26no—
640#117—212no—
641#117—26no—
642#117—26no—
643#117—26no—
644#117—26no—
645#117—26no—
646#117—26no—
647#117—26no—
648#117C2×D413yes—
649#117C2×D413yes—
650#117C2×D416yes—
651#117C2×D413yes—
652#117C2×D416yes—
653#117C2×D413yes—
654#117C2416yes—
655#117C2416yes—
656#117C2416yes—
657#117C24112yes—
658C2×C4⋊C4—23no—
659C2×C4⋊C4—26no—
660C2×C4⋊C4—23no—
661C2×C4⋊C4—23no—
662C2×C4⋊C4—23no—
663C2×C4⋊C4—23no—
664C2×C4⋊C4—26no—
665C2×C4⋊C4—23no—
666C2×C4⋊C4—26no—
667C2×C4⋊C4—23no—
668C2×C4⋊C4—26no—
669C2×C4⋊C4—26no—
670C2×C4⋊C4—212no—
671C2×C4⋊C4—26no—
672C2×C4⋊C4C2×D413yes—
673C2×C4⋊C4C2×D413yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2416yes—
677C2×C4⋊C4C2416yes—
678C2×C22⋊C4—26no—
679C2×C22⋊C4—23no—
680C2×C22⋊C4—26no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—23no—
683C2×C22⋊C4C2×D416yes—
684C2×C42—23no—
685C2×C42—23no—
686C2×C42—26no—
687C2×C42—23no—
688C2×C42—26no—
689C2×C42—26no—
690C2×C42—26no—
691C2×C42—26no—
692C2×C42—26no—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2×D413yes—
697C2×C42C2×D413yes—
698C2×C42C2×D413yes—
699C2×C42C2413yes—
700C2×C42C2411yescharacteristic
701C2×C42C2413yes—
702C2×C42C2413yes—
703C2×C42C2413yes—
704C2×C42C2413yes—
705#107C24112yes—
706#107C24124yes—
707#107C24112yes—
708#106C24112yes—
709#106C24124yes—
710#106C24112yes—
711C4⋊C8C2416yes—
712C4⋊C8C2416yes—
713C4⋊C8C24112yes—
714C4⋊C8C24112yes—
715C4⋊C8C2412yes—
716C4⋊C8C2412yes—
717#103C24124yes—
718#103C24124yes—
719#103C24112yes—
720#103C2414yes—
721#103C24112yes—
722#103C24112yes—
723#102C24112yes—
724#102C24112yes—
725#102C24112yes—
726#102C2414yes—
727C22⋊C8C24112yes—
728C22⋊C8C24112yes—
729#97C24112yes—
730C4×C8C24112yes—
731C24—21no—
732C24C22×D413yes—
733#41—24no—
734#41—24no—
735#41—212no—
736#41—212no—
737#41—24no—
738#41—24no—
739#41—46no—
740#41—46no—
741#41—46no—
742#41—46no—
743#41—412no—
744#41—412no—
745#41—412no—
746#41—424no—
747#41—86no—
748C2×Q8—24no—
749C2×Q8—26no—
750C2×Q8—26no—
751C2×Q8—23no—
752C2×Q8—23no—
753C2×Q8—26no—
754C2×Q8—23no—
755C2×Q8—26no—
756C2×Q8—26no—
757C2×Q8—26no—
758C2×Q8—412no—
759C2×Q8—412no—
760C2×Q8—424no—
761C2×Q8—48no—
762C2×Q8—48no—
763C2×Q8—86no—
764C2×Q8C22×D413yes—
765C2×Q8C22×D411yescharacteristic
766C2×Q8C2516yes—
767C2×Q8C2512yes—
768C2×D4—22no—
769C2×D4—26no—
770C2×D4—26no—
771C2×D4—26no—
772C2×D4—26no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—22no—
777C2×D4—46no—
778C2×D4—412no—
779C2×D4C22×D413yes—
780C2×D4C22×D413yes—
781C2×D4C22×D416yes—
782C2×D42−1+414yescomplemented
783C2×D4C2512yes—
784C2×D4C2512yes—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—21no—
788C22×C4—23no—
789C22×C4—23no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—26no—
799C22×C4—26no—
800C22×C4—26no—
801C22×C4—46no—
802C22×C4—46no—
803C22×C4—412no—
804C22×C4—44no—
805C22×C4—412no—
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D413yes—
810C22×C4C22×D413yes—
811C22×C4C22×D413yes—
812C22×C4C22×D413yes—
813C22×C4C22×D413yes—
814C22×C4C22×D413yes—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D413yes—
817C22×C4C22×D413yes—
818C22×C4C22×D413yes—
819C22×C4C22×D413yes—
820C22×C4C22×D413yes—
821C22×C4C2513yes—
822C22×C4C2513yes—
823C22×C4C2511yescharacteristic
824Q16—412no—
825SD16—28no—
826SD16—412no—
827D8—28no—
828M16—24no—
829M16—212no—
830M16—412no—
831C2×C8—412no—
832C2×C8C2514yes—
833C2×C8C25112yes—
834C4⋊C4—26no—
835C4⋊C4—26no—
836C4⋊C4—212no—
837C4⋊C4—212no—
838C4⋊C4—23no—
839C4⋊C4—23no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—212no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—26no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4—26no—
849C4⋊C4—26no—
850C4⋊C4—26no—
851C4⋊C4—26no—
852C4⋊C4—212no—
853C4⋊C4—26no—
854C4⋊C4—21no—
855C4⋊C4—23no—
856C4⋊C4—26no—
857C4⋊C4—26no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—26no—
861C4⋊C4—26no—
862C4⋊C4—26no—
863C4⋊C4—26no—
864C4⋊C4C22×D413yes—
865C4⋊C4C22×D413yes—
866C4⋊C4C22×D413yes—
867C4⋊C4C22×D416yes—
868C4⋊C4C22×D416yes—
869C4⋊C4C22×D413yes—
870C4⋊C4C2516yes—
871C4⋊C4C2516yes—
872C4⋊C4C2512yes—
873C4⋊C4C2516yes—
874C22⋊C4—26no—
875C22⋊C4—212no—
876C22⋊C4—212no—
877C22⋊C4—26no—
878C22⋊C4—26no—
879C22⋊C4—212no—
880C22⋊C4—26no—
881C22⋊C4—26no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—26no—
885C22⋊C4—26no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—26no—
889C22⋊C4—26no—
890C22⋊C4—26no—
891C22⋊C4—26no—
892C22⋊C4C22×D416yes—
893C22⋊C4C22×D416yes—
894C22⋊C4C22×D416yes—
895C22⋊C4C22×D416yes—
896C42—26no—
897C42—26no—
898C42—26no—
899C42—26no—
900C42—26no—
901C42—26no—
902C42—26no—
903C42—26no—
904C42—212no—
905C42—26no—
906C42C22×D413yes—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C22×D413yes—
910C42C22×D413yes—
911C42C22×D411yescharacteristic
912C42C22×D411yescharacteristic
913C42C22×D413yes—
914C42C22×D413yes—
915C42C22×D413yes—
916C42C22×D413yes—
917C42C22×D413yes—
918C42C2513yes—
919C42C2513yes—
920C42C2511yescharacteristic
921C42C2511yescharacteristic
922C23—22no—
923C23—24no—
924C23—26no—
925C23—22no—
926C23—43no—
927C23—43no—
928C23—42no—
929C23—42no—
930C23C23×D413yes—
931C23C23×D413yes—
932C23C23×D411yescharacteristic
933Q8—26no—
934Q8—22no—
935Q8—26no—
936Q8—26no—
937Q8—22no—
938Q8—412no—
939Q8—46no—
940Q8—46no—
941Q8—46no—
942Q8—412no—
943Q8—412no—
944Q8—86no—
945Q8#57514yes—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—24no—
950D4—26no—
951D4—26no—
952D4—46no—
953D4—42no—
954D4—412no—
955D4—412no—
956D4—412no—
957D4—44no—
958D4—42no—
959D4—86no—
960D4C2×2−1+414yes—
961C2×C4—26no—
962C2×C4—22no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—23no—
966C2×C4—23no—
967C2×C4—23no—
968C2×C4—23no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—26no—
973C2×C4—26no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—26no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—41no—
981C2×C4—43no—
982C2×C4—43no—
983C2×C4—43no—
984C2×C4—43no—
985C2×C4—43no—
986C2×C4—412no—
987C2×C4—412no—
988C2×C4—44no—
989C2×C4—412no—
990C2×C4—42no—
991C2×C4—46no—
992C2×C4—412no—
993C2×C4—46no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—412no—
997C2×C4—412no—
998C2×C4—86no—
999C2×C4—86no—
1000C2×C4C23×D411yescharacteristic
1001C2×C4C23×D413yes—
1002C2×C4C23×D413yes—
1003C2×C4C23×D413yes—
1004C2×C4C23×D413yes—
1005C2×C4C23×D411yescharacteristic
1006C2×C4C23×D411yescharacteristic
1007C2×C4C23×D413yes—
1008C2×C4C23×D411yescharacteristic
1009C2×C4C23×D411yescharacteristic
1010C2×C4C23×D413yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4#58512yes—
1013C2×C4C2611yescharacteristic
1014C8—24no—
1015C8—212no—
1016C22—21no—
1017C22—21no—
1018C22—23no—
1019C22—23no—
1020C22—24no—
1021C22—23no—
1022C22—23no—
1023C22—23no—
1024C22—23no—
1025C22—48no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—86no—
1032C22#348912yes—
1033C22C24×D411yescharacteristic
1034C4—23no—
1035C4—23no—
1036C4—21no—
1037C4—21no—
1038C4—23no—
1039C4—21no—
1040C4—23no—
1041C4—23no—
1042C4—46no—
1043C4—42no—
1044C4—46no—
1045C4—46no—
1046C4—42no—
1047C4—46no—
1048C4#348912yes—
1049C4C2×#57516yes—
1050C4#358612yes—
1051C4C22×2−1+411yescharacteristic
1052C4C2×#58511yescharacteristic
1053C2—22no—
1054C2—43no—
1055C2—43no—
1056C2—44no—
1057C2—82no—
1058C2C2×#348911yescharacteristic
1059C2C22×#57511yescharacteristic
1060C2C2×#358611yescharacteristic
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. #62805C2semidirect
2. C2×#3482C2semidirect
3. #62148C2semidirect
4. #62147C2semidirect
5. #62134C2semidirect
6. #62133C2semidirect
7. #62121C2semidirect
8. #62105C2semidirect
9. Q8×AGL(1,ℤ/8)C2semidirect
10. #61322C2semidirect
11. #61257C2semidirect
12. #61159C2semidirect
13. #60918C2semidirect
14. #60865C2semidirect
15. #60559C2semidirect
16. #60484C2semidirect
17. #60263C2semidirect
20. #3518C22semidirect
21. #3515C22semidirect
22. #3511C22semidirect
23. #3509C22semidirect
24. #3503C22semidirect
25. #3499C22semidirect
55. #3386C22semidirect
56. #3384C22semidirect
57. Q8×SD16C22semidirect
58. Q8×D8C22semidirect
59. #3374C22semidirect
60. #3372C22semidirect
61. #3363C22semidirect
62. #3359C22semidirect
63. #3356C22semidirect
64. #3353C22semidirect
65. #3350C22semidirect
66. #3349C22semidirect
67. #3342C22semidirect
68. #3340C22semidirect
69. #3331C22semidirect
70. #3330C22semidirect
71. #3315C22semidirect
72. #3307C22semidirect
73. #3303C22semidirect
74. #3302C22semidirect
75. #3255C22semidirect
76. #3254C22semidirect
77. #3252C22semidirect
78. #3249C22semidirect
79. #3248C22semidirect
80. #3246C22semidirect
81. #3237C22semidirect
82. #3236C22semidirect
83. #3231C22semidirect
84. #3230C22semidirect
85. #3229C22semidirect
88. #3116C22semidirect
89. #3115C22semidirect
90. #3111C22semidirect
91. #3107C22semidirect
92. #3106C22semidirect
93. #3102C22semidirect
96. #3080C22semidirect
98. #3079C22semidirect
99. #3079C22semidirect
105. #3076C22semidirect
106. #3076C22semidirect
112. #2991C22semidirect
113. #2990C22semidirect
114. #2989C22semidirect
115. #2988C22semidirect
782. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
#628052
C2×#34822
#621482
#621472
#621342
#621332
#621212
#621052
Q8×AGL(1,ℤ/8)2
#613222
#612572
#611592
#609182
#608652
#605592
#604842
#602632