Finite Group Databasebeta

← #10581098

Subgroups — #10581098

Order 512.

6313 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62830C212yesmaximal, complemented
2#62618C214yesmaximal, complemented
3#62610C214yesmaximal, complemented
4#62520C214yesmaximal, complemented
5#62463C214yesmaximal, complemented
6#62365C212yesmaximal, complemented
7#62359C211yesmaximal, characteristic, complemented
8#62358C211yesmaximal, characteristic, complemented
9#62263C214yesmaximal, complemented
10#62259C212yesmaximal, complemented
11#62257C214yesmaximal, complemented
12#62248C211yesmaximal, characteristic, complemented
13#62245C211yesmaximal, characteristic, complemented
14#61555C214yesmaximal, complemented
15#61553C214yesmaximal, complemented
16#61545C214yesmaximal, complemented
17#61539C214yesmaximal, complemented
18#61000C214yesmaximal, complemented
19#60948C211yesmaximal, characteristic, complemented
20#60940C211yesmaximal, characteristic, complemented
21#60707C214yesmaximal, complemented
22#60700C212yesmaximal, complemented
23C2×#2969C211yesmaximal, characteristic, complemented
24#3562—24no—
25#3560—24no—
26#3552C2214yescomplemented
27#3551—24no—
28#3547C2214yescomplemented
29#3546C2214yescomplemented
30#3543C2214yescomplemented
31#3534—24no—
32#3520C2214yescomplemented
33#3519C2218yescomplemented
34#3519C2214yescomplemented
35#3517C2214yescomplemented
36#3514—24no—
37#3514C2214yescomplemented
38#3512—22no—
39#3507C2212yescomplemented
40#3506C2212yescomplemented
41#3505—24no—
42#3500—22no—
43#3497C2212yescomplemented
44#3496C2212yescomplemented
45#3494C2218yescomplemented
46#3489—22no—
47#3488—22no—
48#3444C2212yescomplemented
49C2×#532C2212yescomplemented
50C2×#529C2211yescharacteristic
51#3399C2214yescomplemented
52#3397C2214yescomplemented
53#3394C2214yescomplemented
54#3391C2214yescomplemented
55#3386C2214yescomplemented
56#3384C2214yescomplemented
57#3381C2214yescomplemented
58Q8×D8C2214yescomplemented
59#3373C2214yescomplemented
60#3368C2214yescomplemented
61#3367C2214yescomplemented
62#3366C2214yescomplemented
63#3364C2214yescomplemented
64#3361C2214yescomplemented
65#3358C2214yescomplemented
66#3358C2214yescomplemented
67#3357C2218yescomplemented
68#3355C2218yescomplemented
69#3354C2214yescomplemented
70#3353C2214yescomplemented
71#3347C2218yescomplemented
72#3346C2218yescomplemented
73#3340C2214yescomplemented
74#3334C2214yescomplemented
75#3333C2218yescomplemented
76#3332C2214yescomplemented
77#3330C2214yescomplemented
78#3325C2214yescomplemented
79#3325C2218yescomplemented
80#3324C2214yescomplemented
81#3322C2218yescomplemented
82#3322C2218yescomplemented
83#3319C2218yescomplemented
84#3318C2218yescomplemented
85#3314C2218yescomplemented
86#3309C2218yescomplemented
87#3305C2214yescomplemented
88#3302C2214yescomplemented
89#3294C2214yescomplemented
90#3294C2214yescomplemented
91#3284C2214yescomplemented
92D4×D8C2214yescomplemented
93#3274C2214yescomplemented
94#3274C2218yescomplemented
95#3273C2218yescomplemented
96#3272C2214yescomplemented
97#3268C2218yescomplemented
98#3264C2218yescomplemented
99#3250C2214yescomplemented
100#3249C2211yescharacteristic, complemented
101#3247C2218yescomplemented
102#3246C2212yescomplemented
103#3245C2211yescharacteristic
104#3245C2211yescharacteristic, complemented
105#3245C2212yescomplemented
106#3245C2211yescharacteristic, complemented
107#3245C2214yescomplemented
108#3243C2218yescomplemented
109#3241C2218yescomplemented
110#3233C2214yescomplemented
111#3226C2214yescomplemented
112#3224C2218yescomplemented
113#3220C2218yescomplemented
114#3212C2214yescomplemented
115#3205C2214yescomplemented
116#3191C2214yescomplemented
117#3191C2214yescomplemented
118#3188C2218yescomplemented
119#3186C2214yescomplemented
120#3186C2214yescomplemented
121#3184C2212yescomplemented
122#3184C2212yescomplemented
123#3182C2212yescomplemented
124#3182C2212yescomplemented
125#3180C2214yescomplemented
126#3180C2214yescomplemented
127#3180C2218yescomplemented
128#3179C2218yescomplemented
129#3179C2218yescomplemented
130#3176C2214yescomplemented
131#3176C2214yescomplemented
132#3175C2214yescomplemented
133#3175C2214yescomplemented
134#3171C2214yescomplemented
135#3171C2214yescomplemented
136#3169C2214yescomplemented
137#3169C2212yescomplemented
138#3169C2212yescomplemented
139#3169C2214yescomplemented
140#3168C2214yescomplemented
141#3168C2214yescomplemented
142#3167C2212yescomplemented
143#3167C2212yescomplemented
144#3165C2212yescomplemented
145#3164C2214yescomplemented
146#3155C2214yescomplemented
147#3151C2212yescomplemented
148#3141C2212yescomplemented
149#3138C2212yescomplemented
150#3136C2218yescomplemented
151#3124C2218yescomplemented
152#3122C2218yescomplemented
153#3119C2218yescomplemented
154#3118C2218yescomplemented
155#3107C2214yescomplemented
156#3106C2214yescomplemented
157#3100C2214yescomplemented
158#3100C2214yescomplemented
159#3055C2214yescomplemented
160#3055C2214yescomplemented
161#3055C2218yescomplemented
162#3050C2214yescomplemented
163C2×#466C2214yescomplemented
164#2969C2214yescomplemented
165#2969C2214yescomplemented
166#2969C2214yescomplemented
167#2969C2214yescomplemented
168C2×#446C2211yescharacteristic, complemented
169C2×C8×Q8C2211yescharacteristic, complemented
170#2951C2214yescomplemented
171#2948C2214yescomplemented
172#2946C2218yescomplemented
173C4×AGL(1,ℤ/8)C2214yescomplemented
174C4×AGL(1,ℤ/8)C2214yescomplemented
175C2×#436C2211yescharacteristic, complemented
176C2×#436C2212yescomplemented
177C2×#435C2212yescomplemented
178C2×C8×D4C2211yescharacteristic, complemented
179C2×#433C2212yescomplemented
180C2×#431C2211yescharacteristic, complemented
181C2×#405C2212yescomplemented
182C2×C4×M16C2211yescharacteristic, complemented
183C2×2−1+4—22no—
184C2×H(5,𝔽2)—22no—
185C22×#41—22no—
186C2×AGL(1,ℤ/8)C2314yes—
187C2×AGL(1,ℤ/8)C2314yes—
188C2×AGL(1,ℤ/8)C2318yes—
189C2×#135C2314yes—
190C22×D8C2314yes—
191C22×M16C2311yescharacteristic
192C22×M16C2311yescharacteristic
193C22×M16C2312yes—
194C23×C8C2312yes—
195#563—28no—
196#562—28no—
197#560—28no—
198#560—28no—
199#559—24no—
200#559C2314yes—
201#557C2314yes—
202#556—24no—
203#556C2314yes—
204#556C2314yes—
205#555—28no—
206#555C2314yes—
207#555C2318yes—
208#554C2314yes—
209#554C2318yes—
210#553—28no—
211#553—24no—
212#553—24no—
213#553—24no—
214#553—28no—
215#553—28no—
216#553—28no—
217#553C2318yes—
218#553C2318yes—
219#552—24no—
220#552—24no—
221#552—24no—
222#551—28no—
223#551—28no—
224#551—28no—
225#551—28no—
226#550—24no—
227#550C2314yes—
228#550C2318yes—
229#550C2314yes—
230#550C2314yes—
231D4×Q8—24no—
232D4×Q8C2314yes—
233D4×Q8C2314yes—
234#548—24no—
235#548—24no—
236#548—24no—
237#548—24no—
238#548—24no—
239#548—24no—
240#547—24no—
241#547—28no—
242#547C2314yes—
243#547C2314yes—
244#547C2314yes—
245#546—24no—
246#546—24no—
247#546—28no—
248#546—24no—
249#546—24no—
250#546—24no—
251#546—24no—
252#546—28no—
253#546—28no—
254#546—28no—
255#546—28no—
256#546C2318yes—
257#546C2318yes—
258D42—28no—
259D42—24no—
260D42C2314yes—
261D42C2314yes—
262D42C2318yes—
263#544C2318yes—
264#542—28no—
265#542C2318yes—
266#542C2318yes—
267#541—24no—
268#540—24no—
269#540—28no—
270#540—28no—
271#540C2318yes—
272#540C2318yes—
273#539—28no—
274#539—28no—
275#539—24no—
276#538—28no—
277#538—28no—
278#538—28no—
279#538—28no—
280#538—28no—
281#538—24no—
282#537—24no—
283#537—24no—
284#537—22no—
285#537—22no—
286#537—24no—
287#536—22no—
288#536—24no—
289#536—24no—
290#535—22no—
291#535—24no—
292#535—24no—
293#535C2318yes—
294#534—28no—
295#534—24no—
296#533C2312yes—
297#533C2312yes—
298#533C2312yes—
299#532—24no—
300#532—22no—
301#532—22no—
302#532—22no—
303#532—22no—
304#532C2312yes—
305#532C2312yes—
306#532C2312yes—
307#532C2312yes—
308#532C2312yes—
309#532C2312yes—
310#532C2314yes—
311#532C2312yes—
312#532C2318yes—
313#532C2314yes—
314C2×C4⋊Q8C2312yes—
315C2×#127C2312yes—
316#529—24no—
317#529—24no—
318#529—22no—
319#529—22no—
320#529—22no—
321#529—22no—
322#529D414yes—
323#529D414yes—
324#529C2314yes—
325#529C2318yes—
326#529C2314yes—
327#529C2314yes—
328#529C2314yes—
329C2×#126D412yes—
330C2×#125D411yescharacteristic
331C2×#124—24no—
332C2×#124—22no—
333C2×#124D411yescharacteristic
334#525—22no—
335#525—22no—
336#525—24no—
337#525—24no—
338#525C2318yes—
339#525C2314yes—
340C2×#123D412yes—
341C2×C22⋊Q8—24no—
342C2×C22⋊Q8D411yescharacteristic
343C2×#121—22no—
344C2×#121—24no—
345C2×#121D411yescharacteristic
346C2×#121C2314yes—
347C2×#121C2318yes—
348#520—22no—
349#520—22no—
350#520C2318yes—
351#518—28no—
352#518C2318yes—
353C4×#41—22no—
354C4×#41—22no—
355C4×#41C2314yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×D4—22no—
358C2×C4×D4C2314yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×#117C2312yes—
362C22×C42C2311yescharacteristic
363#501C2318yes—
364#501C2314yes—
365#501C2314yes—
366#500C2312yes—
367#500C2312yes—
368#500C2314yes—
369#500C2314yes—
370#499C2314yes—
371#499C2314yes—
372#498C2312yes—
373#498C2312yes—
374#496C2318yes—
375#496C2314yes—
376#496C2314yes—
377#495C2314yes—
378#495C2314yes—
379#493C2312yes—
380#493C2314yes—
381#493C2312yes—
382#493C2314yes—
383#492C2312yes—
384#492C2312yes—
385#490C2318yes—
386#490C2314yes—
387#490C2314yes—
388#489C2318yes—
389#489C2314yes—
390#489C2314yes—
391#488C2318yes—
392#488C2318yes—
393#487C2312yes—
394#487C2312yes—
395#486C2312yes—
396#486C2318yes—
397#486C2312yes—
398#486C2312yes—
399#486C2312yes—
400#486C2312yes—
401#486C2312yes—
402#486C2318yes—
403#485C2318yes—
404#485C2318yes—
405#484C2318yes—
406#482C2318yes—
407#482C2318yes—
408#482C2318yes—
409#482C2318yes—
410#481C2318yes—
411#480C2318yes—
412#480C2318yes—
413#480C2318yes—
414#480C2318yes—
415#479C2318yes—
416#478C2318yes—
417#478C2318yes—
418#478C2318yes—
419#477C2318yes—
420#477C2314yes—
421#476C2314yes—
422#476C2318yes—
423#475C2314yes—
424#474C2314yes—
425#474C2314yes—
426#474C2314yes—
427#474C2314yes—
428#474C2318yes—
429#474C2318yes—
430#474C2314yes—
431#469C2318yes—
432#469C2314yes—
433#469C2318yes—
434#469C2314yes—
435#469C2314yes—
436#469C2314yes—
437#468C2318yes—
438#468C2314yes—
439#468C2314yes—
440#468C2318yes—
441#468C2314yes—
442#468C2314yes—
443#467C2314yes—
444#467C2314yes—
445#466C2318yes—
446#466C2314yes—
447#466C2314yes—
448#466C2314yes—
449#466C2314yes—
450#466C2314yes—
451#466C2314yes—
452#466C2318yes—
453#466C2314yes—
454#466C2314yes—
455#466C2314yes—
456#466C2314yes—
457#465C2318yes—
458#465C2314yes—
459#465C2314yes—
460#465C2314yes—
461#465C2314yes—
462#465C2318yes—
463#464C2318yes—
464#463C2318yes—
465#463C2318yes—
466#463C2318yes—
467#462C2314yes—
468#461C2314yes—
469#460C2318yes—
470#460C2314yes—
471#459C2314yes—
472#459C2314yes—
473#459C2314yes—
474#459C2314yes—
475#459C2314yes—
476#459C2318yes—
477#459C2318yes—
478#459C2318yes—
479#452C2318yes—
480#452C2318yes—
481#450C2318yes—
482#449C2318yes—
483#449C2318yes—
484#449C2318yes—
485#449C2318yes—
486#447C2318yes—
487#447C2318yes—
488#447C2318yes—
489#447C2318yes—
490#447C2318yes—
491#446C2314yes—
492#446C2314yes—
493C8×Q8C2314yes—
494C8×Q8C2314yes—
495#442C2318yes—
496#442C2318yes—
497#442C2314yes—
498#442C2314yes—
499#442C2314yes—
500#442C2314yes—
501#440C2318yes—
502#440C2318yes—
503#440C2314yes—
504#440C2314yes—
505#440C2314yes—
506#440C2314yes—
507C4×Q16C2314yes—
508C4×Q16C2314yes—
509C4×SD16C2314yes—
510C4×SD16C2314yes—
511C4×SD16C2314yes—
512C4×SD16C2318yes—
513C4×SD16C2318yes—
514C4×SD16C2314yes—
515C4×D8C2314yes—
516C4×D8C2314yes—
517C4×D8C2314yes—
518C4×D8C2318yes—
519C4×D8C2314yes—
520C4×D8C2314yes—
521C4×D8C2318yes—
522C4×D8C2314yes—
523C4×D8C2314yes—
524C4×D8C2314yes—
525C4×D8C2314yes—
526C4×D8C2314yes—
527#436C2314yes—
528#436C2318yes—
529#436C2314yes—
530#436C2318yes—
531#435C2318yes—
532#435C2318yes—
533C8×D4C2314yes—
534C8×D4C2314yes—
535#433C2318yes—
536#433C2318yes—
537#431C2314yes—
538#431C2314yes—
539#428C2314yes—
540#428C2318yes—
541#428C2314yes—
542#427C2314yes—
543C2×#107C2314yes—
544C2×C4⋊C8C2311yescharacteristic
545C2×C4⋊C8C2311yescharacteristic
546C2×C4⋊C8C2312yes—
547C2×C4⋊C8C2312yes—
548#418C2318yes—
549#418C2314yes—
550#418C2314yes—
551#417C2318yes—
552#417C2314yes—
553#417C2314yes—
554#416C2318yes—
555C2×#102C2318yes—
556C2×C22⋊C8C2312yes—
557C2×C22⋊C8C2312yes—
558C2×C22⋊C8C2312yes—
559#405C2314yes—
560#405C2314yes—
561#405C2314yes—
562#405C2314yes—
563C4×M16C2312yes—
564C4×M16C2312yes—
565C4×M16C2312yes—
566C4×M16C2312yes—
567C2×#97C2311yescharacteristic
568C2×#97C2311yescharacteristic
569C2×#97C2312yes—
570C2×C4×C8C2311yescharacteristic
571C2×C4×C8C2311yescharacteristic
572C2×C4×C8C2312yes—
573C2×C4×C8C2312yes—
5742−1+4—88no—
575H(5,𝔽2)—88no—
576C2×#41—24no—
577C2×#41—24no—
578C2×#41—24no—
579C2×#41—24no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—24no—
585C2×#41—24no—
586C2×#41—22no—
587C2×#41—22no—
588C2×#41—28no—
589C2×#41—88no—
590C2×#41C2414yes—
591C2×#41C2418yes—
592C22×Q8—24no—
593C22×Q8—24no—
594C22×Q8—22no—
595C22×Q8C2×D411yescharacteristic
596C22×D4—24no—
597C22×D4—28no—
598C22×D4—28no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—22no—
602C22×D4—22no—
603C22×D4C2×D411yescharacteristic
604C22×D4C2×D412yes—
605C22×D4C2414yes—
606C22×D4C2418yes—
607C23×C4—24no—
608C23×C4C2×D411yescharacteristic
609C23×C4C2×D411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612AGL(1,ℤ/8)—48no—
613AGL(1,ℤ/8)—48no—
614AGL(1,ℤ/8)—416no—
615#135—48no—
616C2×Q16C2414yes—
617C2×SD16C2414yes—
618C2×SD16C2414yes—
619C2×SD16C2414yes—
620C2×SD16C2418yes—
621C2×SD16C2414yes—
622C2×D8—48no—
623C2×D8C2414yes—
624C2×D8C2414yes—
625C2×D8C2414yes—
626C2×D8C2414yes—
627C2×D8C2414yes—
628C2×D8C2414yes—
629C2×D8C2418yes—
630C2×D8C2414yes—
631C2×M16—42no—
632C2×M16—42no—
633C2×M16—44no—
634C2×M16C2412yes—
635C2×M16C2412yes—
636C2×M16C2414yes—
637C2×M16C2412yes—
638C2×M16C2412yes—
639C2×M16C2414yes—
640C22×C8—44no—
641C22×C8C2411yescharacteristic
642C22×C8C2414yes—
643C22×C8C2411yescharacteristic
644C22×C8C2412yes—
645C22×C8C2414yes—
646C22×C8C2411yescharacteristic
647C22×C8C2411yescharacteristic
648C22×C8C2412yes—
649C4⋊Q8—24no—
650C4⋊Q8—28no—
651C4⋊Q8—22no—
652C4⋊Q8—22no—
653C4⋊Q8C2412yes—
654C4⋊Q8C2414yes—
655C4⋊Q8C2412yes—
656C4⋊Q8C2412yes—
657C4⋊Q8C2412yes—
658C4⋊Q8C2412yes—
659C4⋊Q8C2418yes—
660#127—24no—
661#127—28no—
662#127—22no—
663#127—22no—
664#127C2414yes—
665#127C2412yes—
666#127C2412yes—
667#127C2412yes—
668#127C2418yes—
669#126—28no—
670#126—28no—
671#126—28no—
672#126—28no—
673#126—28no—
674#126—28no—
675#126—24no—
676#126—24no—
677#126—28no—
678#126C2×D418yes—
679#126C2×D418yes—
680#125—28no—
681#125—28no—
682#125—28no—
683#125—22no—
684#125—22no—
685#125C2×D414yes—
686#125C2×D414yes—
687#125C2414yes—
688#125C2418yes—
689#124—24no—
690#124—24no—
691#124—28no—
692#124—28no—
693#124—28no—
694#124—28no—
695#124—28no—
696#124—22no—
697#124—22no—
698#124—24no—
699#124—22no—
700#124—22no—
701#124—24no—
702#124—22no—
703#124—22no—
704#124—28no—
705#124C2×D414yes—
706#124C2×D414yes—
707#124C2414yes—
708#124C2418yes—
709#123—24no—
710#123—24no—
711#123—24no—
712#123—28no—
713#123—28no—
714#123—28no—
715#123—28no—
716#123—28no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—28no—
721#123—28no—
722#123—28no—
723#123—28no—
724#123—28no—
725#123—28no—
726#123—28no—
727#123—28no—
728#123C2×D418yes—
729#123C2×D418yes—
730C22⋊Q8—24no—
731C22⋊Q8—24no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—22no—
735C22⋊Q8—22no—
736C22⋊Q8—24no—
737C22⋊Q8—28no—
738C22⋊Q8—24no—
739C22⋊Q8—24no—
740C22⋊Q8—24no—
741C22⋊Q8—28no—
742C22⋊Q8—28no—
743C22⋊Q8—28no—
744C22⋊Q8—28no—
745C22⋊Q8—28no—
746C22⋊Q8—28no—
747C22⋊Q8—28no—
748C22⋊Q8—28no—
749C22⋊Q8C2×D414yes—
750C22⋊Q8C2×D414yes—
751C22⋊Q8C2414yes—
752C22⋊Q8C2414yes—
753C22⋊Q8C2418yes—
754#121—24no—
755#121—28no—
756#121—24no—
757#121—28no—
758#121—28no—
759#121—22no—
760#121—22no—
761#121—22no—
762#121—22no—
763#121—22no—
764#121—24no—
765#121—24no—
766#121—24no—
767#121—24no—
768#121—28no—
769#121—28no—
770#121—22no—
771#121—22no—
772#121—22no—
773#121—28no—
774#121—24no—
775#121—24no—
776#121—24no—
777#121—24no—
778#121—28no—
779#121—28no—
780#121—28no—
781#121—28no—
782#121—28no—
783#121—28no—
784#121—28no—
785#121—28no—
786#121—28no—
787#121—28no—
788#121—28no—
789#121—28no—
790#121—28no—
791#121—28no—
792#121C2×D414yes—
793#121C2×D414yes—
794#121C2414yes—
795#121C2414yes—
796#121C2414yes—
797#121C2414yes—
798#121C2414yes—
799#121C2418yes—
800#121C2418yes—
801#121C2414yes—
802#121C2418yes—
803#120—24no—
804#120—28no—
805#120—28no—
806#120—28no—
807#120—28no—
808#120—28no—
809#120—28no—
810#120—28no—
811#120—28no—
812#120—28no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—22no—
816C4×Q8—22no—
817C4×Q8—22no—
818C4×Q8—22no—
819C4×Q8C2×D414yes—
820C4×Q8C2414yes—
821C4×Q8C2414yes—
822C4×Q8C2418yes—
823C4×Q8C2414yes—
824C4×D4—28no—
825C4×D4—24no—
826C4×D4—24no—
827C4×D4—24no—
828C4×D4—24no—
829C4×D4—24no—
830C4×D4—24no—
831C4×D4—28no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—28no—
835C4×D4—28no—
836C4×D4—28no—
837C4×D4—24no—
838C4×D4—24no—
839C4×D4—28no—
840C4×D4—28no—
841C4×D4—28no—
842C4×D4—28no—
843C4×D4—22no—
844C4×D4—24no—
845C4×D4—22no—
846C4×D4—22no—
847C4×D4—24no—
848C4×D4—22no—
849C4×D4—24no—
850C4×D4—24no—
851C4×D4—22no—
852C4×D4—22no—
853C4×D4—22no—
854C4×D4—22no—
855C4×D4—28no—
856C4×D4C2×D418yes—
857C4×D4C2×D414yes—
858C4×D4C2414yes—
859C4×D4C2414yes—
860C4×D4C2414yes—
861C4×D4C2414yes—
862C4×D4C2414yes—
863C4×D4C2414yes—
864C4×D4C2418yes—
865C4×D4C2418yes—
866C4×D4C2418yes—
867C4×D4C2414yes—
868C4×D4C2418yes—
869#117—22no—
870#117—22no—
871#117—28no—
872#117—24no—
873#117—24no—
874#117—28no—
875#117—24no—
876#117—24no—
877#117—24no—
878#117—28no—
879#117C2×D414yes—
880#117C2×D414yes—
881#117C2414yes—
882#117C2418yes—
883#117C2414yes—
884#117C2414yes—
885C2×C4⋊C4—22no—
886C2×C4⋊C4—24no—
887C2×C4⋊C4—24no—
888C2×C4⋊C4—28no—
889C2×C4⋊C4C2×D412yes—
890C2×C4⋊C4C2×D412yes—
891C2×C4⋊C4C2×D411yescharacteristic
892C2×C4⋊C4C2×D412yes—
893C2×C4⋊C4C2×D411yescharacteristic
894C2×C4⋊C4C2×D412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2418yes—
897C2×C22⋊C4—24no—
898C2×C22⋊C4—24no—
899C2×C22⋊C4—28no—
900C2×C22⋊C4—28no—
901C2×C22⋊C4—28no—
902C2×C22⋊C4—28no—
903C2×C22⋊C4—28no—
904C2×C22⋊C4C2×D412yes—
905C2×C22⋊C4C2×D412yes—
906C2×C22⋊C4C2×D412yes—
907C2×C22⋊C4C2×D412yes—
908C2×C22⋊C4C2×D412yes—
909C2×C42—24no—
910C2×C42C2×D412yes—
911C2×C42C2×D411yescharacteristic
912C2×C42C2×D412yes—
913C2×C42C2×D411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919#107C2414yes—
920#107C2414yes—
921#107C2414yes—
922#107C2414yes—
923#107C2414yes—
924#107C2414yes—
925#107C2414yes—
926#107C2418yes—
927#107C2414yes—
928#106C2414yes—
929#106C2414yes—
930#106C2418yes—
931#106C2414yes—
932#106C2414yes—
933C4⋊C8C2414yes—
934C4⋊C8C2414yes—
935C4⋊C8C2418yes—
936C4⋊C8C2418yes—
937#103C2414yes—
938#103C2418yes—
939#103C2414yes—
940#103C2414yes—
941#103C2414yes—
942#103C2418yes—
943#102C2414yes—
944#102C2414yes—
945#102C2418yes—
946#102C2418yes—
947#102C2414yes—
948#102C2418yes—
949#102C2414yes—
950#102C2414yes—
951#102C2418yes—
952#102C2414yes—
953#102C2414yes—
954#102C2414yes—
955#102C2414yes—
956#102C2414yes—
957#102C2418yes—
958#102C2418yes—
959#102C2414yes—
960#102C2414yes—
961C22⋊C8C2418yes—
962C22⋊C8C2418yes—
963C22⋊C8C2418yes—
964#97C2411yescharacteristic
965#97C2411yescharacteristic
966#97C2411yescharacteristic
967#97C2411yescharacteristic
968#97C2412yes—
969#97C2412yes—
970#97C2414yes—
971#97C2414yes—
972C4×C8C2412yes—
973C4×C8C2412yes—
974C4×C8C2412yes—
975C4×C8C2412yes—
976C4×C8C2414yes—
977C4×C8C2414yes—
978C4×C8C2414yes—
979C4×C8C2414yes—
980C24—24no—
981C24—28no—
982C24C22×D412yes—
983C24C22×D411yescharacteristic
984#41—48no—
985#41—44no—
986#41—48no—
987#41—44no—
988#41—48no—
989#41—48no—
990#41—48no—
991#41—88no—
992#41—88no—
993#41—816no—
994#41—84no—
995#41—84no—
996#41—88no—
997#41—88no—
998#41—84no—
999#41—88no—
1000#41—88no—
1001C2×Q8—24no—
1002C2×Q8—22no—
1003C2×Q8—22no—
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—28no—
1007C2×Q8—24no—
1008C2×Q8—84no—
1009C2×Q8—88no—
1010C2×Q8—88no—
1011C2×Q8C22×D414yes—
1012C2×Q8C2514yes—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—28no—
1018C2×D4—24no—
1019C2×D4—28no—
1020C2×D4—24no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—22no—
1029C2×D4—22no—
1030C2×D4—28no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—28no—
1034C2×D4—22no—
1035C2×D4—28no—
1036C2×D4—24no—
1037C2×D4—48no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—48no—
1041C2×D4—84no—
1042C2×D4—88no—
1043C2×D4—88no—
1044C2×D4—82no—
1045C2×D4—84no—
1046C2×D4—88no—
1047C2×D4—816no—
1048C2×D4—816no—
1049C2×D4C22×D414yes—
1050C2×D4C22×D418yes—
1051C2×D4C2514yes—
1052C2×D4C2514yes—
1053C2×D4C2514yes—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—28no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—24no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—88no—
1073C22×C4—81no—
1074C22×C4C22×D411yescharacteristic
1075C22×C4C22×D412yes—
1076C22×C4C22×D412yes—
1077C22×C4C22×D412yes—
1078C22×C4C22×D412yes—
1079C22×C4C22×D411yescharacteristic
1080C22×C4C22×D412yes—
1081C22×C4C22×D411yescharacteristic
1082C22×C4C22×D411yescharacteristic
1083C22×C4C22×D412yes—
1084C22×C4C22×D412yes—
1085C22×C4C22×D414yes—
1086C22×C4C22×D412yes—
1087C22×C4C22×D411yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2511yescharacteristic
1091Q16—44no—
1092SD16—28no—
1093SD16—28no—
1094SD16—44no—
1095SD16—44no—
1096SD16—48no—
1097D8—28no—
1098D8—28no—
1099D8—44no—
1100D8—44no—
1101D8—44no—
1102D8—44no—
1103D8—48no—
1104D8—44no—
1105M16—24no—
1106M16—24no—
1107M16—28no—
1108M16—42no—
1109M16—42no—
1110M16—44no—
1111C2×C8—22no—
1112C2×C8—28no—
1113C2×C8—22no—
1114C2×C8—44no—
1115C2×C8—42no—
1116C2×C8—41no—
1117C2×C8—41no—
1118C2×C8—42no—
1119C2×C8C2511yescharacteristic
1120C2×C8C2514yes—
1121C2×C8C2511yescharacteristic
1122C2×C8C2512yes—
1123C2×C8C2512yes—
1124C2×C8C2514yes—
1125C2×C8C2511yescharacteristic
1126C2×C8C2511yescharacteristic
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—24no—
1147C4⋊C4C22×D414yes—
1148C4⋊C4C22×D414yes—
1149C4⋊C4C22×D414yes—
1150C4⋊C4C22×D414yes—
1151C4⋊C4C22×D418yes—
1152C4⋊C4C22×D414yes—
1153C4⋊C4C22×D414yes—
1154C4⋊C4C22×D418yes—
1155C4⋊C4C2514yes—
1156C4⋊C4C2514yes—
1157C4⋊C4C2514yes—
1158C4⋊C4C2514yes—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—28no—
1186C22⋊C4C22×D414yes—
1187C22⋊C4C22×D414yes—
1188C22⋊C4C22×D418yes—
1189C22⋊C4C22×D418yes—
1190C22⋊C4C22×D414yes—
1191C22⋊C4C22×D414yes—
1192C22⋊C4C22×D418yes—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—28no—
1197C42—28no—
1198C42C22×D412yes—
1199C42C22×D411yescharacteristic
1200C42C22×D412yes—
1201C42C22×D412yes—
1202C42C22×D411yescharacteristic
1203C42C22×D412yes—
1204C42C22×D412yes—
1205C42C22×D414yes—
1206C42C2511yescharacteristic
1207C42C2511yescharacteristic
1208C42C2512yes—
1209C42C2514yes—
1210C23—22no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—42no—
1216C23—41no—
1217C23—41no—
1218C23—42no—
1219C23—48no—
1220C23—84no—
1221C23—84no—
1222C23—88no—
1223C23—88no—
1224C23—88no—
1225C23C23×D414yes—
1226C23C23×D412yes—
1227C23C23×D411yescharacteristic
1228Q8—28no—
1229Q8—24no—
1230Q8—24no—
1231Q8—44no—
1232Q8—44no—
1233Q8—44no—
1234Q8—88no—
1235Q8—84no—
1236Q8—82no—
1237D4—24no—
1238D4—24no—
1239D4—24no—
1240D4—24no—
1241D4—24no—
1242D4—24no—
1243D4—28no—
1244D4—48no—
1245D4—48no—
1246D4—48no—
1247D4—48no—
1248D4—48no—
1249D4—44no—
1250D4—44no—
1251D4—44no—
1252D4—84no—
1253D4—88no—
1254D4—84no—
1255D4—82no—
1256D4—82no—
1257D4—88no—
1258D4—84no—
1259D4—82no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—84no—
1265D4—84no—
1266D4—88no—
1267D4—84no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—44no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—48no—
1293C2×C4—48no—
1294C2×C4—48no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—88no—
1305C2×C4#57614yes—
1306C2×C4C23×D411yescharacteristic
1307C2×C4C23×D412yes—
1308C2×C4C23×D414yes—
1309C2×C4C23×D414yes—
1310C2×C4C23×D411yescharacteristic
1311C2×C4C23×D412yes—
1312C2×C4C23×D411yescharacteristic
1313C2×C4C23×D411yescharacteristic
1314C2×C4C23×D411yescharacteristic
1315C2×C4C23×D414yes—
1316C2×C4C23×D412yes—
1317C2×C4C2611yescharacteristic
1318C8—21no—
1319C8—24no—
1320C8—21no—
1321C8—22no—
1322C8—22no—
1323C8—24no—
1324C8#58512yes—
1325C8#58512yes—
1326C22—21no—
1327C22—21no—
1328C22—22no—
1329C22—24no—
1330C22—22no—
1331C22—24no—
1332C22—22no—
1333C22—24no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—82no—
1344C22—84no—
1345C22—168no—
1346C22—328no—
1347C22C2×#57612yes—
1348C22C24×D411yescharacteristic
1349C4—21no—
1350C4—24no—
1351C4—22no—
1352C4—21no—
1353C4—21no—
1354C4—24no—
1355C4—21no—
1356C4—21no—
1357C4—22no—
1358C4—24no—
1359C4—44no—
1360C4—44no—
1361C4—44no—
1362C4—44no—
1363C4—44no—
1364C4C2×#57614yes—
1365C4C2×#58511yescharacteristic
1366C4C2×#58511yescharacteristic
1367C2—22no—
1368C2—42no—
1369C2—44no—
1370C2—84no—
1371C2—84no—
1372C2—84no—
1373C2#6281211yescharacteristic
1374C2C22×#57611yescharacteristic
1375C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62830C2semidirect
2. #62618C2semidirect
3. #62610C2semidirect
4. #62520C2semidirect
5. #62463C2semidirect
6. #62365C2semidirect
7. #62359C2semidirect
8. #62358C2semidirect
9. #62263C2semidirect
10. #62259C2semidirect
11. #62257C2semidirect
12. #62248C2semidirect
13. #62245C2semidirect
14. #61555C2semidirect
15. #61553C2semidirect
16. #61545C2semidirect
17. #61539C2semidirect
18. #61000C2semidirect
19. #60948C2semidirect
20. #60940C2semidirect
21. #60707C2semidirect
22. #60700C2semidirect
23. C2×#2969C2semidirect
26. #3552C22semidirect
28. #3547C22semidirect
29. #3546C22semidirect
30. #3543C22semidirect
32. #3520C22semidirect
33. #3519C22semidirect
34. #3519C22semidirect
35. #3517C22semidirect
37. #3514C22semidirect
39. #3507C22semidirect
40. #3506C22semidirect
43. #3497C22semidirect
44. #3496C22semidirect
45. #3494C22semidirect
48. #3444C22semidirect
49. C2×#532C22semidirect
51. #3399C22semidirect
52. #3397C22semidirect
53. #3394C22semidirect
54. #3391C22semidirect
55. #3386C22semidirect
56. #3384C22semidirect
57. #3381C22semidirect
58. Q8×D8C22semidirect
59. #3373C22semidirect
60. #3368C22semidirect
61. #3367C22semidirect
62. #3366C22semidirect
63. #3364C22semidirect
64. #3361C22semidirect
65. #3358C22semidirect
66. #3358C22semidirect
67. #3357C22semidirect
68. #3355C22semidirect
69. #3354C22semidirect
70. #3353C22semidirect
71. #3347C22semidirect
72. #3346C22semidirect
73. #3340C22semidirect
74. #3334C22semidirect
75. #3333C22semidirect
76. #3332C22semidirect
77. #3330C22semidirect
78. #3325C22semidirect
79. #3325C22semidirect
80. #3324C22semidirect
81. #3322C22semidirect
82. #3322C22semidirect
83. #3319C22semidirect
84. #3318C22semidirect
85. #3314C22semidirect
86. #3309C22semidirect
87. #3305C22semidirect
88. #3302C22semidirect
89. #3294C22semidirect
90. #3294C22semidirect
91. #3284C22semidirect
92. D4×D8C22semidirect
93. #3274C22semidirect
94. #3274C22semidirect
95. #3273C22semidirect
96. #3272C22semidirect
97. #3268C22semidirect
98. #3264C22semidirect
99. #3250C22semidirect
100. #3249C22semidirect
101. #3247C22semidirect
102. #3246C22semidirect
104. #3245C22semidirect
105. #3245C22semidirect
106. #3245C22semidirect
107. #3245C22semidirect
108. #3243C22semidirect
109. #3241C22semidirect
110. #3233C22semidirect
111. #3226C22semidirect
112. #3224C22semidirect
113. #3220C22semidirect
114. #3212C22semidirect
115. #3205C22semidirect
116. #3191C22semidirect
117. #3191C22semidirect
118. #3188C22semidirect
119. #3186C22semidirect
120. #3186C22semidirect
121. #3184C22semidirect
122. #3184C22semidirect
123. #3182C22semidirect
124. #3182C22semidirect
125. #3180C22semidirect
126. #3180C22semidirect
127. #3180C22semidirect
128. #3179C22semidirect
129. #3179C22semidirect
130. #3176C22semidirect
131. #3176C22semidirect
132. #3175C22semidirect
133. #3175C22semidirect
134. #3171C22semidirect
135. #3171C22semidirect
136. #3169C22semidirect
137. #3169C22semidirect
138. #3169C22semidirect
139. #3169C22semidirect
140. #3168C22semidirect
141. #3168C22semidirect
142. #3167C22semidirect
143. #3167C22semidirect
144. #3165C22semidirect
145. #3164C22semidirect
146. #3155C22semidirect
147. #3151C22semidirect
148. #3141C22semidirect
149. #3138C22semidirect
150. #3136C22semidirect
151. #3124C22semidirect
152. #3122C22semidirect
153. #3119C22semidirect
154. #3118C22semidirect
155. #3107C22semidirect
156. #3106C22semidirect
157. #3100C22semidirect
158. #3100C22semidirect
159. #3055C22semidirect
160. #3055C22semidirect
161. #3055C22semidirect
162. #3050C22semidirect
163. C2×#466C22semidirect
164. #2969C22semidirect
165. #2969C22semidirect
166. #2969C22semidirect
167. #2969C22semidirect
168. C2×#446C22semidirect
169. C2×C8×Q8C22semidirect
170. #2951C22semidirect
171. #2948C22semidirect
172. #2946C22semidirect
173. C4×AGL(1,ℤ/8)C22semidirect
174. C4×AGL(1,ℤ/8)C22semidirect
175. C2×#436C22semidirect
176. C2×#436C22semidirect
177. C2×#435C22semidirect
178. C2×C8×D4C22semidirect
179. C2×#433C22semidirect
180. C2×#431C22semidirect
181. C2×#405C22semidirect
182. C2×C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#628302
#626182
#626102
#625202
#624632
#623652
#623592
#623582
#622632
#622592
#622572
#622482
#622452
#615552
#615532
#615452
#615392
#610002
#609482
#609402
#607072
#607002
C2×#29692