Finite Group Databasebeta

← #10581393

Subgroups — #10581393

Order 512.

6330 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62834C211yesmaximal, characteristic
2C2×#3550C211yesmaximal, characteristic, complemented
3#62345C218yesmaximal, complemented
4#62343C214yesmaximal, complemented
5#62326C214yesmaximal, complemented
6#61803C214yesmaximal, complemented
7#61789C214yesmaximal, complemented
8#61739C214yesmaximal, complemented
9#61722C212yesmaximal, complemented
10#61701C212yesmaximal, complemented
11#61680C214yesmaximal, complemented
12#61662C214yesmaximal, complemented
13#61593C214yesmaximal, complemented
14#61584C212yesmaximal, complemented
15#61562C212yesmaximal, complemented
16#60969C211yesmaximal, characteristic, complemented
17#60952C211yesmaximal, characteristic, complemented
18#60947C211yesmaximal, characteristic, complemented
19#60941C211yesmaximal, characteristic, complemented
20#60758C218yesmaximal, complemented
21#60236C211yesmaximal, characteristic, complemented
22#3558—22no—
23#3558—22no—
24#3550—22no—
25#3550—22no—
26#3550—22no—
27#3550—22no—
28#3550C2214yescomplemented
29#3550C2214yescomplemented
30#3550C2214yescomplemented
31#3550C2214yescomplemented
32#3549C2212yes—
33#3548C2212yes—
34#3546—22no—
35#3546C2214yes—
36#3537—22no—
37C2×#563—22no—
38#3519—22no—
39#3519C2214yes—
40#3511—21no—
41#3511C2212yes—
42#3508—22no—
43#3506C2212yes—
44#3506C2212yes—
45#3498—21no—
46#3498C2212yes—
47#3496C2212yes—
48#3496C2212yes—
49#3488—22no—
50#3488C2214yes—
51C2×#559—21no—
52C2×Q82—21no—
53C2×#556C2212yescomplemented
54C2×#556C2212yescomplemented
55C2×D4×Q8C2212yescomplemented
56C2×D4×Q8C2212yescomplemented
57C2×#542—22no—
58C2×#542—22no—
59C2×#536C2214yescomplemented
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic, complemented
62C2×#533C2211yescharacteristic, complemented
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic
65#3356C2218yescomplemented
66#3353C2218yescomplemented
67#3353C2218yescomplemented
68#3350C22116yescomplemented
69#3342C2218yescomplemented
70#3340C2218yescomplemented
71#3340C2218yescomplemented
72#3329C2218yescomplemented
73#3329C2218yescomplemented
74#3328C2218yescomplemented
75#3324C2218yescomplemented
76#3324C2218yescomplemented
77#3324C2218yescomplemented
78#3320C22116yescomplemented
79#3311C22116yescomplemented
80#3304C2218yescomplemented
81#3304C2218yescomplemented
82#3302C2218yescomplemented
83#3299C2218yescomplemented
84#3298C2218yescomplemented
85#3298C2218yescomplemented
86D4×SD16C2218yescomplemented
87D4×SD16C2218yescomplemented
88D4×SD16C2218yescomplemented
89#3278C2218yescomplemented
90#3278C2218yescomplemented
91#3276C2218yescomplemented
92#3266C22116yescomplemented
93#3255C2212yescomplemented
94#3254C2212yescomplemented
95#3254C2214yescomplemented
96#3248C2214yescomplemented
97#3246C2214yescomplemented
98#3239C2212yescomplemented
99#3237C2212yescomplemented
100#3231C2212yescomplemented
101#3230C2212yescomplemented
102#3229C2211yescharacteristic, complemented
103#3229C2212yescomplemented
104#3227C2212yescomplemented
105#3226C2212yescomplemented
106#3226C2211yescharacteristic, complemented
107#3218C2212yescomplemented
108#3216C2212yescomplemented
109#3210C2212yescomplemented
110#3209C2211yescharacteristic, complemented
111#3208C2212yescomplemented
112#3208C2212yescomplemented
113#3206C2212yescomplemented
114#3206C2211yescharacteristic, complemented
115#3206C2212yescomplemented
116#3201C22116yescomplemented
117#3201C22116yescomplemented
118#3200C22116yescomplemented
119#3200C22116yescomplemented
120#3196C2214yescomplemented
121#3196C2218yescomplemented
122#3193C2218yescomplemented
123#3193C2214yescomplemented
124#3190C2218yescomplemented
125#3190C2214yescomplemented
126#3187C2214yescomplemented
127#3187C2218yescomplemented
128#3182C2214yescomplemented
129#3172C2214yescomplemented
130#3170C2212yescomplemented
131#3167C2214yescomplemented
132#3167C2212yescomplemented
133#3112C2214yescomplemented
134#3110C2214yescomplemented
135#3108C2214yescomplemented
136#3107C2214yescomplemented
137#3107C2214yescomplemented
138#3104C2212yescomplemented
139#3103C2212yescomplemented
140#3103C2212yescomplemented
141#3103C2212yescomplemented
142#3101C2214yescomplemented
143#3097C22116yescomplemented
144#3094C2218yescomplemented
145#3091C2218yescomplemented
146#3063C22116yescomplemented
147#3057C22116yescomplemented
148#3009C22116yescomplemented
149#3004C2218yescomplemented
150C2×#448C2218yescomplemented
151#2981C2214yescomplemented
152#2979C2214yescomplemented
153#2975C2212yescomplemented
154#2974C2214yescomplemented
155#2972C2212yescomplemented
156#2935C2214yescomplemented
157#2931C2214yescomplemented
158#2920C2211yescharacteristic, complemented
159C2×#431C2211yescharacteristic, complemented
160#2880C2214yescomplemented
161C2×H(5,𝔽2)—22no—
162C2×H(5,𝔽2)C2314yes—
163C22×#41—21no—
164C22×#41C2312yes—
165C23×Q8C2314yes—
166C2×#137C23116yes—
167C22×SD16C23116yes—
168C2×#131C2318yes—
169#563—28no—
170#563—28no—
171#563—28no—
172#563—28no—
173#562—24no—
174H(3,𝔽4)—24no—
175#560—28no—
176#559—24no—
177#559—24no—
178#559—24no—
179#559—24no—
180#559—24no—
181#559—24no—
182Q82—24no—
183Q82—24no—
184Q82—24no—
185Q82—24no—
186#556—22no—
187#556—24no—
188#556—24no—
189#556—24no—
190#556—24no—
191#556C2314yes—
192#556C2318yes—
193#556C2318yes—
194#556C2318yes—
195#556C2318yes—
196#555—22no—
197#555C2314yes—
198#555C2314yes—
199#554—22no—
200#554C2314yes—
201#553—24no—
202#553—24no—
203#553—24no—
204#553C2318yes—
205#550—24no—
206#550—22no—
207#550—22no—
208#550—24no—
209#550C2314yes—
210#550C2314yes—
211D4×Q8—24no—
212D4×Q8—24no—
213D4×Q8—24no—
214D4×Q8—24no—
215D4×Q8C2318yes—
216D4×Q8C2318yes—
217D4×Q8C2318yes—
218D4×Q8C2318yes—
219#548—24no—
220#548—24no—
221#547—22no—
222#547C2314yes—
223#547C2314yes—
224#547C2314yes—
225#546—24no—
226#546—28no—
227#546—24no—
228#546—24no—
229#546—24no—
230#546—24no—
231#546—28no—
232#546C2318yes—
233D42—28no—
234D42—24no—
235D42—24no—
236D42—22no—
237D42—22no—
238D42—24no—
239D42—24no—
240D42C2314yes—
241D42C2314yes—
242D42C2314yes—
243#542—24no—
244#542—24no—
245#542—28no—
246#542—28no—
247#542—28no—
248#542—28no—
249#542—28no—
250#542—28no—
251#542—28no—
252#542—28no—
253#540—24no—
254#540—24no—
255#538—28no—
256#538—24no—
257#538—28no—
258#538—24no—
259#537—24no—
260#537—22no—
261#537C2314yes—
262#537C2318yes—
263#536—28no—
264#536—28no—
265#536C23116yes—
266#536C23116yes—
267#535—22no—
268#535—24no—
269#535—24no—
270#535—24no—
271#535—24no—
272#535C2314yes—
273#535C2318yes—
274#534—24no—
275#534—24no—
276#533—22no—
277#533—21no—
278#533—21no—
279#533—21no—
280#533—21no—
281#533—21no—
282#533—21no—
283#533—21no—
284#533—21no—
285#533C2312yes—
286#533C2311yescharacteristic
287#533C2312yes—
288#533C2312yes—
289#533C2312yes—
290#533C2312yes—
291#533C2312yes—
292#533C2311yescharacteristic
293#533C2312yes—
294#533C2312yes—
295#533C2311yescharacteristic
296#532—22no—
297#532—22no—
298#532—21no—
299#532—21no—
300#532—21no—
301#532—21no—
302#532D412yes—
303#532D412yes—
304#532D412yes—
305#532D412yes—
306#532C2311yescharacteristic
307#532C2312yes—
308#532C2311yescharacteristic
309#532C2312yes—
310#532C2312yes—
311#532C2311yescharacteristic
312#532C2312yes—
313#532C2312yes—
314#532C2312yes—
315#532C2312yes—
316#532C2312yes—
317C2×C4⋊Q8—24no—
318C2×C4⋊Q8—22no—
319C2×C4⋊Q8—22no—
320C2×C4⋊Q8D411yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2311yescharacteristic
324C2×C4⋊Q8C2311yescharacteristic
325C2×C4⋊Q8C2311yescharacteristic
326C2×#127—22no—
327C2×#127D411yescharacteristic
328C2×#127C2311yescharacteristic
329#529—21no—
330#529—21no—
331#529—21no—
332#529—21no—
333#529C2312yes—
334#529C2312yes—
335C2×#126—24no—
336C2×#126—24no—
337C2×#125—21no—
338C2×#125—21no—
339C2×#124—24no—
340C2×#124—22no—
341C2×#124—22no—
342C2×#124—21no—
343C2×#124D412yes—
344#525—21no—
345#525—21no—
346#525—24no—
347#525C2318yes—
348#525C2312yes—
349C2×#123—24no—
350C2×#123—24no—
351C2×C22⋊Q8—21no—
352C2×C22⋊Q8—21no—
353C2×C22⋊Q8—24no—
354C2×C22⋊Q8—24no—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2314yes—
359C2×#121—21no—
360C2×#121—24no—
361C2×#121D412yes—
362C2×#121D412yes—
363C2×#121C2318yes—
364C2×#121C2312yes—
365#520—22no—
366#520C2314yes—
367#518—24no—
368C4×#41—21no—
369C4×#41—21no—
370C4×#41C2312yes—
371C2×C4×Q8—22no—
372C2×C4×Q8—22no—
373C2×C4×Q8—21no—
374C2×C4×Q8—21no—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×D4—22no—
378C2×C4×D4—22no—
379C2×C4×D4—21no—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×#117—21no—
384C2×#117—21no—
385C2×#117C2314yes—
386C22×C42C2311yescharacteristic
387#501C2314yes—
388#500C2314yes—
389#500C2312yes—
390#498C2312yes—
391#498C2314yes—
392#497C2314yes—
393#494C2312yes—
394#492C2314yes—
395#492C2312yes—
396#492C2314yes—
397#491C2314yes—
398#489C2314yes—
399#487C2314yes—
400#487C2312yes—
401#487C2314yes—
402#487C2312yes—
403#487C2312yes—
404#486C2314yes—
405#486C2312yes—
406#486C2314yes—
407#485C23116yes—
408#485C23116yes—
409#485C23116yes—
410#485C2318yes—
411#485C2318yes—
412#484C2314yes—
413#484C2318yes—
414#484C23116yes—
415#483C2314yes—
416#483C23116yes—
417#483C2318yes—
418#482C23116yes—
419#482C23116yes—
420#482C23116yes—
421#481C2314yes—
422#481C2314yes—
423#481C2314yes—
424#480C2318yes—
425#480C2314yes—
426#479C2318yes—
427#477C2314yes—
428#477C2318yes—
429#476C2318yes—
430#475C2314yes—
431#475C2314yes—
432#475C2314yes—
433#475C2314yes—
434#475C2314yes—
435#474C2314yes—
436#474C2318yes—
437#474C2314yes—
438#470C23116yes—
439#470C2318yes—
440#468C23116yes—
441#468C23116yes—
442#468C23116yes—
443#468C2318yes—
444#468C23116yes—
445#467C23116yes—
446#467C2318yes—
447#465C23116yes—
448#465C23116yes—
449#465C23116yes—
450#465C2318yes—
451#465C2318yes—
452#465C2318yes—
453#464C2318yes—
454#462C2314yes—
455#462C2314yes—
456#462C2314yes—
457#461C2314yes—
458#461C2318yes—
459#461C2318yes—
460#461C2314yes—
461#460C2314yes—
462#460C2314yes—
463#460C2314yes—
464#460C2318yes—
465#452C2318yes—
466#452C2318yes—
467#452C23116yes—
468#452C23116yes—
469#451C23116yes—
470#451C2314yes—
471#451C2314yes—
472#450C2318yes—
473#450C2318yes—
474#450C23116yes—
475#450C23116yes—
476#448C23116yes—
477#448C23116yes—
478#448C2314yes—
479#448C2314yes—
480#448C2314yes—
481#448C2314yes—
482#448C2318yes—
483#448C23116yes—
484#440C23116yes—
485C4×Q16C2318yes—
486C4×Q16C2318yes—
487C4×SD16C2318yes—
488C4×SD16C2318yes—
489C4×SD16C2318yes—
490C4×SD16C2318yes—
491#436C2318yes—
492#436C2318yes—
493#436C2318yes—
494#435C23116yes—
495C8×D4C2318yes—
496C8×D4C2318yes—
497C8×D4C2318yes—
498#432C2312yes—
499#432C2312yes—
500#431C2312yes—
501#431C2311yescharacteristic
502#431C2311yescharacteristic
503#431C2312yes—
504#431C2312yes—
505#431C2312yes—
506#431C2312yes—
507#428C23116yes—
508#427C23116yes—
509#423C2312yes—
510C2×C4⋊C8C2312yes—
511#419C23116yes—
512#418C23116yes—
513#416C23116yes—
514C2×#103C23116yes—
515#408C23116yes—
516#408C2318yes—
517#407C2318yes—
518#407C2312yes—
519C2×C22⋊C8C2318yes—
520C2×C22⋊C8C2312yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
523H(5,𝔽2)—88no—
524H(5,𝔽2)—88no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—21no—
529C2×#41—22no—
530C2×#41—21no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—84no—
535C2×#41—84no—
536C2×#41C2×D414yes—
537C2×#41C2×D414yes—
538C2×#41C2412yes—
539C2×#41C2418yes—
540C2×#41C2414yes—
541C2×#41C2414yes—
542C22×Q8—21no—
543C22×Q8—21no—
544C22×Q8—24no—
545C22×Q8—21no—
546C22×Q8—28no—
547C22×Q8—88no—
548C22×Q8C2×D412yes—
549C22×Q8C2412yes—
550C22×Q8C2412yes—
551C22×Q8C24116yes—
552C22×D4—22no—
553C22×D4—28no—
554C22×D4—24no—
555C22×D4—28no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4C2×D412yes—
562C22×D4C2×D412yes—
563C22×D4C2×D414yes—
564C22×D4C2×D412yes—
565C22×D4C2412yes—
566C22×D4C2418yes—
567C23×C4—24no—
568C23×C4—22no—
569C23×C4C2×D411yescharacteristic
570C23×C4C2×D411yescharacteristic
571C23×C4C2414yes—
572C23×C4C2411yescharacteristic
573#137—816no—
574C2×Q16C2418yes—
575C2×Q16C2418yes—
576C2×SD16—816no—
577C2×SD16C2418yes—
578C2×SD16C2418yes—
579C2×SD16C2418yes—
580C2×SD16C24116yes—
581C2×SD16C2418yes—
582#131—88no—
583C2×M16C2414yes—
584C2×M16C24116yes—
585C22×C8C2414yes—
586C22×C8C24116yes—
587C4⋊Q8—216no—
588C4⋊Q8—216no—
589C4⋊Q8—28no—
590C4⋊Q8—28no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593C4⋊Q8—21no—
594C4⋊Q8—21no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597C4⋊Q8—21no—
598C4⋊Q8—21no—
599C4⋊Q8—21no—
600C4⋊Q8—21no—
601C4⋊Q8—21no—
602C4⋊Q8—21no—
603C4⋊Q8C2×D412yes—
604C4⋊Q8C2×D412yes—
605C4⋊Q8C2×D412yes—
606C4⋊Q8C2×D412yes—
607C4⋊Q8C2412yes—
608C4⋊Q8C2412yes—
609C4⋊Q8C2412yes—
610C4⋊Q8C2412yes—
611C4⋊Q8C2411yescharacteristic
612C4⋊Q8C2412yes—
613C4⋊Q8C2412yes—
614C4⋊Q8C2412yes—
615C4⋊Q8C2412yes—
616C4⋊Q8C2412yes—
617C4⋊Q8C2412yes—
618C4⋊Q8C2411yescharacteristic
619C4⋊Q8C2411yescharacteristic
620#127—24no—
621#127—24no—
622#127—24no—
623#127—28no—
624#127—21no—
625#127—21no—
626#127C2×D412yes—
627#127C2×D412yes—
628#127C2×D412yes—
629#127C2×D412yes—
630#127C2412yes—
631#127C2412yes—
632#127C2411yescharacteristic
633#126—28no—
634#126—216no—
635#126—216no—
636#126—216no—
637#126—216no—
638#126—28no—
639#126—22no—
640#126—22no—
641#125—24no—
642#125—22no—
643#125—22no—
644#125—22no—
645#125—22no—
646#125—22no—
647#125—22no—
648#125—22no—
649#125—22no—
650#125—21no—
651#125—21no—
652#125C2412yes—
653#124—24no—
654#124—28no—
655#124—216no—
656#124—216no—
657#124—28no—
658#124—28no—
659#124—28no—
660#124—28no—
661#124—24no—
662#124—28no—
663#124—28no—
664#124—22no—
665#124—22no—
666#124—22no—
667#124—22no—
668#124—21no—
669#124—21no—
670#124C2×D414yes—
671#124C2×D414yes—
672#124C2×D414yes—
673#124C2×D414yes—
674#124C2412yes—
675#123—216no—
676#123—216no—
677#123—216no—
678#123—216no—
679#123—22no—
680#123—22no—
681#123—22no—
682#123—28no—
683#123—28no—
684#123—28no—
685#123—28no—
686#123—28no—
687#123—28no—
688C22⋊Q8—24no—
689C22⋊Q8—28no—
690C22⋊Q8—22no—
691C22⋊Q8—22no—
692C22⋊Q8—22no—
693C22⋊Q8—22no—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8—22no—
697C22⋊Q8—22no—
698C22⋊Q8—22no—
699C22⋊Q8—22no—
700C22⋊Q8—22no—
701C22⋊Q8—22no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—21no—
705C22⋊Q8—21no—
706C22⋊Q8—21no—
707C22⋊Q8—21no—
708C22⋊Q8—24no—
709C22⋊Q8—24no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—28no—
715C22⋊Q8C2414yes—
716C22⋊Q8C2414yes—
717C22⋊Q8C2414yes—
718C22⋊Q8C2414yes—
719C22⋊Q8C24116yes—
720C22⋊Q8C24116yes—
721C22⋊Q8C2412yes—
722C22⋊Q8C2412yes—
723C22⋊Q8C2418yes—
724#121—28no—
725#121—24no—
726#121—24no—
727#121—24no—
728#121—24no—
729#121—28no—
730#121—28no—
731#121—28no—
732#121—28no—
733#121—21no—
734#121—22no—
735#121—22no—
736#121—22no—
737#121—22no—
738#121—22no—
739#121—22no—
740#121—28no—
741#121—28no—
742#121—21no—
743#121—21no—
744#121—21no—
745#121—24no—
746#121—24no—
747#121—24no—
748#121—28no—
749#121—28no—
750#121—28no—
751#121C2×D414yes—
752#121C2×D414yes—
753#121C2×D414yes—
754#121C2×D414yes—
755#121C2×D414yes—
756#121C2×D414yes—
757#121C2×D414yes—
758#121C2×D414yes—
759#121C2412yes—
760#121C2414yes—
761#121C2414yes—
762#121C2418yes—
763#121C2418yes—
764#121C2412yes—
765#121C2418yes—
766#120—22no—
767#120—28no—
768#120—28no—
769#120—28no—
770#120—28no—
771#120—28no—
772#120—28no—
773#120—28no—
774#120—28no—
775C4×Q8—24no—
776C4×Q8—28no—
777C4×Q8—28no—
778C4×Q8—28no—
779C4×Q8—28no—
780C4×Q8—24no—
781C4×Q8—22no—
782C4×Q8—22no—
783C4×Q8—22no—
784C4×Q8—22no—
785C4×Q8—22no—
786C4×Q8—22no—
787C4×Q8—22no—
788C4×Q8—22no—
789C4×Q8—22no—
790C4×Q8—22no—
791C4×Q8—22no—
792C4×Q8—22no—
793C4×Q8—21no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8C2414yes—
798C4×Q8C2414yes—
799C4×Q8C2414yes—
800C4×Q8C2414yes—
801C4×Q8C2412yes—
802C4×Q8C2412yes—
803C4×D4—28no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—24no—
808C4×D4—28no—
809C4×D4—24no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—22no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—24no—
819C4×D4—24no—
820C4×D4—28no—
821C4×D4—22no—
822C4×D4—22no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—22no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4C2×D414yes—
832C4×D4C2×D414yes—
833C4×D4C2×D414yes—
834C4×D4C2×D414yes—
835C4×D4C2414yes—
836C4×D4C2414yes—
837C4×D4C2412yes—
838C4×D4C2412yes—
839C4×D4C2414yes—
840C4×D4C2414yes—
841C4×D4C2414yes—
842C4×D4C2414yes—
843#117—22no—
844#117—22no—
845#117—22no—
846#117—22no—
847#117—22no—
848#117—22no—
849#117—22no—
850#117—22no—
851#117—28no—
852#117—21no—
853#117—21no—
854#117—24no—
855#117—24no—
856#117—22no—
857#117—22no—
858#117—22no—
859#117C24116yes—
860#117C2412yes—
861#117C2418yes—
862C2×C4⋊C4—21no—
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—21no—
868C2×C4⋊C4—21no—
869C2×C4⋊C4—24no—
870C2×C4⋊C4—24no—
871C2×C4⋊C4—22no—
872C2×C4⋊C4—22no—
873C2×C4⋊C4—22no—
874C2×C4⋊C4—22no—
875C2×C4⋊C4—24no—
876C2×C4⋊C4C2×D412yes—
877C2×C4⋊C4C2×D412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2418yes—
882C2×C22⋊C4—22no—
883C2×C22⋊C4—22no—
884C2×C22⋊C4—24no—
885C2×C22⋊C4—24no—
886C2×C22⋊C4—24no—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—22no—
889C2×C22⋊C4—28no—
890C2×C22⋊C4—28no—
891C2×C22⋊C4C2×D414yes—
892C2×C22⋊C4C2×D414yes—
893C2×C42—22no—
894C2×C42—22no—
895C2×C42—24no—
896C2×C42—22no—
897C2×C42C2×D411yescharacteristic
898C2×C42C2×D411yescharacteristic
899C2×C42C2×D411yescharacteristic
900C2×C42C2×D411yescharacteristic
901C2×C42C2×D411yescharacteristic
902C2×C42C2×D411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909#107C2418yes—
910#107C24116yes—
911#107C2418yes—
912#106C2418yes—
913#106C2418yes—
914#106C2418yes—
915#106C2418yes—
916C4⋊C8C2412yes—
917C4⋊C8C2414yes—
918C4⋊C8C2412yes—
919C4⋊C8C2414yes—
920C4⋊C8C2414yes—
921#103C2418yes—
922#103C2418yes—
923#103C2418yes—
924#103C24116yes—
925#103C2418yes—
926#103C2418yes—
927#103C2418yes—
928#103C2418yes—
929#103C2418yes—
930#102C2418yes—
931#102C24116yes—
932#102C2418yes—
933#102C2418yes—
934#102C2418yes—
935C22⋊C8C2412yes—
936C22⋊C8C2414yes—
937C22⋊C8C2412yes—
938C22⋊C8C2414yes—
939C22⋊C8C24116yes—
940C22⋊C8C2414yes—
941C22⋊C8C24116yes—
942#97C2414yes—
943C4×C8C2412yes—
944C4×C8C2414yes—
945C4×C8C2412yes—
946C4×C8C2414yes—
947C24—22no—
948C24—28no—
949C24C22×D411yescharacteristic
950C24C22×D414yes—
951#41—48no—
952#41—48no—
953#41—44no—
954#41—416no—
955#41—48no—
956#41—44no—
957#41—82no—
958#41—84no—
959#41—84no—
960#41—84no—
961#41—84no—
962#41—84no—
963#41—88no—
964#41—88no—
965#41—88no—
966C2×Q8—22no—
967C2×Q8—22no—
968C2×Q8—22no—
969C2×Q8—22no—
970C2×Q8—21no—
971C2×Q8—22no—
972C2×Q8—22no—
973C2×Q8—22no—
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—216no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—416no—
981C2×Q8—416no—
982C2×Q8—44no—
983C2×Q8—82no—
984C2×Q8—82no—
985C2×Q8—88no—
986C2×Q8—816no—
987C2×Q8C22×D414yes—
988C2×Q8C22×D414yes—
989C2×Q8C2512yes—
990C2×Q8C2514yes—
991C2×Q8C2514yes—
992C2×D4—24no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—24no—
999C2×D4—28no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—22no—
1003C2×D4—21no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—21no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4—28no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—416no—
1013C2×D4—82no—
1014C2×D4—82no—
1015C2×D4—88no—
1016C2×D4—88no—
1017C2×D4—88no—
1018C2×D4—82no—
1019C2×D4—84no—
1020C2×D4—88no—
1021C2×D4—84no—
1022C2×D4—816no—
1023C2×D4—816no—
1024C2×D4C22×D414yes—
1025C2×D4C22×D414yes—
1026C2×D4C22×D414yes—
1027C2×D4C22×D414yes—
1028C2×D4C22×D418yes—
1029C2×D4C22×D414yes—
1030C2×D4C22×D414yes—
1031C2×D4C22×D418yes—
1032C2×D4C2512yes—
1033C2×D4C2514yes—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—28no—
1041C22×C4—216no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—42no—
1049C22×C4—48no—
1050C22×C4—42no—
1051C22×C4—84no—
1052C22×C4—88no—
1053C22×C4C22×D411yescharacteristic
1054C22×C4C22×D411yescharacteristic
1055C22×C4C22×D411yescharacteristic
1056C22×C4C22×D411yescharacteristic
1057C22×C4C22×D411yescharacteristic
1058C22×C4C22×D411yescharacteristic
1059C22×C4C22×D411yescharacteristic
1060C22×C4C22×D411yescharacteristic
1061C22×C4C22×D414yes—
1062C22×C4C22×D411yescharacteristic
1063C22×C4C22×D411yescharacteristic
1064C22×C4C22×D411yescharacteristic
1065C22×C4C22×D411yescharacteristic
1066C22×C4C22×D411yescharacteristic
1067C22×C4C22×D411yescharacteristic
1068C22×C4C22×D418yes—
1069C22×C4C22×D411yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2518yes—
1073C22×C4C2511yescharacteristic
1074Q16—48no—
1075Q16—48no—
1076SD16—48no—
1077SD16—48no—
1078SD16—48no—
1079SD16—416no—
1080SD16—48no—
1081M16—44no—
1082M16—416no—
1083C2×C8—44no—
1084C2×C8—416no—
1085C2×C8C2514yes—
1086C2×C8C2514yes—
1087C2×C8C2518yes—
1088C4⋊C4—21no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—28no—
1104C4⋊C4—216no—
1105C4⋊C4—216no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—28no—
1118C4⋊C4—21no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—21no—
1124C4⋊C4—21no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4C22×D414yes—
1128C4⋊C4C22×D414yes—
1129C4⋊C4C22×D414yes—
1130C4⋊C4C22×D414yes—
1131C4⋊C4C2514yes—
1132C4⋊C4C2514yes—
1133C4⋊C4C2512yes—
1134C4⋊C4C2514yes—
1135C4⋊C4C2512yes—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—216no—
1141C22⋊C4—28no—
1142C22⋊C4—216no—
1143C22⋊C4—216no—
1144C22⋊C4—22no—
1145C22⋊C4—22no—
1146C22⋊C4—22no—
1147C22⋊C4—28no—
1148C22⋊C4—22no—
1149C22⋊C4—22no—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—22no—
1157C22⋊C4—22no—
1158C22⋊C4—28no—
1159C22⋊C4—22no—
1160C22⋊C4—22no—
1161C22⋊C4C22×D418yes—
1162C22⋊C4C22×D418yes—
1163C22⋊C4C22×D418yes—
1164C22⋊C4C22×D418yes—
1165C42—22no—
1166C42—22no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—22no—
1172C42—216no—
1173C42—28no—
1174C42C22×D411yescharacteristic
1175C42C22×D411yescharacteristic
1176C42C22×D411yescharacteristic
1177C42C22×D411yescharacteristic
1178C42C22×D411yescharacteristic
1179C42C22×D411yescharacteristic
1180C42C22×D411yescharacteristic
1181C42C22×D411yescharacteristic
1182C42C22×D411yescharacteristic
1183C42C22×D411yescharacteristic
1184C42C22×D411yescharacteristic
1185C42C22×D411yescharacteristic
1186C42C2511yescharacteristic
1187C42C2511yescharacteristic
1188C42C2511yescharacteristic
1189C42C2511yescharacteristic
1190C23—22no—
1191C23—28no—
1192C23—22no—
1193C23—24no—
1194C23—44no—
1195C23—41no—
1196C23—41no—
1197C23—44no—
1198C23—44no—
1199C23—82no—
1200C23—82no—
1201C23—88no—
1202C23—88no—
1203C23—88no—
1204C23C23×D411yescharacteristic
1205C23C23×D411yescharacteristic
1206C23C23×D418yes—
1207C23C23×D411yescharacteristic
1208Q8—24no—
1209Q8—28no—
1210Q8—24no—
1211Q8—24no—
1212Q8—44no—
1213Q8—44no—
1214Q8—44no—
1215Q8—44no—
1216Q8—44no—
1217Q8—44no—
1218Q8—44no—
1219Q8—44no—
1220Q8—44no—
1221Q8—42no—
1222Q8—816no—
1223Q8—82no—
1224Q8—81no—
1225D4—28no—
1226D4—24no—
1227D4—28no—
1228D4—28no—
1229D4—28no—
1230D4—44no—
1231D4—44no—
1232D4—48no—
1233D4—48no—
1234D4—44no—
1235D4—44no—
1236D4—44no—
1237D4—44no—
1238D4—48no—
1239D4—44no—
1240D4—42no—
1241D4—44no—
1242D4—88no—
1243D4—82no—
1244D4—82no—
1245D4—81no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—88no—
1250D4—84no—
1251D4—82no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—216no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—44no—
1277C2×C4—48no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—44no—
1281C2×C4—44no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—44no—
1286C2×C4—48no—
1287C2×C4—44no—
1288C2×C4—84no—
1289C2×C4—88no—
1290C2×C4—82no—
1291C2×C4—816no—
1292C2×C4—88no—
1293C2×C4#57714yes—
1294C2×C4C23×D411yescharacteristic
1295C2×C4C23×D418yes—
1296C2×C4C23×D411yescharacteristic
1297C2×C4C23×D411yescharacteristic
1298C2×C4C23×D411yescharacteristic
1299C2×C4C23×D411yescharacteristic
1300C2×C4C23×D411yescharacteristic
1301C2×C4C23×D411yescharacteristic
1302C2×C4C23×D411yescharacteristic
1303C2×C4C23×D411yescharacteristic
1304C2×C4C23×D411yescharacteristic
1305C2×C4C23×D411yescharacteristic
1306C2×C4C2611yescharacteristic
1307C8—24no—
1308C8—28no—
1309C8—24no—
1310C22—21no—
1311C22—21no—
1312C22—21no—
1313C22—21no—
1314C22—28no—
1315C22—21no—
1316C22—21no—
1317C22—28no—
1318C22—28no—
1319C22—21no—
1320C22—21no—
1321C22—44no—
1322C22—42no—
1323C22—42no—
1324C22—44no—
1325C22—42no—
1326C22—44no—
1327C22—82no—
1328C22—88no—
1329C22—164no—
1330C22—328no—
1331C22C2×#57712yes—
1332C22C24×D411yescharacteristic
1333C4—21no—
1334C4—21no—
1335C4—21no—
1336C4—21no—
1337C4—21no—
1338C4—21no—
1339C4—21no—
1340C4—28no—
1341C4—21no—
1342C4—42no—
1343C4—44no—
1344C4—44no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—44no—
1349C4—44no—
1350C4C2×#57712yes—
1351C4C2×#57712yes—
1352C4#358612yes—
1353C4H(7,𝔽2)12yes—
1354C2—22no—
1355C2—41no—
1356C2—41no—
1357C2—48no—
1358C2—84no—
1359C2—82no—
1360C2#6284211yescharacteristic
1361C2C22×#57711yescharacteristic
1362C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62834C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3550C2semidirect
3. #62345C2semidirect
4. #62343C2semidirect
5. #62326C2semidirect
6. #61803C2semidirect
7. #61789C2semidirect
8. #61739C2semidirect
9. #61722C2semidirect
10. #61701C2semidirect
11. #61680C2semidirect
12. #61662C2semidirect
13. #61593C2semidirect
14. #61584C2semidirect
15. #61562C2semidirect
16. #60969C2semidirect
17. #60952C2semidirect
18. #60947C2semidirect
19. #60941C2semidirect
20. #60758C2semidirect
21. #60236C2semidirect
28. #3550C22semidirect
29. #3550C22semidirect
30. #3550C22semidirect
31. #3550C22semidirect
53. C2×#556C22semidirect
54. C2×#556C22semidirect
55. C2×D4×Q8C22semidirect
56. C2×D4×Q8C22semidirect
59. C2×#536C22semidirect
61. C2×#533C22semidirect
62. C2×#533C22semidirect
65. #3356C22semidirect
66. #3353C22semidirect
67. #3353C22semidirect
68. #3350C22semidirect
69. #3342C22semidirect
70. #3340C22semidirect
71. #3340C22semidirect
72. #3329C22semidirect
73. #3329C22semidirect
74. #3328C22semidirect
75. #3324C22semidirect
76. #3324C22semidirect
77. #3324C22semidirect
78. #3320C22semidirect
79. #3311C22semidirect
80. #3304C22semidirect
81. #3304C22semidirect
82. #3302C22semidirect
83. #3299C22semidirect
84. #3298C22semidirect
85. #3298C22semidirect
86. D4×SD16C22semidirect
87. D4×SD16C22semidirect
88. D4×SD16C22semidirect
89. #3278C22semidirect
90. #3278C22semidirect
91. #3276C22semidirect
92. #3266C22semidirect
93. #3255C22semidirect
94. #3254C22semidirect
95. #3254C22semidirect
96. #3248C22semidirect
97. #3246C22semidirect
98. #3239C22semidirect
99. #3237C22semidirect
100. #3231C22semidirect
101. #3230C22semidirect
102. #3229C22semidirect
103. #3229C22semidirect
104. #3227C22semidirect
105. #3226C22semidirect
106. #3226C22semidirect
107. #3218C22semidirect
108. #3216C22semidirect
109. #3210C22semidirect
110. #3209C22semidirect
111. #3208C22semidirect
112. #3208C22semidirect
113. #3206C22semidirect
114. #3206C22semidirect
115. #3206C22semidirect
116. #3201C22semidirect
117. #3201C22semidirect
118. #3200C22semidirect
119. #3200C22semidirect
120. #3196C22semidirect
121. #3196C22semidirect
122. #3193C22semidirect
123. #3193C22semidirect
124. #3190C22semidirect
125. #3190C22semidirect
126. #3187C22semidirect
127. #3187C22semidirect
128. #3182C22semidirect
129. #3172C22semidirect
130. #3170C22semidirect
131. #3167C22semidirect
132. #3167C22semidirect
133. #3112C22semidirect
134. #3110C22semidirect
135. #3108C22semidirect
136. #3107C22semidirect
137. #3107C22semidirect
138. #3104C22semidirect
139. #3103C22semidirect
140. #3103C22semidirect
141. #3103C22semidirect
142. #3101C22semidirect
143. #3097C22semidirect
144. #3094C22semidirect
145. #3091C22semidirect
146. #3063C22semidirect
147. #3057C22semidirect
148. #3009C22semidirect
149. #3004C22semidirect
150. C2×#448C22semidirect
151. #2981C22semidirect
152. #2979C22semidirect
153. #2975C22semidirect
154. #2974C22semidirect
155. #2972C22semidirect
156. #2935C22semidirect
157. #2931C22semidirect
158. #2920C22semidirect
159. C2×#431C22semidirect
160. #2880C22semidirect

Maximal subgroups

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

subgroupindex
#628342
C2×#35502
#623452
#623432
#623262
#618032
#617892
#617392
#617222
#617012
#616802
#616622
#615932
#615842
#615622
#609692
#609522
#609472
#609412
#607582
#602362