Finite Group Databasebeta

← #10576726

Subgroups — #10576726

Order 512.

6758 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62860C211yesmaximal, characteristic, complemented
2#62855C211yesmaximal, characteristic, complemented
3#61418C218yesmaximal, complemented
4#61417C218yesmaximal, complemented
5#61415C218yesmaximal, complemented
6#61412C218yesmaximal, complemented
7#61410C218yesmaximal, complemented
8#61407C218yesmaximal, complemented
9#60643C211yesmaximal, characteristic, complemented
10C2×#3154C212yesmaximal, complemented
11#60427C212yesmaximal, complemented
12#60426C212yesmaximal, complemented
13#60424C211yesmaximal, characteristic, complemented
14#60423C211yesmaximal, characteristic, complemented
15#60191C211yesmaximal, characteristic, complemented
16#60167C212yesmaximal, complemented
17C2×#2949C211yesmaximal, characteristic, complemented
18C2×#575C2212yes—
19C22×#137C2212yes—
20C22×AGL(1,ℤ/8)C2212yes—
21C22×#135C2212yes—
22C23×SD16C2211yescharacteristic
23#3510C2218yescomplemented
24#3510C2218yescomplemented
25#3509C2218yescomplemented
26#3508C2218yescomplemented
27#3507C2218yescomplemented
28#3506C2218yescomplemented
29#3495—28no—
30#3494—28no—
31#3491—24no—
32#3490—24no—
33#3461—24no—
34#3460—24no—
35#3458C2211yescharacteristic
36#3449C2211yescharacteristic
37#3449C2211yescharacteristic
38C2×#536C2212yes—
39C2×#535C2212yes—
40#3428C2212yes—
41#3428C2212yes—
42C2×#519C2211yescharacteristic
43C2×#518C2211yescharacteristic
44#3403C22132yescomplemented
45#3402C22132yescomplemented
46#3401C22132yescomplemented
47#3400C22132yescomplemented
48#3399C22116yescomplemented
49#3398C22116yescomplemented
50#3397C22132yescomplemented
51#3394C22116yescomplemented
52#3394C22132yescomplemented
53#3392C22116yescomplemented
54#3156C2214yescomplemented
55#3155C2214yescomplemented
56#3154C2218yes—
57#3154C2218yes—
58#3154C2218yescomplemented
59#3154C2218yescomplemented
60#3154C2214yescomplemented
61#3154C2214yescomplemented
62#3150C2214yescomplemented
63C2×#497C2214yescomplemented
64C2×#496C2214yescomplemented
65#3147C2214yescomplemented
66C2×#495C2214yescomplemented
67C2×#492C2214yescomplemented
68#3046C22116yescomplemented
69#3045C22116yescomplemented
70#3044C2218yescomplemented
71#3044C2218yescomplemented
72#3043C2218yescomplemented
73#3043C2218yescomplemented
74#3042C2218yescomplemented
75#3042C2218yescomplemented
76#3041C2218yescomplemented
77#3041C2218yescomplemented
78#3040C2218yescomplemented
79#3040C2218yescomplemented
80#3039C2218yescomplemented
81#3038C2218yescomplemented
82#3037C2218yescomplemented
83#3036C2218yescomplemented
84#2961C2214yescomplemented
85#2961C2218yescomplemented
86#2960C2214yescomplemented
87#2960C2218yescomplemented
88#2952C2218yescomplemented
89#2951C2218yescomplemented
90#2950C2214yescomplemented
91#2949C2218yescomplemented
92#2949C2218yescomplemented
93#2949C2214yescomplemented
94#2949C2214yescomplemented
95#2948C2214yescomplemented
96#2943C2218yescomplemented
97C2×#440C2214yescomplemented
98C4×#135C2218yescomplemented
99C2×C4×SD16C2214yescomplemented
100C2×#427C2211yescharacteristic
101#2905C2211yescharacteristic
102#2905C2212yes—
103#2896C2212yes—
104#2896C2212yes—
105C2×#419C2211yescharacteristic
106C2×#418C2211yescharacteristic
107C2×#405C2211yescharacteristic
108C2×#405C2212yes—
109C22×#41C2312yes—
110C22×#41C2312yes—
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113#575—48no—
114C2×#137—48no—
115C2×#137C2318yes—
116C2×#137C2318yes—
117C2×#137C2314yes—
118C2×#137C2314yes—
119C2×AGL(1,ℤ/8)—48no—
120C2×AGL(1,ℤ/8)C2318yes—
121C2×AGL(1,ℤ/8)C2318yes—
122C2×AGL(1,ℤ/8)C2314yes—
123C2×AGL(1,ℤ/8)C2314yes—
124C2×#135—216no—
125C2×#135C2314yes—
126C2×#135C2314yes—
127C2×#135C2314yes—
128C2×#135C2314yes—
129C2×#135C2318yes—
130C22×Q16C2312yes—
131C22×Q16C2314yes—
132C22×SD16—28no—
133C22×SD16C2312yes—
134C22×SD16C2314yes—
135C22×SD16C2312yes—
136C22×SD16C2314yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2314yes—
140C22×SD16C2314yes—
141C22×D8C2312yes—
142C22×D8C2314yes—
143C22×M16C2311yescharacteristic
144C22×M16C2312yes—
145C23×C8C2311yescharacteristic
146#559C23132yes—
147#559C23116yescomplemented
148#557C23116yescomplemented
149#556—28no—
150#556C23116yes—
151#556C23132yescomplemented
152#555—28no—
153#554—28no—
154#553—216no—
155#552—216no—
156#552—232no—
157#551—232no—
158#551—232no—
159#550C23116yes—
160#547—28no—
161#546—232no—
162#544D414yes—
163#544D418yes—
164#543D414yes—
165#542—216no—
166#542—216no—
167#541—216no—
168#540—216no—
169#539—216no—
170#538—216no—
171#537—22no—
172#537—22no—
173#536—24no—
174#536—24no—
175#536C2318yes—
176#536C2318yes—
177#536C2314yes—
178#536C2314yes—
179#535—24no—
180#535—24no—
181#535C2318yes—
182#535C2318yes—
183#535C2314yes—
184#535C2314yes—
185#534—22no—
186#534—22no—
187#533—216no—
188#533C2314yes—
189#533C2318yes—
190#532—216no—
191#532C2314yes—
192#532C2314yes—
193C2×C4⋊Q8C2314yes—
194C2×#127C2314yes—
195#529—216no—
196#529—216no—
197#529—216no—
198C2×#124C2314yes—
199C2×#124C2314yes—
200#525—216no—
201#525—24no—
202#525—24no—
203C2×#123—24no—
204C2×C22⋊Q8—24no—
205C2×#121—24no—
206C2×#120—24no—
207#520—24no—
208#520—24no—
209#520C2318yes—
210#520C2318yes—
211#519—24no—
212#519C2318yes—
213#519C2314yes—
214#519C2314yes—
215#518—24no—
216#518—24no—
217#518—24no—
218#518C2318yes—
219#518C2314yes—
220#518C2314yes—
221C4×#41—24no—
222C4×#41—24no—
223C4×#41C2318yes—
224C4×#41C2318yes—
225C2×C4×Q8—22no—
226C2×C4×Q8C2314yes—
227C2×C4×D4—22no—
228C2×C4×D4C2314yes—
229C2×#117—24no—
230C2×#117—24no—
231C2×#117—22no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2312yes—
236C22×C22⋊C4—22no—
237#497C23116yes—
238#497C23116yes—
239#497C2318yescomplemented
240#497C2318yescomplemented
241#496C23116yes—
242#496C23116yes—
243#496C2318yescomplemented
244#496C2318yescomplemented
245#495C23116yes—
246#495C23116yes—
247#495C2318yescomplemented
248#495C2318yescomplemented
249#494C2314yescomplemented
250#493C2314yescomplemented
251#492C23116yes—
252#492C23116yes—
253#492C2314yescomplemented
254#492C2314yescomplemented
255#464C23132yes—
256#464C23132yescomplemented
257#464C23132yescomplemented
258#463C23132yes—
259#463C23132yes—
260#463C23132yescomplemented
261#462C23132yescomplemented
262#462C23116yescomplemented
263#461C23116yes—
264#461C23132yescomplemented
265#460C23132yes—
266#460C23116yescomplemented
267#459C23132yes—
268#459C23116yes—
269#446C23132yescomplemented
270#446C23116yescomplemented
271C8×Q8C23116yescomplemented
272#442C23116yescomplemented
273#441C23116yescomplemented
274#440C23132yes—
275#440C23116yescomplemented
276#440C23116yescomplemented
277C4×Q16C23116yescomplemented
278C4×SD16C23116yes—
279C4×SD16C23116yes—
280C4×SD16C23116yescomplemented
281C4×SD16C23116yescomplemented
282C4×D8C23116yescomplemented
283#427C2314yes—
284#427C2314yes—
285C2×#107C2312yes—
286C2×#106C2312yes—
287#424C2318yes—
288#424C2318yes—
289#424C2318yes—
290#423C2314yes—
291#423C2318yes—
292#419C2318yes—
293#419C2314yes—
294#419C2314yes—
295#418C2318yes—
296#418C2314yes—
297#418C2314yes—
298#417C2318yes—
299#417C2318yes—
300#416C2318yes—
301#416C2318yes—
302C2×#103C2314yes—
303C2×#102C2314yes—
304#405C2314yes—
305#405C2314yes—
306#405C2314yes—
307#405C2314yes—
308#405C2314yes—
309#405C2314yes—
310C2×#97C2314yes—
311C2×#97C2312yes—
312C2×C4×C8C2314yes—
313C2×C4×C8C2312yes—
314C25—21no—
315C2×#41—216no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—28no—
321C2×#41—28no—
322C2×#41—28no—
323C2×#41—28no—
324C2×#41C2414yes—
325C2×#41C2414yes—
326C2×#41C2414yes—
327C2×#41C2414yes—
328C22×Q8—21no—
329C22×Q8—22no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8C2412yes—
333C22×Q8C2412yes—
334C22×Q8C2414yes—
335C22×Q8C2412yes—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—28no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4C2412yes—
344C22×D4C2412yes—
345C22×D4C2414yes—
346C22×D4C2412yes—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4C2411yescharacteristic
352#137—416no—
353#137—416no—
354#137—48no—
355#137—48no—
356AGL(1,ℤ/8)—416no—
357AGL(1,ℤ/8)—416no—
358AGL(1,ℤ/8)—48no—
359AGL(1,ℤ/8)—48no—
360#135—216no—
361#135—216no—
362#135—216no—
363#135—216no—
364#135—416no—
365C2×Q16—28no—
366C2×Q16—48no—
367C2×Q16C2414yes—
368C2×Q16C2414yes—
369C2×Q16C24116yes—
370C2×Q16C2418yes—
371C2×SD16—216no—
372C2×SD16—216no—
373C2×SD16—28no—
374C2×SD16—28no—
375C2×SD16—28no—
376C2×SD16—28no—
377C2×SD16—48no—
378C2×SD16—48no—
379C2×SD16C2414yes—
380C2×SD16C2414yes—
381C2×SD16C2418yes—
382C2×SD16C2414yes—
383C2×SD16C2414yes—
384C2×SD16C2414yes—
385C2×SD16C2414yes—
386C2×SD16C24116yes—
387C2×SD16C24116yes—
388C2×SD16C2418yes—
389C2×SD16C2418yes—
390C2×D8—28no—
391C2×D8—48no—
392C2×D8C2414yes—
393C2×D8C2414yes—
394C2×D8C24116yes—
395C2×D8C2418yes—
396C2×M16—28no—
397C2×M16—24no—
398C2×M16C2414yes—
399C2×M16C2414yes—
400C2×M16C2414yes—
401C22×C8#4118yescomplemented
402C22×C8C2414yes—
403C22×C8C2412yes—
404C22×C8C2412yes—
405C22×C8C2412yes—
406C22×C8C2411yescharacteristic
407C22×C8C2411yescharacteristic
408C4⋊Q8—28no—
409C4⋊Q8C2×D4116yes—
410C4⋊Q8C2×D418yes—
411C4⋊Q8C24116yes—
412C4⋊Q8C2414yes—
413C4⋊Q8C2414yes—
414#127—28no—
415#127C24116yes—
416#127C2414yes—
417#127C2414yes—
418#126—232no—
419#126—232no—
420#126—232no—
421#125—216no—
422#125—232no—
423#125C2×D4116yes—
424#125C2×D418yes—
425#124—216no—
426#124—232no—
427#124—28no—
428#124—28no—
429#124C24116yes—
430#124C24116yes—
431#124C2418yes—
432#124C2418yes—
433#123—232no—
434#123—232no—
435#123—232no—
436#123—216no—
437#123—216no—
438#123—28no—
439#123—28no—
440C22⋊Q8—216no—
441C22⋊Q8—232no—
442C22⋊Q8—216no—
443C22⋊Q8—216no—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8C2×D4116yes—
447C22⋊Q8C2×D4132yes—
448#121—28no—
449#121—28no—
450#121—216no—
451#121—216no—
452#121—28no—
453#121—28no—
454#121—216no—
455#121—232no—
456#120—216no—
457#120—216no—
458#120—28no—
459#120—28no—
460C4×Q8—216no—
461C4×Q8—216no—
462C4×Q8—28no—
463C4×Q8—28no—
464C4×Q8—28no—
465C4×Q8C24116yes—
466C4×Q8C24116yes—
467C4×Q8C24116yes—
468C4×Q8C24116yes—
469C4×D4—216no—
470C4×D4—216no—
471C4×D4—216no—
472C4×D4—28no—
473C4×D4—28no—
474C4×D4—232no—
475C4×D4—216no—
476C4×D4—216no—
477C4×D4—216no—
478C4×D4—28no—
479C4×D4—28no—
480C4×D4—28no—
481C4×D4C24116yes—
482C4×D4C24116yes—
483C4×D4C24116yes—
484#117—22no—
485#117—22no—
486#117—28no—
487#117—28no—
488#117—216no—
489#117—232no—
490#117—28no—
491#117—28no—
492#117—216no—
493#117—28no—
494#117—28no—
495#117C2×D414yes—
496#117C2×D414yes—
497#117C2×D414yes—
498#117C2414yes—
499#117C2414yes—
500#117C2414yes—
501#117C2414yes—
502#117C2414yes—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—28no—
507C2×C4⋊C4C2×D412yes—
508C2×C4⋊C4C2×D414yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—28no—
516C2×C22⋊C4—216no—
517C2×C22⋊C4—28no—
518C2×C22⋊C4—28no—
519C2×C22⋊C4C2×D412yes—
520C2×C22⋊C4C2×D414yes—
521C2×C42—24no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42—28no—
525C2×C42—28no—
526C2×C42C2412yes—
527C2×C42C2414yes—
528#107C2418yes—
529#106C2414yes—
530#106C2414yes—
531C4⋊C8C24132yes—
532C4⋊C8C24116yes—
533#103C24116yes—
534#103C24116yes—
535#103C24116yes—
536#102C24116yes—
537#102C24116yes—
538#102C24116yes—
539#97C2418yes—
540#97C2418yes—
541#97C2418yes—
542C4×C8C2418yes—
543C4×C8C2414yes—
544C4×C8C2414yes—
545C4×C8C2418yes—
546C24—22no—
547C24—24no—
548C24—22no—
549C24—22no—
550C24—44no—
551C24—162no—
552C24C22×D411yescharacteristic
553#41—28no—
554#41—28no—
555#41—28no—
556#41—28no—
557#41—28no—
558#41—28no—
559#41—28no—
560#41—28no—
561#41—48no—
562#41—48no—
563#41—48no—
564#41—48no—
565#41—1616no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—24no—
569C2×Q8—22no—
570C2×Q8—28no—
571C2×Q8—24no—
572C2×Q8—24no—
573C2×Q8—24no—
574C2×Q8—24no—
575C2×Q8—28no—
576C2×Q8—24no—
577C2×Q8—24no—
578C2×Q8—48no—
579C2×Q8—44no—
580C2×Q8C22×D4116yes—
581C2×Q8C2514yes—
582C2×Q8C2514yes—
583C2×Q8C2514yes—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—24no—
591C2×D4—22no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—232no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—28no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—28no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—48no—
604C2×D4—48no—
605C2×D4—48no—
606C2×D4—44no—
607C2×D4—168no—
608C2×D4C2514yes—
609C2×D4C2514yes—
610C2×D4C2514yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—216no—
622C22×C4—216no—
623C22×C4—216no—
624C22×C4—44no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—164no—
628C22×C4C22×D414yes—
629C22×C4C22×D418yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D412yes—
632C22×C4C2×#4114yes—
633C22×C4H(5,𝔽2)14yes—
634C22×C4C2511yescharacteristic
635C22×C4C2512yes—
636Q16—28no—
637Q16—28no—
638Q16—416no—
639Q16—48no—
640SD16—28no—
641SD16—216no—
642SD16—28no—
643SD16—28no—
644SD16—28no—
645SD16—28no—
646SD16—28no—
647SD16—416no—
648SD16—416no—
649SD16—48no—
650SD16—48no—
651D8—28no—
652D8—28no—
653D8—416no—
654D8—48no—
655M16—28no—
656M16—28no—
657M16—28no—
658C2×C8—28no—
659C2×C8—24no—
660C2×C8C2×#4118yes—
661C2×C8C2×#4118yes—
662C2×C8C2×#4114yes—
663C2×C8C2×#4114yes—
664C2×C8C2518yes—
665C2×C8C2514yes—
666C2×C8C2511yescharacteristic
667C2×C8C2511yescharacteristic
668C2×C8C2512yes—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—216no—
672C4⋊C4—216no—
673C4⋊C4—216no—
674C4⋊C4—232no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4C22×D418yes—
678C4⋊C4C22×D418yes—
679C4⋊C4C22×D418yes—
680C4⋊C4C22×D4116yes—
681C4⋊C4C22×D4132yes—
682C4⋊C4C2514yes—
683C4⋊C4C2514yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—216no—
687C22⋊C4—216no—
688C22⋊C4—216no—
689C22⋊C4—232no—
690C22⋊C4—232no—
691C22⋊C4—216no—
692C22⋊C4—216no—
693C22⋊C4C22×D418yes—
694C22⋊C4C22×D418yes—
695C22⋊C4C22×D418yes—
696C42—24no—
697C42—24no—
698C42—216no—
699C42—216no—
700C42—216no—
701C42C22×D418yes—
702C42C22×D414yes—
703C42C2518yes—
704C42C2514yes—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—84no—
714C23—84no—
715C23—88no—
716C23—84no—
717C23—168no—
718C23#55014yes—
719C23C23×D412yes—
720C23C23×D411yescharacteristic
721Q8—24no—
722Q8—24no—
723Q8—24no—
724Q8—24no—
725Q8—24no—
726Q8—24no—
727Q8—416no—
728Q8—44no—
729Q8—48no—
730Q8—44no—
731Q8—44no—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—24no—
738D4—48no—
739D4—48no—
740D4—48no—
741D4—48no—
742D4—44no—
743D4—48no—
744D4—44no—
745D4—44no—
746D4—88no—
747D4—832no—
748D4—88no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—44no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—816no—
765C2×C4—816no—
766C2×C4—816no—
767C2×C4—82no—
768C2×C4—82no—
769C2×C4#55018yes—
770C2×C4#55014yes—
771C2×C4C23×D4116yes—
772C2×C4C23×D418yes—
773C2×C4C23×D412yes—
774C2×C4C23×D411yescharacteristic
775C2×C4C22×#4114yes—
776C2×C4C22×#4112yes—
777C2×C4C2×H(5,𝔽2)14yes—
778C2×C4C2×H(5,𝔽2)12yes—
779C2×C4C2611yescharacteristic
780C8—28no—
781C8—24no—
782C8C22×#4112yes—
783C8C22×#4114yes—
784C8C22×#4112yes—
785C22—22no—
786C22—24no—
787C22—44no—
788C22—48no—
789C22—48no—
790C22—48no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—88no—
795C22—164no—
796C22—164no—
797C22—168no—
798C22C2×#55014yes—
799C22C2×#55012yes—
800C22C24×D411yescharacteristic
801C4—28no—
802C4—216no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4C2×#55012yes—
809C4C2×#55014yes—
810C4C23×#4111yescharacteristic
811C4C22×H(5,𝔽2)11yescharacteristic
812C2—22no—
813C2—24no—
814C2—84no—
815C2—84no—
816C2—84no—
817C2C22×#55011yescharacteristic
818C2#6309212yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3458 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62860C2semidirect
2. #62855C2semidirect
3. #61418C2semidirect
4. #61417C2semidirect
5. #61415C2semidirect
6. #61412C2semidirect
7. #61410C2semidirect
8. #61407C2semidirect
9. #60643C2semidirect
10. C2×#3154C2semidirect
11. #60427C2semidirect
12. #60426C2semidirect
13. #60424C2semidirect
14. #60423C2semidirect
15. #60191C2semidirect
16. #60167C2semidirect
17. C2×#2949C2semidirect
23. #3510C22semidirect
24. #3510C22semidirect
25. #3509C22semidirect
26. #3508C22semidirect
27. #3507C22semidirect
28. #3506C22semidirect
44. #3403C22semidirect
45. #3402C22semidirect
46. #3401C22semidirect
47. #3400C22semidirect
48. #3399C22semidirect
49. #3398C22semidirect
50. #3397C22semidirect
51. #3394C22semidirect
52. #3394C22semidirect
53. #3392C22semidirect
54. #3156C22semidirect
55. #3155C22semidirect
58. #3154C22semidirect
59. #3154C22semidirect
60. #3154C22semidirect
61. #3154C22semidirect
62. #3150C22semidirect
63. C2×#497C22semidirect
64. C2×#496C22semidirect
65. #3147C22semidirect
66. C2×#495C22semidirect
67. C2×#492C22semidirect
68. #3046C22semidirect
69. #3045C22semidirect
70. #3044C22semidirect
71. #3044C22semidirect
72. #3043C22semidirect
73. #3043C22semidirect
74. #3042C22semidirect
75. #3042C22semidirect
76. #3041C22semidirect
77. #3041C22semidirect
78. #3040C22semidirect
79. #3040C22semidirect
80. #3039C22semidirect
81. #3038C22semidirect
82. #3037C22semidirect
83. #3036C22semidirect
84. #2961C22semidirect
85. #2961C22semidirect
86. #2960C22semidirect
87. #2960C22semidirect
88. #2952C22semidirect
89. #2951C22semidirect
90. #2950C22semidirect
91. #2949C22semidirect
92. #2949C22semidirect
93. #2949C22semidirect
94. #2949C22semidirect
95. #2948C22semidirect
96. #2943C22semidirect
97. C2×#440C22semidirect
98. C4×#135C22semidirect
99. C2×C4×SD16C22semidirect
147. #559C23semidirect
148. #557C23semidirect
151. #556C23semidirect
239. #497C23semidirect
240. #497C23semidirect
243. #496C23semidirect
244. #496C23semidirect
247. #495C23semidirect
248. #495C23semidirect
249. #494C23semidirect
250. #493C23semidirect
253. #492C23semidirect
254. #492C23semidirect
256. #464C23semidirect
257. #464C23semidirect
260. #463C23semidirect
261. #462C23semidirect
262. #462C23semidirect
264. #461C23semidirect
266. #460C23semidirect
269. #446C23semidirect
270. #446C23semidirect
271. C8×Q8C23semidirect
272. #442C23semidirect
273. #441C23semidirect
275. #440C23semidirect
276. #440C23semidirect
277. C4×Q16C23semidirect
280. C4×SD16C23semidirect
281. C4×SD16C23semidirect
282. C4×D8C23semidirect
401. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#628602
#628552
#614182
#614172
#614152
#614122
#614102
#614072
#606432
C2×#31542
#604272
#604262
#604242
#604232
#601912
#601672
C2×#29492