Finite Group Databasebeta

← #6686493

Subgroups — #6686493

Order 512.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3226C211yesmaximal, characteristic, complemented
2C2×#3179C211yesmaximal, characteristic, complemented
3#37764C211yesmaximal, characteristic, complemented
4#37704C211yesmaximal, characteristic, complemented
5#33215C211yesmaximal, characteristic, complemented
6#30681C211yesmaximal, characteristic, complemented
7#30677C211yesmaximal, characteristic, complemented
8#30665C211yesmaximal, characteristic, complemented
9#30661C211yesmaximal, characteristic, complemented
10#30581C211yesmaximal, characteristic, complemented
11#30573C211yesmaximal, characteristic, complemented
12#30565C211yesmaximal, characteristic, complemented
13#30557C211yesmaximal, characteristic, complemented
14#30289C211yesmaximal, characteristic, complemented
15#29846C211yesmaximal, characteristic, complemented
16#28697C211yesmaximal, characteristic, complemented
17#28627C211yesmaximal, characteristic, complemented
18#26566C211yesmaximal, characteristic, complemented
19#26562C211yesmaximal, characteristic, complemented
20#26550C211yesmaximal, characteristic, complemented
21#26546C211yesmaximal, characteristic, complemented
22#26388C211yesmaximal, characteristic, complemented
23#26384C211yesmaximal, characteristic, complemented
24#26372C211yesmaximal, characteristic, complemented
25#26368C211yesmaximal, characteristic, complemented
26#25816C211yesmaximal, characteristic, complemented
27#25685C211yesmaximal, characteristic, complemented
28#25681C211yesmaximal, characteristic, complemented
29#25602C211yesmaximal, characteristic, complemented
30#22230C211yesmaximal, characteristic, complemented
31#21109C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36#3226—28no—
37#3179—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#500C2211yescharacteristic
41C2×#500C2211yescharacteristic
42C2×#496C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#486C2211yescharacteristic
46C2×#486C2211yescharacteristic
47C2×#480C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#480C2211yescharacteristic
50C2×#480C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#469C2211yescharacteristic
56C2×#468C2211yescharacteristic
57C2×#466C2211yescharacteristic
58C2×#465C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×D8C2211yescharacteristic
63C2×#431C2211yescharacteristic
64C2×#405C2211yescharacteristic
65#2851C2211yescharacteristic
66#2850C2211yescharacteristic
67#2731—21no—
68#2729—21no—
69#2717—21no—
70#2716—21no—
71#2708—21no—
72#2686—21no—
73#2674—21no—
74#2671—21no—
75#2660C2211yescharacteristic
76#2640C2211yescharacteristic
77#2628C2211yescharacteristic
78#2628C2211yescharacteristic
79#2537C2211yescharacteristic
80#2535C2211yescharacteristic
81#2492C2211yescharacteristic
82#2491C2211yescharacteristic
83#2481—21no—
84#2452C2211yescharacteristic
85#2451C2211yescharacteristic
86#2443—21no—
87#2443—21no—
88#2436—21no—
89#2430—21no—
90#2422C2211yescharacteristic
91#2422C2211yescharacteristic
92#2420C2211yescharacteristic
93#2420C2211yescharacteristic
94#2419—21no—
95#2417C2211yescharacteristic
96#2416C2211yescharacteristic
97#2409—21no—
98#2406—21no—
99#2361C2211yescharacteristic
100#2360C2211yescharacteristic
101#2349C2211yescharacteristic
102D4×C4⋊C4C2211yescharacteristic
103#2331C2211yescharacteristic
104#2328C2211yescharacteristic
105#2290C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2095C2211yescharacteristic
109#2095C2211yescharacteristic
110#2093C2211yescharacteristic
111#2093C2211yescharacteristic
112#2092C2211yescharacteristic
113#2092C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2083C2211yescharacteristic
117#2083C2211yescharacteristic
118#2068C2211yescharacteristic
119#2067C2211yescharacteristic
120#2066C2211yescharacteristic
121#2065C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2055C2211yescharacteristic
127#2055C2211yescharacteristic
128#2054C2211yescharacteristic
129#2054C2211yescharacteristic
130#2036C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2035C2211yescharacteristic
134#2034C2211yescharacteristic
135#2034C2211yescharacteristic
136#2034C2211yescharacteristic
137#2033C2211yescharacteristic
138#2033C2211yescharacteristic
139#2033C2211yescharacteristic
140#2033C2211yescharacteristic
141#2033C2211yescharacteristic
142#2000C2211yescharacteristic
143#2000C2211yescharacteristic
144#1999C2211yescharacteristic
145#1999C2211yescharacteristic
146#1993C2211yescharacteristic
147#1993C2211yescharacteristic
148#1993C2211yescharacteristic
149#1991C2211yescharacteristic
150#1961C2211yescharacteristic
151#1958C2211yescharacteristic
152#1949C2211yescharacteristic
153#1949C2211yescharacteristic
154#1947C2211yescharacteristic
155#1947C2211yescharacteristic
156#1944C2211yescharacteristic
157#1944C2211yescharacteristic
158#1942C2211yescharacteristic
159#1942C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1923C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1870C2211yescharacteristic
177#1869C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1853C2211yescharacteristic
191#1853C2211yescharacteristic
192#1852C2211yescharacteristic
193#1852C2211yescharacteristic
194#1851C2211yescharacteristic
195#1850C2211yescharacteristic
196#1846C2211yescharacteristic
197#1809C2211yescharacteristic
198#1809C2211yescharacteristic
199#1808C2211yescharacteristic
200#1808C2211yescharacteristic
201#1768C2211yescharacteristic
202#1750C2211yescharacteristic
203#1749C2211yescharacteristic
204#1746C2211yescharacteristic
205C22×#41—21no—
206C23×Q8—21no—
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#542—24no—
214#542—42no—
215#540—24no—
216#540—42no—
217#532—24no—
218#532—42no—
219C2×C4⋊Q8—24no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#126—21no—
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124—21no—
233C2×#124—21no—
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×#121—21no—
248C2×#121—21no—
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4—21no—
268C22×C4⋊C4—21no—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C42C2311yescharacteristic
272#501—24no—
273#501—42no—
274#500—24no—
275#500—24no—
276#496—24no—
277#489—42no—
278#488—24no—
279#486—24no—
280#486D418yescomplemented
281#480—24no—
282#480—24no—
283#480—24no—
284#480—24no—
285#474—24no—
286#474—24no—
287#474—24no—
288#474—24no—
289#469—24no—
290#468—24no—
291#466—24no—
292#465—24no—
293#442—24no—
294#440—24no—
295C4×SD16—24no—
296C4×D8—24no—
297#431—24no—
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352#405—24no—
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358C2×C4×C8C2311yescharacteristic
359#400—21no—
360#400—21no—
361#400—21no—
362#399—21no—
363#399—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#393—21no—
392#393—21no—
393#393—21no—
394#393—21no—
395#393—21no—
396#393—21no—
397#393—21no—
398#392—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391—21no—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#389—21no—
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388D411yescharacteristic
426#388D411yescharacteristic
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387D411yescharacteristic
434#387D411yescharacteristic
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386D411yescharacteristic
449#386D411yescharacteristic
450#385—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385D411yescharacteristic
462#385D411yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#381—21no—
470#381—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380—21no—
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—21no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487#376C2311yescharacteristic
488C2×#95—21no—
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C2×#41—44no—
516C2×#41—82no—
517C2×#41—82no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—44no—
524C22×Q8—82no—
525C22×Q8—82no—
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C2×D411yescharacteristic
549C23×C4C2×D411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—41no—
563C2×D8—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8—41no—
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—44no—
588C4⋊Q8—44no—
589C4⋊Q8C2×D414yes—
590#127—22no—
591#127C2×D414yes—
592#126—44no—
593#125—22no—
594#125—22no—
595#124—22no—
596#124—22no—
597#124—44no—
598#124—44no—
599#124—82no—
600#123—44no—
601#123—44no—
602#123—44no—
603#123—82no—
604#123—82no—
605C22⋊Q8—22no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—44no—
610C22⋊Q8—82no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—44no—
617#121—44no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—44no—
626#121—82no—
627#121—82no—
628C4×Q8—22no—
629C4×Q8—41no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—44no—
647C4×D4—82no—
648#117—22no—
649#117—22no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—44no—
679C2×C4⋊C4—82no—
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—22no—
739C2×C42—22no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750#107—22no—
751#107—22no—
752#107—22no—
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#107—22no—
758#107—22no—
759#107—22no—
760#107—41no—
761#107—41no—
762#107—41no—
763#107—41no—
764#106—22no—
765#106—22no—
766#106—41no—
767#106—41no—
768#106—41no—
769#106—41no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774#103—22no—
775#103—22no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102C2×D414yes—
795#102C2×D414yes—
796#102C2×D414yes—
797#102C2×D414yes—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—22no—
801C22⋊C8—22no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804#97—22no—
805#97—22no—
806#97—22no—
807C4×C8—22no—
808C4×C8—22no—
809C4×C8C2×D414yes—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855#41—816no—
856C2×Q8—24no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—816no—
878C2×D4—22no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4C22×D412yes—
922C2×D4C22×D412yes—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C2511yescharacteristic
994SD16—44no—
995SD16—44no—
996D8—44no—
997D8—44no—
998M16—44no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—44no—
1020C2×C8C22×D412yes—
1021C2×C8C22×D412yes—
1022C2×C82−1+412yes—
1023C2×C82−1+412yes—
1024C4⋊C4—24no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4C22×D412yes—
1076C4⋊C4C22×D412yes—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C42—22no—
1119C42—22no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—42no—
1129C42—81no—
1130C42—81no—
1131C42C22×D412yes—
1132C42H(5,𝔽2)12yes—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23#57612yes—
1168C23C23×D411yescharacteristic
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—84no—
1174Q8—84no—
1175Q8—84no—
1176Q8—84no—
1177Q8—84no—
1178D4—22no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4—84no—
1192D4—82no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199C2×C4—28no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—44no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—84no—
1285C2×C4—84no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4D4212yes—
1291C2×C4D4212yes—
1292C2×C4#57612yes—
1293C2×C4C23×D411yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×2−1+411yescharacteristic
1296C2×C4C2×2−1+411yescharacteristic
1297C2×C4#58511yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—22no—
1300C8—22no—
1301C8—22no—
1302C8—22no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—42no—
1322C22—42no—
1323C22—41no—
1324C22—42no—
1325C22—42no—
1326C22—41no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22#344911yescharacteristic
1343C22C2×D4211yescharacteristic
1344C22#349911yescharacteristic
1345C22C2×#57611yescharacteristic
1346C22C2×#57611yescharacteristic
1347C22#358611yescharacteristic
1348C22#358611yescharacteristic
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—42no—
1360C4—42no—
1361C4—41no—
1362C4—41no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4#348911yescharacteristic
1375C4#348911yescharacteristic
1376C4#355411yescharacteristic
1377C4#355411yescharacteristic
1378C2—42no—
1379C2—81no—
1380C2—82no—
1381C2—82no—
1382C2—161no—
1383C2#3768011yescharacteristic
1384C2#6097611yescharacteristic
1385C2#6098811yescharacteristic
1386C2#6104911yescharacteristic
1387C2#6106011yescharacteristic
1388C2#6251511yescharacteristic
1389C2#6252011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3226C2semidirect
2. C2×#3179C2semidirect
3. #37764C2semidirect
4. #37704C2semidirect
5. #33215C2semidirect
6. #30681C2semidirect
7. #30677C2semidirect
8. #30665C2semidirect
9. #30661C2semidirect
10. #30581C2semidirect
11. #30573C2semidirect
12. #30565C2semidirect
13. #30557C2semidirect
14. #30289C2semidirect
15. #29846C2semidirect
16. #28697C2semidirect
17. #28627C2semidirect
18. #26566C2semidirect
19. #26562C2semidirect
20. #26550C2semidirect
21. #26546C2semidirect
22. #26388C2semidirect
23. #26384C2semidirect
24. #26372C2semidirect
25. #26368C2semidirect
26. #25816C2semidirect
27. #25685C2semidirect
28. #25681C2semidirect
29. #25602C2semidirect
30. #22230C2semidirect
31. #21109C2semidirect
280. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32262
C2×#31792
#377642
#377042
#332152
#306812
#306772
#306652
#306612
#305812
#305732
#305652
#305572
#302892
#298462
#286972
#286272
#265662
#265622
#265502
#265462
#263882
#263842
#263722
#263682
#258162
#256852
#256812
#256022
#222302
#211092