Finite Group Databasebeta

← #7614418

Subgroups — #7614418

Order 512.

1875 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3377C211yesmaximal, characteristic, complemented
2C2×#3323C211yesmaximal, characteristic
3#45300C211yesmaximal, characteristic, complemented
4#45084C211yesmaximal, characteristic
5#31099C211yesmaximal, characteristic, complemented
6#31094C211yesmaximal, characteristic, complemented
7#30467C211yesmaximal, characteristic, complemented
8#30464C211yesmaximal, characteristic, complemented
9#28920C211yesmaximal, characteristic, complemented
10#28915C211yesmaximal, characteristic, complemented
11#28215C211yesmaximal, characteristic, complemented
12#28195C211yesmaximal, characteristic, complemented
13#28173C211yesmaximal, characteristic, complemented
14#28151C211yesmaximal, characteristic, complemented
15#27284C211yesmaximal, characteristic, complemented
16#27281C211yesmaximal, characteristic, complemented
17#27252C211yesmaximal, characteristic, complemented
18#27238C211yesmaximal, characteristic, complemented
19#26988C211yesmaximal, characteristic, complemented
20#26983C211yesmaximal, characteristic, complemented
21#26952C211yesmaximal, characteristic, complemented
22#26946C211yesmaximal, characteristic, complemented
23#24346C211yesmaximal, characteristic, complemented
24#24259C211yesmaximal, characteristic
25#24207C211yesmaximal, characteristic, complemented
26#24139C211yesmaximal, characteristic, complemented
27#22867C211yesmaximal, characteristic, complemented
28#22864C211yesmaximal, characteristic, complemented
29#21703C211yesmaximal, characteristic, complemented
30#21643C211yesmaximal, characteristic, complemented
31#21636C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#556C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×#546C2211yescharacteristic
36#3377—28no—
37#3323—28no—
38C2×#497C2211yescharacteristic
39C2×#491C2211yescharacteristic, complemented
40C2×#489C2211yescharacteristic
41C2×#488C2211yescharacteristic
42C2×#481C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#479C2211yescharacteristic, complemented
45C2×#477C2211yescharacteristic, complemented
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#470C2211yescharacteristic
49C2×#468C2211yescharacteristic
50C2×#464C2211yescharacteristic
51C2×#464C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#462C2211yescharacteristic, complemented
54C2×#452C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#446C2211yescharacteristic, complemented
59C2×#441C2211yescharacteristic, complemented
60C2×#441C2211yescharacteristic, complemented
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic, complemented
64C2×C4×SD16C2211yescharacteristic
65C2×#436C2211yescharacteristic
66C2×#417C2211yescharacteristic
67C2×#418C2211yescharacteristic
68#2725—21no—
69#2719—21no—
70#2716—21no—
71#2707—21no—
72#2695—21no—
73#2691—21no—
74#2685—21no—
75#2681—21no—
76#2582C2211yescharacteristic, complemented
77#2538C2211yescharacteristic
78#2538C2211yescharacteristic
79#2538C2211yescharacteristic
80#2492C2211yescharacteristic, complemented
81#2489C2211yescharacteristic
82#2480—21no—
83#2475—21no—
84#2470—21no—
85#2458—21no—
86#2453—21no—
87#2442C2211yescharacteristic, complemented
88#2439—21no—
89#2439C2211yescharacteristic
90#2437—21no—
91#2435C2211yescharacteristic
92#2432C2211yescharacteristic
93#2429C2211yescharacteristic
94#2429C2211yescharacteristic
95#2429C2211yescharacteristic, complemented
96#2427C2211yescharacteristic
97#2423C2211yescharacteristic
98#2422C2211yescharacteristic
99#2411—21no—
100#2398C2211yescharacteristic
101#2362C2211yescharacteristic
102#2360C2211yescharacteristic, complemented
103#2341C2211yescharacteristic
104D4×C22⋊C4C2211yescharacteristic
105#2330C2211yescharacteristic, complemented
106#2327C2211yescharacteristic, complemented
107#2326C2211yescharacteristic
108#2326C2211yescharacteristic
109#2088C2211yescharacteristic, complemented
110#2088C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2083C2211yescharacteristic, complemented
113#2075C2211yescharacteristic
114#2075C2211yescharacteristic, complemented
115#2074C2211yescharacteristic, complemented
116#2073C2211yescharacteristic
117#2059C2211yescharacteristic, complemented
118#2057C2211yescharacteristic, complemented
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2043C2211yescharacteristic, complemented
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic, complemented
127#2035C2211yescharacteristic
128#2033C2211yescharacteristic
129#2025C2211yescharacteristic
130#2023C2211yescharacteristic
131#2016C2211yescharacteristic, complemented
132#2016C2211yescharacteristic, complemented
133#2015C2211yescharacteristic
134#2013C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic, complemented
139#2001C2211yescharacteristic, complemented
140#2000C2211yescharacteristic
141#1992C2211yescharacteristic, complemented
142#1985C2211yescharacteristic, complemented
143#1973C2211yescharacteristic
144#1971C2211yescharacteristic, complemented
145#1969C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1959C2211yescharacteristic
148#1958C2211yescharacteristic
149#1956C2211yescharacteristic, complemented
150#1955C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1934C2211yescharacteristic
158#1933C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic, complemented
166#1924C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1894C2211yescharacteristic, complemented
170#1894C2211yescharacteristic, complemented
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1873C2211yescharacteristic
180#1872C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1834C2211yescharacteristic, complemented
189#1832C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic, complemented
203#1753C2211yescharacteristic, complemented
204#1726C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217#557—24no—
218#557—42no—
219#556—24no—
220#556—42no—
221#552—24no—
222#552—42no—
223#546—24no—
224#546—42no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#126—21no—
230C2×#126—21no—
231C2×#126—21no—
232C2×#125—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121—21no—
253C2×#121C2311yescharacteristic
254C2×#120—21no—
255C2×C4×Q8—21no—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117—21no—
269C2×#117—21no—
270C2×#117C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4—21no—
274#497—24no—
275#491—24no—
276#489—24no—
277#488D418yes—
278#485—24no—
279#481—24no—
280#479—24no—
281#478—24no—
282#478—24no—
283#477—24no—
284#470—24no—
285#468—24no—
286#464—24no—
287#464—24no—
288#464—24no—
289#462—24no—
290#452—24no—
291#452—24no—
292#450—24no—
293#450—24no—
294#446—24no—
295#441—24no—
296#441—42no—
297#440—24no—
298#440—42no—
299C4×Q16—24no—
300C4×SD16—24no—
301#436—24no—
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314#418—24no—
315#417—24no—
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362#400—21no—
363#400—21no—
364#400—21no—
365#400D411yescharacteristic
366#400D411yescharacteristic
367#399—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397D411yescharacteristic
379#397D411yescharacteristic
380#396—21no—
381#396—21no—
382#396—21no—
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396—21no—
388#396—21no—
389#396—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394D411yescharacteristic
397#394D411yescharacteristic
398#393—21no—
399#393—21no—
400#393D411yescharacteristic
401#393D411yescharacteristic
402#391—21no—
403#391—21no—
404#391—21no—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#390—21no—
412#390—21no—
413#390—21no—
414#390—21no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#382—21no—
472#382C2311yescharacteristic
473#380—21no—
474#380—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#380C2311yescharacteristic
481#379—21no—
482#379—21no—
483#379—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493#376C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25—21no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8—21no—
526C22×Q8C2×D411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4C2×D411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16#4114yes—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16—41no—
579C2×M16—41no—
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8—41no—
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594C4⋊Q8—44no—
595#126—44no—
596#126—44no—
597#126—44no—
598#125—22no—
599#125—22no—
600#125—41no—
601#125—44no—
602#125—44no—
603#125—44no—
604#125C2×D414yes—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—41no—
609#124—41no—
610#124C2×D414yes—
611#123—44no—
612#123—44no—
613#123—82no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—44no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—82no—
630#121—22no—
631#121—44no—
632#121—41no—
633#120—44no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×Q8—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—44no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659#117—22no—
660#117—44no—
661#117—44no—
662#117—41no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—22no—
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—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4—82no—
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42—21no—
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772#107—22no—
773#107—22no—
774#107—22no—
775#107—41no—
776#106—22no—
777#106—22no—
778#106—22no—
779#106—41no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103C2×D414yes—
803#103C2×D414yes—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—41no—
813#102—41no—
814#102C2×D414yes—
815#102C2×D414yes—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8—22no—
819C22⋊C8—22no—
820C22⋊C8—41no—
821C22⋊C8—41no—
822#97—22no—
823#97—22no—
824#97—22no—
825#97—22no—
826#97—41no—
827C4×C8—41no—
828C4×C8—41no—
829C4×C8C2×D414yes—
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#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868C24—21no—
869C24—21no—
870C24—42no—
871C24—42no—
872C24—42no—
873C24—81no—
874C24—81no—
875C24—81no—
876C24—81no—
877C24C22×D411yescharacteristic
878C24C22×D411yescharacteristic
879#41—44no—
880#41—82no—
881#41—82no—
882#41—82no—
883C2×Q8—22no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—41no—
907C2×Q8—41no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—81no—
911C2×Q8C22×D412yes—
912C2×Q8C2×#4112yes—
913C2×D4—22no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—41no—
925C2×D4—41no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—81no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—82no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4C22×D412yes—
940C2×D4C2×#4112yes—
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—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
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×C4C22×D411yescharacteristic
994C22×C4C2511yescharacteristic
995Q16—44no—
996Q16—44no—
997Q16—44no—
998Q16—82no—
999SD16—44no—
1000SD16—44no—
1001SD16—44no—
1002SD16—82no—
1003M16—82no—
1004M16—82no—
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—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8C22×D412yes—
1027C2×C8C22×D412yes—
1028C2×C8C2×#4112yes—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
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—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
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—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4C22×D412yes—
1088C4⋊C4C22×D412yes—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—81no—
1145C42—81no—
1146C42—81no—
1147C42C22×D412yes—
1148C42H(5,𝔽2)12yes—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—22no—
1163C23—21no—
1164C23—21no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—84no—
1178C23—84no—
1179C23—84no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23C23×D411yescharacteristic
1185Q8—22no—
1186Q8—22no—
1187Q8—22no—
1188Q8—22no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—82no—
1202Q8—84no—
1203D4—22no—
1204D4—22no—
1205D4—22no—
1206D4—22no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—82no—
1212D4—84no—
1213D4—84no—
1214D4—162no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
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—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
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—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4D4212yes—
1305C2×C4D4212yes—
1306C2×C4C23×D411yescharacteristic
1307C2×C4C22×#4111yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C8—22no—
1313C8—22no—
1314C8—22no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—42no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—168no—
1349C22C2×D4211yescharacteristic
1350C22D4×#4111yescharacteristic
1351C22#350011yescharacteristic
1352C22#358511yescharacteristic
1353C22#358611yescharacteristic
1354C22#358611yescharacteristic
1355C22#358611yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4D4×#4111yescharacteristic
1383C4#350011yescharacteristic
1384C4#350511yescharacteristic
1385C4#355111yescharacteristic
1386C2—81no—
1387C2—81no—
1388C2—82no—
1389C2—82no—
1390C2#5981811yescharacteristic
1391C2#6106211yescharacteristic
1392C2#6106411yescharacteristic
1393C2#6150811yescharacteristic
1394C2#6151411yescharacteristic
1395C2#6257111yescharacteristic
1396C2#6257511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3377C2semidirect
3. #45300C2semidirect
5. #31099C2semidirect
6. #31094C2semidirect
7. #30467C2semidirect
8. #30464C2semidirect
9. #28920C2semidirect
10. #28915C2semidirect
11. #28215C2semidirect
12. #28195C2semidirect
13. #28173C2semidirect
14. #28151C2semidirect
15. #27284C2semidirect
16. #27281C2semidirect
17. #27252C2semidirect
18. #27238C2semidirect
19. #26988C2semidirect
20. #26983C2semidirect
21. #26952C2semidirect
22. #26946C2semidirect
23. #24346C2semidirect
25. #24207C2semidirect
26. #24139C2semidirect
27. #22867C2semidirect
28. #22864C2semidirect
29. #21703C2semidirect
30. #21643C2semidirect
31. #21636C2semidirect
32. C2×#557C22semidirect
39. C2×#491C22semidirect
44. C2×#479C22semidirect
45. C2×#477C22semidirect
53. C2×#462C22semidirect
58. C2×#446C22semidirect
59. C2×#441C22semidirect
60. C2×#441C22semidirect
63. C2×C4×Q16C22semidirect
76. #2582C22semidirect
80. #2492C22semidirect
87. #2442C22semidirect
95. #2429C22semidirect
102. #2360C22semidirect
105. #2330C22semidirect
106. #2327C22semidirect
109. #2088C22semidirect
110. #2088C22semidirect
111. #2084C22semidirect
112. #2083C22semidirect
114. #2075C22semidirect
115. #2074C22semidirect
117. #2059C22semidirect
118. #2057C22semidirect
121. #2043C22semidirect
126. #2036C22semidirect
131. #2016C22semidirect
132. #2016C22semidirect
138. #2001C22semidirect
139. #2001C22semidirect
141. #1992C22semidirect
142. #1985C22semidirect
144. #1971C22semidirect
145. #1969C22semidirect
149. #1956C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
158. #1933C22semidirect
159. #1928C22semidirect
160. #1927C22semidirect
165. #1924C22semidirect
166. #1924C22semidirect
169. #1894C22semidirect
170. #1894C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
180. #1872C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
184. #1863C22semidirect
186. #1853C22semidirect
187. #1847C22semidirect
188. #1834C22semidirect
189. #1832C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
196. #1763C22semidirect
198. C4×#103C22semidirect
202. #1753C22semidirect
203. #1753C22semidirect
204. #1726C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33772
C2×#33232
#453002
#450842
#310992
#310942
#304672
#304642
#289202
#289152
#282152
#281952
#281732
#281512
#272842
#272812
#272522
#272382
#269882
#269832
#269522
#269462
#243462
#242592
#242072
#241392
#228672
#228642
#217032
#216432
#216362