Finite Group Databasebeta

← #7199145

Subgroups — #7199145

Order 512.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3377C211yesmaximal, characteristic, complemented
2C2×#3314C211yesmaximal, characteristic
3#45143C211yesmaximal, characteristic, complemented
4#45084C211yesmaximal, characteristic
5#30858C211yesmaximal, characteristic, complemented
6#30853C211yesmaximal, characteristic, complemented
7#30687C211yesmaximal, characteristic, complemented
8#30666C211yesmaximal, characteristic, complemented
9#30651C211yesmaximal, characteristic, complemented
10#30637C211yesmaximal, characteristic, complemented
11#30540C211yesmaximal, characteristic, complemented
12#30531C211yesmaximal, characteristic, complemented
13#28288C211yesmaximal, characteristic, complemented
14#28275C211yesmaximal, characteristic, complemented
15#28258C211yesmaximal, characteristic, complemented
16#28238C211yesmaximal, characteristic, complemented
17#26566C211yesmaximal, characteristic, complemented
18#26559C211yesmaximal, characteristic, complemented
19#25969C211yesmaximal, characteristic, complemented
20#25960C211yesmaximal, characteristic, complemented
21#25176C211yesmaximal, characteristic, complemented
22#25151C211yesmaximal, characteristic, complemented
23#25098C211yesmaximal, characteristic, complemented
24#25084C211yesmaximal, characteristic, complemented
25#24328C211yesmaximal, characteristic, complemented
26#24247C211yesmaximal, characteristic
27#24195C211yesmaximal, characteristic, complemented
28#24122C211yesmaximal, characteristic, complemented
29#23809C211yesmaximal, characteristic, complemented
30#22233C211yesmaximal, characteristic, complemented
31#22217C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#556C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×#546C2211yescharacteristic
36#3377—28no—
37#3314—28no—
38C2×#491C2211yescharacteristic, complemented
39C2×#489C2211yescharacteristic
40C2×#488C2211yescharacteristic
41C2×#484C2211yescharacteristic
42C2×#480C2211yescharacteristic
43C2×#479C2211yescharacteristic, complemented
44C2×#477C2211yescharacteristic, complemented
45C2×#478C2211yescharacteristic
46C2×#474C2211yescharacteristic
47C2×#470C2211yescharacteristic, complemented
48C2×#468C2211yescharacteristic
49C2×#467C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#464C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#462C2211yescharacteristic, complemented
55C2×#462C2211yescharacteristic, complemented
56C2×#461C2211yescharacteristic
57C2×#452C2211yescharacteristic
58C2×#452C2211yescharacteristic
59C2×#450C2211yescharacteristic
60C2×#450C2211yescharacteristic
61C2×#446C2211yescharacteristic, complemented
62C2×#441C2211yescharacteristic, complemented
63C2×#440C2211yescharacteristic
64C2×#440C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic, complemented
66C2×C4×Q16C2211yescharacteristic, complemented
67C2×C4×SD16C2211yescharacteristic
68C2×#435C2211yescharacteristic
69C2×#417C2211yescharacteristic
70C22×#102C2211yescharacteristic
71#2729—21no—
72#2729—21no—
73#2719—21no—
74#2719—21no—
75#2695—21no—
76#2691—21no—
77#2685—21no—
78#2681—21no—
79#2581C2211yescharacteristic, complemented
80#2538C2211yescharacteristic
81#2538C2211yescharacteristic
82#2536C2211yescharacteristic
83#2489C2211yescharacteristic
84#2489C2211yescharacteristic, complemented
85#2480—21no—
86#2470—21no—
87#2460—21no—
88#2460—21no—
89#2442C2211yescharacteristic
90#2442C2211yescharacteristic, complemented
91#2437—21no—
92#2435C2211yescharacteristic
93#2432C2211yescharacteristic
94#2429C2211yescharacteristic
95#2429C2211yescharacteristic
96#2429C2211yescharacteristic, complemented
97#2427C2211yescharacteristic
98#2423C2211yescharacteristic
99#2422C2211yescharacteristic
100#2421—21no—
101#2421—21no—
102#2411—21no—
103#2398C2211yescharacteristic
104#2360C2211yescharacteristic
105#2360C2211yescharacteristic, complemented
106#2341C2211yescharacteristic
107D4×C22⋊C4C2211yescharacteristic
108#2331C2211yescharacteristic, complemented
109#2327C2211yescharacteristic, complemented
110#2326C2211yescharacteristic
111#2326C2211yescharacteristic
112#2097C2211yescharacteristic, complemented
113#2096C2211yescharacteristic, complemented
114#2095C2211yescharacteristic, complemented
115#2092C2211yescharacteristic
116#2068C2211yescharacteristic, complemented
117#2068C2211yescharacteristic, complemented
118#2068C2211yescharacteristic, complemented
119#2067C2211yescharacteristic
120#2067C2211yescharacteristic
121#2067C2211yescharacteristic
122#2066C2211yescharacteristic, complemented
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic, complemented
125#2059C2211yescharacteristic, complemented
126#2056C2211yescharacteristic, complemented
127#2056C2211yescharacteristic, complemented
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2043C2211yescharacteristic, complemented
131#2042C2211yescharacteristic
132#2036C2211yescharacteristic
133#2036C2211yescharacteristic
134#2036C2211yescharacteristic, complemented
135#2036C2211yescharacteristic, complemented
136#2035C2211yescharacteristic
137#2035C2211yescharacteristic
138#2035C2211yescharacteristic, complemented
139#2034C2211yescharacteristic
140#2025C2211yescharacteristic
141#2025C2211yescharacteristic
142#2016C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2013C2211yescharacteristic
148#2001C2211yescharacteristic
149#2001C2211yescharacteristic
150#2001C2211yescharacteristic, complemented
151#2000C2211yescharacteristic
152#1990C2211yescharacteristic, complemented
153#1984C2211yescharacteristic, complemented
154#1983C2211yescharacteristic
155#1983C2211yescharacteristic
156#1973C2211yescharacteristic
157#1968C2211yescharacteristic
158#1958C2211yescharacteristic
159#1954C2211yescharacteristic
160#1947C2211yescharacteristic, complemented
161#1947C2211yescharacteristic, complemented
162#1944C2211yescharacteristic, complemented
163#1942C2211yescharacteristic, complemented
164#1928C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic, complemented
170#1923C2211yescharacteristic
171#1923C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1872C2211yescharacteristic
177#1872C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic, complemented
188#1851C2211yescharacteristic, complemented
189#1851C2211yescharacteristic, complemented
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1847C2211yescharacteristic, complemented
193#1843C2211yescharacteristic, complemented
194#1809C2211yescharacteristic, complemented
195#1807C2211yescharacteristic
196#1805C2211yescharacteristic, complemented
197#1805C2211yescharacteristic, complemented
198#1804C2211yescharacteristic
199#1804C2211yescharacteristic
200#1803C2211yescharacteristic, complemented
201#1803C2211yescharacteristic, complemented
202#1788C2211yescharacteristic
203#1786C2211yescharacteristic
204#1746C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#557—24no—
218#557—42no—
219#556—24no—
220#556—42no—
221#554—24no—
222#554—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×#125—21no—
232C2×#125—21no—
233C2×#125—21no—
234C2×#125C2311yescharacteristic
235C2×#125C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#123—21no—
240C2×#123—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—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×D4—21no—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×#117—21no—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4—21no—
274#491—24no—
275#489D418yes—
276#488—24no—
277#484—24no—
278#480—24no—
279#479—24no—
280#478—24no—
281#477—24no—
282#474—24no—
283#470—42no—
284#468—24no—
285#467—24no—
286#467—42no—
287#464—24no—
288#464—24no—
289#464—24no—
290#462—24no—
291#462—42no—
292#461—42no—
293#452—24no—
294#452—42no—
295#450—24no—
296#450—42no—
297#446—24no—
298#441—24no—
299#440—24no—
300#440—24no—
301C4×Q16—24no—
302C4×Q16—42no—
303C4×SD16—42no—
304#435—24no—
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#107C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325#417—24no—
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#102—24no—
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×C22⋊C8C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×C22⋊C8C2311yescharacteristic
362C2×C22⋊C8C2311yescharacteristic
363C2×C22⋊C8C2311yescharacteristic
364C2×C22⋊C8C2311yescharacteristic
365C2×#97C2311yescharacteristic
366C2×#97C2311yescharacteristic
367C2×C4×C8C2311yescharacteristic
368C2×C4×C8C2311yescharacteristic
369#400—21no—
370#400—21no—
371#400—21no—
372#400—21no—
373#400—21no—
374#400D411yescharacteristic
375#400D411yescharacteristic
376#399—21no—
377#398—21no—
378#398—21no—
379#398—21no—
380#398—21no—
381#398—21no—
382#398—21no—
383#398—21no—
384#397—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#397D411yescharacteristic
389#397D411yescharacteristic
390#396—21no—
391#396—21no—
392#396—21no—
393#396—21no—
394#396—21no—
395#396—21no—
396#396—21no—
397#395—21no—
398#394—21no—
399#394—21no—
400#394—21no—
401#394—21no—
402#394—21no—
403#394—21no—
404#394—21no—
405#394D411yescharacteristic
406#394D411yescharacteristic
407#393D411yescharacteristic
408#393D411yescharacteristic
409#391—21no—
410#391—21no—
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#390—21no—
418#390—21no—
419#390—21no—
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389—21no—
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
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#388—21no—
447#388—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#387—21no—
457#387—21no—
458#387—21no—
459#386—21no—
460#386—21no—
461#386—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385—21no—
466#385—21no—
467#385—21no—
468#385—21no—
469#385—21no—
470#385—21no—
471#385—21no—
472#385—21no—
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#382—21no—
476#382—21no—
477#382C2311yescharacteristic
478#382C2311yescharacteristic
479#380—21no—
480#380—21no—
481#380—21no—
482#380—21no—
483#380—21no—
484#380C2311yescharacteristic
485#380C2311yescharacteristic
486#380C2311yescharacteristic
487#380C2311yescharacteristic
488#379—21no—
489#379—21no—
490#379—21no—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C22⋊C4—21no—
494C4×C22⋊C4—21no—
495C4×C22⋊C4—21no—
496C4×C22⋊C4C2311yescharacteristic
497C4×C22⋊C4C2311yescharacteristic
498C4×C22⋊C4C2311yescharacteristic
499C4×C22⋊C4C2311yescharacteristic
500#376C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#340C2311yescharacteristic
510#340C2311yescharacteristic
511#340C2311yescharacteristic
512#340C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519#336C2311yescharacteristic
520#336C2311yescharacteristic
521C25—21no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—21no—
529C22×Q8C2×D411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4C2×D411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—22no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×M16—22no—
579C2×M16—41no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—22no—
594C4⋊Q8—22no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—44no—
598C4⋊Q8C2×D414yes—
599#126—44no—
600#126—44no—
601#125—22no—
602#125—22no—
603#125—41no—
604#125—41no—
605#125—44no—
606#125—44no—
607#125—44no—
608#124—22no—
609#124—22no—
610#124—22no—
611#124—41no—
612#124—41no—
613#124C2×D414yes—
614#123—44no—
615#123—82no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—44no—
622C22⋊Q8—44no—
623C22⋊Q8—44no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—82no—
634#121—22no—
635#121—44no—
636#121—41no—
637#120—44no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—22no—
642C4×Q8—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—22no—
647C4×Q8—22no—
648C4×Q8—22no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—44no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—44no—
664#117—44no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
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—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
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—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773#107—22no—
774#107—22no—
775#107—22no—
776#107—22no—
777#107—22no—
778#107—41no—
779#107—41no—
780#107—41no—
781#106—22no—
782#106—41no—
783#106—41no—
784#106—41no—
785C4⋊C8—22no—
786C4⋊C8—22no—
787C4⋊C8—22no—
788C4⋊C8—22no—
789C4⋊C8—41no—
790C4⋊C8—41no—
791C4⋊C8—41no—
792C4⋊C8—41no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—41no—
803#103—41no—
804#103—41no—
805#103—41no—
806#103—41no—
807#103—41no—
808#103—41no—
809#103—41no—
810#103—41no—
811#103C2×D414yes—
812#103C2×D414yes—
813#102—22no—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—22no—
818#102—41no—
819#102—41no—
820#102—41no—
821#102—41no—
822#102—41no—
823#102C2×D414yes—
824#102C2×D414yes—
825C22⋊C8—22no—
826C22⋊C8—22no—
827C22⋊C8—41no—
828C22⋊C8—41no—
829C22⋊C8—41no—
830C22⋊C8—41no—
831#97—22no—
832#97C2×D414yes—
833C4×C8—22no—
834C4×C8—22no—
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#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95—21no—
862#95—21no—
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871#95C2×D411yescharacteristic
872#95C2×D411yescharacteristic
873#95C2×D411yescharacteristic
874#95C2×D411yescharacteristic
875C24—21no—
876C24—21no—
877C24—42no—
878C24—42no—
879C24—42no—
880C24—81no—
881C24—81no—
882C24—81no—
883C24—81no—
884C24C22×D411yescharacteristic
885C24C22×D411yescharacteristic
886#41—44no—
887#41—82no—
888#41—82no—
889#41—82no—
890C2×Q8—22no—
891C2×Q8—24no—
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—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—81no—
917C2×Q8—81no—
918C2×Q8C22×D412yes—
919C2×Q8H(5,𝔽2)12yes—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—41no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—81no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4C22×D412yes—
947C2×D42−1+412yes—
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—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C2511yescharacteristic
1005Q16—44no—
1006Q16—44no—
1007Q16—44no—
1008Q16—82no—
1009SD16—44no—
1010SD16—44no—
1011SD16—44no—
1012SD16—82no—
1013M16—82no—
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×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—82no—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C4⋊C4—24no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
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—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
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—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4C22×D412yes—
1097C4⋊C4C22×D412yes—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—81no—
1152C42—81no—
1153C42—81no—
1154C42C22×D412yes—
1155C42H(5,𝔽2)12yes—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—84no—
1184C23—84no—
1185C23—84no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23#57812yes—
1191C23C23×D411yescharacteristic
1192Q8—22no—
1193Q8—22no—
1194Q8—22no—
1195Q8—22no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—82no—
1209Q8—84no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—44no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—84no—
1220D4—84no—
1221D4—162no—
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—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
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—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4D4212yes—
1313C2×C4D4212yes—
1314C2×C4C23×D411yescharacteristic
1315C2×C4C2×H(5,𝔽2)11yescharacteristic
1316C2×C4C2×H(5,𝔽2)11yescharacteristic
1317C2×C4C2×2−1+411yescharacteristic
1318C2×C4#58511yescharacteristic
1319C2×C4#58511yescharacteristic
1320C8—22no—
1321C8—22no—
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—42no—
1337C22—42no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—42no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—168no—
1357C22C2×D4211yescharacteristic
1358C22#348811yescharacteristic
1359C22#348911yescharacteristic
1360C22C2×#57811yescharacteristic
1361C22#358411yescharacteristic
1362C22#358511yescharacteristic
1363C22#358611yescharacteristic
1364C4—22no—
1365C4—22no—
1366C4—41no—
1367C4—41no—
1368C4—42no—
1369C4—42no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—42no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4#348811yescharacteristic
1391C4#348911yescharacteristic
1392C4#353611yescharacteristic
1393C4#354011yescharacteristic
1394C2—42no—
1395C2—81no—
1396C2—82no—
1397C2—82no—
1398C2#4542211yescharacteristic
1399C2#6107411yescharacteristic
1400C2#6107611yescharacteristic
1401C2#6206511yescharacteristic
1402C2#6208511yescharacteristic
1403C2#6216511yescharacteristic
1404C2#6219611yescharacteristic
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. #45143C2semidirect
5. #30858C2semidirect
6. #30853C2semidirect
7. #30687C2semidirect
8. #30666C2semidirect
9. #30651C2semidirect
10. #30637C2semidirect
11. #30540C2semidirect
12. #30531C2semidirect
13. #28288C2semidirect
14. #28275C2semidirect
15. #28258C2semidirect
16. #28238C2semidirect
17. #26566C2semidirect
18. #26559C2semidirect
19. #25969C2semidirect
20. #25960C2semidirect
21. #25176C2semidirect
22. #25151C2semidirect
23. #25098C2semidirect
24. #25084C2semidirect
25. #24328C2semidirect
27. #24195C2semidirect
28. #24122C2semidirect
29. #23809C2semidirect
30. #22233C2semidirect
31. #22217C2semidirect
32. C2×#557C22semidirect
38. C2×#491C22semidirect
43. C2×#479C22semidirect
44. C2×#477C22semidirect
47. C2×#470C22semidirect
54. C2×#462C22semidirect
55. C2×#462C22semidirect
61. C2×#446C22semidirect
62. C2×#441C22semidirect
65. C2×C4×Q16C22semidirect
66. C2×C4×Q16C22semidirect
79. #2581C22semidirect
84. #2489C22semidirect
90. #2442C22semidirect
96. #2429C22semidirect
105. #2360C22semidirect
108. #2331C22semidirect
109. #2327C22semidirect
112. #2097C22semidirect
113. #2096C22semidirect
114. #2095C22semidirect
116. #2068C22semidirect
117. #2068C22semidirect
118. #2068C22semidirect
122. #2066C22semidirect
124. #2059C22semidirect
125. #2059C22semidirect
126. #2056C22semidirect
127. #2056C22semidirect
130. #2043C22semidirect
134. #2036C22semidirect
135. #2036C22semidirect
138. #2035C22semidirect
142. #2016C22semidirect
143. #2016C22semidirect
150. #2001C22semidirect
152. #1990C22semidirect
153. #1984C22semidirect
160. #1947C22semidirect
161. #1947C22semidirect
162. #1944C22semidirect
163. #1942C22semidirect
164. #1928C22semidirect
165. #1927C22semidirect
169. #1924C22semidirect
171. #1923C22semidirect
174. #1878C22semidirect
177. #1872C22semidirect
178. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
187. #1852C22semidirect
188. #1851C22semidirect
189. #1851C22semidirect
192. #1847C22semidirect
193. #1843C22semidirect
194. #1809C22semidirect
196. #1805C22semidirect
197. #1805C22semidirect
200. #1803C22semidirect
201. #1803C22semidirect
204. #1746C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33772
C2×#33142
#451432
#450842
#308582
#308532
#306872
#306662
#306512
#306372
#305402
#305312
#282882
#282752
#282582
#282382
#265662
#265592
#259692
#259602
#251762
#251512
#250982
#250842
#243282
#242472
#241952
#241222
#238092
#222332
#222172