Finite Group Databasebeta

← #6687257

Subgroups — #6687257

Order 512.

1829 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3215C211yesmaximal, characteristic, complemented
2C2×#3178C211yesmaximal, characteristic, complemented
3#37765C211yesmaximal, characteristic, complemented
4#37696C211yesmaximal, characteristic
5#33054C211yesmaximal, characteristic, complemented
6#30618C211yesmaximal, characteristic, complemented
7#30606C211yesmaximal, characteristic, complemented
8#30602C211yesmaximal, characteristic, complemented
9#30590C211yesmaximal, characteristic, complemented
10#30427C211yesmaximal, characteristic, complemented
11#30420C211yesmaximal, characteristic
12#30408C211yesmaximal, characteristic
13#30407C211yesmaximal, characteristic, complemented
14#30289C211yesmaximal, characteristic, complemented
15#29884C211yesmaximal, characteristic, complemented
16#28730C211yesmaximal, characteristic, complemented
17#28628C211yesmaximal, characteristic, complemented
18#26189C211yesmaximal, characteristic, complemented
19#26177C211yesmaximal, characteristic, complemented
20#26169C211yesmaximal, characteristic, complemented
21#26165C211yesmaximal, characteristic, complemented
22#25859C211yesmaximal, characteristic, complemented
23#25681C211yesmaximal, characteristic, complemented
24#25674C211yesmaximal, characteristic, complemented
25#25612C211yesmaximal, characteristic, complemented
26#24922C211yesmaximal, characteristic, complemented
27#24921C211yesmaximal, characteristic, complemented
28#24906C211yesmaximal, characteristic, complemented
29#24905C211yesmaximal, characteristic, complemented
30#22278C211yesmaximal, characteristic, complemented
31#21112C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#541C2211yescharacteristic, complemented
34C2×#533C2211yescharacteristic
35C22×#124C2211yescharacteristic
36#3215—28no—
37#3178—28no—
38C2×#501C2211yescharacteristic, complemented
39C2×#500C2211yescharacteristic, complemented
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#487C2211yescharacteristic, complemented
47C2×#470C2211yescharacteristic, complemented
48C2×#468C2211yescharacteristic
49C2×#467C2211yescharacteristic, complemented
50C2×#465C2211yescharacteristic
51C2×#464C2211yescharacteristic
52C2×#464C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#451C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#450C2211yescharacteristic
59C2×#441C2211yescharacteristic, complemented
60C2×#440C2211yescharacteristic
61C2×C4×Q16C2211yescharacteristic, complemented
62C2×C4×SD16C2211yescharacteristic
63C2×#432C2211yescharacteristic
64C2×#405C2211yescharacteristic, complemented
65#2857C2211yescharacteristic
66#2851C2211yescharacteristic
67#2723—21no—
68#2721—21no—
69#2720—21no—
70#2719—21no—
71#2715—21no—
72#2712—21no—
73#2710—21no—
74#2700—21no—
75#2660C2211yescharacteristic, complemented
76#2640C2211yescharacteristic
77#2628C2211yescharacteristic, complemented
78#2620C2211yescharacteristic
79#2538C2211yescharacteristic
80#2536C2211yescharacteristic
81#2480—21no—
82#2479—21no—
83#2475—21no—
84#2472—21no—
85#2469—21no—
86#2462—21no—
87#2448C2211yescharacteristic
88#2447C2211yescharacteristic
89#2437—21no—
90#2427C2211yescharacteristic
91#2426C2211yescharacteristic
92#2423C2211yescharacteristic
93#2423C2211yescharacteristic, complemented
94#2421C2211yescharacteristic
95#2421C2211yescharacteristic, complemented
96#2412—21no—
97#2409C2211yescharacteristic
98#2408C2211yescharacteristic
99#2351C2211yescharacteristic, complemented
100Q8×C4⋊C4C2211yescharacteristic, complemented
101Q8×C22⋊C4C2211yescharacteristic
102D4×C22⋊C4C2211yescharacteristic
103#2327C2211yescharacteristic, complemented
104#2326C2211yescharacteristic
105#2290C2211yescharacteristic
106#2097C2211yescharacteristic, complemented
107#2097C2211yescharacteristic, complemented
108#2095C2211yescharacteristic, complemented
109#2095C2211yescharacteristic, complemented
110#2093C2211yescharacteristic
111#2093C2211yescharacteristic
112#2092C2211yescharacteristic
113#2092C2211yescharacteristic
114#2088C2211yescharacteristic, complemented
115#2088C2211yescharacteristic, complemented
116#2086C2211yescharacteristic, complemented
117#2086C2211yescharacteristic, complemented
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2076C2211yescharacteristic
121#2076C2211yescharacteristic
122#2074C2211yescharacteristic, complemented
123#2073C2211yescharacteristic
124#2072C2211yescharacteristic, complemented
125#2071C2211yescharacteristic
126#2056C2211yescharacteristic, complemented
127#2056C2211yescharacteristic, complemented
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2036C2211yescharacteristic
135#2036C2211yescharacteristic
136#2036C2211yescharacteristic
137#2036C2211yescharacteristic
138#2036C2211yescharacteristic, complemented
139#2036C2211yescharacteristic, complemented
140#2033C2211yescharacteristic
141#2033C2211yescharacteristic
142#2001C2211yescharacteristic, complemented
143#2001C2211yescharacteristic, complemented
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#1993C2211yescharacteristic, complemented
147#1992C2211yescharacteristic, complemented
148#1990C2211yescharacteristic, complemented
149#1958C2211yescharacteristic
150#1958C2211yescharacteristic
151#1956C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1917C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic, complemented
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1870C2211yescharacteristic
181#1869C2211yescharacteristic
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1851C2211yescharacteristic, complemented
191#1850C2211yescharacteristic, complemented
192#1836C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1803C2211yescharacteristic, complemented
196#1802C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201#1768C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C4×C22⋊C8C2211yescharacteristic
204#1746C2211yescharacteristic, complemented
205C23×Q8C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#542—24no—
218#542—42no—
219#541—24no—
220#541—42no—
221#533—24no—
222#533—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#126—21no—
227C2×#126—21no—
228C2×#126—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#125—21no—
232C2×#125C2311yescharacteristic
233C2×#124—21no—
234C2×#124—24no—
235C2×#124—21no—
236C2×#124—21no—
237C2×#124—42no—
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121C2311yescharacteristic
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×#117—21no—
268C2×#117C2311yescharacteristic
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272C22×C42C2311yescharacteristic
273#501—24no—
274#500—42no—
275#497—24no—
276#497D418yescomplemented
277#489—24no—
278#489—24no—
279#488—24no—
280#488—42no—
281#487—24no—
282#470—24no—
283#468—24no—
284#467—24no—
285#465—24no—
286#464—24no—
287#464—24no—
288#464—24no—
289#464—24no—
290#451—24no—
291#451—24no—
292#450—24no—
293#450—24no—
294#441—24no—
295#440—24no—
296C4×Q16—24no—
297C4×SD16—24no—
298#432—24no—
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349#405—24no—
350C2×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×C4×C8C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356#400—21no—
357#400—21no—
358#400—21no—
359#399—21no—
360#399—21no—
361#399—21no—
362#399—21no—
363#398—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#397—21no—
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#395—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#392—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#390—21no—
406#390—21no—
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388D411yescharacteristic
435#388D411yescharacteristic
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387D411yescharacteristic
447#387D411yescharacteristic
448#386—21no—
449#386—21no—
450#386—21no—
451#386—21no—
452#386D411yescharacteristic
453#386D411yescharacteristic
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385D411yescharacteristic
461#385D411yescharacteristic
462#384—21no—
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#382—21no—
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#381—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#380C2311yescharacteristic
480#379—21no—
481#379—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4C2311yescharacteristic
485C4×C22⋊C4—21no—
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488#376C2311yescharacteristic
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
515C25—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—22no—
520C22×Q8—41no—
521C22×Q8—41no—
522C22×Q8—41no—
523C22×Q8—41no—
524C22×Q8—41no—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4C2×D411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16C2×D414yes—
559C2×Q16C2×D414yes—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16C2×D414yes—
571C2×SD16C2×D414yes—
572C2×M16—22no—
573C2×M16—41no—
574C2×M16—41no—
575C22×C8—22no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—22no—
589C4⋊Q8—22no—
590C4⋊Q8—22no—
591C4⋊Q8C2×D414yes—
592#126—44no—
593#126—44no—
594#126—44no—
595#125—22no—
596#125—22no—
597#125—44no—
598#125—44no—
599#125—44no—
600#124—22no—
601#124—22no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—44no—
606#124—44no—
607#124—41no—
608#124—41no—
609#124—44no—
610#124C2×D414yes—
611#123—44no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—22no—
617C22⋊Q8—44no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—44no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—82no—
627#121—22no—
628#121—41no—
629#121—41no—
630#121—41no—
631#120—82no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—44no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×D4—22no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655#117—22no—
656#117—22no—
657#117—44no—
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—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⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
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⋊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—44no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4—82no—
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C42—22no—
749C2×C42—22no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#107—22no—
766#107—22no—
767#107—41no—
768#107—41no—
769#107—41no—
770#107—41no—
771#106—22no—
772#106—22no—
773C4⋊C8—22no—
774C4⋊C8—22no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
796#103—41no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809C22⋊C8—22no—
810C22⋊C8—22no—
811C22⋊C8—41no—
812C22⋊C8—41no—
813C22⋊C8—41no—
814C22⋊C8—41no—
815#97—22no—
816#97—22no—
817#97C2×D414yes—
818C4×C8—22no—
819C4×C8—22no—
820C4×C8—22no—
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#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#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861C24—21no—
862C24—21no—
863C24—42no—
864C24—42no—
865C24—42no—
866C24—42no—
867C24—81no—
868C24—81no—
869C24—81no—
870C24C22×D411yescharacteristic
871C24C22×D411yescharacteristic
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
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—42no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—81no—
898C2×Q8—81no—
899C2×Q8—81no—
900C2×Q8—81no—
901C2×Q8—81no—
902C2×Q8—82no—
903C2×Q8—82no—
904C2×Q8—82no—
905C2×Q8—82no—
906C2×Q8C22×D412yes—
907C2×Q8C22×D412yes—
908C2×Q8C22×D412yes—
909C2×D4—22no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—81no—
927C2×D4—82no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4C22×D412yes—
937C22×C4—22no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—22no—
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—22no—
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—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
991Q16—44no—
992Q16—44no—
993Q16—82no—
994Q16—82no—
995SD16—44no—
996SD16—44no—
997SD16—82no—
998SD16—82no—
999M16—44no—
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—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—44no—
1023C2×C8C22×D412yes—
1024C2×C8C22×D412yes—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
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—41no—
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—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
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—
1082C22⋊C4—22no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
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—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
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—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C42—22no—
1123C42—22no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—81no—
1140C42C22×D412yes—
1141C42H(5,𝔽2)12yes—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—21no—
1155C23—21no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—84no—
1170C23—84no—
1171C23—84no—
1172C23—84no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23#57812yes—
1177C23C23×D411yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—22no—
1181Q8—22no—
1182Q8—22no—
1183Q8—22no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—84no—
1195Q8—84no—
1196Q8—162no—
1197D4—22no—
1198D4—22no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—82no—
1206D4—84no—
1207D4—162no—
1208D4—162no—
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—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—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—44no—
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—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—82no—
1295C2×C4—84no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4D4212yes—
1299C2×C4D4212yes—
1300C2×C4C23×D411yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C2×C4#58511yescharacteristic
1306C8—22no—
1307C8—22no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—42no—
1330C22—41no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—168no—
1343C22#344911yescharacteristic
1344C22C2×D4211yescharacteristic
1345C22#350011yescharacteristic
1346C22C2×#57811yescharacteristic
1347C22#358411yescharacteristic
1348C22#358511yescharacteristic
1349C22#358611yescharacteristic
1350C4—22no—
1351C4—22no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4#348511yescharacteristic
1377C4#348511yescharacteristic
1378C4#356211yescharacteristic
1379C4#356211yescharacteristic
1380C2—42no—
1381C2—81no—
1382C2—82no—
1383C2—161no—
1384C2#3768211yescharacteristic
1385C2#6098111yescharacteristic
1386C2#6099611yescharacteristic
1387C2#6107611yescharacteristic
1388C2#6107711yescharacteristic
1389C2#6255911yescharacteristic
1390C2#6256811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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×#3215C2semidirect
2. C2×#3178C2semidirect
3. #37765C2semidirect
5. #33054C2semidirect
6. #30618C2semidirect
7. #30606C2semidirect
8. #30602C2semidirect
9. #30590C2semidirect
10. #30427C2semidirect
13. #30407C2semidirect
14. #30289C2semidirect
15. #29884C2semidirect
16. #28730C2semidirect
17. #28628C2semidirect
18. #26189C2semidirect
19. #26177C2semidirect
20. #26169C2semidirect
21. #26165C2semidirect
22. #25859C2semidirect
23. #25681C2semidirect
24. #25674C2semidirect
25. #25612C2semidirect
26. #24922C2semidirect
27. #24921C2semidirect
28. #24906C2semidirect
29. #24905C2semidirect
30. #22278C2semidirect
31. #21112C2semidirect
33. C2×#541C22semidirect
38. C2×#501C22semidirect
39. C2×#500C22semidirect
46. C2×#487C22semidirect
47. C2×#470C22semidirect
49. C2×#467C22semidirect
59. C2×#441C22semidirect
61. C2×C4×Q16C22semidirect
64. C2×#405C22semidirect
75. #2660C22semidirect
77. #2628C22semidirect
93. #2423C22semidirect
95. #2421C22semidirect
99. #2351C22semidirect
100. Q8×C4⋊C4C22semidirect
103. #2327C22semidirect
106. #2097C22semidirect
107. #2097C22semidirect
108. #2095C22semidirect
109. #2095C22semidirect
114. #2088C22semidirect
115. #2088C22semidirect
116. #2086C22semidirect
117. #2086C22semidirect
122. #2074C22semidirect
124. #2072C22semidirect
126. #2056C22semidirect
127. #2056C22semidirect
138. #2036C22semidirect
139. #2036C22semidirect
142. #2001C22semidirect
143. #2001C22semidirect
146. #1993C22semidirect
147. #1992C22semidirect
148. #1990C22semidirect
151. #1956C22semidirect
153. #1935C22semidirect
155. #1933C22semidirect
158. #1917C22semidirect
159. #1916C22semidirect
161. #1894C22semidirect
163. #1892C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
190. #1851C22semidirect
191. #1850C22semidirect
192. #1836C22semidirect
193. #1805C22semidirect
195. #1803C22semidirect
201. #1768C22semidirect
202. #1750C22semidirect
204. #1746C22semidirect
276. #497D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32152
C2×#31782
#377652
#376962
#330542
#306182
#306062
#306022
#305902
#304272
#304202
#304082
#304072
#302892
#298842
#287302
#286282
#261892
#261772
#261692
#261652
#258592
#256812
#256742
#256122
#249222
#249212
#249062
#249052
#222782
#211122