Finite Group Databasebeta

← #6619949

Subgroups — #6619949

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39194C211yesmaximal, characteristic, complemented
2#34309C211yesmaximal, characteristic, complemented
3#33072C211yesmaximal, characteristic, complemented
4#33014C211yesmaximal, characteristic, complemented
5#33012C211yesmaximal, characteristic, complemented
6#29485C211yesmaximal, characteristic, complemented
7#29475C211yesmaximal, characteristic, complemented
8#29426C211yesmaximal, characteristic, complemented
9#29424C211yesmaximal, characteristic, complemented
10#29198C211yesmaximal, characteristic, complemented
11#28163C211yesmaximal, characteristic, complemented
12#27549C211yesmaximal, characteristic, complemented
13#27525C211yesmaximal, characteristic, complemented
14#27061C211yesmaximal, characteristic, complemented
15#27033C211yesmaximal, characteristic, complemented
16#26640C211yesmaximal, characteristic, complemented
17#26623C211yesmaximal, characteristic, complemented
18#25164C211yesmaximal, characteristic, complemented
19#25158C211yesmaximal, characteristic, complemented
20#25027C211yesmaximal, characteristic, complemented
21#24983C211yesmaximal, characteristic, complemented
22#24259C211yesmaximal, characteristic, complemented
23#24257C211yesmaximal, characteristic
24#23109C211yesmaximal, characteristic, complemented
25#23009C211yesmaximal, characteristic, complemented
26#22838C211yesmaximal, characteristic, complemented
27#22780C211yesmaximal, characteristic, complemented
28#22678C211yesmaximal, characteristic, complemented
29#21507C211yesmaximal, characteristic, complemented
30#21465C211yesmaximal, characteristic, complemented
31#21459C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#480C2211yescharacteristic, complemented
37C2×#464C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic
50#2859C2211yescharacteristic, complemented
51#2801—21no—
52#2801—21no—
53#2800—21no—
54#2800—21no—
55#2624C2211yescharacteristic
56#2624C2211yescharacteristic, complemented
57#2538C2211yescharacteristic
58#2537C2211yescharacteristic
59#2500—21no—
60#2494—21no—
61#2494C2211yescharacteristic
62#2494C2211yescharacteristic, complemented
63#2490—21no—
64#2441—21no—
65#2426C2211yescharacteristic
66#2426C2211yescharacteristic, complemented
67#2367C2211yescharacteristic
68#2364—21no—
69#2362C2211yescharacteristic
70#2361C2211yescharacteristic
71#2359—21no—
72#2358—21no—
73#2354C2211yescharacteristic, complemented
74#2352C2211yescharacteristic
75Q8×C4⋊C4C2211yescharacteristic, complemented
76#2349C2211yescharacteristic
77#2342—21no—
78#2339C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2324C2211yescharacteristic
81#2323C2211yescharacteristic
82#2323C2211yescharacteristic
83#2323C2211yescharacteristic, complemented
84#2322—21no—
85#2321—21no—
86C4×#124C2211yescharacteristic
87C4×#124C2211yescharacteristic, complemented
88C4×#121—21no—
89#2293C2211yescharacteristic
90C2×#388—21no—
91C42×D4C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2036C2211yescharacteristic
103#2035C2211yescharacteristic
104#2035C2211yescharacteristic
105#2035C2211yescharacteristic, complemented
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic, complemented
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2015C2211yescharacteristic, complemented
111#2012C2211yescharacteristic
112#2001C2211yescharacteristic
113#2000C2211yescharacteristic
114#2000C2211yescharacteristic
115#1999C2211yescharacteristic
116#1983C2211yescharacteristic, complemented
117#1972C2211yescharacteristic
118#1968C2211yescharacteristic, complemented
119#1959C2211yescharacteristic
120#1959C2211yescharacteristic
121#1955C2211yescharacteristic
122#1955C2211yescharacteristic
123#1949C2211yescharacteristic, complemented
124#1948C2211yescharacteristic, complemented
125#1947C2211yescharacteristic, complemented
126#1943C2211yescharacteristic, complemented
127#1942C2211yescharacteristic, complemented
128#1936C2211yescharacteristic, complemented
129#1935C2211yescharacteristic, complemented
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic, complemented
132#1927C2211yescharacteristic, complemented
133#1927C2211yescharacteristic, complemented
134#1926C2211yescharacteristic
135#1925C2211yescharacteristic, complemented
136#1924C2211yescharacteristic
137#1924C2211yescharacteristic, complemented
138#1923C2211yescharacteristic
139#1923C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1880C2211yescharacteristic
147#1880C2211yescharacteristic, complemented
148#1880C2211yescharacteristic, complemented
149#1879C2211yescharacteristic
150#1879C2211yescharacteristic
151#1879C2211yescharacteristic
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1878C2211yescharacteristic, complemented
155#1878C2211yescharacteristic, complemented
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1873C2211yescharacteristic
159#1872C2211yescharacteristic, complemented
160#1865C2211yescharacteristic, complemented
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1852C2211yescharacteristic, complemented
176#1847C2211yescharacteristic, complemented
177#1836C2211yescharacteristic, complemented
178#1831C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1824C2211yescharacteristic, complemented
181#1818C2211yescharacteristic
182#1818C2211yescharacteristic, complemented
183#1805C2211yescharacteristic, complemented
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1767C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211#546—24no—
212#546—24no—
213C2×#125—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226#520—42no—
227#520—42no—
228#518—42no—
229#518—42no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117—21no—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4—21no—
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C42—21no—
261#482—42no—
262#480—42no—
263#464—24no—
264#463—24no—
265#463—24no—
266#452—24no—
267#450—24no—
268#449—42no—
269#447—42no—
270#442—24no—
271#440—24no—
272#440—42no—
273#440—42no—
274C4×Q16—42no—
275C4×SD16—42no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#401—21no—
333#401—21no—
334#399—21no—
335#399—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390D411yescharacteristic
360#390D411yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389D411yescharacteristic
375#389D411yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388D411yescharacteristic
408#388D411yescharacteristic
409#388D411yescharacteristic
410#388D411yescharacteristic
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C2×#95—21no—
467C2×#95—21no—
468C43C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16#4114yes—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—41no—
552C2×D8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561#125—82no—
562#124—22no—
563#124—22no—
564#124—41no—
565#124#4114yes—
566#123—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—82no—
581#120—28no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—44no—
610C4×D4—44no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4—82no—
614C4×D4#4114yes—
615#117—22no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—44no—
621#117—41no—
622#117—82no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—44no—
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4—28no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—82no—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—22no—
736#107—22no—
737#107—22no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744#106—41no—
745C4⋊C8—22no—
746C4⋊C8—22no—
747C4⋊C8—22no—
748C4⋊C8—41no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785#97—22no—
786#97—22no—
787#97—41no—
788#97—41no—
789C4×C8—41no—
790C4×C8—41no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826C24—21no—
827C24—24no—
828C24—21no—
829C24—21no—
830C24—42no—
831C24—42no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—44no—
839#41—44no—
840#41—44no—
841#41—44no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8C2×#4112yes—
853C2×Q8C2×#4112yes—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—44no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4C2×#4112yes—
891C2×D4C2×#4112yes—
892C2×D4C2×#4112yes—
893C2×D4H(5,𝔽2)12yes—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—24no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—24no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2511yescharacteristic
962Q16—44no—
963SD16—28no—
964SD16—44no—
965SD16—82no—
966D8—44no—
967D8—82no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8C2×#4112yes—
992C4⋊C4—24no—
993C4⋊C4—22no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4C2×#4112yes—
1041C4⋊C4H(5,𝔽2)12yes—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—22no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—22no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—41no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42C2×#4112yes—
1111C42C2×#4112yes—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—48no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23C23×D411yescharacteristic
1155Q8—22no—
1156Q8—22no—
1157Q8—22no—
1158Q8—22no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—22no—
1168D4—48no—
1169D4—48no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—82no—
1177D4—84no—
1178D4—162no—
1179D4—162no—
1180D4#55314yes—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—48no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#52512yes—
1273C2×C4#52512yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—24no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—42no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—168no—
1324C22C2×#52511yescharacteristic
1325C22D4×#4111yescharacteristic
1326C22#348411yescharacteristic
1327C22#358411yescharacteristic
1328C22#358511yescharacteristic
1329C22#358511yescharacteristic
1330C22#358611yescharacteristic
1331C4—22no—
1332C4—22no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—42no—
1337C4—42no—
1338C4—41no—
1339C4—42no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4C2×#55311yescharacteristic
1357C4#348111yescharacteristic
1358C4#350611yescharacteristic
1359C4#351311yescharacteristic
1360C2—44no—
1361C2—81no—
1362C2—81no—
1363C2—82no—
1364C2—161no—
1365C2#3644011yescharacteristic
1366C2#6056711yescharacteristic
1367C2#6060111yescharacteristic
1368C2#6150311yescharacteristic
1369C2#6153111yescharacteristic
1370C2#6166911yescharacteristic
1371C2#6169111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24257C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39194C2semidirect
2. #34309C2semidirect
3. #33072C2semidirect
4. #33014C2semidirect
5. #33012C2semidirect
6. #29485C2semidirect
7. #29475C2semidirect
8. #29426C2semidirect
9. #29424C2semidirect
10. #29198C2semidirect
11. #28163C2semidirect
12. #27549C2semidirect
13. #27525C2semidirect
14. #27061C2semidirect
15. #27033C2semidirect
16. #26640C2semidirect
17. #26623C2semidirect
18. #25164C2semidirect
19. #25158C2semidirect
20. #25027C2semidirect
21. #24983C2semidirect
22. #24259C2semidirect
24. #23109C2semidirect
25. #23009C2semidirect
26. #22838C2semidirect
27. #22780C2semidirect
28. #22678C2semidirect
29. #21507C2semidirect
30. #21465C2semidirect
31. #21459C2semidirect
36. C2×#480C22semidirect
48. C2×C4×Q16C22semidirect
50. #2859C22semidirect
56. #2624C22semidirect
62. #2494C22semidirect
66. #2426C22semidirect
73. #2354C22semidirect
75. Q8×C4⋊C4C22semidirect
83. #2323C22semidirect
87. C4×#124C22semidirect
93. #2077C22semidirect
94. #2077C22semidirect
96. #2074C22semidirect
100. #2066C22semidirect
101. #2066C22semidirect
105. #2035C22semidirect
107. #2034C22semidirect
110. #2015C22semidirect
116. #1983C22semidirect
118. #1968C22semidirect
123. #1949C22semidirect
124. #1948C22semidirect
125. #1947C22semidirect
126. #1943C22semidirect
127. #1942C22semidirect
128. #1936C22semidirect
129. #1935C22semidirect
131. #1934C22semidirect
132. #1927C22semidirect
133. #1927C22semidirect
135. #1925C22semidirect
137. #1924C22semidirect
139. #1923C22semidirect
140. #1921C22semidirect
141. #1921C22semidirect
142. #1920C22semidirect
143. #1919C22semidirect
144. #1919C22semidirect
145. #1919C22semidirect
147. #1880C22semidirect
148. #1880C22semidirect
154. #1878C22semidirect
155. #1878C22semidirect
159. #1872C22semidirect
160. #1865C22semidirect
166. #1863C22semidirect
167. #1863C22semidirect
168. #1863C22semidirect
169. #1863C22semidirect
175. #1852C22semidirect
176. #1847C22semidirect
177. #1836C22semidirect
178. #1831C22semidirect
180. #1824C22semidirect
182. #1818C22semidirect
183. #1805C22semidirect
185. #1804C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1767C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
198. #1762C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#391942
#343092
#330722
#330142
#330122
#294852
#294752
#294262
#294242
#291982
#281632
#275492
#275252
#270612
#270332
#266402
#266232
#251642
#251582
#250272
#249832
#242592
#242572
#231092
#230092
#228382
#227802
#226782
#215072
#214652
#214592