Finite Group Databasebeta

← #7080084

Subgroups — #7080084

Order 512.

1667 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59030C211yesmaximal, characteristic
2#39913C211yesmaximal, characteristic, complemented
3#32186C211yesmaximal, characteristic, complemented
4#31977C211yesmaximal, characteristic, complemented
5#31861C211yesmaximal, characteristic, complemented
6#31755C211yesmaximal, characteristic, complemented
7#31637C211yesmaximal, characteristic, complemented
8#31517C211yesmaximal, characteristic, complemented
9#31474C211yesmaximal, characteristic, complemented
10#31012C211yesmaximal, characteristic, complemented
11#29092C211yesmaximal, characteristic, complemented
12#28997C211yesmaximal, characteristic, complemented
13#28568C211yesmaximal, characteristic, complemented
14#27763C211yesmaximal, characteristic, complemented
15#27534C211yesmaximal, characteristic, complemented
16#27271C211yesmaximal, characteristic, complemented
17#27271C211yesmaximal, characteristic, complemented
18#26762C211yesmaximal, characteristic, complemented
19#26438C211yesmaximal, characteristic, complemented
20#26227C211yesmaximal, characteristic, complemented
21#25505C211yesmaximal, characteristic, complemented
22#25329C211yesmaximal, characteristic, complemented
23#25105C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#24507C211yesmaximal, characteristic, complemented
26#24448C211yesmaximal, characteristic
27#23628C211yesmaximal, characteristic, complemented
28#23141C211yesmaximal, characteristic, complemented
29#22914C211yesmaximal, characteristic, complemented
30#22428C211yesmaximal, characteristic
31#21868C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#470C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#464C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#432C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2855C2211yescharacteristic, complemented
46#2740—21no—
47#2739—21no—
48#2738—21no—
49#2694—21no—
50#2691—21no—
51#2685—21no—
52#2654—21no—
53#2596—21no—
54#2590—21no—
55#2565C2211yescharacteristic, complemented
56#2552C2211yescharacteristic, complemented
57#2544C2211yescharacteristic
58#2534—21no—
59#2511C2211yescharacteristic, complemented
60#2509C2211yescharacteristic, complemented
61#2499C2211yescharacteristic, complemented
62#2495C2211yescharacteristic, complemented
63#2490C2211yescharacteristic
64#2476—21no—
65#2454C2211yescharacteristic
66#2445C2211yescharacteristic
67#2441C2211yescharacteristic, complemented
68#2441C2211yescharacteristic, complemented
69#2435C2211yescharacteristic
70#2435C2211yescharacteristic
71#2426C2211yescharacteristic
72#2423C2211yescharacteristic, complemented
73#2418—21no—
74#2417C2211yescharacteristic
75#2415C2211yescharacteristic
76#2411—21no—
77#2405—21no—
78#2367C2211yescharacteristic
79#2362C2211yescharacteristic, complemented
80#2361C2211yescharacteristic
81#2354C2211yescharacteristic
82D4×C22⋊C4—21no—
83D4×C22⋊C4C2211yescharacteristic
84#2336—21no—
85C4×#123C2211yescharacteristic
86C2×#390C2211yescharacteristic
87#2285C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2075C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2015C2211yescharacteristic, complemented
124#2015C2211yescharacteristic, complemented
125#2014C2211yescharacteristic
126#2001C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1992C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1983C2211yescharacteristic, complemented
132#1982C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic, complemented
135#1959C2211yescharacteristic, complemented
136#1959C2211yescharacteristic, complemented
137#1959C2211yescharacteristic, complemented
138#1957C2211yescharacteristic
139#1939C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic, complemented
145#1934C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1926C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1894C2211yescharacteristic, complemented
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic, complemented
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1873C2211yescharacteristic, complemented
174#1873C2211yescharacteristic, complemented
175#1872C2211yescharacteristic, complemented
176#1870C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1804C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic, complemented
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213D42—24no—
214D42—42no—
215C2×#127C2311yescharacteristic
216#529—24no—
217#529—42no—
218C2×#126—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#488—42no—
255#470—42no—
256#468—24no—
257#464—42no—
258#450—42no—
259#450—42no—
260#436—42no—
261#432—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#418—42no—
272#418—42no—
273#418—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—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#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
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#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—44no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559#127—22no—
560#127—41no—
561#126—44no—
562#125—22no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—44no—
567#124—22no—
568#124—22no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—41no—
573#123—42no—
574#123—44no—
575#123—82no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—41no—
588#121#4114yes—
589#120—44no—
590#120—44no—
591C4×Q8—22no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—44no—
604C4×D4—82no—
605#117—44no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
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—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
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—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4—82no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—41no—
723#107—41no—
724#106—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—41no—
768#97—41no—
769#97—41no—
770C4×C8—41no—
771C4×C8—41no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
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#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—82no—
886C2×D4—81no—
887C2×D4—816no—
888C2×D4C2×#4112yes—
889C2×D4H(5,𝔽2)12yes—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
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—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2×#4112yes—
944C22×C4H(5,𝔽2)12yes—
945C22×C4C2511yescharacteristic
946Q16—82no—
947SD16—82no—
948SD16—82no—
949SD16—82no—
950M16—82no—
951M16—82no—
952M16—82no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
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—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—22no—
1032C22⋊C4—24no—
1033C22⋊C4—22no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C42—22no—
1076C42—22no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—42no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23—84no—
1134C23—84no—
1135C23—84no—
1136C23—162no—
1137C23—162no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23#54612yes—
1144C23C23×D411yescharacteristic
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153D4—22no—
1154D4—22no—
1155D4—22no—
1156D4—22no—
1157D4—44no—
1158D4—48no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
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—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
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—84no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4#54612yes—
1260C2×C4#57512yes—
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C2×C4#58511yescharacteristic
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—168no—
1311C22—168no—
1312C22C2×#54611yescharacteristic
1313C22#348811yescharacteristic
1314C22#350011yescharacteristic
1315C22C2×#57511yescharacteristic
1316C22#358511yescharacteristic
1317C22#358511yescharacteristic
1318C22#358611yescharacteristic
1319C4—22no—
1320C4—22no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4#351311yescharacteristic
1345C4#352111yescharacteristic
1346C4#353411yescharacteristic
1347C4#356011yescharacteristic
1348C2—42no—
1349C2—81no—
1350C2—82no—
1351C2—82no—
1352C2—161no—
1353C2#4399811yescharacteristic
1354C2#6115611yescharacteristic
1355C2#6118011yescharacteristic
1356C2#6197411yescharacteristic
1357C2#6208411yescharacteristic
1358C2#6256411yescharacteristic
1359C2#6259311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39913C2semidirect
3. #32186C2semidirect
4. #31977C2semidirect
5. #31861C2semidirect
6. #31755C2semidirect
7. #31637C2semidirect
8. #31517C2semidirect
9. #31474C2semidirect
10. #31012C2semidirect
11. #29092C2semidirect
12. #28997C2semidirect
13. #28568C2semidirect
14. #27763C2semidirect
15. #27534C2semidirect
16. #27271C2semidirect
17. #27271C2semidirect
18. #26762C2semidirect
19. #26438C2semidirect
20. #26227C2semidirect
21. #25505C2semidirect
22. #25329C2semidirect
23. #25105C2semidirect
24. #24538C2semidirect
25. #24507C2semidirect
27. #23628C2semidirect
28. #23141C2semidirect
29. #22914C2semidirect
31. #21868C2semidirect
35. C2×#470C22semidirect
41. C2×#432C22semidirect
45. #2855C22semidirect
55. #2565C22semidirect
56. #2552C22semidirect
59. #2511C22semidirect
60. #2509C22semidirect
61. #2499C22semidirect
62. #2495C22semidirect
67. #2441C22semidirect
68. #2441C22semidirect
72. #2423C22semidirect
79. #2362C22semidirect
87. #2285C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2088C22semidirect
91. #2086C22semidirect
92. #2077C22semidirect
93. #2075C22semidirect
96. #2073C22semidirect
97. #2073C22semidirect
98. #2072C22semidirect
102. #2071C22semidirect
103. #2071C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2065C22semidirect
108. #2059C22semidirect
109. #2056C22semidirect
112. #2055C22semidirect
115. #2042C22semidirect
116. #2042C22semidirect
118. #2036C22semidirect
120. #2026C22semidirect
121. #2025C22semidirect
122. #2025C22semidirect
123. #2015C22semidirect
124. #2015C22semidirect
126. #2001C22semidirect
128. #1992C22semidirect
129. #1992C22semidirect
130. #1989C22semidirect
131. #1983C22semidirect
134. #1973C22semidirect
135. #1959C22semidirect
136. #1959C22semidirect
137. #1959C22semidirect
139. #1939C22semidirect
142. #1936C22semidirect
143. #1935C22semidirect
144. #1934C22semidirect
145. #1934C22semidirect
146. #1933C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
152. #1921C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
160. #1894C22semidirect
161. #1894C22semidirect
162. #1894C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
165. #1878C22semidirect
167. #1877C22semidirect
168. #1877C22semidirect
172. #1873C22semidirect
173. #1873C22semidirect
174. #1873C22semidirect
175. #1872C22semidirect
177. #1864C22semidirect
178. #1863C22semidirect
180. #1862C22semidirect
181. #1852C22semidirect
182. #1851C22semidirect
183. #1851C22semidirect
184. #1825C22semidirect
185. #1805C22semidirect
186. #1805C22semidirect
187. #1804C22semidirect
188. #1804C22semidirect
190. #1802C22semidirect
194. #1771C22semidirect
195. #1762C22semidirect
196. C4×#103C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
200. #1736C22semidirect
201. #1736C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#590302
#399132
#321862
#319772
#318612
#317552
#316372
#315172
#314742
#310122
#290922
#289972
#285682
#277632
#275342
#272712
#267622
#264382
#262272
#255052
#253292
#251052
#245382
#245072
#244482
#236282
#231412
#229142
#224282
#218682