Finite Group Databasebeta

← #7080481

Subgroups — #7080481

Order 512.

1783 conjugacy classes of subgroups.

The subgroup lattice has 1433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45002C211yesmaximal, characteristic, complemented
2#44988C211yesmaximal, characteristic, complemented
3#32186C211yesmaximal, characteristic, complemented
4#32116C211yesmaximal, characteristic, complemented
5#31905C211yesmaximal, characteristic, complemented
6#31858C211yesmaximal, characteristic, complemented
7#31826C211yesmaximal, characteristic, complemented
8#31654C211yesmaximal, characteristic, complemented
9#30591C211yesmaximal, characteristic, complemented
10#30527C211yesmaximal, characteristic, complemented
11#27593C211yesmaximal, characteristic, complemented
12#27438C211yesmaximal, characteristic, complemented
13#27270C211yesmaximal, characteristic, complemented
14#27078C211yesmaximal, characteristic, complemented
15#26721C211yesmaximal, characteristic, complemented
16#26408C211yesmaximal, characteristic, complemented
17#26202C211yesmaximal, characteristic, complemented
18#25318C211yesmaximal, characteristic, complemented
19#25117C211yesmaximal, characteristic, complemented
20#25076C211yesmaximal, characteristic, complemented
21#24909C211yesmaximal, characteristic, complemented
22#24638C211yesmaximal, characteristic, complemented
23#24530C211yesmaximal, characteristic, complemented
24#24364C211yesmaximal, characteristic, complemented
25#23941C211yesmaximal, characteristic, complemented
26#23850C211yesmaximal, characteristic, complemented
27#23543C211yesmaximal, characteristic, complemented
28#22866C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic, complemented
30#22072C211yesmaximal, characteristic, complemented
31#21897C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#463C2211yescharacteristic, complemented
38C2×#459C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#449C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×#424C2211yescharacteristic, complemented
46C2×#417C2211yescharacteristic
47C2×#417C2211yescharacteristic, complemented
48C22×#102C2211yescharacteristic
49#2746—21no—
50#2746—21no—
51#2738—21no—
52#2728—21no—
53#2706—21no—
54#2693—21no—
55#2688—21no—
56#2668—21no—
57#2598—21no—
58#2564—21no—
59#2544C2211yescharacteristic
60#2542C2211yescharacteristic, complemented
61#2535—21no—
62#2514C2211yescharacteristic, complemented
63#2511C2211yescharacteristic, complemented
64#2502C2211yescharacteristic
65#2492C2211yescharacteristic
66#2489C2211yescharacteristic
67#2463—21no—
68#2454C2211yescharacteristic
69#2447C2211yescharacteristic
70#2440C2211yescharacteristic, complemented
71#2438—21no—
72#2433C2211yescharacteristic
73#2431C2211yescharacteristic
74#2427C2211yescharacteristic
75#2424—21no—
76#2420C2211yescharacteristic
77#2418—21no—
78#2416C2211yescharacteristic
79#2412—21no—
80#2407C2211yescharacteristic
81#2395C2211yescharacteristic
82#2366C2211yescharacteristic
83#2361C2211yescharacteristic
84#2361C2211yescharacteristic
85#2354C2211yescharacteristic, complemented
86D4×C4⋊C4C2211yescharacteristic
87#2339C2211yescharacteristic, complemented
88D4×C22⋊C4C2211yescharacteristic
89#2314C2211yescharacteristic, complemented
90#2311C2211yescharacteristic
91#2311C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2086C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2056C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2026C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2012C2211yescharacteristic
128#2011C2211yescharacteristic
129#2001C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1989C2211yescharacteristic, complemented
133#1989C2211yescharacteristic, complemented
134#1988C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1973C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic
141#1959C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1919C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic, complemented
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic
178#1874C2211yescharacteristic, complemented
179#1872C2211yescharacteristic
180#1869C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1853C2211yescharacteristic, complemented
184#1852C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1824C2211yescharacteristic
189#1818C2211yescharacteristic, complemented
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1786C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—42no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220#546—24no—
221#546—42no—
222#540—24no—
223#540—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248C2×#120—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267#486—42no—
268#466—42no—
269#463—42no—
270#459—42no—
271#450—42no—
272#449—24no—
273#449—42no—
274#447—42no—
275#442—42no—
276#435—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281#424—42no—
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289#417—42no—
290#417—42no—
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#102—42no—
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×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#401—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400D411yescharacteristic
339#399—21no—
340#399—21no—
341#399—21no—
342#399D411yescharacteristic
343#398—21no—
344#398—21no—
345#398—21no—
346#398D411yescharacteristic
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397D411yescharacteristic
353#397D411yescharacteristic
354#397D411yescharacteristic
355#396—21no—
356#396—21no—
357#395—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394D411yescharacteristic
365#394D411yescharacteristic
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
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#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#383—21no—
442#382—21no—
443#382C2311yescharacteristic
444#381—21no—
445#381—21no—
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C2×#95—21no—
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—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8—21no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550#135—416no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—22no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C2×D8—41no—
575C2×M16—22no—
576C2×M16—41no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594#127—22no—
595#127—22no—
596#127—41no—
597#127—41no—
598#125—22no—
599#125—41no—
600#124—22no—
601#124—41no—
602#124—41no—
603#124—41no—
604#123—44no—
605#123—44no—
606#123—44no—
607C22⋊Q8—22no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—82no—
612C22⋊Q8—82no—
613C22⋊Q8—82no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—44no—
619#121—44no—
620#121—44no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—82no—
625#121#4114yes—
626#120—44no—
627#120—82no—
628#120—82no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—82no—
644C4×D4—82no—
645C4×D4—82no—
646C4×D4—82no—
647#117—22no—
648#117—22no—
649#117—82no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
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—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
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—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
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—44no—
728C2×C22⋊C4—82no—
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—41no—
749#107—41no—
750#106—41no—
751#106—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759#103—22no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796#97—41no—
797#97—41no—
798C4×C8—41no—
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#95—21no—
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#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—44no—
853#41—44no—
854#41—44no—
855#41—44no—
856#41—82no—
857#41—82no—
858#41—82no—
859#41—82no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—42no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—24no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—41no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—82no—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4C2×#4112yes—
937C2×D4H(5,𝔽2)12yes—
938C2×D4H(5,𝔽2)12yes—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C2×#4112yes—
1007C22×C4H(5,𝔽2)12yes—
1008C22×C4C2511yescharacteristic
1009Q16—44no—
1010SD16—44no—
1011SD16—44no—
1012SD16—82no—
1013SD16—82no—
1014D8—44no—
1015D8—44no—
1016D8—82no—
1017M16—82no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—44no—
1043C2×C8—82no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4C2×#4112yes—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—24no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
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—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
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—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—21no—
1145C42—42no—
1146C42—42no—
1147C42—81no—
1148C42—81no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—84no—
1190C23—84no—
1191C23—84no—
1192C23—162no—
1193C23—162no—
1194C23—162no—
1195C23—162no—
1196C23#54612yes—
1197C23#57712yes—
1198C23C23×D411yescharacteristic
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—162no—
1208D4—22no—
1209D4—22no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—44no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—84no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—162no—
1232D4—162no—
1233D4—162no—
1234D4—162no—
1235D4—162no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4#54612yes—
1326C2×C4#57612yes—
1327C2×C4C22×#4111yescharacteristic
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4C2×H(5,𝔽2)11yescharacteristic
1330C2×C4C2×H(5,𝔽2)11yescharacteristic
1331C2×C4#58511yescharacteristic
1332C2×C4#58511yescharacteristic
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—168no—
1384C22C2×#54611yescharacteristic
1385C22#348811yescharacteristic
1386C22#348811yescharacteristic
1387C22C2×#57611yescharacteristic
1388C22C2×#57711yescharacteristic
1389C22#358511yescharacteristic
1390C22#358611yescharacteristic
1391C4—22no—
1392C4—22no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—42no—
1400C4—41no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4#351311yescharacteristic
1416C4#351311yescharacteristic
1417C4#353211yescharacteristic
1418C4#354511yescharacteristic
1419C2—42no—
1420C2—42no—
1421C2—82no—
1422C2—82no—
1423C2—82no—
1424C2—161no—
1425C2#4400111yescharacteristic
1426C2#6119211yescharacteristic
1427C2#6119911yescharacteristic
1428C2#6200711yescharacteristic
1429C2#6200811yescharacteristic
1430C2#6205311yescharacteristic
1431C2#6207611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45002C2semidirect
2. #44988C2semidirect
3. #32186C2semidirect
4. #32116C2semidirect
5. #31905C2semidirect
6. #31858C2semidirect
7. #31826C2semidirect
8. #31654C2semidirect
9. #30591C2semidirect
10. #30527C2semidirect
11. #27593C2semidirect
12. #27438C2semidirect
13. #27270C2semidirect
14. #27078C2semidirect
15. #26721C2semidirect
16. #26408C2semidirect
17. #26202C2semidirect
18. #25318C2semidirect
19. #25117C2semidirect
20. #25076C2semidirect
21. #24909C2semidirect
22. #24638C2semidirect
23. #24530C2semidirect
24. #24364C2semidirect
25. #23941C2semidirect
26. #23850C2semidirect
27. #23543C2semidirect
28. #22866C2semidirect
29. #22419C2semidirect
30. #22072C2semidirect
31. #21897C2semidirect
37. C2×#463C22semidirect
40. C2×#449C22semidirect
45. C2×#424C22semidirect
47. C2×#417C22semidirect
60. #2542C22semidirect
62. #2514C22semidirect
63. #2511C22semidirect
70. #2440C22semidirect
85. #2354C22semidirect
87. #2339C22semidirect
89. #2314C22semidirect
91. #2311C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2097C22semidirect
96. #2086C22semidirect
98. #2072C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
104. #2056C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
114. #2054C22semidirect
115. #2042C22semidirect
119. #2026C22semidirect
120. #2025C22semidirect
121. #2024C22semidirect
124. #2015C22semidirect
132. #1989C22semidirect
133. #1989C22semidirect
134. #1988C22semidirect
138. #1973C22semidirect
141. #1959C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
145. #1936C22semidirect
146. #1935C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1927C22semidirect
150. #1927C22semidirect
152. #1926C22semidirect
156. #1919C22semidirect
157. #1918C22semidirect
158. #1917C22semidirect
159. #1917C22semidirect
161. #1895C22semidirect
163. #1893C22semidirect
170. #1879C22semidirect
174. #1877C22semidirect
175. #1877C22semidirect
178. #1874C22semidirect
181. #1864C22semidirect
183. #1853C22semidirect
184. #1852C22semidirect
187. #1850C22semidirect
189. #1818C22semidirect
191. #1804C22semidirect
195. #1802C22semidirect
200. C4×#102C22semidirect
201. #1753C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#450022
#449882
#321862
#321162
#319052
#318582
#318262
#316542
#305912
#305272
#275932
#274382
#272702
#270782
#267212
#264082
#262022
#253182
#251172
#250762
#249092
#246382
#245302
#243642
#239412
#238502
#235432
#228662
#224192
#220722
#218972