Finite Group Databasebeta

← #6770927

Subgroups — #6770927

Order 512.

1771 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#38032C211yesmaximal, characteristic, complemented
2#35522C211yesmaximal, characteristic, complemented
3#33018C211yesmaximal, characteristic, complemented
4#32662C211yesmaximal, characteristic, complemented
5#32621C211yesmaximal, characteristic, complemented
6#32615C211yesmaximal, characteristic, complemented
7#32554C211yesmaximal, characteristic, complemented
8#31411C211yesmaximal, characteristic, complemented
9#30558C211yesmaximal, characteristic, complemented
10#30413C211yesmaximal, characteristic, complemented
11#30402C211yesmaximal, characteristic, complemented
12#30120C211yesmaximal, characteristic, complemented
13#30017C211yesmaximal, characteristic, complemented
14#29481C211yesmaximal, characteristic, complemented
15#29422C211yesmaximal, characteristic, complemented
16#28583C211yesmaximal, characteristic, complemented
17#28119C211yesmaximal, characteristic, complemented
18#28106C211yesmaximal, characteristic, complemented
19#27872C211yesmaximal, characteristic, complemented
20#27593C211yesmaximal, characteristic, complemented
21#25247C211yesmaximal, characteristic, complemented
22#25128C211yesmaximal, characteristic, complemented
23#24957C211yesmaximal, characteristic, complemented
24#24869C211yesmaximal, characteristic, complemented
25#24275C211yesmaximal, characteristic, complemented
26#24043C211yesmaximal, characteristic, complemented
27#23864C211yesmaximal, characteristic, complemented
28#22475C211yesmaximal, characteristic, complemented
29#22193C211yesmaximal, characteristic, complemented
30#22051C211yesmaximal, characteristic, complemented
31#20929C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#518C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2855C2211yescharacteristic, complemented
49#2708—21no—
50#2706—21no—
51#2688—21no—
52#2687—21no—
53#2625C2211yescharacteristic
54#2621C2211yescharacteristic, complemented
55#2580C2211yescharacteristic
56#2580C2211yescharacteristic, complemented
57#2568C2211yescharacteristic, complemented
58#2557—21no—
59#2553—21no—
60#2538C2211yescharacteristic
61#2537C2211yescharacteristic
62#2535C2211yescharacteristic
63#2485C2211yescharacteristic
64#2485C2211yescharacteristic
65#2481—21no—
66#2480—21no—
67#2473—21no—
68#2472—21no—
69#2467—21no—
70#2463—21no—
71#2460—21no—
72#2456—21no—
73#2424—21no—
74#2418—21no—
75#2417C2211yescharacteristic
76#2415C2211yescharacteristic, complemented
77#2408C2211yescharacteristic
78#2408C2211yescharacteristic
79#2407C2211yescharacteristic
80#2407C2211yescharacteristic, complemented
81#2352C2211yescharacteristic
82#2324C2211yescharacteristic
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic, complemented
85#2314C2211yescharacteristic
86#2311C2211yescharacteristic
87C4×#121C2211yescharacteristic
88C4×#121C2211yescharacteristic
89#2297C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2036C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2013C2211yescharacteristic
124#2013C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#1999C2211yescharacteristic
130#1985C2211yescharacteristic, complemented
131#1985C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1972C2211yescharacteristic
135#1944C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic, complemented
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic, complemented
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic, complemented
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1875C2211yescharacteristic
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic, complemented
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic, complemented
188#1818C2211yescharacteristic
189#1818C2211yescharacteristic, complemented
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic, complemented
193#1797C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic, complemented
197#1788C2211yescharacteristic, complemented
198#1786C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#547—42no—
220#547—42no—
221C2×C4⋊Q8C2311yescharacteristic
222#529—42no—
223#529—42no—
224C2×#126D411yescharacteristic
225C2×#126D411yescharacteristic
226C2×#125D411yescharacteristic
227C2×#124D411yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123D411yescharacteristic
231C2×#123D411yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8D411yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121D411yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×#120—21no—
248#518—42no—
249#518—42no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4—21no—
268C22×C4⋊C4C2311yescharacteristic
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271C22×C42C2311yescharacteristic
272#485—42no—
273#482—42no—
274#468—42no—
275#466—24no—
276#465—42no—
277#450—42no—
278#449—24no—
279#449—42no—
280#435—42no—
281#435—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#416—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334#400—21no—
335#400—21no—
336#400—21no—
337#399—21no—
338#399—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
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#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—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#382—21no—
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458#379—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
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—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548AGL(1,ℤ/8)—416no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8#4114yes—
567C2×M16—22no—
568C2×M16—22no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—41no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8—41no—
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589#126—42no—
590#126—42no—
591#125—42no—
592#124—42no—
593#123—42no—
594#123—42no—
595#123—44no—
596#123—44no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—42no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—82no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—42no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—44no—
619#121—82no—
620#120—82no—
621#120—82no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—44no—
641C4×D4—44no—
642C4×D4—82no—
643C4×D4—82no—
644#117—22no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—41no—
649#117—41no—
650#117—41no—
651#117—41no—
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—44no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—44no—
732C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—41no—
749C2×C42—41no—
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756#107—22no—
757#107—41no—
758#107—41no—
759#107—41no—
760#107—41no—
761#107—41no—
762#106—41no—
763#106—41no—
764#106—41no—
765#106—41no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804#97—41no—
805#97—41no—
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#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24C22×D411yescharacteristic
852C24C22×D411yescharacteristic
853C24C22×D411yescharacteristic
854#41—44no—
855#41—44no—
856#41—82no—
857#41—82no—
858#41—82no—
859#41—82no—
860#41—82no—
861#41—82no—
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—21no—
873C2×Q8—21no—
874C2×Q8—41no—
875C2×Q8—41no—
876C2×Q8—41no—
877C2×D4—28no—
878C2×D4—22no—
879C2×D4—22no—
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—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—44no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—41no—
906C2×D4—41no—
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—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4C2×#4112yes—
930C2×D4C2×#4112yes—
931C2×D4H(5,𝔽2)12yes—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
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—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
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×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4H(5,𝔽2)12yes—
1003C22×C4H(5,𝔽2)12yes—
1004C22×C4C2511yescharacteristic
1005SD16—44no—
1006SD16—44no—
1007SD16—82no—
1008SD16—82no—
1009D8—44no—
1010D8—44no—
1011M16—44no—
1012M16—82no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—82no—
1037C2×C8—82no—
1038C2×C8C2×#4112yes—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
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—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
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—
1135C22⋊C4—81no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—41no—
1145C42—41no—
1146C42—42no—
1147C42—81no—
1148C42—81no—
1149C42—81no—
1150C42—81no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—22no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—21no—
1173C23—21no—
1174C23—48no—
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—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—162no—
1194C23—162no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23#53412yes—
1200C23C23×D411yescharacteristic
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—82no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—22no—
1215D4—22no—
1216D4—48no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—82no—
1224D4—82no—
1225D4—82no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
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—21no—
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—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—84no—
1317C2×C4—82no—
1318C2×C4—82no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C2×C4—162no—
1326C2×C4#53412yes—
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—22no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C8—41no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—41no—
1354C22—42no—
1355C22—41no—
1356C22—41no—
1357C22—42no—
1358C22—42no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—42no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
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×#53411yescharacteristic
1385C22D4×#4111yescharacteristic
1386C22#348811yescharacteristic
1387C22#358411yescharacteristic
1388C22#358511yescharacteristic
1389C22#358511yescharacteristic
1390C22#358611yescharacteristic
1391C4—22no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4#349011yescharacteristic
1416C4#351311yescharacteristic
1417C4#353311yescharacteristic
1418C4#353411yescharacteristic
1419C2—42no—
1420C2—81no—
1421C2—81no—
1422C2—82no—
1423C2—82no—
1424C2—82no—
1425C2#3836411yescharacteristic
1426C2#6076711yescharacteristic
1427C2#6077211yescharacteristic
1428C2#6150611yescharacteristic
1429C2#6153211yescharacteristic
1430C2#6201111yescharacteristic
1431C2#6208411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38032C2semidirect
2. #35522C2semidirect
3. #33018C2semidirect
4. #32662C2semidirect
5. #32621C2semidirect
6. #32615C2semidirect
7. #32554C2semidirect
8. #31411C2semidirect
9. #30558C2semidirect
10. #30413C2semidirect
11. #30402C2semidirect
12. #30120C2semidirect
13. #30017C2semidirect
14. #29481C2semidirect
15. #29422C2semidirect
16. #28583C2semidirect
17. #28119C2semidirect
18. #28106C2semidirect
19. #27872C2semidirect
20. #27593C2semidirect
21. #25247C2semidirect
22. #25128C2semidirect
23. #24957C2semidirect
24. #24869C2semidirect
25. #24275C2semidirect
26. #24043C2semidirect
27. #23864C2semidirect
28. #22475C2semidirect
29. #22193C2semidirect
30. #22051C2semidirect
31. #20929C2semidirect
48. #2855C22semidirect
54. #2621C22semidirect
56. #2580C22semidirect
57. #2568C22semidirect
76. #2415C22semidirect
80. #2407C22semidirect
84. #2324C22semidirect
89. #2297C22semidirect
90. #2101C22semidirect
91. #2099C22semidirect
92. #2097C22semidirect
93. #2095C22semidirect
95. #2092C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
101. #2075C22semidirect
102. #2074C22semidirect
104. #2072C22semidirect
105. #2071C22semidirect
106. #2068C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2036C22semidirect
116. #2036C22semidirect
117. #2035C22semidirect
118. #2035C22semidirect
122. #2033C22semidirect
130. #1985C22semidirect
131. #1985C22semidirect
135. #1944C22semidirect
137. #1936C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
145. #1926C22semidirect
147. #1925C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1918C22semidirect
151. #1918C22semidirect
153. #1895C22semidirect
155. #1894C22semidirect
157. #1892C22semidirect
174. #1870C22semidirect
176. #1869C22semidirect
179. #1864C22semidirect
182. #1862C22semidirect
183. #1854C22semidirect
187. #1825C22semidirect
189. #1818C22semidirect
192. #1807C22semidirect
193. #1797C22semidirect
196. #1788C22semidirect
197. #1788C22semidirect
199. #1749C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#380322
#355222
#330182
#326622
#326212
#326152
#325542
#314112
#305582
#304132
#304022
#301202
#300172
#294812
#294222
#285832
#281192
#281062
#278722
#275932
#252472
#251282
#249572
#248692
#242752
#240432
#238642
#224752
#221932
#220512
#209292