Finite Group Databasebeta

← #6508940

Subgroups — #6508940

Order 512.

1941 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3198C211yesmaximal, characteristic
2C2×#3096C211yesmaximal, characteristic, complemented
3#35618C211yesmaximal, characteristic, complemented
4#34411C211yesmaximal, characteristic, complemented
5#28129C211yesmaximal, characteristic, complemented
6#28127C211yesmaximal, characteristic, complemented
7#28116C211yesmaximal, characteristic, complemented
8#28116C211yesmaximal, characteristic, complemented
9#27655C211yesmaximal, characteristic, complemented
10#27654C211yesmaximal, characteristic, complemented
11#27651C211yesmaximal, characteristic, complemented
12#27651C211yesmaximal, characteristic, complemented
13#25230C211yesmaximal, characteristic, complemented
14#25228C211yesmaximal, characteristic, complemented
15#25227C211yesmaximal, characteristic, complemented
16#25225C211yesmaximal, characteristic, complemented
17#25214C211yesmaximal, characteristic, complemented
18#25212C211yesmaximal, characteristic, complemented
19#25207C211yesmaximal, characteristic, complemented
20#25205C211yesmaximal, characteristic, complemented
21#24597C211yesmaximal, characteristic, complemented
22#24593C211yesmaximal, characteristic, complemented
23#24585C211yesmaximal, characteristic, complemented
24#24584C211yesmaximal, characteristic, complemented
25#24539C211yesmaximal, characteristic, complemented
26#24538C211yesmaximal, characteristic, complemented
27#24531C211yesmaximal, characteristic, complemented
28#24527C211yesmaximal, characteristic, complemented
29#21937C211yesmaximal, characteristic, complemented
30#21772C211yesmaximal, characteristic, complemented
31#20703C211yesmaximal, characteristic, complemented
32C2×#537C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#3198—28no—
36#3096—28no—
37C2×#481C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#481C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#482C2211yescharacteristic
42C2×#482C2211yescharacteristic
43C2×#482C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#480C2211yescharacteristic
47C2×#480C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#469C2211yescharacteristic
50C2×#468C2211yescharacteristic
51C2×#466C2211yescharacteristic
52C2×#465C2211yescharacteristic
53C2×#449C2211yescharacteristic
54C2×#449C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#447C2211yescharacteristic
57C2×#428C2211yescharacteristic
58C2×#427C2211yescharacteristic
59C2×#418C2211yescharacteristic
60C22×#102C2211yescharacteristic
61C2×#408C2211yescharacteristic
62C2×#408C2211yescharacteristic
63#2504C2211yescharacteristic
64#2504C2211yescharacteristic, complemented
65#2503C2211yescharacteristic
66#2503C2211yescharacteristic, complemented
67#2500C2211yescharacteristic
68#2500C2211yescharacteristic, complemented
69#2499C2211yescharacteristic
70#2499C2211yescharacteristic, complemented
71#2444—21no—
72#2444—21no—
73#2444—21no—
74#2444—21no—
75#2421—21no—
76#2421—21no—
77#2420—21no—
78#2420—21no—
79#2380—21no—
80#2375—21no—
81#2366—21no—
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic
84#2361C2211yescharacteristic
85#2361C2211yescharacteristic
86#2358—21no—
87#2347C2211yescharacteristic
88#2347C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2337—21no—
92#2337—21no—
93#2324C2211yescharacteristic
94#2324C2211yescharacteristic
95#2321—21no—
96#2321—21no—
97#2317C2211yescharacteristic, complemented
98#2311C2211yescharacteristic
99#2311C2211yescharacteristic, complemented
100C4×#121C2211yescharacteristic
101C4×#121C2211yescharacteristic
102#2297C2211yescharacteristic
103#2297C2211yescharacteristic, complemented
104C2×#382C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2085C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2085C2211yescharacteristic, complemented
110#2085C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2083C2211yescharacteristic, complemented
113#2073C2211yescharacteristic
114#2073C2211yescharacteristic
115#2073C2211yescharacteristic
116#2073C2211yescharacteristic
117#2073C2211yescharacteristic
118#2073C2211yescharacteristic
119#2071C2211yescharacteristic
120#2071C2211yescharacteristic
121#2068C2211yescharacteristic, complemented
122#2068C2211yescharacteristic, complemented
123#2068C2211yescharacteristic, complemented
124#2067C2211yescharacteristic, complemented
125#2066C2211yescharacteristic, complemented
126#2065C2211yescharacteristic, complemented
127#2065C2211yescharacteristic, complemented
128#2065C2211yescharacteristic, complemented
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2055C2211yescharacteristic
132#2055C2211yescharacteristic
133#2054C2211yescharacteristic
134#2054C2211yescharacteristic
135#2054C2211yescharacteristic
136#2054C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1894C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1875C2211yescharacteristic, complemented
166#1874C2211yescharacteristic, complemented
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1851C2211yescharacteristic
170#1851C2211yescharacteristic
171#1851C2211yescharacteristic, complemented
172#1851C2211yescharacteristic, complemented
173#1850C2211yescharacteristic
174#1850C2211yescharacteristic
175#1850C2211yescharacteristic, complemented
176#1850C2211yescharacteristic, complemented
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic, complemented
180#1825C2211yescharacteristic, complemented
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic, complemented
183#1824C2211yescharacteristic, complemented
184#1823C2211yescharacteristic
185#1823C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1798C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1797C2211yescharacteristic, complemented
198#1797C2211yescharacteristic, complemented
199#1788C2211yescharacteristic, complemented
200#1788C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203#1735C2211yescharacteristic, complemented
204C2×#340C2211yescharacteristic, complemented
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C23×D4C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#537—24no—
217#537—24no—
218#535—24no—
219#535D418yes—
220C2×#127—21no—
221C2×#124—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236#520—24no—
237#520—24no—
238C2×C4×Q8—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42C2311yescharacteristic
264#485—24no—
265#482—24no—
266#482—24no—
267#482—24no—
268#482—24no—
269#482—24no—
270#481—24no—
271#481—24no—
272#481—24no—
273#480—24no—
274#480—24no—
275#480—24no—
276#469—24no—
277#468—24no—
278#466—24no—
279#465—24no—
280#450—24no—
281#449—24no—
282#449—24no—
283#447—24no—
284#428—24no—
285#427—24no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306#418—24no—
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#102—24no—
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332#408—24no—
333#408—24no—
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342#400—21no—
343#400—21no—
344#400—21no—
345#400—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#391—21no—
359#391D411yescharacteristic
360#391D411yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390D411yescharacteristic
371#390D411yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—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#386D411yescharacteristic
429#386D411yescharacteristic
430#386D411yescharacteristic
431#386D411yescharacteristic
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#383—21no—
441#383—21no—
442#382—21no—
443#382—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#381—21no—
451#381—21no—
452#381—21no—
453#381—21no—
454#380—21no—
455#380—21no—
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478C2×#95—21no—
479C2×#95—21no—
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512C25—21no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41C2×D414yes—
524C2×#41#4114yes—
525C22×Q8C2×D411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4C2×D414yes—
541C22×D4C2×D411yescharacteristic
542C22×D4C2×D411yescharacteristic
543C22×D4C2×D411yescharacteristic
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C22×D4C2411yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4—21no—
557C23×C4C2×D411yescharacteristic
558C23×C4C2×D411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16—41no—
579C2×M16—41no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594#127—28no—
595#124—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—44no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—44no—
610#121—44no—
611#121—44no—
612#121C2×D414yes—
613#121C2×D414yes—
614#121C2×D414yes—
615#121C2×D414yes—
616#120—28no—
617#120—28no—
618C4×Q8—44no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—44no—
628C4×D4—44no—
629C4×D4—44no—
630C4×D4—82no—
631C4×D4—82no—
632C4×D4—82no—
633C4×D4—82no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—41no—
642#117—41no—
643#117—41no—
644#117—41no—
645#117C2×D414yes—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
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—21no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—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—82no—
723C2×C22⋊C4—82no—
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—41no—
744C2×C42—41no—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—22no—
752#107—22no—
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#106—22no—
758#106—22no—
759#106—22no—
760#106—22no—
761#106—22no—
762#106—22no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771#103—22no—
772#103—22no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—22no—
801C22⋊C8—22no—
802C22⋊C8—22no—
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#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843C24—21no—
844C24—21no—
845C24—24no—
846C24—21no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—82no—
861#41—82no—
862#41—82no—
863#41—82no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—41no—
871C2×Q8—41no—
872C2×Q8#12114yes—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—24no—
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—44no—
895C2×D4—44no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4#12114yes—
924C2×D4#12114yes—
925C2×D4#12114yes—
926C2×D4C22×D412yes—
927C2×D4C22×D412yes—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
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—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
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×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
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×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C2×#4112yes—
1004C22×C4C2×#4112yes—
1005C22×C4C2×#4112yes—
1006C22×C4C2511yescharacteristic
1007SD16—82no—
1008SD16—82no—
1009D8—82no—
1010D8—82no—
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—21no—
1037C2×C8—44no—
1038C2×C8—82no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—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—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4C22×D412yes—
1079C4⋊C4C22×D412yes—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C42—24no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—41no—
1137C42—41no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—81no—
1142C42—81no—
1143C42—81no—
1144C42—81no—
1145C42—81no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
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—21no—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—22no—
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—84no—
1186C23—84no—
1187C23—84no—
1188C23—162no—
1189C23—162no—
1190C23—162no—
1191C23—162no—
1192C23C2×#12112yes—
1193C23C2×#12112yes—
1194C23C2×#12112yes—
1195C23C23×D411yescharacteristic
1196Q8—44no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201D4—22no—
1202D4—22no—
1203D4—22no—
1204D4—22no—
1205D4—44no—
1206D4—44no—
1207D4—44no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—84no—
1217D4—84no—
1218D4—84no—
1219D4—84no—
1220D4—84no—
1221D4—84no—
1222D4—162no—
1223D4—162no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
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—22no—
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—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—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—84no—
1306C2×C4—82no—
1307C2×C4—82no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4—162no—
1316C2×C4—162no—
1317C2×C4C2×#12112yes—
1318C2×C4C2×#12112yes—
1319C2×C4C2×#12112yes—
1320C2×C4C23×D411yescharacteristic
1321C2×C4C22×#4111yescharacteristic
1322C2×C4#58511yescharacteristic
1323C2×C4#58511yescharacteristic
1324C2×C4#58511yescharacteristic
1325C2×C4#58511yescharacteristic
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
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—81no—
1362C22—81no—
1363C22—81no—
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—168no—
1377C22C22×#12111yescharacteristic
1378C22#348511yescharacteristic
1379C22#348511yescharacteristic
1380C22#358411yescharacteristic
1381C22#358411yescharacteristic
1382C22#358511yescharacteristic
1383C22#358511yescharacteristic
1384C4—22no—
1385C4—22no—
1386C4—22no—
1387C4—42no—
1388C4—42no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4#348511yescharacteristic
1409C4#348511yescharacteristic
1410C4#349111yescharacteristic
1411C4#349111yescharacteristic
1412C2—42no—
1413C2—42no—
1414C2—42no—
1415C2—82no—
1416C2—82no—
1417C2—161no—
1418C2#3544711yescharacteristic
1419C2#6043011yescharacteristic
1420C2#6043011yescharacteristic
1421C2#6176911yescharacteristic
1422C2#6177811yescharacteristic
1423C2#6181311yescharacteristic
1424C2#6181311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3198C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3096C2semidirect
3. #35618C2semidirect
4. #34411C2semidirect
5. #28129C2semidirect
6. #28127C2semidirect
7. #28116C2semidirect
8. #28116C2semidirect
9. #27655C2semidirect
10. #27654C2semidirect
11. #27651C2semidirect
12. #27651C2semidirect
13. #25230C2semidirect
14. #25228C2semidirect
15. #25227C2semidirect
16. #25225C2semidirect
17. #25214C2semidirect
18. #25212C2semidirect
19. #25207C2semidirect
20. #25205C2semidirect
21. #24597C2semidirect
22. #24593C2semidirect
23. #24585C2semidirect
24. #24584C2semidirect
25. #24539C2semidirect
26. #24538C2semidirect
27. #24531C2semidirect
28. #24527C2semidirect
29. #21937C2semidirect
30. #21772C2semidirect
31. #20703C2semidirect
64. #2504C22semidirect
66. #2503C22semidirect
68. #2500C22semidirect
70. #2499C22semidirect
97. #2317C22semidirect
99. #2311C22semidirect
103. #2297C22semidirect
104. C2×#382C22semidirect
105. #2085C22semidirect
106. #2085C22semidirect
107. #2085C22semidirect
108. #2085C22semidirect
109. #2085C22semidirect
110. #2085C22semidirect
111. #2084C22semidirect
112. #2083C22semidirect
121. #2068C22semidirect
122. #2068C22semidirect
123. #2068C22semidirect
124. #2067C22semidirect
125. #2066C22semidirect
126. #2065C22semidirect
127. #2065C22semidirect
128. #2065C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1948C22semidirect
144. #1947C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
149. #1926C22semidirect
150. #1925C22semidirect
151. #1925C22semidirect
152. #1925C22semidirect
165. #1875C22semidirect
166. #1874C22semidirect
167. #1873C22semidirect
168. #1872C22semidirect
171. #1851C22semidirect
172. #1851C22semidirect
175. #1850C22semidirect
176. #1850C22semidirect
179. #1825C22semidirect
180. #1825C22semidirect
182. #1824C22semidirect
183. #1824C22semidirect
185. #1823C22semidirect
186. #1823C22semidirect
195. #1798C22semidirect
196. #1798C22semidirect
197. #1797C22semidirect
198. #1797C22semidirect
199. #1788C22semidirect
200. #1788C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect
203. #1735C22semidirect
204. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
C2×#31982
C2×#30962
#356182
#344112
#281292
#281272
#281162
#276552
#276542
#276512
#252302
#252282
#252272
#252252
#252142
#252122
#252072
#252052
#245972
#245932
#245852
#245842
#245392
#245382
#245312
#245272
#219372
#217722
#207032