Finite Group Databasebeta

← #6769767

Subgroups — #6769767

Order 512.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38945C211yesmaximal, characteristic
2#35652C211yesmaximal, characteristic, complemented
3#33116C211yesmaximal, characteristic, complemented
4#32445C211yesmaximal, characteristic, complemented
5#32347C211yesmaximal, characteristic, complemented
6#32303C211yesmaximal, characteristic, complemented
7#32170C211yesmaximal, characteristic, complemented
8#32102C211yesmaximal, characteristic, complemented
9#32071C211yesmaximal, characteristic, complemented
10#31310C211yesmaximal, characteristic, complemented
11#30547C211yesmaximal, characteristic, complemented
12#30123C211yesmaximal, characteristic, complemented
13#30065C211yesmaximal, characteristic, complemented
14#29563C211yesmaximal, characteristic, complemented
15#29367C211yesmaximal, characteristic, complemented
16#28587C211yesmaximal, characteristic, complemented
17#28352C211yesmaximal, characteristic, complemented
18#28131C211yesmaximal, characteristic, complemented
19#27944C211yesmaximal, characteristic, complemented
20#27899C211yesmaximal, characteristic, complemented
21#27717C211yesmaximal, characteristic, complemented
22#27594C211yesmaximal, characteristic, complemented
23#27280C211yesmaximal, characteristic, complemented
24#25535C211yesmaximal, characteristic, complemented
25#24452C211yesmaximal, characteristic, complemented
26#24103C211yesmaximal, characteristic, complemented
27#24037C211yesmaximal, characteristic, complemented
28#22790C211yesmaximal, characteristic, complemented
29#22226C211yesmaximal, characteristic, complemented
30#22052C211yesmaximal, characteristic, complemented
31#21062C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#465C2211yescharacteristic, complemented
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#428C2211yescharacteristic, complemented
43C2×#417C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2861C2211yescharacteristic
46#2705—21no—
47#2705—21no—
48#2678—21no—
49#2678—21no—
50#2620C2211yescharacteristic
51#2619C2211yescharacteristic
52#2595—21no—
53#2594—21no—
54#2585—21no—
55#2577—21no—
56#2566C2211yescharacteristic
57#2544C2211yescharacteristic
58#2531—21no—
59#2528—21no—
60#2525—21no—
61#2514C2211yescharacteristic, complemented
62#2507C2211yescharacteristic, complemented
63#2501C2211yescharacteristic
64#2499C2211yescharacteristic
65#2499C2211yescharacteristic, complemented
66#2494—21no—
67#2494C2211yescharacteristic
68#2489C2211yescharacteristic
69#2485C2211yescharacteristic
70#2456—21no—
71#2456—21no—
72#2442C2211yescharacteristic, complemented
73#2433C2211yescharacteristic
74#2431C2211yescharacteristic
75#2418—21no—
76#2418—21no—
77#2417C2211yescharacteristic
78#2323C2211yescharacteristic
79#2323C2211yescharacteristic, complemented
80#2314C2211yescharacteristic
81#2311C2211yescharacteristic
82#2309C2211yescharacteristic
83C4×#127C2211yescharacteristic
84C4×#125C2211yescharacteristic, complemented
85#2295C2211yescharacteristic, complemented
86#2293C2211yescharacteristic
87#2274C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2059C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2026C2211yescharacteristic, complemented
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1971C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1961C2211yescharacteristic
136#1959C2211yescharacteristic, complemented
137#1958C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1934C2211yescharacteristic
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic, complemented
159#1925C2211yescharacteristic, complemented
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic, complemented
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic, complemented
174#1873C2211yescharacteristic
175#1870C2211yescharacteristic
176#1869C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1839C2211yescharacteristic, complemented
189#1836C2211yescharacteristic, complemented
190#1823C2211yescharacteristic, complemented
191#1818C2211yescharacteristic
192#1798C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199#1750C2211yescharacteristic
200#1745C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—42no—
212#553—42no—
213#546—42no—
214#546—42no—
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251#490—24no—
252#484—42no—
253#482—42no—
254#482—42no—
255#468—42no—
256#465—42no—
257#452—42no—
258#450—24no—
259#428—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274#417—24no—
275#416—42no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#401—21no—
319#401—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390D411yescharacteristic
366#390D411yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389D411yescharacteristic
378#389D411yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388D411yescharacteristic
399#388D411yescharacteristic
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462C43C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554#127—22no—
555#127—41no—
556#127—41no—
557#127—41no—
558#126—44no—
559#125—22no—
560#125—41no—
561#125—41no—
562#125—41no—
563#124—41no—
564#124—41no—
565#124—41no—
566#124—41no—
567#123—44no—
568#123—44no—
569#123—82no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—44no—
582#121—41no—
583#121—41no—
584#121—44no—
585#120—44no—
586#120—82no—
587#120—82no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—44no—
597C4×D4—82no—
598C4×D4—82no—
599#117—22no—
600#117—22no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—44no—
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725#103—22no—
726#103—22no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102#4114yes—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—22no—
764#97—41no—
765#97—41no—
766C4×C8—41no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—44no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×D4—22no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4C2×#4112yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4H(5,𝔽2)12yes—
939C22×C4H(5,𝔽2)12yes—
940C22×C4C2511yescharacteristic
941Q16—82no—
942SD16—82no—
943SD16—82no—
944SD16—82no—
945M16—44no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—82no—
970C2×C8C2×#4112yes—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4C2×#4112yes—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—41no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—21no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—84no—
1121C23—84no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23#53512yes—
1128C23C23×D411yescharacteristic
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137D4—22no—
1138D4—22no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—82no—
1150D4—84no—
1151D4—84no—
1152D4—84no—
1153D4—84no—
1154D4—84no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—84no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4#53512yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22C2×#53511yescharacteristic
1298C22D4×#4111yescharacteristic
1299C22#348511yescharacteristic
1300C22#358411yescharacteristic
1301C22#358511yescharacteristic
1302C22#358511yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4#349411yescharacteristic
1330C4#351311yescharacteristic
1331C4#354511yescharacteristic
1332C4#356011yescharacteristic
1333C2—42no—
1334C2—81no—
1335C2—82no—
1336C2—161no—
1337C2—161no—
1338C2#3836211yescharacteristic
1339C2#6081611yescharacteristic
1340C2#6083011yescharacteristic
1341C2#6150311yescharacteristic
1342C2#6154811yescharacteristic
1343C2#6179311yescharacteristic
1344C2#6181311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38945C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35652C2semidirect
3. #33116C2semidirect
4. #32445C2semidirect
5. #32347C2semidirect
6. #32303C2semidirect
7. #32170C2semidirect
8. #32102C2semidirect
9. #32071C2semidirect
10. #31310C2semidirect
11. #30547C2semidirect
12. #30123C2semidirect
13. #30065C2semidirect
14. #29563C2semidirect
15. #29367C2semidirect
16. #28587C2semidirect
17. #28352C2semidirect
18. #28131C2semidirect
19. #27944C2semidirect
20. #27899C2semidirect
21. #27717C2semidirect
22. #27594C2semidirect
23. #27280C2semidirect
24. #25535C2semidirect
25. #24452C2semidirect
26. #24103C2semidirect
27. #24037C2semidirect
28. #22790C2semidirect
29. #22226C2semidirect
30. #22052C2semidirect
31. #21062C2semidirect
35. C2×#484C22semidirect
37. C2×#482C22semidirect
39. C2×#465C22semidirect
42. C2×#428C22semidirect
61. #2514C22semidirect
62. #2507C22semidirect
65. #2499C22semidirect
72. #2442C22semidirect
79. #2323C22semidirect
84. C4×#125C22semidirect
85. #2295C22semidirect
87. #2274C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2097C22semidirect
91. #2096C22semidirect
92. #2095C22semidirect
96. #2085C22semidirect
97. #2074C22semidirect
100. #2068C22semidirect
102. #2059C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
105. #2056C22semidirect
110. #2042C22semidirect
119. #2026C22semidirect
120. #2026C22semidirect
123. #2015C22semidirect
128. #1992C22semidirect
133. #1971C22semidirect
136. #1959C22semidirect
137. #1958C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
142. #1935C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
153. #1926C22semidirect
158. #1925C22semidirect
159. #1925C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
164. #1895C22semidirect
168. #1880C22semidirect
169. #1878C22semidirect
171. #1877C22semidirect
173. #1874C22semidirect
178. #1864C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
186. #1847C22semidirect
187. #1845C22semidirect
188. #1839C22semidirect
189. #1836C22semidirect
190. #1823C22semidirect
192. #1798C22semidirect
197. #1753C22semidirect
198. #1752C22semidirect
200. #1745C22semidirect
201. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#389452
#356522
#331162
#324452
#323472
#323032
#321702
#321022
#320712
#313102
#305472
#301232
#300652
#295632
#293672
#285872
#283522
#281312
#279442
#278992
#277172
#275942
#272802
#255352
#244522
#241032
#240372
#227902
#222262
#220522
#210622