Finite Group Databasebeta

← #7536941

Subgroups — #7536941

Order 512.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59820C211yesmaximal, characteristic, complemented
2#36420C211yesmaximal, characteristic, complemented
3#32675C211yesmaximal, characteristic, complemented
4#32605C211yesmaximal, characteristic, complemented
5#32379C211yesmaximal, characteristic, complemented
6#31598C211yesmaximal, characteristic, complemented
7#28877C211yesmaximal, characteristic, complemented
8#28579C211yesmaximal, characteristic, complemented
9#28353C211yesmaximal, characteristic
10#28303C211yesmaximal, characteristic, complemented
11#28017C211yesmaximal, characteristic, complemented
12#27944C211yesmaximal, characteristic, complemented
13#27499C211yesmaximal, characteristic, complemented
14#27488C211yesmaximal, characteristic, complemented
15#27190C211yesmaximal, characteristic, complemented
16#27090C211yesmaximal, characteristic, complemented
17#27065C211yesmaximal, characteristic, complemented
18#26593C211yesmaximal, characteristic, complemented
19#26323C211yesmaximal, characteristic, complemented
20#25221C211yesmaximal, characteristic, complemented
21#25093C211yesmaximal, characteristic, complemented
22#25073C211yesmaximal, characteristic, complemented
23#24589C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#23239C211yesmaximal, characteristic, complemented
26#23106C211yesmaximal, characteristic, complemented
27#22947C211yesmaximal, characteristic, complemented
28#22880C211yesmaximal, characteristic, complemented
29#22807C211yesmaximal, characteristic, complemented
30C4×#482C211yesmaximal, characteristic, complemented
31#21060C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#484C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2865—21no—
46#2850C2211yescharacteristic
47#2730—21no—
48#2705—21no—
49#2595—21no—
50#2592C2211yescharacteristic, complemented
51#2578—21no—
52#2570C2211yescharacteristic, complemented
53#2548C2211yescharacteristic
54#2538C2211yescharacteristic
55#2534—21no—
56#2532—21no—
57#2531—21no—
58#2530—21no—
59#2513C2211yescharacteristic, complemented
60#2512C2211yescharacteristic
61#2512C2211yescharacteristic
62#2511C2211yescharacteristic, complemented
63#2501C2211yescharacteristic
64#2500C2211yescharacteristic
65#2499C2211yescharacteristic
66#2477—21no—
67#2471—21no—
68#2467—21no—
69#2445C2211yescharacteristic
70#2445C2211yescharacteristic
71#2433C2211yescharacteristic
72#2412—21no—
73#2411—21no—
74#2367C2211yescharacteristic, complemented
75#2366C2211yescharacteristic
76#2363C2211yescharacteristic
77#2362C2211yescharacteristic
78#2356C2211yescharacteristic, complemented
79#2355C2211yescharacteristic, complemented
80#2354C2211yescharacteristic
81#2354C2211yescharacteristic, complemented
82#2344C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86#2298—21no—
87C2×#390C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2096C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2014C2211yescharacteristic
116#2012C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic, complemented
119#2011C2211yescharacteristic
120#2011C2211yescharacteristic
121#1985C2211yescharacteristic, complemented
122#1984C2211yescharacteristic, complemented
123#1982C2211yescharacteristic
124#1973C2211yescharacteristic, complemented
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1970C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic, complemented
133#1961C2211yescharacteristic
134#1957C2211yescharacteristic
135#1949C2211yescharacteristic, complemented
136#1948C2211yescharacteristic, complemented
137#1948C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1933C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic, complemented
157#1925C2211yescharacteristic, complemented
158#1925C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1895C2211yescharacteristic
168#1894C2211yescharacteristic
169#1880C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic, complemented
173#1879C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1875C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1854C2211yescharacteristic
181#1851C2211yescharacteristic
182#1851C2211yescharacteristic
183#1847C2211yescharacteristic, complemented
184#1845C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic, complemented
189C4×#107C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#551—48no—
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8D411yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#120—21no—
229C2×#120—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117—21no—
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C42C2311yescharacteristic
248#484—24no—
249#482—24no—
250#481—42no—
251#469—42no—
252#468—42no—
253#460—24no—
254#450—42no—
255#447—24no—
256C4×D8—24no—
257#428—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—24no—
277#418—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#392—21no—
341#392—21no—
342#391—21no—
343#391D411yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
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#385—21no—
420#385D411yescharacteristic
421#385D411yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#383—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380D411yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
459#376—21no—
460C43—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551#127—22no—
552#127—41no—
553#127—41no—
554#127—41no—
555#126—44no—
556#126—44no—
557#124—41no—
558#124—41no—
559#124—44no—
560#123—44no—
561#123—44no—
562#123—44no—
563#123—82no—
564C22⋊Q8—24no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—44no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#120—44no—
573#120—82no—
574C4×Q8—22no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587C4×D4—44no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—44no—
592#117—41no—
593#117—44no—
594#117—44no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
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—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—22no—
706#107—22no—
707#107—22no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
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#4114yes—
750C22⋊C8—22no—
751C22⋊C8#4114yes—
752#97—41no—
753#97—41no—
754C4×C8—22no—
755C4×C8—41no—
756C4×C8—41no—
757C4×C8—41no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
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#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—42no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24C22×D411yescharacteristic
809C2×Q8—22no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4C2×#4112yes—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C2×#4112yes—
918C22×C4H(5,𝔽2)12yes—
919C22×C4C2511yescharacteristic
920SD16—82no—
921SD16—82no—
922SD16—82no—
923D8—44no—
924D8—82no—
925D8—82no—
926M16—44no—
927M16—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C2×#4112yes—
950C2×C8C2×#4112yes—
951C2×C8C2×#4112yes—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4AGL(1,ℤ/8)14yes—
998C4⋊C4C2×#4112yes—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—41no—
1058C42—41no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—22no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—84no—
1106C23—84no—
1107C23—84no—
1108C23—84no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23#55012yes—
1113C23C23×D411yescharacteristic
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—82no—
1119D4—22no—
1120D4—22no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—84no—
1136D4—84no—
1137D4—84no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141D4—162no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
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—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
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—82no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—82no—
1221C2×C4—84no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4#55012yes—
1225C2×C4C2×AGL(1,ℤ/8)12yes—
1226C2×C4C2×AGL(1,ℤ/8)12yes—
1227C2×C4C2×AGL(1,ℤ/8)12yes—
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C8—22no—
1235C8—22no—
1236C8—22no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—168no—
1278C22C2×#55011yescharacteristic
1279C22D4×#4111yescharacteristic
1280C22#348511yescharacteristic
1281C22C22×AGL(1,ℤ/8)11yescharacteristic
1282C22#358411yescharacteristic
1283C22#358411yescharacteristic
1284C22#358511yescharacteristic
1285C4—22no—
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4#347511yescharacteristic
1311C4#351311yescharacteristic
1312C4#352111yescharacteristic
1313C4#354511yescharacteristic
1314C2—42no—
1315C2—82no—
1316C2—161no—
1317C2—161no—
1318C2—161no—
1319C2#5904811yescharacteristic
1320C2#6140211yescharacteristic
1321C2#6141311yescharacteristic
1322C2#6143711yescharacteristic
1323C2#6153511yescharacteristic
1324C2#6173311yescharacteristic
1325C2#6174911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28353C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59820C2semidirect
2. #36420C2semidirect
3. #32675C2semidirect
4. #32605C2semidirect
5. #32379C2semidirect
6. #31598C2semidirect
7. #28877C2semidirect
8. #28579C2semidirect
10. #28303C2semidirect
11. #28017C2semidirect
12. #27944C2semidirect
13. #27499C2semidirect
14. #27488C2semidirect
15. #27190C2semidirect
16. #27090C2semidirect
17. #27065C2semidirect
18. #26593C2semidirect
19. #26323C2semidirect
20. #25221C2semidirect
21. #25093C2semidirect
22. #25073C2semidirect
23. #24589C2semidirect
24. #24538C2semidirect
25. #23239C2semidirect
26. #23106C2semidirect
27. #22947C2semidirect
28. #22880C2semidirect
29. #22807C2semidirect
30. C4×#482C2semidirect
31. #21060C2semidirect
50. #2592C22semidirect
52. #2570C22semidirect
59. #2513C22semidirect
62. #2511C22semidirect
74. #2367C22semidirect
78. #2356C22semidirect
79. #2355C22semidirect
81. #2354C22semidirect
89. #2096C22semidirect
90. #2095C22semidirect
92. #2093C22semidirect
96. #2092C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
102. #2073C22semidirect
104. #2071C22semidirect
106. #2067C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
112. #2054C22semidirect
113. #2042C22semidirect
118. #2012C22semidirect
121. #1985C22semidirect
122. #1984C22semidirect
124. #1973C22semidirect
132. #1968C22semidirect
135. #1949C22semidirect
136. #1948C22semidirect
137. #1948C22semidirect
138. #1943C22semidirect
140. #1933C22semidirect
141. #1927C22semidirect
142. #1927C22semidirect
147. #1926C22semidirect
148. #1926C22semidirect
149. #1926C22semidirect
156. #1925C22semidirect
157. #1925C22semidirect
158. #1925C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1918C22semidirect
163. #1917C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
172. #1879C22semidirect
173. #1879C22semidirect
176. #1877C22semidirect
179. #1863C22semidirect
183. #1847C22semidirect
184. #1845C22semidirect
188. #1802C22semidirect
189. C4×#107C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. C8×C4⋊C4C22semidirect
194. #1763C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#598202
#364202
#326752
#326052
#323792
#315982
#288772
#285792
#283532
#283032
#280172
#279442
#274992
#274882
#271902
#270902
#270652
#265932
#263232
#252212
#250932
#250732
#245892
#245382
#232392
#231062
#229472
#228802
#228072
C4×#4822
#210602