Finite Group Databasebeta

← #6877134

Subgroups — #6877134

Order 512.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36536C211yesmaximal, characteristic, complemented
2#36262C211yesmaximal, characteristic, complemented
3#33145C211yesmaximal, characteristic, complemented
4#32212C211yesmaximal, characteristic, complemented
5#32024C211yesmaximal, characteristic, complemented
6#32020C211yesmaximal, characteristic, complemented
7#31625C211yesmaximal, characteristic, complemented
8#30922C211yesmaximal, characteristic, complemented
9#30607C211yesmaximal, characteristic, complemented
10#30424C211yesmaximal, characteristic, complemented
11#30416C211yesmaximal, characteristic
12#30381C211yesmaximal, characteristic, complemented
13#30359C211yesmaximal, characteristic, complemented
14#29576C211yesmaximal, characteristic, complemented
15#29497C211yesmaximal, characteristic, complemented
16#29465C211yesmaximal, characteristic, complemented
17#29461C211yesmaximal, characteristic, complemented
18#27574C211yesmaximal, characteristic, complemented
19#27534C211yesmaximal, characteristic, complemented
20#27510C211yesmaximal, characteristic, complemented
21#27470C211yesmaximal, characteristic, complemented
22#27446C211yesmaximal, characteristic, complemented
23#27406C211yesmaximal, characteristic, complemented
24#26388C211yesmaximal, characteristic, complemented
25#25172C211yesmaximal, characteristic, complemented
26#24700C211yesmaximal, characteristic, complemented
27#24501C211yesmaximal, characteristic, complemented
28#22149C211yesmaximal, characteristic, complemented
29#22040C211yesmaximal, characteristic, complemented
30#21538C211yesmaximal, characteristic, complemented
31#21102C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#474C2211yescharacteristic, complemented
34C2×#469C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×#431C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic, complemented
42#2864C2211yescharacteristic, complemented
43#2860C2211yescharacteristic
44#2857C2211yescharacteristic
45#2855C2211yescharacteristic
46#2855C2211yescharacteristic, complemented
47#2854C2211yescharacteristic
48#2602—21no—
49#2601—21no—
50#2600—21no—
51#2600—21no—
52#2578—21no—
53#2578—21no—
54#2577—21no—
55#2577—21no—
56#2561—21no—
57#2560—21no—
58#2557—21no—
59#2536C2211yescharacteristic
60#2535C2211yescharacteristic
61#2534—21no—
62#2512C2211yescharacteristic
63#2495C2211yescharacteristic
64#2495C2211yescharacteristic, complemented
65#2491C2211yescharacteristic
66#2486C2211yescharacteristic
67#2452C2211yescharacteristic
68#2427C2211yescharacteristic
69#2427C2211yescharacteristic, complemented
70#2422C2211yescharacteristic
71#2408C2211yescharacteristic
72#2356C2211yescharacteristic, complemented
73#2353—21no—
74#2353—21no—
75#2349C2211yescharacteristic, complemented
76#2344C2211yescharacteristic
77#2342—21no—
78D4×C22⋊C4C2211yescharacteristic
79C4×#124C2211yescharacteristic, complemented
80C4×#121C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C4×#121C2211yescharacteristic, complemented
83#2293C2211yescharacteristic
84C2×#390C2211yescharacteristic
85C42×D4C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2024C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1988C2211yescharacteristic, complemented
127#1983C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1970C2211yescharacteristic
130#1970C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1934C2211yescharacteristic, complemented
148#1933C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic, complemented
165#1894C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic
174#1874C2211yescharacteristic
175#1872C2211yescharacteristic
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1851C2211yescharacteristic, complemented
189#1851C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1809C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×C4⋊C8C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic, complemented
200C4×C22⋊C8C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210#551—48no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4D411yescharacteristic
233C2×C4×D4D411yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#474—42no—
249#469—24no—
250#468—42no—
251#463—24no—
252#450—42no—
253#447—24no—
254#442—42no—
255#431—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C4×M16—42no—
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#393—21no—
330#393—21no—
331#392—21no—
332#392—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384C2311yescharacteristic
408#383—21no—
409#383—21no—
410#383—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#381—21no—
417#381—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431#379—21no—
432C4×C4⋊C4D411yescharacteristic
433C4×C4⋊C4D411yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4D411yescharacteristic
446C4×C22⋊C4D411yescharacteristic
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452C2×#95—21no—
453C43C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×D8—22no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8#4114yes—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546#126—44no—
547#126—44no—
548#124—22no—
549#124—41no—
550#124—44no—
551#123—44no—
552#123—44no—
553#123—44no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#120—44no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—24no—
572C4×D4—22no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—42no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—44no—
586C4×D4—44no—
587C4×D4—44no—
588#117—44no—
589#117—44no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
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—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
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—44no—
666C2×C22⋊C4—44no—
667C2×C22⋊C4—44no—
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—41no—
680C2×C42—41no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#107—22no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#106—22no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#103—22no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742#97—22no—
743#97—41no—
744C4×C8—22no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
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#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—21no—
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—42no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×D4—22no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
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—41no—
829C2×D4—41no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4C2×#4112yes—
850C2×D4C2×#4112yes—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
918C22×C4C2511yescharacteristic
919SD16—82no—
920SD16—82no—
921D8—44no—
922D8—82no—
923M16—44no—
924M16—44no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
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×C8C2×#4112yes—
948C2×C8H(5,𝔽2)12yes—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
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—41no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
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—42no—
1027C22⋊C4—42no—
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—
1040C42—22no—
1041C42—22no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—41no—
1053C42—41no—
1054C42—41no—
1055C42—41no—
1056C42—41no—
1057C42—41no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
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—84no—
1098C23—84no—
1099C23—84no—
1100C23—84no—
1101C23—162no—
1102C23—162no—
1103C23—162no—
1104C23C2×AGL(1,ℤ/8)12yes—
1105C23C23×D411yescharacteristic
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—162no—
1111D4—22no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—44no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—84no—
1125D4—84no—
1126D4—84no—
1127D4—84no—
1128D4—162no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
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—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
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—44no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
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—82no—
1211C2×C4—82no—
1212C2×C4—82no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4C2×AGL(1,ℤ/8)12yes—
1220C2×C4C2×AGL(1,ℤ/8)12yes—
1221C2×C4#57512yes—
1222C2×C4C22×#4111yescharacteristic
1223C2×C4C2×H(5,𝔽2)11yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C8—22no—
1229C8—22no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—42no—
1245C22—42no—
1246C22—41no—
1247C22—42no—
1248C22—42no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
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—168no—
1272C22#344911yescharacteristic
1273C22D4×#4111yescharacteristic
1274C22#349611yescharacteristic
1275C22C22×AGL(1,ℤ/8)11yescharacteristic
1276C22C2×#57511yescharacteristic
1277C22#358411yescharacteristic
1278C22#358411yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4#350511yescharacteristic
1305C4#352111yescharacteristic
1306C4#353311yescharacteristic
1307C4#356611yescharacteristic
1308C2—42no—
1309C2—81no—
1310C2—82no—
1311C2—82no—
1312C2—161no—
1313C2#3994211yescharacteristic
1314C2#6096511yescharacteristic
1315C2#6100711yescharacteristic
1316C2#6143711yescharacteristic
1317C2#6144211yescharacteristic
1318C2#6225311yescharacteristic
1319C2#6226111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36536C2semidirect
2. #36262C2semidirect
3. #33145C2semidirect
4. #32212C2semidirect
5. #32024C2semidirect
6. #32020C2semidirect
7. #31625C2semidirect
8. #30922C2semidirect
9. #30607C2semidirect
10. #30424C2semidirect
12. #30381C2semidirect
13. #30359C2semidirect
14. #29576C2semidirect
15. #29497C2semidirect
16. #29465C2semidirect
17. #29461C2semidirect
18. #27574C2semidirect
19. #27534C2semidirect
20. #27510C2semidirect
21. #27470C2semidirect
22. #27446C2semidirect
23. #27406C2semidirect
24. #26388C2semidirect
25. #25172C2semidirect
26. #24700C2semidirect
27. #24501C2semidirect
28. #22149C2semidirect
29. #22040C2semidirect
30. #21538C2semidirect
31. #21102C2semidirect
33. C2×#474C22semidirect
41. C2×C4×M16C22semidirect
42. #2864C22semidirect
46. #2855C22semidirect
64. #2495C22semidirect
69. #2427C22semidirect
72. #2356C22semidirect
75. #2349C22semidirect
79. C4×#124C22semidirect
82. C4×#121C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2099C22semidirect
89. #2096C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
99. #2077C22semidirect
100. #2076C22semidirect
110. #2058C22semidirect
113. #2042C22semidirect
114. #2036C22semidirect
118. #2034C22semidirect
122. #2024C22semidirect
126. #1988C22semidirect
127. #1983C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1942C22semidirect
137. #1942C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
141. #1935C22semidirect
146. #1934C22semidirect
147. #1934C22semidirect
148. #1933C22semidirect
149. #1933C22semidirect
150. #1928C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
164. #1895C22semidirect
165. #1894C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
188. #1851C22semidirect
189. #1851C22semidirect
190. #1809C22semidirect
191. #1809C22semidirect
193. #1802C22semidirect
196. #1776C22semidirect
197. C4×C4⋊C8C22semidirect
199. #1762C22semidirect
201. C4×C22⋊C8C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#365362
#362622
#331452
#322122
#320242
#320202
#316252
#309222
#306072
#304242
#304162
#303812
#303592
#295762
#294972
#294652
#294612
#275742
#275342
#275102
#274702
#274462
#274062
#263882
#251722
#247002
#245012
#221492
#220402
#215382
#211022