Finite Group Databasebeta

← #6793114

Subgroups — #6793114

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36135C211yesmaximal, characteristic, complemented
2#34932C211yesmaximal, characteristic, complemented
3#33199C211yesmaximal, characteristic, complemented
4#31632C211yesmaximal, characteristic, complemented
5#31630C211yesmaximal, characteristic, complemented
6#31604C211yesmaximal, characteristic, complemented
7#31602C211yesmaximal, characteristic, complemented
8#31566C211yesmaximal, characteristic, complemented
9#31564C211yesmaximal, characteristic, complemented
10#31552C211yesmaximal, characteristic, complemented
11#31550C211yesmaximal, characteristic, complemented
12#29944C211yesmaximal, characteristic, complemented
13#29943C211yesmaximal, characteristic, complemented
14#29223C211yesmaximal, characteristic, complemented
15#28282C211yesmaximal, characteristic, complemented
16#28154C211yesmaximal, characteristic, complemented
17#28152C211yesmaximal, characteristic
18#26124C211yesmaximal, characteristic, complemented
19#26122C211yesmaximal, characteristic, complemented
20#25354C211yesmaximal, characteristic, complemented
21#25352C211yesmaximal, characteristic, complemented
22#24841C211yesmaximal, characteristic, complemented
23#24839C211yesmaximal, characteristic, complemented
24#24829C211yesmaximal, characteristic, complemented
25#24827C211yesmaximal, characteristic, complemented
26#24159C211yesmaximal, characteristic, complemented
27#24158C211yesmaximal, characteristic, complemented
28#22648C211yesmaximal, characteristic, complemented
29#21890C211yesmaximal, characteristic, complemented
30#21887C211yesmaximal, characteristic, complemented
31#21507C211yesmaximal, characteristic, complemented
32C2×#529—21no—
33C2×#529C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic
44C2×#423C2211yescharacteristic
45C22×C4⋊C8C2211yescharacteristic
46#2859C2211yescharacteristic
47#2851C2211yescharacteristic
48#2851C2211yescharacteristic
49#2553—21no—
50#2553—21no—
51#2553—21no—
52#2553—21no—
53#2552C2211yescharacteristic
54#2547C2211yescharacteristic
55#2542C2211yescharacteristic
56#2537C2211yescharacteristic
57#2536C2211yescharacteristic
58#2535C2211yescharacteristic
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2489—21no—
62#2478—21no—
63#2478—21no—
64#2455—21no—
65#2455—21no—
66#2427—21no—
67#2423C2211yescharacteristic
68#2423C2211yescharacteristic
69#2422C2211yescharacteristic
70#2422C2211yescharacteristic
71#2422C2211yescharacteristic
72#2422C2211yescharacteristic
73#2395—21no—
74#2395—21no—
75#2359—21no—
76#2359—21no—
77#2351C2211yescharacteristic
78#2349C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic
80C4×#124C2211yescharacteristic
81C4×C22⋊Q8—21no—
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2285C2211yescharacteristic
85#2285C2211yescharacteristic
86C42×D4C2211yescharacteristic
87C42×D4C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2100C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2099C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2077C2211yescharacteristic
108#2076C2211yescharacteristic
109#2076C2211yescharacteristic
110#2075C2211yescharacteristic
111#2075C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1993C2211yescharacteristic
129#1993C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1989C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1927C2211yescharacteristic
149#1925C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1865C2211yescharacteristic
169#1864C2211yescharacteristic
170#1863C2211yescharacteristic
171#1862C2211yescharacteristic
172#1851C2211yescharacteristic
173#1851C2211yescharacteristic
174#1850C2211yescharacteristic
175#1850C2211yescharacteristic
176#1842C2211yescharacteristic
177#1836C2211yescharacteristic
178#1836C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1808C2211yescharacteristic
182#1807C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1802C2211yescharacteristic
198#1797C2211yescharacteristic
199#1797C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1762C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210#529—24no—
211#529—24no—
212#529—42no—
213#529—42no—
214#529—48no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4D411yescharacteristic
248C2×C4×D4D411yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117—21no—
258C2×#117—21no—
259C2×#117—21no—
260C22×C42—21no—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263#478—42no—
264#478—42no—
265#477—42no—
266#476—42no—
267#463—24no—
268#442—42no—
269#440—42no—
270#435—42no—
271#435—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282#423—42no—
283C2×C4⋊C8—42no—
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—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#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#382—21no—
410#382—21no—
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4D411yescharacteristic
434C4×C4⋊C4D411yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C2×#95—21no—
455C43C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—41no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543#126—44no—
544#126—44no—
545#126—44no—
546#126—44no—
547#125—22no—
548#125—22no—
549#125—22no—
550#125—22no—
551#125—44no—
552#124—22no—
553#124—44no—
554#124#4114yes—
555#123—44no—
556#123—44no—
557#123—44no—
558#123—44no—
559#123—44no—
560#123—44no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—44no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—44no—
583C4×D4—24no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—42no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—44no—
603#117—44no—
604#117—44no—
605#117—44no—
606#117—44no—
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⋊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—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
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—21no—
684C2×C22⋊C4—21no—
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×C42—22no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—44no—
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727C4⋊C8—22no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
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—41no—
757#102—41no—
758#102—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—22no—
764#97—22no—
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#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#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—21no—
803C24—21no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8C2×#4112yes—
815C2×D4—22no—
816C2×D4—22no—
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—41no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4C2×#4112yes—
841C2×D42−1+412yes—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
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—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
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—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2511yescharacteristic
911SD16—44no—
912D8—44no—
913M16—82no—
914M16—82no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
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—82no—
940C2×C8—82no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
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—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
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—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
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—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4AGL(1,ℤ/8)14yes—
1038C42—22no—
1039C42—22no—
1040C42—22no—
1041C42—22no—
1042C42—22no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—41no—
1050C42—41no—
1051C42—41no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42C2×#4112yes—
1061C42H(5,𝔽2)12yes—
1062C42H(5,𝔽2)12yes—
1063C422−1+412yes—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—22no—
1074C23—21no—
1075C23—22no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23C2×AGL(1,ℤ/8)12yes—
1092C23C23×D411yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—41no—
1096Q8—41no—
1097Q8—84no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—44no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—84no—
1108D4—84no—
1109D4—84no—
1110D4—84no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
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—82no—
1194C2×C4—84no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—162no—
1200C2×C4#53712yes—
1201C2×C4#53712yes—
1202C2×C4#54612yes—
1203C2×C4#54612yes—
1204C2×C4C2×AGL(1,ℤ/8)12yes—
1205C2×C4C2×AGL(1,ℤ/8)12yes—
1206C2×C4#57512yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4C2×2−1+411yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—42no—
1230C22—42no—
1231C22—41no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—42no—
1236C22—41no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—41no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22C2×#53711yescharacteristic
1250C22C2×#54611yescharacteristic
1251C22#348911yescharacteristic
1252C22C22×AGL(1,ℤ/8)11yescharacteristic
1253C22C2×#57511yescharacteristic
1254C22#358411yescharacteristic
1255C22#358611yescharacteristic
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4#351511yescharacteristic
1283C4#352011yescharacteristic
1284C4#354611yescharacteristic
1285C4#355211yescharacteristic
1286C2—42no—
1287C2—81no—
1288C2—82no—
1289C2—82no—
1290C2#3890811yescharacteristic
1291C2#6091611yescharacteristic
1292C2#6092711yescharacteristic
1293C2#6114111yescharacteristic
1294C2#6116111yescharacteristic
1295C2#6212111yescharacteristic
1296C2#6213711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28152C2
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. #36135C2semidirect
2. #34932C2semidirect
3. #33199C2semidirect
4. #31632C2semidirect
5. #31630C2semidirect
6. #31604C2semidirect
7. #31602C2semidirect
8. #31566C2semidirect
9. #31564C2semidirect
10. #31552C2semidirect
11. #31550C2semidirect
12. #29944C2semidirect
13. #29943C2semidirect
14. #29223C2semidirect
15. #28282C2semidirect
16. #28154C2semidirect
18. #26124C2semidirect
19. #26122C2semidirect
20. #25354C2semidirect
21. #25352C2semidirect
22. #24841C2semidirect
23. #24839C2semidirect
24. #24829C2semidirect
25. #24827C2semidirect
26. #24159C2semidirect
27. #24158C2semidirect
28. #22648C2semidirect
29. #21890C2semidirect
30. #21887C2semidirect
31. #21507C2semidirect

Maximal subgroups

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

subgroupindex
#361352
#349322
#331992
#316322
#316302
#316042
#316022
#315662
#315642
#315522
#315502
#299442
#299432
#292232
#282822
#281542
#281522
#261242
#261222
#253542
#253522
#248412
#248392
#248292
#248272
#241592
#241582
#226482
#218902
#218872
#215072