Finite Group Databasebeta

← #6724893

Subgroups — #6724893

Order 512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39154C211yesmaximal, characteristic
2#36439C211yesmaximal, characteristic
3#32984C211yesmaximal, characteristic, complemented
4#32461C211yesmaximal, characteristic, complemented
5#32303C211yesmaximal, characteristic, complemented
6#32065C211yesmaximal, characteristic, complemented
7#32007C211yesmaximal, characteristic, complemented
8#31424C211yesmaximal, characteristic, complemented
9#31320C211yesmaximal, characteristic, complemented
10#31201C211yesmaximal, characteristic, complemented
11#31103C211yesmaximal, characteristic, complemented
12#29893C211yesmaximal, characteristic, complemented
13#29743C211yesmaximal, characteristic, complemented
14#28782C211yesmaximal, characteristic, complemented
15#28558C211yesmaximal, characteristic, complemented
16#27481C211yesmaximal, characteristic, complemented
17#27356C211yesmaximal, characteristic, complemented
18#27115C211yesmaximal, characteristic, complemented
19#26558C211yesmaximal, characteristic, complemented
20#26431C211yesmaximal, characteristic, complemented
21#26356C211yesmaximal, characteristic, complemented
22#26314C211yesmaximal, characteristic, complemented
23#26223C211yesmaximal, characteristic, complemented
24#26154C211yesmaximal, characteristic, complemented
25#26133C211yesmaximal, characteristic, complemented
26#24123C211yesmaximal, characteristic, complemented
27#24096C211yesmaximal, characteristic, complemented
28#23036C211yesmaximal, characteristic, complemented
29#22662C211yesmaximal, characteristic, complemented
30#22036C211yesmaximal, characteristic
31#20846C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#475C2211yescharacteristic, complemented
38C2×#470C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic, complemented
40C2×#435C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#427C2211yescharacteristic, complemented
44C2×#407C2211yescharacteristic
45#2852—21no—
46#2848C2211yescharacteristic
47#2848C2211yescharacteristic
48#2788—21no—
49#2787—21no—
50#2786—21no—
51#2715—21no—
52#2643—21no—
53#2601—21no—
54#2599—21no—
55#2547C2211yescharacteristic
56#2538C2211yescharacteristic
57#2499C2211yescharacteristic
58#2496C2211yescharacteristic
59#2494C2211yescharacteristic
60#2492C2211yescharacteristic
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic
63#2480—21no—
64#2480—21no—
65#2478—21no—
66#2474—21no—
67#2472—21no—
68#2472—21no—
69#2440C2211yescharacteristic
70#2440C2211yescharacteristic
71#2439C2211yescharacteristic
72#2421C2211yescharacteristic
73#2417C2211yescharacteristic
74#2417C2211yescharacteristic
75#2415C2211yescharacteristic
76#2415C2211yescharacteristic
77#2362C2211yescharacteristic
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80#2354C2211yescharacteristic
81#2352C2211yescharacteristic
82#2352C2211yescharacteristic
83#2347C2211yescharacteristic
84#2329—21no—
85C4×C22⋊Q8—21no—
86C4×#120C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic, complemented
105#2077C2211yescharacteristic, complemented
106#2076C2211yescharacteristic, complemented
107#2072C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2056C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic, complemented
128#1993C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1971C2211yescharacteristic, complemented
132#1955C2211yescharacteristic
133#1954C2211yescharacteristic
134#1949C2211yescharacteristic, complemented
135#1949C2211yescharacteristic, complemented
136#1948C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1892C2211yescharacteristic, complemented
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic
162#1873C2211yescharacteristic, complemented
163#1872C2211yescharacteristic
164#1872C2211yescharacteristic
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1869C2211yescharacteristic
168#1865C2211yescharacteristic, complemented
169#1865C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1863C2211yescharacteristic, complemented
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1853C2211yescharacteristic
186#1853C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic
190#1847C2211yescharacteristic, complemented
191#1825C2211yescharacteristic, complemented
192#1824C2211yescharacteristic
193#1823C2211yescharacteristic
194#1809C2211yescharacteristic
195#1807C2211yescharacteristic, complemented
196#1803C2211yescharacteristic, complemented
197#1779C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199#1776C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#556—42no—
209#556—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#124—21no—
216C2×#124—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#120D411yescharacteristic
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117—42no—
237C2×#117—42no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42—21no—
251#485—42no—
252#484—42no—
253#483—42no—
254#475—42no—
255#470—24no—
256C4×Q16—42no—
257#435—24no—
258#428—42no—
259#428—42no—
260#427—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297#407—24no—
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
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#388—21no—
380#388—21no—
381#388—21no—
382#388—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#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386D411yescharacteristic
401#386D411yescharacteristic
402#386D411yescharacteristic
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#385D411yescharacteristic
415#385D411yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379D411yescharacteristic
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C2×#95—21no—
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#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25C2×D411yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4C2×D411yescharacteristic
499C22×D4C2×D411yescharacteristic
500C22×D4C2×D411yescharacteristic
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—41no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×M16—22no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16#4114yes—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542#126—44no—
543#126—44no—
544#126—82no—
545#124—44no—
546#124—82no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565#120—42no—
566C4×Q8—22no—
567C4×Q8—41no—
568C4×Q8—44no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—22no—
582#117—44no—
583#117—44no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
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—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—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
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—44no—
673C2×C22⋊C4—82no—
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
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—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—44no—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#106—22no—
710#106—22no—
711#106—22no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751#97—22no—
752#97—41no—
753C4×C8—41no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798C24—22no—
799C24—22no—
800C24—41no—
801C24—41no—
802C24—41no—
803C24—41no—
804C24—41no—
805C24C22×D411yescharacteristic
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
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—21no—
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—21no—
876C22×C4—21no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
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×C4—81no—
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×C4C2×#4112yes—
910C22×C42−1+412yes—
911C22×C4C2511yescharacteristic
912Q16—44no—
913M16—44no—
914M16—44no—
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—44no—
938C2×C8C2×#4112yes—
939C2×C8C2×#4112yes—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
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—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
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—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4H(5,𝔽2)12yes—
998C4⋊C4H(5,𝔽2)12yes—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
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—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—
1039C42—24no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—44no—
1084C23—44no—
1085C23—82no—
1086C23—82no—
1087C23—82no—
1088C23—82no—
1089C23—82no—
1090C23#54712yes—
1091C23#57712yes—
1092C23C23×D411yescharacteristic
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—84no—
1102Q8—162no—
1103D4—82no—
1104D4—82no—
1105D4—82no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
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—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
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—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—41no—
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—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4#54712yes—
1206C2×C4#57512yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—88no—
1250C22C2×#54711yescharacteristic
1251C22#348411yescharacteristic
1252C22#348511yescharacteristic
1253C22C2×#57511yescharacteristic
1254C22C2×#57711yescharacteristic
1255C22#358611yescharacteristic
1256C22#358611yescharacteristic
1257C4—22no—
1258C4—22no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
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—81no—
1283C4#345911yescharacteristic
1284C4#350611yescharacteristic
1285C4#354111yescharacteristic
1286C4#354111yescharacteristic
1287C2—42no—
1288C2—42no—
1289C2—81no—
1290C2—81no—
1291C2#3778811yescharacteristic
1292C2#6125711yescharacteristic
1293C2#6127111yescharacteristic
1294C2#6158011yescharacteristic
1295C2#6162011yescharacteristic
1296C2#6173911yescharacteristic
1297C2#6177911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32984C2semidirect
4. #32461C2semidirect
5. #32303C2semidirect
6. #32065C2semidirect
7. #32007C2semidirect
8. #31424C2semidirect
9. #31320C2semidirect
10. #31201C2semidirect
11. #31103C2semidirect
12. #29893C2semidirect
13. #29743C2semidirect
14. #28782C2semidirect
15. #28558C2semidirect
16. #27481C2semidirect
17. #27356C2semidirect
18. #27115C2semidirect
19. #26558C2semidirect
20. #26431C2semidirect
21. #26356C2semidirect
22. #26314C2semidirect
23. #26223C2semidirect
24. #26154C2semidirect
25. #26133C2semidirect
26. #24123C2semidirect
27. #24096C2semidirect
28. #23036C2semidirect
29. #22662C2semidirect
31. #20846C2semidirect
35. C2×#485C22semidirect
37. C2×#475C22semidirect
39. C2×C4×Q16C22semidirect
43. C2×#427C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
104. #2077C22semidirect
105. #2077C22semidirect
106. #2076C22semidirect
107. #2072C22semidirect
108. #2068C22semidirect
109. #2066C22semidirect
110. #2058C22semidirect
111. #2058C22semidirect
112. #2057C22semidirect
113. #2056C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
124. #2024C22semidirect
127. #2001C22semidirect
128. #1993C22semidirect
129. #1990C22semidirect
130. #1987C22semidirect
131. #1971C22semidirect
134. #1949C22semidirect
135. #1949C22semidirect
136. #1948C22semidirect
137. #1943C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
140. #1935C22semidirect
141. #1935C22semidirect
142. #1928C22semidirect
143. #1928C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
153. #1920C22semidirect
156. #1892C22semidirect
157. #1892C22semidirect
162. #1873C22semidirect
168. #1865C22semidirect
169. #1865C22semidirect
170. #1863C22semidirect
171. #1863C22semidirect
180. #1854C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
190. #1847C22semidirect
191. #1825C22semidirect
195. #1807C22semidirect
196. #1803C22semidirect
198. #1776C22semidirect
199. #1776C22semidirect

Maximal subgroups

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

subgroupindex
#391542
#364392
#329842
#324612
#323032
#320652
#320072
#314242
#313202
#312012
#311032
#298932
#297432
#287822
#285582
#274812
#273562
#271152
#265582
#264312
#263562
#263142
#262232
#261542
#261332
#241232
#240962
#230362
#226622
#220362
#208462