Finite Group Databasebeta

← #6725162

Subgroups — #6725162

Order 512.

1545 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39908C211yesmaximal, characteristic
2#36234C211yesmaximal, characteristic
3#32984C211yesmaximal, characteristic, complemented
4#32307C211yesmaximal, characteristic, complemented
5#32267C211yesmaximal, characteristic, complemented
6#31940C211yesmaximal, characteristic, complemented
7#31794C211yesmaximal, characteristic, complemented
8#31792C211yesmaximal, characteristic, complemented
9#31698C211yesmaximal, characteristic, complemented
10#30793C211yesmaximal, characteristic, complemented
11#30569C211yesmaximal, characteristic, complemented
12#29897C211yesmaximal, characteristic, complemented
13#29731C211yesmaximal, characteristic, complemented
14#27462C211yesmaximal, characteristic, complemented
15#27189C211yesmaximal, characteristic, complemented
16#27050C211yesmaximal, characteristic, complemented
17#26790C211yesmaximal, characteristic, complemented
18#26417C211yesmaximal, characteristic, complemented
19#26339C211yesmaximal, characteristic, complemented
20#26201C211yesmaximal, characteristic, complemented
21#26133C211yesmaximal, characteristic, complemented
22#26069C211yesmaximal, characteristic, complemented
23#25716C211yesmaximal, characteristic, complemented
24#25541C211yesmaximal, characteristic, complemented
25#25024C211yesmaximal, characteristic, complemented
26#24939C211yesmaximal, characteristic, complemented
27#24779C211yesmaximal, characteristic, complemented
28#23136C211yesmaximal, characteristic, complemented
29#22704C211yesmaximal, characteristic, complemented
30#22030C211yesmaximal, characteristic
31#20843C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#477C2211yescharacteristic, complemented
39C2×#467C2211yescharacteristic
40C2×#467C2211yescharacteristic, complemented
41C2×C8×D4C2211yescharacteristic
42C2×#427C2211yescharacteristic
43C2×#427C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45#2851—21no—
46#2848C2211yescharacteristic
47#2848C2211yescharacteristic
48#2764—21no—
49#2750—21no—
50#2735—21no—
51#2684—21no—
52#2652—21no—
53#2611—21no—
54#2609—21no—
55#2589—21no—
56#2578—21no—
57#2547C2211yescharacteristic
58#2536C2211yescharacteristic
59#2499C2211yescharacteristic
60#2495C2211yescharacteristic
61#2495C2211yescharacteristic
62#2492C2211yescharacteristic
63#2487C2211yescharacteristic
64#2485C2211yescharacteristic
65#2480—21no—
66#2478—21no—
67#2470—21no—
68#2442C2211yescharacteristic
69#2441C2211yescharacteristic
70#2439C2211yescharacteristic
71#2421C2211yescharacteristic
72#2418—21no—
73#2417C2211yescharacteristic
74#2417C2211yescharacteristic
75#2415C2211yescharacteristic
76#2415C2211yescharacteristic
77#2362C2211yescharacteristic
78#2362C2211yescharacteristic
79#2360C2211yescharacteristic
80#2352C2211yescharacteristic
81#2352C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2346C2211yescharacteristic
84#2337—21no—
85C4×#120C2211yescharacteristic
86#2290—21no—
87#2280C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2026C2211yescharacteristic, complemented
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#1989C2211yescharacteristic, complemented
129#1969C2211yescharacteristic, complemented
130#1955C2211yescharacteristic
131#1955C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1924C2211yescharacteristic
143#1924C2211yescharacteristic
144#1923C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1878C2211yescharacteristic, complemented
155#1878C2211yescharacteristic, complemented
156#1873C2211yescharacteristic
157#1873C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic
162#1872C2211yescharacteristic, complemented
163#1869C2211yescharacteristic
164#1869C2211yescharacteristic
165#1869C2211yescharacteristic
166#1865C2211yescharacteristic, complemented
167#1865C2211yescharacteristic, complemented
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1852C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1835C2211yescharacteristic, complemented
188#1824C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1823C2211yescharacteristic
191#1808C2211yescharacteristic
192#1808C2211yescharacteristic, complemented
193#1807C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1779C2211yescharacteristic
196C4×#107C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#552—42no—
209#552—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#120D411yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117—21no—
234C2×#117—42no—
235C2×#117—42no—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C42—21no—
248#501—42no—
249#484—42no—
250#483—42no—
251#483—42no—
252#477—42no—
253#467—24no—
254#467—42no—
255C8×D4—24no—
256#427—42no—
257#427—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×C22⋊C8—24no—
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
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×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—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#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#393—21no—
342#393—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
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#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#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386D411yescharacteristic
397#386D411yescharacteristic
398#386D411yescharacteristic
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385D411yescharacteristic
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
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#379—21no—
439#379—21no—
440#379—21no—
441#379D411yescharacteristic
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
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
456#376—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×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4C2×D411yescharacteristic
498C22×D4C2×D411yescharacteristic
499C22×D4C2×D411yescharacteristic
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—41no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C2×Q16—22no—
518C2×Q16—41no—
519C2×Q16—41no—
520C22×C8—22no—
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8#4114yes—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539#126—44no—
540#125—22no—
541#125—41no—
542#125—44no—
543#124—44no—
544#123—44no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561#120—42no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573#117—22no—
574#117—22no—
575#117—22no—
576#117—22no—
577#117—44no—
578#117—44no—
579#117—44no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
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—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—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—44no—
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—44no—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—22no—
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#106—22no—
709#106—22no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746#97—41no—
747#97—41no—
748C4×C8—22no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C24—22no—
796C24—22no—
797C24—41no—
798C24—41no—
799C24—41no—
800C24—41no—
801C24—41no—
802C24C22×D411yescharacteristic
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
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—42no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
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—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C2×#4112yes—
904C22×C42−1+412yes—
905C22×C4C2511yescharacteristic
906Q16—82no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
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—44no—
930C2×C8—44no—
931C2×C8—82no—
932C2×C8C2×#4112yes—
933C2×C8C2×#4112yes—
934C4⋊C4—22no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
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—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4H(5,𝔽2)12yes—
991C4⋊C4H(5,𝔽2)12yes—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
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—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C42—24no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
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—44no—
1076C23—44no—
1077C23—82no—
1078C23—82no—
1079C23—82no—
1080C23—82no—
1081C23—82no—
1082C23#54712yes—
1083C23#57512yes—
1084C23#57812yes—
1085C23C23×D411yescharacteristic
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—162no—
1095D4—44no—
1096D4—44no—
1097D4—82no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—22no—
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—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
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—84no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—162no—
1198C2×C4#54712yes—
1199C2×C4C22×#4111yescharacteristic
1200C2×C4C2×H(5,𝔽2)11yescharacteristic
1201C2×C4C2×H(5,𝔽2)11yescharacteristic
1202C2×C4C2×2−1+411yescharacteristic
1203C2×C4#58511yescharacteristic
1204C2×C4#58511yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
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—88no—
1242C22C2×#54711yescharacteristic
1243C22#348411yescharacteristic
1244C22#348511yescharacteristic
1245C22C2×#57511yescharacteristic
1246C22C2×#57811yescharacteristic
1247C22#358411yescharacteristic
1248C22#358411yescharacteristic
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—42no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4#346011yescharacteristic
1276C4#350511yescharacteristic
1277C4#354111yescharacteristic
1278C4#354111yescharacteristic
1279C2—42no—
1280C2—42no—
1281C2—42no—
1282C2—81no—
1283C2#3778911yescharacteristic
1284C2#6124311yescharacteristic
1285C2#6126411yescharacteristic
1286C2#6160611yescharacteristic
1287C2#6164211yescharacteristic
1288C2#6173811yescharacteristic
1289C2#6176911yescharacteristic
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. #32307C2semidirect
5. #32267C2semidirect
6. #31940C2semidirect
7. #31794C2semidirect
8. #31792C2semidirect
9. #31698C2semidirect
10. #30793C2semidirect
11. #30569C2semidirect
12. #29897C2semidirect
13. #29731C2semidirect
14. #27462C2semidirect
15. #27189C2semidirect
16. #27050C2semidirect
17. #26790C2semidirect
18. #26417C2semidirect
19. #26339C2semidirect
20. #26201C2semidirect
21. #26133C2semidirect
22. #26069C2semidirect
23. #25716C2semidirect
24. #25541C2semidirect
25. #25024C2semidirect
26. #24939C2semidirect
27. #24779C2semidirect
28. #23136C2semidirect
29. #22704C2semidirect
31. #20843C2semidirect
34. C2×#501C22semidirect
37. C2×#483C22semidirect
38. C2×#477C22semidirect
40. C2×#467C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2086C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2083C22semidirect
99. #2077C22semidirect
104. #2075C22semidirect
105. #2074C22semidirect
106. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2059C22semidirect
111. #2058C22semidirect
112. #2057C22semidirect
119. #2036C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
125. #2026C22semidirect
128. #1989C22semidirect
129. #1969C22semidirect
132. #1949C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1944C22semidirect
136. #1943C22semidirect
137. #1942C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
146. #1921C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1920C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
154. #1878C22semidirect
155. #1878C22semidirect
162. #1872C22semidirect
166. #1865C22semidirect
167. #1865C22semidirect
182. #1852C22semidirect
183. #1852C22semidirect
184. #1852C22semidirect
186. #1847C22semidirect
187. #1835C22semidirect
189. #1824C22semidirect
192. #1808C22semidirect
193. #1807C22semidirect
194. #1803C22semidirect
196. C4×#107C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#399082
#362342
#329842
#323072
#322672
#319402
#317942
#317922
#316982
#307932
#305692
#298972
#297312
#274622
#271892
#270502
#267902
#264172
#263392
#262012
#261332
#260692
#257162
#255412
#250242
#249392
#247792
#231362
#227042
#220302
#208432