Finite Group Databasebeta

← #7047687

Subgroups — #7047687

Order 512.

1450 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59629C211yesmaximal, characteristic, complemented
2#59224C211yesmaximal, characteristic
3#32047C211yesmaximal, characteristic, complemented
4#31911C211yesmaximal, characteristic, complemented
5#31744C211yesmaximal, characteristic, complemented
6#31680C211yesmaximal, characteristic
7#31663C211yesmaximal, characteristic, complemented
8#30779C211yesmaximal, characteristic, complemented
9#30685C211yesmaximal, characteristic, complemented
10#30510C211yesmaximal, characteristic
11#28883C211yesmaximal, characteristic, complemented
12#28123C211yesmaximal, characteristic, complemented
13#27802C211yesmaximal, characteristic, complemented
14#27635C211yesmaximal, characteristic, complemented
15#27224C211yesmaximal, characteristic, complemented
16#27224C211yesmaximal, characteristic, complemented
17#27213C211yesmaximal, characteristic, complemented
18#27148C211yesmaximal, characteristic, complemented
19#27148C211yesmaximal, characteristic, complemented
20#26814C211yesmaximal, characteristic, complemented
21#26741C211yesmaximal, characteristic, complemented
22#26661C211yesmaximal, characteristic, complemented
23#26249C211yesmaximal, characteristic, complemented
24#25450C211yesmaximal, characteristic, complemented
25#25224C211yesmaximal, characteristic, complemented
26#24952C211yesmaximal, characteristic, complemented
27#23765C211yesmaximal, characteristic, complemented
28#23145C211yesmaximal, characteristic, complemented
29#23067C211yesmaximal, characteristic, complemented
30#22363C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic, complemented
33C2×#484C2211yescharacteristic
34C2×#485C2211yescharacteristic, complemented
35C2×#476C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41#2807—21no—
42#2804—21no—
43#2756—21no—
44#2737—21no—
45#2610—21no—
46#2607—21no—
47#2589—21no—
48#2589—21no—
49#2563C2211yescharacteristic
50#2561—21no—
51#2542C2211yescharacteristic
52#2531—21no—
53#2513C2211yescharacteristic
54#2513C2211yescharacteristic
55#2511—21no—
56#2511—21no—
57#2500C2211yescharacteristic
58#2492C2211yescharacteristic
59#2492C2211yescharacteristic
60#2492C2211yescharacteristic, complemented
61#2492C2211yescharacteristic, complemented
62#2491C2211yescharacteristic
63#2487C2211yescharacteristic
64#2472—21no—
65#2446C2211yescharacteristic, complemented
66#2446C2211yescharacteristic, complemented
67#2440C2211yescharacteristic
68#2420C2211yescharacteristic
69#2412—21no—
70#2408C2211yescharacteristic
71#2374—21no—
72#2369C2211yescharacteristic, complemented
73#2369C2211yescharacteristic, complemented
74#2363C2211yescharacteristic
75#2360C2211yescharacteristic, complemented
76#2360C2211yescharacteristic, complemented
77#2354C2211yescharacteristic
78#2352C2211yescharacteristic
79#2342—21no—
80D4×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2283C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2097C2211yescharacteristic, complemented
89#2095C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2074C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2057C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1990C2211yescharacteristic, complemented
127#1987C2211yescharacteristic, complemented
128#1981C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1960C2211yescharacteristic, complemented
134#1955C2211yescharacteristic
135#1949C2211yescharacteristic, complemented
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1947C2211yescharacteristic, complemented
139#1939C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1933C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1924C2211yescharacteristic, complemented
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1918C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1872C2211yescharacteristic
180#1870C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1824C2211yescharacteristic
185#1823C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1797C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1770C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#124—21no—
214C2×#123D411yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229C2×#117C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235C22×C42C2311yescharacteristic
236#500—42no—
237#485—42no—
238#484—42no—
239#476—24no—
240#476—42no—
241#468—24no—
242#468—42no—
243#450—24no—
244#450—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#399—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#393—21no—
326#393—21no—
327#393—21no—
328#393—21no—
329#392—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
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#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#388—21no—
381#388D411yescharacteristic
382#388D411yescharacteristic
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#387D411yescharacteristic
393#387D411yescharacteristic
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386D411yescharacteristic
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385D411yescharacteristic
408#384—21no—
409#384C2311yescharacteristic
410#383—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#381D411yescharacteristic
417#380—21no—
418#380—21no—
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#376—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544#124—82no—
545#123—24no—
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—82no—
555#121—22no—
556#121—41no—
557#121—41no—
558#121—41no—
559#120—82no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570#117—41no—
571#117—41no—
572#117—82no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4—82no—
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—41no—
669C2×C42—41no—
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677#107—22no—
678#107—22no—
679#107—22no—
680#107—22no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#106—22no—
686#106—22no—
687#106—22no—
688#106—41no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693C4⋊C8—41no—
694#103—22no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102#4114yes—
718C22⋊C8—22no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723C22⋊C8—41no—
724C22⋊C8—41no—
725#97—41no—
726#97—41no—
727#97—41no—
728C4×C8—41no—
729C4×C8—41no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778C24—21no—
779C24—21no—
780C24—42no—
781C24—42no—
782C24—42no—
783C24—42no—
784C24—81no—
785C24—81no—
786C24—81no—
787C24C22×D411yescharacteristic
788C24C22×D411yescharacteristic
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—81no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—82no—
831C2×D4—82no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4C2×#4112yes—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
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—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C2511yescharacteristic
895SD16—82no—
896SD16—82no—
897SD16—82no—
898SD16—82no—
899M16—82no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
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×C8C2×#4112yes—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
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—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4C2×#4112yes—
973C4⋊C4H(5,𝔽2)12yes—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4#13714yes—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—41no—
1024C42—41no—
1025C42—42no—
1026C42—81no—
1027C42—81no—
1028C42—81no—
1029C42—81no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—22no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—84no—
1067C23—162no—
1068C23—162no—
1069C23—162no—
1070C23C2×#13712yes—
1071C23C23×D411yescharacteristic
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—162no—
1081Q8—162no—
1082Q8—162no—
1083D4—22no—
1084D4—22no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—82no—
1092D4—84no—
1093D4—162no—
1094D4—162no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
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—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—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
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—84no—
1180C2×C4—82no—
1181C2×C4—82no—
1182C2×C4—162no—
1183C2×C4—162no—
1184C2×C4—162no—
1185C2×C4C2×#13712yes—
1186C2×C4C2×#13712yes—
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C2×H(5,𝔽2)11yescharacteristic
1189C2×C4#58511yescharacteristic
1190C2×C4#58511yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—42no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—42no—
1217C22—41no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—168no—
1230C22D4×#4111yescharacteristic
1231C22#348511yescharacteristic
1232C22#348811yescharacteristic
1233C22C22×#13711yescharacteristic
1234C22#358411yescharacteristic
1235C22#358511yescharacteristic
1236C22#358511yescharacteristic
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—41no—
1250C4—42no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4#351011yescharacteristic
1264C4#351411yescharacteristic
1265C4#356211yescharacteristic
1266C4#356611yescharacteristic
1267C2—42no—
1268C2—81no—
1269C2—82no—
1270C2—161no—
1271C2#4353711yescharacteristic
1272C2#6145311yescharacteristic
1273C2#6154811yescharacteristic
1274C2#6172111yescharacteristic
1275C2#6176211yescharacteristic
1276C2#6199111yescharacteristic
1277C2#6207911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59629C2semidirect
3. #32047C2semidirect
4. #31911C2semidirect
5. #31744C2semidirect
7. #31663C2semidirect
8. #30779C2semidirect
9. #30685C2semidirect
11. #28883C2semidirect
12. #28123C2semidirect
13. #27802C2semidirect
14. #27635C2semidirect
15. #27224C2semidirect
16. #27224C2semidirect
17. #27213C2semidirect
18. #27148C2semidirect
19. #27148C2semidirect
20. #26814C2semidirect
21. #26741C2semidirect
22. #26661C2semidirect
23. #26249C2semidirect
24. #25450C2semidirect
25. #25224C2semidirect
26. #24952C2semidirect
27. #23765C2semidirect
28. #23145C2semidirect
29. #23067C2semidirect
30. #22363C2semidirect
31. #22049C2semidirect
32. C2×#500C22semidirect
34. C2×#485C22semidirect
60. #2492C22semidirect
61. #2492C22semidirect
65. #2446C22semidirect
66. #2446C22semidirect
72. #2369C22semidirect
73. #2369C22semidirect
75. #2360C22semidirect
76. #2360C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2097C22semidirect
89. #2095C22semidirect
90. #2085C22semidirect
91. #2085C22semidirect
96. #2074C22semidirect
97. #2072C22semidirect
98. #2068C22semidirect
99. #2068C22semidirect
104. #2057C22semidirect
105. #2057C22semidirect
112. #2036C22semidirect
115. #2035C22semidirect
118. #2024C22semidirect
119. #2024C22semidirect
126. #1990C22semidirect
127. #1987C22semidirect
128. #1981C22semidirect
133. #1960C22semidirect
135. #1949C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1947C22semidirect
139. #1939C22semidirect
144. #1933C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
156. #1924C22semidirect
159. #1923C22semidirect
160. #1921C22semidirect
161. #1921C22semidirect
162. #1919C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1918C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
178. #1873C22semidirect
181. #1854C22semidirect
183. #1851C22semidirect
185. #1823C22semidirect
186. #1809C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
192. #1776C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1770C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#596292
#592242
#320472
#319112
#317442
#316802
#316632
#307792
#306852
#305102
#288832
#281232
#278022
#276352
#272242
#272132
#271482
#268142
#267412
#266612
#262492
#254502
#252242
#249522
#237652
#231452
#230672
#223632
#220492