Finite Group Databasebeta

← #6703253

Subgroups — #6703253

Order 512.

1492 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39024C211yesmaximal, characteristic, complemented
2#36464C211yesmaximal, characteristic, complemented
3#33078C211yesmaximal, characteristic, complemented
4#32607C211yesmaximal, characteristic, complemented
5#32559C211yesmaximal, characteristic, complemented
6#32418C211yesmaximal, characteristic, complemented
7#32283C211yesmaximal, characteristic, complemented
8#31498C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#30582C211yesmaximal, characteristic, complemented
11#30396C211yesmaximal, characteristic
12#30383C211yesmaximal, characteristic, complemented
13#30083C211yesmaximal, characteristic, complemented
14#27417C211yesmaximal, characteristic, complemented
15#27188C211yesmaximal, characteristic, complemented
16#27123C211yesmaximal, characteristic, complemented
17#26975C211yesmaximal, characteristic, complemented
18#26938C211yesmaximal, characteristic, complemented
19#26564C211yesmaximal, characteristic, complemented
20#26328C211yesmaximal, characteristic, complemented
21#26211C211yesmaximal, characteristic, complemented
22#25209C211yesmaximal, characteristic, complemented
23#25101C211yesmaximal, characteristic, complemented
24#25056C211yesmaximal, characteristic, complemented
25#25045C211yesmaximal, characteristic, complemented
26#24913C211yesmaximal, characteristic, complemented
27#24886C211yesmaximal, characteristic, complemented
28#22933C211yesmaximal, characteristic, complemented
29#22580C211yesmaximal, characteristic, complemented
30#22391C211yesmaximal, characteristic, complemented
31#21507C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#482C2211yescharacteristic, complemented
34C2×#468C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#440C2211yescharacteristic, complemented
40C2×#418C2211yescharacteristic
41#2860C2211yescharacteristic
42#2859C2211yescharacteristic, complemented
43#2854—21no—
44#2756—21no—
45#2735—21no—
46#2702—21no—
47#2685—21no—
48#2648—21no—
49#2592C2211yescharacteristic
50#2558—21no—
51#2558—21no—
52#2538C2211yescharacteristic
53#2538C2211yescharacteristic, complemented
54#2537C2211yescharacteristic
55#2518—21no—
56#2518—21no—
57#2518—21no—
58#2500C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic, complemented
61#2495—21no—
62#2495C2211yescharacteristic
63#2472—21no—
64#2435C2211yescharacteristic
65#2427C2211yescharacteristic
66#2426—21no—
67#2426C2211yescharacteristic
68#2423C2211yescharacteristic
69#2422C2211yescharacteristic
70#2422C2211yescharacteristic, complemented
71#2415C2211yescharacteristic
72#2408C2211yescharacteristic
73#2363C2211yescharacteristic
74#2363C2211yescharacteristic
75#2363C2211yescharacteristic, complemented
76#2354C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic, complemented
78#2347C2211yescharacteristic
79#2347C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81#2312—21no—
82C4×#124C2211yescharacteristic
83C4×#124C2211yescharacteristic
84C4×C22⋊Q8—21no—
85C42×D4C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2075C2211yescharacteristic
102#2072C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2012C2211yescharacteristic
124#2000C2211yescharacteristic, complemented
125#1999C2211yescharacteristic
126#1985C2211yescharacteristic, complemented
127#1984C2211yescharacteristic, complemented
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1968C2211yescharacteristic, complemented
131#1959C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic, complemented
141#1934C2211yescharacteristic
142#1928C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic, complemented
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic, complemented
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic, complemented
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1851C2211yescharacteristic
185#1850C2211yescharacteristic, complemented
186#1845C2211yescharacteristic, complemented
187#1839C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1767C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×#126—21no—
210C2×#125—21no—
211C2×#124D411yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C42—21no—
240#482—24no—
241#482—42no—
242#468—42no—
243#466—42no—
244#463—24no—
245#447—42no—
246#442—42no—
247#440—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265#418—24no—
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#392—21no—
334#391D411yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390D411yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
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#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388D411yescharacteristic
392#388D411yescharacteristic
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#383—21no—
414#382—21no—
415#382D411yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#379—21no—
428#379—21no—
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C43C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×M16—22no—
522C2×M16—41no—
523C2×M16—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535#126—82no—
536#125—82no—
537#124—22no—
538#124—41no—
539#124—41no—
540#124—41no—
541#124—42no—
542#123—82no—
543#123—82no—
544C22⋊Q8—44no—
545C22⋊Q8—41no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—82no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—82no—
559#120—82no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—82no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577#117—22no—
578#117—22no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
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—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⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×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—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—44no—
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—82no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—22no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102#4114yes—
736C22⋊C8—22no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742#97—41no—
743#97—41no—
744#97—41no—
745C4×C8—41no—
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#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—42no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—41no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
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—41no—
821C2×D4—41no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—81no—
828C2×D4—81no—
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×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4C2×#4112yes—
842C2×D4H(5,𝔽2)12yes—
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—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
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×C4C22×D411yescharacteristic
895C22×C4C2511yescharacteristic
896SD16—44no—
897D8—44no—
898D8—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×C8—82no—
924C2×C8C2×#4112yes—
925C4⋊C4—21no—
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—41no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
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⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4C2×#4112yes—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
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—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C42—22no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—41no—
1038C42—41no—
1039C42—41no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—84no—
1086C23—84no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23C23×D411yescharacteristic
1093Q8—44no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—82no—
1111D4—84no—
1112D4—162no—
1113D4—162no—
1114D4—162no—
1115D4—162no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—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—84no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4#57512yes—
1203C2×C4#57612yes—
1204C2×C4C22×#4111yescharacteristic
1205C2×C4C2×H(5,𝔽2)11yescharacteristic
1206C2×C4#58511yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C2×C4#58511yescharacteristic
1210C8—22no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C22—41no—
1219C22—41no—
1220C22—42no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—41no—
1225C22—41no—
1226C22—42no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—41no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—168no—
1254C22D4×#4111yescharacteristic
1255C22#348511yescharacteristic
1256C22#348811yescharacteristic
1257C22C2×#57511yescharacteristic
1258C22C2×#57611yescharacteristic
1259C22#358511yescharacteristic
1260C22#358611yescharacteristic
1261C4—22no—
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—42no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4#345511yescharacteristic
1287C4#351311yescharacteristic
1288C4#356011yescharacteristic
1289C4#356611yescharacteristic
1290C2—81no—
1291C2—81no—
1292C2—82no—
1293C2—82no—
1294C2—161no—
1295C2#3772811yescharacteristic
1296C2#6145911yescharacteristic
1297C2#6155311yescharacteristic
1298C2#6172711yescharacteristic
1299C2#6179911yescharacteristic
1300C2#6197311yescharacteristic
1301C2#6204011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30396C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39024C2semidirect
2. #36464C2semidirect
3. #33078C2semidirect
4. #32607C2semidirect
5. #32559C2semidirect
6. #32418C2semidirect
7. #32283C2semidirect
8. #31498C2semidirect
9. #31302C2semidirect
10. #30582C2semidirect
12. #30383C2semidirect
13. #30083C2semidirect
14. #27417C2semidirect
15. #27188C2semidirect
16. #27123C2semidirect
17. #26975C2semidirect
18. #26938C2semidirect
19. #26564C2semidirect
20. #26328C2semidirect
21. #26211C2semidirect
22. #25209C2semidirect
23. #25101C2semidirect
24. #25056C2semidirect
25. #25045C2semidirect
26. #24913C2semidirect
27. #24886C2semidirect
28. #22933C2semidirect
29. #22580C2semidirect
30. #22391C2semidirect
31. #21507C2semidirect
33. C2×#482C22semidirect
39. C2×#440C22semidirect
42. #2859C22semidirect
53. #2538C22semidirect
60. #2497C22semidirect
70. #2422C22semidirect
75. #2363C22semidirect
77. Q8×C4⋊C4C22semidirect
79. #2347C22semidirect
85. C42×D4C22semidirect
86. #2100C22semidirect
87. #2100C22semidirect
88. #2096C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2083C22semidirect
99. #2083C22semidirect
102. #2072C22semidirect
103. #2072C22semidirect
106. #2071C22semidirect
109. #2066C22semidirect
117. #2036C22semidirect
124. #2000C22semidirect
126. #1985C22semidirect
127. #1984C22semidirect
130. #1968C22semidirect
132. #1949C22semidirect
133. #1948C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
140. #1936C22semidirect
142. #1928C22semidirect
143. #1927C22semidirect
145. #1926C22semidirect
153. #1924C22semidirect
154. #1923C22semidirect
155. #1920C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
161. #1892C22semidirect
167. #1877C22semidirect
170. #1873C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
185. #1850C22semidirect
186. #1845C22semidirect
187. #1839C22semidirect
191. #1804C22semidirect
195. #1776C22semidirect
196. #1767C22semidirect
197. #1763C22semidirect
201. #1752C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#390242
#364642
#330782
#326072
#325592
#324182
#322832
#314982
#313022
#305822
#303962
#303832
#300832
#274172
#271882
#271232
#269752
#269382
#265642
#263282
#262112
#252092
#251012
#250562
#250452
#249132
#248862
#229332
#225802
#223912
#215072