Finite Group Databasebeta

← #7528248

Subgroups — #7528248

Order 512.

1673 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59248C211yesmaximal, characteristic, complemented
2#36441C211yesmaximal, characteristic
3#31310C211yesmaximal, characteristic
4#31298C211yesmaximal, characteristic, complemented
5#30543C211yesmaximal, characteristic, complemented
6#30527C211yesmaximal, characteristic
7#28894C211yesmaximal, characteristic, complemented
8#28874C211yesmaximal, characteristic, complemented
9#28200C211yesmaximal, characteristic, complemented
10#27895C211yesmaximal, characteristic, complemented
11#27783C211yesmaximal, characteristic, complemented
12#27112C211yesmaximal, characteristic, complemented
13#27101C211yesmaximal, characteristic, complemented
14#27070C211yesmaximal, characteristic, complemented
15#27063C211yesmaximal, characteristic, complemented
16#26743C211yesmaximal, characteristic, complemented
17#26722C211yesmaximal, characteristic, complemented
18#26689C211yesmaximal, characteristic, complemented
19#26688C211yesmaximal, characteristic, complemented
20#26036C211yesmaximal, characteristic, complemented
21#25069C211yesmaximal, characteristic, complemented
22#24655C211yesmaximal, characteristic, complemented
23#24639C211yesmaximal, characteristic, complemented
24#24206C211yesmaximal, characteristic, complemented
25#23226C211yesmaximal, characteristic, complemented
26#23216C211yesmaximal, characteristic, complemented
27#23052C211yesmaximal, characteristic, complemented
28#22819C211yesmaximal, characteristic, complemented
29#22549C211yesmaximal, characteristic, complemented
30#21453C211yesmaximal, characteristic, complemented
31#20732C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#464C2211yescharacteristic, complemented
37C2×#450C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2850C2211yescharacteristic
43#2849—21no—
44#2789—21no—
45#2789—21no—
46#2602—21no—
47#2600—21no—
48#2599—21no—
49#2599—21no—
50#2582C2211yescharacteristic, complemented
51#2580C2211yescharacteristic
52#2551C2211yescharacteristic, complemented
53#2544C2211yescharacteristic
54#2514—21no—
55#2514C2211yescharacteristic, complemented
56#2514C2211yescharacteristic, complemented
57#2494—21no—
58#2494C2211yescharacteristic
59#2494C2211yescharacteristic
60#2492—21no—
61#2492C2211yescharacteristic
62#2492C2211yescharacteristic
63#2472—21no—
64#2459—21no—
65#2455—21no—
66#2447C2211yescharacteristic
67#2445C2211yescharacteristic
68#2435C2211yescharacteristic
69#2433C2211yescharacteristic
70#2418—21no—
71#2367C2211yescharacteristic
72#2366C2211yescharacteristic
73#2365—21no—
74#2365C2211yescharacteristic, complemented
75#2365C2211yescharacteristic, complemented
76#2361C2211yescharacteristic
77#2360C2211yescharacteristic
78#2357C2211yescharacteristic
79#2355C2211yescharacteristic, complemented
80#2355C2211yescharacteristic, complemented
81C4×C22⋊Q8C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#120—21no—
84#2285C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2087C2211yescharacteristic, complemented
88#2086C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2067C2211yescharacteristic
92#2065C2211yescharacteristic
93#2056C2211yescharacteristic, complemented
94#2055C2211yescharacteristic
95#2055C2211yescharacteristic
96#2055C2211yescharacteristic, complemented
97#2042C2211yescharacteristic
98#2042C2211yescharacteristic
99#2041C2211yescharacteristic
100#2041C2211yescharacteristic
101#2036C2211yescharacteristic
102#2036C2211yescharacteristic
103#2035C2211yescharacteristic
104#2034C2211yescharacteristic
105#2034C2211yescharacteristic
106#2033C2211yescharacteristic
107#2024C2211yescharacteristic, complemented
108#2023C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic, complemented
111#2015C2211yescharacteristic
112#2015C2211yescharacteristic
113#2014C2211yescharacteristic
114#2014C2211yescharacteristic
115#2001C2211yescharacteristic
116#2000C2211yescharacteristic
117#1988C2211yescharacteristic, complemented
118#1987C2211yescharacteristic, complemented
119#1985C2211yescharacteristic, complemented
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic, complemented
123#1982C2211yescharacteristic
124#1982C2211yescharacteristic
125#1973C2211yescharacteristic
126#1969C2211yescharacteristic, complemented
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic, complemented
129#1961C2211yescharacteristic
130#1959C2211yescharacteristic, complemented
131#1959C2211yescharacteristic, complemented
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1940C2211yescharacteristic, complemented
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1925C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1921C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1872C2211yescharacteristic
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic, complemented
174#1852C2211yescharacteristic
175#1847C2211yescharacteristic, complemented
176#1836C2211yescharacteristic, complemented
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic
179#1805C2211yescharacteristic, complemented
180#1805C2211yescharacteristic, complemented
181#1804C2211yescharacteristic, complemented
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1776C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#559—24no—
210#559—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—24no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—42no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#489—24no—
251#486—24no—
252#464—42no—
253#450—24no—
254#446—42no—
255#440—24no—
256#440—42no—
257#431—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#401—21no—
317#401—21no—
318#401—21no—
319#401—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#392—21no—
343#392—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391D411yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389—21no—
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
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#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385D411yescharacteristic
419#385D411yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#383—21no—
423#383—21no—
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432#380D411yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—44no—
518C23×C4—82no—
519C23×C4—82no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—44no—
548#127—22no—
549#127—22no—
550#127—41no—
551#127—41no—
552#124—22no—
553#124—22no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#124—44no—
559#123—44no—
560#123—44no—
561#123—82no—
562C22⋊Q8—22no—
563C22⋊Q8—42no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—41no—
568#121—41no—
569#120—44no—
570#120—82no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—41no—
577C4×Q8—82no—
578C4×Q8—82no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—44no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—82no—
592C4×D4—82no—
593C4×D4#4114yes—
594#117—82no—
595C2×C4⋊C4—22no—
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—41no—
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
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×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—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—21no—
672C2×C42—21no—
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×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
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—
740#97—22no—
741#97—22no—
742#97—22no—
743#97—41no—
744C4×C8—22no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
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#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#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C2×Q8—22no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—41no—
822C2×Q8—41no—
823C2×Q8—42no—
824C2×Q8—42no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4C2×#4112yes—
868C2×D4C2×#4112yes—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—816no—
912C22×C4—81no—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C2511yescharacteristic
927Q16—82no—
928SD16—44no—
929SD16—44no—
930SD16—82no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8C2×#4112yes—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C2×#4112yes—
1003C4⋊C4C2×#4112yes—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—24no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C42—22no—
1038C42—22no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42C2×#4112yes—
1061C42H(5,𝔽2)12yes—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—22no—
1070C23—48no—
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—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—84no—
1091C23—84no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23#57712yes—
1097C23C23×D411yescharacteristic
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—82no—
1107Q8—84no—
1108Q8—84no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—48no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—84no—
1123D4—84no—
1124D4—84no—
1125D4—162no—
1126D4—162no—
1127C2×C4—28no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—82no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—162no—
1213C2×C4#54612yes—
1214C2×C4#54612yes—
1215C2×C4#57512yes—
1216C2×C4#57612yes—
1217C2×C4C22×#4111yescharacteristic
1218C2×C4C22×#4111yescharacteristic
1219C2×C4C2×H(5,𝔽2)11yescharacteristic
1220C2×C4#58511yescharacteristic
1221C2×C4#58511yescharacteristic
1222C2×C4#58511yescharacteristic
1223C8—22no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—816no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22C2×#54611yescharacteristic
1261C22D4×#4111yescharacteristic
1262C22#348711yescharacteristic
1263C22C2×#57511yescharacteristic
1264C22C2×#57611yescharacteristic
1265C22C2×#57711yescharacteristic
1266C22#358611yescharacteristic
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—41no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—42no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4#347511yescharacteristic
1294C4#349311yescharacteristic
1295C4#350611yescharacteristic
1296C4#354011yescharacteristic
1297C2—42no—
1298C2—82no—
1299C2—82no—
1300C2—161no—
1301C2#5901711yescharacteristic
1302C2#6116511yescharacteristic
1303C2#6116711yescharacteristic
1304C2#6144411yescharacteristic
1305C2#6152011yescharacteristic
1306C2#6190411yescharacteristic
1307C2#6191211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59248C2semidirect
4. #31298C2semidirect
5. #30543C2semidirect
7. #28894C2semidirect
8. #28874C2semidirect
9. #28200C2semidirect
10. #27895C2semidirect
11. #27783C2semidirect
12. #27112C2semidirect
13. #27101C2semidirect
14. #27070C2semidirect
15. #27063C2semidirect
16. #26743C2semidirect
17. #26722C2semidirect
18. #26689C2semidirect
19. #26688C2semidirect
20. #26036C2semidirect
21. #25069C2semidirect
22. #24655C2semidirect
23. #24639C2semidirect
24. #24206C2semidirect
25. #23226C2semidirect
26. #23216C2semidirect
27. #23052C2semidirect
28. #22819C2semidirect
29. #22549C2semidirect
30. #21453C2semidirect
31. #20732C2semidirect
36. C2×#464C22semidirect
38. C2×#446C22semidirect
50. #2582C22semidirect
52. #2551C22semidirect
55. #2514C22semidirect
56. #2514C22semidirect
74. #2365C22semidirect
75. #2365C22semidirect
79. #2355C22semidirect
80. #2355C22semidirect
87. #2087C22semidirect
88. #2086C22semidirect
89. #2085C22semidirect
90. #2085C22semidirect
93. #2056C22semidirect
96. #2055C22semidirect
107. #2024C22semidirect
110. #2023C22semidirect
117. #1988C22semidirect
118. #1987C22semidirect
119. #1985C22semidirect
122. #1983C22semidirect
126. #1969C22semidirect
128. #1968C22semidirect
130. #1959C22semidirect
131. #1959C22semidirect
133. #1949C22semidirect
134. #1940C22semidirect
136. #1936C22semidirect
137. #1935C22semidirect
139. #1934C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1927C22semidirect
146. #1927C22semidirect
147. #1927C22semidirect
152. #1925C22semidirect
153. #1925C22semidirect
154. #1925C22semidirect
159. #1921C22semidirect
160. #1919C22semidirect
161. #1919C22semidirect
162. #1918C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
165. #1878C22semidirect
168. #1877C22semidirect
170. #1863C22semidirect
173. #1862C22semidirect
175. #1847C22semidirect
176. #1836C22semidirect
179. #1805C22semidirect
180. #1805C22semidirect
181. #1804C22semidirect
189. #1776C22semidirect
190. C4×#107C22semidirect
191. #1771C22semidirect
192. #1771C22semidirect
193. C8×C4⋊C4C22semidirect
194. #1763C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#592482
#364412
#313102
#312982
#305432
#305272
#288942
#288742
#282002
#278952
#277832
#271122
#271012
#270702
#270632
#267432
#267222
#266892
#266882
#260362
#250692
#246552
#246392
#242062
#232262
#232162
#230522
#228192
#225492
#214532
#207322