Finite Group Databasebeta

← #7074297

Subgroups — #7074297

Order 512.

1469 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59637C211yesmaximal, characteristic
2#39665C211yesmaximal, characteristic, complemented
3#32647C211yesmaximal, characteristic, complemented
4#32615C211yesmaximal, characteristic, complemented
5#32540C211yesmaximal, characteristic, complemented
6#32066C211yesmaximal, characteristic, complemented
7#32066C211yesmaximal, characteristic, complemented
8#31290C211yesmaximal, characteristic
9#31166C211yesmaximal, characteristic, complemented
10#30456C211yesmaximal, characteristic
11#29481C211yesmaximal, characteristic, complemented
12#29093C211yesmaximal, characteristic, complemented
13#29085C211yesmaximal, characteristic, complemented
14#28898C211yesmaximal, characteristic, complemented
15#28745C211yesmaximal, characteristic, complemented
16#27508C211yesmaximal, characteristic, complemented
17#27460C211yesmaximal, characteristic, complemented
18#27396C211yesmaximal, characteristic, complemented
19#27245C211yesmaximal, characteristic, complemented
20#27245C211yesmaximal, characteristic, complemented
21#27220C211yesmaximal, characteristic, complemented
22#26912C211yesmaximal, characteristic, complemented
23#26709C211yesmaximal, characteristic, complemented
24#26260C211yesmaximal, characteristic, complemented
25#25481C211yesmaximal, characteristic, complemented
26#24507C211yesmaximal, characteristic, complemented
27#23711C211yesmaximal, characteristic, complemented
28#23101C211yesmaximal, characteristic, complemented
29#23079C211yesmaximal, characteristic, complemented
30#23053C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#492C2211yescharacteristic
33C2×#474C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×#440C2211yescharacteristic, complemented
40C2×#432C2211yescharacteristic
41#2855C2211yescharacteristic
42#2799—21no—
43#2797—21no—
44#2790—21no—
45#2774—21no—
46#2763—21no—
47#2752—21no—
48#2665—21no—
49#2602—21no—
50#2580C2211yescharacteristic
51#2568C2211yescharacteristic, complemented
52#2567C2211yescharacteristic, complemented
53#2557—21no—
54#2548C2211yescharacteristic
55#2520—21no—
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2511—21no—
59#2511C2211yescharacteristic, complemented
60#2504C2211yescharacteristic
61#2497C2211yescharacteristic
62#2492C2211yescharacteristic
63#2492C2211yescharacteristic
64#2472—21no—
65#2451C2211yescharacteristic, complemented
66#2451C2211yescharacteristic, complemented
67#2446C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2445C2211yescharacteristic
70#2433C2211yescharacteristic
71#2429C2211yescharacteristic
72#2418—21no—
73#2412—21no—
74#2369C2211yescharacteristic, complemented
75#2366C2211yescharacteristic
76#2358—21no—
77#2357C2211yescharacteristic
78#2355C2211yescharacteristic, complemented
79#2345C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2332—21no—
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2097C2211yescharacteristic, complemented
87#2097C2211yescharacteristic, complemented
88#2094C2211yescharacteristic
89#2087C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2013C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1993C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1981C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1973C2211yescharacteristic, complemented
139#1973C2211yescharacteristic, complemented
140#1957C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1942C2211yescharacteristic, complemented
146#1940C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1923C2211yescharacteristic
168#1923C2211yescharacteristic
169#1921C2211yescharacteristic, complemented
170#1921C2211yescharacteristic, complemented
171#1921C2211yescharacteristic, complemented
172#1921C2211yescharacteristic, complemented
173#1918C2211yescharacteristic, complemented
174#1917C2211yescharacteristic, complemented
175#1917C2211yescharacteristic, complemented
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic, complemented
184#1872C2211yescharacteristic
185#1872C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#107C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#124—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8D411yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236C22×C42C2311yescharacteristic
237#492—42no—
238#474—24no—
239#474—42no—
240#460—24no—
241#450—24no—
242#450—42no—
243#446—42no—
244#440—42no—
245#432—42no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#393—21no—
336#392—21no—
337#392—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391D411yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389D411yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
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#388—21no—
392#388—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#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#385D411yescharacteristic
424#384—21no—
425#384C2311yescharacteristic
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380D411yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
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×Q8C2×D411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#127—22no—
548#127—41no—
549#127—41no—
550#127—41no—
551#124—82no—
552#123—82no—
553#123—82no—
554C22⋊Q8—24no—
555C22⋊Q8—22no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559#121—41no—
560#121—41no—
561#120—44no—
562#120—82no—
563C4×Q8—22no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—82no—
576C4×D4—82no—
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—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
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×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—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—82no—
651C2×C22⋊C4—82no—
652C2×C22⋊C4—82no—
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—41no—
667C2×C42—41no—
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—22no—
677#107—22no—
678#107—22no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#107—41no—
684#106—41no—
685#106—41no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102#4114yes—
720C22⋊C8—22no—
721C22⋊C8—22no—
722C22⋊C8—41no—
723C22⋊C8—41no—
724#97—22no—
725#97—41no—
726#97—41no—
727#97—41no—
728#97—41no—
729#97—41no—
730C4×C8—22no—
731C4×C8—41no—
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#95—21no—
769#95—21no—
770#95—21no—
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781C24—21no—
782C24—21no—
783C24—21no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24C22×D411yescharacteristic
792C2×Q8—22no—
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—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—41no—
806C2×Q8—41no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
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—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4C2×#4112yes—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C2511yescharacteristic
904SD16—44no—
905SD16—82no—
906SD16—82no—
907SD16—82no—
908SD16—82no—
909SD16—82no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8C2×#4112yes—
933C2×C8H(5,𝔽2)12yes—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4C2×#4112yes—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
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—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—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4#13714yes—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—41no—
1033C42—41no—
1034C42—42no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
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—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—84no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—162no—
1075C23—162no—
1076C23—162no—
1077C23C2×#13712yes—
1078C23C23×D411yescharacteristic
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—41no—
1083Q8—41no—
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—82no—
1088Q8—162no—
1089Q8—162no—
1090D4—22no—
1091D4—22no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—84no—
1103D4—84no—
1104D4—84no—
1105D4—162no—
1106D4—162no—
1107D4—162no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—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—22no—
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—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—82no—
1189C2×C4—82no—
1190C2×C4—162no—
1191C2×C4—162no—
1192C2×C4—162no—
1193C2×C4—162no—
1194C2×C4C2×#13712yes—
1195C2×C4C2×#13712yes—
1196C2×C4C22×#4111yescharacteristic
1197C2×C4C2×H(5,𝔽2)11yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C2×C4#58511yescharacteristic
1202C8—22no—
1203C8—22no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—168no—
1239C22D4×#4111yescharacteristic
1240C22#348711yescharacteristic
1241C22#349611yescharacteristic
1242C22C22×#13711yescharacteristic
1243C22#358511yescharacteristic
1244C22#358511yescharacteristic
1245C22#358511yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4#351011yescharacteristic
1273C4#351411yescharacteristic
1274C4#353311yescharacteristic
1275C4#356611yescharacteristic
1276C2—42no—
1277C2—82no—
1278C2—161no—
1279C2—161no—
1280C2#4392511yescharacteristic
1281C2#6145311yescharacteristic
1282C2#6150611yescharacteristic
1283C2#6189211yescharacteristic
1284C2#6194511yescharacteristic
1285C2#6228611yescharacteristic
1286C2#6229611yescharacteristic
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
2. #39665C2semidirect
3. #32647C2semidirect
4. #32615C2semidirect
5. #32540C2semidirect
6. #32066C2semidirect
7. #32066C2semidirect
9. #31166C2semidirect
11. #29481C2semidirect
12. #29093C2semidirect
13. #29085C2semidirect
14. #28898C2semidirect
15. #28745C2semidirect
16. #27508C2semidirect
17. #27460C2semidirect
18. #27396C2semidirect
19. #27245C2semidirect
20. #27245C2semidirect
21. #27220C2semidirect
22. #26912C2semidirect
23. #26709C2semidirect
24. #26260C2semidirect
25. #25481C2semidirect
26. #24507C2semidirect
27. #23711C2semidirect
28. #23101C2semidirect
29. #23079C2semidirect
30. #23053C2semidirect
31. #22049C2semidirect
38. C2×#446C22semidirect
39. C2×#440C22semidirect
51. #2568C22semidirect
52. #2567C22semidirect
59. #2511C22semidirect
65. #2451C22semidirect
66. #2451C22semidirect
67. #2446C22semidirect
74. #2369C22semidirect
78. #2355C22semidirect
86. #2097C22semidirect
87. #2097C22semidirect
89. #2087C22semidirect
90. #2087C22semidirect
91. #2086C22semidirect
92. #2083C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
99. #2067C22semidirect
100. #2066C22semidirect
107. #2055C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2043C22semidirect
120. #2023C22semidirect
121. #2023C22semidirect
126. #1993C22semidirect
127. #1993C22semidirect
128. #1985C22semidirect
130. #1981C22semidirect
137. #1973C22semidirect
138. #1973C22semidirect
139. #1973C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1947C22semidirect
144. #1944C22semidirect
145. #1942C22semidirect
146. #1940C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
157. #1927C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
169. #1921C22semidirect
170. #1921C22semidirect
171. #1921C22semidirect
172. #1921C22semidirect
173. #1918C22semidirect
174. #1917C22semidirect
175. #1917C22semidirect
183. #1877C22semidirect
186. #1863C22semidirect
187. #1862C22semidirect
192. #1776C22semidirect
193. C4×#107C22semidirect
194. #1771C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
200. #1762C22semidirect
201. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#596372
#396652
#326472
#326152
#325402
#320662
#312902
#311662
#304562
#294812
#290932
#290852
#288982
#287452
#275082
#274602
#273962
#272452
#272202
#269122
#267092
#262602
#254812
#245072
#237112
#231012
#230792
#230532
#220492