Finite Group Databasebeta

← #7015223

Subgroups — #7015223

Order 512.

1450 conjugacy classes of subgroups.

The subgroup lattice has 1297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44978C211yesmaximal, characteristic, complemented
2#42539C211yesmaximal, characteristic
3#32540C211yesmaximal, characteristic, complemented
4#31890C211yesmaximal, characteristic, complemented
5#31779C211yesmaximal, characteristic, complemented
6#31729C211yesmaximal, characteristic, complemented
7#31666C211yesmaximal, characteristic, complemented
8#31348C211yesmaximal, characteristic, complemented
9#31040C211yesmaximal, characteristic, complemented
10#30558C211yesmaximal, characteristic, complemented
11#29491C211yesmaximal, characteristic, complemented
12#29084C211yesmaximal, characteristic, complemented
13#28859C211yesmaximal, characteristic, complemented
14#28082C211yesmaximal, characteristic, complemented
15#28061C211yesmaximal, characteristic, complemented
16#27667C211yesmaximal, characteristic, complemented
17#27479C211yesmaximal, characteristic, complemented
18#27030C211yesmaximal, characteristic, complemented
19#26727C211yesmaximal, characteristic, complemented
20#26311C211yesmaximal, characteristic, complemented
21#26126C211yesmaximal, characteristic, complemented
22#25120C211yesmaximal, characteristic, complemented
23#24977C211yesmaximal, characteristic, complemented
24#24921C211yesmaximal, characteristic, complemented
25#24886C211yesmaximal, characteristic, complemented
26#24612C211yesmaximal, characteristic, complemented
27#23714C211yesmaximal, characteristic, complemented
28#23091C211yesmaximal, characteristic, complemented
29#23032C211yesmaximal, characteristic, complemented
30#22580C211yesmaximal, characteristic, complemented
31#22088C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#433C2211yescharacteristic, complemented
39C22×#107C2211yescharacteristic, complemented
40C2×#418C2211yescharacteristic
41#2827—21no—
42#2796—21no—
43#2772—21no—
44#2770—21no—
45#2756—21no—
46#2749—21no—
47#2735—21no—
48#2718—21no—
49#2678—21no—
50#2635—21no—
51#2624C2211yescharacteristic
52#2622—21no—
53#2602—21no—
54#2562C2211yescharacteristic
55#2535C2211yescharacteristic
56#2515—21no—
57#2513C2211yescharacteristic
58#2511C2211yescharacteristic, complemented
59#2507—21no—
60#2507C2211yescharacteristic, complemented
61#2496C2211yescharacteristic, complemented
62#2495C2211yescharacteristic
63#2490C2211yescharacteristic
64#2486C2211yescharacteristic
65#2486C2211yescharacteristic
66#2468—21no—
67#2454C2211yescharacteristic
68#2423C2211yescharacteristic
69#2418—21no—
70#2417C2211yescharacteristic
71#2416C2211yescharacteristic
72#2415C2211yescharacteristic
73#2415C2211yescharacteristic, complemented
74#2408C2211yescharacteristic
75#2408C2211yescharacteristic
76#2392C2211yescharacteristic
77#2361C2211yescharacteristic
78#2360C2211yescharacteristic, complemented
79#2354C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic, complemented
81#2347C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic, complemented
85#2317C2211yescharacteristic, complemented
86#2097C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2087C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic, complemented
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2026C2211yescharacteristic, complemented
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1955C2211yescharacteristic
131#1955C2211yescharacteristic, complemented
132#1954C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1894C2211yescharacteristic
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic
165#1877C2211yescharacteristic
166#1875C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1872C2211yescharacteristic, complemented
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic, complemented
185#1824C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1823C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1807C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237#482—24no—
238#480—42no—
239#465—24no—
240#450—42no—
241#440—42no—
242#435—42no—
243#433—42no—
244C2×#107—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#418—24no—
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#399—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398D411yescharacteristic
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397D411yescharacteristic
327#396—21no—
328#396—21no—
329#396—21no—
330#396D411yescharacteristic
331#396D411yescharacteristic
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394D411yescharacteristic
342#394D411yescharacteristic
343#394D411yescharacteristic
344#392—21no—
345#392—21no—
346#392—21no—
347#392D411yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
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#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#383—21no—
422#382—21no—
423#382C2311yescharacteristic
424#381—21no—
425#381—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8C2411yescharacteristic
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#126—82no—
534#125—41no—
535#125—41no—
536#123—82no—
537#123—82no—
538C22⋊Q8—22no—
539C22⋊Q8—41no—
540C22⋊Q8—41no—
541C22⋊Q8—41no—
542C22⋊Q8—41no—
543C22⋊Q8—41no—
544#121—22no—
545#121—22no—
546#121—41no—
547#121—41no—
548#121—41no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—82no—
553#120—82no—
554#120—82no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—82no—
568C4×D4—82no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
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—82no—
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684#107—22no—
685#107—22no—
686#107—22no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—22no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702#103—22no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102#4114yes—
722C22⋊C8—22no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732#97—22no—
733#97—41no—
734#97—41no—
735#97—41no—
736C4×C8—41no—
737C4×C8—41no—
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#95—21no—
772#95—21no—
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779C24—21no—
780C24—21no—
781C24—42no—
782C24—42no—
783C24—81no—
784C24—81no—
785C24—81no—
786C24—81no—
787C24—81no—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790C24C22×D411yescharacteristic
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—41no—
811C2×D4—41no—
812C2×D4—41no—
813C2×D4—41no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—82no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4C2×#4112yes—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
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—
897SD16—82no—
898M16—82no—
899C2×C8—21no—
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—44no—
922C2×C8C2×#4112yes—
923C2×C8H(5,𝔽2)12yes—
924C4⋊C4—21no—
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—21no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
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⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4C2×#4112yes—
981C22⋊C4—22no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
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—
1026C22⋊C4—81no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—42no—
1036C42—42no—
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—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—84no—
1078C23—84no—
1079C23—162no—
1080C23—162no—
1081C23—162no—
1082C23—162no—
1083C23—162no—
1084C23#57612yes—
1085C23C23×D411yescharacteristic
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090D4—22no—
1091D4—22no—
1092D4—44no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—82no—
1100D4—82no—
1101D4—84no—
1102D4—84no—
1103D4—162no—
1104D4—162no—
1105D4—162no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—162no—
1194C2×C4—162no—
1195C2×C4—162no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4C22×#4111yescharacteristic
1199C2×C4C2×H(5,𝔽2)11yescharacteristic
1200C2×C4#58511yescharacteristic
1201C2×C4#58511yescharacteristic
1202C2×C4#58511yescharacteristic
1203C2×C4#58511yescharacteristic
1204C8—22no—
1205C8—22no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—42no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—42no—
1226C22—41no—
1227C22—42no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—168no—
1248C22D4×#4111yescharacteristic
1249C22#348511yescharacteristic
1250C22#349611yescharacteristic
1251C22C2×#57611yescharacteristic
1252C22#358511yescharacteristic
1253C22#358611yescharacteristic
1254C22#358611yescharacteristic
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4#349311yescharacteristic
1281C4#351311yescharacteristic
1282C4#356211yescharacteristic
1283C4#356611yescharacteristic
1284C2—42no—
1285C2—81no—
1286C2—81no—
1287C2—82no—
1288C2—161no—
1289C2#4303911yescharacteristic
1290C2#6150911yescharacteristic
1291C2#6152311yescharacteristic
1292C2#6174411yescharacteristic
1293C2#6178011yescharacteristic
1294C2#6231511yescharacteristic
1295C2#6233711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42539C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44978C2semidirect
3. #32540C2semidirect
4. #31890C2semidirect
5. #31779C2semidirect
6. #31729C2semidirect
7. #31666C2semidirect
8. #31348C2semidirect
9. #31040C2semidirect
10. #30558C2semidirect
11. #29491C2semidirect
12. #29084C2semidirect
13. #28859C2semidirect
14. #28082C2semidirect
15. #28061C2semidirect
16. #27667C2semidirect
17. #27479C2semidirect
18. #27030C2semidirect
19. #26727C2semidirect
20. #26311C2semidirect
21. #26126C2semidirect
22. #25120C2semidirect
23. #24977C2semidirect
24. #24921C2semidirect
25. #24886C2semidirect
26. #24612C2semidirect
27. #23714C2semidirect
28. #23091C2semidirect
29. #23032C2semidirect
30. #22580C2semidirect
31. #22088C2semidirect
38. C2×#433C22semidirect
39. C22×#107C22semidirect
58. #2511C22semidirect
60. #2507C22semidirect
61. #2496C22semidirect
73. #2415C22semidirect
78. #2360C22semidirect
80. D4×C4⋊C4C22semidirect
84. #2323C22semidirect
85. #2317C22semidirect
86. #2097C22semidirect
89. #2087C22semidirect
90. #2087C22semidirect
91. #2087C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
94. #2083C22semidirect
95. #2077C22semidirect
98. #2076C22semidirect
101. #2075C22semidirect
106. #2066C22semidirect
108. #2059C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
116. #2035C22semidirect
122. #2026C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
131. #1955C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
137. #1944C22semidirect
138. #1942C22semidirect
139. #1942C22semidirect
140. #1940C22semidirect
145. #1935C22semidirect
149. #1933C22semidirect
150. #1928C22semidirect
156. #1923C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1918C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
170. #1872C22semidirect
172. #1869C22semidirect
174. #1863C22semidirect
179. #1854C22semidirect
180. #1852C22semidirect
181. #1852C22semidirect
182. #1836C22semidirect
184. #1825C22semidirect
185. #1824C22semidirect
186. #1823C22semidirect
187. #1823C22semidirect
190. #1807C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1770C22semidirect
198. C4×#103C22semidirect
201. #1752C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#449782
#425392
#325402
#318902
#317792
#317292
#316662
#313482
#310402
#305582
#294912
#290842
#288592
#280822
#280612
#276672
#274792
#270302
#267272
#263112
#261262
#251202
#249772
#249212
#248862
#246122
#237142
#230912
#230322
#225802
#220882