Finite Group Databasebeta

← #7015015

Subgroups — #7015015

Order 512.

1499 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59440C211yesmaximal, characteristic, complemented
2#39030C211yesmaximal, characteristic
3#32525C211yesmaximal, characteristic, complemented
4#31867C211yesmaximal, characteristic, complemented
5#31778C211yesmaximal, characteristic, complemented
6#31730C211yesmaximal, characteristic, complemented
7#31672C211yesmaximal, characteristic, complemented
8#31326C211yesmaximal, characteristic, complemented
9#31040C211yesmaximal, characteristic, complemented
10#30559C211yesmaximal, characteristic, complemented
11#29466C211yesmaximal, characteristic, complemented
12#29084C211yesmaximal, characteristic, complemented
13#28852C211yesmaximal, characteristic, complemented
14#28082C211yesmaximal, characteristic, complemented
15#28056C211yesmaximal, characteristic, complemented
16#27659C211yesmaximal, characteristic, complemented
17#27477C211yesmaximal, characteristic, complemented
18#27054C211yesmaximal, characteristic, complemented
19#26751C211yesmaximal, characteristic, complemented
20#26310C211yesmaximal, characteristic, complemented
21#26131C211yesmaximal, characteristic, complemented
22#25112C211yesmaximal, characteristic, complemented
23#24982C211yesmaximal, characteristic, complemented
24#24917C211yesmaximal, characteristic, complemented
25#24865C211yesmaximal, characteristic, complemented
26#24608C211yesmaximal, characteristic, complemented
27#23711C211yesmaximal, characteristic, complemented
28#23084C211yesmaximal, characteristic, complemented
29#23033C211yesmaximal, characteristic, complemented
30#22562C211yesmaximal, characteristic, complemented
31#22076C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×#432C2211yescharacteristic, complemented
39C2×#427C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic
41#2854C2211yescharacteristic
42#2779—21no—
43#2772—21no—
44#2739—21no—
45#2703—21no—
46#2697—21no—
47#2685—21no—
48#2648—21no—
49#2601—21no—
50#2590—21no—
51#2569—21no—
52#2562C2211yescharacteristic
53#2537C2211yescharacteristic
54#2512C2211yescharacteristic
55#2511C2211yescharacteristic, complemented
56#2508C2211yescharacteristic, complemented
57#2497C2211yescharacteristic
58#2496C2211yescharacteristic, complemented
59#2490C2211yescharacteristic
60#2485C2211yescharacteristic
61#2485C2211yescharacteristic
62#2481—21no—
63#2467—21no—
64#2454C2211yescharacteristic
65#2444—21no—
66#2424—21no—
67#2421C2211yescharacteristic
68#2417C2211yescharacteristic
69#2417C2211yescharacteristic
70#2417C2211yescharacteristic, complemented
71#2414C2211yescharacteristic
72#2408C2211yescharacteristic
73#2408C2211yescharacteristic
74#2363C2211yescharacteristic
75#2362C2211yescharacteristic, complemented
76#2352—21no—
77#2352C2211yescharacteristic, complemented
78D4×C4⋊C4C2211yescharacteristic
79#2344C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2312—21no—
82C4×C22⋊Q8C2211yescharacteristic, complemented
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#389C2211yescharacteristic, complemented
86#2096C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2087C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2026C2211yescharacteristic, complemented
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1968C2211yescharacteristic
130#1955C2211yescharacteristic
131#1955C2211yescharacteristic, complemented
132#1954C2211yescharacteristic
133#1948C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1939C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1877C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1873C2211yescharacteristic, complemented
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic, complemented
181#1853C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1825C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1824C2211yescharacteristic, complemented
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic, complemented
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#123—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121—21no—
216C2×#121D411yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4—21no—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240#481—24no—
241#480—42no—
242#465—24no—
243#450—42no—
244#440—42no—
245C8×D4—42no—
246#432—42no—
247#427—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
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#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#392—21no—
337#392—21no—
338#392—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390—21no—
344#390—21no—
345#390D411yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389—21no—
355#389D411yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388D411yescharacteristic
384#388D411yescharacteristic
385#387—21no—
386#387—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#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386D411yescharacteristic
408#386D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382C2311yescharacteristic
417#381—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380D411yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C2×#95—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#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×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535#126—82no—
536#126—82no—
537#125—41no—
538#125—41no—
539#123—82no—
540C22⋊Q8—22no—
541C22⋊Q8—41no—
542C22⋊Q8—41no—
543C22⋊Q8—41no—
544C22⋊Q8—41no—
545C22⋊Q8—41no—
546#121—22no—
547#121—22no—
548#121—42no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—82no—
556#120—82no—
557#120—82no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—44no—
571C4×D4—82no—
572#117—41no—
573#117—41no—
574#117—41no—
575#117—41no—
576#117—82no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
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—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—82no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—44no—
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×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—41no—
680C2×C42—41no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—22no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102#4114yes—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—22no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735#97—22no—
736#97—41no—
737#97—41no—
738#97—41no—
739C4×C8—41no—
740C4×C8—41no—
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#95—21no—
774#95—21no—
775#95—21no—
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—42no—
785C24—42no—
786C24—81no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24C22×D411yescharacteristic
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—42no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—82no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—22no—
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—22no—
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—21no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
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×C4C22×D411yescharacteristic
904C22×C4C2511yescharacteristic
905SD16—44no—
906SD16—82no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—44no—
930C2×C8—82no—
931C2×C8C2×#4112yes—
932C2×C8H(5,𝔽2)12yes—
933C4⋊C4—22no—
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—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—21no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
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⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4C2×#4112yes—
988C22⋊C4—22no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
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—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—41no—
1041C42—41no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—22no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—84no—
1084C23—84no—
1085C23—162no—
1086C23—162no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23#57512yes—
1091C23#57712yes—
1092C23C23×D411yescharacteristic
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097D4—22no—
1098D4—22no—
1099D4—44no—
1100D4—44no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—82no—
1108D4—84no—
1109D4—84no—
1110D4—162no—
1111D4—162no—
1112D4—162no—
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—22no—
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—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—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—82no—
1200C2×C4—82no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4#57712yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—41no—
1238C22—42no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—168no—
1257C22D4×#4111yescharacteristic
1258C22#348511yescharacteristic
1259C22#349611yescharacteristic
1260C22C2×#57511yescharacteristic
1261C22C2×#57711yescharacteristic
1262C22C2×#57711yescharacteristic
1263C22#358511yescharacteristic
1264C4—22no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#349311yescharacteristic
1290C4#351311yescharacteristic
1291C4#356211yescharacteristic
1292C4#356611yescharacteristic
1293C2—42no—
1294C2—42no—
1295C2—81no—
1296C2—82no—
1297C2—161no—
1298C2#4303911yescharacteristic
1299C2#6145411yescharacteristic
1300C2#6148111yescharacteristic
1301C2#6172911yescharacteristic
1302C2#6181511yescharacteristic
1303C2#6225611yescharacteristic
1304C2#6231911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39030C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59440C2semidirect
3. #32525C2semidirect
4. #31867C2semidirect
5. #31778C2semidirect
6. #31730C2semidirect
7. #31672C2semidirect
8. #31326C2semidirect
9. #31040C2semidirect
10. #30559C2semidirect
11. #29466C2semidirect
12. #29084C2semidirect
13. #28852C2semidirect
14. #28082C2semidirect
15. #28056C2semidirect
16. #27659C2semidirect
17. #27477C2semidirect
18. #27054C2semidirect
19. #26751C2semidirect
20. #26310C2semidirect
21. #26131C2semidirect
22. #25112C2semidirect
23. #24982C2semidirect
24. #24917C2semidirect
25. #24865C2semidirect
26. #24608C2semidirect
27. #23711C2semidirect
28. #23084C2semidirect
29. #23033C2semidirect
30. #22562C2semidirect
31. #22076C2semidirect
38. C2×#432C22semidirect
39. C2×#427C22semidirect
55. #2511C22semidirect
56. #2508C22semidirect
58. #2496C22semidirect
70. #2417C22semidirect
75. #2362C22semidirect
77. #2352C22semidirect
82. C4×C22⋊Q8C22semidirect
85. C2×#389C22semidirect
86. #2096C22semidirect
89. #2087C22semidirect
90. #2087C22semidirect
91. #2086C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
94. #2084C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
100. #2076C22semidirect
105. #2066C22semidirect
108. #2059C22semidirect
113. #2036C22semidirect
115. #2035C22semidirect
116. #2035C22semidirect
122. #2026C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
131. #1955C22semidirect
133. #1948C22semidirect
134. #1948C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
137. #1941C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
140. #1939C22semidirect
145. #1935C22semidirect
149. #1933C22semidirect
150. #1927C22semidirect
156. #1924C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
170. #1873C22semidirect
172. #1869C22semidirect
173. #1865C22semidirect
177. #1854C22semidirect
180. #1853C22semidirect
181. #1853C22semidirect
182. #1836C22semidirect
183. #1825C22semidirect
184. #1825C22semidirect
185. #1824C22semidirect
187. #1823C22semidirect
190. #1807C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
201. #1752C22semidirect
202. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#594402
#390302
#325252
#318672
#317782
#317302
#316722
#313262
#310402
#305592
#294662
#290842
#288522
#280822
#280562
#276592
#274772
#270542
#267512
#263102
#261312
#251122
#249822
#249172
#248652
#246082
#237112
#230842
#230332
#225622
#220762