Finite Group Databasebeta

← #6543720

Subgroups — #6543720

Order 512.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38260C211yesmaximal, characteristic, complemented
2#34438C211yesmaximal, characteristic, complemented
3#30142C211yesmaximal, characteristic, complemented
4#30082C211yesmaximal, characteristic, complemented
5#29630C211yesmaximal, characteristic
6#29505C211yesmaximal, characteristic, complemented
7#29364C211yesmaximal, characteristic, complemented
8#29130C211yesmaximal, characteristic, complemented
9#28214C211yesmaximal, characteristic, complemented
10#27868C211yesmaximal, characteristic, complemented
11#27622C211yesmaximal, characteristic, complemented
12#27079C211yesmaximal, characteristic, complemented
13#27075C211yesmaximal, characteristic, complemented
14#26917C211yesmaximal, characteristic, complemented
15#26905C211yesmaximal, characteristic, complemented
16#26782C211yesmaximal, characteristic, complemented
17#26780C211yesmaximal, characteristic, complemented
18#26771C211yesmaximal, characteristic, complemented
19#26752C211yesmaximal, characteristic, complemented
20#25976C211yesmaximal, characteristic, complemented
21#25956C211yesmaximal, characteristic, complemented
22#24544C211yesmaximal, characteristic, complemented
23#24526C211yesmaximal, characteristic, complemented
24#23832C211yesmaximal, characteristic, complemented
25#23686C211yesmaximal, characteristic, complemented
26#23509C211yesmaximal, characteristic, complemented
27#22868C211yesmaximal, characteristic, complemented
28#22857C211yesmaximal, characteristic, complemented
29#22598C211yesmaximal, characteristic, complemented
30#22579C211yesmaximal, characteristic, complemented
31#22566C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#478C2211yescharacteristic, complemented
35C2×#449C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#440C2211yescharacteristic, complemented
39C2×#417C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C2×#416C2211yescharacteristic
42C22×#102C2211yescharacteristic
43#2859C2211yescharacteristic, complemented
44#2773—21no—
45#2721—21no—
46#2707—21no—
47#2694—21no—
48#2644C2211yescharacteristic, complemented
49#2624C2211yescharacteristic
50#2553—21no—
51#2517—21no—
52#2512C2211yescharacteristic, complemented
53#2507C2211yescharacteristic, complemented
54#2506C2211yescharacteristic, complemented
55#2501C2211yescharacteristic
56#2470—21no—
57#2454C2211yescharacteristic, complemented
58#2441—21no—
59#2441C2211yescharacteristic
60#2377—21no—
61#2375—21no—
62#2367C2211yescharacteristic
63#2367C2211yescharacteristic
64#2366C2211yescharacteristic
65#2366C2211yescharacteristic
66#2364—21no—
67#2363C2211yescharacteristic
68#2358—21no—
69#2345C2211yescharacteristic
70#2341C2211yescharacteristic
71#2339C2211yescharacteristic
72D4×C22⋊C4C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2333—21no—
75#2330C2211yescharacteristic, complemented
76#2328C2211yescharacteristic
77#2326C2211yescharacteristic
78#2325—21no—
79#2321—21no—
80#2321—21no—
81#2317C2211yescharacteristic
82#2314C2211yescharacteristic
83C4×#127C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2298C2211yescharacteristic
86#2293C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#1972C2211yescharacteristic, complemented
128#1970C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic, complemented
133#1936C2211yescharacteristic, complemented
134#1934C2211yescharacteristic, complemented
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic, complemented
137#1926C2211yescharacteristic, complemented
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic, complemented
141#1925C2211yescharacteristic, complemented
142#1925C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1916C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1893C2211yescharacteristic
155#1880C2211yescharacteristic, complemented
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic, complemented
161#1879C2211yescharacteristic, complemented
162#1879C2211yescharacteristic, complemented
163#1865C2211yescharacteristic, complemented
164#1865C2211yescharacteristic, complemented
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic, complemented
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic, complemented
172#1862C2211yescharacteristic, complemented
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1851C2211yescharacteristic
176#1850C2211yescharacteristic
177#1839C2211yescharacteristic, complemented
178#1832C2211yescharacteristic, complemented
179#1824C2211yescharacteristic
180#1823C2211yescharacteristic
181#1818C2211yescharacteristic
182#1809C2211yescharacteristic
183#1808C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1767C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#535—24no—
212#535—24no—
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×#120—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247#478—42no—
248#478—42no—
249#449—24no—
250#447—24no—
251#442—42no—
252#440—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265#418—42no—
266#417—24no—
267#416—42no—
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#102—24no—
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#399—21no—
309#399—21no—
310#399—21no—
311#399—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—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#394—21no—
326#394—21no—
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#388—21no—
365#388—21no—
366#388—21no—
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#388D411yescharacteristic
379#388D411yescharacteristic
380#388D411yescharacteristic
381#388D411yescharacteristic
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387D411yescharacteristic
392#387D411yescharacteristic
393#387D411yescharacteristic
394#387D411yescharacteristic
395#386—21no—
396#386—21no—
397#386—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#386—21no—
408#386—21no—
409#386—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#384C2311yescharacteristic
421#384C2311yescharacteristic
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376C2311yescharacteristic
452C2×#95—21no—
453C43C2311yescharacteristic
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41#4114yes—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4#4114yes—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551#127—22no—
552#127—22no—
553#127—22no—
554#127—22no—
555#126—82no—
556#125—22no—
557#125—41no—
558#125—82no—
559#125—82no—
560#124—22no—
561#124—22no—
562#124—22no—
563#124—22no—
564#123—82no—
565#123—82no—
566#121—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#120—28no—
571#120—28no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—82no—
591C4×D4—82no—
592C4×D4—82no—
593C4×D4—82no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—41no—
598#117—82no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—82no—
681C2×C22⋊C4—82no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750C22⋊C8—22no—
751C22⋊C8—22no—
752#97—41no—
753#97—41no—
754#97—41no—
755C4×C8—41no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—24no—
797C24—21no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805#41—44no—
806#41—44no—
807#41—82no—
808#41—82no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8C2×#4112yes—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
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—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—42no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4C2×#4112yes—
862C2×D4C2×#4112yes—
863C2×D4C2×#4112yes—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—24no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C2×#4112yes—
921C22×C4C2×#4112yes—
922C22×C4C2511yescharacteristic
923SD16—44no—
924D8—44no—
925D8—82no—
926D8—82no—
927M16—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—82no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4H(5,𝔽2)12yes—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—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—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C42—22no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—42no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—84no—
1108C23—84no—
1109C23—84no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23#52512yes—
1115C23C23×D411yescharacteristic
1116Q8—22no—
1117Q8—22no—
1118Q8—41no—
1119Q8—41no—
1120D4—22no—
1121D4—22no—
1122D4—22no—
1123D4—22no—
1124D4—22no—
1125D4—22no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—162no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4#52512yes—
1230C2×C4#57612yes—
1231C2×C4C22×#4111yescharacteristic
1232C2×C4C22×#4111yescharacteristic
1233C2×C4C2×H(5,𝔽2)11yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22C2×#52511yescharacteristic
1282C22#348811yescharacteristic
1283C22#350011yescharacteristic
1284C22C2×#57611yescharacteristic
1285C22#358511yescharacteristic
1286C22#358511yescharacteristic
1287C22#358611yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—42no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4#349111yescharacteristic
1314C4#349111yescharacteristic
1315C4#350511yescharacteristic
1316C4#350511yescharacteristic
1317C2—42no—
1318C2—82no—
1319C2—82no—
1320C2—82no—
1321C2—161no—
1322C2#3575311yescharacteristic
1323C2#6057511yescharacteristic
1324C2#6059011yescharacteristic
1325C2#6204111yescharacteristic
1326C2#6209311yescharacteristic
1327C2#6256711yescharacteristic
1328C2#6259811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#29630C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38260C2semidirect
2. #34438C2semidirect
3. #30142C2semidirect
4. #30082C2semidirect
6. #29505C2semidirect
7. #29364C2semidirect
8. #29130C2semidirect
9. #28214C2semidirect
10. #27868C2semidirect
11. #27622C2semidirect
12. #27079C2semidirect
13. #27075C2semidirect
14. #26917C2semidirect
15. #26905C2semidirect
16. #26782C2semidirect
17. #26780C2semidirect
18. #26771C2semidirect
19. #26752C2semidirect
20. #25976C2semidirect
21. #25956C2semidirect
22. #24544C2semidirect
23. #24526C2semidirect
24. #23832C2semidirect
25. #23686C2semidirect
26. #23509C2semidirect
27. #22868C2semidirect
28. #22857C2semidirect
29. #22598C2semidirect
30. #22579C2semidirect
31. #22566C2semidirect
34. C2×#478C22semidirect
38. C2×#440C22semidirect
43. #2859C22semidirect
48. #2644C22semidirect
52. #2512C22semidirect
53. #2507C22semidirect
54. #2506C22semidirect
57. #2454C22semidirect
75. #2330C22semidirect
86. #2293C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2095C22semidirect
92. #2093C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2073C22semidirect
97. #2072C22semidirect
98. #2072C22semidirect
101. #2068C22semidirect
104. #2066C22semidirect
105. #2055C22semidirect
106. #2055C22semidirect
121. #2026C22semidirect
127. #1972C22semidirect
132. #1936C22semidirect
133. #1936C22semidirect
134. #1934C22semidirect
136. #1926C22semidirect
137. #1926C22semidirect
140. #1925C22semidirect
141. #1925C22semidirect
142. #1925C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
146. #1919C22semidirect
147. #1918C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
152. #1916C22semidirect
155. #1880C22semidirect
160. #1879C22semidirect
161. #1879C22semidirect
162. #1879C22semidirect
163. #1865C22semidirect
164. #1865C22semidirect
166. #1863C22semidirect
171. #1862C22semidirect
172. #1862C22semidirect
177. #1839C22semidirect
178. #1832C22semidirect
187. #1802C22semidirect
188. #1802C22semidirect
189. #1802C22semidirect
192. #1767C22semidirect
193. #1763C22semidirect
194. #1763C22semidirect
197. C4×#103C22semidirect
201. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#382602
#344382
#301422
#300822
#296302
#295052
#293642
#291302
#282142
#278682
#276222
#270792
#270752
#269172
#269052
#267822
#267802
#267712
#267522
#259762
#259562
#245442
#245262
#238322
#236862
#235092
#228682
#228572
#225982
#225792
#225662