Finite Group Databasebeta

← #7080051

Subgroups — #7080051

Order 512.

1624 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44874C211yesmaximal, characteristic
2#42656C211yesmaximal, characteristic, complemented
3#32186C211yesmaximal, characteristic, complemented
4#31973C211yesmaximal, characteristic, complemented
5#31861C211yesmaximal, characteristic, complemented
6#31739C211yesmaximal, characteristic, complemented
7#31662C211yesmaximal, characteristic, complemented
8#31504C211yesmaximal, characteristic, complemented
9#31479C211yesmaximal, characteristic, complemented
10#30996C211yesmaximal, characteristic, complemented
11#29099C211yesmaximal, characteristic, complemented
12#28998C211yesmaximal, characteristic, complemented
13#28564C211yesmaximal, characteristic, complemented
14#27759C211yesmaximal, characteristic, complemented
15#27541C211yesmaximal, characteristic, complemented
16#27271C211yesmaximal, characteristic, complemented
17#27271C211yesmaximal, characteristic, complemented
18#26777C211yesmaximal, characteristic, complemented
19#26421C211yesmaximal, characteristic, complemented
20#26222C211yesmaximal, characteristic, complemented
21#25514C211yesmaximal, characteristic, complemented
22#25328C211yesmaximal, characteristic, complemented
23#25084C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#24516C211yesmaximal, characteristic, complemented
26#24448C211yesmaximal, characteristic
27#23632C211yesmaximal, characteristic, complemented
28#23142C211yesmaximal, characteristic, complemented
29#22911C211yesmaximal, characteristic, complemented
30#22423C211yesmaximal, characteristic
31#21871C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#467C2211yescharacteristic, complemented
37C2×#464C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#433C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2827—21no—
46#2810—21no—
47#2802—21no—
48#2783—21no—
49#2773—21no—
50#2697—21no—
51#2685—21no—
52#2684—21no—
53#2681—21no—
54#2652—21no—
55#2649—21no—
56#2625C2211yescharacteristic, complemented
57#2571C2211yescharacteristic, complemented
58#2565C2211yescharacteristic, complemented
59#2559—21no—
60#2544C2211yescharacteristic
61#2517—21no—
62#2511C2211yescharacteristic, complemented
63#2508C2211yescharacteristic, complemented
64#2499C2211yescharacteristic, complemented
65#2497C2211yescharacteristic, complemented
66#2491C2211yescharacteristic
67#2472—21no—
68#2452C2211yescharacteristic
69#2445C2211yescharacteristic
70#2441C2211yescharacteristic, complemented
71#2441C2211yescharacteristic, complemented
72#2435—21no—
73#2435C2211yescharacteristic
74#2435C2211yescharacteristic
75#2426C2211yescharacteristic
76#2421C2211yescharacteristic, complemented
77#2415C2211yescharacteristic
78#2415C2211yescharacteristic
79#2405—21no—
80#2395C2211yescharacteristic
81#2367C2211yescharacteristic
82#2363C2211yescharacteristic
83#2360C2211yescharacteristic, complemented
84#2352C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2317C2211yescharacteristic, complemented
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2025C2211yescharacteristic, complemented
121#2025C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2015C2211yescharacteristic, complemented
124#2015C2211yescharacteristic, complemented
125#2014C2211yescharacteristic
126#2001C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1983C2211yescharacteristic, complemented
132#1982C2211yescharacteristic
133#1973C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1961C2211yescharacteristic
136#1959C2211yescharacteristic, complemented
137#1959C2211yescharacteristic, complemented
138#1958C2211yescharacteristic, complemented
139#1939C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic, complemented
146#1934C2211yescharacteristic, complemented
147#1934C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1923C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic, complemented
160#1894C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic, complemented
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1873C2211yescharacteristic, complemented
174#1873C2211yescharacteristic, complemented
175#1872C2211yescharacteristic, complemented
176#1870C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1850C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213D42—24no—
214D42—42no—
215#542—24no—
216#542—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251#488—42no—
252#468—24no—
253#467—42no—
254#464—42no—
255#450—42no—
256#450—42no—
257#435—42no—
258#433—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268#418—42no—
269#418—42no—
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102—42no—
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×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400D411yescharacteristic
322#399—21no—
323#399—21no—
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398D411yescharacteristic
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397D411yescharacteristic
338#397D411yescharacteristic
339#397D411yescharacteristic
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#393—21no—
360#393—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446#379—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4—82no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560#127—22no—
561#127—41no—
562#126—44no—
563#125—41no—
564#125—41no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—44no—
572#124—82no—
573#123—44no—
574#123—82no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—44no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—82no—
585#121—22no—
586#121—22no—
587#121—44no—
588#121—41no—
589#121#4114yes—
590#120—44no—
591#120—44no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604#117—22no—
605#117—22no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
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⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
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—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—41no—
718#107—41no—
719#106—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725#103—22no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762#97—41no—
763#97—41no—
764#97—41no—
765C4×C8—41no—
766C4×C8—41no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—44no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—816no—
888C2×D4C2×#4112yes—
889C2×D4H(5,𝔽2)12yes—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C2×#4112yes—
938C22×C4H(5,𝔽2)12yes—
939C22×C4C2511yescharacteristic
940Q16—82no—
941SD16—82no—
942SD16—82no—
943SD16—82no—
944M16—82no—
945M16—82no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—82no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4C2×#4112yes—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—21no—
1100C23—22no—
1101C23—21no—
1102C23—21no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23#54612yes—
1137C23C23×D411yescharacteristic
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—162no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—22no—
1151D4—44no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—84no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—162no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
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—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
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—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—84no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4#54612yes—
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4#58511yescharacteristic
1257C2×C4#58511yescharacteristic
1258C2×C4#58511yescharacteristic
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—41no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—168no—
1303C22—168no—
1304C22C2×#54611yescharacteristic
1305C22#348811yescharacteristic
1306C22#350011yescharacteristic
1307C22#358411yescharacteristic
1308C22#358511yescharacteristic
1309C22#358511yescharacteristic
1310C22#358611yescharacteristic
1311C4—22no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#351311yescharacteristic
1337C4#352111yescharacteristic
1338C4#353411yescharacteristic
1339C4#356011yescharacteristic
1340C2—42no—
1341C2—81no—
1342C2—82no—
1343C2—82no—
1344C2—161no—
1345C2#4399811yescharacteristic
1346C2#6117511yescharacteristic
1347C2#6120711yescharacteristic
1348C2#6201111yescharacteristic
1349C2#6208411yescharacteristic
1350C2#6257511yescharacteristic
1351C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42656C2semidirect
3. #32186C2semidirect
4. #31973C2semidirect
5. #31861C2semidirect
6. #31739C2semidirect
7. #31662C2semidirect
8. #31504C2semidirect
9. #31479C2semidirect
10. #30996C2semidirect
11. #29099C2semidirect
12. #28998C2semidirect
13. #28564C2semidirect
14. #27759C2semidirect
15. #27541C2semidirect
16. #27271C2semidirect
17. #27271C2semidirect
18. #26777C2semidirect
19. #26421C2semidirect
20. #26222C2semidirect
21. #25514C2semidirect
22. #25328C2semidirect
23. #25084C2semidirect
24. #24538C2semidirect
25. #24516C2semidirect
27. #23632C2semidirect
28. #23142C2semidirect
29. #22911C2semidirect
31. #21871C2semidirect
36. C2×#467C22semidirect
41. C2×#433C22semidirect
56. #2625C22semidirect
57. #2571C22semidirect
58. #2565C22semidirect
62. #2511C22semidirect
63. #2508C22semidirect
64. #2499C22semidirect
65. #2497C22semidirect
70. #2441C22semidirect
71. #2441C22semidirect
76. #2421C22semidirect
83. #2360C22semidirect
86. #2317C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2088C22semidirect
91. #2087C22semidirect
92. #2076C22semidirect
93. #2076C22semidirect
94. #2074C22semidirect
97. #2073C22semidirect
98. #2073C22semidirect
102. #2071C22semidirect
103. #2071C22semidirect
105. #2067C22semidirect
106. #2065C22semidirect
107. #2065C22semidirect
108. #2057C22semidirect
109. #2056C22semidirect
112. #2055C22semidirect
115. #2042C22semidirect
116. #2042C22semidirect
118. #2035C22semidirect
120. #2025C22semidirect
121. #2025C22semidirect
122. #2024C22semidirect
123. #2015C22semidirect
124. #2015C22semidirect
126. #2001C22semidirect
128. #1993C22semidirect
129. #1990C22semidirect
130. #1989C22semidirect
131. #1983C22semidirect
133. #1973C22semidirect
136. #1959C22semidirect
137. #1959C22semidirect
138. #1958C22semidirect
139. #1939C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1934C22semidirect
146. #1934C22semidirect
147. #1934C22semidirect
148. #1928C22semidirect
150. #1924C22semidirect
151. #1923C22semidirect
152. #1921C22semidirect
153. #1920C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
159. #1894C22semidirect
160. #1894C22semidirect
161. #1894C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
165. #1878C22semidirect
167. #1877C22semidirect
168. #1877C22semidirect
172. #1873C22semidirect
173. #1873C22semidirect
174. #1873C22semidirect
175. #1872C22semidirect
177. #1863C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
181. #1854C22semidirect
182. #1851C22semidirect
183. #1850C22semidirect
184. #1825C22semidirect
185. #1805C22semidirect
187. #1804C22semidirect
188. #1803C22semidirect
189. #1802C22semidirect
190. #1802C22semidirect
194. #1771C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
200. #1736C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#448742
#426562
#321862
#319732
#318612
#317392
#316622
#315042
#314792
#309962
#290992
#289982
#285642
#277592
#275412
#272712
#267772
#264212
#262222
#255142
#253282
#250842
#245382
#245162
#244482
#236322
#231422
#229112
#224232
#218712