Finite Group Databasebeta

← #7610421

Subgroups — #7610421

Order 512.

1569 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45096C211yesmaximal, characteristic, complemented
2#44901C211yesmaximal, characteristic, complemented
3#32231C211yesmaximal, characteristic, complemented
4#31846C211yesmaximal, characteristic, complemented
5#31646C211yesmaximal, characteristic, complemented
6#31357C211yesmaximal, characteristic, complemented
7#29094C211yesmaximal, characteristic, complemented
8#28976C211yesmaximal, characteristic, complemented
9#28882C211yesmaximal, characteristic, complemented
10#27819C211yesmaximal, characteristic, complemented
11#27723C211yesmaximal, characteristic, complemented
12#27712C211yesmaximal, characteristic, complemented
13#27619C211yesmaximal, characteristic, complemented
14#27574C211yesmaximal, characteristic, complemented
15#27440C211yesmaximal, characteristic, complemented
16#26976C211yesmaximal, characteristic, complemented
17#26751C211yesmaximal, characteristic, complemented
18#26685C211yesmaximal, characteristic, complemented
19#26423C211yesmaximal, characteristic, complemented
20#26207C211yesmaximal, characteristic, complemented
21#25120C211yesmaximal, characteristic, complemented
22#24527C211yesmaximal, characteristic, complemented
23#23963C211yesmaximal, characteristic
24#23945C211yesmaximal, characteristic, complemented
25#23131C211yesmaximal, characteristic, complemented
26#22868C211yesmaximal, characteristic, complemented
27#22780C211yesmaximal, characteristic, complemented
28#22498C211yesmaximal, characteristic, complemented
29#21568C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#21091C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2797—21no—
43#2735—21no—
44#2718—21no—
45#2705—21no—
46#2701—21no—
47#2698—21no—
48#2686—21no—
49#2685—21no—
50#2601—21no—
51#2595—21no—
52#2566C2211yescharacteristic
53#2550C2211yescharacteristic, complemented
54#2512C2211yescharacteristic
55#2512C2211yescharacteristic
56#2503C2211yescharacteristic
57#2500C2211yescharacteristic
58#2496—21no—
59#2490C2211yescharacteristic
60#2488—21no—
61#2480—21no—
62#2453C2211yescharacteristic, complemented
63#2447—21no—
64#2447C2211yescharacteristic, complemented
65#2441C2211yescharacteristic
66#2439C2211yescharacteristic, complemented
67#2427C2211yescharacteristic, complemented
68#2422C2211yescharacteristic
69#2420C2211yescharacteristic, complemented
70#2419—21no—
71#2415C2211yescharacteristic
72#2411—21no—
73#2408C2211yescharacteristic
74#2395C2211yescharacteristic
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2362C2211yescharacteristic, complemented
78#2354C2211yescharacteristic
79#2354C2211yescharacteristic
80#2349C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82#2317C2211yescharacteristic
83#2314C2211yescharacteristic
84#2309C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2076C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2035C2211yescharacteristic, complemented
105#2033C2211yescharacteristic
106#2026C2211yescharacteristic, complemented
107#2025C2211yescharacteristic
108#2025C2211yescharacteristic
109#2025C2211yescharacteristic, complemented
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#2012C2211yescharacteristic
113#2012C2211yescharacteristic
114#2000C2211yescharacteristic
115#1999C2211yescharacteristic
116#1999C2211yescharacteristic
117#1993C2211yescharacteristic, complemented
118#1992C2211yescharacteristic, complemented
119#1991C2211yescharacteristic, complemented
120#1990C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1989C2211yescharacteristic, complemented
123#1973C2211yescharacteristic
124#1970C2211yescharacteristic
125#1959C2211yescharacteristic, complemented
126#1958C2211yescharacteristic, complemented
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic, complemented
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1894C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic, complemented
156#1892C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic, complemented
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1850C2211yescharacteristic
179#1836C2211yescharacteristic, complemented
180#1825C2211yescharacteristic, complemented
181#1825C2211yescharacteristic, complemented
182#1824C2211yescharacteristic
183#1823C2211yescharacteristic
184#1818C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1762C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—24no—
212#553—42no—
213#542—24no—
214#542—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252#465—24no—
253#450—42no—
254#447—24no—
255#442—24no—
256#435—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264#418—24no—
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102—42no—
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295#405—42no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400D411yescharacteristic
307#399—21no—
308#399D411yescharacteristic
309#398—21no—
310#398—21no—
311#398D411yescharacteristic
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397D411yescharacteristic
322#397D411yescharacteristic
323#397D411yescharacteristic
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#395—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394D411yescharacteristic
340#394D411yescharacteristic
341#393—21no—
342#392—21no—
343#391—21no—
344#391—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
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#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384—21no—
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431#379—21no—
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C2×#95—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2×D411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—41no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—22no—
546C4⋊Q8—41no—
547#126—44no—
548#126—44no—
549#126—82no—
550#126—82no—
551#125—22no—
552#125—41no—
553#125—41no—
554#125—41no—
555#124—22no—
556#124—41no—
557#124—44no—
558#123—44no—
559#123—44no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—44no—
565C22⋊Q8—41no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—41no—
570#121—41no—
571#121—44no—
572#121—41no—
573#121—41no—
574#121#4114yes—
575#120—82no—
576C4×Q8—22no—
577C4×Q8—41no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—44no—
591#117—22no—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—41no—
596#117—41no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—82no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
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⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
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—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—82no—
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—41no—
711#107—41no—
712#106—22no—
713#106—22no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717#103—22no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102#4114yes—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746#97—22no—
747#97—41no—
748#97—41no—
749#97—41no—
750C4×C8—41no—
751C4×C8—41no—
752C4×C8—41no—
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#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
791C24—21no—
792C24—21no—
793C24—21no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24C22×D411yescharacteristic
802C24C22×D411yescharacteristic
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—42no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—82no—
839C2×D4—82no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4C2×#4112yes—
851C2×D4C2×#4112yes—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×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×C4C22×D411yescharacteristic
905C22×C4C2×#4112yes—
906C22×C4H(5,𝔽2)12yes—
907C22×C4C2511yescharacteristic
908SD16—82no—
909SD16—82no—
910D8—44no—
911D8—82no—
912M16—44no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—44no—
937C2×C8—82no—
938C2×C8C2×#4112yes—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
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—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
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⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4C2×#4112yes—
992C4⋊C4C2×#4112yes—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
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—
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—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—21no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
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—84no—
1096C23—84no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23—162no—
1101C23—162no—
1102C23#54612yes—
1103C23C23×D411yescharacteristic
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—162no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—84no—
1122D4—82no—
1123D4—84no—
1124D4—162no—
1125D4—162no—
1126D4—162no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
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—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
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—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
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—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—84no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4#54612yes—
1216C2×C4C22×#4111yescharacteristic
1217C2×C4C22×#4111yescharacteristic
1218C2×C4C2×H(5,𝔽2)11yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C2×C4#58511yescharacteristic
1222C8—22no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—41no—
1242C22—42no—
1243C22—42no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—168no—
1266C22C2×#54611yescharacteristic
1267C22D4×#4111yescharacteristic
1268C22#350011yescharacteristic
1269C22#358411yescharacteristic
1270C22#358411yescharacteristic
1271C22#358511yescharacteristic
1272C22#358511yescharacteristic
1273C4—22no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4#347511yescharacteristic
1299C4#351311yescharacteristic
1300C4#352111yescharacteristic
1301C4#353311yescharacteristic
1302C2—42no—
1303C2—81no—
1304C2—82no—
1305C2—82no—
1306C2—161no—
1307C2#5980511yescharacteristic
1308C2#6118711yescharacteristic
1309C2#6120811yescharacteristic
1310C2#6150111yescharacteristic
1311C2#6150411yescharacteristic
1312C2#6260711yescharacteristic
1313C2#6260711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23963C2
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
1. #45096C2semidirect
2. #44901C2semidirect
3. #32231C2semidirect
4. #31846C2semidirect
5. #31646C2semidirect
6. #31357C2semidirect
7. #29094C2semidirect
8. #28976C2semidirect
9. #28882C2semidirect
10. #27819C2semidirect
11. #27723C2semidirect
12. #27712C2semidirect
13. #27619C2semidirect
14. #27574C2semidirect
15. #27440C2semidirect
16. #26976C2semidirect
17. #26751C2semidirect
18. #26685C2semidirect
19. #26423C2semidirect
20. #26207C2semidirect
21. #25120C2semidirect
22. #24527C2semidirect
24. #23945C2semidirect
25. #23131C2semidirect
26. #22868C2semidirect
27. #22780C2semidirect
28. #22498C2semidirect
29. #21568C2semidirect
30. #21412C2semidirect
31. #21091C2semidirect
53. #2550C22semidirect
62. #2453C22semidirect
64. #2447C22semidirect
66. #2439C22semidirect
67. #2427C22semidirect
69. #2420C22semidirect
77. #2362C22semidirect
80. #2349C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2087C22semidirect
92. #2084C22semidirect
93. #2083C22semidirect
94. #2076C22semidirect
97. #2072C22semidirect
98. #2072C22semidirect
99. #2067C22semidirect
104. #2035C22semidirect
106. #2026C22semidirect
109. #2025C22semidirect
117. #1993C22semidirect
118. #1992C22semidirect
119. #1991C22semidirect
120. #1990C22semidirect
121. #1989C22semidirect
122. #1989C22semidirect
125. #1959C22semidirect
126. #1958C22semidirect
133. #1935C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
141. #1924C22semidirect
142. #1923C22semidirect
143. #1921C22semidirect
144. #1920C22semidirect
145. #1920C22semidirect
146. #1919C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
155. #1893C22semidirect
170. #1875C22semidirect
172. #1873C22semidirect
174. #1864C22semidirect
179. #1836C22semidirect
180. #1825C22semidirect
181. #1825C22semidirect
187. #1802C22semidirect
188. #1802C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1763C22semidirect
192. #1762C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
196. C4×#102C22semidirect
198. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#450962
#449012
#322312
#318462
#316462
#313572
#290942
#289762
#288822
#278192
#277232
#277122
#276192
#275742
#274402
#269762
#267512
#266852
#264232
#262072
#251202
#245272
#239632
#239452
#231312
#228682
#227802
#224982
#215682
#214122
#210912