Finite Group Databasebeta

← #7610399

Subgroups — #7610399

Order 512.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45188C211yesmaximal, characteristic, complemented
2#44875C211yesmaximal, characteristic, complemented
3#32230C211yesmaximal, characteristic, complemented
4#31847C211yesmaximal, characteristic, complemented
5#31645C211yesmaximal, characteristic, complemented
6#31350C211yesmaximal, characteristic, complemented
7#29093C211yesmaximal, characteristic, complemented
8#28975C211yesmaximal, characteristic, complemented
9#28882C211yesmaximal, characteristic, complemented
10#27821C211yesmaximal, characteristic, complemented
11#27721C211yesmaximal, characteristic, complemented
12#27711C211yesmaximal, characteristic, complemented
13#27619C211yesmaximal, characteristic, complemented
14#27568C211yesmaximal, characteristic, complemented
15#27452C211yesmaximal, characteristic, complemented
16#26976C211yesmaximal, characteristic, complemented
17#26741C211yesmaximal, characteristic, complemented
18#26673C211yesmaximal, characteristic, complemented
19#26411C211yesmaximal, characteristic, complemented
20#26201C211yesmaximal, characteristic, complemented
21#25120C211yesmaximal, characteristic, complemented
22#24530C211yesmaximal, characteristic, complemented
23#23960C211yesmaximal, characteristic
24#23945C211yesmaximal, characteristic, complemented
25#23126C211yesmaximal, characteristic, complemented
26#22868C211yesmaximal, characteristic, complemented
27#22774C211yesmaximal, characteristic, complemented
28#22495C211yesmaximal, characteristic, complemented
29#21568C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#21091C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2786—21no—
43#2751—21no—
44#2736—21no—
45#2724—21no—
46#2717—21no—
47#2698—21no—
48#2684—21no—
49#2680—21no—
50#2563C2211yescharacteristic
51#2557—21no—
52#2553—21no—
53#2551C2211yescharacteristic, complemented
54#2534—21no—
55#2513C2211yescharacteristic
56#2512C2211yescharacteristic
57#2504C2211yescharacteristic
58#2502C2211yescharacteristic
59#2491C2211yescharacteristic
60#2480—21no—
61#2467—21no—
62#2451C2211yescharacteristic, complemented
63#2447C2211yescharacteristic, complemented
64#2440—21no—
65#2440C2211yescharacteristic, complemented
66#2439C2211yescharacteristic
67#2432—21no—
68#2427C2211yescharacteristic, complemented
69#2422C2211yescharacteristic
70#2422C2211yescharacteristic, complemented
71#2415C2211yescharacteristic
72#2408C2211yescharacteristic
73#2406—21no—
74#2395C2211yescharacteristic
75#2363C2211yescharacteristic
76#2361C2211yescharacteristic
77#2360C2211yescharacteristic, complemented
78#2357C2211yescharacteristic
79#2352C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82#2317C2211yescharacteristic
83#2314C2211yescharacteristic
84#2309C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2075C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2035C2211yescharacteristic, complemented
105#2033C2211yescharacteristic
106#2024C2211yescharacteristic, complemented
107#2023C2211yescharacteristic
108#2023C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic, complemented
112#2012C2211yescharacteristic
113#2012C2211yescharacteristic
114#2000C2211yescharacteristic
115#1999C2211yescharacteristic
116#1999C2211yescharacteristic
117#1993C2211yescharacteristic, complemented
118#1993C2211yescharacteristic, complemented
119#1990C2211yescharacteristic, complemented
120#1990C2211yescharacteristic, complemented
121#1987C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, 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#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic, complemented
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic, complemented
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1850C2211yescharacteristic
179#1836C2211yescharacteristic, complemented
180#1824C2211yescharacteristic
181#1824C2211yescharacteristic, complemented
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic, complemented
184#1818C2211yescharacteristic
185#1804C2211yescharacteristic, complemented
186#1804C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
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
202C2×#340C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#547—24no—
213#547—42no—
214#542—24no—
215#542—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4—21no—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256#465—24no—
257#450—42no—
258#447—24no—
259#442—24no—
260#435—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268#418—24no—
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299#405—42no—
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400D411yescharacteristic
308#399D411yescharacteristic
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398D411yescharacteristic
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397D411yescharacteristic
326#397D411yescharacteristic
327#397D411yescharacteristic
328#396—21no—
329#396—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394D411yescharacteristic
341#394D411yescharacteristic
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#392—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
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#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#385—21no—
402#385—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#385—21no—
412#385—21no—
413#384—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433#379—21no—
434#379—21no—
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⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
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—
491C2×#41—44no—
492C2×#41—82no—
493C2×#41—82no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—82no—
559#126—44no—
560#126—82no—
561#124—22no—
562#124—41no—
563#124—44no—
564#124—82no—
565#123—44no—
566#123—44no—
567#123—44no—
568#123—82no—
569#123—82no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—41no—
576C22⋊Q8—82no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121#4114yes—
585#120—82no—
586C4×Q8—22no—
587C4×Q8—41no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—82no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—41no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
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⋊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—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—82no—
637C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
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—21no—
693C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
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—41no—
717#107—41no—
718#106—22no—
719#106—22no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
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#4114yescomplemented
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752#97—22no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
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#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809#41—816no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—24no—
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—21no—
843C2×D4—21no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—41no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4C2×#4112yes—
864C2×D4C2×#4112yes—
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—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
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×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
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×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C2×#4112yes—
925C22×C4H(5,𝔽2)12yes—
926C22×C4C2511yescharacteristic
927SD16—82no—
928SD16—82no—
929D8—44no—
930D8—82no—
931M16—44no—
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—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—44no—
956C2×C8—82no—
957C2×C8C2×#4112yes—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
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—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
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⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4C2×#4112yes—
1011C4⋊C4C2×#4112yes—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
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—
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—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
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—41no—
1108C23—41no—
1109C23—84no—
1110C23—84no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23#54612yes—
1117C23#57612yes—
1118C23C23×D411yescharacteristic
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—84no—
1124Q8—162no—
1125Q8—162no—
1126D4—22no—
1127D4—22no—
1128D4—22no—
1129D4—22no—
1130D4—44no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—84no—
1143D4—162no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
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—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
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—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—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—84no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4#54612yes—
1234C2×C4#57712yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4#58511yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—168no—
1285C22C2×#54611yescharacteristic
1286C22D4×#4111yescharacteristic
1287C22#350011yescharacteristic
1288C22C2×#57611yescharacteristic
1289C22C2×#57711yescharacteristic
1290C22#358511yescharacteristic
1291C22#358611yescharacteristic
1292C4—22no—
1293C4—22no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4#347511yescharacteristic
1318C4#351311yescharacteristic
1319C4#352111yescharacteristic
1320C4#353311yescharacteristic
1321C2—42no—
1322C2—42no—
1323C2—82no—
1324C2—82no—
1325C2—161no—
1326C2#5980511yescharacteristic
1327C2#6118311yescharacteristic
1328C2#6120911yescharacteristic
1329C2#6149811yescharacteristic
1330C2#6151011yescharacteristic
1331C2#6260211yescharacteristic
1332C2#6260511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23960C2
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. #45188C2semidirect
2. #44875C2semidirect
3. #32230C2semidirect
4. #31847C2semidirect
5. #31645C2semidirect
6. #31350C2semidirect
7. #29093C2semidirect
8. #28975C2semidirect
9. #28882C2semidirect
10. #27821C2semidirect
11. #27721C2semidirect
12. #27711C2semidirect
13. #27619C2semidirect
14. #27568C2semidirect
15. #27452C2semidirect
16. #26976C2semidirect
17. #26741C2semidirect
18. #26673C2semidirect
19. #26411C2semidirect
20. #26201C2semidirect
21. #25120C2semidirect
22. #24530C2semidirect
24. #23945C2semidirect
25. #23126C2semidirect
26. #22868C2semidirect
27. #22774C2semidirect
28. #22495C2semidirect
29. #21568C2semidirect
30. #21412C2semidirect
31. #21091C2semidirect
53. #2551C22semidirect
62. #2451C22semidirect
63. #2447C22semidirect
65. #2440C22semidirect
68. #2427C22semidirect
70. #2422C22semidirect
77. #2360C22semidirect
80. D4×C4⋊C4C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2086C22semidirect
92. #2084C22semidirect
93. #2083C22semidirect
94. #2075C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
99. #2067C22semidirect
104. #2035C22semidirect
106. #2024C22semidirect
111. #2023C22semidirect
117. #1993C22semidirect
118. #1993C22semidirect
119. #1990C22semidirect
120. #1990C22semidirect
121. #1987C22semidirect
122. #1987C22semidirect
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. #1874C22semidirect
172. #1872C22semidirect
174. #1864C22semidirect
179. #1836C22semidirect
181. #1824C22semidirect
183. #1823C22semidirect
185. #1804C22semidirect
186. #1804C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1763C22semidirect
192. #1762C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
196. C4×#102C22semidirect
198. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
202. C2×#340C22semidirect
746. #102#41semidirect

Maximal subgroups

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

subgroupindex
#451882
#448752
#322302
#318472
#316452
#313502
#290932
#289752
#288822
#278212
#277212
#277112
#276192
#275682
#274522
#269762
#267412
#266732
#264112
#262012
#251202
#245302
#239602
#239452
#231262
#228682
#227742
#224952
#215682
#214122
#210912