Finite Group Databasebeta

← #6509056

Subgroups — #6509056

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35613C211yesmaximal, characteristic, complemented
2#34471C211yesmaximal, characteristic
3#29547C211yesmaximal, characteristic, complemented
4#29413C211yesmaximal, characteristic, complemented
5#29404C211yesmaximal, characteristic, complemented
6#29377C211yesmaximal, characteristic, complemented
7#28214C211yesmaximal, characteristic, complemented
8#28123C211yesmaximal, characteristic, complemented
9#27624C211yesmaximal, characteristic, complemented
10#27585C211yesmaximal, characteristic, complemented
11#27518C211yesmaximal, characteristic, complemented
12#27516C211yesmaximal, characteristic, complemented
13#27369C211yesmaximal, characteristic, complemented
14#27238C211yesmaximal, characteristic, complemented
15#27111C211yesmaximal, characteristic, complemented
16#27064C211yesmaximal, characteristic, complemented
17#26785C211yesmaximal, characteristic, complemented
18#26771C211yesmaximal, characteristic, complemented
19#26345C211yesmaximal, characteristic, complemented
20#26129C211yesmaximal, characteristic, complemented
21#25976C211yesmaximal, characteristic, complemented
22#25223C211yesmaximal, characteristic, complemented
23#24950C211yesmaximal, characteristic, complemented
24#24530C211yesmaximal, characteristic, complemented
25#24448C211yesmaximal, characteristic
26#24032C211yesmaximal, characteristic
27#22200C211yesmaximal, characteristic, complemented
28#22052C211yesmaximal, characteristic, complemented
29#22006C211yesmaximal, characteristic, complemented
30#21586C211yesmaximal, characteristic, complemented
31#21065C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#484C2211yescharacteristic, complemented
34C2×#480C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#427C2211yescharacteristic, complemented
41C2×#418C2211yescharacteristic
42C22×#102C2211yescharacteristic
43#2590—21no—
44#2577—21no—
45#2575—21no—
46#2553—21no—
47#2515—21no—
48#2511C2211yescharacteristic, complemented
49#2508—21no—
50#2507C2211yescharacteristic, complemented
51#2502C2211yescharacteristic, complemented
52#2496C2211yescharacteristic, complemented
53#2489C2211yescharacteristic, complemented
54#2486C2211yescharacteristic
55#2478—21no—
56#2470—21no—
57#2441C2211yescharacteristic, complemented
58#2415C2211yescharacteristic
59#2377—21no—
60#2375—21no—
61#2366C2211yescharacteristic
62#2363C2211yescharacteristic
63#2361C2211yescharacteristic
64#2358—21no—
65#2357C2211yescharacteristic
66#2352C2211yescharacteristic
67D4×C22⋊C4—21no—
68D4×C22⋊C4C2211yescharacteristic
69D4×C22⋊C4C2211yescharacteristic
70#2333—21no—
71#2330C2211yescharacteristic, complemented
72#2328C2211yescharacteristic
73#2324C2211yescharacteristic
74#2323C2211yescharacteristic, complemented
75#2321—21no—
76#2321—21no—
77#2320C2211yescharacteristic, complemented
78#2319C2211yescharacteristic
79#2309C2211yescharacteristic
80#2308—21no—
81C4×C22⋊Q8C2211yescharacteristic, complemented
82C4×#121C2211yescharacteristic
83C2×#390C2211yescharacteristic
84#2290C2211yescharacteristic
85#2285C2211yescharacteristic, complemented
86#2274C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2097C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2075C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic, complemented
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2035C2211yescharacteristic, complemented
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2014C2211yescharacteristic
118#2000C2211yescharacteristic
119#1973C2211yescharacteristic
120#1968C2211yescharacteristic, complemented
121#1947C2211yescharacteristic, complemented
122#1947C2211yescharacteristic, complemented
123#1936C2211yescharacteristic, complemented
124#1934C2211yescharacteristic
125#1928C2211yescharacteristic, complemented
126#1927C2211yescharacteristic, complemented
127#1927C2211yescharacteristic, complemented
128#1926C2211yescharacteristic
129#1926C2211yescharacteristic
130#1926C2211yescharacteristic
131#1926C2211yescharacteristic, complemented
132#1926C2211yescharacteristic, complemented
133#1926C2211yescharacteristic, complemented
134#1926C2211yescharacteristic, complemented
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic, complemented
138#1925C2211yescharacteristic, complemented
139#1925C2211yescharacteristic, complemented
140#1925C2211yescharacteristic, complemented
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1918C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1916C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1892C2211yescharacteristic, complemented
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic, complemented
157#1880C2211yescharacteristic, complemented
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1877C2211yescharacteristic, complemented
162#1877C2211yescharacteristic, complemented
163#1875C2211yescharacteristic
164#1873C2211yescharacteristic, complemented
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1864C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1853C2211yescharacteristic, complemented
178#1853C2211yescharacteristic, complemented
179#1851C2211yescharacteristic, complemented
180#1850C2211yescharacteristic, complemented
181#1840C2211yescharacteristic, complemented
182#1832C2211yescharacteristic, complemented
183#1824C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1817C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1802C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1797C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×#107C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1750C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211D42—24no—
212D42—24no—
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C42C2311yescharacteristic
245#484—42no—
246#480—24no—
247#478—42no—
248#478—42no—
249#468—24no—
250#450—24no—
251#450—42no—
252#427—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#418—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102—24no—
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#394—21no—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388D411yescharacteristic
369#388D411yescharacteristic
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387D411yescharacteristic
383#387D411yescharacteristic
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386D411yescharacteristic
400#386D411yescharacteristic
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385D411yescharacteristic
407#385D411yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#382—21no—
413#382—21no—
414#382—21no—
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#379—21no—
428#379—21no—
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—28no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—82no—
512C22×D4—82no—
513C22×D4C2×D411yescharacteristic
514C22×D4#4114yes—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552#127—22no—
553#127—22no—
554#126—82no—
555#125—22no—
556#125—41no—
557#123—82no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562#121—28no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121#4114yes—
567#120—28no—
568#120—28no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—82no—
584C4×D4—82no—
585C4×D4—82no—
586#117—22no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—82no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—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—82no—
669C2×C22⋊C4—82no—
670C2×C22⋊C4—82no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—22no—
701#107—22no—
702#107—22no—
703#107—22no—
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713C4⋊C8—41no—
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#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749#97—41no—
750C4×C8—41no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—24no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—24no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—41no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—82no—
857C2×D4—82no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—816no—
863C2×D4C2×#4112yes—
864C2×D4C2×#4112yes—
865C2×D4C2×#4112yes—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—24no—
874C22×C4—22no—
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—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
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×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
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×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2×#4112yes—
929C22×C4C2×#4112yes—
930C22×C4C2511yescharacteristic
931SD16—82no—
932SD16—82no—
933SD16—82no—
934M16—82no—
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—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—44no—
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—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4C2×#4112yes—
1009C4⋊C4H(5,𝔽2)12yes—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—41no—
1062C42—41no—
1063C42—42no—
1064C42—42no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—48no—
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—84no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23#52512yes—
1122C23#57612yes—
1123C23C23×D411yescharacteristic
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—44no—
1135D4—48no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—44no—
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—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—84no—
1230C2×C4—82no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#52512yes—
1238C2×C4#57712yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—168no—
1289C22—168no—
1290C22C2×#52511yescharacteristic
1291C22#348511yescharacteristic
1292C22#348811yescharacteristic
1293C22C2×#57611yescharacteristic
1294C22C2×#57711yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#349111yescharacteristic
1323C4#350511yescharacteristic
1324C4#351411yescharacteristic
1325C4#352111yescharacteristic
1326C2—42no—
1327C2—42no—
1328C2—82no—
1329C2—82no—
1330C2—82no—
1331C2#3544911yescharacteristic
1332C2#6057811yescharacteristic
1333C2#6059111yescharacteristic
1334C2#6176611yescharacteristic
1335C2#6178011yescharacteristic
1336C2#6202211yescharacteristic
1337C2#6203311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35613C2semidirect
3. #29547C2semidirect
4. #29413C2semidirect
5. #29404C2semidirect
6. #29377C2semidirect
7. #28214C2semidirect
8. #28123C2semidirect
9. #27624C2semidirect
10. #27585C2semidirect
11. #27518C2semidirect
12. #27516C2semidirect
13. #27369C2semidirect
14. #27238C2semidirect
15. #27111C2semidirect
16. #27064C2semidirect
17. #26785C2semidirect
18. #26771C2semidirect
19. #26345C2semidirect
20. #26129C2semidirect
21. #25976C2semidirect
22. #25223C2semidirect
23. #24950C2semidirect
24. #24530C2semidirect
27. #22200C2semidirect
28. #22052C2semidirect
29. #22006C2semidirect
30. #21586C2semidirect
31. #21065C2semidirect
33. C2×#484C22semidirect
35. C2×#478C22semidirect
36. C2×#478C22semidirect
40. C2×#427C22semidirect
48. #2511C22semidirect
50. #2507C22semidirect
51. #2502C22semidirect
52. #2496C22semidirect
53. #2489C22semidirect
57. #2441C22semidirect
71. #2330C22semidirect
74. #2323C22semidirect
77. #2320C22semidirect
81. C4×C22⋊Q8C22semidirect
85. #2285C22semidirect
86. #2274C22semidirect
87. #2101C22semidirect
88. #2097C22semidirect
90. #2094C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2083C22semidirect
95. #2075C22semidirect
96. #2075C22semidirect
97. #2075C22semidirect
100. #2071C22semidirect
101. #2068C22semidirect
104. #2067C22semidirect
105. #2059C22semidirect
108. #2055C22semidirect
112. #2035C22semidirect
120. #1968C22semidirect
121. #1947C22semidirect
122. #1947C22semidirect
123. #1936C22semidirect
125. #1928C22semidirect
126. #1927C22semidirect
127. #1927C22semidirect
131. #1926C22semidirect
132. #1926C22semidirect
133. #1926C22semidirect
134. #1926C22semidirect
137. #1925C22semidirect
138. #1925C22semidirect
139. #1925C22semidirect
140. #1925C22semidirect
141. #1924C22semidirect
142. #1923C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1920C22semidirect
148. #1919C22semidirect
149. #1918C22semidirect
150. #1918C22semidirect
151. #1917C22semidirect
152. #1916C22semidirect
154. #1892C22semidirect
156. #1880C22semidirect
157. #1880C22semidirect
159. #1877C22semidirect
160. #1877C22semidirect
161. #1877C22semidirect
162. #1877C22semidirect
164. #1873C22semidirect
167. #1864C22semidirect
168. #1863C22semidirect
172. #1862C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
177. #1853C22semidirect
178. #1853C22semidirect
179. #1851C22semidirect
180. #1850C22semidirect
181. #1840C22semidirect
182. #1832C22semidirect
183. #1824C22semidirect
184. #1824C22semidirect
185. #1817C22semidirect
186. #1809C22semidirect
187. #1802C22semidirect
188. #1802C22semidirect
189. #1802C22semidirect
190. #1802C22semidirect
191. #1797C22semidirect
196. #1776C22semidirect
197. C4×#107C22semidirect
198. #1762C22semidirect
199. C4×#102C22semidirect
200. #1750C22semidirect
201. #1736C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#356132
#344712
#295472
#294132
#294042
#293772
#282142
#281232
#276242
#275852
#275182
#275162
#273692
#272382
#271112
#270642
#267852
#267712
#263452
#261292
#259762
#252232
#249502
#245302
#244482
#240322
#222002
#220522
#220062
#215862
#210652