Finite Group Databasebeta

← #6549956

Subgroups — #6549956

Order 512.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37858C211yesmaximal, characteristic, complemented
2#34391C211yesmaximal, characteristic, complemented
3#30181C211yesmaximal, characteristic, complemented
4#30023C211yesmaximal, characteristic, complemented
5#29896C211yesmaximal, characteristic, complemented
6#29491C211yesmaximal, characteristic, complemented
7#29418C211yesmaximal, characteristic, complemented
8#27639C211yesmaximal, characteristic, complemented
9#27527C211yesmaximal, characteristic, complemented
10#27526C211yesmaximal, characteristic, complemented
11#27479C211yesmaximal, characteristic, complemented
12#27478C211yesmaximal, characteristic, complemented
13#27335C211yesmaximal, characteristic, complemented
14#27246C211yesmaximal, characteristic, complemented
15#27166C211yesmaximal, characteristic, complemented
16#26415C211yesmaximal, characteristic, complemented
17#26341C211yesmaximal, characteristic, complemented
18#25209C211yesmaximal, characteristic, complemented
19#25203C211yesmaximal, characteristic, complemented
20#24912C211yesmaximal, characteristic, complemented
21#24712C211yesmaximal, characteristic, complemented
22#24382C211yesmaximal, characteristic
23#24008C211yesmaximal, characteristic, complemented
24#23771C211yesmaximal, characteristic, complemented
25#23714C211yesmaximal, characteristic, complemented
26#23638C211yesmaximal, characteristic, complemented
27#23130C211yesmaximal, characteristic, complemented
28#23033C211yesmaximal, characteristic, complemented
29#22933C211yesmaximal, characteristic, complemented
30#22919C211yesmaximal, characteristic, complemented
31#22558C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#474C2211yescharacteristic, complemented
36C2×#466C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#440C2211yescharacteristic, complemented
40C2×#433C2211yescharacteristic
41C2×#427C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43#2847C2211yescharacteristic
44#2743—21no—
45#2737—21no—
46#2685—21no—
47#2684—21no—
48#2628C2211yescharacteristic
49#2624C2211yescharacteristic
50#2578—21no—
51#2572—21no—
52#2521—21no—
53#2516—21no—
54#2500C2211yescharacteristic
55#2496C2211yescharacteristic
56#2495C2211yescharacteristic
57#2491C2211yescharacteristic
58#2439C2211yescharacteristic
59#2420C2211yescharacteristic
60#2375—21no—
61#2375—21no—
62#2363C2211yescharacteristic
63#2363C2211yescharacteristic
64#2363C2211yescharacteristic
65#2362C2211yescharacteristic
66#2362C2211yescharacteristic
67#2357—21no—
68#2353—21no—
69#2347C2211yescharacteristic
70#2347C2211yescharacteristic
71#2346C2211yescharacteristic
72#2341C2211yescharacteristic
73#2339C2211yescharacteristic
74#2335—21no—
75#2335—21no—
76#2324C2211yescharacteristic
77#2324C2211yescharacteristic
78#2324C2211yescharacteristic
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2319—21no—
82#2318—21no—
83#2314C2211yescharacteristic
84#2280C2211yescharacteristic
85#2280C2211yescharacteristic
86#2280C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2074C2211yescharacteristic, complemented
106#2071C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2024C2211yescharacteristic, complemented
125#2000C2211yescharacteristic
126#1999C2211yescharacteristic
127#1987C2211yescharacteristic, complemented
128#1973C2211yescharacteristic, complemented
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1923C2211yescharacteristic
149#1921C2211yescharacteristic, complemented
150#1921C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1893C2211yescharacteristic
158#1892C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1879C2211yescharacteristic, complemented
161#1879C2211yescharacteristic, complemented
162#1879C2211yescharacteristic, complemented
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1875C2211yescharacteristic
167#1873C2211yescharacteristic
168#1865C2211yescharacteristic, complemented
169#1865C2211yescharacteristic, complemented
170#1864C2211yescharacteristic, complemented
171#1864C2211yescharacteristic, complemented
172#1864C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1818C2211yescharacteristic
182#1805C2211yescharacteristic, complemented
183#1804C2211yescharacteristic, complemented
184#1803C2211yescharacteristic, complemented
185#1798C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1779C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1750C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#124—21no—
212#525—24no—
213#525—24no—
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238#485—24no—
239#482—24no—
240#474—42no—
241#466—24no—
242#465—24no—
243#449—42no—
244#440—42no—
245#433—42no—
246#427—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
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×C22⋊C8—42no—
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#399—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#395—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#391—21no—
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#390—21no—
324#390—21no—
325#390—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
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#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—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#386—21no—
382#386—21no—
383#386—21no—
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#385—21no—
394#385—21no—
395#385—21no—
396#384C2311yescharacteristic
397#383—21no—
398#383—21no—
399#383—21no—
400#382—21no—
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#381—21no—
406#381—21no—
407#381D411yescharacteristic
408#381D411yescharacteristic
409#380—21no—
410#380D411yescharacteristic
411#380D411yescharacteristic
412#380D411yescharacteristic
413#380D411yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#379—21no—
426#379—21no—
427#379D411yescharacteristic
428#379D411yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#376—21no—
453C2×#95—21no—
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#126—82no—
546#124—82no—
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8#4114yes—
552#121—22no—
553#121—22no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121#4114yes—
562#120—28no—
563#120—82no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689#107—22no—
690#107—22no—
691#107—22no—
692#107—22no—
693#107—22no—
694#107—41no—
695#107—41no—
696#106—22no—
697#106—22no—
698#106—22no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—22no—
738#97—41no—
739C4×C8—41no—
740C4×C8—41no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
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#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24—22no—
786C24—21no—
787C24—41no—
788C24—41no—
789C24—41no—
790C24—41no—
791C24—41no—
792C24—41no—
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C24C22×D411yescharacteristic
796#41—82no—
797#41—82no—
798#41—82no—
799#41—82no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8C2×#4112yes—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—21no—
813C2×D4—21no—
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—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4C2×#4112yes—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—24no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
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—22no—
861C22×C4—22no—
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—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—82no—
880C22×C4—82no—
881C22×C4—82no—
882C22×C4—82no—
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×C4—81no—
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×C4C2×#4112yes—
907C22×C4C2511yescharacteristic
908SD16—44no—
909D8—82no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
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—44no—
934C2×C8—82no—
935C2×C8H(5,𝔽2)12yes—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
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—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4C2×#4112yes—
981C4⋊C4C2×#4112yes—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
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—
1030C42—24no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—42no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—44no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—82no—
1088C23—82no—
1089C23—82no—
1090C23—82no—
1091C23—82no—
1092C23—82no—
1093C23#52512yes—
1094C23C23×D411yescharacteristic
1095Q8—22no—
1096Q8—22no—
1097Q8—41no—
1098Q8—41no—
1099Q8—162no—
1100D4—22no—
1101D4—22no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—84no—
1109D4—84no—
1110D4—84no—
1111D4—162no—
1112D4—162no—
1113D4—162no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
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—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—82no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—84no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4#52512yes—
1208C2×C4C22×#4111yescharacteristic
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—42no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—42no—
1246C22—88no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#52511yescharacteristic
1259C22#348511yescharacteristic
1260C22#349611yescharacteristic
1261C22#358411yescharacteristic
1262C22#358411yescharacteristic
1263C22#358411yescharacteristic
1264C22#358511yescharacteristic
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—42no—
1275C4—42no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#351311yescharacteristic
1291C4#351411yescharacteristic
1292C4#352111yescharacteristic
1293C4#352111yescharacteristic
1294C2—42no—
1295C2—81no—
1296C2—81no—
1297C2—82no—
1298C2—161no—
1299C2#3579211yescharacteristic
1300C2#6055711yescharacteristic
1301C2#6058011yescharacteristic
1302C2#6176111yescharacteristic
1303C2#6176911yescharacteristic
1304C2#6228211yescharacteristic
1305C2#6231811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24382C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37858C2semidirect
2. #34391C2semidirect
3. #30181C2semidirect
4. #30023C2semidirect
5. #29896C2semidirect
6. #29491C2semidirect
7. #29418C2semidirect
8. #27639C2semidirect
9. #27527C2semidirect
10. #27526C2semidirect
11. #27479C2semidirect
12. #27478C2semidirect
13. #27335C2semidirect
14. #27246C2semidirect
15. #27166C2semidirect
16. #26415C2semidirect
17. #26341C2semidirect
18. #25209C2semidirect
19. #25203C2semidirect
20. #24912C2semidirect
21. #24712C2semidirect
23. #24008C2semidirect
24. #23771C2semidirect
25. #23714C2semidirect
26. #23638C2semidirect
27. #23130C2semidirect
28. #23033C2semidirect
29. #22933C2semidirect
30. #22919C2semidirect
31. #22558C2semidirect
35. C2×#474C22semidirect
39. C2×#440C22semidirect
87. #2101C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2084C22semidirect
105. #2074C22semidirect
106. #2071C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2058C22semidirect
112. #2055C22semidirect
113. #2054C22semidirect
124. #2024C22semidirect
127. #1987C22semidirect
128. #1973C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
133. #1944C22semidirect
134. #1942C22semidirect
135. #1936C22semidirect
136. #1934C22semidirect
137. #1934C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
140. #1927C22semidirect
141. #1926C22semidirect
142. #1926C22semidirect
143. #1926C22semidirect
144. #1925C22semidirect
149. #1921C22semidirect
150. #1921C22semidirect
151. #1920C22semidirect
152. #1919C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
159. #1880C22semidirect
160. #1879C22semidirect
161. #1879C22semidirect
162. #1879C22semidirect
168. #1865C22semidirect
169. #1865C22semidirect
170. #1864C22semidirect
171. #1864C22semidirect
172. #1864C22semidirect
173. #1863C22semidirect
182. #1805C22semidirect
183. #1804C22semidirect
184. #1803C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. C4×#106C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
195. C4×#102C22semidirect
196. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#378582
#343912
#301812
#300232
#298962
#294912
#294182
#276392
#275272
#275262
#274792
#274782
#273352
#272462
#271662
#264152
#263412
#252092
#252032
#249122
#247122
#243822
#240082
#237712
#237142
#236382
#231302
#230332
#229332
#229192
#225582