Finite Group Databasebeta

← #7505481

Subgroups — #7505481

Order 512.

1618 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34917C211yesmaximal, characteristic, complemented
2#34720C211yesmaximal, characteristic, complemented
3#31660C211yesmaximal, characteristic, complemented
4#31616C211yesmaximal, characteristic, complemented
5#31596C211yesmaximal, characteristic, complemented
6#31559C211yesmaximal, characteristic, complemented
7#31542C211yesmaximal, characteristic, complemented
8#31498C211yesmaximal, characteristic, complemented
9#31478C211yesmaximal, characteristic, complemented
10#31447C211yesmaximal, characteristic, complemented
11#31387C211yesmaximal, characteristic, complemented
12#31379C211yesmaximal, characteristic, complemented
13#31319C211yesmaximal, characteristic, complemented
14#31311C211yesmaximal, characteristic, complemented
15#31264C211yesmaximal, characteristic, complemented
16#31003C211yesmaximal, characteristic, complemented
17#30595C211yesmaximal, characteristic, complemented
18#30398C211yesmaximal, characteristic
19#23826C211yesmaximal, characteristic, complemented
20#23785C211yesmaximal, characteristic, complemented
21#23764C211yesmaximal, characteristic, complemented
22#23762C211yesmaximal, characteristic, complemented
23#23711C211yesmaximal, characteristic, complemented
24#23574C211yesmaximal, characteristic, complemented
25#21526C211yesmaximal, characteristic, complemented
26#21507C211yesmaximal, characteristic, complemented
27#21456C211yesmaximal, characteristic, complemented
28#21407C211yesmaximal, characteristic, complemented
29#21121C211yesmaximal, characteristic, complemented
30#21107C211yesmaximal, characteristic, complemented
31#20743C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#466C2211yescharacteristic
35C2×#463C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#432C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2578—21no—
43#2576—21no—
44#2570C2211yescharacteristic
45#2566C2211yescharacteristic
46#2562C2211yescharacteristic
47#2535C2211yescharacteristic
48#2515—21no—
49#2497C2211yescharacteristic
50#2494C2211yescharacteristic
51#2477—21no—
52#2475—21no—
53#2463—21no—
54#2460—21no—
55#2457—21no—
56#2452C2211yescharacteristic
57#2446C2211yescharacteristic
58#2439C2211yescharacteristic
59#2432C2211yescharacteristic
60#2427C2211yescharacteristic
61#2422C2211yescharacteristic
62#2421C2211yescharacteristic
63#2420C2211yescharacteristic
64#2415C2211yescharacteristic
65#2407C2211yescharacteristic
66#2401—21no—
67#2398—21no—
68#2392—21no—
69#2392—21no—
70C4×#125C2211yescharacteristic
71C4×#124C2211yescharacteristic
72C4×C22⋊Q8—21no—
73C4×C22⋊Q8C2211yescharacteristic
74C4×#123—21no—
75C4×#121C2211yescharacteristic
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78#2295C2211yescharacteristic
79#2290—21no—
80#2290—21no—
81#2285C2211yescharacteristic
82#2283C2211yescharacteristic
83C42×D4C2211yescharacteristic
84C42×D4C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2097C2211yescharacteristic
91#2095C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2074C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2059C2211yescharacteristic
112#2057C2211yescharacteristic
113#2055C2211yescharacteristic
114#2043C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2026C2211yescharacteristic
126#2026C2211yescharacteristic
127#2025C2211yescharacteristic
128#2023C2211yescharacteristic
129#2013C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1993C2211yescharacteristic
134#1993C2211yescharacteristic
135#1983C2211yescharacteristic
136#1972C2211yescharacteristic
137#1960C2211yescharacteristic
138#1960C2211yescharacteristic
139#1949C2211yescharacteristic
140#1943C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1928C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1921C2211yescharacteristic
150#1918C2211yescharacteristic
151#1917C2211yescharacteristic
152#1917C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1880C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1875C2211yescharacteristic
166#1869C2211yescharacteristic
167#1869C2211yescharacteristic
168#1865C2211yescharacteristic
169#1864C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1854C2211yescharacteristic
173#1850C2211yescharacteristic
174#1850C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1807C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic
180#1803C2211yescharacteristic
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1788C2211yescharacteristic
184#1788C2211yescharacteristic
185#1788C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1767C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic
202#1745C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#533—24no—
210#533—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C4×#41—24no—
226C4×#41—42no—
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4D411yescharacteristic
237C2×C4×D4D411yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C22×C42—21no—
249C22×C42—21no—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#466—24no—
253#463—24no—
254#449—24no—
255#442—42no—
256#440—24no—
257#440—42no—
258#432—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
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×#97—42no—
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311#401—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#398—21no—
318#398—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#392—21no—
342#392—21no—
343#391—21no—
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#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#387—21no—
383#387—21no—
384#387—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#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4D411yescharacteristic
446C4×C22⋊C4D411yescharacteristic
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452#376—21no—
453C43C2311yescharacteristic
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
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8#4114yes—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#125—41no—
546#125—41no—
547#125—44no—
548#124—22no—
549#124—41no—
550#123—44no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—41no—
563#121—41no—
564#121—41no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—44no—
570C4×Q8—41no—
571C4×Q8#4114yes—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—44no—
585C4×D4—42no—
586C4×D4—42no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—82no—
591#117—22no—
592#117—44no—
593#117—44no—
594#117—41no—
595#117—82no—
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—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
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×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⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
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×C42—21no—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—22no—
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—44no—
685C2×C42—82no—
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—22no—
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708C4⋊C8—22no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744#97—22no—
745#97—22no—
746#97—22no—
747#97—22no—
748#97—41no—
749#97—41no—
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#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798#41—44no—
799#41—44no—
800#41—44no—
801#41—44no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×Q8—81no—
816C2×Q8C2×#4112yes—
817C2×D4—22no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4C2×#4112yes—
843C2×D4C2×#4112yes—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
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—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—42no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
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—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2511yescharacteristic
913SD16—44no—
914SD16—44no—
915D8—44no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—44no—
940C2×C8—44no—
941C2×C8C2×#4112yes—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4C2×#4112yes—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C42—22no—
1029C42—22no—
1030C42—22no—
1031C42—22no—
1032C42—24no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—41no—
1042C42—41no—
1043C42—41no—
1044C42—41no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42C2×#4112yes—
1055C42H(5,𝔽2)12yes—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—22no—
1067C23—22no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23#57512yes—
1084C23C23×D411yescharacteristic
1085Q8—22no—
1086Q8—22no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—41no—
1093Q8—84no—
1094D4—22no—
1095D4—22no—
1096D4—22no—
1097D4—22no—
1098D4—44no—
1099D4—48no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—84no—
1105D4—84no—
1106D4—84no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
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—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—48no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
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—82no—
1194C2×C4—82no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4#54612yes—
1201C2×C4#54612yes—
1202C2×C4#57512yes—
1203C2×C4C22×#4111yescharacteristic
1204C2×C4C22×#4111yescharacteristic
1205C2×C4C2×H(5,𝔽2)11yescharacteristic
1206C2×C4#58511yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C8—22no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—42no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—42no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—41no—
1234C22—42no—
1235C22—41no—
1236C22—41no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22#344911yescharacteristic
1246C22C2×#54611yescharacteristic
1247C22D4×#4111yescharacteristic
1248C22C2×#57511yescharacteristic
1249C22C2×#57511yescharacteristic
1250C22#358511yescharacteristic
1251C22#358611yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—42no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4#345511yescharacteristic
1279C4#345911yescharacteristic
1280C4#347511yescharacteristic
1281C4#352911yescharacteristic
1282C2—42no—
1283C2—81no—
1284C2—82no—
1285C2—82no—
1286C2#5211711yescharacteristic
1287C2#6096111yescharacteristic
1288C2#6097311yescharacteristic
1289C2#6115811yescharacteristic
1290C2#6116411yescharacteristic
1291C2#6145411yescharacteristic
1292C2#6146111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30398C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34917C2semidirect
2. #34720C2semidirect
3. #31660C2semidirect
4. #31616C2semidirect
5. #31596C2semidirect
6. #31559C2semidirect
7. #31542C2semidirect
8. #31498C2semidirect
9. #31478C2semidirect
10. #31447C2semidirect
11. #31387C2semidirect
12. #31379C2semidirect
13. #31319C2semidirect
14. #31311C2semidirect
15. #31264C2semidirect
16. #31003C2semidirect
17. #30595C2semidirect
19. #23826C2semidirect
20. #23785C2semidirect
21. #23764C2semidirect
22. #23762C2semidirect
23. #23711C2semidirect
24. #23574C2semidirect
25. #21526C2semidirect
26. #21507C2semidirect
27. #21456C2semidirect
28. #21407C2semidirect
29. #21121C2semidirect
30. #21107C2semidirect
31. #20743C2semidirect

Maximal subgroups

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

subgroupindex
#349172
#347202
#316602
#316162
#315962
#315592
#315422
#314982
#314782
#314472
#313872
#313792
#313192
#313112
#312642
#310032
#305952
#303982
#238262
#237852
#237642
#237622
#237112
#235742
#215262
#215072
#214562
#214072
#211212
#211072
#207432