Finite Group Databasebeta

← #7101095

Subgroups — #7101095

Order 512.

1551 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59765C211yesmaximal, characteristic, complemented
2#40056C211yesmaximal, characteristic, complemented
3#32616C211yesmaximal, characteristic, complemented
4#32558C211yesmaximal, characteristic, complemented
5#32298C211yesmaximal, characteristic, complemented
6#31794C211yesmaximal, characteristic, complemented
7#31607C211yesmaximal, characteristic, complemented
8#31506C211yesmaximal, characteristic, complemented
9#31063C211yesmaximal, characteristic
10#30996C211yesmaximal, characteristic, complemented
11#29451C211yesmaximal, characteristic, complemented
12#29445C211yesmaximal, characteristic, complemented
13#29065C211yesmaximal, characteristic, complemented
14#28277C211yesmaximal, characteristic, complemented
15#28104C211yesmaximal, characteristic, complemented
16#27048C211yesmaximal, characteristic, complemented
17#27033C211yesmaximal, characteristic, complemented
18#26678C211yesmaximal, characteristic, complemented
19#25298C211yesmaximal, characteristic, complemented
20#25178C211yesmaximal, characteristic, complemented
21#25167C211yesmaximal, characteristic, complemented
22#25121C211yesmaximal, characteristic, complemented
23#25088C211yesmaximal, characteristic, complemented
24#25041C211yesmaximal, characteristic, complemented
25#24913C211yesmaximal, characteristic, complemented
26#24547C211yesmaximal, characteristic, complemented
27#23686C211yesmaximal, characteristic, complemented
28#23207C211yesmaximal, characteristic, complemented
29#22866C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#22156C211yesmaximal, characteristic, complemented
32C2×#465C2211yescharacteristic
33C2×#464C2211yescharacteristic
34C2×#463C2211yescharacteristic
35C2×#452C2211yescharacteristic, complemented
36C2×#449C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#446C2211yescharacteristic, complemented
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#417C2211yescharacteristic, complemented
46C22×#102C2211yescharacteristic
47#2860C2211yescharacteristic
48#2796—21no—
49#2781—21no—
50#2778—21no—
51#2746—21no—
52#2735—21no—
53#2684—21no—
54#2653—21no—
55#2603—21no—
56#2592C2211yescharacteristic
57#2582C2211yescharacteristic, complemented
58#2580C2211yescharacteristic
59#2580C2211yescharacteristic, complemented
60#2557—21no—
61#2527—21no—
62#2505—21no—
63#2504C2211yescharacteristic
64#2496C2211yescharacteristic, complemented
65#2494C2211yescharacteristic
66#2494C2211yescharacteristic, complemented
67#2487C2211yescharacteristic
68#2480—21no—
69#2479—21no—
70#2467—21no—
71#2435C2211yescharacteristic
72#2427C2211yescharacteristic
73#2426C2211yescharacteristic
74#2422C2211yescharacteristic
75#2421C2211yescharacteristic
76#2421C2211yescharacteristic
77#2417C2211yescharacteristic
78#2408C2211yescharacteristic
79#2407C2211yescharacteristic
80#2361C2211yescharacteristic
81#2361C2211yescharacteristic
82#2360C2211yescharacteristic
83#2359—21no—
84#2341C2211yescharacteristic, complemented
85#2339C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2321—21no—
88C4×#124C2211yescharacteristic
89C4×#124C2211yescharacteristic
90#2295C2211yescharacteristic, complemented
91#2293C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2073C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2015C2211yescharacteristic
130#2012C2211yescharacteristic
131#2001C2211yescharacteristic
132#1985C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1971C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1958C2211yescharacteristic
141#1955C2211yescharacteristic
142#1949C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic, complemented
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic, complemented
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1872C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1853C2211yescharacteristic, complemented
184#1853C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic, complemented
191#1808C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1786C2211yescharacteristic
196#1767C2211yescharacteristic, complemented
197#1767C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1752C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#124D411yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241#465—42no—
242#464—24no—
243#463—42no—
244#452—42no—
245#450—24no—
246#449—24no—
247#449—42no—
248#447—42no—
249#446—42no—
250#442—42no—
251#440—42no—
252#440—42no—
253#435—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#417—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102—42no—
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×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#401—21no—
313#401—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#392—21no—
347#392—21no—
348#391—21no—
349#391D411yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390D411yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388D411yescharacteristic
397#388D411yescharacteristic
398#388D411yescharacteristic
399#388D411yescharacteristic
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#382D411yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376—21no—
463C2×#95—21no—
464C43C2311yescharacteristic
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#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
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×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16#4114yes—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559#126—82no—
560#126—82no—
561#124—22no—
562#124—41no—
563#124—41no—
564#124—41no—
565#124—42no—
566#123—44no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573#121—22no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#120—44no—
580C4×Q8—22no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—22no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—82no—
599C4×D4—82no—
600#117—82no—
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⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
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—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—22no—
755#97—41no—
756#97—41no—
757#97—41no—
758#97—41no—
759C4×C8—41no—
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#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—21no—
806C24—42no—
807C24—42no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24C22×D411yescharacteristic
814C24C22×D411yescharacteristic
815#41—44no—
816#41—82no—
817#41—82no—
818#41—82no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—41no—
831C2×Q8—41no—
832C2×Q8—41no—
833C2×Q8C2×#4112yes—
834C2×D4—22no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—44no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—82no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4C2×#4112yes—
873C2×D4H(5,𝔽2)12yes—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
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×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
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×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C2511yescharacteristic
933Q16—82no—
934SD16—44no—
935SD16—44no—
936SD16—82no—
937D8—44no—
938D8—82no—
939M16—82no—
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—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—82no—
963C2×C8C2×#4112yes—
964C2×C8H(5,𝔽2)12yes—
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—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
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—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
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—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—84no—
1114C23—84no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23#57512yes—
1121C23C23×D411yescharacteristic
1122Q8—22no—
1123Q8—22no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—82no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—82no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
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—21no—
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—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—22no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—42no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
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—
1289C22D4×#4111yescharacteristic
1290C22#348811yescharacteristic
1291C22#349611yescharacteristic
1292C22C2×#57511yescharacteristic
1293C22#358511yescharacteristic
1294C22#358511yescharacteristic
1295C22#358611yescharacteristic
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4#350511yescharacteristic
1322C4#351311yescharacteristic
1323C4#353411yescharacteristic
1324C4#356811yescharacteristic
1325C2—42no—
1326C2—81no—
1327C2—82no—
1328C2—82no—
1329C2—161no—
1330C2#4439811yescharacteristic
1331C2#6145611yescharacteristic
1332C2#6151811yescharacteristic
1333C2#6197111yescharacteristic
1334C2#6208911yescharacteristic
1335C2#6229711yescharacteristic
1336C2#6233411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31063C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59765C2semidirect
2. #40056C2semidirect
3. #32616C2semidirect
4. #32558C2semidirect
5. #32298C2semidirect
6. #31794C2semidirect
7. #31607C2semidirect
8. #31506C2semidirect
10. #30996C2semidirect
11. #29451C2semidirect
12. #29445C2semidirect
13. #29065C2semidirect
14. #28277C2semidirect
15. #28104C2semidirect
16. #27048C2semidirect
17. #27033C2semidirect
18. #26678C2semidirect
19. #25298C2semidirect
20. #25178C2semidirect
21. #25167C2semidirect
22. #25121C2semidirect
23. #25088C2semidirect
24. #25041C2semidirect
25. #24913C2semidirect
26. #24547C2semidirect
27. #23686C2semidirect
28. #23207C2semidirect
29. #22866C2semidirect
30. #22854C2semidirect
31. #22156C2semidirect
35. C2×#452C22semidirect
40. C2×#446C22semidirect
43. C2×#440C22semidirect
45. C2×#417C22semidirect
57. #2582C22semidirect
59. #2580C22semidirect
64. #2496C22semidirect
66. #2494C22semidirect
84. #2341C22semidirect
85. #2339C22semidirect
90. #2295C22semidirect
91. #2293C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
95. #2088C22semidirect
96. #2086C22semidirect
97. #2085C22semidirect
100. #2073C22semidirect
101. #2073C22semidirect
102. #2072C22semidirect
103. #2068C22semidirect
106. #2067C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
113. #2055C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
132. #1985C22semidirect
136. #1973C22semidirect
138. #1971C22semidirect
142. #1949C22semidirect
143. #1949C22semidirect
144. #1944C22semidirect
145. #1943C22semidirect
146. #1942C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
154. #1927C22semidirect
158. #1924C22semidirect
159. #1924C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
166. #1894C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
182. #1862C22semidirect
183. #1853C22semidirect
184. #1853C22semidirect
186. #1851C22semidirect
188. #1847C22semidirect
190. #1823C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
196. #1767C22semidirect
197. #1767C22semidirect
198. #1763C22semidirect
200. C4×#102C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#597652
#400562
#326162
#325582
#322982
#317942
#316072
#315062
#310632
#309962
#294512
#294452
#290652
#282772
#281042
#270482
#270332
#266782
#252982
#251782
#251672
#251212
#250882
#250412
#249132
#245472
#236862
#232072
#228662
#228542
#221562