Finite Group Databasebeta

← #6743133

Subgroups — #6743133

Order 512.

1626 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#39784C211yesmaximal, characteristic, complemented
2#36528C211yesmaximal, characteristic
3#32956C211yesmaximal, characteristic, complemented
4#31806C211yesmaximal, characteristic, complemented
5#31294C211yesmaximal, characteristic, complemented
6#31276C211yesmaximal, characteristic
7#31044C211yesmaximal, characteristic
8#30974C211yesmaximal, characteristic, complemented
9#30930C211yesmaximal, characteristic, complemented
10#30640C211yesmaximal, characteristic, complemented
11#30531C211yesmaximal, characteristic, complemented
12#30367C211yesmaximal, characteristic, complemented
13#30021C211yesmaximal, characteristic, complemented
14#27455C211yesmaximal, characteristic, complemented
15#27415C211yesmaximal, characteristic, complemented
16#27327C211yesmaximal, characteristic, complemented
17#27092C211yesmaximal, characteristic, complemented
18#27026C211yesmaximal, characteristic, complemented
19#26986C211yesmaximal, characteristic, complemented
20#26914C211yesmaximal, characteristic, complemented
21#26786C211yesmaximal, characteristic, complemented
22#26570C211yesmaximal, characteristic, complemented
23#26499C211yesmaximal, characteristic, complemented
24#26469C211yesmaximal, characteristic, complemented
25#26438C211yesmaximal, characteristic, complemented
26#25712C211yesmaximal, characteristic, complemented
27#25561C211yesmaximal, characteristic, complemented
28#23225C211yesmaximal, characteristic, complemented
29#22944C211yesmaximal, characteristic, complemented
30#22363C211yesmaximal, characteristic, complemented
31#21453C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#488C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#479C2211yescharacteristic, complemented
39C2×#476C2211yescharacteristic
40C2×#476C2211yescharacteristic
41C2×#470C2211yescharacteristic, complemented
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic
45#2857C2211yescharacteristic
46#2855C2211yescharacteristic
47#2848—21no—
48#2779—21no—
49#2770—21no—
50#2758—21no—
51#2754—21no—
52#2663—21no—
53#2562C2211yescharacteristic
54#2561—21no—
55#2550C2211yescharacteristic, complemented
56#2534—21no—
57#2525—21no—
58#2511C2211yescharacteristic, complemented
59#2509—21no—
60#2495C2211yescharacteristic
61#2492C2211yescharacteristic, complemented
62#2489C2211yescharacteristic
63#2463—21no—
64#2463—21no—
65#2460—21no—
66#2460—21no—
67#2453C2211yescharacteristic, complemented
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic
70#2441C2211yescharacteristic, complemented
71#2435C2211yescharacteristic
72#2427C2211yescharacteristic
73#2427C2211yescharacteristic
74#2421C2211yescharacteristic, complemented
75#2415C2211yescharacteristic
76#2408C2211yescharacteristic
77#2370C2211yescharacteristic, complemented
78#2367C2211yescharacteristic
79#2367C2211yescharacteristic
80#2361C2211yescharacteristic
81#2361C2211yescharacteristic
82#2347C2211yescharacteristic, complemented
83#2345C2211yescharacteristic
84#2332—21no—
85C4×C22⋊Q8C2211yescharacteristic
86C4×#123C2211yescharacteristic
87C4×#120—21no—
88#2100C2211yescharacteristic, complemented
89#2095C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic, complemented
103#2058C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1989C2211yescharacteristic, complemented
129#1988C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1973C2211yescharacteristic
133#1968C2211yescharacteristic
134#1958C2211yescharacteristic
135#1955C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1939C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1875C2211yescharacteristic
171#1873C2211yescharacteristic, complemented
172#1872C2211yescharacteristic
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic, complemented
187#1851C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1797C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#554—42no—
210#554—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123D411yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—42no—
239C2×C4×D4—42no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#501—42no—
251#488—24no—
252#483—42no—
253#482—24no—
254#479—42no—
255#476—42no—
256#476—42no—
257#470—42no—
258#450—24no—
259#440—42no—
260#440—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#398—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#396—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387D411yescharacteristic
408#387D411yescharacteristic
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#383—21no—
426#382—21no—
427#382C2311yescharacteristic
428#381—21no—
429#381D411yescharacteristic
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
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
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#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—44no—
517C23×C4—82no—
518C23×C4—82no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—22no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#125—22no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—44no—
552#124—22no—
553#124—22no—
554#124—41no—
555#124—41no—
556#123—42no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—82no—
569C22⋊Q8—82no—
570#121—22no—
571#121—22no—
572#121—41no—
573#121—41no—
574#120—44no—
575C4×Q8—22no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—82no—
593C4×D4—82no—
594#117—22no—
595#117—41no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
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⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
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—44no—
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—22no—
700#107—22no—
701#107—22no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102#4114yes—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750#97—41no—
751#97—41no—
752#97—41no—
753C4×C8—22no—
754C4×C8—41no—
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#95—21no—
789#95—21no—
790#95—21no—
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—42no—
825C2×Q8—42no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4C2×#4112yes—
857C2×D42−1+412yes—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—24no—
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—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—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—816no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2511yescharacteristic
922Q16—82no—
923SD16—44no—
924SD16—44no—
925M16—82no—
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—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C2×#4112yes—
950C4⋊C4—24no—
951C4⋊C4—22no—
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—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
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—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C2×#4112yes—
1003C4⋊C4H(5,𝔽2)12yes—
1004C4⋊C4H(5,𝔽2)12yes—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
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—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—41no—
1053C42—41no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—48no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—84no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—84no—
1097C23#57512yes—
1098C23C23×D411yescharacteristic
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—162no—
1108Q8—162no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—44no—
1114D4—48no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120D4—84no—
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—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
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—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—44no—
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—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—82no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—162no—
1214C2×C4#57712yes—
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4C2×H(5,𝔽2)11yescharacteristic
1218C2×C4C2×2−1+411yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—42no—
1246C22—41no—
1247C22—42no—
1248C22—42no—
1249C22—816no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22D4×#4111yescharacteristic
1259C22#348411yescharacteristic
1260C22#348911yescharacteristic
1261C22C2×#57511yescharacteristic
1262C22C2×#57711yescharacteristic
1263C22#358511yescharacteristic
1264C22#358611yescharacteristic
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—42no—
1276C4—42no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4#346011yescharacteristic
1292C4#352011yescharacteristic
1293C4#354011yescharacteristic
1294C4#354111yescharacteristic
1295C2—42no—
1296C2—81no—
1297C2—82no—
1298C2—82no—
1299C2#3782711yescharacteristic
1300C2#6145611yescharacteristic
1301C2#6154111yescharacteristic
1302C2#6158311yescharacteristic
1303C2#6161011yescharacteristic
1304C2#6212611yescharacteristic
1305C2#6222411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39784C2semidirect
3. #32956C2semidirect
4. #31806C2semidirect
5. #31294C2semidirect
8. #30974C2semidirect
9. #30930C2semidirect
10. #30640C2semidirect
11. #30531C2semidirect
12. #30367C2semidirect
13. #30021C2semidirect
14. #27455C2semidirect
15. #27415C2semidirect
16. #27327C2semidirect
17. #27092C2semidirect
18. #27026C2semidirect
19. #26986C2semidirect
20. #26914C2semidirect
21. #26786C2semidirect
22. #26570C2semidirect
23. #26499C2semidirect
24. #26469C2semidirect
25. #26438C2semidirect
26. #25712C2semidirect
27. #25561C2semidirect
28. #23225C2semidirect
29. #22944C2semidirect
30. #22363C2semidirect
31. #21453C2semidirect
34. C2×#501C22semidirect
37. C2×#483C22semidirect
38. C2×#479C22semidirect
41. C2×#470C22semidirect
55. #2550C22semidirect
58. #2511C22semidirect
61. #2492C22semidirect
67. #2453C22semidirect
70. #2441C22semidirect
74. #2421C22semidirect
77. #2370C22semidirect
82. #2347C22semidirect
88. #2100C22semidirect
89. #2095C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
98. #2066C22semidirect
99. #2066C22semidirect
100. #2066C22semidirect
102. #2059C22semidirect
103. #2058C22semidirect
104. #2058C22semidirect
105. #2056C22semidirect
111. #2036C22semidirect
115. #2035C22semidirect
121. #2024C22semidirect
122. #2024C22semidirect
128. #1989C22semidirect
129. #1988C22semidirect
136. #1949C22semidirect
137. #1943C22semidirect
138. #1943C22semidirect
139. #1942C22semidirect
140. #1939C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
153. #1924C22semidirect
156. #1923C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
171. #1873C22semidirect
174. #1865C22semidirect
179. #1863C22semidirect
184. #1853C22semidirect
186. #1852C22semidirect
187. #1851C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#397842
#365282
#329562
#318062
#312942
#312762
#310442
#309742
#309302
#306402
#305312
#303672
#300212
#274552
#274152
#273272
#270922
#270262
#269862
#269142
#267862
#265702
#264992
#264692
#264382
#257122
#255612
#232252
#229442
#223632
#214532