Finite Group Databasebeta

← #7205982

Subgroups — #7205982

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45626C211yesmaximal, characteristic, complemented
2#36162C211yesmaximal, characteristic
3#32959C211yesmaximal, characteristic, complemented
4#32905C211yesmaximal, characteristic, complemented
5#32748C211yesmaximal, characteristic, complemented
6#32725C211yesmaximal, characteristic, complemented
7#31843C211yesmaximal, characteristic, complemented
8#31531C211yesmaximal, characteristic, complemented
9#31462C211yesmaximal, characteristic, complemented
10#31251C211yesmaximal, characteristic, complemented
11#31157C211yesmaximal, characteristic, complemented
12#31024C211yesmaximal, characteristic
13#30996C211yesmaximal, characteristic, complemented
14#30927C211yesmaximal, characteristic, complemented
15#30858C211yesmaximal, characteristic, complemented
16#30655C211yesmaximal, characteristic, complemented
17#30543C211yesmaximal, characteristic, complemented
18#30424C211yesmaximal, characteristic
19#27328C211yesmaximal, characteristic, complemented
20#27176C211yesmaximal, characteristic, complemented
21#26956C211yesmaximal, characteristic, complemented
22#26892C211yesmaximal, characteristic, complemented
23#26796C211yesmaximal, characteristic, complemented
24#26599C211yesmaximal, characteristic, complemented
25#26537C211yesmaximal, characteristic, complemented
26#26427C211yesmaximal, characteristic, complemented
27#25562C211yesmaximal, characteristic, complemented
28#25337C211yesmaximal, characteristic, complemented
29#25225C211yesmaximal, characteristic, complemented
30#24127C211yesmaximal, characteristic, complemented
31#23320C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#470C2211yescharacteristic, complemented
41C2×#468C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#461C2211yescharacteristic
44C2×#461C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic, complemented
48#2857C2211yescharacteristic
49#2855C2211yescharacteristic
50#2851C2211yescharacteristic
51#2849—21no—
52#2839—21no—
53#2788—21no—
54#2755—21no—
55#2750—21no—
56#2744—21no—
57#2739—21no—
58#2687—21no—
59#2570C2211yescharacteristic, complemented
60#2568C2211yescharacteristic, complemented
61#2536C2211yescharacteristic
62#2503C2211yescharacteristic, complemented
63#2492C2211yescharacteristic
64#2489C2211yescharacteristic, complemented
65#2482—21no—
66#2467—21no—
67#2467—21no—
68#2460—21no—
69#2460—21no—
70#2454C2211yescharacteristic
71#2454C2211yescharacteristic
72#2453C2211yescharacteristic, complemented
73#2446C2211yescharacteristic, complemented
74#2440C2211yescharacteristic, complemented
75#2435C2211yescharacteristic
76#2429C2211yescharacteristic, complemented
77#2427C2211yescharacteristic
78#2427C2211yescharacteristic
79#2421C2211yescharacteristic
80#2417C2211yescharacteristic
81#2411—21no—
82#2408C2211yescharacteristic
83#2378—21no—
84#2367C2211yescharacteristic
85#2367C2211yescharacteristic
86#2363C2211yescharacteristic
87#2363C2211yescharacteristic
88#2344C2211yescharacteristic
89C4×#123C2211yescharacteristic
90#2280—21no—
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2075C2211yescharacteristic
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2058C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2056C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2043C2211yescharacteristic, complemented
119#2042C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic, complemented
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2034C2211yescharacteristic
126#2026C2211yescharacteristic, complemented
127#2026C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2016C2211yescharacteristic, complemented
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic, complemented
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1991C2211yescharacteristic, complemented
140#1987C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1973C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1958C2211yescharacteristic
146#1954C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1943C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1939C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic, complemented
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1895C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1874C2211yescharacteristic
175#1873C2211yescharacteristic, complemented
176#1872C2211yescharacteristic
177#1872C2211yescharacteristic
178#1872C2211yescharacteristic, complemented
179#1870C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic, complemented
190#1851C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1797C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200C4×#106C2211yescharacteristic, complemented
201#1763C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#552—42no—
213#552—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123D411yescharacteristic
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—42no—
240C2×C4×D4—42no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#489—42no—
254#485—42no—
255#481—42no—
256#479—42no—
257#478—42no—
258#478—42no—
259#470—42no—
260#468—42no—
261#464—42no—
262#461—42no—
263#461—42no—
264#450—42no—
265#450—42no—
266C4×Q16—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#392—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
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#388—21no—
397#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387D411yescharacteristic
414#387D411yescharacteristic
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386D411yescharacteristic
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#385D411yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#381—21no—
438#381—21no—
439#381D411yescharacteristic
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—44no—
520C23×C4—44no—
521C23×C4—82no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#126—44no—
560#125—22no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—44no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—41no—
569#123—42no—
570#123—44no—
571C22⋊Q8—22no—
572C22⋊Q8—44no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584#121—22no—
585#121—22no—
586#121—41no—
587#121—41no—
588#120—82no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—44no—
606C4×D4—44no—
607#117—22no—
608#117—41no—
609#117—44no—
610#117—82no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
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—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—41no—
705C2×C42—41no—
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—22no—
715#107—41no—
716#107—41no—
717#106—22no—
718#106—22no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765#97—41no—
766C4×C8—41no—
767C4×C8—41no—
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#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—42no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×D4—22no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4H(5,𝔽2)12yes—
874C2×D42−1+412yes—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—22no—
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—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—816no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C2511yescharacteristic
939Q16—44no—
940Q16—82no—
941SD16—82no—
942SD16—82no—
943SD16—82no—
944SD16—82no—
945M16—82no—
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—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C4⋊C4—24no—
971C4⋊C4—22no—
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—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4H(5,𝔽2)12yes—
1024C4⋊C4H(5,𝔽2)12yes—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
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—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—41no—
1073C42—41no—
1074C42—42no—
1075C42—42no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—22no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—48no—
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—84no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23#57712yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—48no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—82no—
1140D4—162no—
1141D4—162no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
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—44no—
1180C2×C4—48no—
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—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—82no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4#57512yes—
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×2−1+411yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—41no—
1260C22—42no—
1261C22—41no—
1262C22—42no—
1263C22—41no—
1264C22—42no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—816no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22#348411yescharacteristic
1280C22#348811yescharacteristic
1281C22#348911yescharacteristic
1282C22C2×#57511yescharacteristic
1283C22C2×#57711yescharacteristic
1284C22#358411yescharacteristic
1285C22#358611yescharacteristic
1286C4—22no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—42no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#352911yescharacteristic
1313C4#353611yescharacteristic
1314C4#354111yescharacteristic
1315C4#354211yescharacteristic
1316C2—42no—
1317C2—81no—
1318C2—82no—
1319C2—82no—
1320C2#4545111yescharacteristic
1321C2#6160111yescharacteristic
1322C2#6161511yescharacteristic
1323C2#6200411yescharacteristic
1324C2#6200811yescharacteristic
1325C2#6211611yescharacteristic
1326C2#6221211yescharacteristic
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. #45626C2semidirect
3. #32959C2semidirect
4. #32905C2semidirect
5. #32748C2semidirect
6. #32725C2semidirect
7. #31843C2semidirect
8. #31531C2semidirect
9. #31462C2semidirect
10. #31251C2semidirect
11. #31157C2semidirect
13. #30996C2semidirect
14. #30927C2semidirect
15. #30858C2semidirect
16. #30655C2semidirect
17. #30543C2semidirect
19. #27328C2semidirect
20. #27176C2semidirect
21. #26956C2semidirect
22. #26892C2semidirect
23. #26796C2semidirect
24. #26599C2semidirect
25. #26537C2semidirect
26. #26427C2semidirect
27. #25562C2semidirect
28. #25337C2semidirect
29. #25225C2semidirect
30. #24127C2semidirect
31. #23320C2semidirect
36. C2×#485C22semidirect
37. C2×#479C22semidirect
40. C2×#470C22semidirect
47. C2×C4×Q16C22semidirect
59. #2570C22semidirect
60. #2568C22semidirect
62. #2503C22semidirect
64. #2489C22semidirect
72. #2453C22semidirect
73. #2446C22semidirect
74. #2440C22semidirect
76. #2429C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
93. #2096C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2085C22semidirect
100. #2074C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
111. #2059C22semidirect
112. #2059C22semidirect
113. #2058C22semidirect
114. #2056C22semidirect
115. #2056C22semidirect
118. #2043C22semidirect
121. #2036C22semidirect
126. #2026C22semidirect
127. #2026C22semidirect
129. #2016C22semidirect
135. #2001C22semidirect
139. #1991C22semidirect
140. #1987C22semidirect
147. #1949C22semidirect
148. #1943C22semidirect
149. #1940C22semidirect
150. #1939C22semidirect
152. #1933C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
158. #1924C22semidirect
160. #1923C22semidirect
161. #1921C22semidirect
162. #1919C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
169. #1878C22semidirect
175. #1873C22semidirect
178. #1872C22semidirect
180. #1865C22semidirect
183. #1863C22semidirect
186. #1854C22semidirect
189. #1851C22semidirect
190. #1851C22semidirect
191. #1805C22semidirect
200. C4×#106C22semidirect
201. #1763C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#456262
#361622
#329592
#329052
#327482
#327252
#318432
#315312
#314622
#312512
#311572
#310242
#309962
#309272
#308582
#306552
#305432
#304242
#273282
#271762
#269562
#268922
#267962
#265992
#265372
#264272
#255622
#253372
#252252
#241272
#233202