Finite Group Databasebeta

← #7257537

Subgroups — #7257537

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39960C211yesmaximal, characteristic
2#39902C211yesmaximal, characteristic, complemented
3#32778C211yesmaximal, characteristic, complemented
4#31799C211yesmaximal, characteristic, complemented
5#31785C211yesmaximal, characteristic, complemented
6#31347C211yesmaximal, characteristic, complemented
7#31325C211yesmaximal, characteristic, complemented
8#31308C211yesmaximal, characteristic, complemented
9#31306C211yesmaximal, characteristic, complemented
10#31277C211yesmaximal, characteristic, complemented
11#31266C211yesmaximal, characteristic, complemented
12#31109C211yesmaximal, characteristic, complemented
13#31096C211yesmaximal, characteristic, complemented
14#30830C211yesmaximal, characteristic, complemented
15#30809C211yesmaximal, characteristic, complemented
16#29114C211yesmaximal, characteristic, complemented
17#28860C211yesmaximal, characteristic, complemented
18#28850C211yesmaximal, characteristic, complemented
19#27894C211yesmaximal, characteristic, complemented
20#27584C211yesmaximal, characteristic, complemented
21#27271C211yesmaximal, characteristic, complemented
22#27266C211yesmaximal, characteristic, complemented
23#26713C211yesmaximal, characteristic, complemented
24#26702C211yesmaximal, characteristic, complemented
25#25897C211yesmaximal, characteristic, complemented
26#25889C211yesmaximal, characteristic, complemented
27#24878C211yesmaximal, characteristic, complemented
28#24871C211yesmaximal, characteristic, complemented
29#24050C211yesmaximal, characteristic, complemented
30#24036C211yesmaximal, characteristic, complemented
31#22335C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#474C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C22×#103C2211yescharacteristic, complemented
42#2851C2211yescharacteristic, complemented
43#2850C2211yescharacteristic
44#2767—21no—
45#2742—21no—
46#2723—21no—
47#2691—21no—
48#2688—21no—
49#2686—21no—
50#2684—21no—
51#2668—21no—
52#2663—21no—
53#2650—21no—
54#2602—21no—
55#2563C2211yescharacteristic
56#2562C2211yescharacteristic
57#2562C2211yescharacteristic, complemented
58#2561—21no—
59#2550C2211yescharacteristic, complemented
60#2496C2211yescharacteristic
61#2496C2211yescharacteristic, complemented
62#2487C2211yescharacteristic, complemented
63#2485C2211yescharacteristic
64#2479—21no—
65#2477—21no—
66#2448C2211yescharacteristic
67#2447C2211yescharacteristic
68#2441C2211yescharacteristic
69#2440C2211yescharacteristic, complemented
70#2436C2211yescharacteristic
71#2435C2211yescharacteristic
72#2421C2211yescharacteristic
73#2420C2211yescharacteristic
74#2415C2211yescharacteristic
75#2414C2211yescharacteristic
76#2409C2211yescharacteristic
77#2408C2211yescharacteristic
78#2370C2211yescharacteristic, complemented
79#2352C2211yescharacteristic
80#2334—21no—
81#2321—21no—
82C4×#121C2211yescharacteristic
83#2297C2211yescharacteristic
84#2285C2211yescharacteristic, complemented
85#2097C2211yescharacteristic, complemented
86#2095C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2026C2211yescharacteristic, complemented
128#2026C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2025C2211yescharacteristic
132#2024C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic
137#1955C2211yescharacteristic
138#1954C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1942C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1874C2211yescharacteristic
168#1873C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1825C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1817C2211yescharacteristic, complemented
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic, complemented
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1787C2211yescharacteristic, complemented
193#1787C2211yescharacteristic, complemented
194#1787C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#548—42no—
209#548—42no—
210#546—42no—
211#546—42no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#489—42no—
248#488—42no—
249#485—42no—
250#481—42no—
251#479—42no—
252#474—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#418—42no—
268C2×#103—42no—
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#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×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—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#397—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#392—21no—
354#392—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390D411yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389D411yescharacteristic
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#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#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386D411yescharacteristic
416#386D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432#380D411yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#126—44no—
549#126—82no—
550#125—41no—
551#125—41no—
552#125—41no—
553#125—41no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—41no—
560#124—44no—
561#123—44no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—82no—
570#121—22no—
571#121—42no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—44no—
576#121—44no—
577#121—41no—
578#121—41no—
579#120—44no—
580#120—44no—
581C4×Q8—22no—
582C4×Q8—41no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—44no—
592#117—41no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—82no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊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—44no—
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×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#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—41no—
743#102—41no—
744#102—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—41no—
756#97—41no—
757#97—41no—
758C4×C8—41no—
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#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
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813#41—82no—
814#41—82no—
815#41—82no—
816#41—82no—
817C2×Q8—21no—
818C2×Q8—21no—
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—42no—
829C2×Q8—44no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—82no—
836C2×Q8—82no—
837C2×Q8—82no—
838C2×Q8H(5,𝔽2)12yes—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
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—21no—
852C2×D4—21no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4H(5,𝔽2)12yes—
879C22×C4—21no—
880C22×C4—24no—
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—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
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×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2511yescharacteristic
941M16—82no—
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—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—82no—
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—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
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—42no—
1006C4⋊C4—42no—
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—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
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—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—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—41no—
1072C42—41no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
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—41no—
1114C23—84no—
1115C23—84no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23#57512yes—
1122C23C23×D411yescharacteristic
1123Q8—22no—
1124Q8—22no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—84no—
1132Q8—162no—
1133D4—22no—
1134D4—22no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—82no—
1142D4—82no—
1143D4—84no—
1144D4—82no—
1145D4—84no—
1146D4—84no—
1147D4—162no—
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—22no—
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—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—44no—
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—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—84no—
1238C2×C4—82no—
1239C2×C4—84no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4#58511yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—42no—
1278C22—41no—
1279C22—41no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—168no—
1292C22#348411yescharacteristic
1293C22#348511yescharacteristic
1294C22#350011yescharacteristic
1295C22C2×#57511yescharacteristic
1296C22#358411yescharacteristic
1297C22#358511yescharacteristic
1298C22#358611yescharacteristic
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—41no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#353311yescharacteristic
1325C4#353311yescharacteristic
1326C4#354511yescharacteristic
1327C4#354511yescharacteristic
1328C2—42no—
1329C2—81no—
1330C2—81no—
1331C2—82no—
1332C2—161no—
1333C2#4681411yescharacteristic
1334C2#6158011yescharacteristic
1335C2#6169011yescharacteristic
1336C2#6174111yescharacteristic
1337C2#6177511yescharacteristic
1338C2#6258411yescharacteristic
1339C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39960C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39902C2semidirect
3. #32778C2semidirect
4. #31799C2semidirect
5. #31785C2semidirect
6. #31347C2semidirect
7. #31325C2semidirect
8. #31308C2semidirect
9. #31306C2semidirect
10. #31277C2semidirect
11. #31266C2semidirect
12. #31109C2semidirect
13. #31096C2semidirect
14. #30830C2semidirect
15. #30809C2semidirect
16. #29114C2semidirect
17. #28860C2semidirect
18. #28850C2semidirect
19. #27894C2semidirect
20. #27584C2semidirect
21. #27271C2semidirect
22. #27266C2semidirect
23. #26713C2semidirect
24. #26702C2semidirect
25. #25897C2semidirect
26. #25889C2semidirect
27. #24878C2semidirect
28. #24871C2semidirect
29. #24050C2semidirect
30. #24036C2semidirect
31. #22335C2semidirect
38. C2×#479C22semidirect
41. C22×#103C22semidirect
42. #2851C22semidirect
57. #2562C22semidirect
59. #2550C22semidirect
61. #2496C22semidirect
62. #2487C22semidirect
69. #2440C22semidirect
78. #2370C22semidirect
84. #2285C22semidirect
85. #2097C22semidirect
86. #2095C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
94. #2077C22semidirect
96. #2076C22semidirect
97. #2074C22semidirect
99. #2072C22semidirect
101. #2068C22semidirect
103. #2059C22semidirect
104. #2058C22semidirect
113. #2036C22semidirect
116. #2035C22semidirect
117. #2035C22semidirect
118. #2035C22semidirect
127. #2026C22semidirect
128. #2026C22semidirect
132. #2024C22semidirect
138. #1954C22semidirect
139. #1944C22semidirect
140. #1942C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
158. #1924C22semidirect
159. #1919C22semidirect
160. #1918C22semidirect
161. #1917C22semidirect
162. #1916C22semidirect
172. #1869C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
180. #1852C22semidirect
181. #1847C22semidirect
182. #1836C22semidirect
183. #1825C22semidirect
184. #1825C22semidirect
185. #1817C22semidirect
187. #1807C22semidirect
192. #1787C22semidirect
193. #1787C22semidirect
194. #1787C22semidirect
199. C4×#103C22semidirect
201. #1752C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#399602
#399022
#327782
#317992
#317852
#313472
#313252
#313082
#313062
#312772
#312662
#311092
#310962
#308302
#308092
#291142
#288602
#288502
#278942
#275842
#272712
#272662
#267132
#267022
#258972
#258892
#248782
#248712
#240502
#240362
#223352