Finite Group Databasebeta

← #6771502

Subgroups — #6771502

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38051C211yesmaximal, characteristic, complemented
2#35522C211yesmaximal, characteristic
3#33018C211yesmaximal, characteristic, complemented
4#32663C211yesmaximal, characteristic, complemented
5#32593C211yesmaximal, characteristic, complemented
6#32580C211yesmaximal, characteristic, complemented
7#32556C211yesmaximal, characteristic, complemented
8#32019C211yesmaximal, characteristic, complemented
9#31995C211yesmaximal, characteristic, complemented
10#31393C211yesmaximal, characteristic, complemented
11#30576C211yesmaximal, characteristic, complemented
12#30177C211yesmaximal, characteristic, complemented
13#30016C211yesmaximal, characteristic, complemented
14#29480C211yesmaximal, characteristic, complemented
15#29420C211yesmaximal, characteristic, complemented
16#29236C211yesmaximal, characteristic, complemented
17#29174C211yesmaximal, characteristic, complemented
18#28100C211yesmaximal, characteristic, complemented
19#27870C211yesmaximal, characteristic, complemented
20#27664C211yesmaximal, characteristic, complemented
21#27623C211yesmaximal, characteristic, complemented
22#25247C211yesmaximal, characteristic, complemented
23#25128C211yesmaximal, characteristic, complemented
24#24957C211yesmaximal, characteristic, complemented
25#24869C211yesmaximal, characteristic, complemented
26#24096C211yesmaximal, characteristic, complemented
27#23979C211yesmaximal, characteristic, complemented
28#22475C211yesmaximal, characteristic, complemented
29#22201C211yesmaximal, characteristic, complemented
30#22086C211yesmaximal, characteristic, complemented
31#20879C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#427C2211yescharacteristic
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44#2855C2211yescharacteristic, complemented
45#2718—21no—
46#2717—21no—
47#2689—21no—
48#2686—21no—
49#2628C2211yescharacteristic, complemented
50#2625C2211yescharacteristic
51#2581C2211yescharacteristic, complemented
52#2580C2211yescharacteristic
53#2567C2211yescharacteristic, complemented
54#2538C2211yescharacteristic
55#2537C2211yescharacteristic
56#2535C2211yescharacteristic
57#2521—21no—
58#2496—21no—
59#2485C2211yescharacteristic
60#2485C2211yescharacteristic
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic, complemented
63#2480—21no—
64#2472—21no—
65#2469—21no—
66#2467—21no—
67#2463—21no—
68#2462—21no—
69#2460—21no—
70#2456—21no—
71#2424—21no—
72#2418—21no—
73#2417C2211yescharacteristic
74#2415C2211yescharacteristic, complemented
75#2408C2211yescharacteristic
76#2408C2211yescharacteristic
77#2352C2211yescharacteristic
78#2324C2211yescharacteristic
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic, complemented
81#2316C2211yescharacteristic
82#2314C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2296C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1985C2211yescharacteristic, complemented
127#1985C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1944C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1943C2211yescharacteristic, complemented
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic, complemented
136#1928C2211yescharacteristic, complemented
137#1928C2211yescharacteristic, complemented
138#1926C2211yescharacteristic
139#1925C2211yescharacteristic
140#1921C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1920C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1918C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1893C2211yescharacteristic
151#1893C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic, complemented
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1870C2211yescharacteristic
164#1870C2211yescharacteristic, complemented
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic, complemented
167#1865C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1818C2211yescharacteristic
191#1818C2211yescharacteristic, complemented
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic, complemented
194#1809C2211yescharacteristic, complemented
195#1808C2211yescharacteristic
196#1807C2211yescharacteristic, complemented
197#1797C2211yescharacteristic, complemented
198#1786C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#556—42no—
211#556—42no—
212C2×C4⋊Q8C2311yescharacteristic
213#529—42no—
214#529—42no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126D411yescharacteristic
218C2×#126D411yescharacteristic
219C2×#125D411yescharacteristic
220C2×#124—21no—
221C2×#124D411yescharacteristic
222C2×#123D411yescharacteristic
223C2×#123D411yescharacteristic
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8D411yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121D411yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237#518—42no—
238#518—42no—
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263#485—42no—
264#482—24no—
265#468—24no—
266#450—42no—
267#435—42no—
268#435—42no—
269#427—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#418—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102—24no—
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—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#394—21no—
349#393—21no—
350#393—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#391—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
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#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#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#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384—21no—
423#384C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
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×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551#126—42no—
552#126—42no—
553#126—44no—
554#126—44no—
555#125—42no—
556#124—42no—
557#124—44no—
558#123—42no—
559#123—42no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—42no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—82no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—42no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—82no—
578#120—82no—
579#120—82no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—44no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—82no—
602C4×D4—82no—
603#117—22no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615C2×C4⋊C4—22no—
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—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
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—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—22no—
732#106—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
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—
758#102#4114yes—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—41no—
768#97—41no—
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#95—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—41no—
825C2×Q8—41no—
826C2×Q8—41no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×D4—28no—
831C2×D4—22no—
832C2×D4—22no—
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—21no—
842C2×D4—21no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4C2×#4112yes—
869C2×D42−1+412yes—
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—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—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4H(5,𝔽2)12yes—
933C22×C4H(5,𝔽2)12yes—
934C22×C4C2511yescharacteristic
935SD16—82no—
936SD16—82no—
937M16—82no—
938M16—82no—
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×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—44no—
963C2×C8—82no—
964C2×C8C2×#4112yes—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
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—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
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⋊C4C2×#4112yes—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
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—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
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—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—41no—
1075C42—41no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—21no—
1105C23—21no—
1106C23—48no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23#53412yes—
1126C23C23×D411yescharacteristic
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—82no—
1132Q8—84no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—48no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—82no—
1143D4—82no—
1144D4—82no—
1145D4—84no—
1146D4—84no—
1147D4—162no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—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—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—82no—
1236C2×C4—82no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4#53412yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—22no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—168no—
1293C22C2×#53411yescharacteristic
1294C22D4×#4111yescharacteristic
1295C22#348911yescharacteristic
1296C22#358411yescharacteristic
1297C22#358511yescharacteristic
1298C22#358511yescharacteristic
1299C22#358611yescharacteristic
1300C4—22no—
1301C4—42no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
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—81no—
1325C4#349211yescharacteristic
1326C4#351311yescharacteristic
1327C4#353311yescharacteristic
1328C4#353511yescharacteristic
1329C2—42no—
1330C2—81no—
1331C2—81no—
1332C2—82no—
1333C2—82no—
1334C2#3836511yescharacteristic
1335C2#6076711yescharacteristic
1336C2#6077211yescharacteristic
1337C2#6150311yescharacteristic
1338C2#6152911yescharacteristic
1339C2#6217211yescharacteristic
1340C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35522C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38051C2semidirect
3. #33018C2semidirect
4. #32663C2semidirect
5. #32593C2semidirect
6. #32580C2semidirect
7. #32556C2semidirect
8. #32019C2semidirect
9. #31995C2semidirect
10. #31393C2semidirect
11. #30576C2semidirect
12. #30177C2semidirect
13. #30016C2semidirect
14. #29480C2semidirect
15. #29420C2semidirect
16. #29236C2semidirect
17. #29174C2semidirect
18. #28100C2semidirect
19. #27870C2semidirect
20. #27664C2semidirect
21. #27623C2semidirect
22. #25247C2semidirect
23. #25128C2semidirect
24. #24957C2semidirect
25. #24869C2semidirect
26. #24096C2semidirect
27. #23979C2semidirect
28. #22475C2semidirect
29. #22201C2semidirect
30. #22086C2semidirect
31. #20879C2semidirect
44. #2855C22semidirect
49. #2628C22semidirect
51. #2581C22semidirect
53. #2567C22semidirect
62. #2485C22semidirect
74. #2415C22semidirect
80. #2323C22semidirect
85. #2296C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2097C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2083C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
101. #2076C22semidirect
102. #2075C22semidirect
103. #2075C22semidirect
105. #2072C22semidirect
108. #2066C22semidirect
110. #2058C22semidirect
111. #2057C22semidirect
113. #2036C22semidirect
114. #2035C22semidirect
115. #2035C22semidirect
126. #1985C22semidirect
127. #1985C22semidirect
129. #1944C22semidirect
130. #1943C22semidirect
131. #1943C22semidirect
135. #1935C22semidirect
136. #1928C22semidirect
137. #1928C22semidirect
140. #1921C22semidirect
141. #1921C22semidirect
142. #1920C22semidirect
143. #1920C22semidirect
144. #1919C22semidirect
145. #1918C22semidirect
146. #1918C22semidirect
147. #1918C22semidirect
153. #1892C22semidirect
164. #1870C22semidirect
166. #1869C22semidirect
167. #1865C22semidirect
174. #1863C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
189. #1825C22semidirect
191. #1818C22semidirect
193. #1809C22semidirect
194. #1809C22semidirect
196. #1807C22semidirect
197. #1797C22semidirect
199. #1749C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#380512
#355222
#330182
#326632
#325932
#325802
#325562
#320192
#319952
#313932
#305762
#301772
#300162
#294802
#294202
#292362
#291742
#281002
#278702
#276642
#276232
#252472
#251282
#249572
#248692
#240962
#239792
#224752
#222012
#220862
#208792