Finite Group Databasebeta

← #7044070

Subgroups — #7044070

Order 512.

1581 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45023C211yesmaximal, characteristic
2#44972C211yesmaximal, characteristic, complemented
3#32225C211yesmaximal, characteristic, complemented
4#32070C211yesmaximal, characteristic, complemented
5#31861C211yesmaximal, characteristic, complemented
6#31592C211yesmaximal, characteristic, complemented
7#31508C211yesmaximal, characteristic, complemented
8#31470C211yesmaximal, characteristic, complemented
9#31400C211yesmaximal, characteristic, complemented
10#30426C211yesmaximal, characteristic, complemented
11#28130C211yesmaximal, characteristic, complemented
12#27690C211yesmaximal, characteristic, complemented
13#27543C211yesmaximal, characteristic, complemented
14#27451C211yesmaximal, characteristic, complemented
15#27221C211yesmaximal, characteristic, complemented
16#27047C211yesmaximal, characteristic, complemented
17#26219C211yesmaximal, characteristic, complemented
18#25562C211yesmaximal, characteristic, complemented
19#25251C211yesmaximal, characteristic, complemented
20#25216C211yesmaximal, characteristic, complemented
21#25128C211yesmaximal, characteristic, complemented
22#24951C211yesmaximal, characteristic, complemented
23#24890C211yesmaximal, characteristic, complemented
24#24889C211yesmaximal, characteristic, complemented
25#24546C211yesmaximal, characteristic, complemented
26#24442C211yesmaximal, characteristic, complemented
27#23632C211yesmaximal, characteristic, complemented
28#22496C211yesmaximal, characteristic, complemented
29#22419C211yesmaximal, characteristic, complemented
30#22198C211yesmaximal, characteristic, complemented
31#22177C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2770—21no—
46#2757—21no—
47#2757—21no—
48#2725—21no—
49#2711—21no—
50#2707—21no—
51#2685—21no—
52#2678—21no—
53#2606—21no—
54#2603—21no—
55#2587—21no—
56#2552C2211yescharacteristic, complemented
57#2538C2211yescharacteristic, complemented
58#2502C2211yescharacteristic, complemented
59#2499C2211yescharacteristic, complemented
60#2496C2211yescharacteristic, complemented
61#2495C2211yescharacteristic, complemented
62#2490C2211yescharacteristic
63#2485C2211yescharacteristic
64#2480—21no—
65#2471—21no—
66#2460—21no—
67#2454C2211yescharacteristic
68#2448C2211yescharacteristic
69#2426C2211yescharacteristic
70#2418—21no—
71#2417C2211yescharacteristic
72#2416C2211yescharacteristic
73#2415C2211yescharacteristic
74#2414—21no—
75#2408C2211yescharacteristic
76#2407C2211yescharacteristic
77#2392C2211yescharacteristic
78#2361C2211yescharacteristic
79#2356C2211yescharacteristic, complemented
80#2354C2211yescharacteristic
81#2352C2211yescharacteristic, complemented
82D4×C4⋊C4C2211yescharacteristic
83#2341C2211yescharacteristic
84#2323C2211yescharacteristic
85#2323C2211yescharacteristic
86#2317C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2036C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic, complemented
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic
132#1959C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1925C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1924C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1894C2211yescharacteristic, complemented
155#1894C2211yescharacteristic, complemented
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1878C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic, complemented
173#1870C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1798C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#552—24no—
213#552—42no—
214#546—24no—
215#546—42no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254#485—42no—
255#482—42no—
256#470—24no—
257#468—42no—
258#452—42no—
259#450—42no—
260#435—42no—
261#435—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275#418—42no—
276#417—42no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102—42no—
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314#400—21no—
315#400—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398D411yescharacteristic
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397D411yescharacteristic
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396D411yescharacteristic
340#396D411yescharacteristic
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394D411yescharacteristic
349#394D411yescharacteristic
350#394D411yescharacteristic
351#392—21no—
352#392—21no—
353#392D411yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
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#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#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#383—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#380—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#126—44no—
556#126—82no—
557#125—22no—
558#125—41no—
559#125—44no—
560#125—82no—
561#124—22no—
562#124—41no—
563#123—44no—
564#123—44no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8#4114yes—
575#121—22no—
576#121—22no—
577#121—44no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—82no—
583#120—44no—
584#120—82no—
585C4×Q8—22no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—82no—
600C4×D4—82no—
601#117—22no—
602#117—22no—
603#117—41no—
604#117—41no—
605#117—44no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—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—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
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×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—41no—
730#106—41no—
731#106—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—22no—
737#103—22no—
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#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770#97—41no—
771#97—41no—
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#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—82no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
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×Q8C2×#4112yes—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4H(5,𝔽2)12yes—
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—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
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×C4C2×#4112yes—
933C22×C4H(5,𝔽2)12yes—
934C22×C4C2511yescharacteristic
935Q16—82no—
936SD16—82no—
937SD16—82no—
938M16—82no—
939M16—82no—
940M16—82no—
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—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—82no—
966C4⋊C4—24no—
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—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
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—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⋊C4C2×#4112yes—
1024C22⋊C4—24no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
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—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—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
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—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—21no—
1108C23—21no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—84no—
1123C23—84no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23#54612yes—
1130C23C23×D411yescharacteristic
1131Q8—22no—
1132Q8—22no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139D4—22no—
1140D4—22no—
1141D4—44no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—84no—
1149D4—82no—
1150D4—82no—
1151D4—84no—
1152D4—84no—
1153D4—162no—
1154D4—162no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
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—22no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
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—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—84no—
1242C2×C4—84no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4#54612yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22C2×#54611yescharacteristic
1298C22#348511yescharacteristic
1299C22#348811yescharacteristic
1300C22#358511yescharacteristic
1301C22#358511yescharacteristic
1302C22#358611yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4#351311yescharacteristic
1330C4#352111yescharacteristic
1331C4#353411yescharacteristic
1332C4#356011yescharacteristic
1333C2—42no—
1334C2—81no—
1335C2—81no—
1336C2—82no—
1337C2—161no—
1338C2#4353011yescharacteristic
1339C2#6117811yescharacteristic
1340C2#6118011yescharacteristic
1341C2#6178011yescharacteristic
1342C2#6179911yescharacteristic
1343C2#6208011yescharacteristic
1344C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45023C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #44972C2semidirect
3. #32225C2semidirect
4. #32070C2semidirect
5. #31861C2semidirect
6. #31592C2semidirect
7. #31508C2semidirect
8. #31470C2semidirect
9. #31400C2semidirect
10. #30426C2semidirect
11. #28130C2semidirect
12. #27690C2semidirect
13. #27543C2semidirect
14. #27451C2semidirect
15. #27221C2semidirect
16. #27047C2semidirect
17. #26219C2semidirect
18. #25562C2semidirect
19. #25251C2semidirect
20. #25216C2semidirect
21. #25128C2semidirect
22. #24951C2semidirect
23. #24890C2semidirect
24. #24889C2semidirect
25. #24546C2semidirect
26. #24442C2semidirect
27. #23632C2semidirect
28. #22496C2semidirect
29. #22419C2semidirect
30. #22198C2semidirect
31. #22177C2semidirect
56. #2552C22semidirect
57. #2538C22semidirect
58. #2502C22semidirect
59. #2499C22semidirect
60. #2496C22semidirect
61. #2495C22semidirect
79. #2356C22semidirect
81. #2352C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2095C22semidirect
94. #2087C22semidirect
95. #2083C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2075C22semidirect
110. #2066C22semidirect
112. #2059C22semidirect
117. #2036C22semidirect
118. #2036C22semidirect
123. #2026C22semidirect
125. #2001C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1943C22semidirect
137. #1935C22semidirect
138. #1928C22semidirect
139. #1928C22semidirect
144. #1924C22semidirect
145. #1924C22semidirect
146. #1921C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
154. #1894C22semidirect
155. #1894C22semidirect
160. #1878C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
167. #1873C22semidirect
169. #1872C22semidirect
172. #1870C22semidirect
173. #1870C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
179. #1853C22semidirect
181. #1852C22semidirect
182. #1851C22semidirect
183. #1851C22semidirect
185. #1824C22semidirect
186. #1823C22semidirect
188. #1809C22semidirect
189. #1805C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
197. #1763C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#450232
#449722
#322252
#320702
#318612
#315922
#315082
#314702
#314002
#304262
#281302
#276902
#275432
#274512
#272212
#270472
#262192
#255622
#252512
#252162
#251282
#249512
#248902
#248892
#245462
#244422
#236322
#224962
#224192
#221982
#221772