Finite Group Databasebeta

← #6479590

Subgroups — #6479590

Order 512.

1552 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35255C211yesmaximal, characteristic
2#34060C211yesmaximal, characteristic, complemented
3#33101C211yesmaximal, characteristic, complemented
4#33098C211yesmaximal, characteristic, complemented
5#33097C211yesmaximal, characteristic, complemented
6#33096C211yesmaximal, characteristic, complemented
7#29919C211yesmaximal, characteristic, complemented
8#29918C211yesmaximal, characteristic, complemented
9#29916C211yesmaximal, characteristic, complemented
10#29916C211yesmaximal, characteristic, complemented
11#27873C211yesmaximal, characteristic, complemented
12#27872C211yesmaximal, characteristic, complemented
13#27871C211yesmaximal, characteristic, complemented
14#27869C211yesmaximal, characteristic, complemented
15#27866C211yesmaximal, characteristic, complemented
16#27863C211yesmaximal, characteristic, complemented
17#27859C211yesmaximal, characteristic, complemented
18#27855C211yesmaximal, characteristic, complemented
19#27622C211yesmaximal, characteristic, complemented
20#27619C211yesmaximal, characteristic, complemented
21#27616C211yesmaximal, characteristic, complemented
22#27611C211yesmaximal, characteristic, complemented
23#27597C211yesmaximal, characteristic, complemented
24#27593C211yesmaximal, characteristic, complemented
25#27590C211yesmaximal, characteristic, complemented
26#27584C211yesmaximal, characteristic, complemented
27#21946C211yesmaximal, characteristic, complemented
28#21945C211yesmaximal, characteristic, complemented
29#21772C211yesmaximal, characteristic
30#21772C211yesmaximal, characteristic
31#20684C211yesmaximal, characteristic, complemented
32C2×#537C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#408C2211yescharacteristic
35C2×#408C2211yescharacteristic
36#2855C2211yescharacteristic
37#2855C2211yescharacteristic
38#2854C2211yescharacteristic
39#2854C2211yescharacteristic
40#2625C2211yescharacteristic
41#2625C2211yescharacteristic
42#2624C2211yescharacteristic
43#2624C2211yescharacteristic
44#2444—21no—
45#2444—21no—
46#2443—21no—
47#2443—21no—
48#2423—21no—
49#2422—21no—
50#2421—21no—
51#2420—21no—
52#2320—21no—
53#2319—21no—
54#2318—21no—
55#2318—21no—
56#2317C2211yescharacteristic
57#2317C2211yescharacteristic
58#2317C2211yescharacteristic
59#2314C2211yescharacteristic
60#2314C2211yescharacteristic
61#2314C2211yescharacteristic
62#2314C2211yescharacteristic
63#2311C2211yescharacteristic
64#2311C2211yescharacteristic
65#2311C2211yescharacteristic
66#2311C2211yescharacteristic
67#2297C2211yescharacteristic
68#2295—21no—
69#2293—21no—
70C2×#389C2211yescharacteristic
71#2290—21no—
72#2290—21no—
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2283C2211yescharacteristic
76#2283C2211yescharacteristic
77C4×#117C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2095C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic
111#1928C2211yescharacteristic
112#1928C2211yescharacteristic
113#1927C2211yescharacteristic
114#1927C2211yescharacteristic
115#1927C2211yescharacteristic
116#1927C2211yescharacteristic
117#1927C2211yescharacteristic
118#1927C2211yescharacteristic
119#1926C2211yescharacteristic
120#1926C2211yescharacteristic
121#1926C2211yescharacteristic
122#1926C2211yescharacteristic
123#1925C2211yescharacteristic
124#1925C2211yescharacteristic
125#1925C2211yescharacteristic
126#1925C2211yescharacteristic
127#1921C2211yescharacteristic
128#1921C2211yescharacteristic
129#1921C2211yescharacteristic
130#1921C2211yescharacteristic
131#1920C2211yescharacteristic
132#1920C2211yescharacteristic
133#1920C2211yescharacteristic
134#1920C2211yescharacteristic
135#1920C2211yescharacteristic
136#1920C2211yescharacteristic
137#1920C2211yescharacteristic
138#1920C2211yescharacteristic
139#1919C2211yescharacteristic
140#1919C2211yescharacteristic
141#1918C2211yescharacteristic
142#1918C2211yescharacteristic
143#1895C2211yescharacteristic
144#1895C2211yescharacteristic
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic
149#1892C2211yescharacteristic
150#1892C2211yescharacteristic
151#1875C2211yescharacteristic
152#1875C2211yescharacteristic
153#1874C2211yescharacteristic
154#1874C2211yescharacteristic
155#1873C2211yescharacteristic
156#1873C2211yescharacteristic
157#1872C2211yescharacteristic
158#1872C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1824C2211yescharacteristic
176#1824C2211yescharacteristic
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic
179#1818C2211yescharacteristic
180#1818C2211yescharacteristic
181#1818C2211yescharacteristic
182#1818C2211yescharacteristic
183#1817C2211yescharacteristic
184#1817C2211yescharacteristic
185#1817C2211yescharacteristic
186#1817C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1807C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#537—24no—
210#537—24no—
211C2×#123—21no—
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C4×#41—24no—
222C4×#41—24no—
223C2×C4×Q8D411yescharacteristic
224C2×C4×Q8D411yescharacteristic
225C2×C4×D4D411yescharacteristic
226C2×C4×D4D411yescharacteristic
227C2×C4×D4D411yescharacteristic
228C2×C4×D4D411yescharacteristic
229C2×C4×D4D411yescharacteristic
230C2×C4×D4D411yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C42—21no—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280#408—24no—
281#408—24no—
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#394—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#390—21no—
314#390—21no—
315#390—21no—
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#386—21no—
359#386—21no—
360#386—21no—
361#386—21no—
362#386—21no—
363#386—21no—
364#386—21no—
365#386—21no—
366#386—21no—
367#386—21no—
368#386—21no—
369#386—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#384—21no—
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#383—21no—
384#383—21no—
385#382—21no—
386#382—21no—
387#382—21no—
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#381—21no—
393#381—21no—
394#381—21no—
395#381—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430#376—21no—
431#376—21no—
432#376—21no—
433C2×#95—21no—
434C2×#95—21no—
435C43—21no—
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41#4114yes—
495C2×#41#4114yes—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539#123—82no—
540#123—82no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—44no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—44no—
551#121—44no—
552#121—44no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—24no—
561#117—22no—
562#117—22no—
563#117—22no—
564#117—22no—
565#117—22no—
566#117—22no—
567#117—41no—
568#117—41no—
569#117—41no—
570#117—41no—
571#117—41no—
572#117—41no—
573#117—82no—
574#117—82no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—82no—
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C42—22no—
660C2×C42—22no—
661C2×C42—22no—
662C2×C42—22no—
663C2×C42—22no—
664C2×C42—22no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—82no—
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722C22⋊C8—22no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771C24—21no—
772C24C22×D411yescharacteristic
773C24C22×D411yescharacteristic
774C24C22×D411yescharacteristic
775#41—44no—
776#41—44no—
777#41—44no—
778#41—44no—
779#41—82no—
780#41—82no—
781#41—82no—
782#41—82no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8#12314yes—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4#12314yes—
814C2×D4#12314yes—
815C2×D4#12314yes—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C2×#4112yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4C2×#4112yes—
891C22×C4C2×#4112yes—
892C22×C4C2×#4112yes—
893C22×C4C2511yescharacteristic
894M16—82no—
895M16—82no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—82no—
921C2×C8—82no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—42no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—42no—
1031C42—42no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23C2×#12312yes—
1062C23C2×#12312yes—
1063C23C2×#12312yes—
1064C23C23×D411yescharacteristic
1065Q8—44no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070D4—44no—
1071D4—44no—
1072D4—44no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—84no—
1078D4—162no—
1079D4—162no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—84no—
1170C2×C4—82no—
1171C2×C4—82no—
1172C2×C4—82no—
1173C2×C4—84no—
1174C2×C4—84no—
1175C2×C4—84no—
1176C2×C4—162no—
1177C2×C4C2×#12312yes—
1178C2×C4C2×#12312yes—
1179C2×C4C2×#12312yes—
1180C2×C4#57712yes—
1181C2×C4C22×#4111yescharacteristic
1182C2×C4C22×#4111yescharacteristic
1183C2×C4#58511yescharacteristic
1184C2×C4#58511yescharacteristic
1185C2×C4#58511yescharacteristic
1186C2×C4#58511yescharacteristic
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22C22×#12311yescharacteristic
1224C22#344911yescharacteristic
1225C22#344911yescharacteristic
1226C22C2×#57711yescharacteristic
1227C22#358411yescharacteristic
1228C22#358511yescharacteristic
1229C22#358611yescharacteristic
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4#349111yescharacteristic
1257C4#349111yescharacteristic
1258C4#349111yescharacteristic
1259C4#349111yescharacteristic
1260C2—42no—
1261C2—42no—
1262C2—42no—
1263C2—161no—
1264C2#3509711yescharacteristic
1265C2#6052211yescharacteristic
1266C2#6052311yescharacteristic
1267C2#6095611yescharacteristic
1268C2#6097311yescharacteristic
1269C2#6098911yescharacteristic
1270C2#6099911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34060C2semidirect
3. #33101C2semidirect
4. #33098C2semidirect
5. #33097C2semidirect
6. #33096C2semidirect
7. #29919C2semidirect
8. #29918C2semidirect
9. #29916C2semidirect
10. #29916C2semidirect
11. #27873C2semidirect
12. #27872C2semidirect
13. #27871C2semidirect
14. #27869C2semidirect
15. #27866C2semidirect
16. #27863C2semidirect
17. #27859C2semidirect
18. #27855C2semidirect
19. #27622C2semidirect
20. #27619C2semidirect
21. #27616C2semidirect
22. #27611C2semidirect
23. #27597C2semidirect
24. #27593C2semidirect
25. #27590C2semidirect
26. #27584C2semidirect
27. #21946C2semidirect
28. #21945C2semidirect
31. #20684C2semidirect

Maximal subgroups

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

subgroupindex
#352552
#340602
#331012
#330982
#330972
#330962
#299192
#299182
#299162
#278732
#278722
#278712
#278692
#278662
#278632
#278592
#278552
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