Finite Group Databasebeta

← #6777313

Subgroups — #6777313

Order 512.

1485 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36263C211yesmaximal, characteristic
2#34945C211yesmaximal, characteristic, complemented
3#33081C211yesmaximal, characteristic, complemented
4#32367C211yesmaximal, characteristic, complemented
5#32335C211yesmaximal, characteristic, complemented
6#31661C211yesmaximal, characteristic, complemented
7#31597C211yesmaximal, characteristic, complemented
8#31386C211yesmaximal, characteristic, complemented
9#31318C211yesmaximal, characteristic, complemented
10#31318C211yesmaximal, characteristic, complemented
11#30561C211yesmaximal, characteristic, complemented
12#30115C211yesmaximal, characteristic, complemented
13#30018C211yesmaximal, characteristic, complemented
14#29521C211yesmaximal, characteristic, complemented
15#29393C211yesmaximal, characteristic, complemented
16#29047C211yesmaximal, characteristic, complemented
17#28856C211yesmaximal, characteristic, complemented
18#27897C211yesmaximal, characteristic, complemented
19#27859C211yesmaximal, characteristic, complemented
20#27847C211yesmaximal, characteristic, complemented
21#27633C211yesmaximal, characteristic, complemented
22#27616C211yesmaximal, characteristic, complemented
23#27112C211yesmaximal, characteristic, complemented
24#27048C211yesmaximal, characteristic, complemented
25#26978C211yesmaximal, characteristic, complemented
26#26674C211yesmaximal, characteristic, complemented
27#26570C211yesmaximal, characteristic, complemented
28#22787C211yesmaximal, characteristic, complemented
29#22185C211yesmaximal, characteristic, complemented
30#22084C211yesmaximal, characteristic, complemented
31#21124C211yesmaximal, characteristic, complemented
32C2×#553—21no—
33C2×#483C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#440C2211yescharacteristic
36#2860C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854C2211yescharacteristic
39#2602—21no—
40#2601—21no—
41#2591—21no—
42#2573—21no—
43#2573—21no—
44#2571C2211yescharacteristic
45#2568C2211yescharacteristic
46#2559—21no—
47#2558—21no—
48#2547C2211yescharacteristic
49#2543—21no—
50#2538C2211yescharacteristic
51#2514—21no—
52#2506C2211yescharacteristic
53#2496C2211yescharacteristic
54#2494C2211yescharacteristic
55#2494C2211yescharacteristic
56#2447—21no—
57#2445C2211yescharacteristic
58#2428C2211yescharacteristic
59#2421C2211yescharacteristic
60#2421C2211yescharacteristic
61#2416C2211yescharacteristic
62#2416C2211yescharacteristic
63#2401—21no—
64#2401—21no—
65#2364—21no—
66#2361C2211yescharacteristic
67#2361C2211yescharacteristic
68C4×C4⋊Q8C2211yescharacteristic
69C4×#124—21no—
70C4×C22⋊Q8C2211yescharacteristic
71C4×C22⋊Q8C2211yescharacteristic
72C4×#121C2211yescharacteristic
73#2295—21no—
74#2293C2211yescharacteristic
75C2×#389C2211yescharacteristic
76#2283C2211yescharacteristic
77#2283C2211yescharacteristic
78C42×Q8C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2095C2211yescharacteristic
86#2094C2211yescharacteristic
87#2092C2211yescharacteristic
88#2087C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2077C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2068C2211yescharacteristic
99#2065C2211yescharacteristic
100#2057C2211yescharacteristic
101#2057C2211yescharacteristic
102#2055C2211yescharacteristic
103#2041C2211yescharacteristic
104#2035C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2014C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#1961C2211yescharacteristic
121#1961C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1944C2211yescharacteristic
125#1944C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1928C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1924C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1877C2211yescharacteristic
168#1872C2211yescharacteristic
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1847C2211yescharacteristic
183#1839C2211yescharacteristic
184#1836C2211yescharacteristic
185#1823C2211yescharacteristic
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic
188#1817C2211yescharacteristic
189#1808C2211yescharacteristic
190#1808C2211yescharacteristic
191#1807C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1797C2211yescharacteristic
195#1776C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201#1745C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#553—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125—21no—
213C2×#124—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121—21no—
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4D411yescharacteristic
235C2×C4×D4D411yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245#483—24no—
246#465—24no—
247#440—24no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294#401—21no—
295#401—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#392—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390—21no—
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#383—21no—
391#383—21no—
392#382—21no—
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#381—21no—
398#381—21no—
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4D411yescharacteristic
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4D411yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435#376—21no—
436#376—21no—
437C2×#95—21no—
438C43—21no—
439C43C2311yescharacteristic
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
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C2×D411yescharacteristic
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#127—41no—
526#127—41no—
527#126—44no—
528#126—44no—
529#125—44no—
530#124—44no—
531#123—44no—
532#123—44no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537#121—22no—
538#121—44no—
539#121—41no—
540#121—41no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—44no—
545#121—44no—
546#121—44no—
547#121—44no—
548#121—41no—
549#121—41no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—44no—
557C4×D4—24no—
558C4×D4—22no—
559C4×D4—41no—
560C4×D4—42no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—44no—
566C4×D4—44no—
567C4×D4—44no—
568#117—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
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—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—41no—
659C2×C42—41no—
660C2×C42—41no—
661C2×C42—41no—
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#107—22no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#106—22no—
684#106—22no—
685#106—22no—
686#106—41no—
687#106—41no—
688#106—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691#103—22no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103#4114yes—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716C22⋊C8—41no—
717#97—22no—
718#97—41no—
719#97—41no—
720#97—41no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
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#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766C24—21no—
767C24—21no—
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8C2×#4112yes—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—41no—
792C2×D4—41no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4AGL(1,ℤ/8)14yes—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
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—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C2511yescharacteristic
875SD16—44no—
876SD16—82no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—82no—
901C2×C8—82no—
902C2×C8C2×#4112yes—
903C4⋊C4—22no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4C2×#4112yes—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C42—22no—
991C42—22no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—42no—
1017C42—81no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23C2×AGL(1,ℤ/8)12yes—
1045C23C2×AGL(1,ℤ/8)12yes—
1046C23C23×D411yescharacteristic
1047Q8—22no—
1048Q8—22no—
1049Q8—41no—
1050Q8—41no—
1051Q8—84no—
1052D4—44no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—84no—
1062D4—84no—
1063D4—84no—
1064D4—162no—
1065D4—162no—
1066D4—162no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
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—82no—
1152C2×C4—82no—
1153C2×C4—82no—
1154C2×C4—82no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—162no—
1158C2×C4—162no—
1159C2×C4C2×AGL(1,ℤ/8)12yes—
1160C2×C4#57512yes—
1161C2×C4C22×#4111yescharacteristic
1162C2×C4#58511yescharacteristic
1163C2×C4#58511yescharacteristic
1164C2×C4#58511yescharacteristic
1165C2×C4#58511yescharacteristic
1166C2×C4#58511yescharacteristic
1167C8—22no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22#344911yescharacteristic
1204C22D4×#4111yescharacteristic
1205C22#348511yescharacteristic
1206C22C22×AGL(1,ℤ/8)11yescharacteristic
1207C22C2×#57511yescharacteristic
1208C22#358411yescharacteristic
1209C22#358611yescharacteristic
1210C4—22no—
1211C4—22no—
1212C4—41no—
1213C4—41no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—42no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4#349311yescharacteristic
1237C4#352111yescharacteristic
1238C4#356611yescharacteristic
1239C4#356711yescharacteristic
1240C2—42no—
1241C2—42no—
1242C2—161no—
1243C2—161no—
1244C2#3837711yescharacteristic
1245C2#6095811yescharacteristic
1246C2#6099911yescharacteristic
1247C2#6144311yescharacteristic
1248C2#6145211yescharacteristic
1249C2#6171211yescharacteristic
1250C2#6173311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36263C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34945C2semidirect
3. #33081C2semidirect
4. #32367C2semidirect
5. #32335C2semidirect
6. #31661C2semidirect
7. #31597C2semidirect
8. #31386C2semidirect
9. #31318C2semidirect
10. #31318C2semidirect
11. #30561C2semidirect
12. #30115C2semidirect
13. #30018C2semidirect
14. #29521C2semidirect
15. #29393C2semidirect
16. #29047C2semidirect
17. #28856C2semidirect
18. #27897C2semidirect
19. #27859C2semidirect
20. #27847C2semidirect
21. #27633C2semidirect
22. #27616C2semidirect
23. #27112C2semidirect
24. #27048C2semidirect
25. #26978C2semidirect
26. #26674C2semidirect
27. #26570C2semidirect
28. #22787C2semidirect
29. #22185C2semidirect
30. #22084C2semidirect
31. #21124C2semidirect

Maximal subgroups

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

subgroupindex
#362632
#349452
#330812
#323672
#323352
#316612
#315972
#313862
#313182
#305612
#301152
#300182
#295212
#293932
#290472
#288562
#278972
#278592
#278472
#276332
#276162
#271122
#270482
#269782
#266742
#265702
#227872
#221852
#220842
#211242