Finite Group Databasebeta

← #6794595

Subgroups — #6794595

Order 512.

1432 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36201C211yesmaximal, characteristic, complemented
2#34932C211yesmaximal, characteristic
3#33070C211yesmaximal, characteristic, complemented
4#32344C211yesmaximal, characteristic, complemented
5#32342C211yesmaximal, characteristic, complemented
6#32312C211yesmaximal, characteristic, complemented
7#32310C211yesmaximal, characteristic, complemented
8#32276C211yesmaximal, characteristic, complemented
9#32276C211yesmaximal, characteristic, complemented
10#32021C211yesmaximal, characteristic
11#32019C211yesmaximal, characteristic
12#29943C211yesmaximal, characteristic, complemented
13#29943C211yesmaximal, characteristic, complemented
14#29317C211yesmaximal, characteristic, complemented
15#29280C211yesmaximal, characteristic, complemented
16#28869C211yesmaximal, characteristic, complemented
17#28865C211yesmaximal, characteristic, complemented
18#27853C211yesmaximal, characteristic, complemented
19#27852C211yesmaximal, characteristic, complemented
20#27683C211yesmaximal, characteristic, complemented
21#27632C211yesmaximal, characteristic, complemented
22#27482C211yesmaximal, characteristic, complemented
23#27478C211yesmaximal, characteristic, complemented
24#27186C211yesmaximal, characteristic, complemented
25#27182C211yesmaximal, characteristic, complemented
26#24841C211yesmaximal, characteristic, complemented
27#24704C211yesmaximal, characteristic, complemented
28#22749C211yesmaximal, characteristic, complemented
29#21984C211yesmaximal, characteristic, complemented
30#21963C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic, complemented
32C2×#529—21no—
33C2×#478C2211yescharacteristic
34C2×#431C2211yescharacteristic
35C2×#423C2211yescharacteristic
36#2864C2211yescharacteristic
37#2851C2211yescharacteristic
38#2851C2211yescharacteristic
39#2577—21no—
40#2553—21no—
41#2553—21no—
42#2552C2211yescharacteristic
43#2547C2211yescharacteristic
44#2542C2211yescharacteristic
45#2537C2211yescharacteristic
46#2530—21no—
47#2524—21no—
48#2515—21no—
49#2507C2211yescharacteristic
50#2506C2211yescharacteristic
51#2497C2211yescharacteristic
52#2496C2211yescharacteristic
53#2496C2211yescharacteristic
54#2496C2211yescharacteristic
55#2489—21no—
56#2485C2211yescharacteristic
57#2485C2211yescharacteristic
58#2468—21no—
59#2460—21no—
60#2427—21no—
61#2422C2211yescharacteristic
62#2422C2211yescharacteristic
63#2395—21no—
64#2395—21no—
65#2373—21no—
66#2371—21no—
67#2347C2211yescharacteristic
68#2346C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C4×#125C2211yescharacteristic
71C4×C22⋊Q8—21no—
72C4×#121C2211yescharacteristic
73C4×#121C2211yescharacteristic
74#2285C2211yescharacteristic
75#2285C2211yescharacteristic
76#2285C2211yescharacteristic
77#2283C2211yescharacteristic
78C42×D4C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2100C2211yescharacteristic
81#2099C2211yescharacteristic
82#2099C2211yescharacteristic
83#2099C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2093C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2076C2211yescharacteristic
109#2076C2211yescharacteristic
110#2067C2211yescharacteristic
111#2065C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#1989C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1870C2211yescharacteristic
167#1870C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1845C2211yescharacteristic
181#1844C2211yescharacteristic
182#1834C2211yescharacteristic
183#1834C2211yescharacteristic
184#1831C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1797C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1767C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206#529—48no—
207C2×#126—21no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4D411yescharacteristic
225C2×C4×D4D411yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C42—21no—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#478—24no—
238#431—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259#423—24no—
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#399—21no—
290#399—21no—
291#398—21no—
292#398—21no—
293#398—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#397—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#391—21no—
313#391—21no—
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#389—21no—
317#389—21no—
318#389—21no—
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
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#387—21no—
343#387—21no—
344#387—21no—
345#387—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#387—21no—
359#387—21no—
360#386—21no—
361#386—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#384C2311yescharacteristic
369#384C2311yescharacteristic
370#384C2311yescharacteristic
371#384C2311yescharacteristic
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#383—21no—
376#383—21no—
377#382—21no—
378#382—21no—
379#382—21no—
380#382C2311yescharacteristic
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#381—21no—
384#380—21no—
385#380—21no—
386#380—21no—
387#380—21no—
388#380—21no—
389#380C2311yescharacteristic
390#380C2311yescharacteristic
391#380C2311yescharacteristic
392#380C2311yescharacteristic
393#380C2311yescharacteristic
394#380C2311yescharacteristic
395#380C2311yescharacteristic
396#380C2311yescharacteristic
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4D411yescharacteristic
410C4×C4⋊C4D411yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4D411yescharacteristic
428C4×C22⋊C4D411yescharacteristic
429C4×C22⋊C4D411yescharacteristic
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4C2311yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433#376—21no—
434#376—21no—
435C43C2311yescharacteristic
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#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C22×Q8—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2×D411yescharacteristic
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2×D411yescharacteristic
493C23×C4C2×D411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512#126—44no—
513#126—44no—
514#126—44no—
515#125—22no—
516#125—22no—
517#125—44no—
518#125—44no—
519#124—44no—
520#123—44no—
521#123—44no—
522C22⋊Q8—44no—
523C22⋊Q8—44no—
524#121—22no—
525#121—22no—
526#121—41no—
527#121—41no—
528#121—44no—
529C4×Q8—44no—
530C4×D4—24no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—42no—
540C4×D4—44no—
541C4×D4—44no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—44no—
547#117—44no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—44no—
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8#4114yes—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695#97—41no—
696#97—41no—
697C4×C8—22no—
698C4×C8—22no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24C22×D411yescharacteristic
748C24C22×D411yescharacteristic
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×D4—22no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—81no—
765C2×D4—81no—
766C2×D42−1+412yes—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—81no—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C2511yescharacteristic
828M16—82no—
829M16—82no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8C2×#4112yes—
853C2×C8C2×#4112yes—
854C4⋊C4—22no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—41no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4AGL(1,ℤ/8)14yes—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—41no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—81no—
973C42—81no—
974C42C2×#4112yes—
975C422−1+412yes—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—22no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23C23×D411yescharacteristic
998Q8—84no—
999D4—22no—
1000D4—22no—
1001D4—44no—
1002D4—41no—
1003D4—41no—
1004D4—84no—
1005D4—84no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—82no—
1093C2×C4—84no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4#54712yes—
1097C2×C4#54712yes—
1098C2×C4C2×AGL(1,ℤ/8)12yes—
1099C2×C4C2×AGL(1,ℤ/8)12yes—
1100C2×C4C2×AGL(1,ℤ/8)12yes—
1101C2×C4#57512yes—
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C2×2−1+411yescharacteristic
1104C2×C4C2×2−1+411yescharacteristic
1105C2×C4#58511yescharacteristic
1106C2×C4#58511yescharacteristic
1107C2×C4#58511yescharacteristic
1108C8—22no—
1109C8—22no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C22—41no—
1117C22—41no—
1118C22—42no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—41no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22#344911yescharacteristic
1138C22C2×#54711yescharacteristic
1139C22#348911yescharacteristic
1140C22C22×AGL(1,ℤ/8)11yescharacteristic
1141C22C2×#57511yescharacteristic
1142C22#358411yescharacteristic
1143C22#358611yescharacteristic
1144C4—22no—
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4#351611yescharacteristic
1172C4#352111yescharacteristic
1173C4#356311yescharacteristic
1174C4#356511yescharacteristic
1175C2—81no—
1176C2—81no—
1177C2—82no—
1178C2#3891511yescharacteristic
1179C2#6096511yescharacteristic
1180C2#6099911yescharacteristic
1181C2#6124311yescharacteristic
1182C2#6125211yescharacteristic
1183C2#6212111yescharacteristic
1184C2#6215111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
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
1. #36201C2semidirect
3. #33070C2semidirect
4. #32344C2semidirect
5. #32342C2semidirect
6. #32312C2semidirect
7. #32310C2semidirect
8. #32276C2semidirect
9. #32276C2semidirect
12. #29943C2semidirect
13. #29943C2semidirect
14. #29317C2semidirect
15. #29280C2semidirect
16. #28869C2semidirect
17. #28865C2semidirect
18. #27853C2semidirect
19. #27852C2semidirect
20. #27683C2semidirect
21. #27632C2semidirect
22. #27482C2semidirect
23. #27478C2semidirect
24. #27186C2semidirect
25. #27182C2semidirect
26. #24841C2semidirect
27. #24704C2semidirect
28. #22749C2semidirect
29. #21984C2semidirect
30. #21963C2semidirect
31. #21617C2semidirect

Maximal subgroups

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

subgroupindex
#362012
#349322
#330702
#323442
#323422
#323122
#323102
#322762
#320212
#320192
#299432
#293172
#292802
#288692
#288652
#278532
#278522
#276832
#276322
#274822
#274782
#271862
#271822
#248412
#247042
#227492
#219842
#219632
#216172