Finite Group Databasebeta

← #7592836

Subgroups — #7592836

Order 512.

1383 conjugacy classes of subgroups.

The subgroup lattice has 1163 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59330C211yesmaximal, characteristic, complemented
2#59302C211yesmaximal, characteristic
3#32381C211yesmaximal, characteristic, complemented
4#32379C211yesmaximal, characteristic, complemented
5#32378C211yesmaximal, characteristic, complemented
6#32377C211yesmaximal, characteristic, complemented
7#28840C211yesmaximal, characteristic, complemented
8#28837C211yesmaximal, characteristic, complemented
9#28832C211yesmaximal, characteristic, complemented
10#28275C211yesmaximal, characteristic, complemented
11#28025C211yesmaximal, characteristic, complemented
12#28010C211yesmaximal, characteristic, complemented
13#27947C211yesmaximal, characteristic
14#27947C211yesmaximal, characteristic
15#27650C211yesmaximal, characteristic
16#27647C211yesmaximal, characteristic, complemented
17#26105C211yesmaximal, characteristic, complemented
18#26099C211yesmaximal, characteristic, complemented
19#25073C211yesmaximal, characteristic, complemented
20#25071C211yesmaximal, characteristic, complemented
21#24599C211yesmaximal, characteristic
22#24597C211yesmaximal, characteristic
23#24590C211yesmaximal, characteristic, complemented
24#24590C211yesmaximal, characteristic, complemented
25#22820C211yesmaximal, characteristic, complemented
26#22730C211yesmaximal, characteristic, complemented
27#22623C211yesmaximal, characteristic, complemented
28#22621C211yesmaximal, characteristic, complemented
29#21600C211yesmaximal, characteristic, complemented
30#21540C211yesmaximal, characteristic
31#20800C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#483C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#446C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic
44#2793—21no—
45#2793—21no—
46#2747—21no—
47#2690—21no—
48#2581C2211yescharacteristic
49#2577—21no—
50#2571C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2570C2211yescharacteristic
55#2552C2211yescharacteristic
56#2538C2211yescharacteristic
57#2533—21no—
58#2530—21no—
59#2524—21no—
60#2520—21no—
61#2512C2211yescharacteristic
62#2512C2211yescharacteristic
63#2511C2211yescharacteristic
64#2511C2211yescharacteristic
65#2504C2211yescharacteristic
66#2504C2211yescharacteristic
67#2499—21no—
68#2499C2211yescharacteristic
69#2499C2211yescharacteristic
70#2496—21no—
71#2481—21no—
72#2481—21no—
73#2417—21no—
74#2371—21no—
75#2356C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2354C2211yescharacteristic
79#2352—21no—
80#2347C2211yescharacteristic
81#2346C2211yescharacteristic
82#2345C2211yescharacteristic
83#2345C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×#121C2211yescharacteristic
87#2285C2211yescharacteristic
88C2×#384C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2083C2211yescharacteristic
109#2072C2211yescharacteristic
110#2072C2211yescharacteristic
111#2071C2211yescharacteristic
112#2071C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#1985C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1968C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1941C2211yescharacteristic
144#1940C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic
167#1851C2211yescharacteristic
168#1851C2211yescharacteristic
169#1847C2211yescharacteristic
170#1847C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1846C2211yescharacteristic
176#1846C2211yescharacteristic
177#1845C2211yescharacteristic
178#1845C2211yescharacteristic
179#1844C2211yescharacteristic
180#1844C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1809C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1797C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8D411yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×#121C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4—21no—
216C2×C4×D4C2311yescharacteristic
217C2×#117—21no—
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C4⋊C4—21no—
221C22×C4⋊C4—21no—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#483—42no—
226#483—42no—
227#482—42no—
228#482—42no—
229#468—24no—
230#446—24no—
231#440—24no—
232#428—24no—
233#428—24no—
234#428—42no—
235#428—42no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C4×M16—24no—
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—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#400—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#395—21no—
326#391—21no—
327#391—21no—
328#391D411yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389—21no—
340#389—21no—
341#389D411yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—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#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387D411yescharacteristic
391#387D411yescharacteristic
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385D411yescharacteristic
399#385D411yescharacteristic
400#384—21no—
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#383—21no—
412#382—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380D411yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457#376—21no—
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8C2×D411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16#4114yes—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517#126—82no—
518#126—82no—
519#125—44no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—42no—
523C22⋊Q8—82no—
524#121—22no—
525#121—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—44no—
533#117—22no—
534#117—22no—
535#117—22no—
536#117—22no—
537#117—82no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
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—82no—
573C2×C4⋊C4—82no—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641#107—22no—
642#107—22no—
643#107—22no—
644#107—22no—
645#107—22no—
646#107—22no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—22no—
657#106—22no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688C22⋊C8—22no—
689C22⋊C8—22no—
690#97—22no—
691#97—22no—
692#97—22no—
693#97#4114yes—
694C4×C8—22no—
695C4×C8—22no—
696C4×C8—22no—
697C4×C8—22no—
698#95—21no—
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#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C24C22×D411yescharacteristic
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—41no—
766C2×Q8—41no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—42no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
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—41no—
800C22×C4—41no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
824C22×C4H(5,𝔽2)12yes—
825C22×C4C2511yescharacteristic
826SD16—44no—
827M16—28no—
828M16—28no—
829C2×C8—21no—
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×C8C2×#4112yes—
848C2×C8C2×#4112yes—
849C2×C8C2×#4112yes—
850C2×C8C2×#4112yes—
851C2×C82−1+412yes—
852C2×C82−1+412yes—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
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—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
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—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
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⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C22⋊C4—41no—
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—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C42—22no—
942C42—22no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42C2×#4112yes—
967C422−1+412yes—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23#55012yes—
982C23C23×D411yescharacteristic
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—82no—
988D4—41no—
989D4—41no—
990D4—41no—
991D4—41no—
992D4—84no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
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—44no—
1032C2×C4—44no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
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—84no—
1079C2×C4—162no—
1080C2×C4—162no—
1081C2×C4#54712yes—
1082C2×C4#54712yes—
1083C2×C4#55012yes—
1084C2×C4#57512yes—
1085C2×C4#57712yes—
1086C2×C4C22×#4111yescharacteristic
1087C2×C4C22×#4111yescharacteristic
1088C2×C4C2×H(5,𝔽2)11yescharacteristic
1089C2×C4C2×2−1+411yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C8—22no—
1093C8—22no—
1094C8—22no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8#55214yes—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22C2×#54711yescharacteristic
1115C22C2×#55011yescharacteristic
1116C22#349911yescharacteristic
1117C22C2×#57511yescharacteristic
1118C22C2×#57711yescharacteristic
1119C22#358511yescharacteristic
1120C22#358611yescharacteristic
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4C2×#55211yescharacteristic
1150C4#349211yescharacteristic
1151C4#350911yescharacteristic
1152C4#354411yescharacteristic
1153C2—42no—
1154C2—161no—
1155C2#5931211yescharacteristic
1156C2#6125511yescharacteristic
1157C2#6127111yescharacteristic
1158C2#6140311yescharacteristic
1159C2#6142111yescharacteristic
1160C2#6248311yescharacteristic
1161C2#6249811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59330C2semidirect
3. #32381C2semidirect
4. #32379C2semidirect
5. #32378C2semidirect
6. #32377C2semidirect
7. #28840C2semidirect
8. #28837C2semidirect
9. #28832C2semidirect
10. #28275C2semidirect
11. #28025C2semidirect
12. #28010C2semidirect
16. #27647C2semidirect
17. #26105C2semidirect
18. #26099C2semidirect
19. #25073C2semidirect
20. #25071C2semidirect
23. #24590C2semidirect
24. #24590C2semidirect
25. #22820C2semidirect
26. #22730C2semidirect
27. #22623C2semidirect
28. #22621C2semidirect
29. #21600C2semidirect
31. #20800C2semidirect

Maximal subgroups

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

subgroupindex
#593302
#593022
#323812
#323792
#323782
#323772
#288402
#288372
#288322
#282752
#280252
#280102
#279472
#276502
#276472
#261052
#260992
#250732
#250712
#245992
#245972
#245902
#228202
#227302
#226232
#226212
#216002
#215402
#208002