Finite Group Databasebeta

← #6565239

Subgroups — #6565239

Order 512.

1617 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36190C211yesmaximal, characteristic, complemented
2#36183C211yesmaximal, characteristic
3#30359C211yesmaximal, characteristic, complemented
4#30357C211yesmaximal, characteristic, complemented
5#29734C211yesmaximal, characteristic
6#29466C211yesmaximal, characteristic, complemented
7#29464C211yesmaximal, characteristic, complemented
8#28981C211yesmaximal, characteristic, complemented
9#28979C211yesmaximal, characteristic, complemented
10#28847C211yesmaximal, characteristic, complemented
11#28845C211yesmaximal, characteristic, complemented
12#28771C211yesmaximal, characteristic, complemented
13#28066C211yesmaximal, characteristic, complemented
14#28062C211yesmaximal, characteristic, complemented
15#27924C211yesmaximal, characteristic, complemented
16#27876C211yesmaximal, characteristic, complemented
17#27875C211yesmaximal, characteristic, complemented
18#27835C211yesmaximal, characteristic, complemented
19#27835C211yesmaximal, characteristic, complemented
20#27697C211yesmaximal, characteristic, complemented
21#27695C211yesmaximal, characteristic, complemented
22#24553C211yesmaximal, characteristic
23#24551C211yesmaximal, characteristic, complemented
24#23756C211yesmaximal, characteristic, complemented
25#23755C211yesmaximal, characteristic, complemented
26C2×#2077C211yesmaximal, characteristic, complemented
27#23126C211yesmaximal, characteristic, complemented
28#22920C211yesmaximal, characteristic, complemented
29#22918C211yesmaximal, characteristic, complemented
30#22609C211yesmaximal, characteristic, complemented
31#20523C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#481C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C22×#106C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2855C2211yescharacteristic
42#2854C2211yescharacteristic
43#2848C2211yescharacteristic
44#2847C2211yescharacteristic
45#2574—21no—
46#2569—21no—
47#2564—21no—
48#2553—21no—
49#2522—21no—
50#2521—21no—
51#2505—21no—
52#2502C2211yescharacteristic
53#2501C2211yescharacteristic
54#2498—21no—
55#2497C2211yescharacteristic
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic
58#2496C2211yescharacteristic
59#2492C2211yescharacteristic
60#2491C2211yescharacteristic
61#2488—21no—
62#2440C2211yescharacteristic
63#2440C2211yescharacteristic
64#2438—21no—
65#2437—21no—
66#2423C2211yescharacteristic
67#2422C2211yescharacteristic
68#2412—21no—
69#2368—21no—
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic
72#2359—21no—
73#2345C2211yescharacteristic
74#2344C2211yescharacteristic
75#2342—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×#121C2211yescharacteristic
78#2285C2211yescharacteristic
79#2285C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83#2100C2211yescharacteristic, complemented
84#2100C2211yescharacteristic, complemented
85#2099C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2096C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2094C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2072C2211yescharacteristic, complemented
108#2071C2211yescharacteristic, complemented
109#2058C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic, complemented
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#1990C2211yescharacteristic, complemented
124#1990C2211yescharacteristic, complemented
125#1990C2211yescharacteristic, complemented
126#1990C2211yescharacteristic, complemented
127#1968C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1941C2211yescharacteristic, complemented
130#1941C2211yescharacteristic, complemented
131#1941C2211yescharacteristic, complemented
132#1941C2211yescharacteristic, complemented
133#1941C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1934C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1926C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1892C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic, complemented
162#1877C2211yescharacteristic, complemented
163#1874C2211yescharacteristic
164#1872C2211yescharacteristic
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1844C2211yescharacteristic, complemented
170#1844C2211yescharacteristic, complemented
171#1834C2211yescharacteristic, complemented
172#1834C2211yescharacteristic, complemented
173#1824C2211yescharacteristic
174#1823C2211yescharacteristic
175#1807C2211yescharacteristic
176#1807C2211yescharacteristic
177#1807C2211yescharacteristic
178#1807C2211yescharacteristic
179#1807C2211yescharacteristic
180C4×#106C2211yescharacteristic, complemented
181C4×#106C2211yescharacteristic, complemented
182C4×#106C2211yescharacteristic, complemented
183C4×#106C2211yescharacteristic, complemented
184C4×#103C2211yescharacteristic, complemented
185C4×#103C2211yescharacteristic, complemented
186C4×#102C2211yescharacteristic, complemented
187C4×#102C2211yescharacteristic, complemented
188C8×C22⋊C4C2211yescharacteristic
189C8×C22⋊C4C2211yescharacteristic
190C8×C22⋊C4C2211yescharacteristic
191C8×C22⋊C4C2211yescharacteristic
192C8×C22⋊C4C2211yescharacteristic
193C8×C22⋊C4C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C4×C22⋊C8C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#551—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#124—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117—21no—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4D411yescharacteristic
244C22×C22⋊C4D411yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#483—24no—
248#481—24no—
249#465—24no—
250C2×#106—24no—
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×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×C22⋊C8—24no—
281C2×C22⋊C8—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
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#399—21no—
305#399—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#396—21no—
315#396—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#393—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#389—21no—
332#389—21no—
333#389—21no—
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#386—21no—
367#386—21no—
368#386—21no—
369#386—21no—
370#386—21no—
371#386—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#382—21no—
391#382—21no—
392#381—21no—
393#381—21no—
394#380—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#379—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4D411yescharacteristic
433C4×C22⋊C4D411yescharacteristic
434C4×C22⋊C4D411yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439C2×#95—21no—
440C2×#95—21no—
441C2×#95D411yescharacteristic
442C2×#95D411yescharacteristic
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#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C25C2×D411yescharacteristic
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—41no—
501C23×C4—41no—
502C23×C4—41no—
503C23×C4—41no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8#4114yes—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#126—44no—
542#126—44no—
543#124—44no—
544#123—44no—
545#123—44no—
546#123—44no—
547#123—44no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—82no—
558#121—22no—
559#121—22no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#120—44no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—44no—
570C4×D4—44no—
571#117—44no—
572#117—44no—
573#117—82no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
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—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—24no—
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⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—44no—
657C2×C22⋊C4—82no—
658C2×C22⋊C4SD1618yescomplemented
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#106—22no—
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715C22⋊C8—22no—
716C22⋊C8—22no—
717C22⋊C8—22no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722C22⋊C8#4114yes—
723C4×C8—41no—
724C4×C8—41no—
725C4×C8—41no—
726C4×C8—41no—
727C4×C8—41no—
728C4×C8—41no—
729C4×C8—41no—
730C4×C8—41no—
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#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775C24—22no—
776C24—22no—
777C24—21no—
778C24—41no—
779C24—41no—
780C24—41no—
781C24—41no—
782C24C2×SD1614yes—
783C24C22×D411yescharacteristic
784C24C22×D411yescharacteristic
785C24C22×D411yescharacteristic
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—81no—
812C2×D4—81no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
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—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
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—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
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—41no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—82no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4—82no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4C2×SD1614yes—
883C22×C4C2×SD1614yes—
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2511yescharacteristic
898SD16—82no—
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—44no—
920C2×C8—82no—
921C2×C8—82no—
922C2×C8—82no—
923C2×C8C2×#4112yes—
924C2×C8C2×#4112yes—
925C2×C8C2×#4112yes—
926C2×C8C2×#4112yes—
927C4⋊C4—21no—
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—42no—
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—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4C2×SD1614yes—
1018C22⋊C4C2×SD1614yes—
1019C22⋊C4C2×SD1614yes—
1020C22⋊C4C2×SD1614yes—
1021C22⋊C4#13514yes—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
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—21no—
1055C23—21no—
1056C23—21no—
1057C23—28no—
1058C23—44no—
1059C23—44no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—82no—
1068C23—82no—
1069C23—82no—
1070C23—82no—
1071C23#53212yes—
1072C23C22×SD1612yes—
1073C23C22×SD1612yes—
1074C23C22×SD1612yes—
1075C23C2×#13512yes—
1076C23C23×D411yescharacteristic
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—162no—
1082Q8—162no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—84no—
1088D4—84no—
1089D4—162no—
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—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
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—44no—
1121C2×C4—44no—
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—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—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—82no—
1176C2×C4—82no—
1177C2×C4—82no—
1178C2×C4—82no—
1179C2×C4—82no—
1180C2×C4—84no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4—162no—
1184C2×C4—162no—
1185C2×C4#53212yes—
1186C2×C4C22×SD1612yes—
1187C2×C4C22×SD1612yes—
1188C2×C4C22×SD1612yes—
1189C2×C4C22×SD1612yes—
1190C2×C4C2×#13512yes—
1191C2×C4C2×#13512yes—
1192C2×C4C22×#4111yescharacteristic
1193C2×C4C22×#4111yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C8—22no—
1199C8—22no—
1200C8—22no—
1201C8—22no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—88no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22#316714yes—
1235C22C2×#53211yescharacteristic
1236C22#348511yescharacteristic
1237C22#348511yescharacteristic
1238C22C23×SD1611yescharacteristic
1239C22C22×#13511yescharacteristic
1240C22#358511yescharacteristic
1241C22#358611yescharacteristic
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4#349111yescharacteristic
1269C4#351011yescharacteristic
1270C4#352111yescharacteristic
1271C4#352111yescharacteristic
1272C2—24no—
1273C2—42no—
1274C2—42no—
1275C2—161no—
1276C2#3601211yescharacteristic
1277C2C2×#316711yescharacteristic
1278C2#6070911yescharacteristic
1279C2#6169511yescharacteristic
1280C2#6169711yescharacteristic
1281C2#6170211yescharacteristic
1282C2#6170311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36190C2semidirect
3. #30359C2semidirect
4. #30357C2semidirect
6. #29466C2semidirect
7. #29464C2semidirect
8. #28981C2semidirect
9. #28979C2semidirect
10. #28847C2semidirect
11. #28845C2semidirect
12. #28771C2semidirect
13. #28066C2semidirect
14. #28062C2semidirect
15. #27924C2semidirect
16. #27876C2semidirect
17. #27875C2semidirect
18. #27835C2semidirect
19. #27835C2semidirect
20. #27697C2semidirect
21. #27695C2semidirect
23. #24551C2semidirect
24. #23756C2semidirect
25. #23755C2semidirect
26. C2×#2077C2semidirect
27. #23126C2semidirect
28. #22920C2semidirect
29. #22918C2semidirect
30. #22609C2semidirect
31. #20523C2semidirect
83. #2100C22semidirect
84. #2100C22semidirect
85. #2099C22semidirect
86. #2099C22semidirect
87. #2096C22semidirect
88. #2096C22semidirect
89. #2094C22semidirect
90. #2094C22semidirect
91. #2084C22semidirect
92. #2084C22semidirect
107. #2072C22semidirect
108. #2071C22semidirect
109. #2058C22semidirect
110. #2058C22semidirect
119. #2024C22semidirect
120. #2023C22semidirect
123. #1990C22semidirect
124. #1990C22semidirect
125. #1990C22semidirect
126. #1990C22semidirect
127. #1968C22semidirect
128. #1968C22semidirect
129. #1941C22semidirect
130. #1941C22semidirect
131. #1941C22semidirect
132. #1941C22semidirect
133. #1941C22semidirect
134. #1941C22semidirect
135. #1934C22semidirect
136. #1934C22semidirect
137. #1934C22semidirect
138. #1934C22semidirect
139. #1933C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1927C22semidirect
144. #1926C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1919C22semidirect
161. #1880C22semidirect
162. #1877C22semidirect
165. #1865C22semidirect
166. #1864C22semidirect
169. #1844C22semidirect
170. #1844C22semidirect
171. #1834C22semidirect
172. #1834C22semidirect
180. C4×#106C22semidirect
181. C4×#106C22semidirect
182. C4×#106C22semidirect
183. C4×#106C22semidirect
184. C4×#103C22semidirect
185. C4×#103C22semidirect
186. C4×#102C22semidirect
187. C4×#102C22semidirect
658. C2×C22⋊C4SD16semidirect

Maximal subgroups

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

subgroupindex
#361902
#361832
#303592
#303572
#297342
#294662
#294642
#289812
#289792
#288472
#288452
#287712
#280662
#280622
#279242
#278762
#278752
#278352
#276972
#276952
#245532
#245512
#237562
#237552
C2×#20772
#231262
#229202
#229182
#226092
#205232