Finite Group Databasebeta

← #7224343

Subgroups — #7224343

Order 512.

1582 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45997C211yesmaximal, characteristic, complemented
2#36239C211yesmaximal, characteristic, complemented
3#33030C211yesmaximal, characteristic, complemented
4#33024C211yesmaximal, characteristic, complemented
5#32823C211yesmaximal, characteristic, complemented
6#32823C211yesmaximal, characteristic, complemented
7#32096C211yesmaximal, characteristic, complemented
8#32094C211yesmaximal, characteristic, complemented
9#32080C211yesmaximal, characteristic, complemented
10#32078C211yesmaximal, characteristic, complemented
11#31891C211yesmaximal, characteristic, complemented
12#31886C211yesmaximal, characteristic, complemented
13#31875C211yesmaximal, characteristic, complemented
14#31870C211yesmaximal, characteristic, complemented
15#31598C211yesmaximal, characteristic, complemented
16#31594C211yesmaximal, characteristic, complemented
17#31577C211yesmaximal, characteristic, complemented
18#31573C211yesmaximal, characteristic, complemented
19#26392C211yesmaximal, characteristic, complemented
20#26388C211yesmaximal, characteristic, complemented
21#26380C211yesmaximal, characteristic, complemented
22#26368C211yesmaximal, characteristic, complemented
23#26178C211yesmaximal, characteristic, complemented
24#26178C211yesmaximal, characteristic, complemented
25#26162C211yesmaximal, characteristic, complemented
26#26162C211yesmaximal, characteristic, complemented
27#24744C211yesmaximal, characteristic, complemented
28#24744C211yesmaximal, characteristic, complemented
29#24726C211yesmaximal, characteristic, complemented
30#24726C211yesmaximal, characteristic, complemented
31#23370C211yesmaximal, characteristic, complemented
32C2×#562—21no—
33C2×#476C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#459C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45#2864C2211yescharacteristic
46#2858C2211yescharacteristic
47#2858C2211yescharacteristic
48#2851—21no—
49#2819—21no—
50#2682—21no—
51#2682—21no—
52#2676—21no—
53#2676—21no—
54#2676—21no—
55#2676—21no—
56#2570C2211yescharacteristic
57#2570C2211yescharacteristic
58#2569—21no—
59#2569—21no—
60#2541C2211yescharacteristic
61#2541C2211yescharacteristic
62#2541C2211yescharacteristic
63#2541C2211yescharacteristic
64#2509C2211yescharacteristic
65#2508C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506C2211yescharacteristic
68#2505—21no—
69#2505—21no—
70#2473—21no—
71#2473—21no—
72#2452C2211yescharacteristic
73#2452C2211yescharacteristic
74#2452C2211yescharacteristic
75#2452C2211yescharacteristic
76#2445C2211yescharacteristic
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic
80#2349C2211yescharacteristic
81#2349C2211yescharacteristic
82#2349C2211yescharacteristic
83#2349C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic
86C4×#125C2211yescharacteristic
87C2×#387—21no—
88C42×D4C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2087C2211yescharacteristic
100#2087C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2084C2211yescharacteristic
104#2083C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2041C2211yescharacteristic
126#2041C2211yescharacteristic
127#2041C2211yescharacteristic
128#2041C2211yescharacteristic
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic
131#2041C2211yescharacteristic
132#2041C2211yescharacteristic
133#2041C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2041C2211yescharacteristic
137#1988C2211yescharacteristic
138#1987C2211yescharacteristic
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic
141#1961C2211yescharacteristic
142#1961C2211yescharacteristic
143#1957C2211yescharacteristic
144#1957C2211yescharacteristic
145#1944C2211yescharacteristic
146#1943C2211yescharacteristic
147#1942C2211yescharacteristic
148#1941C2211yescharacteristic
149#1940C2211yescharacteristic
150#1940C2211yescharacteristic
151#1939C2211yescharacteristic
152#1939C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1879C2211yescharacteristic
183#1879C2211yescharacteristic
184#1879C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic
190#1864C2211yescharacteristic
191#1862C2211yescharacteristic
192#1862C2211yescharacteristic
193#1862C2211yescharacteristic
194#1862C2211yescharacteristic
195#1862C2211yescharacteristic
196#1862C2211yescharacteristic
197#1831C2211yescharacteristic
198#1831C2211yescharacteristic
199#1804C2211yescharacteristic
200#1804C2211yescharacteristic
201#1802C2211yescharacteristic
202#1802C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207#562—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#125—21no—
217C2×#125D411yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4—21no—
251C22×C42—21no—
252#476—42no—
253#474—42no—
254#459—42no—
255#459—42no—
256#459—42no—
257#459—42no—
258#459—42no—
259#459—42no—
260#442—42no—
261#442—42no—
262C4×D8—42no—
263C4×D8—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389D411yescharacteristic
375#389D411yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387D411yescharacteristic
405#387D411yescharacteristic
406#387D411yescharacteristic
407#387D411yescharacteristic
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382D411yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
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×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C2×#95—21no—
455C2×#95—21no—
456C2×#95—21no—
457C2×#95—21no—
458C43C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C2×D8—22no—
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#127—41no—
546#127—41no—
547#127—41no—
548#127—41no—
549#127—41no—
550#127—41no—
551#127—41no—
552#127—41no—
553#127—41no—
554#127—41no—
555#127—41no—
556#127—41no—
557#125—24no—
558#125—82no—
559#124—44no—
560#124—44no—
561#124—82no—
562#124—82no—
563#123—44no—
564#123—44no—
565#123—44no—
566#123—44no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571#121—44no—
572#121—44no—
573#121—44no—
574#121—44no—
575#121—82no—
576#121—82no—
577#121—82no—
578#121—82no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
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—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—82no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
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—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—82no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#97—41no—
751#97—41no—
752C4×C8—41no—
753C4×C8—41no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4H(5,𝔽2)12yes—
868C2×D4H(5,𝔽2)12yes—
869C2×D42−1+412yes—
870C22×C4—21no—
871C22×C4—24no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2511yescharacteristic
929D8—44no—
930D8—44no—
931D8—44no—
932D8—44no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4AGL(1,ℤ/8)14yes—
1012C4⋊C42−1+412yes—
1013C22⋊C4—24no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C42—22no—
1049C42—22no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—41no—
1065C42—41no—
1066C42—42no—
1067C42—81no—
1068C42—81no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23C23×D411yescharacteristic
1105Q8—162no—
1106Q8—162no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—162no—
1127D4—162no—
1128D4—162no—
1129D4—162no—
1130D4—162no—
1131D4—162no—
1132D4—162no—
1133D4—162no—
1134D4—162no—
1135D4—162no—
1136D4—162no—
1137D4—162no—
1138D4#56214yescomplemented
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4C2×AGL(1,ℤ/8)12yes—
1222C2×C4C2×AGL(1,ℤ/8)12yes—
1223C2×C4C2×AGL(1,ℤ/8)12yes—
1224C2×C4#57612yes—
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4C2×H(5,𝔽2)11yescharacteristic
1227C2×C4C2×2−1+411yescharacteristic
1228C2×C4C2×2−1+411yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C22—24no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22#348611yescharacteristic
1275C22#348811yescharacteristic
1276C22#348811yescharacteristic
1277C22C22×AGL(1,ℤ/8)11yescharacteristic
1278C22C2×#57611yescharacteristic
1279C22#358411yescharacteristic
1280C22#358511yescharacteristic
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4C2×#56211yescharacteristic
1307C4#355311yescharacteristic
1308C4#355911yescharacteristic
1309C4#355911yescharacteristic
1310C2—44no—
1311C2—161no—
1312C2—161no—
1313C2—161no—
1314C2—161no—
1315C2#4597811yescharacteristic
1316C2#6184011yescharacteristic
1317C2#6184711yescharacteristic
1318C2#6195911yescharacteristic
1319C2#6197911yescharacteristic
1320C2#6204711yescharacteristic
1321C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45997C2semidirect
2. #36239C2semidirect
3. #33030C2semidirect
4. #33024C2semidirect
5. #32823C2semidirect
6. #32823C2semidirect
7. #32096C2semidirect
8. #32094C2semidirect
9. #32080C2semidirect
10. #32078C2semidirect
11. #31891C2semidirect
12. #31886C2semidirect
13. #31875C2semidirect
14. #31870C2semidirect
15. #31598C2semidirect
16. #31594C2semidirect
17. #31577C2semidirect
18. #31573C2semidirect
19. #26392C2semidirect
20. #26388C2semidirect
21. #26380C2semidirect
22. #26368C2semidirect
23. #26178C2semidirect
24. #26178C2semidirect
25. #26162C2semidirect
26. #26162C2semidirect
27. #24744C2semidirect
28. #24744C2semidirect
29. #24726C2semidirect
30. #24726C2semidirect
31. #23370C2semidirect
1138. D4#562semidirect

Maximal subgroups

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

subgroupindex
#459972
#362392
#330302
#330242
#328232
#320962
#320942
#320802
#320782
#318912
#318862
#318752
#318702
#315982
#315942
#315772
#315732
#263922
#263882
#263802
#263682
#261782
#261622
#247442
#247262
#233702