Finite Group Databasebeta

← #7085938

Subgroups — #7085938

Order 512.

1605 conjugacy classes of subgroups.

The subgroup lattice has 1311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59476C211yesmaximal, characteristic
2#40224C211yesmaximal, characteristic, complemented
3#32448C211yesmaximal, characteristic, complemented
4#32300C211yesmaximal, characteristic, complemented
5#31661C211yesmaximal, characteristic, complemented
6#31598C211yesmaximal, characteristic, complemented
7#31220C211yesmaximal, characteristic, complemented
8#31004C211yesmaximal, characteristic
9#30909C211yesmaximal, characteristic, complemented
10#30773C211yesmaximal, characteristic, complemented
11#29582C211yesmaximal, characteristic, complemented
12#29195C211yesmaximal, characteristic, complemented
13#28881C211yesmaximal, characteristic, complemented
14#28856C211yesmaximal, characteristic, complemented
15#28540C211yesmaximal, characteristic, complemented
16#28344C211yesmaximal, characteristic
17#27213C211yesmaximal, characteristic, complemented
18#26912C211yesmaximal, characteristic, complemented
19#26566C211yesmaximal, characteristic, complemented
20#26495C211yesmaximal, characteristic, complemented
21#26385C211yesmaximal, characteristic, complemented
22#26098C211yesmaximal, characteristic, complemented
23#25950C211yesmaximal, characteristic, complemented
24#25156C211yesmaximal, characteristic, complemented
25#25041C211yesmaximal, characteristic, complemented
26#24917C211yesmaximal, characteristic, complemented
27#23803C211yesmaximal, characteristic, complemented
28#23292C211yesmaximal, characteristic, complemented
29#23010C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#22152C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#500C2211yescharacteristic, complemented
34C2×#480C2211yescharacteristic
35C2×#475C2211yescharacteristic, complemented
36C2×#474C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2864C2211yescharacteristic, complemented
49#2805—21no—
50#2769—21no—
51#2765—21no—
52#2696—21no—
53#2689—21no—
54#2685—21no—
55#2655—21no—
56#2598—21no—
57#2588—21no—
58#2573—21no—
59#2570C2211yescharacteristic, complemented
60#2568C2211yescharacteristic, complemented
61#2542C2211yescharacteristic
62#2514C2211yescharacteristic, complemented
63#2503C2211yescharacteristic
64#2496C2211yescharacteristic
65#2491C2211yescharacteristic
66#2472—21no—
67#2471—21no—
68#2463—21no—
69#2452C2211yescharacteristic
70#2451C2211yescharacteristic, complemented
71#2446C2211yescharacteristic, complemented
72#2445C2211yescharacteristic
73#2445C2211yescharacteristic
74#2440C2211yescharacteristic
75#2433C2211yescharacteristic
76#2429C2211yescharacteristic
77#2422C2211yescharacteristic
78#2421C2211yescharacteristic
79#2421C2211yescharacteristic
80#2418—21no—
81#2366C2211yescharacteristic
82#2360C2211yescharacteristic
83#2354C2211yescharacteristic
84#2351C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2332—21no—
88C4×C4⋊Q8C2211yescharacteristic, complemented
89C4×#127C2211yescharacteristic
90C4×#126C2211yescharacteristic
91#2293C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic, complemented
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic, complemented
114#2057C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic, complemented
117#2055C2211yescharacteristic, complemented
118#2041C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic, complemented
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2013C2211yescharacteristic
130#2013C2211yescharacteristic, complemented
131#2000C2211yescharacteristic
132#1981C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1961C2211yescharacteristic
140#1961C2211yescharacteristic
141#1961C2211yescharacteristic
142#1949C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1847C2211yescharacteristic, complemented
190#1836C2211yescharacteristic, complemented
191#1808C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1786C2211yescharacteristic
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1767C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#551—48no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#126D411yescharacteristic
219C2×#124—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249#500—42no—
250#480—42no—
251#475—42no—
252#474—42no—
253#465—42no—
254#461—24no—
255#460—24no—
256#450—24no—
257#450—42no—
258#440—42no—
259#440—42no—
260#440—42no—
261#440—42no—
262C4×SD16—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#401—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#395—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#393—21no—
354#393—21no—
355#392—21no—
356#392—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388D411yescharacteristic
402#388D411yescharacteristic
403#388D411yescharacteristic
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
420#387D411yescharacteristic
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#383—21no—
437#383D411yescharacteristic
438#382—21no—
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C43C2311yescharacteristic
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16#4114yes—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#126—24no—
561#126—44no—
562#124—44no—
563#123—44no—
564#123—44no—
565#123—44no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—82no—
574#121—41no—
575#121—41no—
576#120—44no—
577#120—82no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—44no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—44no—
598C4×D4—82no—
599#117—44no—
600#117—44no—
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—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
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⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
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×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—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—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—22no—
701#107—22no—
702#107—22no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
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—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750#97—22no—
751#97—22no—
752#97—41no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—22no—
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#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8C2×#4112yes—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4C2×#4112yes—
872C2×D42−1+412yes—
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—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
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×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
924SD16—44no—
925SD16—44no—
926SD16—44no—
927SD16—44no—
928SD16—44no—
929SD16—82no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
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—82no—
952C2×C8C2×#4112yes—
953C2×C8H(5,𝔽2)12yes—
954C2×C8H(5,𝔽2)12yes—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
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—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
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—42no—
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—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
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—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4AGL(1,ℤ/8)14yes—
1044C42—22no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—41no—
1058C42—41no—
1059C42—41no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—22no—
1074C23—22no—
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—84no—
1095C23—84no—
1096C23—84no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23—162no—
1101C23C2×AGL(1,ℤ/8)12yes—
1102C23C23×D411yescharacteristic
1103Q8—22no—
1104Q8—22no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—162no—
1112Q8—162no—
1113D4—22no—
1114D4—22no—
1115D4—22no—
1116D4—22no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—162no—
1130D4—162no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
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—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
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—41no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4C2×AGL(1,ℤ/8)12yes—
1218C2×C4C2×AGL(1,ℤ/8)12yes—
1219C2×C4C22×#4111yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C2×C4#58511yescharacteristic
1224C2×C4#58511yescharacteristic
1225C8—22no—
1226C8—22no—
1227C8—22no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
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—168no—
1262C22D4×#4111yescharacteristic
1263C22#348911yescharacteristic
1264C22#349811yescharacteristic
1265C22C22×AGL(1,ℤ/8)11yescharacteristic
1266C22#358511yescharacteristic
1267C22#358611yescharacteristic
1268C22#358611yescharacteristic
1269C4—22no—
1270C4—22no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4#350511yescharacteristic
1296C4#352011yescharacteristic
1297C4#353311yescharacteristic
1298C4#353511yescharacteristic
1299C2—42no—
1300C2—82no—
1301C2—82no—
1302C2—161no—
1303C2#4416211yescharacteristic
1304C2#6145211yescharacteristic
1305C2#6151311yescharacteristic
1306C2#6210911yescharacteristic
1307C2#6223211yescharacteristic
1308C2#6244211yescharacteristic
1309C2#6244711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #40224C2semidirect
3. #32448C2semidirect
4. #32300C2semidirect
5. #31661C2semidirect
6. #31598C2semidirect
7. #31220C2semidirect
9. #30909C2semidirect
10. #30773C2semidirect
11. #29582C2semidirect
12. #29195C2semidirect
13. #28881C2semidirect
14. #28856C2semidirect
15. #28540C2semidirect
17. #27213C2semidirect
18. #26912C2semidirect
19. #26566C2semidirect
20. #26495C2semidirect
21. #26385C2semidirect
22. #26098C2semidirect
23. #25950C2semidirect
24. #25156C2semidirect
25. #25041C2semidirect
26. #24917C2semidirect
27. #23803C2semidirect
28. #23292C2semidirect
29. #23010C2semidirect
30. #22854C2semidirect
31. #22152C2semidirect
33. C2×#500C22semidirect
35. C2×#475C22semidirect
44. C2×#440C22semidirect
45. C2×#440C22semidirect
48. #2864C22semidirect
59. #2570C22semidirect
60. #2568C22semidirect
62. #2514C22semidirect
70. #2451C22semidirect
71. #2446C22semidirect
84. #2351C22semidirect
88. C4×C4⋊Q8C22semidirect
92. #2101C22semidirect
93. #2095C22semidirect
94. #2095C22semidirect
95. #2095C22semidirect
97. #2093C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
105. #2073C22semidirect
106. #2072C22semidirect
107. #2068C22semidirect
111. #2067C22semidirect
113. #2065C22semidirect
114. #2057C22semidirect
116. #2055C22semidirect
117. #2055C22semidirect
123. #2024C22semidirect
125. #2023C22semidirect
130. #2013C22semidirect
132. #1981C22semidirect
137. #1973C22semidirect
142. #1949C22semidirect
143. #1947C22semidirect
144. #1947C22semidirect
145. #1944C22semidirect
146. #1943C22semidirect
147. #1943C22semidirect
148. #1940C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
153. #1934C22semidirect
154. #1928C22semidirect
155. #1926C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1918C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
171. #1880C22semidirect
177. #1864C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
184. #1862C22semidirect
188. #1847C22semidirect
189. #1847C22semidirect
190. #1836C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1767C22semidirect
198. #1763C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#594762
#402242
#324482
#323002
#316612
#315982
#312202
#310042
#309092
#307732
#295822
#291952
#288812
#288562
#285402
#283442
#272132
#269122
#265662
#264952
#263852
#260982
#259502
#251562
#250412
#249172
#238032
#232922
#230102
#228542
#221522