Finite Group Databasebeta

← #6602538

Subgroups — #6602538

Order 512.

1680 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39066C211yesmaximal, characteristic, complemented
2#34284C211yesmaximal, characteristic, complemented
3#33102C211yesmaximal, characteristic, complemented
4#33080C211yesmaximal, characteristic, complemented
5#33039C211yesmaximal, characteristic, complemented
6#29564C211yesmaximal, characteristic, complemented
7#29542C211yesmaximal, characteristic, complemented
8#29450C211yesmaximal, characteristic, complemented
9#29366C211yesmaximal, characteristic, complemented
10#27130C211yesmaximal, characteristic, complemented
11#27090C211yesmaximal, characteristic, complemented
12#27014C211yesmaximal, characteristic, complemented
13#26906C211yesmaximal, characteristic, complemented
14#26709C211yesmaximal, characteristic, complemented
15#26705C211yesmaximal, characteristic, complemented
16#26608C211yesmaximal, characteristic, complemented
17#26597C211yesmaximal, characteristic, complemented
18#26423C211yesmaximal, characteristic, complemented
19#26360C211yesmaximal, characteristic, complemented
20#25513C211yesmaximal, characteristic, complemented
21#25097C211yesmaximal, characteristic
22#25080C211yesmaximal, characteristic, complemented
23#23945C211yesmaximal, characteristic, complemented
24#23135C211yesmaximal, characteristic, complemented
25#23039C211yesmaximal, characteristic, complemented
26#22884C211yesmaximal, characteristic, complemented
27#22858C211yesmaximal, characteristic, complemented
28#22598C211yesmaximal, characteristic, complemented
29#21503C211yesmaximal, characteristic, complemented
30#21131C211yesmaximal, characteristic, complemented
31#21063C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#479C2211yescharacteristic, complemented
34C2×#469C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#442C2211yescharacteristic, complemented
42C2×C4×SD16C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C22×#102C2211yescharacteristic
46#2860C2211yescharacteristic
47#2752—21no—
48#2705—21no—
49#2685—21no—
50#2685—21no—
51#2641C2211yescharacteristic
52#2624C2211yescharacteristic
53#2602—21no—
54#2534—21no—
55#2512C2211yescharacteristic
56#2467—21no—
57#2454C2211yescharacteristic
58#2445C2211yescharacteristic
59#2445C2211yescharacteristic
60#2441C2211yescharacteristic
61#2433C2211yescharacteristic
62#2418—21no—
63#2373—21no—
64#2373—21no—
65#2372—21no—
66#2369C2211yescharacteristic, complemented
67#2367—21no—
68#2367C2211yescharacteristic, complemented
69#2367C2211yescharacteristic, complemented
70#2365C2211yescharacteristic, complemented
71#2363C2211yescharacteristic
72#2363C2211yescharacteristic
73#2362C2211yescharacteristic
74#2361C2211yescharacteristic
75#2360C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77#2335—21no—
78#2332—21no—
79#2319C2211yescharacteristic
80#2319C2211yescharacteristic, complemented
81#2309C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×C22⋊Q8—21no—
84C4×#123—21no—
85#2298C2211yescharacteristic
86#2295C2211yescharacteristic, complemented
87#2276C2211yescharacteristic, complemented
88#2274C2211yescharacteristic
89C42×D4C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2067C2211yescharacteristic, complemented
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2059C2211yescharacteristic, complemented
99#2058C2211yescharacteristic, complemented
100#2055C2211yescharacteristic
101#2054C2211yescharacteristic
102#2042C2211yescharacteristic, complemented
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2025C2211yescharacteristic, complemented
106#2023C2211yescharacteristic
107#2023C2211yescharacteristic
108#2023C2211yescharacteristic, complemented
109#2014C2211yescharacteristic
110#2012C2211yescharacteristic
111#2012C2211yescharacteristic
112#2012C2211yescharacteristic, complemented
113#2011C2211yescharacteristic
114#1989C2211yescharacteristic, complemented
115#1982C2211yescharacteristic
116#1982C2211yescharacteristic
117#1973C2211yescharacteristic
118#1972C2211yescharacteristic
119#1970C2211yescharacteristic, complemented
120#1948C2211yescharacteristic, complemented
121#1944C2211yescharacteristic, complemented
122#1936C2211yescharacteristic
123#1936C2211yescharacteristic, complemented
124#1935C2211yescharacteristic, complemented
125#1934C2211yescharacteristic
126#1926C2211yescharacteristic
127#1926C2211yescharacteristic
128#1926C2211yescharacteristic
129#1926C2211yescharacteristic
130#1926C2211yescharacteristic
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic, complemented
135#1926C2211yescharacteristic, complemented
136#1926C2211yescharacteristic, complemented
137#1926C2211yescharacteristic, complemented
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic, complemented
143#1925C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1917C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1894C2211yescharacteristic
157#1893C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic, complemented
163#1880C2211yescharacteristic, complemented
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic, complemented
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic, complemented
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1874C2211yescharacteristic
175#1873C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1839C2211yescharacteristic, complemented
189#1832C2211yescharacteristic, complemented
190#1818C2211yescharacteristic
191#1802C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1767C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1746C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#542—24no—
213#542—24no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×C4×Q8—21no—
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×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C42—21no—
251#479—42no—
252#469—24no—
253#465—24no—
254#460—42no—
255#459—24no—
256#450—24no—
257#447—24no—
258#442—42no—
259#442—42no—
260C4×SD16—24no—
261#428—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—24no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102—42no—
283C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#399—21no—
313#399—21no—
314#399—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#392—21no—
331#392—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388D411yescharacteristic
386#388D411yescharacteristic
387#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387D411yescharacteristic
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#379—21no—
420#379—21no—
421#379—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454#376—21no—
455#376C2311yescharacteristic
456C43C2311yescharacteristic
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
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
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—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555#127—22no—
556#127—41no—
557#127—41no—
558#127—41no—
559#126—28no—
560#126—82no—
561#126—82no—
562#125—41no—
563#125—41no—
564#124—28no—
565#124—22no—
566#124—22no—
567#123—28no—
568#123—82no—
569#123—82no—
570C22⋊Q8—28no—
571C22⋊Q8—22no—
572C22⋊Q8#4114yes—
573#121—22no—
574#121—22no—
575#121—22no—
576#121#4114yes—
577#120—82no—
578#120—82no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—82no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—82no—
599C4×D4—82no—
600C4×D4—82no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—41no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
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×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—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×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—82no—
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—82no—
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—41no—
719#107—41no—
720#106—22no—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—41no—
726#106—41no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102#4114yes—
759C22⋊C8—22no—
760C22⋊C8—22no—
761#97—41no—
762#97—41no—
763#97—41no—
764C4×C8—22no—
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#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—42no—
805C24—42no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C2×Q8—24no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8C2×#4112yes—
821C2×D4—24no—
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—21no—
832C2×D4—21no—
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—44no—
845C2×D4—44no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—82no—
854C2×D4—82no—
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×D4—81no—
868C2×D4C2×#4112yes—
869C2×D4C2×#4112yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—24no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
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—81no—
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×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
921C22×C4C2×#4112yes—
922C22×C4C2511yescharacteristic
923SD16—44no—
924SD16—82no—
925SD16—82no—
926D8—44no—
927D8—44no—
928D8—82no—
929M16—44no—
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—21no—
952C2×C8—21no—
953C2×C8—82no—
954C2×C8C2×#4112yes—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
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—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4C2×#4112yes—
999C4⋊C4C2×#4112yes—
1000C4⋊C4C2×#4112yes—
1001C4⋊C4H(5,𝔽2)12yes—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
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⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C42—24no—
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—41no—
1063C42—41no—
1064C42—41no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
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—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23#52512yes—
1120C23C23×D411yescharacteristic
1121Q8—22no—
1122Q8—22no—
1123Q8—41no—
1124Q8—41no—
1125Q8—84no—
1126D4—22no—
1127D4—22no—
1128D4—22no—
1129D4—22no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—162no—
1147D4—162no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
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—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
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—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4#52512yes—
1234C2×C4#57712yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
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—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—168no—
1285C22C2×#52511yescharacteristic
1286C22D4×#4111yescharacteristic
1287C22#348811yescharacteristic
1288C22C2×#57711yescharacteristic
1289C22#358511yescharacteristic
1290C22#358511yescharacteristic
1291C22#358511yescharacteristic
1292C4—22no—
1293C4—22no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4#347511yescharacteristic
1318C4#348111yescharacteristic
1319C4#351411yescharacteristic
1320C4#352111yescharacteristic
1321C2—42no—
1322C2—82no—
1323C2—82no—
1324C2—161no—
1325C2—161no—
1326C2#3622611yescharacteristic
1327C2#6057411yescharacteristic
1328C2#6059311yescharacteristic
1329C2#6150411yescharacteristic
1330C2#6152211yescharacteristic
1331C2#6203511yescharacteristic
1332C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25097C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39066C2semidirect
2. #34284C2semidirect
3. #33102C2semidirect
4. #33080C2semidirect
5. #33039C2semidirect
6. #29564C2semidirect
7. #29542C2semidirect
8. #29450C2semidirect
9. #29366C2semidirect
10. #27130C2semidirect
11. #27090C2semidirect
12. #27014C2semidirect
13. #26906C2semidirect
14. #26709C2semidirect
15. #26705C2semidirect
16. #26608C2semidirect
17. #26597C2semidirect
18. #26423C2semidirect
19. #26360C2semidirect
20. #25513C2semidirect
22. #25080C2semidirect
23. #23945C2semidirect
24. #23135C2semidirect
25. #23039C2semidirect
26. #22884C2semidirect
27. #22858C2semidirect
28. #22598C2semidirect
29. #21503C2semidirect
30. #21131C2semidirect
31. #21063C2semidirect
33. C2×#479C22semidirect
41. C2×#442C22semidirect
66. #2369C22semidirect
68. #2367C22semidirect
69. #2367C22semidirect
70. #2365C22semidirect
80. #2319C22semidirect
86. #2295C22semidirect
87. #2276C22semidirect
89. C42×D4C22semidirect
90. #2099C22semidirect
91. #2096C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2068C22semidirect
95. #2067C22semidirect
98. #2059C22semidirect
99. #2058C22semidirect
102. #2042C22semidirect
105. #2025C22semidirect
108. #2023C22semidirect
112. #2012C22semidirect
114. #1989C22semidirect
119. #1970C22semidirect
120. #1948C22semidirect
121. #1944C22semidirect
123. #1936C22semidirect
124. #1935C22semidirect
134. #1926C22semidirect
135. #1926C22semidirect
136. #1926C22semidirect
137. #1926C22semidirect
142. #1925C22semidirect
143. #1925C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1917C22semidirect
153. #1917C22semidirect
154. #1917C22semidirect
155. #1916C22semidirect
162. #1880C22semidirect
163. #1880C22semidirect
169. #1879C22semidirect
171. #1877C22semidirect
176. #1865C22semidirect
177. #1865C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
183. #1862C22semidirect
188. #1839C22semidirect
189. #1832C22semidirect
191. #1802C22semidirect
192. C4×#106C22semidirect
193. #1767C22semidirect
194. #1763C22semidirect
197. #1762C22semidirect
200. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#390662
#342842
#331022
#330802
#330392
#295642
#295422
#294502
#293662
#271302
#270902
#270142
#269062
#267092
#267052
#266082
#265972
#264232
#263602
#255132
#250972
#250802
#239452
#231352
#230392
#228842
#228582
#225982
#215032
#211312
#210632