Finite Group Databasebeta

← #6592765

Subgroups — #6592765

Order 512.

1867 conjugacy classes of subgroups.

The subgroup lattice has 1411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37893C211yesmaximal, characteristic, complemented
2#34292C211yesmaximal, characteristic, complemented
3#33076C211yesmaximal, characteristic, complemented
4#32911C211yesmaximal, characteristic, complemented
5#32904C211yesmaximal, characteristic, complemented
6#29134C211yesmaximal, characteristic, complemented
7#28167C211yesmaximal, characteristic, complemented
8#27684C211yesmaximal, characteristic, complemented
9#27638C211yesmaximal, characteristic, complemented
10#27568C211yesmaximal, characteristic, complemented
11#27557C211yesmaximal, characteristic, complemented
12#27089C211yesmaximal, characteristic, complemented
13#27072C211yesmaximal, characteristic, complemented
14#26681C211yesmaximal, characteristic, complemented
15#26664C211yesmaximal, characteristic, complemented
16#26229C211yesmaximal, characteristic, complemented
17#26225C211yesmaximal, characteristic, complemented
18#24909C211yesmaximal, characteristic, complemented
19#24897C211yesmaximal, characteristic, complemented
20#24758C211yesmaximal, characteristic, complemented
21#24668C211yesmaximal, characteristic, complemented
22#24444C211yesmaximal, characteristic, complemented
23#24444C211yesmaximal, characteristic, complemented
24#23143C211yesmaximal, characteristic, complemented
25#23140C211yesmaximal, characteristic, complemented
26#22878C211yesmaximal, characteristic, complemented
27#22866C211yesmaximal, characteristic, complemented
28#22755C211yesmaximal, characteristic, complemented
29#21513C211yesmaximal, characteristic, complemented
30#20744C211yesmaximal, characteristic, complemented
31#20649C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#460C2211yescharacteristic, complemented
38C2×#459C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic
46C2×#433C2211yescharacteristic
47C2×#423C2211yescharacteristic, complemented
48C2×#417C2211yescharacteristic
49C2×#417C2211yescharacteristic
50#2856C2211yescharacteristic, complemented
51#2761—21no—
52#2761—21no—
53#2753—21no—
54#2753—21no—
55#2647C2211yescharacteristic, complemented
56#2619C2211yescharacteristic
57#2543—21no—
58#2543—21no—
59#2513C2211yescharacteristic, complemented
60#2513C2211yescharacteristic, complemented
61#2444—21no—
62#2444—21no—
63#2420C2211yescharacteristic
64#2420C2211yescharacteristic
65#2416C2211yescharacteristic
66#2416C2211yescharacteristic
67#2367C2211yescharacteristic
68#2363C2211yescharacteristic
69#2362C2211yescharacteristic
70#2361—21no—
71#2361C2211yescharacteristic, complemented
72#2361C2211yescharacteristic, complemented
73#2359—21no—
74#2358—21no—
75#2354C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2342—21no—
78#2339C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2328C2211yescharacteristic, complemented
81#2326C2211yescharacteristic
82#2325—21no—
83#2323C2211yescharacteristic
84#2321—21no—
85#2314C2211yescharacteristic
86C4×#123—21no—
87C4×#121C2211yescharacteristic
88#2290C2211yescharacteristic
89C2×#388—21no—
90C2×#382C2211yescharacteristic, complemented
91#2275C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2099C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2012C2211yescharacteristic
113#2012C2211yescharacteristic
114#2000C2211yescharacteristic
115#2000C2211yescharacteristic
116#1982C2211yescharacteristic, complemented
117#1973C2211yescharacteristic, complemented
118#1968C2211yescharacteristic, complemented
119#1949C2211yescharacteristic, complemented
120#1949C2211yescharacteristic, complemented
121#1948C2211yescharacteristic, complemented
122#1936C2211yescharacteristic
123#1936C2211yescharacteristic, complemented
124#1935C2211yescharacteristic, complemented
125#1934C2211yescharacteristic
126#1934C2211yescharacteristic, complemented
127#1933C2211yescharacteristic, complemented
128#1928C2211yescharacteristic, complemented
129#1927C2211yescharacteristic, complemented
130#1926C2211yescharacteristic, complemented
131#1925C2211yescharacteristic, complemented
132#1924C2211yescharacteristic
133#1923C2211yescharacteristic
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1919C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1919C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1917C2211yescharacteristic, complemented
141#1916C2211yescharacteristic, complemented
142#1895C2211yescharacteristic, complemented
143#1895C2211yescharacteristic, complemented
144#1880C2211yescharacteristic, complemented
145#1880C2211yescharacteristic, complemented
146#1879C2211yescharacteristic
147#1879C2211yescharacteristic
148#1879C2211yescharacteristic
149#1879C2211yescharacteristic
150#1879C2211yescharacteristic
151#1879C2211yescharacteristic
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1877C2211yescharacteristic, complemented
157#1877C2211yescharacteristic, complemented
158#1875C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic, complemented
161#1875C2211yescharacteristic, complemented
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1870C2211yescharacteristic
165#1870C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1862C2211yescharacteristic
170#1853C2211yescharacteristic, complemented
171#1852C2211yescharacteristic, complemented
172#1832C2211yescharacteristic, complemented
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1805C2211yescharacteristic, complemented
176#1805C2211yescharacteristic, complemented
177#1805C2211yescharacteristic, complemented
178#1805C2211yescharacteristic, complemented
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1798C2211yescharacteristic
189#1797C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1768C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#546—24no—
214#546—24no—
215C2×#127C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230#518—24no—
231#518—42no—
232C4×#41—24no—
233C4×#41—42no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C42—21no—
265C22×C42C2311yescharacteristic
266#469—24no—
267#469—24no—
268#460—42no—
269#459—24no—
270#459—42no—
271#449—24no—
272#449—24no—
273#447—42no—
274#447—42no—
275#442—42no—
276C4×D8—42no—
277#433—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284#423—42no—
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#417—42no—
292#417—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#396—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#392—21no—
350#392—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
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#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
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#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386D411yescharacteristic
417#386D411yescharacteristic
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#381—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#376C2311yescharacteristic
461C2×#95—21no—
462C2×#95—21no—
463C2×#95—21no—
464C2×#95—21no—
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41#4114yes—
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2×D411yescharacteristic
540C23×C4C2×D411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575#127—22no—
576#127—22no—
577#124—22no—
578#124—22no—
579#123—28no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—82no—
593#121—82no—
594#121—82no—
595#121—82no—
596#121#4114yes—
597#120—28no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—44no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—82no—
626C4×D4—82no—
627C4×D4—82no—
628C4×D4#4114yes—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—44no—
634#117—41no—
635#117—41no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—82no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C22⋊C4—28no—
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—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—44no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—82no—
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—44no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#107—41no—
743#107—41no—
744#106—22no—
745#106—22no—
746#106—41no—
747#106—41no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754#103—22no—
755#103—22no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—41no—
789#97—41no—
790C4×C8—41no—
791C4×C8—41no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—24no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—28no—
843#41—44no—
844#41—44no—
845#41—44no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8C2×#4112yes—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4C2×#4112yes—
907C2×D4C2×#4112yes—
908C2×D4C2×#4112yes—
909C2×D4H(5,𝔽2)12yes—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C2×#4112yes—
987C22×C4C2×#4112yes—
988C22×C4C2511yescharacteristic
989SD16—82no—
990SD16—82no—
991D8—44no—
992D8—44no—
993D8—82no—
994D8—82no—
995M16—82no—
996M16—82no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C4⋊C4—24no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4C2×#4112yes—
1062C4⋊C4C2×#4112yes—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C42—22no—
1111C42—22no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C42—81no—
1128C42—81no—
1129C42C2×#4112yes—
1130C42H(5,𝔽2)12yes—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—22no—
1136C23—22no—
1137C23—21no—
1138C23—22no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—21no—
1148C23—48no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—84no—
1174C23—84no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23#52512yes—
1180C23C23×D411yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—41no—
1184Q8—41no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—48no—
1191D4—48no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—82no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4#55314yes—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—48no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—82no—
1290C2×C4—82no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4#52512yes—
1303C2×C4#54612yes—
1304C2×C4#54612yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C22×#4111yescharacteristic
1307C2×C4C22×#4111yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—24no—
1321C22—22no—
1322C22—22no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—168no—
1362C22C2×#52511yescharacteristic
1363C22C2×#54611yescharacteristic
1364C22#348811yescharacteristic
1365C22#358411yescharacteristic
1366C22#358511yescharacteristic
1367C22#358511yescharacteristic
1368C22#358511yescharacteristic
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—42no—
1382C4—41no—
1383C4—41no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4C2×#55311yescharacteristic
1394C4#347511yescharacteristic
1395C4#350511yescharacteristic
1396C4#351911yescharacteristic
1397C2—42no—
1398C2—44no—
1399C2—81no—
1400C2—82no—
1401C2—161no—
1402C2—161no—
1403C2#3615711yescharacteristic
1404C2#6056811yescharacteristic
1405C2#6060111yescharacteristic
1406C2#6117911yescharacteristic
1407C2#6118711yescharacteristic
1408C2#6204711yescharacteristic
1409C2#6208811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37893C2semidirect
2. #34292C2semidirect
3. #33076C2semidirect
4. #32911C2semidirect
5. #32904C2semidirect
6. #29134C2semidirect
7. #28167C2semidirect
8. #27684C2semidirect
9. #27638C2semidirect
10. #27568C2semidirect
11. #27557C2semidirect
12. #27089C2semidirect
13. #27072C2semidirect
14. #26681C2semidirect
15. #26664C2semidirect
16. #26229C2semidirect
17. #26225C2semidirect
18. #24909C2semidirect
19. #24897C2semidirect
20. #24758C2semidirect
21. #24668C2semidirect
22. #24444C2semidirect
23. #24444C2semidirect
24. #23143C2semidirect
25. #23140C2semidirect
26. #22878C2semidirect
27. #22866C2semidirect
28. #22755C2semidirect
29. #21513C2semidirect
30. #20744C2semidirect
31. #20649C2semidirect
37. C2×#460C22semidirect
47. C2×#423C22semidirect
50. #2856C22semidirect
55. #2647C22semidirect
59. #2513C22semidirect
60. #2513C22semidirect
71. #2361C22semidirect
72. #2361C22semidirect
80. #2328C22semidirect
90. C2×#382C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
94. #2100C22semidirect
95. #2099C22semidirect
100. #2071C22semidirect
101. #2071C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
116. #1982C22semidirect
117. #1973C22semidirect
118. #1968C22semidirect
119. #1949C22semidirect
120. #1949C22semidirect
121. #1948C22semidirect
123. #1936C22semidirect
124. #1935C22semidirect
126. #1934C22semidirect
127. #1933C22semidirect
128. #1928C22semidirect
129. #1927C22semidirect
130. #1926C22semidirect
131. #1925C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1919C22semidirect
137. #1919C22semidirect
138. #1919C22semidirect
139. #1918C22semidirect
140. #1917C22semidirect
141. #1916C22semidirect
142. #1895C22semidirect
143. #1895C22semidirect
144. #1880C22semidirect
145. #1880C22semidirect
156. #1877C22semidirect
157. #1877C22semidirect
160. #1875C22semidirect
161. #1875C22semidirect
170. #1853C22semidirect
171. #1852C22semidirect
172. #1832C22semidirect
175. #1805C22semidirect
176. #1805C22semidirect
177. #1805C22semidirect
178. #1805C22semidirect
185. #1803C22semidirect
189. #1797C22semidirect
192. #1768C22semidirect
195. #1762C22semidirect
198. C4×#102C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#378932
#342922
#330762
#329112
#329042
#291342
#281672
#276842
#276382
#275682
#275572
#270892
#270722
#266812
#266642
#262292
#262252
#249092
#248972
#247582
#246682
#244442
#231432
#231402
#228782
#228662
#227552
#215132
#207442
#206492