Finite Group Databasebeta

← #7614695

Subgroups — #7614695

Order 512.

1623 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59567C211yesmaximal, characteristic, complemented
2#59424C211yesmaximal, characteristic, complemented
3#32673C211yesmaximal, characteristic, complemented
4#32655C211yesmaximal, characteristic, complemented
5#32525C211yesmaximal, characteristic, complemented
6#31210C211yesmaximal, characteristic, complemented
7#28900C211yesmaximal, characteristic, complemented
8#28899C211yesmaximal, characteristic, complemented
9#28886C211yesmaximal, characteristic, complemented
10#28882C211yesmaximal, characteristic, complemented
11#28362C211yesmaximal, characteristic, complemented
12#28361C211yesmaximal, characteristic, complemented
13#28122C211yesmaximal, characteristic, complemented
14#28120C211yesmaximal, characteristic, complemented
15#27507C211yesmaximal, characteristic, complemented
16#27502C211yesmaximal, characteristic, complemented
17#26615C211yesmaximal, characteristic, complemented
18#26614C211yesmaximal, characteristic, complemented
19#25296C211yesmaximal, characteristic, complemented
20#25293C211yesmaximal, characteristic, complemented
21#24598C211yesmaximal, characteristic, complemented
22#24590C211yesmaximal, characteristic, complemented
23#24373C211yesmaximal, characteristic
24#24367C211yesmaximal, characteristic
25#23109C211yesmaximal, characteristic, complemented
26#23109C211yesmaximal, characteristic, complemented
27#22584C211yesmaximal, characteristic, complemented
28#22578C211yesmaximal, characteristic, complemented
29#21596C211yesmaximal, characteristic, complemented
30#21539C211yesmaximal, characteristic, complemented
31#21236C211yesmaximal, characteristic
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×C8×Q8C2211yescharacteristic, complemented
43C2×#441C2211yescharacteristic, complemented
44C2×#428C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×C4×M16C2211yescharacteristic
48#2786—21no—
49#2782—21no—
50#2746—21no—
51#2740—21no—
52#2601—21no—
53#2592C2211yescharacteristic
54#2580C2211yescharacteristic, complemented
55#2578—21no—
56#2575—21no—
57#2568C2211yescharacteristic, complemented
58#2560—21no—
59#2538C2211yescharacteristic
60#2527—21no—
61#2514C2211yescharacteristic, complemented
62#2512C2211yescharacteristic
63#2512C2211yescharacteristic
64#2511C2211yescharacteristic, complemented
65#2505—21no—
66#2502C2211yescharacteristic
67#2499C2211yescharacteristic
68#2480—21no—
69#2480—21no—
70#2477—21no—
71#2448C2211yescharacteristic
72#2447C2211yescharacteristic
73#2447C2211yescharacteristic, complemented
74#2446C2211yescharacteristic, complemented
75#2437—21no—
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2367C2211yescharacteristic
79#2367C2211yescharacteristic, complemented
80#2354C2211yescharacteristic
81#2354C2211yescharacteristic, complemented
82#2346C2211yescharacteristic
83#2345C2211yescharacteristic
84#2343—21no—
85#2342—21no—
86#2339C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×C22⋊Q8C2211yescharacteristic
91#2297C2211yescharacteristic
92C2×#390C2211yescharacteristic
93#2096C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic, complemented
116#2054C2211yescharacteristic
117#2016C2211yescharacteristic, complemented
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic, complemented
123#2013C2211yescharacteristic
124#2012C2211yescharacteristic
125#1984C2211yescharacteristic, complemented
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1971C2211yescharacteristic, complemented
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1969C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic, complemented
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1956C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1948C2211yescharacteristic, complemented
145#1948C2211yescharacteristic, complemented
146#1948C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic, complemented
166#1925C2211yescharacteristic
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic, complemented
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1851C2211yescharacteristic
185#1825C2211yescharacteristic
186#1823C2211yescharacteristic
187#1809C2211yescharacteristic
188#1797C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8D411yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C42C2311yescharacteristic
244#485—42no—
245#483—42no—
246#470—24no—
247#463—24no—
248#463—24no—
249#463—42no—
250#461—42no—
251#452—42no—
252#450—42no—
253C8×Q8—42no—
254#441—42no—
255#428—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—24no—
274#417—24no—
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C4×M16—42no—
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#401—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#393—21no—
347#393—21no—
348#391—21no—
349#391D411yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389D411yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
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#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387D411yescharacteristic
409#387D411yescharacteristic
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#385D411yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#383—21no—
434#382—21no—
435#382—21no—
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380D411yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376—21no—
471C2×#95—21no—
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527AGL(1,ℤ/8)—416no—
528C2×Q16—22no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8#4114yes—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—22no—
558C2×M16—41no—
559C2×M16—41no—
560C2×M16#4114yes—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#126—82no—
572#126—82no—
573#124—22no—
574#124—22no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—42no—
584C22⋊Q8—82no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599#117—22no—
600#117—22no—
601#117—44no—
602#117—82no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—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—44no—
681C2×C22⋊C4—82no—
682C2×C22⋊C4—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—22no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
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—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755#97—22no—
756#97—41no—
757#97—41no—
758#97—41no—
759C4×C8—22no—
760C4×C8—41no—
761C4×C8—41no—
762C4×C8—41no—
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#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#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822#41—44no—
823#41—44no—
824#41—82no—
825#41—82no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—41no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4C2×#4112yes—
874C2×D4C2×#4112yes—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—22no—
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—21no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C2×#4112yes—
930C22×C4H(5,𝔽2)12yes—
931C22×C4C2511yescharacteristic
932Q16—44no—
933Q16—82no—
934SD16—44no—
935SD16—44no—
936SD16—82no—
937SD16—82no—
938SD16—82no—
939D8—44no—
940D8—44no—
941M16—28no—
942M16—44no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8C2×#4112yes—
964C2×C8C2×#4112yes—
965C2×C8C2×#4112yes—
966C2×C8H(5,𝔽2)12yes—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C22⋊C4—22no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
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—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
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—84no—
1107C23—84no—
1108C23—84no—
1109C23—84no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23#55012yes—
1114C23C23×D411yescharacteristic
1115Q8—44no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4—84no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—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—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
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—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—82no—
1222C2×C4—84no—
1223C2×C4—82no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4#55012yes—
1230C2×C4#57512yes—
1231C2×C4#57712yes—
1232C2×C4C22×#4111yescharacteristic
1233C2×C4C22×#4111yescharacteristic
1234C2×C4C2×H(5,𝔽2)11yescharacteristic
1235C2×C4C2×H(5,𝔽2)11yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C8—22no—
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—168no—
1275C22C2×#55011yescharacteristic
1276C22D4×#4111yescharacteristic
1277C22#349611yescharacteristic
1278C22C2×#57511yescharacteristic
1279C22C2×#57711yescharacteristic
1280C22#358511yescharacteristic
1281C22#358611yescharacteristic
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4#347511yescharacteristic
1309C4#349011yescharacteristic
1310C4#350511yescharacteristic
1311C4#354511yescharacteristic
1312C2—42no—
1313C2—82no—
1314C2—82no—
1315C2—161no—
1316C2#5981911yescharacteristic
1317C2#6140311yescharacteristic
1318C2#6142111yescharacteristic
1319C2#6146411yescharacteristic
1320C2#6154111yescharacteristic
1321C2#6225611yescharacteristic
1322C2#6229411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59567C2semidirect
2. #59424C2semidirect
3. #32673C2semidirect
4. #32655C2semidirect
5. #32525C2semidirect
6. #31210C2semidirect
7. #28900C2semidirect
8. #28899C2semidirect
9. #28886C2semidirect
10. #28882C2semidirect
11. #28362C2semidirect
12. #28361C2semidirect
13. #28122C2semidirect
14. #28120C2semidirect
15. #27507C2semidirect
16. #27502C2semidirect
17. #26615C2semidirect
18. #26614C2semidirect
19. #25296C2semidirect
20. #25293C2semidirect
21. #24598C2semidirect
22. #24590C2semidirect
25. #23109C2semidirect
26. #23109C2semidirect
27. #22584C2semidirect
28. #22578C2semidirect
29. #21596C2semidirect
30. #21539C2semidirect
42. C2×C8×Q8C22semidirect
43. C2×#441C22semidirect
54. #2580C22semidirect
57. #2568C22semidirect
61. #2514C22semidirect
64. #2511C22semidirect
73. #2447C22semidirect
74. #2446C22semidirect
79. #2367C22semidirect
81. #2354C22semidirect
93. #2096C22semidirect
95. #2094C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2067C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
109. #2056C22semidirect
115. #2055C22semidirect
117. #2016C22semidirect
122. #2015C22semidirect
125. #1984C22semidirect
131. #1971C22semidirect
134. #1969C22semidirect
138. #1968C22semidirect
140. #1959C22semidirect
142. #1956C22semidirect
143. #1949C22semidirect
144. #1948C22semidirect
145. #1948C22semidirect
146. #1948C22semidirect
147. #1941C22semidirect
148. #1939C22semidirect
150. #1935C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1933C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
161. #1927C22semidirect
165. #1926C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
173. #1880C22semidirect
177. #1878C22semidirect
180. #1864C22semidirect
182. #1862C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
198. #1762C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#595672
#594242
#326732
#326552
#325252
#312102
#289002
#288992
#288862
#288822
#283622
#283612
#281222
#281202
#275072
#275022
#266152
#266142
#252962
#252932
#245982
#245902
#243732
#243672
#231092
#225842
#225782
#215962
#215392
#212362