Finite Group Databasebeta

← #6598338

Subgroups — #6598338

Order 512.

1899 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3344C211yesmaximal, characteristic
2C2×#3312C211yesmaximal, characteristic
3#36276C211yesmaximal, characteristic
4C4×#552C211yesmaximal, characteristic
5#33114C211yesmaximal, characteristic, complemented
6#33108C211yesmaximal, characteristic, complemented
7#33033C211yesmaximal, characteristic, complemented
8#28660C211yesmaximal, characteristic, complemented
9#28581C211yesmaximal, characteristic, complemented
10#28575C211yesmaximal, characteristic, complemented
11#28209C211yesmaximal, characteristic, complemented
12#28124C211yesmaximal, characteristic, complemented
13#28121C211yesmaximal, characteristic, complemented
14#25467C211yesmaximal, characteristic, complemented
15#25290C211yesmaximal, characteristic, complemented
16#25219C211yesmaximal, characteristic, complemented
17#25206C211yesmaximal, characteristic, complemented
18#25095C211yesmaximal, characteristic, complemented
19#25082C211yesmaximal, characteristic, complemented
20#24698C211yesmaximal, characteristic, complemented
21#24648C211yesmaximal, characteristic, complemented
22#24598C211yesmaximal, characteristic, complemented
23#24580C211yesmaximal, characteristic, complemented
24#24498C211yesmaximal, characteristic, complemented
25#24480C211yesmaximal, characteristic, complemented
26#22698C211yesmaximal, characteristic
27#22497C211yesmaximal, characteristic
28#22425C211yesmaximal, characteristic
29#21506C211yesmaximal, characteristic, complemented
30#21061C211yesmaximal, characteristic, complemented
31C2×#1927C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35#3344—28no—
36#3312—28no—
37C2×#501C2211yescharacteristic
38C2×#491C2211yescharacteristic
39C2×#484C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#483C2211yescharacteristic
43C2×#483C2211yescharacteristic
44C2×#483C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#475C2211yescharacteristic
48C2×#470C2211yescharacteristic
49C2×#470C2211yescharacteristic
50C2×#467C2211yescharacteristic
51C2×#467C2211yescharacteristic
52C2×#462C2211yescharacteristic
53C2×#462C2211yescharacteristic
54C2×#451C2211yescharacteristic
55C2×#451C2211yescharacteristic
56C2×#441C2211yescharacteristic
57C2×#441C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#435C2211yescharacteristic
60C2×#428C2211yescharacteristic
61C22×#106C2211yescharacteristic
62C2×#419C2211yescharacteristic
63C2×#419C2211yescharacteristic
64C22×#103C2211yescharacteristic
65C22×#103C2211yescharacteristic
66#2862C2211yescharacteristic
67#2857C2211yescharacteristic
68#2857C2211yescharacteristic
69#2567C2211yescharacteristic
70#2550—21no—
71#2550—21no—
72#2549—21no—
73#2549—21no—
74#2549—21no—
75#2549—21no—
76#2546C2211yescharacteristic
77#2502C2211yescharacteristic
78#2502C2211yescharacteristic
79#2434C2211yescharacteristic
80#2434C2211yescharacteristic
81#2373—21no—
82#2371—21no—
83#2370C2211yescharacteristic
84#2362C2211yescharacteristic
85#2360C2211yescharacteristic
86#2359—21no—
87#2356C2211yescharacteristic
88#2352C2211yescharacteristic
89#2349—21no—
90#2349—21no—
91#2346C2211yescharacteristic
92#2344C2211yescharacteristic
93#2343—21no—
94C4×C4⋊Q8C2211yescharacteristic
95C4×#125—21no—
96C4×#125C2211yescharacteristic
97C4×#126—21no—
98C4×C22⋊Q8C2211yescharacteristic
99C4×C22⋊Q8C2211yescharacteristic
100C4×#123—21no—
101C2×#391C2211yescharacteristic
102C2×#391C2211yescharacteristic
103C42×Q8C2211yescharacteristic
104C42×D4C2211yescharacteristic
105C4×#117—21no—
106C4×#117C2211yescharacteristic
107C2×C4×C4⋊C4C2211yescharacteristic
108#2084C2211yescharacteristic
109#2084C2211yescharacteristic
110#2083C2211yescharacteristic
111#2083C2211yescharacteristic
112#2072C2211yescharacteristic
113#2072C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2056C2211yescharacteristic
123#2056C2211yescharacteristic
124#2056C2211yescharacteristic
125#2056C2211yescharacteristic
126#2043C2211yescharacteristic
127#2043C2211yescharacteristic
128#2043C2211yescharacteristic
129#2043C2211yescharacteristic
130#2016C2211yescharacteristic
131#2016C2211yescharacteristic
132#1993C2211yescharacteristic
133#1988C2211yescharacteristic
134#1981C2211yescharacteristic
135#1981C2211yescharacteristic
136#1981C2211yescharacteristic
137#1981C2211yescharacteristic
138#1981C2211yescharacteristic
139#1981C2211yescharacteristic
140#1960C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1831C2211yescharacteristic
189#1824C2211yescharacteristic
190#1823C2211yescharacteristic
191#1805C2211yescharacteristic
192#1805C2211yescharacteristic
193#1803C2211yescharacteristic
194#1797C2211yescharacteristic
195#1797C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1767C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203#1728C2211yescharacteristic
204C2×#336C2211yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#554—24no—
216#554—24no—
217#552—24no—
218#552D418yes—
219D4×Q8—24no—
220D4×Q8—24no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#126—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4D411yescharacteristic
250C2×C4×D4D411yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C42—21no—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263#501—24no—
264#491—24no—
265#485—24no—
266#485—24no—
267#484—24no—
268#483—24no—
269#483—24no—
270#483—24no—
271#479—24no—
272#479—24no—
273#475—24no—
274#470—24no—
275#470—24no—
276#467—24no—
277#467—24no—
278#462—24no—
279#462—24no—
280#451—24no—
281#451—24no—
282#441—24no—
283#441—24no—
284#435—24no—
285#435—24no—
286#428—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#106—24no—
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308#419—24no—
309#419—24no—
310C2×#103—24no—
311C2×#103—24no—
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×C22⋊C8C2311yescharacteristic
346C2×C22⋊C8C2311yescharacteristic
347C2×C22⋊C8C2311yescharacteristic
348C2×#97C2311yescharacteristic
349C2×#97C2311yescharacteristic
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#395—21no—
360#395—21no—
361#395—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#382—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4D411yescharacteristic
455C4×C4⋊C4D411yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4D411yescharacteristic
473C4×C22⋊C4D411yescharacteristic
474C4×C22⋊C4D411yescharacteristic
475C4×C22⋊C4D411yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478#376—21no—
479#376—21no—
480#376—21no—
481C2×#95—21no—
482C2×#95—21no—
483C2×#95—21no—
484C2×#95—21no—
485C2×#95—21no—
486C43—21no—
487C43—21no—
488C43C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—22no—
519C22×Q8—22no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—22no—
524C22×Q8—41no—
525C22×Q8—41no—
526C22×Q8—41no—
527C22×Q8—41no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×D4C2×D411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2×D411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589C4⋊Q8—41no—
590C4⋊Q8—44no—
591#126—28no—
592#125—28no—
593#125—22no—
594#125—44no—
595#125C2×D414yes—
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—44no—
608C22⋊Q8—44no—
609C22⋊Q8—44no—
610C22⋊Q8—44no—
611C22⋊Q8C2×D414yes—
612C22⋊Q8C2×D414yes—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—22no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8C2×D414yes—
623C4×D4—24no—
624C4×D4—24no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4C2×D414yes—
628C4×D4#4114yes—
629#117—22no—
630#117—28no—
631#117—22no—
632#117—41no—
633#117—44no—
634#117C2×D414yes—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D414yes—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42—44no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#107—22no—
744#107—22no—
745#107—22no—
746#107—22no—
747#106—22no—
748#106—22no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103#4114yes—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799#97—22no—
800#97—22no—
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#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848C24C22×D411yescharacteristic
849C24C22×D411yescharacteristic
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—44no—
881C2×Q8—44no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—81no—
888C2×Q8—81no—
889C2×Q8—81no—
890C2×Q8—81no—
891C2×Q8—82no—
892C2×Q8—82no—
893C2×Q8—82no—
894C2×Q8—82no—
895C2×Q8C22×D412yes—
896C2×Q8C2×#4112yes—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4#12114yes—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—24no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4#13714yes—
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D412yes—
963C22×C4C22×D412yes—
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C2×#4112yes—
969C22×C4C2×#4112yes—
970C22×C4C2511yescharacteristic
971Q16—44no—
972Q16—44no—
973Q16—82no—
974Q16—82no—
975M16—44no—
976M16—82no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—44no—
1001C2×C8—82no—
1002C2×C8C2×#4112yes—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
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#12114yes—
1060C4⋊C4C22×D412yes—
1061C4⋊C4C22×D412yes—
1062C4⋊C4C22×D412yes—
1063C4⋊C4C2×#4112yes—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—81no—
1077C22⋊C4#12114yes—
1078C22⋊C4#12114yes—
1079C22⋊C4#13714yes—
1080C42—24no—
1081C42—24no—
1082C42—22no—
1083C42—22no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—41no—
1093C42—41no—
1094C42—41no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—81no—
1111C42—81no—
1112C42C22×D412yes—
1113C42C2×#4112yes—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23C2×#12112yes—
1125C23C2×#12112yes—
1126C23C2×#13712yes—
1127C23C2×#13712yes—
1128C23C23×D411yescharacteristic
1129Q8—22no—
1130Q8—22no—
1131Q8—22no—
1132Q8—22no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—84no—
1150Q8—84no—
1151Q8—162no—
1152D4—28no—
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—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—44no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—48no—
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—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—82no—
1240C2×C4—82no—
1241C2×C4—82no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4C2×#12112yes—
1248C2×C4C2×#12112yes—
1249C2×C4C2×#12112yes—
1250C2×C4C2×#12112yes—
1251C2×C4C2×#13712yes—
1252C2×C4C2×#13712yes—
1253C2×C4C2×#13712yes—
1254C2×C4C2×#13712yes—
1255C2×C4C23×D411yescharacteristic
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C22×#4111yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22#303914yes—
1283C22C22×#12111yescharacteristic
1284C22D4×#4111yescharacteristic
1285C22#348511yescharacteristic
1286C22C22×#13711yescharacteristic
1287C22C22×#13711yescharacteristic
1288C22#358411yescharacteristic
1289C22#358611yescharacteristic
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—41no—
1307C4—42no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4D4×#4111yescharacteristic
1319C4#347511yescharacteristic
1320C4#350011yescharacteristic
1321C4#352111yescharacteristic
1322C2—24no—
1323C2—42no—
1324C2#3621811yescharacteristic
1325C2C2×#303911yescharacteristic
1326C2#6043311yescharacteristic
1327C2#6143811yescharacteristic
1328C2#6145711yescharacteristic
1329C2#6170511yescharacteristic
1330C2#6174211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #33114C2semidirect
6. #33108C2semidirect
7. #33033C2semidirect
8. #28660C2semidirect
9. #28581C2semidirect
10. #28575C2semidirect
11. #28209C2semidirect
12. #28124C2semidirect
13. #28121C2semidirect
14. #25467C2semidirect
15. #25290C2semidirect
16. #25219C2semidirect
17. #25206C2semidirect
18. #25095C2semidirect
19. #25082C2semidirect
20. #24698C2semidirect
21. #24648C2semidirect
22. #24598C2semidirect
23. #24580C2semidirect
24. #24498C2semidirect
25. #24480C2semidirect
29. #21506C2semidirect
30. #21061C2semidirect
31. C2×#1927C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33442
C2×#33122
#362762
C4×#5522
#331142
#331082
#330332
#286602
#285812
#285752
#282092
#281242
#281212
#254672
#252902
#252192
#252062
#250952
#250822
#246982
#246482
#245982
#245802
#244982
#244802
#226982
#224972
#224252
#215062
#210612
C2×#19272