Finite Group Databasebeta

← #6476889

Subgroups — #6476889

Order 512.

1747 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35325C211yesmaximal, characteristic
2#34203C211yesmaximal, characteristic
3#33155C211yesmaximal, characteristic, complemented
4#33117C211yesmaximal, characteristic, complemented
5#32964C211yesmaximal, characteristic, complemented
6#32915C211yesmaximal, characteristic, complemented
7#30021C211yesmaximal, characteristic, complemented
8#30020C211yesmaximal, characteristic, complemented
9#30013C211yesmaximal, characteristic, complemented
10#30012C211yesmaximal, characteristic, complemented
11#29252C211yesmaximal, characteristic, complemented
12#29250C211yesmaximal, characteristic, complemented
13#28132C211yesmaximal, characteristic, complemented
14#28132C211yesmaximal, characteristic, complemented
15#27635C211yesmaximal, characteristic, complemented
16#27634C211yesmaximal, characteristic, complemented
17#24853C211yesmaximal, characteristic, complemented
18#24849C211yesmaximal, characteristic, complemented
19#24764C211yesmaximal, characteristic, complemented
20#24764C211yesmaximal, characteristic, complemented
21#24561C211yesmaximal, characteristic
22#24554C211yesmaximal, characteristic
23#24386C211yesmaximal, characteristic
24#24380C211yesmaximal, characteristic
25#24157C211yesmaximal, characteristic, complemented
26#24155C211yesmaximal, characteristic, complemented
27#22203C211yesmaximal, characteristic, complemented
28#22198C211yesmaximal, characteristic, complemented
29#22197C211yesmaximal, characteristic, complemented
30#22192C211yesmaximal, characteristic, complemented
31#20628C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#475C2211yescharacteristic, complemented
40C2×#470C2211yescharacteristic
41C2×#470C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#467C2211yescharacteristic
44C2×#462C2211yescharacteristic, complemented
45C2×#462C2211yescharacteristic, complemented
46C2×#451C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#424C2211yescharacteristic
49C2×#424C2211yescharacteristic
50C2×#407C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52#2855C2211yescharacteristic
53#2855C2211yescharacteristic
54#2848C2211yescharacteristic
55#2848C2211yescharacteristic
56#2628C2211yescharacteristic
57#2628C2211yescharacteristic
58#2621C2211yescharacteristic
59#2621C2211yescharacteristic
60#2611—21no—
61#2611—21no—
62#2599—21no—
63#2599—21no—
64#2583—21no—
65#2561—21no—
66#2484—21no—
67#2482—21no—
68#2362—21no—
69#2362—21no—
70#2360—21no—
71#2360—21no—
72#2344—21no—
73#2344—21no—
74#2342—21no—
75#2342—21no—
76#2323C2211yescharacteristic
77#2323C2211yescharacteristic
78#2323C2211yescharacteristic
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2323C2211yescharacteristic
82#2323C2211yescharacteristic
83#2323C2211yescharacteristic
84#2316C2211yescharacteristic
85#2310C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90#2283C2211yescharacteristic
91#2280C2211yescharacteristic
92#2274C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2001C2211yescharacteristic
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic
124#2001C2211yescharacteristic
125#1988C2211yescharacteristic, complemented
126#1987C2211yescharacteristic, complemented
127#1981C2211yescharacteristic, complemented
128#1981C2211yescharacteristic, complemented
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1949C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1928C2211yescharacteristic, complemented
134#1928C2211yescharacteristic, complemented
135#1928C2211yescharacteristic, complemented
136#1928C2211yescharacteristic, complemented
137#1927C2211yescharacteristic, complemented
138#1927C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1920C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1894C2211yescharacteristic
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic
152#1894C2211yescharacteristic
153#1892C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1878C2211yescharacteristic, complemented
158#1878C2211yescharacteristic, complemented
159#1878C2211yescharacteristic, complemented
160#1878C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic, complemented
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1865C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1797C2211yescharacteristic
197#1797C2211yescharacteristic
198#1797C2211yescharacteristic
199#1787C2211yescharacteristic
200#1787C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#533—42no—
214#533—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#125—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—24no—
221C2×C22⋊Q8—24no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233#519—42no—
234#519—42no—
235C2×C4×Q8—21no—
236C2×C4×Q8—21no—
237C2×C4×Q8—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—21no—
247C2×#117—42no—
248C2×#117—42no—
249C2×#117D411yescharacteristic
250C2×#117D411yescharacteristic
251C2×#117D411yescharacteristic
252C2×#117D411yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C22×C4⋊C4—21no—
260C22×C4⋊C4D411yescharacteristic
261C22×C4⋊C4D411yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4D411yescharacteristic
265C22×C22⋊C4D411yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#485—42no—
269#485—42no—
270#477—42no—
271#475—42no—
272#470—24no—
273#470—24no—
274#467—24no—
275#467—24no—
276#462—42no—
277#462—42no—
278#451—42no—
279#451—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292#424—42no—
293#424—42no—
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
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
326#407—42no—
327C2×C22⋊C8—42no—
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336#400—21no—
337#400—21no—
338#399—21no—
339#399—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#395—21no—
349#395—21no—
350#393—21no—
351#393—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
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#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—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#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#385—21no—
413#385—21no—
414#385—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#383—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—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⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469#376—21no—
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25C2×D411yescharacteristic
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—22no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—22no—
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#125—44no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—44no—
591C22⋊Q8#4114yes—
592C22⋊Q8#4114yes—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—44no—
606C4×Q8—44no—
607C4×Q8—44no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—42no—
619#117—42no—
620#117—42no—
621#117—42no—
622#117—44no—
623#117—44no—
624#117—41no—
625#117—41no—
626#117—44no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
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—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—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—42no—
659C2×C4⋊C4—42no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4—28no—
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—42no—
704C2×C22⋊C4—42no—
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—22no—
714C2×C42—22no—
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—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—22no—
740#107—22no—
741#107—41no—
742#107—41no—
743#107—41no—
744#107—41no—
745#106—22no—
746#106—22no—
747#106—41no—
748#106—41no—
749#106—41no—
750#106—41no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
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#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—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—41no—
839C24—41no—
840C24—41no—
841C24—41no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C2×Q8—24no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
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—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8C2×#4112yes—
878C2×Q8C2×#4112yes—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—24no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—24no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
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—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4C2×#4112yes—
953C22×C4H(5,𝔽2)12yes—
954C22×C42−1+412yes—
955C22×C4C2511yescharacteristic
956Q16—82no—
957Q16—82no—
958Q16—82no—
959Q16—82no—
960M16—82no—
961M16—82no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
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—82no—
987C2×C8—82no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
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—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
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—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4C2×#4112yes—
1047C4⋊C4C2×#4112yes—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C42—22no—
1079C42—22no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—41no—
1087C42—41no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42H(5,𝔽2)12yes—
1103C42H(5,𝔽2)12yes—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—44no—
1123C23—44no—
1124C23—44no—
1125C23—82no—
1126C23—82no—
1127C23—82no—
1128C23—82no—
1129C23#52512yes—
1130C23#53712yes—
1131C23#57812yes—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—22no—
1136Q8—22no—
1137Q8—48no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—84no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—48no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—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—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—82no—
1246C2×C4—82no—
1247C2×C4—84no—
1248C2×C4—82no—
1249C2×C4#52512yes—
1250C2×C4#53412yes—
1251C2×C4#53412yes—
1252C2×C4#53712yes—
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×2−1+411yescharacteristic
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—88no—
1289C22C2×#52511yescharacteristic
1290C22C2×#53411yescharacteristic
1291C22C2×#53711yescharacteristic
1292C22C2×#57811yescharacteristic
1293C22#358411yescharacteristic
1294C22#358611yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—41no—
1301C4—42no—
1302C4—42no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4#351911yescharacteristic
1324C4#351911yescharacteristic
1325C4#352011yescharacteristic
1326C4#352011yescharacteristic
1327C2—42no—
1328C2—42no—
1329C2—42no—
1330C2#3507711yescharacteristic
1331C2#6058311yescharacteristic
1332C2#6058611yescharacteristic
1333C2#6075911yescharacteristic
1334C2#6076111yescharacteristic
1335C2#6093611yescharacteristic
1336C2#6093911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33155C2semidirect
4. #33117C2semidirect
5. #32964C2semidirect
6. #32915C2semidirect
7. #30021C2semidirect
8. #30020C2semidirect
9. #30013C2semidirect
10. #30012C2semidirect
11. #29252C2semidirect
12. #29250C2semidirect
13. #28132C2semidirect
14. #28132C2semidirect
15. #27635C2semidirect
16. #27634C2semidirect
17. #24853C2semidirect
18. #24849C2semidirect
19. #24764C2semidirect
20. #24764C2semidirect
25. #24157C2semidirect
26. #24155C2semidirect
27. #22203C2semidirect
28. #22198C2semidirect
29. #22197C2semidirect
30. #22192C2semidirect
38. C2×#477C22semidirect
39. C2×#475C22semidirect
44. C2×#462C22semidirect
45. C2×#462C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2056C22semidirect
110. #2056C22semidirect
111. #2056C22semidirect
112. #2056C22semidirect
125. #1988C22semidirect
126. #1987C22semidirect
127. #1981C22semidirect
128. #1981C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1949C22semidirect
132. #1949C22semidirect
133. #1928C22semidirect
134. #1928C22semidirect
135. #1928C22semidirect
136. #1928C22semidirect
137. #1927C22semidirect
138. #1927C22semidirect
139. #1927C22semidirect
140. #1927C22semidirect
141. #1921C22semidirect
142. #1921C22semidirect
143. #1920C22semidirect
144. #1920C22semidirect
145. #1919C22semidirect
146. #1919C22semidirect
147. #1918C22semidirect
148. #1918C22semidirect
157. #1878C22semidirect
158. #1878C22semidirect
159. #1878C22semidirect
160. #1878C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
169. #1865C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
172. #1865C22semidirect
173. #1863C22semidirect
174. #1863C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
189. #1805C22semidirect
190. #1805C22semidirect

Maximal subgroups

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

subgroupindex
#353252
#342032
#331552
#331172
#329642
#329152
#300212
#300202
#300132
#300122
#292522
#292502
#281322
#276352
#276342
#248532
#248492
#247642
#245612
#245542
#243862
#243802
#241572
#241552
#222032
#221982
#221972
#221922
#206282