Finite Group Databasebeta

← #7565220

Subgroups — #7565220

Order 512.

1902 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3375C211yesmaximal, characteristic, complemented
2C2×#3136C211yesmaximal, characteristic
3#45097C211yesmaximal, characteristic
4#44894C211yesmaximal, characteristic, complemented
5#30885C211yesmaximal, characteristic, complemented
6#30877C211yesmaximal, characteristic, complemented
7#30809C211yesmaximal, characteristic, complemented
8#30805C211yesmaximal, characteristic, complemented
9#28643C211yesmaximal, characteristic, complemented
10#28407C211yesmaximal, characteristic, complemented
11#27776C211yesmaximal, characteristic, complemented
12#27773C211yesmaximal, characteristic, complemented
13#27281C211yesmaximal, characteristic, complemented
14#27278C211yesmaximal, characteristic, complemented
15#26841C211yesmaximal, characteristic, complemented
16#26840C211yesmaximal, characteristic, complemented
17#25954C211yesmaximal, characteristic, complemented
18#25950C211yesmaximal, characteristic, complemented
19#25942C211yesmaximal, characteristic, complemented
20#25658C211yesmaximal, characteristic, complemented
21#25332C211yesmaximal, characteristic, complemented
22#25286C211yesmaximal, characteristic, complemented
23#25089C211yesmaximal, characteristic, complemented
24#25084C211yesmaximal, characteristic, complemented
25#24311C211yesmaximal, characteristic, complemented
26#24220C211yesmaximal, characteristic
27#23216C211yesmaximal, characteristic, complemented
28#22864C211yesmaximal, characteristic, complemented
29#22862C211yesmaximal, characteristic, complemented
30#21604C211yesmaximal, characteristic, complemented
31#21525C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic, complemented
34C2×#544C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3375—28no—
37#3136—28no—
38C2×#490C2211yescharacteristic
39C2×#490C2211yescharacteristic
40C2×#489C2211yescharacteristic
41C2×#489C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#489C2211yescharacteristic, complemented
44C2×#488C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#486C2211yescharacteristic
47C2×#486C2211yescharacteristic
48C2×#479C2211yescharacteristic, complemented
49C2×#477C2211yescharacteristic, complemented
50C2×#474C2211yescharacteristic
51C2×#474C2211yescharacteristic, complemented
52C2×#467C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#464C2211yescharacteristic, complemented
56C2×#460C2211yescharacteristic
57C2×#452C2211yescharacteristic
58C2×#450C2211yescharacteristic
59C2×#446C2211yescharacteristic, complemented
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic, complemented
62C2×C4×Q16C2211yescharacteristic, complemented
63C2×#417C2211yescharacteristic
64C2×#418C2211yescharacteristic
65C2×#416C2211yescharacteristic
66C22×#102C2211yescharacteristic
67C2×#405C2211yescharacteristic
68#2734—21no—
69#2729—21no—
70#2713—21no—
71#2701—21no—
72#2697—21no—
73#2686—21no—
74#2684—21no—
75#2677—21no—
76#2592C2211yescharacteristic
77#2584C2211yescharacteristic, complemented
78#2565C2211yescharacteristic, complemented
79#2551C2211yescharacteristic, complemented
80#2550C2211yescharacteristic, complemented
81#2547C2211yescharacteristic
82#2546—21no—
83#2545C2211yescharacteristic
84#2544C2211yescharacteristic
85#2534—21no—
86#2465—21no—
87#2462—21no—
88#2453C2211yescharacteristic, complemented
89#2451C2211yescharacteristic, complemented
90#2447C2211yescharacteristic
91#2445C2211yescharacteristic
92#2444—21no—
93#2440C2211yescharacteristic
94#2439C2211yescharacteristic
95#2435C2211yescharacteristic
96#2432C2211yescharacteristic
97#2429—21no—
98#2425—21no—
99#2418—21no—
100#2396C2211yescharacteristic
101#2366C2211yescharacteristic
102#2365C2211yescharacteristic, complemented
103#2362C2211yescharacteristic
104#2360C2211yescharacteristic
105#2339C2211yescharacteristic
106D4×C22⋊C4C2211yescharacteristic
107#2323C2211yescharacteristic
108#2323C2211yescharacteristic
109#2097C2211yescharacteristic, complemented
110#2093C2211yescharacteristic
111#2073C2211yescharacteristic
112#2071C2211yescharacteristic, complemented
113#2068C2211yescharacteristic, complemented
114#2068C2211yescharacteristic, complemented
115#2068C2211yescharacteristic, complemented
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2059C2211yescharacteristic, complemented
120#2057C2211yescharacteristic, complemented
121#2055C2211yescharacteristic
122#2055C2211yescharacteristic, complemented
123#2043C2211yescharacteristic, complemented
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2042C2211yescharacteristic
127#2042C2211yescharacteristic
128#2042C2211yescharacteristic, complemented
129#2042C2211yescharacteristic, complemented
130#2041C2211yescharacteristic
131#2026C2211yescharacteristic, complemented
132#2024C2211yescharacteristic, complemented
133#2024C2211yescharacteristic, complemented
134#2024C2211yescharacteristic, complemented
135#2023C2211yescharacteristic
136#2023C2211yescharacteristic
137#2016C2211yescharacteristic, complemented
138#2015C2211yescharacteristic
139#2015C2211yescharacteristic
140#2014C2211yescharacteristic
141#1989C2211yescharacteristic, complemented
142#1988C2211yescharacteristic, complemented
143#1985C2211yescharacteristic, complemented
144#1983C2211yescharacteristic
145#1983C2211yescharacteristic
146#1982C2211yescharacteristic
147#1981C2211yescharacteristic, complemented
148#1969C2211yescharacteristic, complemented
149#1969C2211yescharacteristic, complemented
150#1968C2211yescharacteristic
151#1958C2211yescharacteristic
152#1956C2211yescharacteristic, complemented
153#1942C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic
157#1935C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1935C2211yescharacteristic, complemented
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic, complemented
163#1928C2211yescharacteristic, complemented
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1873C2211yescharacteristic
178#1872C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1808C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1798C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195C4×#107C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic, complemented
203#1753C2211yescharacteristic
204#1753C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#559—24no—
215#559—42no—
216Q82—24no—
217Q82—42no—
218#544—24no—
219#544—42no—
220#535—24no—
221#535—42no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8—21no—
226C2×C4⋊Q8—21no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#125—21no—
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#124—21no—
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#123—21no—
244C2×#123—21no—
245C2×#123—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×#121—21no—
252C2×#121—21no—
253C2×#120—21no—
254C2×#120—21no—
255C2×C4×Q8—21no—
256C2×C4×Q8—21no—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4—21no—
272#490—24no—
273#490—24no—
274#489—24no—
275#489—24no—
276#489—24no—
277#489—24no—
278#488—24no—
279#488—24no—
280#486—24no—
281#486D418yes—
282#479—42no—
283#477—24no—
284#474—24no—
285#474—24no—
286#467—24no—
287#464—24no—
288#464—24no—
289#464—42no—
290#460—24no—
291#452—24no—
292#450—24no—
293#446—24no—
294#440—24no—
295#440—24no—
296C4×Q16—24no—
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310#418—24no—
311#417—24no—
312#416—24no—
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×#102—24no—
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×C22⋊C8C2311yescharacteristic
353C2×C22⋊C8C2311yescharacteristic
354#405—24no—
355C2×#97C2311yescharacteristic
356C2×#97C2311yescharacteristic
357C2×#97C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362C2×C4×C8C2311yescharacteristic
363#400—21no—
364#400D411yescharacteristic
365#399D411yescharacteristic
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398D411yescharacteristic
374#398D411yescharacteristic
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#396—21no—
381#396—21no—
382#396—21no—
383#396D411yescharacteristic
384#396D411yescharacteristic
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395D411yescharacteristic
392#394—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394—21no—
398#394—21no—
399#394—21no—
400#393—21no—
401#393—21no—
402#393D411yescharacteristic
403#391—21no—
404#391—21no—
405#391—21no—
406#391—21no—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#390—21no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#386—21no—
458#386—21no—
459#386—21no—
460#386—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#386—21no—
466#385—21no—
467#385—21no—
468#385—21no—
469#385—21no—
470#385—21no—
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#381—21no—
474#381—21no—
475#380—21no—
476#380—21no—
477#380C2311yescharacteristic
478#380C2311yescharacteristic
479#379—21no—
480#379—21no—
481#379—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C22⋊C4—21no—
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493C2×#95—21no—
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518C25—21no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8C2×D411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4C2411yescharacteristic
546C22×D4C2411yescharacteristic
547C22×D4C2411yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C2411yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—41no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—41no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C4⋊Q8—22no—
585C4⋊Q8—22no—
586C4⋊Q8—22no—
587C4⋊Q8—22no—
588C4⋊Q8—41no—
589C4⋊Q8—41no—
590C4⋊Q8—41no—
591C4⋊Q8—41no—
592C4⋊Q8—41no—
593C4⋊Q8—44no—
594C4⋊Q8—44no—
595C4⋊Q8—44no—
596C4⋊Q8—44no—
597C4⋊Q8—82no—
598C4⋊Q8C2×D414yes—
599#127—22no—
600#127—22no—
601#127—41no—
602#127C2×D414yes—
603#125—22no—
604#125—22no—
605#125—22no—
606#125—41no—
607#125—44no—
608#124—22no—
609#124—22no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—41no—
618#124—44no—
619#123—44no—
620#123—44no—
621#123—82no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—44no—
626C22⋊Q8—44no—
627C22⋊Q8—82no—
628C22⋊Q8#4114yes—
629#121—44no—
630#121—44no—
631#120—44no—
632#120—44no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—22no—
640C4×Q8—22no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—44no—
644C4×Q8—82no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—44no—
654C4×D4—82no—
655#117—22no—
656#117—22no—
657#117—22no—
658#117—41no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—22no—
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—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—82no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760#107—22no—
761#107—22no—
762#107—22no—
763#107—22no—
764#107—41no—
765#107—41no—
766#106—41no—
767C4⋊C8—22no—
768C4⋊C8—22no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8—41no—
772C4⋊C8—41no—
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—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102C2×D414yes—
808#102C2×D414yes—
809#102C2×D414yes—
810#102C2×D414yes—
811C22⋊C8—22no—
812C22⋊C8—22no—
813#97—22no—
814#97—22no—
815#97—22no—
816#97—22no—
817C4×C8—22no—
818C4×C8—41no—
819C4×C8—41no—
820C4×C8C2×D414yes—
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#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861C24—21no—
862C24—21no—
863C24—21no—
864C24—42no—
865C24—42no—
866C24—81no—
867C24—81no—
868C24—81no—
869C24—81no—
870C24—81no—
871C24C22×D411yescharacteristic
872#41—44no—
873#41—44no—
874#41—82no—
875#41—82no—
876C2×Q8—22no—
877C2×Q8—24no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—41no—
896C2×Q8—41no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—81no—
901C2×Q8—81no—
902C2×Q8—81no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—81no—
906C2×Q8—81no—
907C2×Q8—81no—
908C2×Q8C2×#4112yes—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—82no—
936C2×D4—82no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4C22×D412yes—
948C2×D4C22×D412yes—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C2×#4112yes—
998C22×C42−1+412yes—
999C22×C4C2511yescharacteristic
1000Q16—44no—
1001Q16—82no—
1002SD16—44no—
1003SD16—44no—
1004SD16—82no—
1005M16—44no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—44no—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C4⋊C4—24no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—24no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4C22×D412yes—
1087C4⋊C4C22×D412yes—
1088C4⋊C4C2×#4112yes—
1089C22⋊C4—24no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—81no—
1141C42—81no—
1142C42—81no—
1143C42C22×D412yes—
1144C42H(5,𝔽2)12yes—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—22no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—84no—
1173C23—84no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23#54812yes—
1180C23C23×D411yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—44no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—84no—
1195Q8—162no—
1196Q8—162no—
1197Q8—162no—
1198D4—22no—
1199D4—22no—
1200D4—22no—
1201D4—22no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—84no—
1211D4—84no—
1212D4—84no—
1213D4—84no—
1214D4—162no—
1215D4—162no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—84no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4D4212yes—
1301C2×C4D4212yes—
1302C2×C4#54812yes—
1303C2×C4#57612yes—
1304C2×C4C23×D411yescharacteristic
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×2−1+411yescharacteristic
1308C2×C4#58511yescharacteristic
1309C2×C4#58511yescharacteristic
1310C8—22no—
1311C8—22no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—168no—
1347C22C2×D4211yescharacteristic
1348C22C2×#54811yescharacteristic
1349C22#350011yescharacteristic
1350C22C2×#57611yescharacteristic
1351C22#358411yescharacteristic
1352C22#358611yescharacteristic
1353C22#358611yescharacteristic
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4D4×#4111yescharacteristic
1381C4#348911yescharacteristic
1382C4#351411yescharacteristic
1383C4#356111yescharacteristic
1384C2—42no—
1385C2—82no—
1386C2—82no—
1387C2—161no—
1388C2#5913011yescharacteristic
1389C2#6106011yescharacteristic
1390C2#6108411yescharacteristic
1391C2#6134411yescharacteristic
1392C2#6134511yescharacteristic
1393C2#6260011yescharacteristic
1394C2#6260511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3375C2semidirect
4. #44894C2semidirect
5. #30885C2semidirect
6. #30877C2semidirect
7. #30809C2semidirect
8. #30805C2semidirect
9. #28643C2semidirect
10. #28407C2semidirect
11. #27776C2semidirect
12. #27773C2semidirect
13. #27281C2semidirect
14. #27278C2semidirect
15. #26841C2semidirect
16. #26840C2semidirect
17. #25954C2semidirect
18. #25950C2semidirect
19. #25942C2semidirect
20. #25658C2semidirect
21. #25332C2semidirect
22. #25286C2semidirect
23. #25089C2semidirect
24. #25084C2semidirect
25. #24311C2semidirect
27. #23216C2semidirect
28. #22864C2semidirect
29. #22862C2semidirect
30. #21604C2semidirect
31. #21525C2semidirect
33. C2×Q82C22semidirect
43. C2×#489C22semidirect
48. C2×#479C22semidirect
49. C2×#477C22semidirect
51. C2×#474C22semidirect
55. C2×#464C22semidirect
59. C2×#446C22semidirect
61. C2×#440C22semidirect
62. C2×C4×Q16C22semidirect
77. #2584C22semidirect
78. #2565C22semidirect
79. #2551C22semidirect
80. #2550C22semidirect
88. #2453C22semidirect
89. #2451C22semidirect
102. #2365C22semidirect
109. #2097C22semidirect
112. #2071C22semidirect
113. #2068C22semidirect
114. #2068C22semidirect
115. #2068C22semidirect
119. #2059C22semidirect
120. #2057C22semidirect
122. #2055C22semidirect
123. #2043C22semidirect
128. #2042C22semidirect
129. #2042C22semidirect
131. #2026C22semidirect
132. #2024C22semidirect
133. #2024C22semidirect
134. #2024C22semidirect
137. #2016C22semidirect
141. #1989C22semidirect
142. #1988C22semidirect
143. #1985C22semidirect
147. #1981C22semidirect
148. #1969C22semidirect
149. #1969C22semidirect
152. #1956C22semidirect
153. #1942C22semidirect
154. #1940C22semidirect
157. #1935C22semidirect
158. #1935C22semidirect
159. #1935C22semidirect
160. #1935C22semidirect
162. #1934C22semidirect
163. #1928C22semidirect
166. #1925C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
176. #1877C22semidirect
180. #1864C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
190. #1804C22semidirect
195. C4×#107C22semidirect
196. #1770C22semidirect
197. #1770C22semidirect
198. C8×C4⋊C4C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33752
C2×#31362
#450972
#448942
#308852
#308772
#308092
#308052
#286432
#284072
#277762
#277732
#272812
#272782
#268412
#268402
#259542
#259502
#259422
#256582
#253322
#252862
#250892
#250842
#243112
#242202
#232162
#228642
#228622
#216042
#215252