Finite Group Databasebeta

← #6783129

Subgroups — #6783129

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38117C211yesmaximal, characteristic, complemented
2#38090C211yesmaximal, characteristic, complemented
3#33042C211yesmaximal, characteristic, complemented
4#32426C211yesmaximal, characteristic, complemented
5#32163C211yesmaximal, characteristic, complemented
6#32053C211yesmaximal, characteristic, complemented
7#31935C211yesmaximal, characteristic, complemented
8#31520C211yesmaximal, characteristic, complemented
9#30988C211yesmaximal, characteristic, complemented
10#30877C211yesmaximal, characteristic, complemented
11#30519C211yesmaximal, characteristic, complemented
12#30354C211yesmaximal, characteristic, complemented
13#30332C211yesmaximal, characteristic, complemented
14#29567C211yesmaximal, characteristic, complemented
15#29505C211yesmaximal, characteristic, complemented
16#29113C211yesmaximal, characteristic, complemented
17#28316C211yesmaximal, characteristic, complemented
18#24665C211yesmaximal, characteristic, complemented
19#24585C211yesmaximal, characteristic, complemented
20#24535C211yesmaximal, characteristic, complemented
21#24512C211yesmaximal, characteristic, complemented
22#24484C211yesmaximal, characteristic, complemented
23#24362C211yesmaximal, characteristic, complemented
24#24093C211yesmaximal, characteristic, complemented
25#24037C211yesmaximal, characteristic, complemented
26#23965C211yesmaximal, characteristic, complemented
27#23850C211yesmaximal, characteristic, complemented
28#22160C211yesmaximal, characteristic, complemented
29#22052C211yesmaximal, characteristic, complemented
30#21224C211yesmaximal, characteristic, complemented
31#21103C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#555C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic, complemented
39C2×#460C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic, complemented
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#433C2211yescharacteristic
45C2×#427C2211yescharacteristic, complemented
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic, complemented
48C22×C4×C8C2211yescharacteristic, complemented
49#2857C2211yescharacteristic, complemented
50#2856C2211yescharacteristic
51#2786—21no—
52#2756—21no—
53#2730—21no—
54#2723—21no—
55#2676—21no—
56#2676—21no—
57#2668—21no—
58#2668—21no—
59#2644C2211yescharacteristic, complemented
60#2640C2211yescharacteristic
61#2624C2211yescharacteristic
62#2620C2211yescharacteristic
63#2544C2211yescharacteristic
64#2542C2211yescharacteristic
65#2523—21no—
66#2522—21no—
67#2521—21no—
68#2518—21no—
69#2512C2211yescharacteristic, complemented
70#2500C2211yescharacteristic
71#2499C2211yescharacteristic
72#2491C2211yescharacteristic
73#2485C2211yescharacteristic
74#2472—21no—
75#2472—21no—
76#2471—21no—
77#2471—21no—
78#2451C2211yescharacteristic, complemented
79#2433C2211yescharacteristic
80#2431C2211yescharacteristic
81#2423C2211yescharacteristic
82#2407C2211yescharacteristic
83#2347C2211yescharacteristic, complemented
84#2341C2211yescharacteristic, complemented
85#2328C2211yescharacteristic
86#2323C2211yescharacteristic
87#2320C2211yescharacteristic, complemented
88#2309C2211yescharacteristic
89#2297C2211yescharacteristic
90#2297C2211yescharacteristic, complemented
91#2290C2211yescharacteristic
92#2096C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2058C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2015C2211yescharacteristic
123#2014C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic, complemented
126#2011C2211yescharacteristic
127#2011C2211yescharacteristic
128#2001C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#1999C2211yescharacteristic
132#1990C2211yescharacteristic, complemented
133#1983C2211yescharacteristic, complemented
134#1982C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic, complemented
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic
141#1969C2211yescharacteristic, complemented
142#1969C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic, complemented
146#1968C2211yescharacteristic, complemented
147#1957C2211yescharacteristic
148#1949C2211yescharacteristic, complemented
149#1947C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic, complemented
157#1934C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic, complemented
169#1893C2211yescharacteristic, complemented
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1875C2211yescharacteristic
179#1873C2211yescharacteristic
180#1869C2211yescharacteristic
181#1869C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1850C2211yescharacteristic, complemented
189#1850C2211yescharacteristic, complemented
190#1834C2211yescharacteristic, complemented
191#1825C2211yescharacteristic, complemented
192#1825C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1768C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—24no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#555—42no—
220#555—42no—
221#546—42no—
222#546—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#126—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#120—21no—
248C2×#120—21no—
249C2×#120—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C42C2311yescharacteristic
262#486—42no—
263#482—42no—
264#482—42no—
265#464—42no—
266#460—24no—
267#450—24no—
268#449—42no—
269#449—42no—
270#447—42no—
271#433—42no—
272#427—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#416—42no—
286#416—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8—42no—
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#391—21no—
373#391—21no—
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388D411yescharacteristic
417#388D411yescharacteristic
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387D411yescharacteristic
427#387D411yescharacteristic
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386D411yescharacteristic
442#386D411yescharacteristic
443#385—21no—
444#385D411yescharacteristic
445#385D411yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#383—21no—
450#383—21no—
451#382—21no—
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#376C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C2×D411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546#135—416no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16#4114yes—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—41no—
576C22×C8—41no—
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589#127—22no—
590#127—41no—
591#127—41no—
592#127—41no—
593#126—82no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—44no—
599#124—44no—
600#124—82no—
601#123—44no—
602C22⋊Q8—22no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—82no—
607C22⋊Q8—82no—
608C22⋊Q8—82no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—44no—
614#121—41no—
615#121—41no—
616#121—44no—
617#121—41no—
618#121—41no—
619#121—82no—
620#121—82no—
621#120—44no—
622#120—82no—
623#120—82no—
624C4×Q8—22no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
642#117—44no—
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—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—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—44no—
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—41no—
736C2×C42—41no—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—41no—
745#107—41no—
746#107—41no—
747#107—41no—
748#106—41no—
749#106—41no—
750#106—41no—
751#106—41no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794#97—41no—
795#97—41no—
796C4×C8—22no—
797C4×C8—22no—
798C4×C8—41no—
799C4×C8—41no—
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#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C24C22×D411yescharacteristic
849#41—44no—
850#41—44no—
851#41—44no—
852#41—44no—
853#41—82no—
854#41—82no—
855#41—82no—
856#41—82no—
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—42no—
869C2×Q8—42no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8C2×#4112yes—
875C2×D4—22no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—82no—
924C2×D4—82no—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4C2×#4112yes—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
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—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4H(5,𝔽2)12yes—
992C22×C4H(5,𝔽2)12yes—
993C22×C4C2511yescharacteristic
994Q16—44no—
995SD16—44no—
996SD16—44no—
997SD16—82no—
998SD16—82no—
999D8—44no—
1000D8—82no—
1001D8—82no—
1002C2×C8—28no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—44no—
1026C2×C8C2×#4112yes—
1027C2×C8H(5,𝔽2)12yes—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
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—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—41no—
1133C42—41no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—81no—
1139C42—81no—
1140C42—81no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—84no—
1183C23—84no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23#53512yes—
1190C23C23×D411yescharacteristic
1191Q8—22no—
1192Q8—22no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—162no—
1200Q8—162no—
1201D4—22no—
1202D4—22no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—82no—
1218D4—84no—
1219D4—84no—
1220D4—84no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
1227D4—162no—
1228D4—162no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
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—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—44no—
1268C2×C4—44no—
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—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—84no—
1311C2×C4—162no—
1312C2×C4#53512yes—
1313C2×C4#57612yes—
1314C2×C4#57712yes—
1315C2×C4C22×#4111yescharacteristic
1316C2×C4C2×H(5,𝔽2)11yescharacteristic
1317C2×C4C2×H(5,𝔽2)11yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4#58511yescharacteristic
1320C2×C4#58511yescharacteristic
1321C8—22no—
1322C8—22no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—168no—
1372C22C2×#53511yescharacteristic
1373C22D4×#4111yescharacteristic
1374C22#349611yescharacteristic
1375C22C2×#57611yescharacteristic
1376C22C2×#57711yescharacteristic
1377C22#358411yescharacteristic
1378C22#358411yescharacteristic
1379C4—22no—
1380C4—22no—
1381C4—22no—
1382C4—41no—
1383C4—42no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4#349011yescharacteristic
1404C4#351311yescharacteristic
1405C4#354211yescharacteristic
1406C4#354511yescharacteristic
1407C2—42no—
1408C2—81no—
1409C2—82no—
1410C2—161no—
1411C2—161no—
1412C2—161no—
1413C2#3842011yescharacteristic
1414C2#6079711yescharacteristic
1415C2#6082211yescharacteristic
1416C2#6147411yescharacteristic
1417C2#6149411yescharacteristic
1418C2#6226611yescharacteristic
1419C2#6227711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38117C2semidirect
2. #38090C2semidirect
3. #33042C2semidirect
4. #32426C2semidirect
5. #32163C2semidirect
6. #32053C2semidirect
7. #31935C2semidirect
8. #31520C2semidirect
9. #30988C2semidirect
10. #30877C2semidirect
11. #30519C2semidirect
12. #30354C2semidirect
13. #30332C2semidirect
14. #29567C2semidirect
15. #29505C2semidirect
16. #29113C2semidirect
17. #28316C2semidirect
18. #24665C2semidirect
19. #24585C2semidirect
20. #24535C2semidirect
21. #24512C2semidirect
22. #24484C2semidirect
23. #24362C2semidirect
24. #24093C2semidirect
25. #24037C2semidirect
26. #23965C2semidirect
27. #23850C2semidirect
28. #22160C2semidirect
29. #22052C2semidirect
30. #21224C2semidirect
31. #21103C2semidirect
37. C2×#482C22semidirect
38. C2×#464C22semidirect
41. C2×#449C22semidirect
45. C2×#427C22semidirect
47. C2×#416C22semidirect
48. C22×C4×C8C22semidirect
49. #2857C22semidirect
59. #2644C22semidirect
69. #2512C22semidirect
78. #2451C22semidirect
83. #2347C22semidirect
84. #2341C22semidirect
87. #2320C22semidirect
90. #2297C22semidirect
92. #2096C22semidirect
93. #2093C22semidirect
94. #2085C22semidirect
95. #2084C22semidirect
96. #2073C22semidirect
97. #2072C22semidirect
99. #2071C22semidirect
101. #2066C22semidirect
104. #2058C22semidirect
105. #2057C22semidirect
106. #2055C22semidirect
112. #2042C22semidirect
118. #2024C22semidirect
119. #2024C22semidirect
121. #2023C22semidirect
125. #2012C22semidirect
132. #1990C22semidirect
133. #1983C22semidirect
136. #1973C22semidirect
138. #1972C22semidirect
141. #1969C22semidirect
142. #1969C22semidirect
145. #1968C22semidirect
146. #1968C22semidirect
148. #1949C22semidirect
149. #1947C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
156. #1934C22semidirect
157. #1934C22semidirect
158. #1928C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
168. #1893C22semidirect
169. #1893C22semidirect
174. #1879C22semidirect
175. #1878C22semidirect
177. #1877C22semidirect
183. #1864C22semidirect
185. #1862C22semidirect
188. #1850C22semidirect
189. #1850C22semidirect
190. #1834C22semidirect
191. #1825C22semidirect
192. #1825C22semidirect
193. #1805C22semidirect
194. #1803C22semidirect
199. #1768C22semidirect
201. #1749C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#381172
#380902
#330422
#324262
#321632
#320532
#319352
#315202
#309882
#308772
#305192
#303542
#303322
#295672
#295052
#291132
#283162
#246652
#245852
#245352
#245122
#244842
#243622
#240932
#240372
#239652
#238502
#221602
#220522
#212242
#211032