Finite Group Databasebeta

← #6784519

Subgroups — #6784519

Order 512.

1737 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36386C211yesmaximal, characteristic, complemented
2#36369C211yesmaximal, characteristic, complemented
3#33183C211yesmaximal, characteristic, complemented
4#32366C211yesmaximal, characteristic, complemented
5#32296C211yesmaximal, characteristic, complemented
6#32106C211yesmaximal, characteristic, complemented
7#31855C211yesmaximal, characteristic, complemented
8#31658C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#30761C211yesmaximal, characteristic, complemented
11#30468C211yesmaximal, characteristic, complemented
12#30346C211yesmaximal, characteristic, complemented
13#30325C211yesmaximal, characteristic, complemented
14#29562C211yesmaximal, characteristic, complemented
15#29503C211yesmaximal, characteristic, complemented
16#29339C211yesmaximal, characteristic, complemented
17#28316C211yesmaximal, characteristic, complemented
18#25544C211yesmaximal, characteristic, complemented
19#25544C211yesmaximal, characteristic, complemented
20#25209C211yesmaximal, characteristic, complemented
21#25207C211yesmaximal, characteristic, complemented
22#25085C211yesmaximal, characteristic, complemented
23#25083C211yesmaximal, characteristic, complemented
24#24659C211yesmaximal, characteristic, complemented
25#24506C211yesmaximal, characteristic, complemented
26#24428C211yesmaximal, characteristic, complemented
27#24428C211yesmaximal, characteristic, complemented
28#22155C211yesmaximal, characteristic, complemented
29#22046C211yesmaximal, characteristic, complemented
30#21107C211yesmaximal, characteristic, complemented
31#21086C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic, complemented
37C2×#466C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic, complemented
40C2×#465C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#461C2211yescharacteristic, complemented
43C2×#449C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#432C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C2×#416C2211yescharacteristic
50C22×#97C2211yescharacteristic, complemented
51#2861C2211yescharacteristic
52#2860C2211yescharacteristic, complemented
53#2857C2211yescharacteristic
54#2856C2211yescharacteristic, complemented
55#2854C2211yescharacteristic
56#2850C2211yescharacteristic
57#2593—21no—
58#2566C2211yescharacteristic
59#2559—21no—
60#2559—21no—
61#2559—21no—
62#2558—21no—
63#2558—21no—
64#2554—21no—
65#2545C2211yescharacteristic
66#2534—21no—
67#2534—21no—
68#2507C2211yescharacteristic, complemented
69#2503C2211yescharacteristic
70#2500C2211yescharacteristic
71#2497C2211yescharacteristic
72#2476—21no—
73#2464—21no—
74#2456—21no—
75#2445C2211yescharacteristic, complemented
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2428C2211yescharacteristic
79#2414C2211yescharacteristic
80#2414C2211yescharacteristic
81#2374—21no—
82#2363—21no—
83#2363C2211yescharacteristic, complemented
84#2363C2211yescharacteristic, complemented
85#2342—21no—
86#2342—21no—
87C4×#124C2211yescharacteristic
88C4×#121C2211yescharacteristic
89#2297C2211yescharacteristic
90#2296C2211yescharacteristic, complemented
91#2293C2211yescharacteristic, complemented
92C2×#390C2211yescharacteristic
93C42×D4C2211yescharacteristic
94#2101C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2096C2211yescharacteristic, complemented
97#2093C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2025C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2014C2211yescharacteristic, complemented
125#2013C2211yescharacteristic, complemented
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2011C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1983C2211yescharacteristic
135#1981C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1973C2211yescharacteristic, complemented
138#1973C2211yescharacteristic, complemented
139#1973C2211yescharacteristic, complemented
140#1972C2211yescharacteristic
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic
143#1972C2211yescharacteristic
144#1961C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1873C2211yescharacteristic, complemented
181#1873C2211yescharacteristic, complemented
182#1869C2211yescharacteristic
183#1869C2211yescharacteristic
184#1865C2211yescharacteristic, complemented
185#1865C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1853C2211yescharacteristic
189#1853C2211yescharacteristic
190#1850C2211yescharacteristic, complemented
191#1850C2211yescharacteristic, complemented
192#1847C2211yescharacteristic, complemented
193#1804C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1767C2211yescharacteristic, complemented
198#1749C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200#1745C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#552—42no—
216#552—42no—
217#546—42no—
218#546—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4D411yescharacteristic
248C2×C4×D4D411yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#496—42no—
265#482—42no—
266#482—42no—
267#466—42no—
268#466—42no—
269#465—42no—
270#465—42no—
271#463—24no—
272#461—42no—
273#449—42no—
274#449—42no—
275#447—24no—
276#447—42no—
277#432—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#416—24no—
291#416—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97—42no—
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337#400—21no—
338#400—21no—
339#400—21no—
340#398—21no—
341#398—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
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#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4D411yescharacteristic
454C4×C4⋊C4D411yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
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⋊C4D411yescharacteristic
467C4×C22⋊C4D411yescharacteristic
468C4×C22⋊C4D411yescharacteristic
469C4×C22⋊C4D411yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C43C2311yescharacteristic
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—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—22no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579#127—41no—
580#127—41no—
581#126—44no—
582#126—82no—
583#125—41no—
584#125—41no—
585#125—44no—
586#124—22no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#123—44no—
593#123—44no—
594#123—44no—
595#123—82no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—44no—
610#121—44no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—82no—
615#121—82no—
616#120—44no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—42no—
628C4×D4—42no—
629C4×D4—82no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—44no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—82no—
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—21no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—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—21no—
720C2×C22⋊C4—44no—
721C2×C22⋊C4—44no—
722C2×C22⋊C4—44no—
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
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×C42—41no—
738C2×C42—41no—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107—41no—
753#107—41no—
754#107—41no—
755#107—41no—
756#106—41no—
757#106—41no—
758#106—41no—
759#106—41no—
760C4⋊C8—22no—
761C4⋊C8—22no—
762C4⋊C8—41no—
763C4⋊C8—41no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
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#102—22no—
777#102—22no—
778#102—22no—
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—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102#4114yes—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802#97—22no—
803#97—22no—
804#97—41no—
805#97—41no—
806#97—41no—
807#97—41no—
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#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851#41—44no—
852#41—44no—
853#41—82no—
854#41—82no—
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×D4—22no—
868C2×D4—22no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
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—41no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
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—81no—
924C2×D4C2×#4112yes—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—22no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—22no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4H(5,𝔽2)12yes—
987C22×C4H(5,𝔽2)12yes—
988C22×C4C2511yescharacteristic
989SD16—82no—
990SD16—82no—
991SD16—82no—
992SD16—82no—
993D8—82no—
994D8—82no—
995D8—82no—
996D8—82no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
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—44no—
1020C2×C8—44no—
1021C2×C8C2×#4112yes—
1022C2×C8H(5,𝔽2)12yes—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
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—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4C2×#4112yes—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
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—42no—
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—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—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—41no—
1130C42—41no—
1131C42—41no—
1132C42—41no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—41no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—81no—
1141C42—81no—
1142C42—81no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
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—41no—
1183C23—84no—
1184C23—84no—
1185C23—84no—
1186C23—84no—
1187C23—162no—
1188C23—162no—
1189C23—162no—
1190C23#53512yes—
1191C23#57512yes—
1192C23C23×D411yescharacteristic
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201D4—22no—
1202D4—22no—
1203D4—44no—
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—41no—
1218D4—84no—
1219D4—84no—
1220D4—84no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
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—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
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—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—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—82no—
1306C2×C4—84no—
1307C2×C4—82no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4#53512yes—
1315C2×C4#57512yes—
1316C2×C4C22×#4111yescharacteristic
1317C2×C4C2×H(5,𝔽2)11yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4#58511yescharacteristic
1321C2×C4#58511yescharacteristic
1322C8—22no—
1323C8—22no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
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—81no—
1372C22—168no—
1373C22C2×#53511yescharacteristic
1374C22D4×#4111yescharacteristic
1375C22#349611yescharacteristic
1376C22C2×#57511yescharacteristic
1377C22C2×#57511yescharacteristic
1378C22#358511yescharacteristic
1379C22#358511yescharacteristic
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—41no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4#349411yescharacteristic
1405C4#351911yescharacteristic
1406C4#353411yescharacteristic
1407C4#356011yescharacteristic
1408C2—42no—
1409C2—42no—
1410C2—82no—
1411C2—161no—
1412C2—161no—
1413C2—161no—
1414C2#3842311yescharacteristic
1415C2#6079011yescharacteristic
1416C2#6082511yescharacteristic
1417C2#6145411yescharacteristic
1418C2#6145911yescharacteristic
1419C2#6229811yescharacteristic
1420C2#6230111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36386C2semidirect
2. #36369C2semidirect
3. #33183C2semidirect
4. #32366C2semidirect
5. #32296C2semidirect
6. #32106C2semidirect
7. #31855C2semidirect
8. #31658C2semidirect
9. #31302C2semidirect
10. #30761C2semidirect
11. #30468C2semidirect
12. #30346C2semidirect
13. #30325C2semidirect
14. #29562C2semidirect
15. #29503C2semidirect
16. #29339C2semidirect
17. #28316C2semidirect
18. #25544C2semidirect
19. #25544C2semidirect
20. #25209C2semidirect
21. #25207C2semidirect
22. #25085C2semidirect
23. #25083C2semidirect
24. #24659C2semidirect
25. #24506C2semidirect
26. #24428C2semidirect
27. #24428C2semidirect
28. #22155C2semidirect
29. #22046C2semidirect
30. #21107C2semidirect
31. #21086C2semidirect
35. C2×#482C22semidirect
36. C2×#482C22semidirect
39. C2×#465C22semidirect
40. C2×#465C22semidirect
42. C2×#461C22semidirect
50. C22×#97C22semidirect
52. #2860C22semidirect
54. #2856C22semidirect
68. #2507C22semidirect
75. #2445C22semidirect
83. #2363C22semidirect
84. #2363C22semidirect
90. #2296C22semidirect
91. #2293C22semidirect
94. #2101C22semidirect
95. #2101C22semidirect
96. #2096C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
100. #2073C22semidirect
101. #2071C22semidirect
103. #2066C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2055C22semidirect
112. #2043C22semidirect
122. #2025C22semidirect
123. #2025C22semidirect
124. #2014C22semidirect
125. #2013C22semidirect
135. #1981C22semidirect
136. #1973C22semidirect
137. #1973C22semidirect
138. #1973C22semidirect
139. #1973C22semidirect
144. #1961C22semidirect
146. #1949C22semidirect
147. #1947C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
157. #1935C22semidirect
158. #1935C22semidirect
159. #1935C22semidirect
160. #1927C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
175. #1877C22semidirect
180. #1873C22semidirect
181. #1873C22semidirect
184. #1865C22semidirect
185. #1865C22semidirect
190. #1850C22semidirect
191. #1850C22semidirect
192. #1847C22semidirect
193. #1804C22semidirect
194. #1802C22semidirect
197. #1767C22semidirect
199. #1749C22semidirect
200. #1745C22semidirect
201. #1735C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#363862
#363692
#331832
#323662
#322962
#321062
#318552
#316582
#313022
#307612
#304682
#303462
#303252
#295622
#295032
#293392
#283162
#255442
#252092
#252072
#250852
#250832
#246592
#245062
#244282
#221552
#220462
#211072
#210862