Finite Group Databasebeta

← #7080689

Subgroups — #7080689

Order 512.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59239C211yesmaximal, characteristic, complemented
2#59099C211yesmaximal, characteristic
3#32170C211yesmaximal, characteristic, complemented
4#32124C211yesmaximal, characteristic, complemented
5#31905C211yesmaximal, characteristic, complemented
6#31859C211yesmaximal, characteristic, complemented
7#31827C211yesmaximal, characteristic, complemented
8#31649C211yesmaximal, characteristic, complemented
9#30610C211yesmaximal, characteristic, complemented
10#30527C211yesmaximal, characteristic, complemented
11#27590C211yesmaximal, characteristic, complemented
12#27426C211yesmaximal, characteristic, complemented
13#27270C211yesmaximal, characteristic, complemented
14#27063C211yesmaximal, characteristic, complemented
15#26735C211yesmaximal, characteristic, complemented
16#26425C211yesmaximal, characteristic, complemented
17#26228C211yesmaximal, characteristic, complemented
18#25325C211yesmaximal, characteristic, complemented
19#25138C211yesmaximal, characteristic, complemented
20#25093C211yesmaximal, characteristic, complemented
21#24917C211yesmaximal, characteristic, complemented
22#24639C211yesmaximal, characteristic, complemented
23#24538C211yesmaximal, characteristic, complemented
24#24368C211yesmaximal, characteristic, complemented
25#23931C211yesmaximal, characteristic, complemented
26#23862C211yesmaximal, characteristic, complemented
27#23547C211yesmaximal, characteristic, complemented
28#22865C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22073C211yesmaximal, characteristic, complemented
31#21891C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#464C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic
39C2×#448C2211yescharacteristic
40C2×#448C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#423C2211yescharacteristic, complemented
46C2×#417C2211yescharacteristic
47C2×#419C2211yescharacteristic, complemented
48C2×#418C2211yescharacteristic
49#2762—21no—
50#2759—21no—
51#2688—21no—
52#2678—21no—
53#2605—21no—
54#2568C2211yescharacteristic, complemented
55#2557—21no—
56#2544C2211yescharacteristic
57#2532—21no—
58#2514C2211yescharacteristic, complemented
59#2514C2211yescharacteristic, complemented
60#2510—21no—
61#2499C2211yescharacteristic
62#2493—21no—
63#2492C2211yescharacteristic
64#2492C2211yescharacteristic
65#2488—21no—
66#2472—21no—
67#2457—21no—
68#2452C2211yescharacteristic
69#2447C2211yescharacteristic
70#2440C2211yescharacteristic, complemented
71#2433C2211yescharacteristic
72#2431C2211yescharacteristic
73#2427C2211yescharacteristic
74#2421C2211yescharacteristic
75#2414C2211yescharacteristic
76#2409C2211yescharacteristic
77#2407—21no—
78#2404—21no—
79#2368—21no—
80#2366C2211yescharacteristic
81#2363C2211yescharacteristic
82#2362C2211yescharacteristic
83#2358—21no—
84#2355C2211yescharacteristic, complemented
85#2352C2211yescharacteristic
86Q8×C22⋊C4C2211yescharacteristic, complemented
87D4×C22⋊C4C2211yescharacteristic
88C4×#123C2211yescharacteristic
89#2297C2211yescharacteristic
90C2×#391C2211yescharacteristic, complemented
91#2283C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2092C2211yescharacteristic
96#2087C2211yescharacteristic, complemented
97#2075C2211yescharacteristic
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2056C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic, complemented
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic
131#2000C2211yescharacteristic
132#1988C2211yescharacteristic, complemented
133#1988C2211yescharacteristic, complemented
134#1988C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1959C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1919C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic, complemented
163#1895C2211yescharacteristic, complemented
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1874C2211yescharacteristic
178#1874C2211yescharacteristic, complemented
179#1873C2211yescharacteristic
180#1870C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1817C2211yescharacteristic, complemented
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C2×#137—42no—
208C2×#137—42no—
209C2×#137—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C22×M16C2311yescharacteristic
220C22×M16C2311yescharacteristic
221#546—24no—
222#546—42no—
223#532—24no—
224#532—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#124—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123D411yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C42C2311yescharacteristic
262#486—42no—
263#468—42no—
264#464—42no—
265#460—42no—
266#450—42no—
267#450—42no—
268#448—24no—
269#448—42no—
270#440—42no—
271#436—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276#423—42no—
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#419—42no—
285#418—42no—
286#417—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#401—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#395—21no—
345#395—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390—21no—
379#390—21no—
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388D411yescharacteristic
399#388D411yescharacteristic
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386D411yescharacteristic
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385D411yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#383—21no—
434#383—21no—
435#382—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#381—21no—
441#381D411yescharacteristic
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#376—21no—
467C2×#95—21no—
468C2×#95—21no—
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#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—44no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—82no—
508C2×#41—82no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—21no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—22no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4C2×D411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C2×D411yescharacteristic
548C23×C4C2×D411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551#137—416no—
552C2×Q16—22no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×M16—22no—
577C2×M16—22no—
578C2×M16—41no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16—41no—
582C2×M16—41no—
583C2×M16—41no—
584C2×M16—41no—
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597#127—22no—
598#127—22no—
599#127—41no—
600#127—41no—
601#124—22no—
602#124—44no—
603#124—41no—
604#124—41no—
605#124—41no—
606#123—42no—
607#123—44no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—44no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—82no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—44no—
620#121—44no—
621#121—41no—
622#121—41no—
623#121#4114yes—
624#120—44no—
625#120—44no—
626#120—82no—
627C4×Q8—22no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—44no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—82no—
643#117—41no—
644#117—41no—
645#117—41no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×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—44no—
709C2×C22⋊C4—82no—
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#107—41no—
736#107—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—41no—
784C4×C8—41no—
785C4×C8—41no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#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—42no—
840C24—42no—
841C24—42no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24C22×D411yescharacteristic
847C24C22×D411yescharacteristic
848#41—44no—
849#41—44no—
850#41—82no—
851#41—82no—
852#41—816no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×Q8—81no—
880C2×Q8—81no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×Q8H(5,𝔽2)12yes—
884C2×D4—22no—
885C2×D4—24no—
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—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—44no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
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×D4C2×#4112yes—
935C2×D4H(5,𝔽2)12yes—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—22no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—21no—
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—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
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×C4—81no—
985C22×C4—81no—
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×C4C22×D411yescharacteristic
998C22×C4C2×#4112yes—
999C22×C4H(5,𝔽2)12yes—
1000C22×C4C2511yescharacteristic
1001Q16—44no—
1002Q16—44no—
1003SD16—44no—
1004SD16—44no—
1005SD16—44no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009M16—44no—
1010M16—82no—
1011M16—82no—
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—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
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—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4C2×#4112yes—
1075C22⋊C4—22no—
1076C22⋊C4—24no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
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—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—
1113C42—22no—
1114C42—22no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—42no—
1126C42—42no—
1127C42—81no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C42—81no—
1132C42—81no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—22no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—21no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
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—84no—
1168C23—84no—
1169C23—84no—
1170C23—162no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23#54612yes—
1175C23C23×D411yescharacteristic
1176Q8—22no—
1177Q8—22no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—84no—
1189Q8—84no—
1190Q8—162no—
1191D4—22no—
1192D4—22no—
1193D4—22no—
1194D4—22no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—84no—
1204D4—84no—
1205D4—82no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—162no—
1212D4—162no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
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—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
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—44no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
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—82no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4#54612yes—
1303C2×C4#57512yes—
1304C2×C4#57712yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—42no—
1337C22—41no—
1338C22—42no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—168no—
1355C22C2×#54611yescharacteristic
1356C22#348811yescharacteristic
1357C22#348811yescharacteristic
1358C22C2×#57511yescharacteristic
1359C22C2×#57711yescharacteristic
1360C22#358511yescharacteristic
1361C22#358611yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4#351311yescharacteristic
1388C4#351311yescharacteristic
1389C4#353211yescharacteristic
1390C4#354511yescharacteristic
1391C2—42no—
1392C2—81no—
1393C2—82no—
1394C2—82no—
1395C2—161no—
1396C2#4400111yescharacteristic
1397C2#6116511yescharacteristic
1398C2#6118411yescharacteristic
1399C2#6197111yescharacteristic
1400C2#6199711yescharacteristic
1401C2#6203211yescharacteristic
1402C2#6208511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59099C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59239C2semidirect
3. #32170C2semidirect
4. #32124C2semidirect
5. #31905C2semidirect
6. #31859C2semidirect
7. #31827C2semidirect
8. #31649C2semidirect
9. #30610C2semidirect
10. #30527C2semidirect
11. #27590C2semidirect
12. #27426C2semidirect
13. #27270C2semidirect
14. #27063C2semidirect
15. #26735C2semidirect
16. #26425C2semidirect
17. #26228C2semidirect
18. #25325C2semidirect
19. #25138C2semidirect
20. #25093C2semidirect
21. #24917C2semidirect
22. #24639C2semidirect
23. #24538C2semidirect
24. #24368C2semidirect
25. #23931C2semidirect
26. #23862C2semidirect
27. #23547C2semidirect
28. #22865C2semidirect
29. #22427C2semidirect
30. #22073C2semidirect
31. #21891C2semidirect
37. C2×#464C22semidirect
40. C2×#448C22semidirect
45. C2×#423C22semidirect
47. C2×#419C22semidirect
54. #2568C22semidirect
58. #2514C22semidirect
59. #2514C22semidirect
70. #2440C22semidirect
84. #2355C22semidirect
86. Q8×C22⋊C4C22semidirect
90. C2×#391C22semidirect
91. #2283C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2097C22semidirect
96. #2087C22semidirect
98. #2074C22semidirect
100. #2073C22semidirect
102. #2068C22semidirect
104. #2056C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
108. #2056C22semidirect
114. #2055C22semidirect
115. #2042C22semidirect
119. #2024C22semidirect
120. #2024C22semidirect
121. #2024C22semidirect
125. #2015C22semidirect
132. #1988C22semidirect
133. #1988C22semidirect
134. #1988C22semidirect
139. #1968C22semidirect
140. #1959C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
145. #1935C22semidirect
146. #1933C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
153. #1925C22semidirect
156. #1919C22semidirect
157. #1919C22semidirect
158. #1916C22semidirect
159. #1916C22semidirect
162. #1895C22semidirect
163. #1895C22semidirect
168. #1878C22semidirect
174. #1877C22semidirect
175. #1877C22semidirect
178. #1874C22semidirect
181. #1865C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
187. #1851C22semidirect
189. #1817C22semidirect
193. #1804C22semidirect
194. #1804C22semidirect
199. C4×#103C22semidirect
201. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#592392
#590992
#321702
#321242
#319052
#318592
#318272
#316492
#306102
#305272
#275902
#274262
#272702
#270632
#267352
#264252
#262282
#253252
#251382
#250932
#249172
#246392
#245382
#243682
#239312
#238622
#235472
#228652
#224272
#220732
#218912