Finite Group Databasebeta

← #6563091

Subgroups — #6563091

Order 512.

1647 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38254C211yesmaximal, characteristic, complemented
2#34431C211yesmaximal, characteristic, complemented
3#30137C211yesmaximal, characteristic, complemented
4#30065C211yesmaximal, characteristic, complemented
5#29919C211yesmaximal, characteristic, complemented
6#29530C211yesmaximal, characteristic, complemented
7#29365C211yesmaximal, characteristic, complemented
8#29269C211yesmaximal, characteristic, complemented
9#28378C211yesmaximal, characteristic, complemented
10#27514C211yesmaximal, characteristic, complemented
11#27507C211yesmaximal, characteristic, complemented
12#27215C211yesmaximal, characteristic, complemented
13#27206C211yesmaximal, characteristic, complemented
14#26390C211yesmaximal, characteristic, complemented
15#26370C211yesmaximal, characteristic, complemented
16#26366C211yesmaximal, characteristic, complemented
17#26347C211yesmaximal, characteristic, complemented
18#26184C211yesmaximal, characteristic, complemented
19#26172C211yesmaximal, characteristic, complemented
20#25507C211yesmaximal, characteristic, complemented
21#25101C211yesmaximal, characteristic, complemented
22#25088C211yesmaximal, characteristic, complemented
23#23939C211yesmaximal, characteristic
24#23808C211yesmaximal, characteristic, complemented
25#23784C211yesmaximal, characteristic, complemented
26#23735C211yesmaximal, characteristic, complemented
27#23034C211yesmaximal, characteristic, complemented
28#23033C211yesmaximal, characteristic, complemented
29#22880C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#22598C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#478C2211yescharacteristic, complemented
34C2×#478C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic
45C2×#428C2211yescharacteristic
46C2×#427C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C22×#102C2211yescharacteristic
49#2861C2211yescharacteristic
50#2796—21no—
51#2786—21no—
52#2735—21no—
53#2735—21no—
54#2644C2211yescharacteristic
55#2625C2211yescharacteristic
56#2601—21no—
57#2516—21no—
58#2512C2211yescharacteristic
59#2482—21no—
60#2480—21no—
61#2454C2211yescharacteristic
62#2448C2211yescharacteristic
63#2447C2211yescharacteristic
64#2441C2211yescharacteristic
65#2435C2211yescharacteristic
66#2377—21no—
67#2376—21no—
68#2363C2211yescharacteristic
69#2363C2211yescharacteristic
70#2362C2211yescharacteristic
71#2361—21no—
72#2361C2211yescharacteristic
73#2361C2211yescharacteristic
74#2359—21no—
75#2357C2211yescharacteristic, complemented
76#2354C2211yescharacteristic, complemented
77#2349C2211yescharacteristic, complemented
78D4×C4⋊C4C2211yescharacteristic, complemented
79D4×C22⋊C4C2211yescharacteristic
80#2335—21no—
81#2330C2211yescharacteristic, complemented
82#2328C2211yescharacteristic, complemented
83#2326C2211yescharacteristic
84#2325—21no—
85#2324—21no—
86#2322—21no—
87#2317C2211yescharacteristic
88#2309C2211yescharacteristic
89C4×#127C2211yescharacteristic, complemented
90C4×#125C2211yescharacteristic, complemented
91#2298C2211yescharacteristic
92#2293C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2096C2211yescharacteristic, complemented
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic, complemented
103#2092C2211yescharacteristic
104#2092C2211yescharacteristic
105#2092C2211yescharacteristic
106#2092C2211yescharacteristic
107#2088C2211yescharacteristic, complemented
108#2086C2211yescharacteristic, complemented
109#2085C2211yescharacteristic, complemented
110#2084C2211yescharacteristic, complemented
111#2074C2211yescharacteristic, complemented
112#2072C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic, complemented
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic, complemented
117#2059C2211yescharacteristic, complemented
118#2059C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2041C2211yescharacteristic, complemented
125#2026C2211yescharacteristic, complemented
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2014C2211yescharacteristic, complemented
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1973C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1948C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1934C2211yescharacteristic
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic, complemented
150#1926C2211yescharacteristic, complemented
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1893C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1877C2211yescharacteristic, complemented
172#1877C2211yescharacteristic, complemented
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic
175#1873C2211yescharacteristic
176#1872C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1864C2211yescharacteristic, complemented
184#1864C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1854C2211yescharacteristic
188#1853C2211yescharacteristic
189#1851C2211yescharacteristic
190#1850C2211yescharacteristic
191#1839C2211yescharacteristic, complemented
192#1832C2211yescharacteristic, complemented
193#1818C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1776C2211yescharacteristic, complemented
196#1767C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#540—24no—
213#540—24no—
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248#478—42no—
249#478—42no—
250#468—24no—
251#465—24no—
252#463—42no—
253#463—42no—
254#447—24no—
255#447—24no—
256#442—42no—
257#440—42no—
258C4×SD16—42no—
259C4×D8—42no—
260#428—42no—
261#427—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#418—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102—42no—
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#394—21no—
335#394—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387D411yescharacteristic
403#387D411yescharacteristic
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2311yescharacteristic
462C2×#95—21no—
463C43C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#127—22no—
556#127—22no—
557#126—82no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125—41no—
562#124—22no—
563#124—41no—
564#124—41no—
565#124—41no—
566#123—28no—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570#121—28no—
571#121—28no—
572#121—22no—
573#121—22no—
574#121#4114yes—
575#121#4114yes—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—82no—
595C4×D4—82no—
596C4×D4—82no—
597C4×D4—82no—
598#117—22no—
599#117—22no—
600#117—41no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—82no—
605#117—82no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—82no—
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
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—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—22no—
716#107—22no—
717#107—22no—
718#107—22no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—22no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#103—22no—
734#103—22no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763#97—22no—
764#97—41no—
765#97—41no—
766C4×C8—22no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4C2×#4112yes—
863C2×D4C2×#4112yes—
864C2×D42−1+412yes—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2×#4112yes—
922C22×C4C2×#4112yes—
923C22×C4C2511yescharacteristic
924SD16—44no—
925SD16—44no—
926D8—44no—
927D8—44no—
928D8—82no—
929D8—82no—
930M16—44no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—44no—
954C2×C8H(5,𝔽2)12yes—
955C2×C8H(5,𝔽2)12yes—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4C2×#4112yes—
1005C4⋊C4C2×#4112yes—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23#52512yes—
1120C23C23×D411yescharacteristic
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125D4—22no—
1126D4—22no—
1127D4—22no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—84no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4#52512yes—
1234C2×C4C22×#4111yescharacteristic
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×2−1+411yescharacteristic
1239C2×C4#58511yescharacteristic
1240C8—22no—
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—168no—
1284C22C2×#52511yescharacteristic
1285C22#348911yescharacteristic
1286C22#349811yescharacteristic
1287C22#358411yescharacteristic
1288C22#358511yescharacteristic
1289C22#358511yescharacteristic
1290C22#358511yescharacteristic
1291C4—22no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4#351311yescharacteristic
1317C4#351311yescharacteristic
1318C4#352011yescharacteristic
1319C4#352011yescharacteristic
1320C2—42no—
1321C2—82no—
1322C2—82no—
1323C2—82no—
1324C2—161no—
1325C2#3599011yescharacteristic
1326C2#6057411yescharacteristic
1327C2#6059211yescharacteristic
1328C2#6219511yescharacteristic
1329C2#6223111yescharacteristic
1330C2#6244111yescharacteristic
1331C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23939C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38254C2semidirect
2. #34431C2semidirect
3. #30137C2semidirect
4. #30065C2semidirect
5. #29919C2semidirect
6. #29530C2semidirect
7. #29365C2semidirect
8. #29269C2semidirect
9. #28378C2semidirect
10. #27514C2semidirect
11. #27507C2semidirect
12. #27215C2semidirect
13. #27206C2semidirect
14. #26390C2semidirect
15. #26370C2semidirect
16. #26366C2semidirect
17. #26347C2semidirect
18. #26184C2semidirect
19. #26172C2semidirect
20. #25507C2semidirect
21. #25101C2semidirect
22. #25088C2semidirect
24. #23808C2semidirect
25. #23784C2semidirect
26. #23735C2semidirect
27. #23034C2semidirect
28. #23033C2semidirect
29. #22880C2semidirect
30. #22858C2semidirect
31. #22598C2semidirect
33. C2×#478C22semidirect
34. C2×#478C22semidirect
42. C2×#440C22semidirect
43. C2×C4×SD16C22semidirect
75. #2357C22semidirect
76. #2354C22semidirect
77. #2349C22semidirect
78. D4×C4⋊C4C22semidirect
81. #2330C22semidirect
82. #2328C22semidirect
89. C4×#127C22semidirect
90. C4×#125C22semidirect
93. #2101C22semidirect
94. #2100C22semidirect
95. #2097C22semidirect
96. #2096C22semidirect
99. #2094C22semidirect
102. #2093C22semidirect
107. #2088C22semidirect
108. #2086C22semidirect
109. #2085C22semidirect
110. #2084C22semidirect
111. #2074C22semidirect
112. #2072C22semidirect
114. #2067C22semidirect
116. #2065C22semidirect
117. #2059C22semidirect
118. #2059C22semidirect
119. #2059C22semidirect
124. #2041C22semidirect
125. #2026C22semidirect
128. #2014C22semidirect
135. #1973C22semidirect
136. #1973C22semidirect
139. #1948C22semidirect
140. #1948C22semidirect
141. #1944C22semidirect
142. #1942C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
149. #1926C22semidirect
150. #1926C22semidirect
153. #1921C22semidirect
154. #1918C22semidirect
155. #1917C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
158. #1916C22semidirect
171. #1877C22semidirect
172. #1877C22semidirect
177. #1865C22semidirect
178. #1865C22semidirect
181. #1864C22semidirect
182. #1864C22semidirect
183. #1864C22semidirect
184. #1864C22semidirect
185. #1862C22semidirect
186. #1862C22semidirect
191. #1839C22semidirect
192. #1832C22semidirect
194. #1776C22semidirect
195. #1776C22semidirect
196. #1767C22semidirect
201. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#382542
#344312
#301372
#300652
#299192
#295302
#293652
#292692
#283782
#275142
#275072
#272152
#272062
#263902
#263702
#263662
#263472
#261842
#261722
#255072
#251012
#250882
#239392
#238082
#237842
#237352
#230342
#230332
#228802
#228582
#225982