Finite Group Databasebeta

← #7078243

Subgroups — #7078243

Order 512.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59281C211yesmaximal, characteristic, complemented
2#59273C211yesmaximal, characteristic, complemented
3#32543C211yesmaximal, characteristic, complemented
4#32531C211yesmaximal, characteristic, complemented
5#32457C211yesmaximal, characteristic, complemented
6#32448C211yesmaximal, characteristic, complemented
7#32064C211yesmaximal, characteristic, complemented
8#32050C211yesmaximal, characteristic, complemented
9#30673C211yesmaximal, characteristic, complemented
10#30669C211yesmaximal, characteristic, complemented
11#28784C211yesmaximal, characteristic, complemented
12#27588C211yesmaximal, characteristic, complemented
13#27587C211yesmaximal, characteristic, complemented
14#27514C211yesmaximal, characteristic, complemented
15#27502C211yesmaximal, characteristic, complemented
16#26562C211yesmaximal, characteristic, complemented
17#26546C211yesmaximal, characteristic, complemented
18#25978C211yesmaximal, characteristic, complemented
19#25974C211yesmaximal, characteristic, complemented
20#25212C211yesmaximal, characteristic, complemented
21#25200C211yesmaximal, characteristic, complemented
22#24882C211yesmaximal, characteristic, complemented
23#24877C211yesmaximal, characteristic, complemented
24#24692C211yesmaximal, characteristic, complemented
25#24677C211yesmaximal, characteristic, complemented
26#24275C211yesmaximal, characteristic
27#23546C211yesmaximal, characteristic, complemented
28#22711C211yesmaximal, characteristic, complemented
29#22442C211yesmaximal, characteristic, complemented
30#22071C211yesmaximal, characteristic, complemented
31#21963C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#551—21no—
34C2×#480C2211yescharacteristic
35C2×#480C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#476C2211yescharacteristic, complemented
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#423C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#418C2211yescharacteristic
46#2760—21no—
47#2750—21no—
48#2723—21no—
49#2706—21no—
50#2572—21no—
51#2572—21no—
52#2563C2211yescharacteristic, complemented
53#2542C2211yescharacteristic
54#2527—21no—
55#2514C2211yescharacteristic, complemented
56#2514C2211yescharacteristic, complemented
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2503C2211yescharacteristic, complemented
60#2501C2211yescharacteristic
61#2493—21no—
62#2492C2211yescharacteristic, complemented
63#2491C2211yescharacteristic
64#2482—21no—
65#2479—21no—
66#2461—21no—
67#2457—21no—
68#2440C2211yescharacteristic
69#2439C2211yescharacteristic
70#2437—21no—
71#2422C2211yescharacteristic
72#2420C2211yescharacteristic, complemented
73#2418—21no—
74#2408C2211yescharacteristic
75#2407C2211yescharacteristic
76#2361C2211yescharacteristic
77#2361C2211yescharacteristic, complemented
78#2357C2211yescharacteristic, complemented
79#2354C2211yescharacteristic
80#2353—21no—
81#2352C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2339C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×#123C2211yescharacteristic
86#2297C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2285C2211yescharacteristic
89#2283C2211yescharacteristic
90#2096C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2093C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic, complemented
126#2024C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2000C2211yescharacteristic
129#1999C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1972C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1923C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1872C2211yescharacteristic, complemented
172#1870C2211yescharacteristic
173#1864C2211yescharacteristic, complemented
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic, complemented
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1850C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1817C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1807C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1776C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#551—48no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123D411yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#480—42no—
252#480—42no—
253#476—42no—
254#476—42no—
255#466—42no—
256#465—42no—
257#442—42no—
258C4×D8—42no—
259#435—24no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
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
276#423—24no—
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#418—42no—
285#417—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#401—21no—
319#401—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
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#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387D411yescharacteristic
393#387D411yescharacteristic
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386D411yescharacteristic
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#381—21no—
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376—21no—
463C2×#95—21no—
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531AGL(1,ℤ/8)—416no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16#4114yes—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565#126—44no—
566#126—44no—
567#124—44no—
568#123—24no—
569#123—44no—
570#123—44no—
571#123—82no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—82no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#120—44no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—44no—
596C4×D4—44no—
597#117—44no—
598#117—44no—
599#117—41no—
600#117—41no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
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—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
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—44no—
680C2×C22⋊C4—44no—
681C2×C22⋊C4—82no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—22no—
691C2×C42—22no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—22no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—22no—
759#97—41no—
760C4×C8—41no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
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#95—21no—
793#95—21no—
794#95—21no—
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
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817#41—44no—
818#41—44no—
819#41—82no—
820#41—82no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×D4—22no—
834C2×D4—22no—
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—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—41no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4H(5,𝔽2)12yes—
872C2×D4H(5,𝔽2)12yes—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C2×#4112yes—
939C22×C42−1+412yes—
940C22×C4C2511yescharacteristic
941SD16—44no—
942SD16—44no—
943D8—28no—
944D8—44no—
945M16—44no—
946M16—82no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—82no—
970C2×C8C2×#4112yes—
971C2×C8C2×#4112yes—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
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—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4AGL(1,ℤ/8)14yescomplemented
1064C42—22no—
1065C42—22no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—22no—
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—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23#54712yes—
1124C23C2×AGL(1,ℤ/8)12yes—
1125C23C23×D411yescharacteristic
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—162no—
1131Q8—162no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—44no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—162no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
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—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—44no—
1188C2×C4—41no—
1189C2×C4—41no—
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—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—82no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4#54712yes—
1241C2×C4C2×AGL(1,ℤ/8)12yes—
1242C2×C4C2×AGL(1,ℤ/8)12yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—22no—
1250C8—22no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—168no—
1293C22C2×#54711yescharacteristic
1294C22#348811yescharacteristic
1295C22#348811yescharacteristic
1296C22C22×AGL(1,ℤ/8)11yescharacteristic
1297C22#358411yescharacteristic
1298C22#358511yescharacteristic
1299C22#358611yescharacteristic
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4#349011yescharacteristic
1326C4#351011yescharacteristic
1327C4#353511yescharacteristic
1328C4#353511yescharacteristic
1329C2—42no—
1330C2—42no—
1331C2—82no—
1332C2—82no—
1333C2—161no—
1334C2#4395911yescharacteristic
1335C2#6125211yescharacteristic
1336C2#6127411yescharacteristic
1337C2#6195911yescharacteristic
1338C2#6198911yescharacteristic
1339C2#6204811yescharacteristic
1340C2#6207611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24275C2
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. #59281C2semidirect
2. #59273C2semidirect
3. #32543C2semidirect
4. #32531C2semidirect
5. #32457C2semidirect
6. #32448C2semidirect
7. #32064C2semidirect
8. #32050C2semidirect
9. #30673C2semidirect
10. #30669C2semidirect
11. #28784C2semidirect
12. #27588C2semidirect
13. #27587C2semidirect
14. #27514C2semidirect
15. #27502C2semidirect
16. #26562C2semidirect
17. #26546C2semidirect
18. #25978C2semidirect
19. #25974C2semidirect
20. #25212C2semidirect
21. #25200C2semidirect
22. #24882C2semidirect
23. #24877C2semidirect
24. #24692C2semidirect
25. #24677C2semidirect
27. #23546C2semidirect
28. #22711C2semidirect
29. #22442C2semidirect
30. #22071C2semidirect
31. #21963C2semidirect
35. C2×#480C22semidirect
37. C2×#476C22semidirect
52. #2563C22semidirect
55. #2514C22semidirect
56. #2514C22semidirect
59. #2503C22semidirect
62. #2492C22semidirect
72. #2420C22semidirect
77. #2361C22semidirect
78. #2357C22semidirect
90. #2096C22semidirect
91. #2096C22semidirect
92. #2095C22semidirect
93. #2093C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
103. #2072C22semidirect
104. #2071C22semidirect
105. #2071C22semidirect
106. #2068C22semidirect
108. #2066C22semidirect
110. #2058C22semidirect
111. #2057C22semidirect
122. #2035C22semidirect
125. #2033C22semidirect
126. #2024C22semidirect
130. #1993C22semidirect
131. #1990C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1948C22semidirect
142. #1948C22semidirect
143. #1948C22semidirect
144. #1947C22semidirect
145. #1947C22semidirect
146. #1944C22semidirect
147. #1942C22semidirect
148. #1940C22semidirect
149. #1939C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
158. #1926C22semidirect
162. #1924C22semidirect
163. #1923C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
171. #1872C22semidirect
173. #1864C22semidirect
176. #1862C22semidirect
180. #1853C22semidirect
182. #1852C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
186. #1836C22semidirect
192. #1807C22semidirect
194. #1802C22semidirect
199. #1776C22semidirect
202. C2×#340C22semidirect
1063. C22⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#592812
#592732
#325432
#325312
#324572
#324482
#320642
#320502
#306732
#306692
#287842
#275882
#275872
#275142
#275022
#265622
#265462
#259782
#259742
#252122
#252002
#248822
#248772
#246922
#246772
#242752
#235462
#227112
#224422
#220712
#219632