Finite Group Databasebeta

← #7078250

Subgroups — #7078250

Order 512.

1696 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59277C211yesmaximal, characteristic, complemented
2#59273C211yesmaximal, characteristic, complemented
3#32536C211yesmaximal, characteristic, complemented
4#32533C211yesmaximal, characteristic, complemented
5#32456C211yesmaximal, characteristic, complemented
6#32446C211yesmaximal, characteristic, complemented
7#32072C211yesmaximal, characteristic, complemented
8#32046C211yesmaximal, characteristic, complemented
9#30675C211yesmaximal, characteristic, complemented
10#30664C211yesmaximal, characteristic, complemented
11#28783C211yesmaximal, characteristic, complemented
12#27585C211yesmaximal, characteristic, complemented
13#27584C211yesmaximal, characteristic, complemented
14#27507C211yesmaximal, characteristic, complemented
15#27503C211yesmaximal, characteristic, complemented
16#26566C211yesmaximal, characteristic, complemented
17#26554C211yesmaximal, characteristic, complemented
18#25968C211yesmaximal, characteristic, complemented
19#25967C211yesmaximal, characteristic, complemented
20#25204C211yesmaximal, characteristic, complemented
21#25200C211yesmaximal, characteristic, complemented
22#24882C211yesmaximal, characteristic, complemented
23#24879C211yesmaximal, characteristic, complemented
24#24690C211yesmaximal, characteristic, complemented
25#24678C211yesmaximal, characteristic, complemented
26#24275C211yesmaximal, characteristic
27#23546C211yesmaximal, characteristic, complemented
28#22711C211yesmaximal, characteristic, complemented
29#22443C211yesmaximal, characteristic, complemented
30#22071C211yesmaximal, characteristic, complemented
31#21964C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#551—21no—
34C2×#483C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C4×SD16C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#423C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#418C2211yescharacteristic
46#2740—21no—
47#2723—21no—
48#2706—21no—
49#2706—21no—
50#2565C2211yescharacteristic, complemented
51#2553—21no—
52#2542C2211yescharacteristic
53#2522—21no—
54#2517—21no—
55#2513C2211yescharacteristic, complemented
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic, complemented
59#2501C2211yescharacteristic
60#2501C2211yescharacteristic, complemented
61#2491C2211yescharacteristic
62#2490C2211yescharacteristic, complemented
63#2482—21no—
64#2479—21no—
65#2479—21no—
66#2471—21no—
67#2461—21no—
68#2441C2211yescharacteristic
69#2440C2211yescharacteristic
70#2437—21no—
71#2423C2211yescharacteristic, complemented
72#2422C2211yescharacteristic
73#2418—21no—
74#2408C2211yescharacteristic
75#2407C2211yescharacteristic
76#2374—21no—
77#2361C2211yescharacteristic
78#2360C2211yescharacteristic, complemented
79#2355C2211yescharacteristic, complemented
80#2354C2211yescharacteristic
81#2352C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2341C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×#123C2211yescharacteristic
86#2297C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2285C2211yescharacteristic
89#2285C2211yescharacteristic
90#2095C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2094C2211yescharacteristic, complemented
94#2094C2211yescharacteristic, complemented
95#2094C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, 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#2025C2211yescharacteristic
127#2023C2211yescharacteristic, complemented
128#2000C2211yescharacteristic
129#1999C2211yescharacteristic
130#1992C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1970C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1948C2211yescharacteristic, complemented
138#1948C2211yescharacteristic, complemented
139#1948C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic, complemented
163#1923C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic, complemented
172#1870C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
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#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
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×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117—21no—
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#483—42no—
255#480—42no—
256#478—42no—
257#475—42no—
258#466—42no—
259#465—42no—
260#440—42no—
261C4×SD16—42no—
262#435—24no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279#423—24no—
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#418—42no—
288#417—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#399—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#392—21no—
352#392—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
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#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387D411yescharacteristic
404#387D411yescharacteristic
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386D411yescharacteristic
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385D411yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382—21no—
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
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⋊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×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
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×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528AGL(1,ℤ/8)—416no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—41no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16#4114yes—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#126—44no—
561#126—44no—
562#126—82no—
563#125—41no—
564#125—41no—
565#124—44no—
566#123—24no—
567#123—44no—
568#123—44no—
569#123—44no—
570#123—82no—
571#123—82no—
572C22⋊Q8—22no—
573C22⋊Q8—44no—
574C22⋊Q8—41no—
575C22⋊Q8—44no—
576C22⋊Q8—82no—
577#121—22no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#120—44no—
584C4×Q8—22no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—44no—
596#117—44no—
597#117—44no—
598#117—41no—
599#117—41no—
600#117—82no—
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—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—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
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—44no—
691C2×C22⋊C4—44no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
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—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—22no—
772#97—41no—
773C4×C8—41no—
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#95—21no—
796#95—21no—
797#95—21no—
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—44no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—42no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8H(5,𝔽2)12yes—
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—21no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—41no—
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×D4—81no—
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—21no—
880C22×C4—22no—
881C22×C4—22no—
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—21no—
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—81no—
911C22×C4—81no—
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×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C2×#4112yes—
933C22×C42−1+412yes—
934C22×C4C2511yescharacteristic
935SD16—28no—
936SD16—44no—
937D8—44no—
938D8—44no—
939M16—44no—
940M16—82no—
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—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—82no—
964C2×C8C2×#4112yes—
965C2×C8C2×#4112yes—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
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—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—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—81no—
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—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
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—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
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⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4AGL(1,ℤ/8)14yescomplemented
1069C42—22no—
1070C42—22no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
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—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23#54712yes—
1131C23C2×AGL(1,ℤ/8)12yes—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—41no—
1136Q8—41no—
1137Q8—162no—
1138D4—22no—
1139D4—22no—
1140D4—44no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—84no—
1152D4—84no—
1153D4—84no—
1154D4—162no—
1155D4—162no—
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—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
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—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—44no—
1194C2×C4—44no—
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—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4#54712yes—
1244C2×C4C2×AGL(1,ℤ/8)12yes—
1245C2×C4C2×AGL(1,ℤ/8)12yes—
1246C2×C4#57712yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×2−1+411yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—22no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
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—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22C2×#54711yescharacteristic
1298C22#348811yescharacteristic
1299C22#348811yescharacteristic
1300C22C22×AGL(1,ℤ/8)11yescharacteristic
1301C22C2×#57711yescharacteristic
1302C22#358511yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4#349011yescharacteristic
1330C4#351011yescharacteristic
1331C4#353511yescharacteristic
1332C4#353511yescharacteristic
1333C2—42no—
1334C2—42no—
1335C2—82no—
1336C2—161no—
1337C2—161no—
1338C2#4395911yescharacteristic
1339C2#6125211yescharacteristic
1340C2#6127211yescharacteristic
1341C2#6196111yescharacteristic
1342C2#6198311yescharacteristic
1343C2#6204211yescharacteristic
1344C2#6209411yescharacteristic
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. #59277C2semidirect
2. #59273C2semidirect
3. #32536C2semidirect
4. #32533C2semidirect
5. #32456C2semidirect
6. #32446C2semidirect
7. #32072C2semidirect
8. #32046C2semidirect
9. #30675C2semidirect
10. #30664C2semidirect
11. #28783C2semidirect
12. #27585C2semidirect
13. #27584C2semidirect
14. #27507C2semidirect
15. #27503C2semidirect
16. #26566C2semidirect
17. #26554C2semidirect
18. #25968C2semidirect
19. #25967C2semidirect
20. #25204C2semidirect
21. #25200C2semidirect
22. #24882C2semidirect
23. #24879C2semidirect
24. #24690C2semidirect
25. #24678C2semidirect
27. #23546C2semidirect
28. #22711C2semidirect
29. #22443C2semidirect
30. #22071C2semidirect
31. #21964C2semidirect
34. C2×#483C22semidirect
36. C2×#475C22semidirect
50. #2565C22semidirect
55. #2513C22semidirect
58. #2512C22semidirect
60. #2501C22semidirect
62. #2490C22semidirect
71. #2423C22semidirect
78. #2360C22semidirect
79. #2355C22semidirect
90. #2095C22semidirect
93. #2094C22semidirect
94. #2094C22semidirect
95. #2094C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
101. #2072C22semidirect
102. #2072C22semidirect
105. #2071C22semidirect
106. #2067C22semidirect
109. #2065C22semidirect
110. #2059C22semidirect
111. #2058C22semidirect
122. #2035C22semidirect
125. #2033C22semidirect
127. #2023C22semidirect
130. #1992C22semidirect
131. #1990C22semidirect
136. #1949C22semidirect
137. #1948C22semidirect
138. #1948C22semidirect
139. #1948C22semidirect
140. #1948C22semidirect
141. #1948C22semidirect
142. #1947C22semidirect
143. #1947C22semidirect
144. #1947C22semidirect
145. #1947C22semidirect
146. #1944C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
149. #1939C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
158. #1926C22semidirect
160. #1925C22semidirect
161. #1925C22semidirect
162. #1924C22semidirect
163. #1923C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
171. #1874C22semidirect
173. #1865C22semidirect
175. #1863C22semidirect
181. #1853C22semidirect
182. #1852C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
186. #1836C22semidirect
192. #1807C22semidirect
193. #1803C22semidirect
199. #1776C22semidirect
202. C2×#340C22semidirect
1068. 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
#592772
#592732
#325362
#325332
#324562
#324462
#320722
#320462
#306752
#306642
#287832
#275852
#275842
#275072
#275032
#265662
#265542
#259682
#259672
#252042
#252002
#248822
#248792
#246902
#246782
#242752
#235462
#227112
#224432
#220712
#219642