Finite Group Databasebeta

← #7044067

Subgroups — #7044067

Order 512.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45353C211yesmaximal, characteristic, complemented
2#44907C211yesmaximal, characteristic, complemented
3#32214C211yesmaximal, characteristic, complemented
4#32063C211yesmaximal, characteristic, complemented
5#31863C211yesmaximal, characteristic, complemented
6#31589C211yesmaximal, characteristic, complemented
7#31506C211yesmaximal, characteristic, complemented
8#31482C211yesmaximal, characteristic, complemented
9#31408C211yesmaximal, characteristic, complemented
10#30416C211yesmaximal, characteristic, complemented
11#28127C211yesmaximal, characteristic, complemented
12#27687C211yesmaximal, characteristic, complemented
13#27536C211yesmaximal, characteristic, complemented
14#27443C211yesmaximal, characteristic, complemented
15#27206C211yesmaximal, characteristic, complemented
16#27047C211yesmaximal, characteristic, complemented
17#26223C211yesmaximal, characteristic, complemented
18#25549C211yesmaximal, characteristic, complemented
19#25252C211yesmaximal, characteristic, complemented
20#25218C211yesmaximal, characteristic, complemented
21#25125C211yesmaximal, characteristic, complemented
22#24964C211yesmaximal, characteristic, complemented
23#24890C211yesmaximal, characteristic, complemented
24#24889C211yesmaximal, characteristic, complemented
25#24539C211yesmaximal, characteristic, complemented
26#24444C211yesmaximal, characteristic, complemented
27#23634C211yesmaximal, characteristic, complemented
28#22495C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#22202C211yesmaximal, characteristic, complemented
31#22177C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#481C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic, complemented
42C2×#417C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2803—21no—
46#2779—21no—
47#2778—21no—
48#2714—21no—
49#2708—21no—
50#2697—21no—
51#2693—21no—
52#2687—21no—
53#2601—21no—
54#2597—21no—
55#2594—21no—
56#2570C2211yescharacteristic, complemented
57#2535C2211yescharacteristic
58#2500C2211yescharacteristic
59#2500C2211yescharacteristic, complemented
60#2496C2211yescharacteristic, complemented
61#2494C2211yescharacteristic
62#2492C2211yescharacteristic
63#2487C2211yescharacteristic
64#2476—21no—
65#2452C2211yescharacteristic
66#2447C2211yescharacteristic
67#2437—21no—
68#2427C2211yescharacteristic
69#2418—21no—
70#2417C2211yescharacteristic
71#2416C2211yescharacteristic
72#2414C2211yescharacteristic, complemented
73#2408C2211yescharacteristic
74#2407—21no—
75#2407C2211yescharacteristic
76#2404—21no—
77#2392C2211yescharacteristic
78#2361C2211yescharacteristic
79#2354C2211yescharacteristic
80#2354C2211yescharacteristic
81#2354C2211yescharacteristic, complemented
82#2352C2211yescharacteristic, complemented
83D4×C22⋊C4C2211yescharacteristic
84#2324C2211yescharacteristic
85#2324C2211yescharacteristic, complemented
86#2317C2211yescharacteristic, complemented
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2058C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2023C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#1999C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1987C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic, complemented
132#1959C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic, complemented
143#1925C2211yescharacteristic
144#1924C2211yescharacteristic
145#1924C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic, complemented
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1877C2211yescharacteristic, complemented
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic, complemented
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1870C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic, complemented
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1798C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#547—24no—
214#547—42no—
215#546—24no—
216#546—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255#482—42no—
256#481—42no—
257#469—24no—
258#469—42no—
259#449—42no—
260#447—42no—
261#435—42no—
262#435—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277#417—42no—
278#416—42no—
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398D411yescharacteristic
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397D411yescharacteristic
331#396—21no—
332#396—21no—
333#396—21no—
334#396D411yescharacteristic
335#396D411yescharacteristic
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394D411yescharacteristic
346#394D411yescharacteristic
347#394D411yescharacteristic
348#393—21no—
349#393—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#392D411yescharacteristic
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
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#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
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#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#380—21no—
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#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—44no—
501C2×#41—82no—
502C2×#41—82no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×M16—22no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—22no—
566C4⋊Q8—41no—
567#126—82no—
568#124—22no—
569#124—41no—
570#123—44no—
571#123—44no—
572#123—44no—
573C22⋊Q8—22no—
574C22⋊Q8—44no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—82no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—44no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—82no—
592#121#4114yes—
593#120—44no—
594#120—82no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—82no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—82no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
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—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
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—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—82no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
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—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773#97—41no—
774#97—41no—
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#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824#41—44no—
825#41—44no—
826#41—82no—
827#41—82no—
828#41—816no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—24no—
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—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—81no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4C2×#4112yes—
892C2×D4H(5,𝔽2)12yes—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C2×#4112yes—
958C22×C4H(5,𝔽2)12yes—
959C22×C4C2511yescharacteristic
960SD16—82no—
961D8—82no—
962D8—82no—
963M16—82no—
964M16—82no—
965M16—82no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—82no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4C2×#4112yes—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—42no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—22no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23#54612yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—84no—
1161D4—22no—
1162D4—22no—
1163D4—22no—
1164D4—22no—
1165D4—44no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—82no—
1175D4—84no—
1176D4—82no—
1177D4—84no—
1178D4—84no—
1179D4—84no—
1180D4—84no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
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—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4#54612yes—
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—42no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—41no—
1309C22—42no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—168no—
1333C22C2×#54611yescharacteristic
1334C22#348511yescharacteristic
1335C22#348811yescharacteristic
1336C22#358511yescharacteristic
1337C22#358511yescharacteristic
1338C22#358511yescharacteristic
1339C22#358611yescharacteristic
1340C4—22no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—42no—
1350C4—41no—
1351C4—41no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#351311yescharacteristic
1365C4#352111yescharacteristic
1366C4#353411yescharacteristic
1367C4#356011yescharacteristic
1368C2—42no—
1369C2—81no—
1370C2—81no—
1371C2—82no—
1372C2—82no—
1373C2—161no—
1374C2#4353011yescharacteristic
1375C2#6117511yescharacteristic
1376C2#6118211yescharacteristic
1377C2#6177611yescharacteristic
1378C2#6179511yescharacteristic
1379C2#6207611yescharacteristic
1380C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45353C2semidirect
2. #44907C2semidirect
3. #32214C2semidirect
4. #32063C2semidirect
5. #31863C2semidirect
6. #31589C2semidirect
7. #31506C2semidirect
8. #31482C2semidirect
9. #31408C2semidirect
10. #30416C2semidirect
11. #28127C2semidirect
12. #27687C2semidirect
13. #27536C2semidirect
14. #27443C2semidirect
15. #27206C2semidirect
16. #27047C2semidirect
17. #26223C2semidirect
18. #25549C2semidirect
19. #25252C2semidirect
20. #25218C2semidirect
21. #25125C2semidirect
22. #24964C2semidirect
23. #24890C2semidirect
24. #24889C2semidirect
25. #24539C2semidirect
26. #24444C2semidirect
27. #23634C2semidirect
28. #22495C2semidirect
29. #22424C2semidirect
30. #22202C2semidirect
31. #22177C2semidirect
34. C2×#481C22semidirect
41. C2×#435C22semidirect
56. #2570C22semidirect
59. #2500C22semidirect
60. #2496C22semidirect
72. #2414C22semidirect
81. #2354C22semidirect
82. #2352C22semidirect
85. #2324C22semidirect
86. #2317C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
94. #2088C22semidirect
95. #2084C22semidirect
99. #2074C22semidirect
100. #2074C22semidirect
104. #2072C22semidirect
105. #2072C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
112. #2058C22semidirect
113. #2055C22semidirect
117. #2036C22semidirect
123. #2023C22semidirect
126. #2000C22semidirect
128. #1993C22semidirect
129. #1987C22semidirect
131. #1973C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1943C22semidirect
137. #1936C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
142. #1926C22semidirect
145. #1924C22semidirect
146. #1921C22semidirect
147. #1921C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
155. #1894C22semidirect
157. #1893C22semidirect
163. #1877C22semidirect
167. #1874C22semidirect
169. #1873C22semidirect
173. #1870C22semidirect
177. #1862C22semidirect
179. #1854C22semidirect
180. #1853C22semidirect
181. #1852C22semidirect
183. #1851C22semidirect
185. #1824C22semidirect
186. #1823C22semidirect
188. #1809C22semidirect
193. #1798C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#453532
#449072
#322142
#320632
#318632
#315892
#315062
#314822
#314082
#304162
#281272
#276872
#275362
#274432
#272062
#270472
#262232
#255492
#252522
#252182
#251252
#249642
#248902
#248892
#245392
#244442
#236342
#224952
#224242
#222022
#221772