Finite Group Databasebeta

← #7005465

Subgroups — #7005465

Order 512.

1687 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59028C211yesmaximal, characteristic
2#39477C211yesmaximal, characteristic, complemented
3#32127C211yesmaximal, characteristic, complemented
4#32011C211yesmaximal, characteristic, complemented
5#31696C211yesmaximal, characteristic, complemented
6#31625C211yesmaximal, characteristic, complemented
7#31410C211yesmaximal, characteristic, complemented
8#31360C211yesmaximal, characteristic, complemented
9#31276C211yesmaximal, characteristic, complemented
10#31044C211yesmaximal, characteristic, complemented
11#28995C211yesmaximal, characteristic, complemented
12#28570C211yesmaximal, characteristic, complemented
13#28147C211yesmaximal, characteristic, complemented
14#28086C211yesmaximal, characteristic, complemented
15#27710C211yesmaximal, characteristic, complemented
16#27525C211yesmaximal, characteristic, complemented
17#26439C211yesmaximal, characteristic, complemented
18#26308C211yesmaximal, characteristic, complemented
19#26220C211yesmaximal, characteristic, complemented
20#26156C211yesmaximal, characteristic, complemented
21#25548C211yesmaximal, characteristic, complemented
22#25263C211yesmaximal, characteristic, complemented
23#25224C211yesmaximal, characteristic, complemented
24#24905C211yesmaximal, characteristic, complemented
25#24561C211yesmaximal, characteristic, complemented
26#24385C211yesmaximal, characteristic, complemented
27#23642C211yesmaximal, characteristic, complemented
28#23035C211yesmaximal, characteristic, complemented
29#22852C211yesmaximal, characteristic, complemented
30#22501C211yesmaximal, characteristic, complemented
31#21764C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C2×#485C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic, complemented
40C2×#436C2211yescharacteristic, complemented
41C2×#436C2211yescharacteristic, complemented
42C2×#428C2211yescharacteristic, complemented
43C2×#407C2211yescharacteristic
44C2×#407C2211yescharacteristic
45#2848C2211yescharacteristic
46#2787—21no—
47#2781—21no—
48#2779—21no—
49#2770—21no—
50#2701—21no—
51#2688—21no—
52#2622—21no—
53#2562C2211yescharacteristic
54#2559—21no—
55#2536C2211yescharacteristic, complemented
56#2535C2211yescharacteristic
57#2510—21no—
58#2505—21no—
59#2500C2211yescharacteristic
60#2495C2211yescharacteristic, complemented
61#2494C2211yescharacteristic
62#2490C2211yescharacteristic
63#2489C2211yescharacteristic, complemented
64#2485C2211yescharacteristic, complemented
65#2480—21no—
66#2464—21no—
67#2442C2211yescharacteristic
68#2442C2211yescharacteristic, complemented
69#2422C2211yescharacteristic
70#2421C2211yescharacteristic
71#2417C2211yescharacteristic, complemented
72#2416C2211yescharacteristic
73#2415C2211yescharacteristic
74#2414C2211yescharacteristic
75#2408—21no—
76#2408C2211yescharacteristic
77#2405—21no—
78#2363C2211yescharacteristic
79#2360C2211yescharacteristic, complemented
80#2358—21no—
81#2352C2211yescharacteristic, complemented
82D4×C4⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2312—21no—
85C4×#120C2211yescharacteristic
86#2280C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2076C2211yescharacteristic, complemented
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic, complemented
108#2073C2211yescharacteristic, complemented
109#2072C2211yescharacteristic, complemented
110#2067C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic, complemented
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#2000C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1991C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1989C2211yescharacteristic, complemented
132#1973C2211yescharacteristic, complemented
133#1955C2211yescharacteristic
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1925C2211yescharacteristic, complemented
144#1923C2211yescharacteristic
145#1923C2211yescharacteristic
146#1918C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic, complemented
155#1895C2211yescharacteristic, complemented
156#1894C2211yescharacteristic, complemented
157#1894C2211yescharacteristic, complemented
158#1894C2211yescharacteristic, complemented
159#1880C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1875C2211yescharacteristic, complemented
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic, complemented
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic, complemented
171#1870C2211yescharacteristic, complemented
172#1864C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1835C2211yescharacteristic, complemented
183#1825C2211yescharacteristic, complemented
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic
186#1823C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#553—24no—
214#553—42no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—24no—
229C2×#121—42no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120D411yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#485—42no—
257#482—42no—
258#468—24no—
259#468—42no—
260#450—42no—
261C4×SD16—42no—
262#436—42no—
263#436—42no—
264#428—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298#407—42no—
299#407—42no—
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
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#394—21no—
346#394—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386D411yescharacteristic
398#386D411yescharacteristic
399#386D411yescharacteristic
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385D411yescharacteristic
410#385D411yescharacteristic
411#385D411yescharacteristic
412#384C2311yescharacteristic
413#383—21no—
414#382—21no—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439#379—21no—
440#379—21no—
441#379—21no—
442#379D411yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C2×#95—21no—
455#340C2311yescharacteristic
456#340C2311yescharacteristic
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—44no—
510C22×D4—82no—
511C22×D4—82no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—41no—
526C23×C4—41no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565#126—44no—
566#125—22no—
567#125—41no—
568#125—41no—
569#125—41no—
570#123—44no—
571#123—82no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—44no—
591#121—44no—
592#121—41no—
593#121—41no—
594#121—82no—
595#121#4114yes—
596#120—42no—
597#120—44no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—44no—
611C4×D4—82no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
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—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—21no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
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—44no—
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
725#107—22no—
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—22no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738#103—22no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769#97—41no—
770C4×C8—22no—
771C4×C8—41no—
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#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—22no—
813C24—22no—
814C24—21no—
815C24—41no—
816C24—41no—
817C24—41no—
818C24—41no—
819C24—41no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—24no—
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—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—816no—
883C2×D4C2×#4112yes—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
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—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—22no—
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—21no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—82no—
936C22×C4—82no—
937C22×C4—82no—
938C22×C4—82no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2×#4112yes—
962C22×C4H(5,𝔽2)12yes—
963C22×C4C2511yescharacteristic
964SD16—44no—
965SD16—82no—
966M16—44no—
967M16—82no—
968M16—82no—
969M16—82no—
970M16—82no—
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—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8H(5,𝔽2)12yes—
995C4⋊C4—22no—
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—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
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⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4C2×#4112yes—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—24no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
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—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—42no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
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—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—44no—
1135C23—44no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23—84no—
1153C23—84no—
1154C23—82no—
1155C23—82no—
1156C23—84no—
1157C23—84no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23#54612yes—
1162C23#57512yes—
1163C23C23×D411yescharacteristic
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168D4—22no—
1169D4—22no—
1170D4—44no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—82no—
1178D4—84no—
1179D4—82no—
1180D4—84no—
1181D4—84no—
1182D4—84no—
1183D4—84no—
1184D4—84no—
1185D4—162no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
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—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
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—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—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—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—82no—
1274C2×C4—82no—
1275C2×C4—82no—
1276C2×C4—84no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4#54612yes—
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4#58511yescharacteristic
1287C2×C4#58511yescharacteristic
1288C2×C4#58511yescharacteristic
1289C8—22no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—88no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—168no—
1341C22C2×#54611yescharacteristic
1342C22#348511yescharacteristic
1343C22#349611yescharacteristic
1344C22C2×#57511yescharacteristic
1345C22#358511yescharacteristic
1346C22#358511yescharacteristic
1347C22#358611yescharacteristic
1348C4—22no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4#351311yescharacteristic
1373C4#352111yescharacteristic
1374C4#355811yescharacteristic
1375C4#356011yescharacteristic
1376C2—42no—
1377C2—42no—
1378C2—81no—
1379C2—81no—
1380C2—82no—
1381C2—161no—
1382C2#4302111yescharacteristic
1383C2#6116311yescharacteristic
1384C2#6117511yescharacteristic
1385C2#6171811yescharacteristic
1386C2#6178211yescharacteristic
1387C2#6228511yescharacteristic
1388C2#6229811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59028C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39477C2semidirect
3. #32127C2semidirect
4. #32011C2semidirect
5. #31696C2semidirect
6. #31625C2semidirect
7. #31410C2semidirect
8. #31360C2semidirect
9. #31276C2semidirect
10. #31044C2semidirect
11. #28995C2semidirect
12. #28570C2semidirect
13. #28147C2semidirect
14. #28086C2semidirect
15. #27710C2semidirect
16. #27525C2semidirect
17. #26439C2semidirect
18. #26308C2semidirect
19. #26220C2semidirect
20. #26156C2semidirect
21. #25548C2semidirect
22. #25263C2semidirect
23. #25224C2semidirect
24. #24905C2semidirect
25. #24561C2semidirect
26. #24385C2semidirect
27. #23642C2semidirect
28. #23035C2semidirect
29. #22852C2semidirect
30. #22501C2semidirect
31. #21764C2semidirect
34. C2×#485C22semidirect
35. C2×#482C22semidirect
39. C2×C4×SD16C22semidirect
40. C2×#436C22semidirect
41. C2×#436C22semidirect
42. C2×#428C22semidirect
55. #2536C22semidirect
60. #2495C22semidirect
63. #2489C22semidirect
64. #2485C22semidirect
68. #2442C22semidirect
71. #2417C22semidirect
79. #2360C22semidirect
81. #2352C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2099C22semidirect
91. #2092C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2076C22semidirect
104. #2076C22semidirect
107. #2075C22semidirect
108. #2073C22semidirect
109. #2072C22semidirect
110. #2067C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2055C22semidirect
114. #2055C22semidirect
117. #2034C22semidirect
120. #2033C22semidirect
121. #2026C22semidirect
122. #2025C22semidirect
123. #2025C22semidirect
126. #2000C22semidirect
127. #2000C22semidirect
128. #1992C22semidirect
129. #1991C22semidirect
130. #1989C22semidirect
131. #1989C22semidirect
132. #1973C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
136. #1936C22semidirect
137. #1934C22semidirect
138. #1934C22semidirect
139. #1933C22semidirect
140. #1927C22semidirect
141. #1926C22semidirect
142. #1926C22semidirect
143. #1925C22semidirect
146. #1918C22semidirect
147. #1918C22semidirect
154. #1895C22semidirect
155. #1895C22semidirect
156. #1894C22semidirect
157. #1894C22semidirect
158. #1894C22semidirect
159. #1880C22semidirect
160. #1877C22semidirect
161. #1875C22semidirect
166. #1873C22semidirect
168. #1872C22semidirect
170. #1870C22semidirect
171. #1870C22semidirect
172. #1864C22semidirect
173. #1863C22semidirect
174. #1862C22semidirect
175. #1862C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
179. #1852C22semidirect
180. #1851C22semidirect
181. #1851C22semidirect
182. #1835C22semidirect
183. #1825C22semidirect
186. #1823C22semidirect
187. #1809C22semidirect
188. #1809C22semidirect
189. #1805C22semidirect
190. #1804C22semidirect
191. #1804C22semidirect
195. #1776C22semidirect
196. C4×#102C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#590282
#394772
#321272
#320112
#316962
#316252
#314102
#313602
#312762
#310442
#289952
#285702
#281472
#280862
#277102
#275252
#264392
#263082
#262202
#261562
#255482
#252632
#252242
#249052
#245612
#243852
#236422
#230352
#228522
#225012
#217642