Finite Group Databasebeta

← #7532792

Subgroups — #7532792

Order 512.

1593 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45010C211yesmaximal, characteristic
2#35833C211yesmaximal, characteristic, complemented
3#31582C211yesmaximal, characteristic, complemented
4#31471C211yesmaximal, characteristic, complemented
5#31333C211yesmaximal, characteristic, complemented
6#31260C211yesmaximal, characteristic, complemented
7#29175C211yesmaximal, characteristic, complemented
8#29120C211yesmaximal, characteristic, complemented
9#29040C211yesmaximal, characteristic, complemented
10#28103C211yesmaximal, characteristic, complemented
11#28081C211yesmaximal, characteristic, complemented
12#27661C211yesmaximal, characteristic, complemented
13#27518C211yesmaximal, characteristic, complemented
14#27419C211yesmaximal, characteristic, complemented
15#27327C211yesmaximal, characteristic, complemented
16#27125C211yesmaximal, characteristic, complemented
17#27003C211yesmaximal, characteristic, complemented
18#26708C211yesmaximal, characteristic, complemented
19#26201C211yesmaximal, characteristic, complemented
20#24950C211yesmaximal, characteristic, complemented
21#24874C211yesmaximal, characteristic, complemented
22#24869C211yesmaximal, characteristic, complemented
23#24092C211yesmaximal, characteristic, complemented
24#24048C211yesmaximal, characteristic, complemented
25#23123C211yesmaximal, characteristic, complemented
26#22921C211yesmaximal, characteristic, complemented
27#22566C211yesmaximal, characteristic, complemented
28#22498C211yesmaximal, characteristic, complemented
29#22414C211yesmaximal, characteristic, complemented
30#21584C211yesmaximal, characteristic, complemented
31#21067C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#435C2211yescharacteristic, complemented
37C2×C8×D4C2211yescharacteristic
38C22×#107C2211yescharacteristic, complemented
39C2×#417C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2706—21no—
43#2695—21no—
44#2688—21no—
45#2678—21no—
46#2654—21no—
47#2628C2211yescharacteristic, complemented
48#2570C2211yescharacteristic, complemented
49#2557—21no—
50#2553—21no—
51#2547C2211yescharacteristic
52#2527—21no—
53#2521—21no—
54#2520—21no—
55#2516—21no—
56#2496C2211yescharacteristic
57#2494C2211yescharacteristic, complemented
58#2489C2211yescharacteristic
59#2487C2211yescharacteristic, complemented
60#2486C2211yescharacteristic
61#2486C2211yescharacteristic
62#2480—21no—
63#2454C2211yescharacteristic
64#2447C2211yescharacteristic
65#2427C2211yescharacteristic
66#2420—21no—
67#2418—21no—
68#2415C2211yescharacteristic
69#2412—21no—
70#2408C2211yescharacteristic
71#2407C2211yescharacteristic
72#2401—21no—
73#2392C2211yescharacteristic
74#2369C2211yescharacteristic, complemented
75#2363C2211yescharacteristic
76#2354C2211yescharacteristic, complemented
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2346C2211yescharacteristic, complemented
80#2345C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82#2324C2211yescharacteristic
83#2311C2211yescharacteristic
84#2274C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2095C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2086C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2075C2211yescharacteristic
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2059C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic, complemented
107#2036C2211yescharacteristic, complemented
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2024C2211yescharacteristic, complemented
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1992C2211yescharacteristic, complemented
118#1989C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1958C2211yescharacteristic
121#1942C2211yescharacteristic, complemented
122#1942C2211yescharacteristic, complemented
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1935C2211yescharacteristic, complemented
126#1935C2211yescharacteristic, complemented
127#1934C2211yescharacteristic
128#1933C2211yescharacteristic, complemented
129#1928C2211yescharacteristic, complemented
130#1928C2211yescharacteristic, complemented
131#1928C2211yescharacteristic, complemented
132#1928C2211yescharacteristic, complemented
133#1927C2211yescharacteristic, complemented
134#1926C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1875C2211yescharacteristic
158#1875C2211yescharacteristic
159#1873C2211yescharacteristic, complemented
160#1872C2211yescharacteristic
161#1870C2211yescharacteristic
162#1869C2211yescharacteristic
163#1869C2211yescharacteristic
164#1869C2211yescharacteristic, complemented
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic, complemented
172#1854C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1853C2211yescharacteristic
175#1825C2211yescharacteristic, complemented
176#1824C2211yescharacteristic
177#1824C2211yescharacteristic, complemented
178#1823C2211yescharacteristic, complemented
179#1823C2211yescharacteristic, complemented
180#1809C2211yescharacteristic, complemented
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic
183#1808C2211yescharacteristic, complemented
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic, complemented
199#1750C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#553—24no—
210#553—42no—
211#546—24no—
212#546—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248#482—24no—
249#481—24no—
250#435—42no—
251C8×D4—42no—
252C2×#107—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#417—42no—
268#416—24no—
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102—24no—
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#399—21no—
314#399—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398D411yescharacteristic
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397D411yescharacteristic
331#396—21no—
332#396D411yescharacteristic
333#396D411yescharacteristic
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394D411yescharacteristic
340#394D411yescharacteristic
341#394D411yescharacteristic
342#393—21no—
343#392—21no—
344#392—21no—
345#392D411yescharacteristic
346#391—21no—
347#391—21no—
348#391—21no—
349#391C2311yescharacteristic
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#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
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#387—21no—
382#387—21no—
383#387—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#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C2311yescharacteristic
406#382—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#126—44no—
548#126—82no—
549#125—22no—
550#125—41no—
551#124—22no—
552#124—41no—
553#124—82no—
554#123—44no—
555#123—44no—
556#123—82no—
557#123—82no—
558C22⋊Q8—22no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—44no—
566#121—41no—
567#121—41no—
568#121—44no—
569#121#4114yes—
570#120—44no—
571#120—82no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—44no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
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—41no—
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#103—22no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102#4114yes—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744#97—41no—
745#97—41no—
746C4×C8—41no—
747C4×C8—41no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C24C22×D411yescharacteristic
803#41—44no—
804#41—44no—
805#41—82no—
806#41—82no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—42no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—44no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—81no—
844C2×D4—82no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4C2×#4112yes—
855C2×D4C2×#4112yes—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C2×#4112yes—
919C22×C4H(5,𝔽2)12yes—
920C22×C4C2511yescharacteristic
921M16—82no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—44no—
946C2×C8—82no—
947C2×C8—82no—
948C2×C8C2×#4112yes—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4C2×#4112yes—
1000C4⋊C4C2×#4112yes—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—24no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—22no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—21no—
1083C23—21no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—162no—
1100C23—162no—
1101C23—162no—
1102C23—162no—
1103C23#54612yes—
1104C23#57612yes—
1105C23C23×D411yescharacteristic
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—162no—
1111D4—22no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—44no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—82no—
1121D4—82no—
1122D4—84no—
1123D4—84no—
1124D4—84no—
1125D4—162no—
1126D4—162no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—84no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4#54612yes—
1221C2×C4C22×#4111yescharacteristic
1222C2×C4C22×#4111yescharacteristic
1223C2×C4C2×H(5,𝔽2)11yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C2×C4#58511yescharacteristic
1227C8—22no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—42no—
1251C22—41no—
1252C22—42no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—41no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—168no—
1271C22C2×#54611yescharacteristic
1272C22D4×#4111yescharacteristic
1273C22#348511yescharacteristic
1274C22C2×#57611yescharacteristic
1275C22#358411yescharacteristic
1276C22#358411yescharacteristic
1277C22#358611yescharacteristic
1278C4—22no—
1279C4—41no—
1280C4—41no—
1281C4—42no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4#347511yescharacteristic
1304C4#351311yescharacteristic
1305C4#352111yescharacteristic
1306C4#354511yescharacteristic
1307C2—42no—
1308C2—42no—
1309C2—81no—
1310C2—82no—
1311C2—82no—
1312C2#5903211yescharacteristic
1313C2#6117111yescharacteristic
1314C2#6118811yescharacteristic
1315C2#6148711yescharacteristic
1316C2#6152311yescharacteristic
1317C2#6177211yescharacteristic
1318C2#6180111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45010C2
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
2. #35833C2semidirect
3. #31582C2semidirect
4. #31471C2semidirect
5. #31333C2semidirect
6. #31260C2semidirect
7. #29175C2semidirect
8. #29120C2semidirect
9. #29040C2semidirect
10. #28103C2semidirect
11. #28081C2semidirect
12. #27661C2semidirect
13. #27518C2semidirect
14. #27419C2semidirect
15. #27327C2semidirect
16. #27125C2semidirect
17. #27003C2semidirect
18. #26708C2semidirect
19. #26201C2semidirect
20. #24950C2semidirect
21. #24874C2semidirect
22. #24869C2semidirect
23. #24092C2semidirect
24. #24048C2semidirect
25. #23123C2semidirect
26. #22921C2semidirect
27. #22566C2semidirect
28. #22498C2semidirect
29. #22414C2semidirect
30. #21584C2semidirect
31. #21067C2semidirect
36. C2×#435C22semidirect
38. C22×#107C22semidirect
47. #2628C22semidirect
48. #2570C22semidirect
57. #2494C22semidirect
59. #2487C22semidirect
74. #2369C22semidirect
76. #2354C22semidirect
79. #2346C22semidirect
84. #2274C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2095C22semidirect
89. #2086C22semidirect
90. #2086C22semidirect
91. #2085C22semidirect
96. #2074C22semidirect
100. #2066C22semidirect
101. #2059C22semidirect
102. #2059C22semidirect
103. #2057C22semidirect
106. #2036C22semidirect
107. #2036C22semidirect
114. #2024C22semidirect
117. #1992C22semidirect
118. #1989C22semidirect
121. #1942C22semidirect
122. #1942C22semidirect
125. #1935C22semidirect
126. #1935C22semidirect
128. #1933C22semidirect
129. #1928C22semidirect
130. #1928C22semidirect
131. #1928C22semidirect
132. #1928C22semidirect
133. #1927C22semidirect
141. #1924C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1920C22semidirect
148. #1919C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
156. #1892C22semidirect
159. #1873C22semidirect
164. #1869C22semidirect
171. #1854C22semidirect
172. #1854C22semidirect
173. #1854C22semidirect
175. #1825C22semidirect
177. #1824C22semidirect
178. #1823C22semidirect
179. #1823C22semidirect
180. #1809C22semidirect
183. #1808C22semidirect
191. #1776C22semidirect
192. C4×#106C22semidirect
198. C8×C22⋊C4C22semidirect
199. #1750C22semidirect
200. #1736C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#450102
#358332
#315822
#314712
#313332
#312602
#291752
#291202
#290402
#281032
#280812
#276612
#275182
#274192
#273272
#271252
#270032
#267082
#262012
#249502
#248742
#248692
#240922
#240482
#231232
#229212
#225662
#224982
#224142
#215842
#210672