Finite Group Databasebeta

← #7301954

Subgroups — #7301954

Order 512.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59023C211yesmaximal, characteristic, complemented
2#38938C211yesmaximal, characteristic, complemented
3#32286C211yesmaximal, characteristic, complemented
4#32064C211yesmaximal, characteristic, complemented
5#31778C211yesmaximal, characteristic, complemented
6#31742C211yesmaximal, characteristic, complemented
7#31720C211yesmaximal, characteristic, complemented
8#31429C211yesmaximal, characteristic, complemented
9#31406C211yesmaximal, characteristic, complemented
10#31402C211yesmaximal, characteristic, complemented
11#31374C211yesmaximal, characteristic, complemented
12#31279C211yesmaximal, characteristic, complemented
13#31082C211yesmaximal, characteristic, complemented
14#31046C211yesmaximal, characteristic, complemented
15#29892C211yesmaximal, characteristic, complemented
16#29600C211yesmaximal, characteristic, complemented
17#27600C211yesmaximal, characteristic, complemented
18#27533C211yesmaximal, characteristic, complemented
19#27110C211yesmaximal, characteristic, complemented
20#26803C211yesmaximal, characteristic, complemented
21#26720C211yesmaximal, characteristic, complemented
22#26547C211yesmaximal, characteristic, complemented
23#26315C211yesmaximal, characteristic, complemented
24#26152C211yesmaximal, characteristic, complemented
25#26145C211yesmaximal, characteristic, complemented
26#25018C211yesmaximal, characteristic, complemented
27#24895C211yesmaximal, characteristic, complemented
28#24116C211yesmaximal, characteristic, complemented
29#24100C211yesmaximal, characteristic, complemented
30#24007C211yesmaximal, characteristic, complemented
31#23308C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic, complemented
39C2×#449C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic, complemented
41C2×#428C2211yescharacteristic, complemented
42#2847C2211yescharacteristic
43#2784—21no—
44#2781—21no—
45#2756—21no—
46#2693—21no—
47#2687—21no—
48#2686—21no—
49#2639—21no—
50#2563C2211yescharacteristic
51#2537C2211yescharacteristic
52#2535C2211yescharacteristic
53#2534—21no—
54#2503C2211yescharacteristic
55#2497C2211yescharacteristic
56#2495C2211yescharacteristic
57#2492C2211yescharacteristic
58#2491C2211yescharacteristic
59#2485C2211yescharacteristic
60#2472—21no—
61#2457—21no—
62#2450—21no—
63#2440C2211yescharacteristic
64#2439C2211yescharacteristic
65#2424—21no—
66#2420C2211yescharacteristic
67#2420C2211yescharacteristic
68#2419—21no—
69#2417C2211yescharacteristic
70#2417C2211yescharacteristic
71#2416C2211yescharacteristic
72#2414C2211yescharacteristic
73#2407C2211yescharacteristic
74#2404—21no—
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2339—21no—
80#2339C2211yescharacteristic
81#2318—21no—
82C4×#120C2211yescharacteristic
83C2×#380C2211yescharacteristic
84C2×#380C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2097C2211yescharacteristic, complemented
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2058C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic, complemented
111#2036C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic, complemented
125#2024C2211yescharacteristic, complemented
126#2023C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic, complemented
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1999C2211yescharacteristic, complemented
133#1993C2211yescharacteristic, complemented
134#1990C2211yescharacteristic, complemented
135#1988C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1955C2211yescharacteristic
138#1954C2211yescharacteristic
139#1954C2211yescharacteristic
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1895C2211yescharacteristic, complemented
160#1895C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1879C2211yescharacteristic, complemented
163#1877C2211yescharacteristic, complemented
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic, complemented
168#1873C2211yescharacteristic, complemented
169#1872C2211yescharacteristic
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1864C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1862C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1823C2211yescharacteristic
191#1823C2211yescharacteristic
192#1823C2211yescharacteristic
193#1823C2211yescharacteristic
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1779C2211yescharacteristic
200#1779C2211yescharacteristic
201#1776C2211yescharacteristic, complemented
202C4×#102C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#547—42no—
210#547—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#124—21no—
214#525—42no—
215#525—42no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×#120D411yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255#484—42no—
256#482—42no—
257#482—42no—
258#481—42no—
259#474—42no—
260#449—42no—
261C4×D8—42no—
262#428—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
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×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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—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#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
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#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—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#386—21no—
401#386—21no—
402#386D411yescharacteristic
403#386D411yescharacteristic
404#386D411yescharacteristic
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#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379D411yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C2×#95—21no—
454C2×#95—21no—
455C2×#95—21no—
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—44no—
498C2×#41—44no—
499C2×#41—82no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
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×C4—41no—
530C23×C4—41no—
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#124—82no—
560#123—44no—
561#123—44no—
562#123—44no—
563C22⋊Q8—22no—
564C22⋊Q8—44no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—82no—
586#121—82no—
587#120—42no—
588#120—44no—
589#120—82no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—82no—
606#117—22no—
607#117—41no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—82no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—22no—
712#107—22no—
713#107—41no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—22no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—41no—
764C4×C8—41no—
765C4×C8—41no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807C24—21no—
808C24—22no—
809C24—22no—
810C24—21no—
811C24—41no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24—41no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—82no—
821#41—82no—
822#41—82no—
823#41—82no—
824#41—816no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
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—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—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—81no—
872C2×D4—81no—
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×D4H(5,𝔽2)12yes—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—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—41no—
921C22×C4—41no—
922C22×C4—41no—
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—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—82no—
950C22×C4—82no—
951C22×C4—82no—
952C22×C4—82no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2511yescharacteristic
971SD16—82no—
972D8—44no—
973M16—44no—
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×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—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—21no—
1022C4⋊C4—21no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1045C22⋊C4—24no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
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—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—
1091C22⋊C4—81no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—42no—
1099C42—42no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—44no—
1131C23—44no—
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—82no—
1146C23—82no—
1147C23—82no—
1148C23—82no—
1149C23—82no—
1150C23#57612yes—
1151C23#57712yes—
1152C23C23×D411yescharacteristic
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—84no—
1158Q8—162no—
1159D4—22no—
1160D4—22no—
1161D4—44no—
1162D4—48no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—82no—
1170D4—82no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
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—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—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—84no—
1266C2×C4—82no—
1267C2×C4—82no—
1268C2×C4—82no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4#57512yes—
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—88no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22#348411yescharacteristic
1336C22#348511yescharacteristic
1337C22#348511yescharacteristic
1338C22C2×#57511yescharacteristic
1339C22C2×#57611yescharacteristic
1340C22C2×#57711yescharacteristic
1341C22#358611yescharacteristic
1342C4—22no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4#353311yescharacteristic
1367C4#354011yescharacteristic
1368C4#356011yescharacteristic
1369C4#356211yescharacteristic
1370C2—42no—
1371C2—42no—
1372C2—81no—
1373C2—81no—
1374C2—82no—
1375C2—161no—
1376C2#4782811yescharacteristic
1377C2#6159211yescharacteristic
1378C2#6162011yescharacteristic
1379C2#6172411yescharacteristic
1380C2#6173111yescharacteristic
1381C2#6174411yescharacteristic
1382C2#6176611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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
1. #59023C2semidirect
2. #38938C2semidirect
3. #32286C2semidirect
4. #32064C2semidirect
5. #31778C2semidirect
6. #31742C2semidirect
7. #31720C2semidirect
8. #31429C2semidirect
9. #31406C2semidirect
10. #31402C2semidirect
11. #31374C2semidirect
12. #31279C2semidirect
13. #31082C2semidirect
14. #31046C2semidirect
15. #29892C2semidirect
16. #29600C2semidirect
17. #27600C2semidirect
18. #27533C2semidirect
19. #27110C2semidirect
20. #26803C2semidirect
21. #26720C2semidirect
22. #26547C2semidirect
23. #26315C2semidirect
24. #26152C2semidirect
25. #26145C2semidirect
26. #25018C2semidirect
27. #24895C2semidirect
28. #24116C2semidirect
29. #24100C2semidirect
30. #24007C2semidirect
31. #23308C2semidirect
37. C2×#482C22semidirect
38. C2×#474C22semidirect
40. C2×C4×D8C22semidirect
41. C2×#428C22semidirect
85. #2101C22semidirect
86. #2100C22semidirect
87. #2097C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
103. #2073C22semidirect
104. #2072C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2058C22semidirect
108. #2057C22semidirect
109. #2055C22semidirect
110. #2054C22semidirect
115. #2035C22semidirect
124. #2033C22semidirect
125. #2024C22semidirect
126. #2023C22semidirect
129. #2000C22semidirect
132. #1999C22semidirect
133. #1993C22semidirect
134. #1990C22semidirect
135. #1988C22semidirect
136. #1973C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1941C22semidirect
143. #1936C22semidirect
144. #1934C22semidirect
145. #1933C22semidirect
146. #1933C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1926C22semidirect
150. #1925C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1895C22semidirect
160. #1895C22semidirect
161. #1894C22semidirect
162. #1879C22semidirect
163. #1877C22semidirect
167. #1874C22semidirect
168. #1873C22semidirect
173. #1864C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1862C22semidirect
179. #1854C22semidirect
186. #1852C22semidirect
187. #1846C22semidirect
189. #1824C22semidirect
194. #1804C22semidirect
195. #1802C22semidirect
201. #1776C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#590232
#389382
#322862
#320642
#317782
#317422
#317202
#314292
#314062
#314022
#313742
#312792
#310822
#310462
#298922
#296002
#276002
#275332
#271102
#268032
#267202
#265472
#263152
#261522
#261452
#250182
#248952
#241162
#241002
#240072
#233082