Finite Group Databasebeta

← #7083317

Subgroups — #7083317

Order 512.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59324C211yesmaximal, characteristic, complemented
2#39511C211yesmaximal, characteristic
3#32626C211yesmaximal, characteristic, complemented
4#32601C211yesmaximal, characteristic, complemented
5#32430C211yesmaximal, characteristic, complemented
6#32427C211yesmaximal, characteristic, complemented
7#32085C211yesmaximal, characteristic, complemented
8#32083C211yesmaximal, characteristic, complemented
9#30830C211yesmaximal, characteristic, complemented
10#30812C211yesmaximal, characteristic, complemented
11#28581C211yesmaximal, characteristic, complemented
12#28432C211yesmaximal, characteristic, complemented
13#28407C211yesmaximal, characteristic, complemented
14#28052C211yesmaximal, characteristic, complemented
15#28034C211yesmaximal, characteristic, complemented
16#27975C211yesmaximal, characteristic, complemented
17#27281C211yesmaximal, characteristic
18#27271C211yesmaximal, characteristic
19#26360C211yesmaximal, characteristic, complemented
20#26356C211yesmaximal, characteristic, complemented
21#26331C211yesmaximal, characteristic, complemented
22#26324C211yesmaximal, characteristic, complemented
23#26189C211yesmaximal, characteristic, complemented
24#26173C211yesmaximal, characteristic, complemented
25#25105C211yesmaximal, characteristic
26#25105C211yesmaximal, characteristic
27#23731C211yesmaximal, characteristic
28#23239C211yesmaximal, characteristic, complemented
29#23038C211yesmaximal, characteristic, complemented
30#23036C211yesmaximal, characteristic, complemented
31#22043C211yesmaximal, characteristic
32C2×#489C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#479C2211yescharacteristic, complemented
35C2×#475C2211yescharacteristic, complemented
36C2×#470C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#441C2211yescharacteristic, complemented
42C2×C4×Q16C2211yescharacteristic, complemented
43C2×#428C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#418C2211yescharacteristic
47#2857C2211yescharacteristic
48#2808—21no—
49#2800—21no—
50#2800—21no—
51#2742—21no—
52#2727—21no—
53#2704—21no—
54#2626—21no—
55#2592C2211yescharacteristic
56#2592C2211yescharacteristic
57#2590—21no—
58#2586—21no—
59#2581C2211yescharacteristic, complemented
60#2574—21no—
61#2567C2211yescharacteristic, complemented
62#2565C2211yescharacteristic, complemented
63#2550C2211yescharacteristic, complemented
64#2545C2211yescharacteristic
65#2545C2211yescharacteristic
66#2522—21no—
67#2520—21no—
68#2512C2211yescharacteristic
69#2512C2211yescharacteristic
70#2507C2211yescharacteristic, complemented
71#2506C2211yescharacteristic, complemented
72#2480—21no—
73#2480—21no—
74#2448C2211yescharacteristic
75#2448C2211yescharacteristic
76#2441C2211yescharacteristic
77#2439C2211yescharacteristic
78#2435C2211yescharacteristic
79#2435C2211yescharacteristic
80#2370—21no—
81#2362C2211yescharacteristic
82#2362C2211yescharacteristic
83#2360C2211yescharacteristic
84#2360C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2351C2211yescharacteristic, complemented
87#2312—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C2×#390C2211yescharacteristic
91#2285C2211yescharacteristic
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2088C2211yescharacteristic, complemented
103#2087C2211yescharacteristic, complemented
104#2084C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2074C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2074C2211yescharacteristic, complemented
109#2073C2211yescharacteristic
110#2072C2211yescharacteristic, complemented
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic, complemented
113#2066C2211yescharacteristic, complemented
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic, complemented
117#2058C2211yescharacteristic, complemented
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2043C2211yescharacteristic, complemented
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2042C2211yescharacteristic
127#2025C2211yescharacteristic
128#2023C2211yescharacteristic
129#2016C2211yescharacteristic, complemented
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#1985C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1971C2211yescharacteristic, complemented
137#1969C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic
141#1958C2211yescharacteristic
142#1956C2211yescharacteristic, complemented
143#1956C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1948C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1920C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1873C2211yescharacteristic
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1865C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1853C2211yescharacteristic
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1834C2211yescharacteristic, complemented
193#1834C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235C22×C42C2311yescharacteristic
236#489—42no—
237#488—42no—
238#479—42no—
239#475—42no—
240#470—24no—
241#470—24no—
242#464—42no—
243#464—42no—
244#450—24no—
245#441—42no—
246C4×Q16—42no—
247#428—42no—
248#428—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265#418—42no—
266#418—42no—
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
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
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#400—21no—
309#399—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391D411yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389D411yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#385D411yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380D411yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—41no—
529C2×M16—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542#126—82no—
543#126—82no—
544#125—41no—
545#125—41no—
546#125—44no—
547#124—41no—
548#124—41no—
549#124—41no—
550#124—41no—
551#124—41no—
552#124—41no—
553#124—41no—
554#124—41no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—42no—
561C22⋊Q8#4114yes—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574#117—41no—
575#117—41no—
576#117—41no—
577#117—41no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
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—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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—44no—
662C2×C22⋊C4—82no—
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—41no—
680C2×C42—41no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689#107—22no—
690#107—22no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739#97—22no—
740#97—41no—
741C4×C8—22no—
742C4×C8—41no—
743C4×C8—41no—
744C4×C8—41no—
745#95—21no—
746#95—21no—
747#95—21no—
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#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—21no—
791C24—21no—
792C24—42no—
793C24—42no—
794C24—42no—
795C24—81no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24C22×D411yescharacteristic
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8C2×#4112yes—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—82no—
840C2×D4—82no—
841C2×D4—81no—
842C2×D4—81no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C2×#4112yes—
884C22×C42−1+412yes—
885C22×C4C2511yescharacteristic
886Q16—44no—
887Q16—44no—
888SD16—82no—
889SD16—82no—
890M16—44no—
891M16—44no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8H(5,𝔽2)12yes—
915C2×C8H(5,𝔽2)12yes—
916C4⋊C4—24no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4C2×#4112yes—
978C22⋊C4—24no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—41no—
1025C42—41no—
1026C42—42no—
1027C42—42no—
1028C42—81no—
1029C42—81no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—84no—
1059C23—84no—
1060C23—84no—
1061C23—162no—
1062C23—162no—
1063C23—162no—
1064C23—162no—
1065C23#54812yes—
1066C23C23×D411yescharacteristic
1067Q8—22no—
1068Q8—22no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—82no—
1080Q8—162no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—84no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—82no—
1173C2×C4—82no—
1174C2×C4—162no—
1175C2×C4#54812yes—
1176C2×C4#57512yes—
1177C2×C4#57712yes—
1178C2×C4C22×#4111yescharacteristic
1179C2×C4C2×H(5,𝔽2)11yescharacteristic
1180C2×C4C2×H(5,𝔽2)11yescharacteristic
1181C2×C4C2×2−1+411yescharacteristic
1182C2×C4#58511yescharacteristic
1183C2×C4#58511yescharacteristic
1184C8—22no—
1185C8—22no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—168no—
1214C22C2×#54811yescharacteristic
1215C22#348511yescharacteristic
1216C22#349811yescharacteristic
1217C22C2×#57511yescharacteristic
1218C22C2×#57711yescharacteristic
1219C22#358411yescharacteristic
1220C22#358611yescharacteristic
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—42no—
1233C4—42no—
1234C4—41no—
1235C4—41no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4#351311yescharacteristic
1249C4#351311yescharacteristic
1250C4#354111yescharacteristic
1251C4#354111yescharacteristic
1252C2—42no—
1253C2—161no—
1254C2—161no—
1255C2#4410311yescharacteristic
1256C2#6132311yescharacteristic
1257C2#6132711yescharacteristic
1258C2#6174111yescharacteristic
1259C2#6175511yescharacteristic
1260C2#6242711yescharacteristic
1261C2#6246711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59324C2semidirect
3. #32626C2semidirect
4. #32601C2semidirect
5. #32430C2semidirect
6. #32427C2semidirect
7. #32085C2semidirect
8. #32083C2semidirect
9. #30830C2semidirect
10. #30812C2semidirect
11. #28581C2semidirect
12. #28432C2semidirect
13. #28407C2semidirect
14. #28052C2semidirect
15. #28034C2semidirect
16. #27975C2semidirect
19. #26360C2semidirect
20. #26356C2semidirect
21. #26331C2semidirect
22. #26324C2semidirect
23. #26189C2semidirect
24. #26173C2semidirect
28. #23239C2semidirect
29. #23038C2semidirect
30. #23036C2semidirect
34. C2×#479C22semidirect
35. C2×#475C22semidirect
41. C2×#441C22semidirect
42. C2×C4×Q16C22semidirect
59. #2581C22semidirect
61. #2567C22semidirect
62. #2565C22semidirect
63. #2550C22semidirect
70. #2507C22semidirect
71. #2506C22semidirect
85. #2355C22semidirect
86. #2351C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
102. #2088C22semidirect
103. #2087C22semidirect
104. #2084C22semidirect
105. #2074C22semidirect
106. #2074C22semidirect
107. #2074C22semidirect
108. #2074C22semidirect
110. #2072C22semidirect
112. #2068C22semidirect
113. #2066C22semidirect
116. #2059C22semidirect
117. #2058C22semidirect
120. #2043C22semidirect
129. #2016C22semidirect
132. #1985C22semidirect
133. #1984C22semidirect
136. #1971C22semidirect
137. #1969C22semidirect
142. #1956C22semidirect
143. #1956C22semidirect
144. #1949C22semidirect
145. #1948C22semidirect
146. #1944C22semidirect
147. #1941C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
164. #1921C22semidirect
165. #1920C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
183. #1865C22semidirect
184. #1865C22semidirect
185. #1865C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
192. #1834C22semidirect
193. #1834C22semidirect
195. #1776C22semidirect
196. C4×#106C22semidirect
197. #1771C22semidirect
198. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#593242
#395112
#326262
#326012
#324302
#324272
#320852
#320832
#308302
#308122
#285812
#284322
#284072
#280522
#280342
#279752
#272812
#272712
#263602
#263562
#263312
#263242
#261892
#261732
#251052
#237312
#232392
#230382
#230362
#220432