Finite Group Databasebeta

← #7082908

Subgroups — #7082908

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45017C211yesmaximal, characteristic, complemented
2#44874C211yesmaximal, characteristic
3#32222C211yesmaximal, characteristic, complemented
4#32097C211yesmaximal, characteristic, complemented
5#31978C211yesmaximal, characteristic, complemented
6#31891C211yesmaximal, characteristic, complemented
7#31601C211yesmaximal, characteristic, complemented
8#31508C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#30660C211yesmaximal, characteristic, complemented
11#27591C211yesmaximal, characteristic, complemented
12#27539C211yesmaximal, characteristic, complemented
13#27350C211yesmaximal, characteristic, complemented
14#27262C211yesmaximal, characteristic, complemented
15#27015C211yesmaximal, characteristic, complemented
16#26778C211yesmaximal, characteristic, complemented
17#26543C211yesmaximal, characteristic, complemented
18#26359C211yesmaximal, characteristic, complemented
19#26150C211yesmaximal, characteristic, complemented
20#25974C211yesmaximal, characteristic, complemented
21#25284C211yesmaximal, characteristic, complemented
22#25251C211yesmaximal, characteristic, complemented
23#24495C211yesmaximal, characteristic, complemented
24#24495C211yesmaximal, characteristic, complemented
25#24075C211yesmaximal, characteristic, complemented
26#24044C211yesmaximal, characteristic
27#23614C211yesmaximal, characteristic, complemented
28#22935C211yesmaximal, characteristic, complemented
29#22423C211yesmaximal, characteristic
30#22070C211yesmaximal, characteristic, complemented
31#21896C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#489C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic, complemented
36C2×#485C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#476C2211yescharacteristic, complemented
39C2×#435C2211yescharacteristic
40C2×#428C2211yescharacteristic, complemented
41C2×#424C2211yescharacteristic, complemented
42C2×#418C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2781—21no—
46#2772—21no—
47#2767—21no—
48#2702—21no—
49#2697—21no—
50#2685—21no—
51#2684—21no—
52#2681—21no—
53#2612—21no—
54#2604—21no—
55#2571C2211yescharacteristic, complemented
56#2559—21no—
57#2544C2211yescharacteristic
58#2530—21no—
59#2509C2211yescharacteristic, complemented
60#2507C2211yescharacteristic, complemented
61#2497C2211yescharacteristic, complemented
62#2496C2211yescharacteristic, complemented
63#2491C2211yescharacteristic
64#2485C2211yescharacteristic
65#2472—21no—
66#2452C2211yescharacteristic
67#2445C2211yescharacteristic
68#2440C2211yescharacteristic, complemented
69#2439C2211yescharacteristic, complemented
70#2435—21no—
71#2435C2211yescharacteristic
72#2435C2211yescharacteristic
73#2426C2211yescharacteristic
74#2421—21no—
75#2415C2211yescharacteristic
76#2405—21no—
77#2395C2211yescharacteristic
78#2367C2211yescharacteristic
79#2365C2211yescharacteristic, complemented
80#2363C2211yescharacteristic
81#2352C2211yescharacteristic
82#2346C2211yescharacteristic, complemented
83#2346C2211yescharacteristic, complemented
84D4×C22⋊C4C2211yescharacteristic
85#2316C2211yescharacteristic, complemented
86#2314C2211yescharacteristic, complemented
87#2309C2211yescharacteristic
88#2097C2211yescharacteristic, complemented
89#2093C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic, complemented
99#2071C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2058C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2057C2211yescharacteristic, complemented
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2042C2211yescharacteristic, complemented
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2036C2211yescharacteristic, complemented
124#2036C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2023C2211yescharacteristic
128#1988C2211yescharacteristic, complemented
129#1987C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic, complemented
132#1983C2211yescharacteristic, complemented
133#1983C2211yescharacteristic, complemented
134#1982C2211yescharacteristic
135#1961C2211yescharacteristic
136#1959C2211yescharacteristic
137#1948C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1940C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1936C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic, complemented
150#1926C2211yescharacteristic, complemented
151#1926C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1924C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1894C2211yescharacteristic, complemented
165#1894C2211yescharacteristic, complemented
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic, complemented
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1872C2211yescharacteristic, complemented
171#1870C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1851C2211yescharacteristic, complemented
185#1851C2211yescharacteristic, complemented
186#1818C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209D42—24no—
210D42—42no—
211#542—24no—
212#542—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#124—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247#489—42no—
248#485—42no—
249#485—42no—
250#482—24no—
251#476—42no—
252#435—42no—
253#428—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266#424—42no—
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274#418—42no—
275#418—42no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102—42no—
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×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400D411yescharacteristic
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398D411yescharacteristic
329#397—21no—
330#397—21no—
331#397—21no—
332#397D411yescharacteristic
333#397D411yescharacteristic
334#397D411yescharacteristic
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394D411yescharacteristic
353#394D411yescharacteristic
354#393—21no—
355#393—21no—
356#393—21no—
357#391—21no—
358#391—21no—
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
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#388—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#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#382—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446#379—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462#376—21no—
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4—82no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×M16—22no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550#127—22no—
551#127—41no—
552#126—44no—
553#126—82no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—41no—
560#124—44no—
561#124—82no—
562#123—44no—
563#123—82no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121—44no—
574#121—41no—
575#121#4114yes—
576#120—44no—
577#120—44no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—82no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—22no—
594#117—41no—
595#117—41no—
596#117—41no—
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—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
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—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#106—22no—
709#106—22no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
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—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—41no—
759#97—41no—
760#97—41no—
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#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24—21no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—42no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×D4—22no—
833C2×D4—24no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—816no—
878C2×D4C2×#4112yes—
879C2×D42−1+412yes—
880C22×C4—21no—
881C22×C4—21no—
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—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2×#4112yes—
928C22×C4H(5,𝔽2)12yes—
929C22×C4C2511yescharacteristic
930M16—44no—
931M16—82no—
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—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—82no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
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—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4C2×#4112yes—
1009C4⋊C4H(5,𝔽2)12yes—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
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—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
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—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—22no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—21no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23#54612yes—
1125C23C23×D411yescharacteristic
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—84no—
1131Q8—162no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—44no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
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—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
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—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—84no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#54612yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—42no—
1261C22—42no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—42no—
1266C22—42no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—168no—
1288C22—168no—
1289C22C2×#54611yescharacteristic
1290C22#348811yescharacteristic
1291C22#348911yescharacteristic
1292C22#358511yescharacteristic
1293C22#358511yescharacteristic
1294C22#358511yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4#352011yescharacteristic
1322C4#352111yescharacteristic
1323C4#353511yescharacteristic
1324C4#354211yescharacteristic
1325C2—42no—
1326C2—81no—
1327C2—82no—
1328C2—82no—
1329C2—161no—
1330C2#4404411yescharacteristic
1331C2#6117511yescharacteristic
1332C2#6122211yescharacteristic
1333C2#6208311yescharacteristic
1334C2#6209211yescharacteristic
1335C2#6223111yescharacteristic
1336C2#6223611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45017C2semidirect
3. #32222C2semidirect
4. #32097C2semidirect
5. #31978C2semidirect
6. #31891C2semidirect
7. #31601C2semidirect
8. #31508C2semidirect
9. #31302C2semidirect
10. #30660C2semidirect
11. #27591C2semidirect
12. #27539C2semidirect
13. #27350C2semidirect
14. #27262C2semidirect
15. #27015C2semidirect
16. #26778C2semidirect
17. #26543C2semidirect
18. #26359C2semidirect
19. #26150C2semidirect
20. #25974C2semidirect
21. #25284C2semidirect
22. #25251C2semidirect
23. #24495C2semidirect
24. #24495C2semidirect
25. #24075C2semidirect
27. #23614C2semidirect
28. #22935C2semidirect
30. #22070C2semidirect
31. #21896C2semidirect
34. C2×#489C22semidirect
35. C2×#485C22semidirect
36. C2×#485C22semidirect
38. C2×#476C22semidirect
40. C2×#428C22semidirect
41. C2×#424C22semidirect
55. #2571C22semidirect
59. #2509C22semidirect
60. #2507C22semidirect
61. #2497C22semidirect
62. #2496C22semidirect
68. #2440C22semidirect
69. #2439C22semidirect
79. #2365C22semidirect
82. #2346C22semidirect
83. #2346C22semidirect
85. #2316C22semidirect
86. #2314C22semidirect
88. #2097C22semidirect
89. #2093C22semidirect
91. #2092C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2077C22semidirect
96. #2077C22semidirect
98. #2071C22semidirect
99. #2071C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2066C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
112. #2058C22semidirect
113. #2057C22semidirect
114. #2057C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
120. #2042C22semidirect
123. #2036C22semidirect
124. #2036C22semidirect
128. #1988C22semidirect
129. #1987C22semidirect
131. #1983C22semidirect
132. #1983C22semidirect
133. #1983C22semidirect
137. #1948C22semidirect
138. #1943C22semidirect
139. #1943C22semidirect
140. #1940C22semidirect
141. #1940C22semidirect
143. #1936C22semidirect
144. #1936C22semidirect
145. #1935C22semidirect
146. #1927C22semidirect
149. #1926C22semidirect
150. #1926C22semidirect
151. #1926C22semidirect
153. #1925C22semidirect
154. #1924C22semidirect
155. #1924C22semidirect
156. #1921C22semidirect
157. #1919C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
164. #1894C22semidirect
165. #1894C22semidirect
167. #1892C22semidirect
170. #1872C22semidirect
172. #1865C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1863C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
180. #1854C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
183. #1851C22semidirect
184. #1851C22semidirect
185. #1851C22semidirect
186. #1818C22semidirect
187. #1809C22semidirect
188. #1805C22semidirect
190. #1804C22semidirect
191. #1803C22semidirect
192. #1802C22semidirect
198. #1776C22semidirect
200. #1762C22semidirect
201. #1752C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#450172
#448742
#322222
#320972
#319782
#318912
#316012
#315082
#313022
#306602
#275912
#275392
#273502
#272622
#270152
#267782
#265432
#263592
#261502
#259742
#252842
#252512
#244952
#240752
#240442
#236142
#229352
#224232
#220702
#218962