Finite Group Databasebeta

← #7082586

Subgroups — #7082586

Order 512.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59288C211yesmaximal, characteristic, complemented
2#59046C211yesmaximal, characteristic
3#32195C211yesmaximal, characteristic, complemented
4#32093C211yesmaximal, characteristic, complemented
5#31992C211yesmaximal, characteristic, complemented
6#31887C211yesmaximal, characteristic, complemented
7#31584C211yesmaximal, characteristic, complemented
8#31486C211yesmaximal, characteristic, complemented
9#31317C211yesmaximal, characteristic, complemented
10#30646C211yesmaximal, characteristic, complemented
11#27585C211yesmaximal, characteristic, complemented
12#27546C211yesmaximal, characteristic, complemented
13#27357C211yesmaximal, characteristic, complemented
14#27264C211yesmaximal, characteristic, complemented
15#27010C211yesmaximal, characteristic, complemented
16#26752C211yesmaximal, characteristic, complemented
17#26538C211yesmaximal, characteristic, complemented
18#26344C211yesmaximal, characteristic, complemented
19#26140C211yesmaximal, characteristic, complemented
20#25953C211yesmaximal, characteristic, complemented
21#25291C211yesmaximal, characteristic, complemented
22#25238C211yesmaximal, characteristic, complemented
23#24486C211yesmaximal, characteristic, complemented
24#24478C211yesmaximal, characteristic, complemented
25#24067C211yesmaximal, characteristic, complemented
26#24039C211yesmaximal, characteristic, complemented
27C2×#2067C211yesmaximal, characteristic, complemented
28#22932C211yesmaximal, characteristic, complemented
29#22414C211yesmaximal, characteristic, complemented
30#22065C211yesmaximal, characteristic, complemented
31#21887C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#479C2211yescharacteristic, complemented
39C2×C8×D4C2211yescharacteristic
40C22×#107C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2773—21no—
46#2767—21no—
47#2714—21no—
48#2705—21no—
49#2570C2211yescharacteristic, complemented
50#2548C2211yescharacteristic
51#2539—21no—
52#2533—21no—
53#2519—21no—
54#2508C2211yescharacteristic, complemented
55#2506C2211yescharacteristic, complemented
56#2498—21no—
57#2496C2211yescharacteristic, complemented
58#2495C2211yescharacteristic, complemented
59#2490C2211yescharacteristic
60#2487C2211yescharacteristic
61#2481—21no—
62#2471—21no—
63#2454C2211yescharacteristic
64#2448C2211yescharacteristic
65#2442—21no—
66#2442C2211yescharacteristic
67#2441C2211yescharacteristic, complemented
68#2433C2211yescharacteristic
69#2431C2211yescharacteristic
70#2428C2211yescharacteristic
71#2424—21no—
72#2416C2211yescharacteristic
73#2414—21no—
74#2412—21no—
75#2370C2211yescharacteristic, complemented
76#2366C2211yescharacteristic
77#2360C2211yescharacteristic
78#2358—21no—
79#2352C2211yescharacteristic
80#2346C2211yescharacteristic, complemented
81#2345C2211yescharacteristic
82#2343—21no—
83#2341C2211yescharacteristic
84C4×#123C2211yescharacteristic
85C2×#390C2211yescharacteristic
86C2×#389C2211yescharacteristic
87#2285C2211yescharacteristic
88#2097C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic
91#2092C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2034C2211yescharacteristic, complemented
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic, complemented
127#2025C2211yescharacteristic
128#1989C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic, complemented
132#1983C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic
135#1961C2211yescharacteristic
136#1958C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1940C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1924C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1872C2211yescharacteristic
171#1869C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1850C2211yescharacteristic, complemented
186#1817C2211yescharacteristic
187#1807C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1802C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#546—24no—
209#546—42no—
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212#529—24no—
213#529—42no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C22×C4⋊C4—21no—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252#490—42no—
253#484—24no—
254#482—42no—
255#481—42no—
256#479—42no—
257C8×D4—42no—
258C2×#107—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8—42no—
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#416—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102—42no—
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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387D411yescharacteristic
409#387D411yescharacteristic
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#383—21no—
427#382—21no—
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462C2×#95—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—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—21no—
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×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547#127—22no—
548#127—41no—
549#127—41no—
550#127—41no—
551#126—44no—
552#126—82no—
553#125—22no—
554#125—22no—
555#125—41no—
556#125—41no—
557#125—82no—
558#124—22no—
559#124—22no—
560#124—41no—
561#124—41no—
562#123—42no—
563#123—44no—
564#123—44no—
565C22⋊Q8—22no—
566C22⋊Q8#4114yes—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—44no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—82no—
575#121—82no—
576#120—44no—
577#120—44no—
578#120—82no—
579C4×Q8—22no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590C4×D4—82no—
591#117—22no—
592#117—44no—
593#117—41no—
594#117—44no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
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—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—82no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
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—44no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4—82no—
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—22no—
688C2×C42—22no—
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×C42—21no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#107—22no—
706#107—22no—
707#107—22no—
708#107—22no—
709#107—41no—
710#107—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
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—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761#97—41no—
762#97—41no—
763C4×C8—41no—
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#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—82no—
818#41—82no—
819#41—82no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8C2×#4112yes—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
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—44no—
847C2×D4—44no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D42−1+412yes—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—41no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C2×#4112yes—
938C22×C4H(5,𝔽2)12yes—
939C22×C4C2511yescharacteristic
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—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—44no—
965C2×C8—82no—
966C2×C8—82no—
967C4⋊C4—24no—
968C4⋊C4—22no—
969C4⋊C4—22no—
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—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4C2×#4112yes—
1021C4⋊C4H(5,𝔽2)12yes—
1022C22⋊C4—24no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
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—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C42—22no—
1062C42—22no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
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—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—84no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23#54612yes—
1122C23#57512yes—
1123C23#57712yes—
1124C23C23×D411yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—41no—
1128Q8—41no—
1129D4—22no—
1130D4—22no—
1131D4—44no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—162no—
1147D4—162no—
1148D4—162no—
1149D4—162no—
1150D4—162no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
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—22no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
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—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—44no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—44no—
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—41no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4#54612yes—
1241C2×C4#57612yes—
1242C2×C4C22×#4111yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×2−1+411yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—42no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
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—81no—
1288C22—81no—
1289C22—81no—
1290C22—168no—
1291C22#331714yes—
1292C22C2×#54611yescharacteristic
1293C22#348811yescharacteristic
1294C22#348911yescharacteristic
1295C22C2×#57511yescharacteristic
1296C22C2×#57611yescharacteristic
1297C22C2×#57711yescharacteristic
1298C22#358411yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#352011yescharacteristic
1325C4#352111yescharacteristic
1326C4#353511yescharacteristic
1327C4#354211yescharacteristic
1328C2—24no—
1329C2—81no—
1330C2—82no—
1331C2—161no—
1332C2—161no—
1333C2#4404411yescharacteristic
1334C2C2×#331711yescharacteristic
1335C2#6117111yescharacteristic
1336C2#6199211yescharacteristic
1337C2#6205311yescharacteristic
1338C2#6212511yescharacteristic
1339C2#6221211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59046C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59288C2semidirect
3. #32195C2semidirect
4. #32093C2semidirect
5. #31992C2semidirect
6. #31887C2semidirect
7. #31584C2semidirect
8. #31486C2semidirect
9. #31317C2semidirect
10. #30646C2semidirect
11. #27585C2semidirect
12. #27546C2semidirect
13. #27357C2semidirect
14. #27264C2semidirect
15. #27010C2semidirect
16. #26752C2semidirect
17. #26538C2semidirect
18. #26344C2semidirect
19. #26140C2semidirect
20. #25953C2semidirect
21. #25291C2semidirect
22. #25238C2semidirect
23. #24486C2semidirect
24. #24478C2semidirect
25. #24067C2semidirect
26. #24039C2semidirect
27. C2×#2067C2semidirect
28. #22932C2semidirect
29. #22414C2semidirect
30. #22065C2semidirect
31. #21887C2semidirect
37. C2×#482C22semidirect
38. C2×#479C22semidirect
49. #2570C22semidirect
54. #2508C22semidirect
55. #2506C22semidirect
57. #2496C22semidirect
58. #2495C22semidirect
67. #2441C22semidirect
75. #2370C22semidirect
80. #2346C22semidirect
88. #2097C22semidirect
91. #2092C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2077C22semidirect
96. #2076C22semidirect
100. #2068C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
114. #2059C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
123. #2034C22semidirect
126. #2033C22semidirect
128. #1989C22semidirect
129. #1989C22semidirect
131. #1983C22semidirect
132. #1983C22semidirect
137. #1949C22semidirect
138. #1943C22semidirect
139. #1941C22semidirect
140. #1940C22semidirect
141. #1940C22semidirect
144. #1935C22semidirect
145. #1934C22semidirect
146. #1927C22semidirect
153. #1925C22semidirect
154. #1924C22semidirect
155. #1924C22semidirect
156. #1921C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
165. #1893C22semidirect
172. #1865C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
175. #1863C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
180. #1854C22semidirect
184. #1850C22semidirect
185. #1850C22semidirect
187. #1807C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
191. #1802C22semidirect
192. #1802C22semidirect
198. #1776C22semidirect
199. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#592882
#590462
#321952
#320932
#319922
#318872
#315842
#314862
#313172
#306462
#275852
#275462
#273572
#272642
#270102
#267522
#265382
#263442
#261402
#259532
#252912
#252382
#244862
#244782
#240672
#240392
C2×#20672
#229322
#224142
#220652
#218872