Finite Group Databasebeta

← #6924349

Subgroups — #6924349

Order 512.

1585 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38110C211yesmaximal, characteristic, complemented
2#37862C211yesmaximal, characteristic, complemented
3#32845C211yesmaximal, characteristic, complemented
4#32735C211yesmaximal, characteristic, complemented
5#32427C211yesmaximal, characteristic, complemented
6#32426C211yesmaximal, characteristic, complemented
7#32053C211yesmaximal, characteristic, complemented
8#32046C211yesmaximal, characteristic, complemented
9#31937C211yesmaximal, characteristic, complemented
10#31930C211yesmaximal, characteristic, complemented
11#31519C211yesmaximal, characteristic, complemented
12#31518C211yesmaximal, characteristic, complemented
13#30188C211yesmaximal, characteristic, complemented
14#30142C211yesmaximal, characteristic, complemented
15#30119C211yesmaximal, characteristic, complemented
16#29991C211yesmaximal, characteristic, complemented
17#29917C211yesmaximal, characteristic, complemented
18#29381C211yesmaximal, characteristic, complemented
19#28303C211yesmaximal, characteristic, complemented
20#27961C211yesmaximal, characteristic, complemented
21#27687C211yesmaximal, characteristic, complemented
22#24583C211yesmaximal, characteristic, complemented
23#24582C211yesmaximal, characteristic, complemented
24#24531C211yesmaximal, characteristic, complemented
25#24530C211yesmaximal, characteristic, complemented
26#24098C211yesmaximal, characteristic, complemented
27#24092C211yesmaximal, characteristic, complemented
28#23969C211yesmaximal, characteristic, complemented
29#23963C211yesmaximal, characteristic
30C2×#2093C211yesmaximal, characteristic, complemented
31#21997C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C22×#107C2211yescharacteristic
39C22×#107C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2857C2211yescharacteristic
43#2850C2211yescharacteristic
44#2796—21no—
45#2751—21no—
46#2730—21no—
47#2721—21no—
48#2721—21no—
49#2705—21no—
50#2680—21no—
51#2680—21no—
52#2660C2211yescharacteristic, complemented
53#2644C2211yescharacteristic
54#2624C2211yescharacteristic
55#2620C2211yescharacteristic, complemented
56#2565C2211yescharacteristic, complemented
57#2542C2211yescharacteristic, complemented
58#2512C2211yescharacteristic
59#2504C2211yescharacteristic
60#2502C2211yescharacteristic
61#2501C2211yescharacteristic, complemented
62#2499C2211yescharacteristic, complemented
63#2491C2211yescharacteristic
64#2487C2211yescharacteristic
65#2480—21no—
66#2472—21no—
67#2452C2211yescharacteristic
68#2449—21no—
69#2449—21no—
70#2443—21no—
71#2443—21no—
72#2437—21no—
73#2422C2211yescharacteristic
74#2412—21no—
75#2408C2211yescharacteristic
76#2345C2211yescharacteristic
77D4×C22⋊C4C2211yescharacteristic
78#2326C2211yescharacteristic, complemented
79#2324C2211yescharacteristic
80#2319C2211yescharacteristic
81#2317C2211yescharacteristic, complemented
82C2×#390C2211yescharacteristic
83#2290C2211yescharacteristic
84C2×#384C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic
95#2093C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2083C2211yescharacteristic, complemented
104#2083C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic, complemented
108#2071C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic, complemented
111#2068C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2067C2211yescharacteristic, complemented
114#2067C2211yescharacteristic, complemented
115#2059C2211yescharacteristic, complemented
116#2059C2211yescharacteristic, complemented
117#2057C2211yescharacteristic, complemented
118#2057C2211yescharacteristic, complemented
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2054C2211yescharacteristic
122#2054C2211yescharacteristic
123#2042C2211yescharacteristic, complemented
124#2042C2211yescharacteristic, complemented
125#2036C2211yescharacteristic, complemented
126#2036C2211yescharacteristic, complemented
127#2033C2211yescharacteristic, complemented
128#2033C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2024C2211yescharacteristic, complemented
132#2023C2211yescharacteristic
133#2023C2211yescharacteristic
134#2023C2211yescharacteristic, complemented
135#2012C2211yescharacteristic
136#2012C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic
141#1990C2211yescharacteristic, complemented
142#1990C2211yescharacteristic, complemented
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1949C2211yescharacteristic, complemented
149#1947C2211yescharacteristic, complemented
150#1947C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1925C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1852C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1850C2211yescharacteristic
187#1840C2211yescharacteristic, complemented
188#1834C2211yescharacteristic, complemented
189#1834C2211yescharacteristic, complemented
190#1832C2211yescharacteristic, complemented
191#1824C2211yescharacteristic
192#1824C2211yescharacteristic
193#1824C2211yescharacteristic
194#1824C2211yescharacteristic
195#1818C2211yescharacteristic, complemented
196#1804C2211yescharacteristic
197#1804C2211yescharacteristic
198#1802C2211yescharacteristic
199#1802C2211yescharacteristic
200#1798C2211yescharacteristic, complemented
201C4×C22⋊C8C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#554—42no—
211#554—42no—
212#553—42no—
213#553—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C42C2311yescharacteristic
259#484—42no—
260#481—42no—
261#450—42no—
262#447—42no—
263C2×#107—42no—
264C2×#107—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102—42no—
288C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#395—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#393—21no—
353#393—21no—
354#392—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388D411yescharacteristic
392#388D411yescharacteristic
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387D411yescharacteristic
400#387D411yescharacteristic
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386D411yescharacteristic
410#386D411yescharacteristic
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385D411yescharacteristic
422#385D411yescharacteristic
423#384—21no—
424#384—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550#126—44no—
551#126—82no—
552#125—41no—
553#125—41no—
554#125—44no—
555#124—41no—
556#124—41no—
557#124—82no—
558#123—44no—
559#123—82no—
560#123—82no—
561#123—82no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—82no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571C22⋊Q8—82no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—44no—
579#121—41no—
580#121—41no—
581#120—82no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—44no—
593C4×D4—44no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—41no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
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—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—82no—
638C2×C4⋊C4—82no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4—82no—
696C2×C22⋊C4—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—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—
756#102—41no—
757#102—41no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C4×C8—41no—
765C4×C8—41no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95C2×D411yescharacteristic
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
800C24—21no—
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
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—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D42−1+412yes—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)12yes—
927C22×C4H(5,𝔽2)12yes—
928C22×C4C2511yescharacteristic
929SD16—82no—
930SD16—82no—
931D8—82no—
932D8—82no—
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—21no—
957C2×C8—44no—
958C2×C8—44no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
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—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
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—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
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—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
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—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—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—41no—
1076C42—41no—
1077C42—42no—
1078C42—42no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—22no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
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—41no—
1111C23—41no—
1112C23—41no—
1113C23—84no—
1114C23—84no—
1115C23—84no—
1116C23—84no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23#53512yes—
1121C23#57712yes—
1122C23#57812yes—
1123C23C23×D411yescharacteristic
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—162no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—44no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—84no—
1144D4—84no—
1145D4—162no—
1146D4—162no—
1147D4—162no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
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—21no—
1184C2×C4—21no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—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—162no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#53512yes—
1238C2×C4#57612yes—
1239C2×C4#57612yes—
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C2×C4#58511yescharacteristic
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—42no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
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—168no—
1289C22#322514yes—
1290C22C2×#53511yescharacteristic
1291C22#348511yescharacteristic
1292C22#348911yescharacteristic
1293C22C2×#57611yescharacteristic
1294C22C2×#57611yescharacteristic
1295C22C2×#57711yescharacteristic
1296C22C2×#57811yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#353311yescharacteristic
1323C4#353311yescharacteristic
1324C4#353511yescharacteristic
1325C4#353511yescharacteristic
1326C2—24no—
1327C2—81no—
1328C2—82no—
1329C2—161no—
1330C2—161no—
1331C2#4140911yescharacteristic
1332C2C2×#322511yescharacteristic
1333C2#6081711yescharacteristic
1334C2#6176411yescharacteristic
1335C2#6176611yescharacteristic
1336C2#6219911yescharacteristic
1337C2#6220111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23963C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38110C2semidirect
2. #37862C2semidirect
3. #32845C2semidirect
4. #32735C2semidirect
5. #32427C2semidirect
6. #32426C2semidirect
7. #32053C2semidirect
8. #32046C2semidirect
9. #31937C2semidirect
10. #31930C2semidirect
11. #31519C2semidirect
12. #31518C2semidirect
13. #30188C2semidirect
14. #30142C2semidirect
15. #30119C2semidirect
16. #29991C2semidirect
17. #29917C2semidirect
18. #29381C2semidirect
19. #28303C2semidirect
20. #27961C2semidirect
21. #27687C2semidirect
22. #24583C2semidirect
23. #24582C2semidirect
24. #24531C2semidirect
25. #24530C2semidirect
26. #24098C2semidirect
27. #24092C2semidirect
28. #23969C2semidirect
30. C2×#2093C2semidirect
31. #21997C2semidirect
52. #2660C22semidirect
55. #2620C22semidirect
56. #2565C22semidirect
57. #2542C22semidirect
61. #2501C22semidirect
62. #2499C22semidirect
78. #2326C22semidirect
81. #2317C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
103. #2083C22semidirect
104. #2083C22semidirect
107. #2072C22semidirect
110. #2071C22semidirect
111. #2068C22semidirect
112. #2068C22semidirect
113. #2067C22semidirect
114. #2067C22semidirect
115. #2059C22semidirect
116. #2059C22semidirect
117. #2057C22semidirect
118. #2057C22semidirect
123. #2042C22semidirect
124. #2042C22semidirect
125. #2036C22semidirect
126. #2036C22semidirect
127. #2033C22semidirect
128. #2033C22semidirect
131. #2024C22semidirect
134. #2023C22semidirect
141. #1990C22semidirect
142. #1990C22semidirect
147. #1949C22semidirect
148. #1949C22semidirect
149. #1947C22semidirect
150. #1947C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1925C22semidirect
154. #1925C22semidirect
155. #1923C22semidirect
156. #1923C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
181. #1854C22semidirect
182. #1854C22semidirect
183. #1852C22semidirect
184. #1852C22semidirect
187. #1840C22semidirect
188. #1834C22semidirect
189. #1834C22semidirect
190. #1832C22semidirect
195. #1818C22semidirect
200. #1798C22semidirect

Maximal subgroups

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

subgroupindex
#381102
#378622
#328452
#327352
#324272
#324262
#320532
#320462
#319372
#319302
#315192
#315182
#301882
#301422
#301192
#299912
#299172
#293812
#283032
#279612
#276872
#245832
#245822
#245312
#245302
#240982
#240922
#239692
#239632
C2×#20932
#219972