Finite Group Databasebeta

← #6661086

Subgroups — #6661086

Order 512.

1651 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35301C211yesmaximal, characteristic
2#35253C211yesmaximal, characteristic, complemented
3#32747C211yesmaximal, characteristic, complemented
4#32746C211yesmaximal, characteristic, complemented
5#32742C211yesmaximal, characteristic, complemented
6#32739C211yesmaximal, characteristic, complemented
7#30302C211yesmaximal, characteristic, complemented
8#30299C211yesmaximal, characteristic, complemented
9#30194C211yesmaximal, characteristic, complemented
10#30192C211yesmaximal, characteristic, complemented
11#29977C211yesmaximal, characteristic, complemented
12#29975C211yesmaximal, characteristic, complemented
13#29941C211yesmaximal, characteristic, complemented
14#29940C211yesmaximal, characteristic, complemented
15#29765C211yesmaximal, characteristic, complemented
16#29763C211yesmaximal, characteristic, complemented
17#29694C211yesmaximal, characteristic, complemented
18#29690C211yesmaximal, characteristic, complemented
19#27655C211yesmaximal, characteristic, complemented
20#27654C211yesmaximal, characteristic, complemented
21#24852C211yesmaximal, characteristic, complemented
22#24851C211yesmaximal, characteristic, complemented
23#24851C211yesmaximal, characteristic, complemented
24#24848C211yesmaximal, characteristic, complemented
25#24560C211yesmaximal, characteristic, complemented
26#24558C211yesmaximal, characteristic, complemented
27#24555C211yesmaximal, characteristic, complemented
28#24553C211yesmaximal, characteristic, complemented
29#24309C211yesmaximal, characteristic, complemented
30#24309C211yesmaximal, characteristic, complemented
31#20628C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#478C2211yescharacteristic, complemented
40C2×#478C2211yescharacteristic, complemented
41C2×#476C2211yescharacteristic, complemented
42C2×#476C2211yescharacteristic, complemented
43C2×#424C2211yescharacteristic
44C2×#424C2211yescharacteristic
45C2×#407C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2854C2211yescharacteristic
50#2854C2211yescharacteristic
51#2851C2211yescharacteristic
52#2851C2211yescharacteristic
53#2847C2211yescharacteristic
54#2847C2211yescharacteristic
55#2629C2211yescharacteristic
56#2629C2211yescharacteristic
57#2628C2211yescharacteristic
58#2628C2211yescharacteristic
59#2628C2211yescharacteristic
60#2628C2211yescharacteristic
61#2619C2211yescharacteristic
62#2619C2211yescharacteristic
63#2610—21no—
64#2610—21no—
65#2598—21no—
66#2598—21no—
67#2591—21no—
68#2539—21no—
69#2442—21no—
70#2441—21no—
71#2440—21no—
72#2439—21no—
73#2438—21no—
74#2438—21no—
75#2437—21no—
76#2437—21no—
77#2406—21no—
78#2404—21no—
79#2324C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2324C2211yescharacteristic
83#2317C2211yescharacteristic
84#2317C2211yescharacteristic
85#2316C2211yescharacteristic
86#2283C2211yescharacteristic
87#2280C2211yescharacteristic
88C2×#380C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2087C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2085C2211yescharacteristic, complemented
104#2085C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2085C2211yescharacteristic, complemented
107#2084C2211yescharacteristic, complemented
108#2083C2211yescharacteristic, complemented
109#2077C2211yescharacteristic
110#2077C2211yescharacteristic
111#2077C2211yescharacteristic
112#2077C2211yescharacteristic
113#2076C2211yescharacteristic
114#2076C2211yescharacteristic
115#2076C2211yescharacteristic
116#2075C2211yescharacteristic
117#2073C2211yescharacteristic, complemented
118#2073C2211yescharacteristic, complemented
119#2071C2211yescharacteristic, complemented
120#2071C2211yescharacteristic, complemented
121#2067C2211yescharacteristic, complemented
122#2067C2211yescharacteristic, complemented
123#2067C2211yescharacteristic, complemented
124#2067C2211yescharacteristic, complemented
125#2065C2211yescharacteristic, complemented
126#2065C2211yescharacteristic, complemented
127#2065C2211yescharacteristic, complemented
128#2065C2211yescharacteristic, complemented
129#2059C2211yescharacteristic, complemented
130#2059C2211yescharacteristic, complemented
131#2058C2211yescharacteristic, complemented
132#2058C2211yescharacteristic, complemented
133#2058C2211yescharacteristic, complemented
134#2058C2211yescharacteristic, complemented
135#2058C2211yescharacteristic, complemented
136#2057C2211yescharacteristic, complemented
137#2041C2211yescharacteristic, complemented
138#2041C2211yescharacteristic, complemented
139#2041C2211yescharacteristic, complemented
140#2041C2211yescharacteristic, complemented
141#2034C2211yescharacteristic
142#2034C2211yescharacteristic
143#2034C2211yescharacteristic
144#2034C2211yescharacteristic
145#2034C2211yescharacteristic
146#2034C2211yescharacteristic
147#2033C2211yescharacteristic
148#2033C2211yescharacteristic
149#2025C2211yescharacteristic, complemented
150#2025C2211yescharacteristic, complemented
151#2023C2211yescharacteristic, complemented
152#2023C2211yescharacteristic, complemented
153#1989C2211yescharacteristic, complemented
154#1989C2211yescharacteristic, complemented
155#1988C2211yescharacteristic, complemented
156#1988C2211yescharacteristic, complemented
157#1949C2211yescharacteristic, complemented
158#1949C2211yescharacteristic, complemented
159#1948C2211yescharacteristic, complemented
160#1947C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1824C2211yescharacteristic
180#1823C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1804C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic, complemented
192#1802C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1798C2211yescharacteristic
196#1798C2211yescharacteristic
197#1797C2211yescharacteristic
198#1797C2211yescharacteristic
199#1797C2211yescharacteristic
200#1797C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41—21no—
204C24×C4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#544—42no—
210#544—42no—
211#532—42no—
212#532—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—42no—
241C2×#117—42no—
242C2×#117D411yescharacteristic
243C2×#117D411yescharacteristic
244C2×#117D411yescharacteristic
245C2×#117D411yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4D411yescharacteristic
253C22×C4⋊C4D411yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C22⋊C4D411yescharacteristic
258C22×C22⋊C4D411yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261#482—42no—
262#482—42no—
263#481—42no—
264#480—42no—
265#478—42no—
266#478—42no—
267#476—42no—
268#476—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285#424—42no—
286#424—42no—
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
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
311#407—42no—
312C2×C22⋊C8—42no—
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#392—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#391—21no—
354#391—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#381—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454#376—21no—
455C2×#95—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—44no—
498C2×#41—82no—
499C2×#41—82no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—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×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—44no—
560#127—41no—
561#127—41no—
562#125—22no—
563#125—22no—
564#125—41no—
565#125—41no—
566#125—44no—
567#124—44no—
568#123—82no—
569#123—82no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572C22⋊Q8—82no—
573C22⋊Q8—82no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—44no—
587#120—82no—
588#120—82no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—44no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—41no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—42no—
605#117—42no—
606#117—42no—
607#117—42no—
608#117—41no—
609#117—41no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
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—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
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—21no—
695C2×C22⋊C4—42no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—22no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745C4⋊C8—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—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806C24—22no—
807C24—22no—
808C24—22no—
809C24—21no—
810C24—21no—
811C24—41no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818#41—816no—
819C2×Q8—42no—
820C2×Q8—42no—
821C2×Q8—42no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
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—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
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×D4—81no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—22no—
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—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
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×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4H(5,𝔽2)12yes—
941C22×C42−1+412yes—
942C22×C42−1+412yes—
943C22×C42−1+412yes—
944C22×C4C2511yescharacteristic
945M16—82no—
946M16—82no—
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—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—82no—
972C2×C8—82no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
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—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C42—22no—
1075C42—22no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—41no—
1083C42—41no—
1084C42—42no—
1085C42—42no—
1086C42—81no—
1087C42—81no—
1088C42H(5,𝔽2)12yes—
1089C42H(5,𝔽2)12yes—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—44no—
1109C23—44no—
1110C23—44no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—82no—
1126C23—82no—
1127C23—82no—
1128C23—82no—
1129C23#53612yes—
1130C23#53712yes—
1131C23#57712yes—
1132C23C23×D411yescharacteristic
1133Q8—84no—
1134Q8—162no—
1135Q8—162no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—162no—
1149D4—162no—
1150D4—162no—
1151D4—162no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
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—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
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—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—82no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—82no—
1243C2×C4—82no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4#53412yes—
1247C2×C4#53412yes—
1248C2×C4#53612yes—
1249C2×C4#53712yes—
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4C2×H(5,𝔽2)11yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4C2×2−1+411yescharacteristic
1254C2×C4C2×2−1+411yescharacteristic
1255C2×C4C2×2−1+411yescharacteristic
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—88no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22C2×#53411yescharacteristic
1301C22C2×#53611yescharacteristic
1302C22C2×#53711yescharacteristic
1303C22C2×#57711yescharacteristic
1304C22#358411yescharacteristic
1305C22#358511yescharacteristic
1306C22#358511yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#353611yescharacteristic
1333C4#353611yescharacteristic
1334C4#353811yescharacteristic
1335C4#353811yescharacteristic
1336C2—42no—
1337C2—42no—
1338C2—42no—
1339C2—161no—
1340C2—161no—
1341C2#3744211yescharacteristic
1342C2#6075711yescharacteristic
1343C2#6076711yescharacteristic
1344C2#6087311yescharacteristic
1345C2#6087511yescharacteristic
1346C2#6093511yescharacteristic
1347C2#6093711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35301C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35253C2semidirect
3. #32747C2semidirect
4. #32746C2semidirect
5. #32742C2semidirect
6. #32739C2semidirect
7. #30302C2semidirect
8. #30299C2semidirect
9. #30194C2semidirect
10. #30192C2semidirect
11. #29977C2semidirect
12. #29975C2semidirect
13. #29941C2semidirect
14. #29940C2semidirect
15. #29765C2semidirect
16. #29763C2semidirect
17. #29694C2semidirect
18. #29690C2semidirect
19. #27655C2semidirect
20. #27654C2semidirect
21. #24852C2semidirect
22. #24851C2semidirect
23. #24851C2semidirect
24. #24848C2semidirect
25. #24560C2semidirect
26. #24558C2semidirect
27. #24555C2semidirect
28. #24553C2semidirect
29. #24309C2semidirect
30. #24309C2semidirect
31. #20628C2semidirect
39. C2×#478C22semidirect
40. C2×#478C22semidirect
41. C2×#476C22semidirect
42. C2×#476C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2087C22semidirect
100. #2086C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
103. #2085C22semidirect
104. #2085C22semidirect
105. #2085C22semidirect
106. #2085C22semidirect
107. #2084C22semidirect
108. #2083C22semidirect
117. #2073C22semidirect
118. #2073C22semidirect
119. #2071C22semidirect
120. #2071C22semidirect
121. #2067C22semidirect
122. #2067C22semidirect
123. #2067C22semidirect
124. #2067C22semidirect
125. #2065C22semidirect
126. #2065C22semidirect
127. #2065C22semidirect
128. #2065C22semidirect
129. #2059C22semidirect
130. #2059C22semidirect
131. #2058C22semidirect
132. #2058C22semidirect
133. #2058C22semidirect
134. #2058C22semidirect
135. #2058C22semidirect
136. #2057C22semidirect
137. #2041C22semidirect
138. #2041C22semidirect
139. #2041C22semidirect
140. #2041C22semidirect
149. #2025C22semidirect
150. #2025C22semidirect
151. #2023C22semidirect
152. #2023C22semidirect
153. #1989C22semidirect
154. #1989C22semidirect
155. #1988C22semidirect
156. #1988C22semidirect
157. #1949C22semidirect
158. #1949C22semidirect
159. #1948C22semidirect
160. #1947C22semidirect
189. #1804C22semidirect
190. #1804C22semidirect
191. #1802C22semidirect
192. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#353012
#352532
#327472
#327462
#327422
#327392
#303022
#302992
#301942
#301922
#299772
#299752
#299412
#299402
#297652
#297632
#296942
#296902
#276552
#276542
#248522
#248512
#248482
#245602
#245582
#245552
#245532
#243092
#206282