Finite Group Databasebeta

← #6556365

Subgroups — #6556365

Order 512.

1610 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#38090C211yesmaximal, characteristic
2#37875C211yesmaximal, characteristic, complemented
3#30211C211yesmaximal, characteristic, complemented
4#30197C211yesmaximal, characteristic, complemented
5#30195C211yesmaximal, characteristic, complemented
6#29362C211yesmaximal, characteristic, complemented
7#29116C211yesmaximal, characteristic, complemented
8#29113C211yesmaximal, characteristic, complemented
9#28728C211yesmaximal, characteristic, complemented
10#27984C211yesmaximal, characteristic, complemented
11#27982C211yesmaximal, characteristic, complemented
12#27759C211yesmaximal, characteristic, complemented
13#27753C211yesmaximal, characteristic, complemented
14#27744C211yesmaximal, characteristic, complemented
15#27736C211yesmaximal, characteristic, complemented
16#27726C211yesmaximal, characteristic, complemented
17#27724C211yesmaximal, characteristic, complemented
18#27714C211yesmaximal, characteristic, complemented
19#27704C211yesmaximal, characteristic, complemented
20#27280C211yesmaximal, characteristic, complemented
21#27273C211yesmaximal, characteristic, complemented
22#27270C211yesmaximal, characteristic, complemented
23#27264C211yesmaximal, characteristic, complemented
24#23828C211yesmaximal, characteristic, complemented
25#23632C211yesmaximal, characteristic, complemented
26#23631C211yesmaximal, characteristic, complemented
27#22503C211yesmaximal, characteristic, complemented
28#22492C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic, complemented
31#20564C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#436C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#417C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2857C2211yescharacteristic, complemented
43#2856C2211yescharacteristic
44#2774—21no—
45#2768—21no—
46#2763—21no—
47#2755—21no—
48#2676—21no—
49#2676—21no—
50#2668—21no—
51#2668—21no—
52#2660C2211yescharacteristic, complemented
53#2640C2211yescharacteristic
54#2628C2211yescharacteristic
55#2620C2211yescharacteristic
56#2571C2211yescharacteristic, complemented
57#2570C2211yescharacteristic, complemented
58#2564—21no—
59#2549—21no—
60#2544C2211yescharacteristic
61#2542C2211yescharacteristic
62#2505—21no—
63#2500C2211yescharacteristic
64#2499C2211yescharacteristic
65#2472—21no—
66#2472—21no—
67#2471—21no—
68#2471—21no—
69#2450—21no—
70#2442C2211yescharacteristic
71#2442C2211yescharacteristic, complemented
72#2440C2211yescharacteristic, complemented
73#2439C2211yescharacteristic
74#2433C2211yescharacteristic
75#2431C2211yescharacteristic
76#2352C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2331C2211yescharacteristic, complemented
79#2328C2211yescharacteristic
80#2317C2211yescharacteristic
81#2309C2211yescharacteristic
82#2297C2211yescharacteristic
83#2290C2211yescharacteristic
84C2×#382C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2074C2211yescharacteristic, complemented
92#2074C2211yescharacteristic, complemented
93#2074C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2073C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2071C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#1993C2211yescharacteristic, complemented
126#1993C2211yescharacteristic, complemented
127#1991C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1988C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1961C2211yescharacteristic
134#1961C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic, complemented
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic, complemented
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic, complemented
155#1895C2211yescharacteristic, complemented
156#1894C2211yescharacteristic
157#1893C2211yescharacteristic
158#1892C2211yescharacteristic
159#1875C2211yescharacteristic
160#1874C2211yescharacteristic
161#1874C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic, complemented
164#1874C2211yescharacteristic, complemented
165#1873C2211yescharacteristic
166#1872C2211yescharacteristic
167#1836C2211yescharacteristic, complemented
168#1836C2211yescharacteristic, complemented
169#1836C2211yescharacteristic, complemented
170#1834C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1825C2211yescharacteristic, complemented
174#1825C2211yescharacteristic, complemented
175#1804C2211yescharacteristic
176#1804C2211yescharacteristic, complemented
177#1802C2211yescharacteristic
178#1802C2211yescharacteristic, complemented
179#1788C2211yescharacteristic
180#1788C2211yescharacteristic
181#1786C2211yescharacteristic
182#1786C2211yescharacteristic
183#1771C2211yescharacteristic, complemented
184#1770C2211yescharacteristic, complemented
185#1768C2211yescharacteristic, complemented
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic, complemented
188C4×#102C2211yescharacteristic
189C4×#102C2211yescharacteristic, complemented
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194#1750C2211yescharacteristic
195#1749C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#555—24no—
210#555—24no—
211#546—24no—
212#546—24no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#490—42no—
254#486—42no—
255#436—24no—
256#435—24no—
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259#418—42no—
260#417—42no—
261#417—42no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102—42no—
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#386—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#386D411yescharacteristic
403#386D411yescharacteristic
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#382—21no—
419#382—21no—
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376C2311yescharacteristic
446C2×#95—21no—
447C2×#95—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
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
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#127—22no—
557#127—41no—
558#127—41no—
559#127—41no—
560#125—41no—
561#125—41no—
562#124—22no—
563#124—22no—
564#124—41no—
565#124—41no—
566#124—44no—
567#124—44no—
568#123—44no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—82no—
572C22⋊Q8—82no—
573C22⋊Q8—82no—
574C22⋊Q8—82no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—44no—
582#121—44no—
583#121—82no—
584#121—82no—
585#120—44no—
586#120—82no—
587#120—82no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—82no—
593C4×D4#4114yes—
594C4×D4#4114yes—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—41no—
600#117—41no—
601#117—44no—
602#117—41no—
603#117—41no—
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—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
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×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—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—44no—
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C4⋊C8—22no—
707C4⋊C8—22no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744#97—22no—
745#97—41no—
746#97—41no—
747#97—41no—
748#97—41no—
749C4×C8—22no—
750C4×C8—41no—
751C4×C8—41no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806#41—44no—
807#41—44no—
808#41—82no—
809#41—82no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—42no—
847C2×D4—42no—
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—82no—
858C2×D4—82no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
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#12414yes—
876C2×D4H(5,𝔽2)12yes—
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—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
935C22×C4C2×#4112yes—
936C22×C4C2×#4112yes—
937C22×C4C2×#4112yes—
938C22×C4C2511yescharacteristic
939M16—82no—
940M16—82no—
941M16—82no—
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—21no—
965C2×C8—21no—
966C2×C8—82no—
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—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
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—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
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—
1019C4⋊C4—81no—
1020C4⋊C4#12414yes—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
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—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4#12414yes—
1059C22⋊C4#12414yes—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42C2×#4112yes—
1076C42C2×#4112yes—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—84no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23C2×#12412yes—
1118C23C2×#12412yes—
1119C23C23×D411yescharacteristic
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—162no—
1125Q8—162no—
1126Q8—162no—
1127D4—22no—
1128D4—22no—
1129D4—44no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4—84no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145D4—162no—
1146D4—162no—
1147D4—162no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
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—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
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—84no—
1229C2×C4—84no—
1230C2×C4—82no—
1231C2×C4—82no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4C2×#12412yes—
1237C2×C4C2×#12412yes—
1238C2×C4C2×#12412yes—
1239C2×C4C2×#12412yes—
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C22×#4111yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
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—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
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—81no—
1289C22—168no—
1290C22C22×#12411yescharacteristic
1291C22#348511yescharacteristic
1292C22#348811yescharacteristic
1293C22#358511yescharacteristic
1294C22#358511yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
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#351311yescharacteristic
1323C4#351311yescharacteristic
1324C4#352111yescharacteristic
1325C4#352111yescharacteristic
1326C2—42no—
1327C2—42no—
1328C2—82no—
1329C2—161no—
1330C2—161no—
1331C2#3584711yescharacteristic
1332C2#6062111yescharacteristic
1333C2#6062611yescharacteristic
1334C2#6178011yescharacteristic
1335C2#6178311yescharacteristic
1336C2#6208711yescharacteristic
1337C2#6208811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38090C2
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
2. #37875C2semidirect
3. #30211C2semidirect
4. #30197C2semidirect
5. #30195C2semidirect
6. #29362C2semidirect
7. #29116C2semidirect
8. #29113C2semidirect
9. #28728C2semidirect
10. #27984C2semidirect
11. #27982C2semidirect
12. #27759C2semidirect
13. #27753C2semidirect
14. #27744C2semidirect
15. #27736C2semidirect
16. #27726C2semidirect
17. #27724C2semidirect
18. #27714C2semidirect
19. #27704C2semidirect
20. #27280C2semidirect
21. #27273C2semidirect
22. #27270C2semidirect
23. #27264C2semidirect
24. #23828C2semidirect
25. #23632C2semidirect
26. #23631C2semidirect
27. #22503C2semidirect
28. #22492C2semidirect
29. #22427C2semidirect
30. #22419C2semidirect
31. #20564C2semidirect
42. #2857C22semidirect
52. #2660C22semidirect
56. #2571C22semidirect
57. #2570C22semidirect
71. #2442C22semidirect
72. #2440C22semidirect
78. #2331C22semidirect
84. C2×#382C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2074C22semidirect
92. #2074C22semidirect
93. #2074C22semidirect
94. #2074C22semidirect
103. #2073C22semidirect
104. #2073C22semidirect
105. #2072C22semidirect
110. #2071C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
117. #2026C22semidirect
119. #2024C22semidirect
120. #2024C22semidirect
124. #2023C22semidirect
125. #1993C22semidirect
126. #1993C22semidirect
127. #1991C22semidirect
128. #1990C22semidirect
129. #1988C22semidirect
130. #1987C22semidirect
136. #1959C22semidirect
138. #1958C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
150. #1933C22semidirect
154. #1895C22semidirect
155. #1895C22semidirect
163. #1874C22semidirect
164. #1874C22semidirect
167. #1836C22semidirect
168. #1836C22semidirect
169. #1836C22semidirect
170. #1834C22semidirect
173. #1825C22semidirect
174. #1825C22semidirect
176. #1804C22semidirect
178. #1802C22semidirect
183. #1771C22semidirect
184. #1770C22semidirect
185. #1768C22semidirect
187. #1762C22semidirect
189. C4×#102C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
195. #1749C22semidirect
196. #1746C22semidirect
198. #1736C22semidirect
199. #1736C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#380902
#378752
#302112
#301972
#301952
#293622
#291162
#291132
#287282
#279842
#279822
#277592
#277532
#277442
#277362
#277262
#277242
#277142
#277042
#272802
#272732
#272702
#272642
#238282
#236322
#236312
#225032
#224922
#224272
#224192
#205642