Finite Group Databasebeta

← #6556220

Subgroups — #6556220

Order 512.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39498C211yesmaximal, characteristic, complemented
2#38945C211yesmaximal, characteristic
3#30217C211yesmaximal, characteristic, complemented
4#30195C211yesmaximal, characteristic, complemented
5#30192C211yesmaximal, characteristic, complemented
6#29352C211yesmaximal, characteristic, complemented
7#29120C211yesmaximal, characteristic, complemented
8#29116C211yesmaximal, characteristic, complemented
9#28724C211yesmaximal, characteristic, complemented
10#27986C211yesmaximal, characteristic, complemented
11#27984C211yesmaximal, characteristic, complemented
12#27763C211yesmaximal, characteristic, complemented
13#27759C211yesmaximal, characteristic, complemented
14#27743C211yesmaximal, characteristic, complemented
15#27739C211yesmaximal, characteristic, complemented
16#27717C211yesmaximal, characteristic, complemented
17#27716C211yesmaximal, characteristic, complemented
18#27709C211yesmaximal, characteristic, complemented
19#27708C211yesmaximal, characteristic, complemented
20#27280C211yesmaximal, characteristic, complemented
21#27279C211yesmaximal, characteristic, complemented
22#27264C211yesmaximal, characteristic, complemented
23#27263C211yesmaximal, characteristic, complemented
24#23822C211yesmaximal, characteristic, complemented
25#23634C211yesmaximal, characteristic, complemented
26#23632C211yesmaximal, characteristic, complemented
27#22498C211yesmaximal, characteristic, complemented
28#22493C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic, complemented
31#20563C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#417C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2861C2211yescharacteristic
43#2859C2211yescharacteristic, complemented
44#2807—21no—
45#2807—21no—
46#2788—21no—
47#2788—21no—
48#2705—21no—
49#2705—21no—
50#2678—21no—
51#2678—21no—
52#2628C2211yescharacteristic
53#2628C2211yescharacteristic, complemented
54#2620C2211yescharacteristic
55#2619C2211yescharacteristic
56#2584—21no—
57#2580—21no—
58#2571C2211yescharacteristic, complemented
59#2566C2211yescharacteristic
60#2552C2211yescharacteristic, complemented
61#2544C2211yescharacteristic
62#2509—21no—
63#2501C2211yescharacteristic
64#2499C2211yescharacteristic
65#2456—21no—
66#2456—21no—
67#2454—21no—
68#2442C2211yescharacteristic
69#2442C2211yescharacteristic, complemented
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic, complemented
72#2433C2211yescharacteristic
73#2431C2211yescharacteristic
74#2418—21no—
75#2418—21no—
76#2354C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic, complemented
80#2311C2211yescharacteristic
81#2309C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic, complemented
83C4×#127C2211yescharacteristic
84#2293C2211yescharacteristic
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#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
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#2026C2211yescharacteristic, complemented
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#1992C2211yescharacteristic, complemented
126#1992C2211yescharacteristic, complemented
127#1992C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1961C2211yescharacteristic
134#1959C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic, complemented
137#1958C2211yescharacteristic, complemented
138#1957C2211yescharacteristic
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, complemented
154#1894C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic, complemented
158#1892C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic, complemented
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic, complemented
165#1873C2211yescharacteristic
166#1872C2211yescharacteristic
167#1836C2211yescharacteristic, complemented
168#1836C2211yescharacteristic, complemented
169#1835C2211yescharacteristic, complemented
170#1834C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1824C2211yescharacteristic, complemented
174#1823C2211yescharacteristic, complemented
175#1802C2211yescharacteristic
176#1802C2211yescharacteristic
177#1802C2211yescharacteristic, complemented
178#1802C2211yescharacteristic, complemented
179#1788C2211yescharacteristic
180#1788C2211yescharacteristic
181#1786C2211yescharacteristic
182#1786C2211yescharacteristic
183#1771C2211yescharacteristic, complemented
184#1771C2211yescharacteristic, complemented
185#1767C2211yescharacteristic, complemented
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic
188#1762C2211yescharacteristic, complemented
189#1762C2211yescharacteristic, complemented
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic, complemented
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic, complemented
194#1750C2211yescharacteristic
195#1750C2211yescharacteristic, complemented
196#1745C2211yescharacteristic, complemented
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic, complemented
199#1735C2211yescharacteristic
200C2×#340C2211yescharacteristic, complemented
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#553—24no—
210#553—24no—
211#546—24no—
212#546—24no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253#490—42no—
254#490—42no—
255#435—24no—
256#435—24no—
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259#418—42no—
260#417—42no—
261#416—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×#97C2311yescharacteristic
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#399—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—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#392—21no—
342#392—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390—21no—
356#390D411yescharacteristic
357#390D411yescharacteristic
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#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389D411yescharacteristic
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#388D411yescharacteristic
396#388D411yescharacteristic
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—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#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439#379—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C43C2311yescharacteristic
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×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—41no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—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—
548#127—22no—
549#127—41no—
550#127—41no—
551#127—41no—
552#126—44no—
553#125—22no—
554#125—22no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—82no—
560#124—22no—
561#124—22no—
562#124—41no—
563#124—41no—
564#123—44no—
565#123—44no—
566#123—82no—
567#123—82no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—44no—
577#121—44no—
578#120—44no—
579#120—82no—
580#120—82no—
581C4×Q8—82no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—44no—
587C4×D4—82no—
588C4×D4—82no—
589C4×D4—82no—
590C4×D4#4114yes—
591C4×D4#4114yes—
592#117—22no—
593#117—22no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—41no—
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—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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—44no—
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C4⋊C8—22no—
715C4⋊C8—22no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
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—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—22no—
752#97—22no—
753#97—22no—
754#97—41no—
755#97—41no—
756#97—41no—
757#97—41no—
758C4×C8—41no—
759C4×C8—41no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
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—81no—
818C2×Q8—81no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
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—44no—
837C2×D4—44no—
838C2×D4—41no—
839C2×D4—41no—
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—82no—
852C2×D4—82no—
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—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4#12414yes—
870C2×D4H(5,𝔽2)12yes—
871C22×C4—21no—
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—21no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—81no—
898C22×C4—81no—
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×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2511yescharacteristic
927M16—82no—
928M16—82no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—82no—
954C2×C8—82no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊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#12414yes—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
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—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4#12414yes—
1057C22⋊C4#12414yes—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
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—84no—
1125D4—22no—
1126D4—22no—
1127D4—44no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—84no—
1143D4—162no—
1144D4—162no—
1145D4—162no—
1146D4—162no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
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—21no—
1186C2×C4—21no—
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—84no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4C2×#12412yes—
1233C2×C4C2×#12412yes—
1234C2×C4C2×#12412yes—
1235C2×C4C2×#12412yes—
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
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—168no—
1286C22C22×#12411yescharacteristic
1287C22#348511yescharacteristic
1288C22#348811yescharacteristic
1289C22#358511yescharacteristic
1290C22#358511yescharacteristic
1291C22#358511yescharacteristic
1292C22#358611yescharacteristic
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4#351311yescharacteristic
1319C4#351311yescharacteristic
1320C4#352111yescharacteristic
1321C4#352111yescharacteristic
1322C2—42no—
1323C2—42no—
1324C2—82no—
1325C2—161no—
1326C2—161no—
1327C2#3584711yescharacteristic
1328C2#6062111yescharacteristic
1329C2#6062611yescharacteristic
1330C2#6179311yescharacteristic
1331C2#6179511yescharacteristic
1332C2#6208311yescharacteristic
1333C2#6208411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38945C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39498C2semidirect
3. #30217C2semidirect
4. #30195C2semidirect
5. #30192C2semidirect
6. #29352C2semidirect
7. #29120C2semidirect
8. #29116C2semidirect
9. #28724C2semidirect
10. #27986C2semidirect
11. #27984C2semidirect
12. #27763C2semidirect
13. #27759C2semidirect
14. #27743C2semidirect
15. #27739C2semidirect
16. #27717C2semidirect
17. #27716C2semidirect
18. #27709C2semidirect
19. #27708C2semidirect
20. #27280C2semidirect
21. #27279C2semidirect
22. #27264C2semidirect
23. #27263C2semidirect
24. #23822C2semidirect
25. #23634C2semidirect
26. #23632C2semidirect
27. #22498C2semidirect
28. #22493C2semidirect
29. #22424C2semidirect
30. #22419C2semidirect
31. #20563C2semidirect
43. #2859C22semidirect
53. #2628C22semidirect
58. #2571C22semidirect
60. #2552C22semidirect
69. #2442C22semidirect
71. #2441C22semidirect
79. #2317C22semidirect
82. C4×C4⋊Q8C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2074C22semidirect
92. #2074C22semidirect
93. #2074C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
103. #2072C22semidirect
104. #2072C22semidirect
110. #2071C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
117. #2026C22semidirect
118. #2026C22semidirect
121. #2024C22semidirect
124. #2023C22semidirect
125. #1992C22semidirect
126. #1992C22semidirect
127. #1992C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1989C22semidirect
136. #1959C22semidirect
137. #1958C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
150. #1933C22semidirect
153. #1895C22semidirect
157. #1893C22semidirect
161. #1875C22semidirect
164. #1874C22semidirect
167. #1836C22semidirect
168. #1836C22semidirect
169. #1835C22semidirect
170. #1834C22semidirect
173. #1824C22semidirect
174. #1823C22semidirect
177. #1802C22semidirect
178. #1802C22semidirect
183. #1771C22semidirect
184. #1771C22semidirect
185. #1767C22semidirect
188. #1762C22semidirect
189. #1762C22semidirect
191. #1753C22semidirect
193. #1752C22semidirect
195. #1750C22semidirect
196. #1745C22semidirect
198. #1736C22semidirect
200. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#394982
#389452
#302172
#301952
#301922
#293522
#291202
#291162
#287242
#279862
#279842
#277632
#277592
#277432
#277392
#277172
#277162
#277092
#277082
#272802
#272792
#272642
#272632
#238222
#236342
#236322
#224982
#224932
#224242
#224192
#205632