Finite Group Databasebeta

← #6678840

Subgroups — #6678840

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39732C211yesmaximal, characteristic, complemented
2#36216C211yesmaximal, characteristic, complemented
3#33006C211yesmaximal, characteristic, complemented
4#31988C211yesmaximal, characteristic, complemented
5#31944C211yesmaximal, characteristic, complemented
6#31912C211yesmaximal, characteristic, complemented
7#31648C211yesmaximal, characteristic, complemented
8#31620C211yesmaximal, characteristic, complemented
9#31584C211yesmaximal, characteristic, complemented
10#31566C211yesmaximal, characteristic, complemented
11#31371C211yesmaximal, characteristic, complemented
12#29907C211yesmaximal, characteristic, complemented
13#29782C211yesmaximal, characteristic, complemented
14#27710C211yesmaximal, characteristic, complemented
15#27563C211yesmaximal, characteristic, complemented
16#27520C211yesmaximal, characteristic, complemented
17#27296C211yesmaximal, characteristic, complemented
18#26117C211yesmaximal, characteristic, complemented
19#25976C211yesmaximal, characteristic, complemented
20#25972C211yesmaximal, characteristic, complemented
21#25257C211yesmaximal, characteristic, complemented
22#25218C211yesmaximal, characteristic, complemented
23#24959C211yesmaximal, characteristic, complemented
24#24913C211yesmaximal, characteristic, complemented
25#24823C211yesmaximal, characteristic, complemented
26#24539C211yesmaximal, characteristic, complemented
27#24444C211yesmaximal, characteristic
28#22866C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22073C211yesmaximal, characteristic, complemented
31#20648C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#482C2211yescharacteristic, complemented
35C2×#478C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#423C2211yescharacteristic, complemented
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2854C2211yescharacteristic
46#2854C2211yescharacteristic, complemented
47#2853—21no—
48#2795—21no—
49#2793—21no—
50#2790—21no—
51#2718—21no—
52#2618—21no—
53#2570C2211yescharacteristic, complemented
54#2566C2211yescharacteristic, complemented
55#2512C2211yescharacteristic, complemented
56#2507C2211yescharacteristic, complemented
57#2500C2211yescharacteristic
58#2500C2211yescharacteristic
59#2498—21no—
60#2497C2211yescharacteristic
61#2485C2211yescharacteristic
62#2482—21no—
63#2481—21no—
64#2448C2211yescharacteristic
65#2448C2211yescharacteristic
66#2444—21no—
67#2443—21no—
68#2443—21no—
69#2442C2211yescharacteristic, complemented
70#2441C2211yescharacteristic
71#2423C2211yescharacteristic
72#2422C2211yescharacteristic
73#2421C2211yescharacteristic
74#2418—21no—
75#2418—21no—
76#2416C2211yescharacteristic
77#2361C2211yescharacteristic, complemented
78#2352C2211yescharacteristic
79#2349C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2339C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2322—21no—
85C4×#123C2211yescharacteristic
86C2×#388—21no—
87C2×#384C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2084C2211yescharacteristic, complemented
102#2084C2211yescharacteristic, complemented
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic, complemented
108#2071C2211yescharacteristic
109#2071C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic, complemented
113#2066C2211yescharacteristic, complemented
114#2066C2211yescharacteristic, complemented
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic, complemented
117#2065C2211yescharacteristic, complemented
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2042C2211yescharacteristic
122#2035C2211yescharacteristic
123#2034C2211yescharacteristic
124#2026C2211yescharacteristic, complemented
125#2025C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1968C2211yescharacteristic, complemented
131#1958C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1941C2211yescharacteristic, complemented
134#1940C2211yescharacteristic, complemented
135#1939C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1920C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1916C2211yescharacteristic, complemented
147#1916C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic, complemented
151#1894C2211yescharacteristic
152#1880C2211yescharacteristic, complemented
153#1880C2211yescharacteristic, complemented
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1874C2211yescharacteristic
161#1874C2211yescharacteristic
162#1873C2211yescharacteristic
163#1870C2211yescharacteristic
164#1865C2211yescharacteristic, complemented
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic, complemented
174#1853C2211yescharacteristic, complemented
175#1851C2211yescharacteristic
176#1851C2211yescharacteristic
177#1851C2211yescharacteristic, complemented
178#1835C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic, complemented
181#1817C2211yescharacteristic, complemented
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic, complemented
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#546—24no—
212#546—42no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121—21no—
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C4×#41—24no—
229C4×#41—42no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4—21no—
246C22×C4⋊C4—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42—21no—
254C22×C42C2311yescharacteristic
255#482—42no—
256#478—42no—
257#469—42no—
258#449—24no—
259#447—42no—
260#442—42no—
261#436—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271#423—42no—
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#418—42no—
280#417—42no—
281#417—42no—
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
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#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385D411yescharacteristic
424#384—21no—
425#384—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
456C2×#95—21no—
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41#4114yes—
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#126—82no—
556#125—41no—
557#125—41no—
558#124—22no—
559#124—41no—
560#123—42no—
561#123—44no—
562#123—44no—
563#123—82no—
564#123—82no—
565C22⋊Q8—22no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—44no—
572#121—41no—
573#121—41no—
574#121—82no—
575#120—44no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—44no—
596C4×D4—82no—
597#117—22no—
598#117—22no—
599#117—44no—
600#117—41no—
601#117—41no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—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—82no—
634C2×C4⋊C4—82no—
635C2×C4⋊C4—82no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—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⋊C4—44no—
691C2×C22⋊C4—82no—
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—22no—
701C2×C42—22no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—44no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—41no—
717#107—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—41no—
764C4×C8—41no—
765C4×C8—41no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—28no—
817#41—44no—
818#41—44no—
819#41—44no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8C2×#4112yes—
826C2×D4—24no—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—82no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4C2×#4112yes—
864C2×D4H(5,𝔽2)12yes—
865C2×D42−1+412yes—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—24no—
874C22×C4—22no—
875C22×C4—22no—
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—21no—
893C22×C4—21no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—81no—
909C22×C4—81no—
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×C4H(5,𝔽2)12yes—
936C22×C4C2511yescharacteristic
937SD16—82no—
938D8—44no—
939D8—82no—
940M16—82no—
941M16—82no—
942M16—82no—
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—21no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—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—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C42—22no—
1068C42—22no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C23—21no—
1086C23—21no—
1087C23—22no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23#54612yes—
1127C23C23×D411yescharacteristic
1128Q8—22no—
1129Q8—22no—
1130Q8—41no—
1131Q8—41no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—48no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—82no—
1145D4—84no—
1146D4—84no—
1147D4—162no—
1148D4—162no—
1149D4#53914yes—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
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—44no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4#54612yes—
1242C2×C4#57512yes—
1243C2×C4#57712yes—
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×H(5,𝔽2)11yescharacteristic
1247C2×C4C2×2−1+411yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—22no—
1259C22—22no—
1260C22—24no—
1261C22—22no—
1262C22—42no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—168no—
1294C22C2×#54611yescharacteristic
1295C22#348811yescharacteristic
1296C22#348911yescharacteristic
1297C22C2×#57511yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358511yescharacteristic
1300C22#358511yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4C2×#53911yescharacteristic
1327C4#349111yescharacteristic
1328C4#353411yescharacteristic
1329C4#353511yescharacteristic
1330C2—42no—
1331C2—44no—
1332C2—81no—
1333C2—161no—
1334C2—161no—
1335C2#3766111yescharacteristic
1336C2#6116411yescharacteristic
1337C2#6119211yescharacteristic
1338C2#6199611yescharacteristic
1339C2#6207911yescharacteristic
1340C2#6211511yescharacteristic
1341C2#6217911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24444C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39732C2semidirect
2. #36216C2semidirect
3. #33006C2semidirect
4. #31988C2semidirect
5. #31944C2semidirect
6. #31912C2semidirect
7. #31648C2semidirect
8. #31620C2semidirect
9. #31584C2semidirect
10. #31566C2semidirect
11. #31371C2semidirect
12. #29907C2semidirect
13. #29782C2semidirect
14. #27710C2semidirect
15. #27563C2semidirect
16. #27520C2semidirect
17. #27296C2semidirect
18. #26117C2semidirect
19. #25976C2semidirect
20. #25972C2semidirect
21. #25257C2semidirect
22. #25218C2semidirect
23. #24959C2semidirect
24. #24913C2semidirect
25. #24823C2semidirect
26. #24539C2semidirect
28. #22866C2semidirect
29. #22427C2semidirect
30. #22073C2semidirect
31. #20648C2semidirect
34. C2×#482C22semidirect
41. C2×#423C22semidirect
46. #2854C22semidirect
53. #2570C22semidirect
54. #2566C22semidirect
55. #2512C22semidirect
56. #2507C22semidirect
69. #2442C22semidirect
77. #2361C22semidirect
87. C2×#384C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2100C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
98. #2086C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
101. #2084C22semidirect
102. #2084C22semidirect
107. #2073C22semidirect
112. #2067C22semidirect
113. #2066C22semidirect
114. #2066C22semidirect
116. #2065C22semidirect
117. #2065C22semidirect
124. #2026C22semidirect
128. #1992C22semidirect
130. #1968C22semidirect
132. #1949C22semidirect
133. #1941C22semidirect
134. #1940C22semidirect
135. #1939C22semidirect
137. #1935C22semidirect
139. #1934C22semidirect
140. #1927C22semidirect
144. #1920C22semidirect
145. #1919C22semidirect
146. #1916C22semidirect
147. #1916C22semidirect
150. #1895C22semidirect
152. #1880C22semidirect
153. #1880C22semidirect
159. #1877C22semidirect
164. #1865C22semidirect
170. #1863C22semidirect
173. #1853C22semidirect
174. #1853C22semidirect
177. #1851C22semidirect
178. #1835C22semidirect
180. #1825C22semidirect
181. #1817C22semidirect
183. #1809C22semidirect
186. #1803C22semidirect
187. #1803C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
194. #1802C22semidirect
200. #1753C22semidirect
201. #1736C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#397322
#362162
#330062
#319882
#319442
#319122
#316482
#316202
#315842
#315662
#313712
#299072
#297822
#277102
#275632
#275202
#272962
#261172
#259762
#259722
#252572
#252182
#249592
#249132
#248232
#245392
#244442
#228662
#224272
#220732
#206482