Finite Group Databasebeta

← #7532843

Subgroups — #7532843

Order 512.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59650C211yesmaximal, characteristic
2#36301C211yesmaximal, characteristic, complemented
3#31579C211yesmaximal, characteristic, complemented
4#31479C211yesmaximal, characteristic, complemented
5#31336C211yesmaximal, characteristic, complemented
6#31268C211yesmaximal, characteristic, complemented
7#29166C211yesmaximal, characteristic, complemented
8#29103C211yesmaximal, characteristic, complemented
9#29046C211yesmaximal, characteristic, complemented
10#28100C211yesmaximal, characteristic, complemented
11#28074C211yesmaximal, characteristic, complemented
12#27671C211yesmaximal, characteristic, complemented
13#27532C211yesmaximal, characteristic, complemented
14#27397C211yesmaximal, characteristic, complemented
15#27326C211yesmaximal, characteristic, complemented
16#27097C211yesmaximal, characteristic, complemented
17#27002C211yesmaximal, characteristic, complemented
18#26710C211yesmaximal, characteristic, complemented
19#26202C211yesmaximal, characteristic, complemented
20#24952C211yesmaximal, characteristic, complemented
21#24882C211yesmaximal, characteristic, complemented
22#24877C211yesmaximal, characteristic, complemented
23#24109C211yesmaximal, characteristic, complemented
24#24050C211yesmaximal, characteristic, complemented
25#23118C211yesmaximal, characteristic, complemented
26#22916C211yesmaximal, characteristic, complemented
27#22583C211yesmaximal, characteristic, complemented
28#22497C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30C4×#485C211yesmaximal, characteristic, complemented
31#21060C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#436C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C2×#418C2211yescharacteristic
42#2864—21no—
43#2857C2211yescharacteristic
44#2711—21no—
45#2696—21no—
46#2571C2211yescharacteristic, complemented
47#2563C2211yescharacteristic, complemented
48#2558—21no—
49#2540—21no—
50#2527—21no—
51#2527—21no—
52#2494—21no—
53#2494C2211yescharacteristic, complemented
54#2494C2211yescharacteristic, complemented
55#2491C2211yescharacteristic
56#2487C2211yescharacteristic
57#2485C2211yescharacteristic
58#2485C2211yescharacteristic
59#2477—21no—
60#2477—21no—
61#2472—21no—
62#2452C2211yescharacteristic
63#2448C2211yescharacteristic
64#2437—21no—
65#2426C2211yescharacteristic
66#2424—21no—
67#2420—21no—
68#2416C2211yescharacteristic
69#2408C2211yescharacteristic
70#2407C2211yescharacteristic
71#2369C2211yescharacteristic, complemented
72#2361C2211yescharacteristic
73#2358—21no—
74#2352C2211yescharacteristic
75#2352C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic, complemented
77#2344C2211yescharacteristic, complemented
78#2344C2211yescharacteristic, complemented
79#2341C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2293—21no—
83C2×#390C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2095C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2058C2211yescharacteristic, complemented
102#2058C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic, complemented
107#2035C2211yescharacteristic, complemented
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2024C2211yescharacteristic, complemented
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic, complemented
118#1988C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1958C2211yescharacteristic
121#1942C2211yescharacteristic, complemented
122#1941C2211yescharacteristic, complemented
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1934C2211yescharacteristic
126#1934C2211yescharacteristic
127#1934C2211yescharacteristic
128#1934C2211yescharacteristic
129#1928C2211yescharacteristic, complemented
130#1927C2211yescharacteristic, complemented
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1926C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1923C2211yescharacteristic, complemented
142#1923C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1918C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1894C2211yescharacteristic
153#1894C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1874C2211yescharacteristic
158#1874C2211yescharacteristic
159#1873C2211yescharacteristic
160#1872C2211yescharacteristic, complemented
161#1870C2211yescharacteristic
162#1870C2211yescharacteristic
163#1870C2211yescharacteristic, complemented
164#1869C2211yescharacteristic, complemented
165#1865C2211yescharacteristic, complemented
166#1865C2211yescharacteristic, complemented
167#1865C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1853C2211yescharacteristic, complemented
173#1852C2211yescharacteristic, complemented
174#1852C2211yescharacteristic, complemented
175#1825C2211yescharacteristic
176#1824C2211yescharacteristic, complemented
177#1824C2211yescharacteristic, complemented
178#1823C2211yescharacteristic
179#1823C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1805C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191C4×#107C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic, complemented
199C4×C22⋊C8C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic, complemented
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#554—24no—
210#554—42no—
211#546—24no—
212#546—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#125—21no—
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121D411yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#485—24no—
255#480—24no—
256#436—42no—
257#435—42no—
258#428—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—24no—
274#418—42no—
275#417—24no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#401—21no—
313#401—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#393—21no—
335#393—21no—
336#393—21no—
337#393—21no—
338#392—21no—
339#392—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390D411yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389D411yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
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#388D411yescharacteristic
383#388D411yescharacteristic
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386D411yescharacteristic
402#386D411yescharacteristic
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#382—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#380—21no—
418#380—21no—
419#380D411yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376—21no—
451C43—21no—
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—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—22no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551#125—44no—
552#124—22no—
553#124—41no—
554#124—82no—
555#123—44no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—44no—
559C22⋊Q8—44no—
560C22⋊Q8—41no—
561C22⋊Q8—82no—
562C22⋊Q8—82no—
563C22⋊Q8#4114yes—
564#121—22no—
565#121—22no—
566#121—44no—
567#121—42no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—82no—
573#120—44no—
574#120—44no—
575C4×Q8—22no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—82no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—41no—
594#117—82no—
595#117—82no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
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—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
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—44no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—41no—
701C2×C42—41no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—22no—
710#107—22no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—22no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722#103—22no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
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#4114yes—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—41no—
755C4×C8—41no—
756C4×C8—41no—
757C4×C8—41no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809#41—44no—
810#41—82no—
811#41—82no—
812#41—82no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8C2×#4112yes—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
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—44no—
842C2×D4—44no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—41no—
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—82no—
856C2×D4—82no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4C2×#4112yes—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
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—22no—
885C22×C4—22no—
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—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
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×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
931C22×C4H(5,𝔽2)12yes—
932C22×C4C2511yescharacteristic
933M16—44no—
934M16—82no—
935M16—82no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—82no—
960C2×C8C2×#4112yes—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4C2×#4112yes—
1012C4⋊C4C2×#4112yes—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—42no—
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—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—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—41no—
1065C42—41no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
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—21no—
1090C23—21no—
1091C23—22no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
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—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23#54612yes—
1118C23#57512yes—
1119C23C23×D411yescharacteristic
1120Q8—22no—
1121Q8—22no—
1122Q8—41no—
1123Q8—41no—
1124Q8—162no—
1125Q8—162no—
1126D4—22no—
1127D4—22no—
1128D4—44no—
1129D4—44no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—82no—
1138D4—84no—
1139D4—84no—
1140D4—162no—
1141D4—162no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
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—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
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—82no—
1227C2×C4—82no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4#54612yes—
1235C2×C4#57612yes—
1236C2×C4#57712yes—
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C2×C4#58511yescharacteristic
1243C8—22no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—168no—
1287C22C2×#54611yescharacteristic
1288C22D4×#4111yescharacteristic
1289C22#348511yescharacteristic
1290C22C2×#57511yescharacteristic
1291C22C2×#57611yescharacteristic
1292C22C2×#57711yescharacteristic
1293C22#358611yescharacteristic
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4#347511yescharacteristic
1320C4#351311yescharacteristic
1321C4#352111yescharacteristic
1322C4#354511yescharacteristic
1323C2—42no—
1324C2—42no—
1325C2—81no—
1326C2—82no—
1327C2—161no—
1328C2#5903211yescharacteristic
1329C2#6115811yescharacteristic
1330C2#6121511yescharacteristic
1331C2#6144411yescharacteristic
1332C2#6155711yescharacteristic
1333C2#6172911yescharacteristic
1334C2#6175911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59650C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36301C2semidirect
3. #31579C2semidirect
4. #31479C2semidirect
5. #31336C2semidirect
6. #31268C2semidirect
7. #29166C2semidirect
8. #29103C2semidirect
9. #29046C2semidirect
10. #28100C2semidirect
11. #28074C2semidirect
12. #27671C2semidirect
13. #27532C2semidirect
14. #27397C2semidirect
15. #27326C2semidirect
16. #27097C2semidirect
17. #27002C2semidirect
18. #26710C2semidirect
19. #26202C2semidirect
20. #24952C2semidirect
21. #24882C2semidirect
22. #24877C2semidirect
23. #24109C2semidirect
24. #24050C2semidirect
25. #23118C2semidirect
26. #22916C2semidirect
27. #22583C2semidirect
28. #22497C2semidirect
29. #22427C2semidirect
30. C4×#485C2semidirect
31. #21060C2semidirect
46. #2571C22semidirect
47. #2563C22semidirect
53. #2494C22semidirect
54. #2494C22semidirect
71. #2369C22semidirect
76. D4×C4⋊C4C22semidirect
77. #2344C22semidirect
78. #2344C22semidirect
85. #2101C22semidirect
86. #2100C22semidirect
87. #2095C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
94. #2077C22semidirect
95. #2075C22semidirect
101. #2058C22semidirect
102. #2058C22semidirect
103. #2057C22semidirect
106. #2036C22semidirect
107. #2035C22semidirect
114. #2024C22semidirect
117. #1993C22semidirect
118. #1988C22semidirect
121. #1942C22semidirect
122. #1941C22semidirect
129. #1928C22semidirect
130. #1927C22semidirect
141. #1923C22semidirect
142. #1923C22semidirect
143. #1919C22semidirect
144. #1919C22semidirect
145. #1918C22semidirect
146. #1918C22semidirect
147. #1918C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
156. #1892C22semidirect
160. #1872C22semidirect
163. #1870C22semidirect
164. #1869C22semidirect
165. #1865C22semidirect
166. #1865C22semidirect
167. #1865C22semidirect
169. #1863C22semidirect
172. #1853C22semidirect
173. #1852C22semidirect
174. #1852C22semidirect
176. #1824C22semidirect
177. #1824C22semidirect
182. #1809C22semidirect
183. #1809C22semidirect
184. #1805C22semidirect
191. C4×#107C22semidirect
192. C4×#106C22semidirect
193. #1763C22semidirect
194. C4×#103C22semidirect
195. C4×#103C22semidirect
197. #1753C22semidirect
198. C8×C22⋊C4C22semidirect
201. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#596502
#363012
#315792
#314792
#313362
#312682
#291662
#291032
#290462
#281002
#280742
#276712
#275322
#273972
#273262
#270972
#270022
#267102
#262022
#249522
#248822
#248772
#241092
#240502
#231182
#229162
#225832
#224972
#224272
C4×#4852
#210602