Finite Group Databasebeta

← #6622486

Subgroups — #6622486

Order 512.

1541 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36513C211yesmaximal, characteristic, complemented
2#36473C211yesmaximal, characteristic, complemented
3#33269C211yesmaximal, characteristic, complemented
4#33268C211yesmaximal, characteristic, complemented
5#33051C211yesmaximal, characteristic, complemented
6#29519C211yesmaximal, characteristic, complemented
7#29518C211yesmaximal, characteristic, complemented
8#29503C211yesmaximal, characteristic, complemented
9#29500C211yesmaximal, characteristic, complemented
10#29054C211yesmaximal, characteristic, complemented
11#29045C211yesmaximal, characteristic, complemented
12#28990C211yesmaximal, characteristic, complemented
13#28975C211yesmaximal, characteristic
14#28933C211yesmaximal, characteristic
15#28909C211yesmaximal, characteristic, complemented
16#28856C211yesmaximal, characteristic, complemented
17#28841C211yesmaximal, characteristic, complemented
18#28803C211yesmaximal, characteristic, complemented
19#28426C211yesmaximal, characteristic, complemented
20#27785C211yesmaximal, characteristic, complemented
21#27744C211yesmaximal, characteristic, complemented
22#24711C211yesmaximal, characteristic, complemented
23#24656C211yesmaximal, characteristic
24#23226C211yesmaximal, characteristic, complemented
25#23109C211yesmaximal, characteristic, complemented
26#22977C211yesmaximal, characteristic, complemented
27#22781C211yesmaximal, characteristic, complemented
28C4×#489C211yesmaximal, characteristic, complemented
29#21647C211yesmaximal, characteristic, complemented
30#21528C211yesmaximal, characteristic, complemented
31#20479C211yesmaximal, characteristic, complemented
32C2×#556—21no—
33C2×#489C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#432C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2863C2211yescharacteristic
43#2860C2211yescharacteristic
44#2860C2211yescharacteristic
45#2860C2211yescharacteristic
46#2857C2211yescharacteristic
47#2850C2211yescharacteristic
48#2604—21no—
49#2604—21no—
50#2601—21no—
51#2587—21no—
52#2570C2211yescharacteristic
53#2551C2211yescharacteristic
54#2545C2211yescharacteristic
55#2542C2211yescharacteristic
56#2529—21no—
57#2525—21no—
58#2521—21no—
59#2521—21no—
60#2518—21no—
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2492—21no—
64#2491C2211yescharacteristic
65#2491C2211yescharacteristic
66#2470—21no—
67#2429C2211yescharacteristic
68#2426C2211yescharacteristic
69#2422C2211yescharacteristic
70#2421C2211yescharacteristic
71#2415—21no—
72#2374—21no—
73#2373—21no—
74#2367C2211yescharacteristic
75#2365C2211yescharacteristic
76#2362—21no—
77#2354C2211yescharacteristic
78#2351C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic
80C4×C4⋊Q8C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×#124C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2095C2211yescharacteristic
89#2093C2211yescharacteristic
90#2085C2211yescharacteristic
91#2083C2211yescharacteristic
92#2075C2211yescharacteristic
93#2075C2211yescharacteristic
94#2073C2211yescharacteristic
95#2071C2211yescharacteristic
96#2058C2211yescharacteristic
97#2058C2211yescharacteristic
98#2043C2211yescharacteristic
99#2042C2211yescharacteristic
100#2035C2211yescharacteristic
101#2035C2211yescharacteristic
102#2035C2211yescharacteristic
103#2033C2211yescharacteristic
104#2024C2211yescharacteristic
105#2023C2211yescharacteristic
106#2013C2211yescharacteristic
107#2012C2211yescharacteristic
108#2000C2211yescharacteristic
109#1999C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1990C2211yescharacteristic
113#1987C2211yescharacteristic
114#1983C2211yescharacteristic
115#1973C2211yescharacteristic
116#1973C2211yescharacteristic
117#1973C2211yescharacteristic
118#1972C2211yescharacteristic
119#1972C2211yescharacteristic
120#1970C2211yescharacteristic
121#1968C2211yescharacteristic
122#1959C2211yescharacteristic
123#1959C2211yescharacteristic
124#1956C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1944C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1943C2211yescharacteristic
131#1943C2211yescharacteristic
132#1942C2211yescharacteristic
133#1941C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1879C2211yescharacteristic
170#1865C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1862C2211yescharacteristic
174#1836C2211yescharacteristic
175#1836C2211yescharacteristic
176#1834C2211yescharacteristic
177#1808C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic
180#1776C2211yescharacteristic
181#1771C2211yescharacteristic
182#1771C2211yescharacteristic
183#1771C2211yescharacteristic
184#1771C2211yescharacteristic
185#1763C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1762C2211yescharacteristic
191C4×#103C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195#1752C2211yescharacteristic
196#1752C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1745C2211yescharacteristic
200#1745C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#556—48no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#124—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×C4×Q8—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117D411yescharacteristic
243C2×#117D411yescharacteristic
244C22×C42C2311yescharacteristic
245#489—24no—
246#489—24no—
247#487—24no—
248#477—24no—
249#465—24no—
250#463—24no—
251#440—24no—
252#432—24no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97—24no—
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#399—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#393—21no—
330#393—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390—21no—
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
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#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4D411yescharacteristic
432C4×C4⋊C4D411yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4D411yescharacteristic
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376D411yescharacteristic
451#376D411yescharacteristic
452C43C2311yescharacteristic
453C43C2311yescharacteristic
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
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—44no—
534#126—44no—
535#126—44no—
536#126—44no—
537#126—44no—
538#126—44no—
539#124—22no—
540#124—22no—
541#124—22no—
542#124—41no—
543#124—44no—
544#124—44no—
545#123—44no—
546C22⋊Q8—22no—
547C22⋊Q8—41no—
548C22⋊Q8—44no—
549C22⋊Q8—44no—
550C22⋊Q8—44no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553#121—22no—
554#121—41no—
555#121—41no—
556#121—41no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—44no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573#117—24no—
574#117—42no—
575#117—44no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C42—22no—
658C2×C42—22no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—22no—
688#107—41no—
689#107—41no—
690#106—22no—
691#106—41no—
692#106—41no—
693#106—41no—
694C4⋊C8—22no—
695C4⋊C8#4114yes—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103#4114yes—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722C22⋊C8—22no—
723C22⋊C8—22no—
724#97—22no—
725#97—22no—
726#97—22no—
727#97—22no—
728#97—22no—
729#97—22no—
730#97—41no—
731#97—41no—
732#97—41no—
733#97#4114yes—
734C4×C8—22no—
735C4×C8—41no—
736C4×C8—41no—
737C4×C8—41no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C24C22×D411yescharacteristic
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—42no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8C2×#4112yes—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C2511yescharacteristic
868SD16—44no—
869SD16—82no—
870D8—82no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—44no—
891C2×C8—44no—
892C2×C8C2×#4112yes—
893C2×C8C2×#4112yes—
894C2×C8C2×#4112yes—
895C2×C8C2×#4112yes—
896C2×C8C2×#4112yes—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4C2×#4112yes—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—41no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4AGL(1,ℤ/8)14yes—
990C42—22no—
991C42—22no—
992C42—22no—
993C42—22no—
994C42—22no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42—41no—
1009C42—41no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C42C2×#4112yes—
1021C42C2×#4112yes—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23C2×AGL(1,ℤ/8)12yes—
1043C23C23×D411yescharacteristic
1044Q8—22no—
1045Q8—22no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—84no—
1053Q8—84no—
1054Q8—84no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—84no—
1064D4—162no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—44no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—82no—
1147C2×C4—84no—
1148C2×C4—162no—
1149C2×C4#53212yes—
1150C2×C4#53212yes—
1151C2×C4C2×AGL(1,ℤ/8)12yes—
1152C2×C4C2×AGL(1,ℤ/8)12yes—
1153C2×C4#57512yes—
1154C2×C4C22×#4111yescharacteristic
1155C2×C4C22×#4111yescharacteristic
1156C2×C4C22×#4111yescharacteristic
1157C2×C4#58511yescharacteristic
1158C2×C4#58511yescharacteristic
1159C2×C4#58511yescharacteristic
1160C8—22no—
1161C8—22no—
1162C8—22no—
1163C8—22no—
1164C8—22no—
1165C8—41no—
1166C8—41no—
1167C8—41no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22C2×#53211yescharacteristic
1190C22D4×#4111yescharacteristic
1191C22#350011yescharacteristic
1192C22C22×AGL(1,ℤ/8)11yescharacteristic
1193C22C2×#57511yescharacteristic
1194C22#358611yescharacteristic
1195C22#358611yescharacteristic
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—22no—
1201C4—41no—
1202C4—42no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—42no—
1210C4—41no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4#347511yescharacteristic
1224C4#348011yescharacteristic
1225C4#349311yescharacteristic
1226C4#352111yescharacteristic
1227C2—42no—
1228C2—161no—
1229C2—161no—
1230C2#3647011yescharacteristic
1231C2#6070011yescharacteristic
1232C2#6071111yescharacteristic
1233C2#6145211yescharacteristic
1234C2#6145811yescharacteristic
1235C2#6258111yescharacteristic
1236C2#6258311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36513C2semidirect
2. #36473C2semidirect
3. #33269C2semidirect
4. #33268C2semidirect
5. #33051C2semidirect
6. #29519C2semidirect
7. #29518C2semidirect
8. #29503C2semidirect
9. #29500C2semidirect
10. #29054C2semidirect
11. #29045C2semidirect
12. #28990C2semidirect
15. #28909C2semidirect
16. #28856C2semidirect
17. #28841C2semidirect
18. #28803C2semidirect
19. #28426C2semidirect
20. #27785C2semidirect
21. #27744C2semidirect
22. #24711C2semidirect
24. #23226C2semidirect
25. #23109C2semidirect
26. #22977C2semidirect
27. #22781C2semidirect
28. C4×#489C2semidirect
29. #21647C2semidirect
30. #21528C2semidirect
31. #20479C2semidirect

Maximal subgroups

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

subgroupindex
#365132
#364732
#332692
#332682
#330512
#295192
#295182
#295032
#295002
#290542
#290452
#289902
#289752
#289332
#289092
#288562
#288412
#288032
#284262
#277852
#277442
#247112
#246562
#232262
#231092
#229772
#227812
C4×#4892
#216472
#215282
#204792