Finite Group Databasebeta

← #6820595

Subgroups — #6820595

Order 512.

1283 conjugacy classes of subgroups.

The subgroup lattice has 1173 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40024C211yesmaximal, characteristic, complemented
2#39513C211yesmaximal, characteristic
3#33232C211yesmaximal, characteristic, complemented
4#32185C211yesmaximal, characteristic
5#32185C211yesmaximal, characteristic
6#32169C211yesmaximal, characteristic
7#32169C211yesmaximal, characteristic
8#31596C211yesmaximal, characteristic, complemented
9#31595C211yesmaximal, characteristic, complemented
10#31576C211yesmaximal, characteristic, complemented
11#31575C211yesmaximal, characteristic, complemented
12#29870C211yesmaximal, characteristic
13#29799C211yesmaximal, characteristic, complemented
14#28904C211yesmaximal, characteristic, complemented
15#28892C211yesmaximal, characteristic, complemented
16#28887C211yesmaximal, characteristic, complemented
17#28875C211yesmaximal, characteristic, complemented
18#28427C211yesmaximal, characteristic
19#28427C211yesmaximal, characteristic
20#27765C211yesmaximal, characteristic
21#27761C211yesmaximal, characteristic
22#27754C211yesmaximal, characteristic
23#27752C211yesmaximal, characteristic
24#25333C211yesmaximal, characteristic, complemented
25#25333C211yesmaximal, characteristic, complemented
26#25289C211yesmaximal, characteristic
27#25289C211yesmaximal, characteristic
28#23233C211yesmaximal, characteristic, complemented
29#23227C211yesmaximal, characteristic, complemented
30#21674C211yesmaximal, characteristic, complemented
31#21288C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#491C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#462C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#440C2211yescharacteristic
41#2868C2211yescharacteristic
42#2859C2211yescharacteristic
43#2802—21no—
44#2793—21no—
45#2793—21no—
46#2793—21no—
47#2793—21no—
48#2776—21no—
49#2766—21no—
50#2719—21no—
51#2655—21no—
52#2629—21no—
53#2571C2211yescharacteristic
54#2570C2211yescharacteristic
55#2570C2211yescharacteristic
56#2565C2211yescharacteristic
57#2565C2211yescharacteristic
58#2552C2211yescharacteristic
59#2547C2211yescharacteristic
60#2547C2211yescharacteristic
61#2545C2211yescharacteristic
62#2545C2211yescharacteristic
63#2545C2211yescharacteristic
64#2545C2211yescharacteristic
65#2533—21no—
66#2528—21no—
67#2514C2211yescharacteristic
68#2514C2211yescharacteristic
69#2511C2211yescharacteristic
70#2511C2211yescharacteristic
71#2497—21no—
72#2497—21no—
73#2446C2211yescharacteristic
74#2446C2211yescharacteristic
75#2446C2211yescharacteristic
76#2446C2211yescharacteristic
77#2370C2211yescharacteristic
78#2370C2211yescharacteristic
79#2365C2211yescharacteristic
80#2365C2211yescharacteristic
81#2336—21no—
82#2314—21no—
83C4×#125C2211yescharacteristic
84#2295C2211yescharacteristic
85#2293C2211yescharacteristic
86#2097C2211yescharacteristic
87#2097C2211yescharacteristic
88#2095C2211yescharacteristic
89#2095C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2083C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2056C2211yescharacteristic
107#2056C2211yescharacteristic
108#2056C2211yescharacteristic
109#2056C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2043C2211yescharacteristic
113#2043C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2016C2211yescharacteristic
119#2016C2211yescharacteristic
120#2016C2211yescharacteristic
121#2016C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1981C2211yescharacteristic
133#1981C2211yescharacteristic
134#1973C2211yescharacteristic
135#1971C2211yescharacteristic
136#1971C2211yescharacteristic
137#1969C2211yescharacteristic
138#1969C2211yescharacteristic
139#1968C2211yescharacteristic
140#1960C2211yescharacteristic
141#1960C2211yescharacteristic
142#1960C2211yescharacteristic
143#1960C2211yescharacteristic
144#1959C2211yescharacteristic
145#1959C2211yescharacteristic
146#1958C2211yescharacteristic
147#1958C2211yescharacteristic
148#1956C2211yescharacteristic
149#1956C2211yescharacteristic
150#1956C2211yescharacteristic
151#1956C2211yescharacteristic
152#1943C2211yescharacteristic
153#1942C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1936C2211yescharacteristic
157#1935C2211yescharacteristic
158#1935C2211yescharacteristic
159#1935C2211yescharacteristic
160#1934C2211yescharacteristic
161#1933C2211yescharacteristic
162#1933C2211yescharacteristic
163#1933C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1928C2211yescharacteristic
168#1927C2211yescharacteristic
169#1927C2211yescharacteristic
170#1927C2211yescharacteristic
171#1927C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1831C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1776C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1770C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125D411yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229#491—24no—
230#491—24no—
231#491—42no—
232#491—42no—
233#478—42no—
234#478—42no—
235#462—42no—
236#462—42no—
237#440—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#401—21no—
300#401—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389D411yescharacteristic
366#389D411yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
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#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#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#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387D411yescharacteristic
418#387D411yescharacteristic
419#387D411yescharacteristic
420#387D411yescharacteristic
421#384—21no—
422#384—21no—
423#384—21no—
424#384—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#383—21no—
431#382—21no—
432#382D411yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459#376—21no—
460C43C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C2×Q16—41no—
495C2×Q16—41no—
496C2×Q16—41no—
497C2×Q16—41no—
498C2×Q16—41no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×SD16—22no—
507C2×SD16—41no—
508C2×SD16—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—42no—
534#125—44no—
535#124—41no—
536#124—41no—
537#124—41no—
538#124—41no—
539#124—41no—
540#124—41no—
541#124—41no—
542#124—41no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555#117—44no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650#107—22no—
651#107—41no—
652#107—41no—
653#107—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#102—22no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#97—22no—
702#97—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706#97#4114yes—
707C4×C8—41no—
708C4×C8—41no—
709C4×C8—41no—
710C4×C8—41no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
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#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
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—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C2511yescharacteristic
843Q16—82no—
844Q16—82no—
845Q16—82no—
846Q16—82no—
847SD16—44no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8C2×#4112yes—
871C2×C8C2×#4112yes—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C42—22no—
955C42—22no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—41no—
969C42—41no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42C2×#4112yes—
982C42H(5,𝔽2)12yes—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23C23×D411yescharacteristic
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—84no—
1099C2×C4#55012yes—
1100C2×C4#55012yes—
1101C2×C4#57512yes—
1102C2×C4#57812yes—
1103C2×C4C22×#4111yescharacteristic
1104C2×C4C2×H(5,𝔽2)11yescharacteristic
1105C2×C4#58511yescharacteristic
1106C2×C4#58511yescharacteristic
1107C2×C4#58511yescharacteristic
1108C2×C4#58511yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22C2×#55011yescharacteristic
1125C22#350011yescharacteristic
1126C22#350011yescharacteristic
1127C22C2×#57511yescharacteristic
1128C22C2×#57811yescharacteristic
1129C22#358611yescharacteristic
1130C22#358611yescharacteristic
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4#345511yescharacteristic
1161C4#351211yescharacteristic
1162C4#356211yescharacteristic
1163C4#356211yescharacteristic
1164C2—161no—
1165C2#3938211yescharacteristic
1166C2#6140311yescharacteristic
1167C2#6142211yescharacteristic
1168C2#6254511yescharacteristic
1169C2#6256511yescharacteristic
1170C2#6257911yescharacteristic
1171C2#6259911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40024C2semidirect
3. #33232C2semidirect
8. #31596C2semidirect
9. #31595C2semidirect
10. #31576C2semidirect
11. #31575C2semidirect
13. #29799C2semidirect
14. #28904C2semidirect
15. #28892C2semidirect
16. #28887C2semidirect
17. #28875C2semidirect
24. #25333C2semidirect
25. #25333C2semidirect
28. #23233C2semidirect
29. #23227C2semidirect
30. #21674C2semidirect

Maximal subgroups

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

subgroupindex
#400242
#395132
#332322
#321852
#321692
#315962
#315952
#315762
#315752
#298702
#297992
#289042
#288922
#288872
#288752
#284272
#277652
#277612
#277542
#277522
#253332
#252892
#232332
#232272
#216742
#212882