Finite Group Databasebeta

← #6802882

Subgroups — #6802882

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39731C211yesmaximal, characteristic
2#35286C211yesmaximal, characteristic, complemented
3#33112C211yesmaximal, characteristic
4#32403C211yesmaximal, characteristic, complemented
5#32390C211yesmaximal, characteristic, complemented
6#32389C211yesmaximal, characteristic, complemented
7#32376C211yesmaximal, characteristic, complemented
8#31599C211yesmaximal, characteristic, complemented
9#31586C211yesmaximal, characteristic, complemented
10#31585C211yesmaximal, characteristic, complemented
11#31572C211yesmaximal, characteristic, complemented
12#29768C211yesmaximal, characteristic
13#29764C211yesmaximal, characteristic, complemented
14#28840C211yesmaximal, characteristic, complemented
15#28837C211yesmaximal, characteristic, complemented
16#27922C211yesmaximal, characteristic, complemented
17#27920C211yesmaximal, characteristic
18#27913C211yesmaximal, characteristic
19#27765C211yesmaximal, characteristic, complemented
20#27761C211yesmaximal, characteristic, complemented
21#27656C211yesmaximal, characteristic, complemented
22#27654C211yesmaximal, characteristic
23#27647C211yesmaximal, characteristic, complemented
24#26544C211yesmaximal, characteristic, complemented
25#26543C211yesmaximal, characteristic, complemented
26#26105C211yesmaximal, characteristic, complemented
27#26104C211yesmaximal, characteristic, complemented
28#22628C211yesmaximal, characteristic, complemented
29#22091C211yesmaximal, characteristic
30#22087C211yesmaximal, characteristic, complemented
31#21583C211yesmaximal, characteristic, complemented
32C2×#484C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#483C2211yescharacteristic
40C2×#483C2211yescharacteristic
41#2859—21no—
42#2859—21no—
43#2850C2211yescharacteristic
44#2793—21no—
45#2790—21no—
46#2786—21no—
47#2750—21no—
48#2647—21no—
49#2647—21no—
50#2621C2211yescharacteristic
51#2620C2211yescharacteristic
52#2578—21no—
53#2571C2211yescharacteristic
54#2571C2211yescharacteristic
55#2571C2211yescharacteristic
56#2571C2211yescharacteristic
57#2570C2211yescharacteristic
58#2552C2211yescharacteristic
59#2552C2211yescharacteristic
60#2552C2211yescharacteristic
61#2552C2211yescharacteristic
62#2545C2211yescharacteristic
63#2531—21no—
64#2529—21no—
65#2515—21no—
66#2513C2211yescharacteristic
67#2511C2211yescharacteristic
68#2447C2211yescharacteristic
69#2446C2211yescharacteristic
70#2442—21no—
71#2442—21no—
72#2442—21no—
73#2442—21no—
74#2367C2211yescharacteristic
75#2356C2211yescharacteristic
76#2324C2211yescharacteristic
77#2323C2211yescharacteristic
78#2317C2211yescharacteristic
79#2317C2211yescharacteristic
80#2316C2211yescharacteristic
81#2316C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83#2285C2211yescharacteristic
84C2×#384C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2097C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2096C2211yescharacteristic
93#2095C2211yescharacteristic
94#2094C2211yescharacteristic
95#2093C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2083C2211yescharacteristic
108#2074C2211yescharacteristic
109#2073C2211yescharacteristic
110#2072C2211yescharacteristic
111#2072C2211yescharacteristic
112#2072C2211yescharacteristic
113#2071C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2043C2211yescharacteristic
123#2043C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1960C2211yescharacteristic
129#1959C2211yescharacteristic
130#1959C2211yescharacteristic
131#1959C2211yescharacteristic
132#1958C2211yescharacteristic
133#1956C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1947C2211yescharacteristic
142#1944C2211yescharacteristic
143#1943C2211yescharacteristic
144#1942C2211yescharacteristic
145#1941C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1847C2211yescharacteristic
180#1846C2211yescharacteristic
181#1844C2211yescharacteristic
182#1825C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1805C2211yescharacteristic
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—21no—
205C2×#125—21no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#124C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×#121C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C4⋊C4—21no—
221C22×C4⋊C4—21no—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#485—24no—
226#485—42no—
227#484—24no—
228#484—42no—
229#483—42no—
230#483—42no—
231#482—42no—
232#481—24no—
233#481—42no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—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#396—21no—
328#394—21no—
329#394—21no—
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
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#388—21no—
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#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#384—21no—
401#384—21no—
402#384D411yescharacteristic
403#384D411yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#383—21no—
414#382—21no—
415#382—21no—
416#382—21no—
417#382—21no—
418#382D411yescharacteristic
419#382D411yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380D411yescharacteristic
432#380D411yescharacteristic
433#380D411yescharacteristic
434#380D411yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452#376—21no—
453#376—21no—
454C43—21no—
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#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×D4—21no—
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507#125—82no—
508#125—82no—
509#125—82no—
510#125—82no—
511#124—22no—
512#124—22no—
513#124—41no—
514#124—41no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519#121—22no—
520#121—22no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×D4—41no—
526C4×D4—41no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
531#117—41no—
532#117—41no—
533#117—41no—
534#117—41no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
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—82no—
577C2×C4⋊C4—82no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—21no—
627C2×C42—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×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—22no—
646#107—22no—
647#107—22no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—41no—
657#106—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665C4⋊C8—22no—
666C4⋊C8—22no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
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#102—22no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8#4114yes—
699#97—22no—
700#97—22no—
701#97—41no—
702#97—41no—
703C4×C8—41no—
704C4×C8—41no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
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#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C24C22×D411yescharacteristic
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—42no—
777C2×D4—81no—
778C2×D4—81no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C2×#4112yes—
827C22×C4H(5,𝔽2)12yes—
828C22×C4C2511yescharacteristic
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8C2×#4112yes—
852C2×C8C2×#4112yes—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C42—22no—
950C42—22no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C422−1+412yes—
973C422−1+412yes—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23#55012yes—
988C23C23×D411yescharacteristic
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997D4—41no—
998D4—41no—
999D4—41no—
1000D4—41no—
1001D4—162no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
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—44no—
1042C2×C4—44no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
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—162no—
1089C2×C4—162no—
1090C2×C4—162no—
1091C2×C4#53612yes—
1092C2×C4#53612yes—
1093C2×C4#55012yes—
1094C2×C4#57712yes—
1095C2×C4C22×#4111yescharacteristic
1096C2×C4C2×H(5,𝔽2)11yescharacteristic
1097C2×C4C2×2−1+411yescharacteristic
1098C2×C4C2×2−1+411yescharacteristic
1099C2×C4#58511yescharacteristic
1100C2×C4#58511yescharacteristic
1101C8—22no—
1102C8—22no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22C2×#53611yescharacteristic
1124C22C2×#55011yescharacteristic
1125C22#348511yescharacteristic
1126C22C2×#57711yescharacteristic
1127C22#358511yescharacteristic
1128C22#358611yescharacteristic
1129C22#358611yescharacteristic
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—81no—
1144C4—81no—
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#351511yescharacteristic
1159C4#351511yescharacteristic
1160C4#355911yescharacteristic
1161C4#355911yescharacteristic
1162C2—42no—
1163C2—161no—
1164C2#3913411yescharacteristic
1165C2#6086711yescharacteristic
1166C2#6087211yescharacteristic
1167C2#6141811yescharacteristic
1168C2#6142111yescharacteristic
1169C2#6179911yescharacteristic
1170C2#6181211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35286C2semidirect
4. #32403C2semidirect
5. #32390C2semidirect
6. #32389C2semidirect
7. #32376C2semidirect
8. #31599C2semidirect
9. #31586C2semidirect
10. #31585C2semidirect
11. #31572C2semidirect
13. #29764C2semidirect
14. #28840C2semidirect
15. #28837C2semidirect
16. #27922C2semidirect
19. #27765C2semidirect
20. #27761C2semidirect
21. #27656C2semidirect
23. #27647C2semidirect
24. #26544C2semidirect
25. #26543C2semidirect
26. #26105C2semidirect
27. #26104C2semidirect
28. #22628C2semidirect
30. #22087C2semidirect
31. #21583C2semidirect

Maximal subgroups

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

subgroupindex
#397312
#352862
#331122
#324032
#323902
#323892
#323762
#315992
#315862
#315852
#315722
#297682
#297642
#288402
#288372
#279222
#279202
#279132
#277652
#277612
#276562
#276542
#276472
#265442
#265432
#261052
#261042
#226282
#220912
#220872
#215832