Finite Group Databasebeta

← #6480097

Subgroups — #6480097

Order 512.

1379 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34629C211yesmaximal, characteristic
2#34254C211yesmaximal, characteristic
3#33105C211yesmaximal, characteristic
4#33104C211yesmaximal, characteristic
5#33019C211yesmaximal, characteristic
6#33019C211yesmaximal, characteristic
7#29979C211yesmaximal, characteristic
8#29963C211yesmaximal, characteristic
9#29766C211yesmaximal, characteristic
10#29724C211yesmaximal, characteristic
11#29589C211yesmaximal, characteristic, complemented
12#29585C211yesmaximal, characteristic, complemented
13#29565C211yesmaximal, characteristic, complemented
14#29565C211yesmaximal, characteristic, complemented
15#29541C211yesmaximal, characteristic, complemented
16#29541C211yesmaximal, characteristic, complemented
17#29540C211yesmaximal, characteristic, complemented
18#29539C211yesmaximal, characteristic, complemented
19#29455C211yesmaximal, characteristic, complemented
20#29454C211yesmaximal, characteristic, complemented
21#29439C211yesmaximal, characteristic, complemented
22#29438C211yesmaximal, characteristic, complemented
23#29399C211yesmaximal, characteristic, complemented
24#29398C211yesmaximal, characteristic, complemented
25#29371C211yesmaximal, characteristic, complemented
26#29370C211yesmaximal, characteristic, complemented
27#22083C211yesmaximal, characteristic
28#22077C211yesmaximal, characteristic
29#22050C211yesmaximal, characteristic
30#22044C211yesmaximal, characteristic
31#20784C211yesmaximal, characteristic
32C2×#519C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#451C2211yescharacteristic
36C2×#451C2211yescharacteristic
37#2655—21no—
38#2655—21no—
39#2652—21no—
40#2652—21no—
41#2647C2211yescharacteristic
42#2645C2211yescharacteristic
43#2645C2211yescharacteristic
44#2642C2211yescharacteristic
45#2629C2211yescharacteristic
46#2625C2211yescharacteristic
47#2625C2211yescharacteristic
48#2621C2211yescharacteristic
49#2402—21no—
50#2402—21no—
51#2401—21no—
52#2401—21no—
53#2356—21no—
54#2356—21no—
55#2355—21no—
56#2355—21no—
57#2343—21no—
58#2343—21no—
59#2343—21no—
60#2343—21no—
61#2320C2211yescharacteristic
62#2320C2211yescharacteristic
63#2320C2211yescharacteristic
64#2320C2211yescharacteristic
65#2317C2211yescharacteristic
66#2310C2211yescharacteristic
67C4×C4⋊Q8C2211yescharacteristic
68C4×#125C2211yescharacteristic
69C4×C22⋊Q8C2211yescharacteristic
70C4×C22⋊Q8C2211yescharacteristic
71#2296C2211yescharacteristic
72#2295C2211yescharacteristic
73#2295C2211yescharacteristic
74#2295C2211yescharacteristic
75#2295C2211yescharacteristic
76#2295C2211yescharacteristic
77#2295C2211yescharacteristic
78C2×#391C2211yescharacteristic
79#2274C2211yescharacteristic
80C4×#117C2211yescharacteristic
81#2100C2211yescharacteristic
82#2099C2211yescharacteristic
83#2096C2211yescharacteristic
84#2095C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2074C2211yescharacteristic
92#2074C2211yescharacteristic
93#2068C2211yescharacteristic
94#2068C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2066C2211yescharacteristic
98#2066C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2056C2211yescharacteristic
104#2056C2211yescharacteristic
105#2056C2211yescharacteristic
106#2056C2211yescharacteristic
107#2043C2211yescharacteristic
108#2043C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2016C2211yescharacteristic
112#2016C2211yescharacteristic
113#1971C2211yescharacteristic
114#1971C2211yescharacteristic
115#1969C2211yescharacteristic
116#1969C2211yescharacteristic
117#1944C2211yescharacteristic
118#1943C2211yescharacteristic
119#1942C2211yescharacteristic
120#1941C2211yescharacteristic
121#1935C2211yescharacteristic
122#1935C2211yescharacteristic
123#1935C2211yescharacteristic
124#1935C2211yescharacteristic
125#1933C2211yescharacteristic
126#1933C2211yescharacteristic
127#1933C2211yescharacteristic
128#1933C2211yescharacteristic
129#1928C2211yescharacteristic
130#1928C2211yescharacteristic
131#1928C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1928C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1927C2211yescharacteristic
138#1927C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1918C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1878C2211yescharacteristic
154#1878C2211yescharacteristic
155#1878C2211yescharacteristic
156#1878C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1839C2211yescharacteristic
186#1839C2211yescharacteristic
187#1831C2211yescharacteristic
188#1831C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1818C2211yescharacteristic
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199#1749C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212#519—24no—
213#519—24no—
214C2×C4×Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×#117—21no—
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#485—24no—
231#485—24no—
232#451—24no—
233#451—24no—
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#401—21no—
283#401—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#385—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#384—21no—
383#384C2311yescharacteristic
384#383—21no—
385#383—21no—
386#383—21no—
387#383—21no—
388#382—21no—
389#382—21no—
390#382—21no—
391#382—21no—
392#382—21no—
393#382C2311yescharacteristic
394#381—21no—
395#381—21no—
396#380C2311yescharacteristic
397#380C2311yescharacteristic
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4D411yescharacteristic
415C4×C4⋊C4D411yescharacteristic
416C4×C4⋊C4D411yescharacteristic
417C4×C4⋊C4D411yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4D411yescharacteristic
429C4×C22⋊C4D411yescharacteristic
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432#376—21no—
433#376—21no—
434#376—21no—
435#376—21no—
436#376—21no—
437#376—21no—
438#376C2311yescharacteristic
439#376C2311yescharacteristic
440C2×#95—21no—
441C2×#95—21no—
442C43C2311yescharacteristic
443C43C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8—41no—
489C22×Q8—41no—
490C22×Q8#4114yes—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522#125—41no—
523#125—41no—
524C22⋊Q8—22no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C4×Q8—28no—
529C4×Q8—28no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542#117—28no—
543#117—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117#4114yes—
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—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—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#107—22no—
644#107—22no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#106—22no—
650#106—22no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
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—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686C22⋊C8—22no—
687#97—41no—
688#97—41no—
689C4×C8—41no—
690C4×C8—41no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
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#95—21no—
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757C24C22×D411yescharacteristic
758C2×Q8—24no—
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×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8C2×#4112yes—
788C2×Q8C2×#4112yes—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—24no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C2×#4112yes—
835C22×C4C2×#4112yes—
836C22×C4C2511yescharacteristic
837Q16—82no—
838Q16—82no—
839Q16—82no—
840Q16—82no—
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×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—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—22no—
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—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—41no—
894C4⋊C4—41no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
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⋊C4C2×#4112yes—
923C4⋊C4C2×#4112yes—
924C22⋊C4—24no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—22no—
940C42—22no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23#52512yes—
977C23C23×D411yescharacteristic
978Q8—22no—
979Q8—22no—
980Q8—22no—
981Q8—22no—
982Q8—48no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
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—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
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—48no—
1041C2×C4—41no—
1042C2×C4—41no—
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—82no—
1086C2×C4—82no—
1087C2×C4—162no—
1088C2×C4#52512yes—
1089C2×C4#57812yes—
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C22×#4111yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C2×C4#58511yescharacteristic
1095C2×C4#58511yescharacteristic
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22C2×#52511yescharacteristic
1112C22#344911yescharacteristic
1113C22#344911yescharacteristic
1114C22C2×#57811yescharacteristic
1115C22#358411yescharacteristic
1116C22#358611yescharacteristic
1117C22#358611yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—42no—
1121C4—42no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—42no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4#349111yescharacteristic
1148C4#349111yescharacteristic
1149C4#349311yescharacteristic
1150C4#349311yescharacteristic
1151C2—42no—
1152C2#3511811yescharacteristic
1153C2#6057311yescharacteristic
1154C2#6057711yescharacteristic
1155C2#6098311yescharacteristic
1156C2#6098711yescharacteristic
1157C2#6099511yescharacteristic
1158C2#6099611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
11. #29589C2semidirect
12. #29585C2semidirect
13. #29565C2semidirect
14. #29565C2semidirect
15. #29541C2semidirect
16. #29541C2semidirect
17. #29540C2semidirect
18. #29539C2semidirect
19. #29455C2semidirect
20. #29454C2semidirect
21. #29439C2semidirect
22. #29438C2semidirect
23. #29399C2semidirect
24. #29398C2semidirect
25. #29371C2semidirect
26. #29370C2semidirect

Maximal subgroups

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

subgroupindex
#346292
#342542
#331052
#331042
#330192
#299792
#299632
#297662
#297242
#295892
#295852
#295652
#295412
#295402
#295392
#294552
#294542
#294392
#294382
#293992
#293982
#293712
#293702
#220832
#220772
#220502
#220442
#207842