Finite Group Databasebeta

← #6489451

Subgroups — #6489451

Order 512.

1345 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#35344C211yesmaximal, characteristic, complemented
2#35290C211yesmaximal, characteristic
3#33215C211yesmaximal, characteristic, complemented
4#33213C211yesmaximal, characteristic, complemented
5#33054C211yesmaximal, characteristic
6#33054C211yesmaximal, characteristic
7#30387C211yesmaximal, characteristic, complemented
8#30386C211yesmaximal, characteristic, complemented
9#30381C211yesmaximal, characteristic, complemented
10#30380C211yesmaximal, characteristic, complemented
11#29224C211yesmaximal, characteristic, complemented
12#29187C211yesmaximal, characteristic, complemented
13#29187C211yesmaximal, characteristic, complemented
14#28727C211yesmaximal, characteristic, complemented
15#28688C211yesmaximal, characteristic, complemented
16#28663C211yesmaximal, characteristic, complemented
17#28662C211yesmaximal, characteristic, complemented
18#28510C211yesmaximal, characteristic, complemented
19#27866C211yesmaximal, characteristic, complemented
20#27865C211yesmaximal, characteristic
21#27860C211yesmaximal, characteristic, complemented
22#27859C211yesmaximal, characteristic
23#24853C211yesmaximal, characteristic, complemented
24#24851C211yesmaximal, characteristic
25#24849C211yesmaximal, characteristic, complemented
26#24847C211yesmaximal, characteristic
27#22129C211yesmaximal, characteristic, complemented
28#22127C211yesmaximal, characteristic, complemented
29#22125C211yesmaximal, characteristic, complemented
30#22123C211yesmaximal, characteristic, complemented
31#20430C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#498C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#424C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#405C2211yescharacteristic
43C2×#405C2211yescharacteristic
44#2864C2211yescharacteristic
45#2864C2211yescharacteristic
46#2863C2211yescharacteristic
47#2862C2211yescharacteristic
48#2862C2211yescharacteristic
49#2860C2211yescharacteristic
50#2855C2211yescharacteristic
51#2854C2211yescharacteristic
52#2647C2211yescharacteristic
53#2640C2211yescharacteristic
54#2628C2211yescharacteristic
55#2628C2211yescharacteristic
56#2628C2211yescharacteristic
57#2628C2211yescharacteristic
58#2628C2211yescharacteristic
59#2620C2211yescharacteristic
60#2607—21no—
61#2607—21no—
62#2607—21no—
63#2607—21no—
64#2605—21no—
65#2605—21no—
66#2605—21no—
67#2605—21no—
68#2574—21no—
69#2573—21no—
70#2572—21no—
71#2553—21no—
72#2525—21no—
73#2516—21no—
74#2469—21no—
75#2458—21no—
76#2331C2211yescharacteristic
77#2331C2211yescharacteristic
78#2331C2211yescharacteristic
79#2331C2211yescharacteristic
80#2324C2211yescharacteristic
81#2323C2211yescharacteristic
82#2320C2211yescharacteristic
83#2319C2211yescharacteristic
84C4×C4⋊Q8C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2283C2211yescharacteristic
87#2283C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2101C2211yescharacteristic
92#2101C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2087C2211yescharacteristic
102#2087C2211yescharacteristic
103#2086C2211yescharacteristic
104#2086C2211yescharacteristic
105#2085C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2074C2211yescharacteristic
110#2074C2211yescharacteristic
111#2073C2211yescharacteristic
112#2073C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#1993C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1993C2211yescharacteristic
125#1990C2211yescharacteristic
126#1990C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1958C2211yescharacteristic
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1941C2211yescharacteristic
144#1941C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1919C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1895C2211yescharacteristic
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1894C2211yescharacteristic
173#1893C2211yescharacteristic
174#1893C2211yescharacteristic
175#1892C2211yescharacteristic
176#1892C2211yescharacteristic
177#1846C2211yescharacteristic
178#1846C2211yescharacteristic
179#1836C2211yescharacteristic
180#1836C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1768C2211yescharacteristic
197#1767C2211yescharacteristic
198#1767C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201#1728C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#500—42no—
224#498—42no—
225#489—42no—
226#489—42no—
227#477—24no—
228#476—24no—
229#475—24no—
230#474—24no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247#424—24no—
248#424—24no—
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273#405—42no—
274#405—42no—
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#399—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#396—21no—
300#396—21no—
301#395—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#395—21no—
306#394—21no—
307#394—21no—
308#393—21no—
309#393—21no—
310#393—21no—
311#393—21no—
312#393—21no—
313#393—21no—
314#393—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—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#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#384C2311yescharacteristic
400#383—21no—
401#383—21no—
402#383—21no—
403#383—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#381—21no—
417#381—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4D411yescharacteristic
429C4×C4⋊C4D411yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4D411yescharacteristic
442C4×C22⋊C4D411yescharacteristic
443C4×C22⋊C4D411yescharacteristic
444#376—21no—
445#376—21no—
446#376C2311yescharacteristic
447#376C2311yescharacteristic
448C43C2311yescharacteristic
449C43C2311yescharacteristic
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#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532#126—82no—
533#124—22no—
534#124—22no—
535#123—82no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538#121—22no—
539#121—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—82no—
543C4×D4—22no—
544C4×D4—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—22no—
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⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
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⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640#107—22no—
641#107—22no—
642#107—22no—
643#107—22no—
644#107—41no—
645#107—41no—
646#107—41no—
647#107—41no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656C4⋊C8—22no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8#4114yes—
663C4⋊C8#4114yes—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#97—22no—
681#97—22no—
682#97—41no—
683#97—41no—
684C4×C8—22no—
685C4×C8—22no—
686C4×C8—41no—
687C4×C8—41no—
688#95—21no—
689#95—21no—
690#95—21no—
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#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750C24—21no—
751C24C22×D411yescharacteristic
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—42no—
780C2×D4—81no—
781C2×D4—81no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
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—21no—
802C22×C4—21no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—42no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
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×C42−1+412yes—
824C22×C42−1+412yes—
825C22×C4C2511yescharacteristic
826M16—44no—
827M16—44no—
828C2×C8—21no—
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—44no—
849C2×C8—44no—
850C2×C8C2×#4112yes—
851C2×C8C2×#4112yes—
852C2×C8C2×#4112yes—
853C2×C8C2×#4112yes—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
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—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
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—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—22no—
935C42—22no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—41no—
950C42—41no—
951C42—41no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42C2×#4112yes—
960C42C2×#4112yes—
961C42H(5,𝔽2)12yes—
962C422−1+412yes—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23#53612yes—
977C23C23×D411yescharacteristic
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—84no—
983Q8—162no—
984Q8—162no—
985Q8—162no—
986Q8—162no—
987D4—41no—
988D4—41no—
989D4—41no—
990D4—41no—
991D4—162no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
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—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
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—82no—
1076C2×C4—82no—
1077C2×C4—162no—
1078C2×C4#53212yes—
1079C2×C4#53212yes—
1080C2×C4#53612yes—
1081C2×C4#53712yes—
1082C2×C4#53712yes—
1083C2×C4C22×#4111yescharacteristic
1084C2×C4C22×#4111yescharacteristic
1085C2×C4C2×H(5,𝔽2)11yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4C2×2−1+411yescharacteristic
1088C2×C4C2×2−1+411yescharacteristic
1089C8—22no—
1090C8—22no—
1091C8—22no—
1092C8—22no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22C2×#53211yescharacteristic
1112C22C2×#53611yescharacteristic
1113C22C2×#53711yescharacteristic
1114C22#358411yescharacteristic
1115C22#358411yescharacteristic
1116C22#358511yescharacteristic
1117C22#358611yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4#352011yescharacteristic
1147C4#352011yescharacteristic
1148C4#352311yescharacteristic
1149C4#352311yescharacteristic
1150C2—42no—
1151C2—161no—
1152C2#3524111yescharacteristic
1153C2#6071311yescharacteristic
1154C2#6072711yescharacteristic
1155C2#6087511yescharacteristic
1156C2#6087611yescharacteristic
1157C2#6092611yescharacteristic
1158C2#6092711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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. #35344C2semidirect
3. #33215C2semidirect
4. #33213C2semidirect
7. #30387C2semidirect
8. #30386C2semidirect
9. #30381C2semidirect
10. #30380C2semidirect
11. #29224C2semidirect
12. #29187C2semidirect
13. #29187C2semidirect
14. #28727C2semidirect
15. #28688C2semidirect
16. #28663C2semidirect
17. #28662C2semidirect
18. #28510C2semidirect
19. #27866C2semidirect
21. #27860C2semidirect
23. #24853C2semidirect
25. #24849C2semidirect
27. #22129C2semidirect
28. #22127C2semidirect
29. #22125C2semidirect
30. #22123C2semidirect
31. #20430C2semidirect

Maximal subgroups

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

subgroupindex
#353442
#352902
#332152
#332132
#330542
#303872
#303862
#303812
#303802
#292242
#291872
#287272
#286882
#286632
#286622
#285102
#278662
#278652
#278602
#278592
#248532
#248512
#248492
#248472
#221292
#221272
#221252
#221232
#204302