Finite Group Databasebeta

← #6566457

Subgroups — #6566457

Order 512.

1461 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36201C211yesmaximal, characteristic, complemented
2#34321C211yesmaximal, characteristic
3#30171C211yesmaximal, characteristic, complemented
4#30096C211yesmaximal, characteristic, complemented
5#29974C211yesmaximal, characteristic, complemented
6#29576C211yesmaximal, characteristic, complemented
7#29396C211yesmaximal, characteristic, complemented
8#29300C211yesmaximal, characteristic, complemented
9#29161C211yesmaximal, characteristic, complemented
10#27646C211yesmaximal, characteristic, complemented
11#27618C211yesmaximal, characteristic, complemented
12#27465C211yesmaximal, characteristic, complemented
13#27463C211yesmaximal, characteristic, complemented
14#27296C211yesmaximal, characteristic, complemented
15#27294C211yesmaximal, characteristic, complemented
16#27109C211yesmaximal, characteristic, complemented
17#27107C211yesmaximal, characteristic, complemented
18#26862C211yesmaximal, characteristic, complemented
19#26860C211yesmaximal, characteristic, complemented
20#24944C211yesmaximal, characteristic, complemented
21#24942C211yesmaximal, characteristic, complemented
22#24093C211yesmaximal, characteristic
23#24093C211yesmaximal, characteristic
24#23838C211yesmaximal, characteristic, complemented
25#23758C211yesmaximal, characteristic, complemented
26#23656C211yesmaximal, characteristic, complemented
27#22923C211yesmaximal, characteristic, complemented
28#22921C211yesmaximal, characteristic, complemented
29#22785C211yesmaximal, characteristic, complemented
30#22614C211yesmaximal, characteristic, complemented
31#22610C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#427C2211yescharacteristic
36C2×#427C2211yescharacteristic
37#2864C2211yescharacteristic
38#2851C2211yescharacteristic
39#2851C2211yescharacteristic
40#2577—21no—
41#2530—21no—
42#2524—21no—
43#2515—21no—
44#2507C2211yescharacteristic
45#2506C2211yescharacteristic
46#2497C2211yescharacteristic
47#2496C2211yescharacteristic
48#2485C2211yescharacteristic
49#2485C2211yescharacteristic
50#2468—21no—
51#2460—21no—
52#2373—21no—
53#2371—21no—
54#2369C2211yescharacteristic
55#2367—21no—
56#2367—21no—
57#2363C2211yescharacteristic
58#2363C2211yescharacteristic
59#2361—21no—
60#2354C2211yescharacteristic
61D4×C4⋊C4C2211yescharacteristic
62#2347—21no—
63#2347C2211yescharacteristic
64#2347C2211yescharacteristic
65#2347C2211yescharacteristic
66#2346C2211yescharacteristic
67#2337—21no—
68#2337—21no—
69#2324—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×#125C2211yescharacteristic
72C4×#121C2211yescharacteristic
73C4×#121C2211yescharacteristic
74#2296C2211yescharacteristic
75#2296C2211yescharacteristic
76#2293C2211yescharacteristic
77#2285C2211yescharacteristic
78#2283C2211yescharacteristic
79#2274—21no—
80C42×D4C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2025C2211yescharacteristic
121#1948C2211yescharacteristic
122#1947C2211yescharacteristic
123#1942C2211yescharacteristic
124#1942C2211yescharacteristic
125#1942C2211yescharacteristic
126#1941C2211yescharacteristic
127#1941C2211yescharacteristic
128#1941C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1926C2211yescharacteristic
132#1925C2211yescharacteristic
133#1923C2211yescharacteristic
134#1923C2211yescharacteristic
135#1921C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1921C2211yescharacteristic
142#1920C2211yescharacteristic
143#1919C2211yescharacteristic
144#1919C2211yescharacteristic
145#1919C2211yescharacteristic
146#1919C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1916C2211yescharacteristic
154#1916C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1869C2211yescharacteristic
158#1869C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1862C2211yescharacteristic
164#1862C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1839C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1817C2211yescharacteristic
183#1808C2211yescharacteristic
184#1807C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1797C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199#1744C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×C8C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#555—24no—
206#555—24no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#124—21no—
212C2×#124—21no—
213C2×#121—21no—
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×D4—21no—
218C2×C4×D4—21no—
219C2×C4×D4D411yescharacteristic
220C2×C4×D4D411yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117—21no—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C22×C4⋊C4—21no—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#482—24no—
237#482—24no—
238#427—24no—
239#427—24no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280#400—21no—
281#400—21no—
282#400—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#397—21no—
287#397—21no—
288#397—21no—
289#396—21no—
290#394—21no—
291#394—21no—
292#391—21no—
293#391—21no—
294#391—21no—
295#390—21no—
296#390—21no—
297#390—21no—
298#390C2311yescharacteristic
299#390C2311yescharacteristic
300#389—21no—
301#389—21no—
302#389—21no—
303#389C2311yescharacteristic
304#389C2311yescharacteristic
305#389C2311yescharacteristic
306#389C2311yescharacteristic
307#389C2311yescharacteristic
308#389C2311yescharacteristic
309#389C2311yescharacteristic
310#389C2311yescharacteristic
311#389C2311yescharacteristic
312#389C2311yescharacteristic
313#389C2311yescharacteristic
314#389C2311yescharacteristic
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#388—21no—
322#388—21no—
323#388—21no—
324#388—21no—
325#388—21no—
326#388—21no—
327#388—21no—
328#388—21no—
329#388—21no—
330#388—21no—
331#388—21no—
332#388—21no—
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#386—21no—
357#386—21no—
358#386—21no—
359#386—21no—
360#385—21no—
361#385—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#384C2311yescharacteristic
371#384C2311yescharacteristic
372#384C2311yescharacteristic
373#383—21no—
374#383—21no—
375#383—21no—
376#383—21no—
377#382—21no—
378#382C2311yescharacteristic
379#382C2311yescharacteristic
380#382C2311yescharacteristic
381#381—21no—
382#380—21no—
383#380—21no—
384#380—21no—
385#380C2311yescharacteristic
386#380C2311yescharacteristic
387#380C2311yescharacteristic
388#380C2311yescharacteristic
389#380C2311yescharacteristic
390#380C2311yescharacteristic
391#380C2311yescharacteristic
392#380C2311yescharacteristic
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4D411yescharacteristic
426C4×C22⋊C4D411yescharacteristic
427C4×C22⋊C4D411yescharacteristic
428C4×C22⋊C4D411yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431#376—21no—
432#376—21no—
433C43C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#340C2311yescharacteristic
469#340C2311yescharacteristic
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×D4—21no—
486C22×D4—21no—
487C22×D4C2×D411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C2×D411yescharacteristic
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2×D411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514#126—44no—
515#125—41no—
516#125—41no—
517#125—44no—
518#124—28no—
519#124—28no—
520#121—28no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121#4114yes—
525C4×Q8—82no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—24no—
530C4×D4—22no—
531C4×D4—42no—
532C4×D4—41no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—82no—
537C4×D4—82no—
538#117—28no—
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—22no—
544#117—22no—
545#117—22no—
546#117—44no—
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—44no—
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4—21no—
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—41no—
643C2×C42—41no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—22no—
666#107—41no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—22no—
671#106—22no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—41no—
688#102—41no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—22no—
692C22⋊C8—22no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C4×C8—22no—
696C4×C8—22no—
697C4×C8—41no—
698C4×C8—41no—
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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24C22×D411yescharacteristic
748C24C22×D411yescharacteristic
749C2×Q8—24no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×D4—22no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—22no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—41no—
762C2×D4—81no—
763C2×D4—81no—
764C2×D4—81no—
765C2×D4—81no—
766C2×D4C2×#4112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
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—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
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×C4C2×#4112yes—
826C22×C4C2×#4112yes—
827C22×C4C2511yescharacteristic
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—21no—
849C2×C8—21no—
850C2×C8—44no—
851C2×C8—44no—
852C2×C82−1+412yes—
853C2×C82−1+412yes—
854C4⋊C4—24no—
855C4⋊C4—22no—
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—21no—
882C4⋊C4—21no—
883C4⋊C4—41no—
884C4⋊C4—42no—
885C4⋊C4—42no—
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—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
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#13514yes—
911C4⋊C4C2×#4112yes—
912C4⋊C4C2×#4112yes—
913C4⋊C4C2×#4112yes—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—22no—
919C22⋊C4—24no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C42—24no—
944C42—24no—
945C42—22no—
946C42—22no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—22no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23#52512yes—
997C23C23×D411yescharacteristic
998Q8—84no—
999D4—22no—
1000D4—22no—
1001D4—44no—
1002D4—41no—
1003D4—41no—
1004D4—84no—
1005D4—84no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
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—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
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—48no—
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—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—82no—
1092C2×C4—82no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—162no—
1096C2×C4—162no—
1097C2×C4#52512yes—
1098C2×C4C2×#13512yes—
1099C2×C4C2×#13512yes—
1100C2×C4C2×#13512yes—
1101C2×C4#57512yes—
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C22×#4111yescharacteristic
1104C2×C4C2×2−1+411yescharacteristic
1105C2×C4C2×2−1+411yescharacteristic
1106C2×C4#58511yescharacteristic
1107C2×C4#58511yescharacteristic
1108C8—22no—
1109C8—22no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—41no—
1130C22—42no—
1131C22—41no—
1132C22—42no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22C2×#52511yescharacteristic
1138C22#348511yescharacteristic
1139C22#349911yescharacteristic
1140C22C22×#13511yescharacteristic
1141C22C2×#57511yescharacteristic
1142C22#358411yescharacteristic
1143C22#358511yescharacteristic
1144C4—22no—
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4#349511yescharacteristic
1172C4#349511yescharacteristic
1173C4#351511yescharacteristic
1174C4#351511yescharacteristic
1175C2—42no—
1176C2—81no—
1177C2—82no—
1178C2#3602111yescharacteristic
1179C2#6053611yescharacteristic
1180C2#6060111yescharacteristic
1181C2#6170211yescharacteristic
1182C2#6174311yescharacteristic
1183C2#6247611yescharacteristic
1184C2#6250611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#555C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36201C2semidirect
3. #30171C2semidirect
4. #30096C2semidirect
5. #29974C2semidirect
6. #29576C2semidirect
7. #29396C2semidirect
8. #29300C2semidirect
9. #29161C2semidirect
10. #27646C2semidirect
11. #27618C2semidirect
12. #27465C2semidirect
13. #27463C2semidirect
14. #27296C2semidirect
15. #27294C2semidirect
16. #27109C2semidirect
17. #27107C2semidirect
18. #26862C2semidirect
19. #26860C2semidirect
20. #24944C2semidirect
21. #24942C2semidirect
24. #23838C2semidirect
25. #23758C2semidirect
26. #23656C2semidirect
27. #22923C2semidirect
28. #22921C2semidirect
29. #22785C2semidirect
30. #22614C2semidirect
31. #22610C2semidirect

Maximal subgroups

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

subgroupindex
#362012
#343212
#301712
#300962
#299742
#295762
#293962
#293002
#291612
#276462
#276182
#274652
#274632
#272962
#272942
#271092
#271072
#268622
#268602
#249442
#249422
#240932
#238382
#237582
#236562
#229232
#229212
#227852
#226142
#226102