Finite Group Databasebeta

← #7180249

Subgroups — #7180249

Order 512.

1307 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59333C211yesmaximal, characteristic, complemented
2#39736C211yesmaximal, characteristic
3#32445C211yesmaximal, characteristic, complemented
4#32445C211yesmaximal, characteristic, complemented
5#32405C211yesmaximal, characteristic, complemented
6#32404C211yesmaximal, characteristic, complemented
7#32070C211yesmaximal, characteristic, complemented
8#32054C211yesmaximal, characteristic, complemented
9#31954C211yesmaximal, characteristic, complemented
10#31941C211yesmaximal, characteristic, complemented
11#28807C211yesmaximal, characteristic, complemented
12#28026C211yesmaximal, characteristic, complemented
13#28019C211yesmaximal, characteristic, complemented
14#27982C211yesmaximal, characteristic
15#27743C211yesmaximal, characteristic, complemented
16#27733C211yesmaximal, characteristic, complemented
17#27344C211yesmaximal, characteristic, complemented
18#27329C211yesmaximal, characteristic, complemented
19#27174C211yesmaximal, characteristic, complemented
20#27159C211yesmaximal, characteristic, complemented
21#26541C211yesmaximal, characteristic, complemented
22#26332C211yesmaximal, characteristic, complemented
23#26039C211yesmaximal, characteristic, complemented
24#25310C211yesmaximal, characteristic, complemented
25#25005C211yesmaximal, characteristic, complemented
26#24661C211yesmaximal, characteristic
27#23763C211yesmaximal, characteristic, complemented
28#23106C211yesmaximal, characteristic, complemented
29#23053C211yesmaximal, characteristic, complemented
30#22744C211yesmaximal, characteristic, complemented
31#21986C211yesmaximal, characteristic, complemented
32C2×#460C2211yescharacteristic
33C2×#446C2211yescharacteristic
34C2×#432C2211yescharacteristic
35#2856C2211yescharacteristic
36#2767—21no—
37#2762—21no—
38#2761—21no—
39#2761—21no—
40#2691—21no—
41#2691—21no—
42#2620—21no—
43#2581C2211yescharacteristic
44#2571C2211yescharacteristic
45#2570C2211yescharacteristic
46#2570C2211yescharacteristic
47#2566C2211yescharacteristic
48#2566C2211yescharacteristic
49#2552C2211yescharacteristic
50#2548C2211yescharacteristic
51#2528—21no—
52#2524—21no—
53#2514C2211yescharacteristic
54#2514C2211yescharacteristic
55#2512—21no—
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic
58#2503C2211yescharacteristic
59#2502C2211yescharacteristic
60#2493—21no—
61#2493—21no—
62#2490C2211yescharacteristic
63#2490C2211yescharacteristic
64#2447—21no—
65#2438—21no—
66#2420C2211yescharacteristic
67#2420C2211yescharacteristic
68#2366C2211yescharacteristic
69#2356C2211yescharacteristic
70#2355C2211yescharacteristic
71#2355C2211yescharacteristic
72#2345C2211yescharacteristic
73#2344C2211yescharacteristic
74#2343—21no—
75#2324—21no—
76C4×C22⋊Q8C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78#2285C2211yescharacteristic
79C2×#382C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2099C2211yescharacteristic
83#2096C2211yescharacteristic
84#2093C2211yescharacteristic
85#2093C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2085C2211yescharacteristic
89#2083C2211yescharacteristic
90#2083C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1985C2211yescharacteristic
125#1982C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1968C2211yescharacteristic
131#1968C2211yescharacteristic
132#1961C2211yescharacteristic
133#1961C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1947C2211yescharacteristic
142#1947C2211yescharacteristic
143#1944C2211yescharacteristic
144#1942C2211yescharacteristic
145#1940C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1934C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1917C2211yescharacteristic
167#1917C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1836C2211yescharacteristic
183#1836C2211yescharacteristic
184#1836C2211yescharacteristic
185#1836C2211yescharacteristic
186#1836C2211yescharacteristic
187#1835C2211yescharacteristic
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195#1771C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124—21no—
211C2×C22⋊Q8D411yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121—21no—
214C2×#121—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117—21no—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#460—24no—
228#446—24no—
229#432—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
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#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#395—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#391—21no—
319#391—21no—
320#391D411yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#389—21no—
341#389—21no—
342#389D411yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—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#387D411yescharacteristic
374#387D411yescharacteristic
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385D411yescharacteristic
387#385D411yescharacteristic
388#384—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#383—21no—
395#383—21no—
396#383—21no—
397#382—21no—
398#382—21no—
399#382—21no—
400#382—21no—
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381—21no—
411#381—21no—
412#381—21no—
413#381—21no—
414#380—21no—
415#380—21no—
416#380D411yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376—21no—
441C2×#95—21no—
442C2×#95—21no—
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#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2×D411yescharacteristic
482C22×Q8C2411yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2411yescharacteristic
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510#127—22no—
511#127—22no—
512#126—82no—
513#126—82no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#124—82no—
519C22⋊Q8—42no—
520C22⋊Q8—41no—
521C22⋊Q8—41no—
522#121—44no—
523#121—41no—
524#121—41no—
525#121—41no—
526#121—41no—
527#121—82no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×D4—41no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—82no—
537#117—44no—
538#117—82no—
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—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
591C2×C22⋊C4—21no—
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⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654C4⋊C8—22no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8#4114yes—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#102—22no—
665#102—22no—
666#102—41no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—41no—
681C22⋊C8—41no—
682#97—22no—
683#97—22no—
684#97—22no—
685#97—22no—
686#97—22no—
687#97—41no—
688C4×C8—22no—
689C4×C8—41no—
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#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745C24—21no—
746C24—21no—
747C24C22×D411yescharacteristic
748C2×Q8—22no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—41no—
756C2×Q8—41no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—81no—
776C2×D4—81no—
777C2×D4—81no—
778C2×D4—81no—
779C2×D4—81no—
780C2×D4—81no—
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—22no—
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—21no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
833SD16—82no—
834SD16—82no—
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×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8C2×#4112yes—
858C2×C8C2×#4112yes—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
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—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
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—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
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—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C42—22no—
948C42—22no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42C2×#4112yes—
970C422−1+412yes—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23#57512yes—
992C23C23×D411yescharacteristic
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—82no—
998D4—41no—
999D4—41no—
1000D4—41no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—84no—
1007D4—162no—
1008D4—162no—
1009D4—162no—
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—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—44no—
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—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—82no—
1095C2×C4—84no—
1096C2×C4—162no—
1097C2×C4—162no—
1098C2×C4—162no—
1099C2×C4#54712yes—
1100C2×C4#54712yes—
1101C2×C4C22×#4111yescharacteristic
1102C2×C4C2×2−1+411yescharacteristic
1103C2×C4#58511yescharacteristic
1104C2×C4#58511yescharacteristic
1105C2×C4#58511yescharacteristic
1106C2×C4#58511yescharacteristic
1107C8—22no—
1108C8—22no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22C2×#54711yescharacteristic
1137C22#348711yescharacteristic
1138C22#350011yescharacteristic
1139C22C2×#57511yescharacteristic
1140C22#358511yescharacteristic
1141C22#358511yescharacteristic
1142C22#358611yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4#352111yescharacteristic
1171C4#352411yescharacteristic
1172C4#356511yescharacteristic
1173C4#356511yescharacteristic
1174C2—42no—
1175C2—161no—
1176C2—161no—
1177C2#4523911yescharacteristic
1178C2#6125511yescharacteristic
1179C2#6126811yescharacteristic
1180C2#6189411yescharacteristic
1181C2#6194211yescharacteristic
1182C2#6257511yescharacteristic
1183C2#6257811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59333C2semidirect
3. #32445C2semidirect
4. #32445C2semidirect
5. #32405C2semidirect
6. #32404C2semidirect
7. #32070C2semidirect
8. #32054C2semidirect
9. #31954C2semidirect
10. #31941C2semidirect
11. #28807C2semidirect
12. #28026C2semidirect
13. #28019C2semidirect
15. #27743C2semidirect
16. #27733C2semidirect
17. #27344C2semidirect
18. #27329C2semidirect
19. #27174C2semidirect
20. #27159C2semidirect
21. #26541C2semidirect
22. #26332C2semidirect
23. #26039C2semidirect
24. #25310C2semidirect
25. #25005C2semidirect
27. #23763C2semidirect
28. #23106C2semidirect
29. #23053C2semidirect
30. #22744C2semidirect
31. #21986C2semidirect

Maximal subgroups

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

subgroupindex
#593332
#397362
#324452
#324052
#324042
#320702
#320542
#319542
#319412
#288072
#280262
#280192
#279822
#277432
#277332
#273442
#273292
#271742
#271592
#265412
#263322
#260392
#253102
#250052
#246612
#237632
#231062
#230532
#227442
#219862