Finite Group Databasebeta

← #6480084

Subgroups — #6480084

Order 512.

1451 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35270C211yesmaximal, characteristic, complemented
2#34056C211yesmaximal, characteristic, complemented
3#33101C211yesmaximal, characteristic, complemented
4#33097C211yesmaximal, characteristic, complemented
5#33011C211yesmaximal, characteristic, complemented
6#33006C211yesmaximal, characteristic
7#29971C211yesmaximal, characteristic, complemented
8#29954C211yesmaximal, characteristic, complemented
9#29762C211yesmaximal, characteristic, complemented
10#29720C211yesmaximal, characteristic
11#29588C211yesmaximal, characteristic, complemented
12#29585C211yesmaximal, characteristic, complemented
13#29570C211yesmaximal, characteristic, complemented
14#29567C211yesmaximal, characteristic, complemented
15#29549C211yesmaximal, characteristic, complemented
16#29548C211yesmaximal, characteristic, complemented
17#29546C211yesmaximal, characteristic, complemented
18#29543C211yesmaximal, characteristic, complemented
19#29459C211yesmaximal, characteristic, complemented
20#29453C211yesmaximal, characteristic, complemented
21#29441C211yesmaximal, characteristic, complemented
22#29439C211yesmaximal, characteristic, complemented
23#29403C211yesmaximal, characteristic, complemented
24#29401C211yesmaximal, characteristic, complemented
25#29382C211yesmaximal, characteristic, complemented
26#29380C211yesmaximal, characteristic, complemented
27#22083C211yesmaximal, characteristic, complemented
28#22080C211yesmaximal, characteristic, complemented
29#22051C211yesmaximal, characteristic
30#22042C211yesmaximal, characteristic, complemented
31#20779C211yesmaximal, characteristic, complemented
32C2×C4×#41C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#452C2211yescharacteristic
36C2×#449C2211yescharacteristic
37#2857C2211yescharacteristic
38#2855C2211yescharacteristic
39#2854C2211yescharacteristic
40#2850C2211yescharacteristic
41#2647C2211yescharacteristic
42#2645C2211yescharacteristic
43#2644C2211yescharacteristic
44#2640C2211yescharacteristic
45#2532—21no—
46#2530—21no—
47#2529—21no—
48#2527—21no—
49#2510—21no—
50#2488—21no—
51#2450—21no—
52#2419—21no—
53#2331C2211yescharacteristic
54#2326C2211yescharacteristic
55#2320C2211yescharacteristic
56#2320C2211yescharacteristic
57#2320C2211yescharacteristic
58#2320C2211yescharacteristic
59#2320C2211yescharacteristic
60#2319C2211yescharacteristic
61#2319C2211yescharacteristic
62#2319C2211yescharacteristic
63#2319C2211yescharacteristic
64#2319C2211yescharacteristic
65#2318—21no—
66#2318—21no—
67#2318—21no—
68#2318—21no—
69C4×C22⋊Q8C2211yescharacteristic
70C4×#121C2211yescharacteristic
71#2298—21no—
72#2298—21no—
73#2297C2211yescharacteristic
74#2297C2211yescharacteristic
75#2296C2211yescharacteristic
76#2296C2211yescharacteristic
77#2283—21no—
78#2283—21no—
79C4×#117C2211yescharacteristic
80C2×#376C2211yescharacteristic
81#2099C2211yescharacteristic
82#2099C2211yescharacteristic
83#2095C2211yescharacteristic
84#2094C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2087C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2074C2211yescharacteristic
92#2073C2211yescharacteristic
93#2068C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2066C2211yescharacteristic
98#2066C2211yescharacteristic
99#2066C2211yescharacteristic
100#2065C2211yescharacteristic
101#2058C2211yescharacteristic
102#2057C2211yescharacteristic
103#2056C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2054C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2024C2211yescharacteristic
110#2023C2211yescharacteristic
111#2015C2211yescharacteristic
112#2012C2211yescharacteristic
113#1973C2211yescharacteristic
114#1972C2211yescharacteristic
115#1969C2211yescharacteristic
116#1968C2211yescharacteristic
117#1944C2211yescharacteristic
118#1943C2211yescharacteristic
119#1942C2211yescharacteristic
120#1941C2211yescharacteristic
121#1936C2211yescharacteristic
122#1935C2211yescharacteristic
123#1935C2211yescharacteristic
124#1935C2211yescharacteristic
125#1934C2211yescharacteristic
126#1934C2211yescharacteristic
127#1934C2211yescharacteristic
128#1933C2211yescharacteristic
129#1928C2211yescharacteristic
130#1928C2211yescharacteristic
131#1927C2211yescharacteristic
132#1927C2211yescharacteristic
133#1927C2211yescharacteristic
134#1927C2211yescharacteristic
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1875C2211yescharacteristic
166#1875C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1840C2211yescharacteristic
186#1840C2211yescharacteristic
187#1832C2211yescharacteristic
188#1832C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1817C2211yescharacteristic
192#1817C2211yescharacteristic
193#1797C2211yescharacteristic
194#1797C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199#1749C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×#123—21no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C4×#41—24no—
215C4×#41—24no—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C42—21no—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#485—24no—
234#482—24no—
235#452—24no—
236#449—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#396—21no—
299#393—21no—
300#393—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#389—21no—
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
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#386—21no—
370#386—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#384C2311yescharacteristic
386#383—21no—
387#383—21no—
388#383—21no—
389#383—21no—
390#383—21no—
391#382—21no—
392#382—21no—
393#382—21no—
394#382—21no—
395#382—21no—
396#382C2311yescharacteristic
397#381—21no—
398#381—21no—
399#381—21no—
400#381—21no—
401#381—21no—
402#381—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380—21no—
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430#376—21no—
431#376D411yescharacteristic
432#376D411yescharacteristic
433#376D411yescharacteristic
434#376D411yescharacteristic
435#376C2311yescharacteristic
436#376C2311yescharacteristic
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439C2×#95D411yescharacteristic
440C2×#95D411yescharacteristic
441C2×#95D411yescharacteristic
442C2×#95D411yescharacteristic
443C43—21no—
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
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41#4114yes—
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×Q16—22no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#124—41no—
531#124—41no—
532#123—82no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—82no—
536#121—22no—
537#121—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—82no—
553#117—28no—
554#117—22no—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—41no—
559#117#4114yes—
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⋊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×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⋊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⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C42—28no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—22no—
628C2×C42—22no—
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—41no—
639C2×C42—41no—
640C2×C42—41no—
641C2×C42—41no—
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654#107—22no—
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#106—22no—
661#106—22no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
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#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694C22⋊C8—22no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698#97—41no—
699#97—41no—
700C4×C8—41no—
701C4×C8—41no—
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#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760C24—21no—
761C24—21no—
762C24C22×D411yescharacteristic
763#41—44no—
764#41—44no—
765#41—44no—
766#41—44no—
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—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8C2×#4112yes—
782C2×D4—24no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4C2×#4112yes—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2511yescharacteristic
864Q16—82no—
865SD16—82no—
866SD16—82no—
867D8—82no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4C2×#4112yes—
938C4⋊C4C2×#4112yes—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C42—24no—
968C42—24no—
969C42—22no—
970C42—24no—
971C42—22no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—41no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23#52512yes—
1018C23C23×D411yescharacteristic
1019Q8—22no—
1020Q8—22no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—162no—
1028D4—22no—
1029D4—22no—
1030D4—48no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—84no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—48no—
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—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—84no—
1126C2×C4—84no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—162no—
1132C2×C4#52512yes—
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C22×#4111yescharacteristic
1135C2×C4#58511yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22C2×#52511yescharacteristic
1169C22#344911yescharacteristic
1170C22#344911yescharacteristic
1171C22#358411yescharacteristic
1172C22#358411yescharacteristic
1173C22#358511yescharacteristic
1174C22#358611yescharacteristic
1175C4—22no—
1176C4—42no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—42no—
1188C4—41no—
1189C4—41no—
1190C4—42no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4#349111yescharacteristic
1203C4#349111yescharacteristic
1204C4#349311yescharacteristic
1205C4#349311yescharacteristic
1206C2—42no—
1207C2—82no—
1208C2—161no—
1209C2#3511811yescharacteristic
1210C2#6055711yescharacteristic
1211C2#6056711yescharacteristic
1212C2#6098511yescharacteristic
1213C2#6098511yescharacteristic
1214C2#6098711yescharacteristic
1215C2#6098711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35270C2semidirect
2. #34056C2semidirect
3. #33101C2semidirect
4. #33097C2semidirect
5. #33011C2semidirect
7. #29971C2semidirect
8. #29954C2semidirect
9. #29762C2semidirect
11. #29588C2semidirect
12. #29585C2semidirect
13. #29570C2semidirect
14. #29567C2semidirect
15. #29549C2semidirect
16. #29548C2semidirect
17. #29546C2semidirect
18. #29543C2semidirect
19. #29459C2semidirect
20. #29453C2semidirect
21. #29441C2semidirect
22. #29439C2semidirect
23. #29403C2semidirect
24. #29401C2semidirect
25. #29382C2semidirect
26. #29380C2semidirect
27. #22083C2semidirect
28. #22080C2semidirect
30. #22042C2semidirect
31. #20779C2semidirect

Maximal subgroups

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

subgroupindex
#352702
#340562
#331012
#330972
#330112
#330062
#299712
#299542
#297622
#297202
#295882
#295852
#295702
#295672
#295492
#295482
#295462
#295432
#294592
#294532
#294412
#294392
#294032
#294012
#293822
#293802
#220832
#220802
#220512
#220422
#207792