Finite Group Databasebeta

← #6515613

Subgroups — #6515613

Order 512.

1703 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35218C211yesmaximal, characteristic, complemented
2#34493C211yesmaximal, characteristic, complemented
3#29422C211yesmaximal, characteristic, complemented
4#29421C211yesmaximal, characteristic, complemented
5#28126C211yesmaximal, characteristic, complemented
6#28126C211yesmaximal, characteristic, complemented
7#27640C211yesmaximal, characteristic, complemented
8#27637C211yesmaximal, characteristic, complemented
9#27594C211yesmaximal, characteristic, complemented
10#27591C211yesmaximal, characteristic, complemented
11#27523C211yesmaximal, characteristic, complemented
12#27518C211yesmaximal, characteristic, complemented
13#27039C211yesmaximal, characteristic, complemented
14#27038C211yesmaximal, characteristic, complemented
15#26549C211yesmaximal, characteristic, complemented
16#26548C211yesmaximal, characteristic, complemented
17#26538C211yesmaximal, characteristic, complemented
18#26311C211yesmaximal, characteristic, complemented
19#26098C211yesmaximal, characteristic, complemented
20#25891C211yesmaximal, characteristic, complemented
21#25330C211yesmaximal, characteristic, complemented
22#25023C211yesmaximal, characteristic, complemented
23#24897C211yesmaximal, characteristic, complemented
24#24893C211yesmaximal, characteristic, complemented
25#24688C211yesmaximal, characteristic, complemented
26#24248C211yesmaximal, characteristic
27#22226C211yesmaximal, characteristic, complemented
28#22114C211yesmaximal, characteristic, complemented
29#22011C211yesmaximal, characteristic, complemented
30C4×#459C211yesmaximal, characteristic, complemented
31#21122C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#490C2211yescharacteristic
34C2×#482C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic, complemented
42C2×C4×D8C2211yescharacteristic, complemented
43#2853—21no—
44#2852—21no—
45#2652—21no—
46#2648—21no—
47#2597—21no—
48#2595—21no—
49#2573—21no—
50#2570C2211yescharacteristic, complemented
51#2566C2211yescharacteristic, complemented
52#2562C2211yescharacteristic
53#2554—21no—
54#2535C2211yescharacteristic
55#2496C2211yescharacteristic, complemented
56#2495C2211yescharacteristic, complemented
57#2422C2211yescharacteristic, complemented
58#2420C2211yescharacteristic, complemented
59#2375—21no—
60#2375—21no—
61#2366C2211yescharacteristic
62#2363—21no—
63#2363C2211yescharacteristic
64#2363C2211yescharacteristic
65#2354C2211yescharacteristic
66#2354C2211yescharacteristic
67D4×C22⋊C4—21no—
68D4×C22⋊C4C2211yescharacteristic
69D4×C22⋊C4C2211yescharacteristic
70#2324—21no—
71#2324C2211yescharacteristic
72#2324C2211yescharacteristic
73#2324C2211yescharacteristic, complemented
74#2324C2211yescharacteristic, complemented
75#2321—21no—
76#2321—21no—
77#2314C2211yescharacteristic, complemented
78#2314C2211yescharacteristic, complemented
79#2309—21no—
80#2309C2211yescharacteristic
81#2309C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic, complemented
84#2293C2211yescharacteristic
85#2293C2211yescharacteristic
86C42×D4C2211yescharacteristic, complemented
87#2094C2211yescharacteristic, complemented
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic, complemented
91#2077C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2075C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2075C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic, complemented
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic, complemented
108#2054C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic, complemented
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic, complemented
117#1999C2211yescharacteristic
118#1999C2211yescharacteristic
119#1992C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1982C2211yescharacteristic
122#1961C2211yescharacteristic
123#1955C2211yescharacteristic
124#1955C2211yescharacteristic
125#1949C2211yescharacteristic, complemented
126#1949C2211yescharacteristic, complemented
127#1949C2211yescharacteristic, complemented
128#1948C2211yescharacteristic, complemented
129#1947C2211yescharacteristic, complemented
130#1947C2211yescharacteristic, complemented
131#1942C2211yescharacteristic, complemented
132#1941C2211yescharacteristic, complemented
133#1940C2211yescharacteristic, complemented
134#1940C2211yescharacteristic, complemented
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1926C2211yescharacteristic, complemented
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic, complemented
145#1925C2211yescharacteristic, complemented
146#1925C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1923C2211yescharacteristic, complemented
152#1923C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic, complemented
162#1879C2211yescharacteristic, complemented
163#1879C2211yescharacteristic, complemented
164#1879C2211yescharacteristic, complemented
165#1864C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1864C2211yescharacteristic, complemented
168#1862C2211yescharacteristic, complemented
169#1862C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1862C2211yescharacteristic, complemented
172#1862C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1854C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1847C2211yescharacteristic, complemented
178#1825C2211yescharacteristic, complemented
179#1825C2211yescharacteristic, complemented
180#1818C2211yescharacteristic, complemented
181#1818C2211yescharacteristic, complemented
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic, complemented
184#1804C2211yescharacteristic, complemented
185#1802C2211yescharacteristic, complemented
186#1802C2211yescharacteristic, complemented
187#1802C2211yescharacteristic, complemented
188#1798C2211yescharacteristic, complemented
189#1798C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×C4⋊C8C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1745C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209D42—24no—
210D42—24no—
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×#121—21no—
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117—21no—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C42—21no—
243#490—24no—
244#482—42no—
245#482—42no—
246#478—24no—
247#459—24no—
248#447—42no—
249#447—42no—
250#442—24no—
251C4×D8—42no—
252C4×D8—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#392—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390D411yescharacteristic
341#390D411yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389D411yescharacteristic
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
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#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#388D411yescharacteristic
382#388D411yescharacteristic
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#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#383—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433#379—21no—
434#379—21no—
435#379—21no—
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×D4—28no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—82no—
514C22×D4—82no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547#127—22no—
548#127#4114yes—
549#126—82no—
550#125—22no—
551#125—22no—
552#123—82no—
553#121—28no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—22no—
559#121—22no—
560#121—41no—
561#121—41no—
562#120—28no—
563#120—28no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—82no—
582C4×D4—82no—
583C4×D4—82no—
584C4×D4#4114yes—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—41no—
593#117—82no—
594#117—82no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—82no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—82no—
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#106—22no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—22no—
756#97—22no—
757C4×C8—41no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—24no—
794C24—24no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—22no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—82no—
858C2×D4—82no—
859C2×D4—82no—
860C2×D4—816no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4C2×#4112yes—
870C2×D4C2×#4112yes—
871C2×D4C2×#4112yes—
872C2×D4H(5,𝔽2)12yes—
873C22×C4—21no—
874C22×C4—24no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2511yescharacteristic
934D8—44no—
935D8—44no—
936D8—44no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4C2×#4112yes—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C42—22no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42C2×#4112yes—
1081C42C2×#4112yes—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—162no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23—162no—
1138C23C23×D411yescharacteristic
1139D4—22no—
1140D4—22no—
1141D4—22no—
1142D4—22no—
1143D4—22no—
1144D4—22no—
1145D4—22no—
1146D4—22no—
1147D4—48no—
1148D4—44no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—84no—
1158D4—84no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162D4—162no—
1163D4—162no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—48no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4#52512yes—
1250C2×C4#52512yes—
1251C2×C4#57612yes—
1252C2×C4C22×#4111yescharacteristic
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4#58511yescharacteristic
1256C2×C4#58511yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C22—42no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—168no—
1309C22—168no—
1310C22C2×#52511yescharacteristic
1311C22#348511yescharacteristic
1312C22#348811yescharacteristic
1313C22C2×#57611yescharacteristic
1314C22#358411yescharacteristic
1315C22#358511yescharacteristic
1316C22#358511yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—42no—
1328C4—41no—
1329C4—41no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4#349411yescharacteristic
1342C4#351011yescharacteristic
1343C4#351311yescharacteristic
1344C4#352111yescharacteristic
1345C2—81no—
1346C2—81no—
1347C2—82no—
1348C2—82no—
1349C2—82no—
1350C2—82no—
1351C2#3552311yescharacteristic
1352C2#6056411yescharacteristic
1353C2#6057011yescharacteristic
1354C2#6180211yescharacteristic
1355C2#6181311yescharacteristic
1356C2#6200711yescharacteristic
1357C2#6202411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24248C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35218C2semidirect
2. #34493C2semidirect
3. #29422C2semidirect
4. #29421C2semidirect
5. #28126C2semidirect
6. #28126C2semidirect
7. #27640C2semidirect
8. #27637C2semidirect
9. #27594C2semidirect
10. #27591C2semidirect
11. #27523C2semidirect
12. #27518C2semidirect
13. #27039C2semidirect
14. #27038C2semidirect
15. #26549C2semidirect
16. #26548C2semidirect
17. #26538C2semidirect
18. #26311C2semidirect
19. #26098C2semidirect
20. #25891C2semidirect
21. #25330C2semidirect
22. #25023C2semidirect
23. #24897C2semidirect
24. #24893C2semidirect
25. #24688C2semidirect
27. #22226C2semidirect
28. #22114C2semidirect
29. #22011C2semidirect
30. C4×#459C2semidirect
31. #21122C2semidirect
34. C2×#482C22semidirect
35. C2×#482C22semidirect
41. C2×C4×D8C22semidirect
42. C2×C4×D8C22semidirect
50. #2570C22semidirect
51. #2566C22semidirect
55. #2496C22semidirect
56. #2495C22semidirect
57. #2422C22semidirect
58. #2420C22semidirect
73. #2324C22semidirect
74. #2324C22semidirect
77. #2314C22semidirect
78. #2314C22semidirect
83. C4×#125C22semidirect
86. C42×D4C22semidirect
87. #2094C22semidirect
90. #2092C22semidirect
91. #2077C22semidirect
92. #2076C22semidirect
93. #2076C22semidirect
94. #2075C22semidirect
95. #2075C22semidirect
96. #2075C22semidirect
98. #2073C22semidirect
100. #2071C22semidirect
102. #2067C22semidirect
104. #2065C22semidirect
107. #2054C22semidirect
108. #2054C22semidirect
113. #2034C22semidirect
116. #2033C22semidirect
119. #1992C22semidirect
120. #1989C22semidirect
125. #1949C22semidirect
126. #1949C22semidirect
127. #1949C22semidirect
128. #1948C22semidirect
129. #1947C22semidirect
130. #1947C22semidirect
131. #1942C22semidirect
132. #1941C22semidirect
133. #1940C22semidirect
134. #1940C22semidirect
139. #1926C22semidirect
140. #1926C22semidirect
141. #1926C22semidirect
144. #1925C22semidirect
145. #1925C22semidirect
146. #1925C22semidirect
147. #1925C22semidirect
148. #1925C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1923C22semidirect
152. #1923C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1920C22semidirect
156. #1920C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
161. #1879C22semidirect
162. #1879C22semidirect
163. #1879C22semidirect
164. #1879C22semidirect
165. #1864C22semidirect
166. #1864C22semidirect
167. #1864C22semidirect
168. #1862C22semidirect
169. #1862C22semidirect
170. #1862C22semidirect
171. #1862C22semidirect
172. #1862C22semidirect
173. #1854C22semidirect
174. #1854C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
177. #1847C22semidirect
178. #1825C22semidirect
179. #1825C22semidirect
180. #1818C22semidirect
181. #1818C22semidirect
183. #1804C22semidirect
184. #1804C22semidirect
185. #1802C22semidirect
186. #1802C22semidirect
187. #1802C22semidirect
188. #1798C22semidirect
189. #1798C22semidirect
196. #1776C22semidirect
197. C4×C4⋊C8C22semidirect
199. #1762C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#352182
#344932
#294222
#294212
#281262
#276402
#276372
#275942
#275912
#275232
#275182
#270392
#270382
#265492
#265482
#265382
#263112
#260982
#258912
#253302
#250232
#248972
#248932
#246882
#242482
#222262
#221142
#220112
C4×#4592
#211222