Finite Group Databasebeta

← #6629904

Subgroups — #6629904

Order 512.

2004 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35299C211yesmaximal, characteristic, complemented
2C4×#518C211yesmaximal, characteristic, complemented
3#33154C211yesmaximal, characteristic, complemented
4#33112C211yesmaximal, characteristic, complemented
5#33105C211yesmaximal, characteristic, complemented
6#33102C211yesmaximal, characteristic, complemented
7#33084C211yesmaximal, characteristic, complemented
8#33082C211yesmaximal, characteristic, complemented
9#33080C211yesmaximal, characteristic, complemented
10#33080C211yesmaximal, characteristic, complemented
11#33076C211yesmaximal, characteristic, complemented
12#33074C211yesmaximal, characteristic, complemented
13#33034C211yesmaximal, characteristic, complemented
14#33034C211yesmaximal, characteristic, complemented
15#33018C211yesmaximal, characteristic, complemented
16#33014C211yesmaximal, characteristic
17#32956C211yesmaximal, characteristic, complemented
18#32908C211yesmaximal, characteristic
19#21623C211yesmaximal, characteristic, complemented
20#21623C211yesmaximal, characteristic, complemented
21#21591C211yesmaximal, characteristic, complemented
22#21588C211yesmaximal, characteristic, complemented
23#21510C211yesmaximal, characteristic, complemented
24#21509C211yesmaximal, characteristic, complemented
25#21459C211yesmaximal, characteristic, complemented
26#21458C211yesmaximal, characteristic
27#21122C211yesmaximal, characteristic, complemented
28#21121C211yesmaximal, characteristic, complemented
29#21118C211yesmaximal, characteristic, complemented
30#21117C211yesmaximal, characteristic, complemented
31#20785C211yesmaximal, characteristic, complemented
32C2×#518C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47#2863C2211yescharacteristic, complemented
48#2860C2211yescharacteristic, complemented
49#2857C2211yescharacteristic
50#2850C2211yescharacteristic
51#2647C2211yescharacteristic, complemented
52#2640C2211yescharacteristic, complemented
53#2625C2211yescharacteristic
54#2624C2211yescharacteristic
55#2596—21no—
56#2589—21no—
57#2578—21no—
58#2560—21no—
59#2532—21no—
60#2531—21no—
61#2478—21no—
62#2477—21no—
63#2331C2211yescharacteristic, complemented
64#2326C2211yescharacteristic, complemented
65#2324C2211yescharacteristic
66#2323C2211yescharacteristic
67#2295C2211yescharacteristic, complemented
68#2293C2211yescharacteristic, complemented
69#2275—21no—
70#2275—21no—
71#2275C2211yescharacteristic
72#2275C2211yescharacteristic
73#2275C2211yescharacteristic
74#2275C2211yescharacteristic
75#2274C2211yescharacteristic
76#2274C2211yescharacteristic
77#2273—21no—
78#2273—21no—
79C42×D4—21no—
80C42×D4—21no—
81C42×D4C2211yescharacteristic
82C42×D4C2211yescharacteristic
83C42×D4C2211yescharacteristic
84C42×D4C2211yescharacteristic
85C4×#117C2211yescharacteristic
86C4×#117C2211yescharacteristic
87C2×C4×C22⋊C4—21no—
88C2×C4×C22⋊C4—21no—
89#1988C2211yescharacteristic, complemented
90#1988C2211yescharacteristic, complemented
91#1983C2211yescharacteristic, complemented
92#1983C2211yescharacteristic, complemented
93#1949C2211yescharacteristic, complemented
94#1949C2211yescharacteristic, complemented
95#1948C2211yescharacteristic, complemented
96#1947C2211yescharacteristic, complemented
97#1928C2211yescharacteristic, complemented
98#1928C2211yescharacteristic, complemented
99#1927C2211yescharacteristic, complemented
100#1927C2211yescharacteristic, complemented
101#1927C2211yescharacteristic, complemented
102#1927C2211yescharacteristic, complemented
103#1927C2211yescharacteristic, complemented
104#1927C2211yescharacteristic, complemented
105#1926C2211yescharacteristic, complemented
106#1926C2211yescharacteristic, complemented
107#1926C2211yescharacteristic, complemented
108#1926C2211yescharacteristic, complemented
109#1926C2211yescharacteristic, complemented
110#1926C2211yescharacteristic, complemented
111#1925C2211yescharacteristic, complemented
112#1925C2211yescharacteristic, complemented
113#1921C2211yescharacteristic, complemented
114#1921C2211yescharacteristic, complemented
115#1921C2211yescharacteristic, complemented
116#1921C2211yescharacteristic, complemented
117#1920C2211yescharacteristic, complemented
118#1920C2211yescharacteristic, complemented
119#1920C2211yescharacteristic, complemented
120#1920C2211yescharacteristic, complemented
121#1920C2211yescharacteristic, complemented
122#1920C2211yescharacteristic, complemented
123#1919C2211yescharacteristic, complemented
124#1919C2211yescharacteristic, complemented
125#1919C2211yescharacteristic, complemented
126#1919C2211yescharacteristic, complemented
127#1918C2211yescharacteristic, complemented
128#1918C2211yescharacteristic, complemented
129#1879C2211yescharacteristic
130#1879C2211yescharacteristic
131#1879C2211yescharacteristic
132#1879C2211yescharacteristic
133#1879C2211yescharacteristic
134#1879C2211yescharacteristic
135#1879C2211yescharacteristic
136#1879C2211yescharacteristic
137#1877C2211yescharacteristic
138#1877C2211yescharacteristic
139#1877C2211yescharacteristic
140#1877C2211yescharacteristic
141#1877C2211yescharacteristic
142#1877C2211yescharacteristic
143#1877C2211yescharacteristic
144#1877C2211yescharacteristic
145#1875C2211yescharacteristic
146#1874C2211yescharacteristic
147#1873C2211yescharacteristic
148#1872C2211yescharacteristic
149#1864C2211yescharacteristic
150#1864C2211yescharacteristic
151#1864C2211yescharacteristic
152#1864C2211yescharacteristic
153#1864C2211yescharacteristic
154#1864C2211yescharacteristic
155#1864C2211yescharacteristic
156#1864C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1862C2211yescharacteristic
160#1862C2211yescharacteristic
161#1862C2211yescharacteristic
162#1862C2211yescharacteristic
163#1862C2211yescharacteristic
164#1862C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1839C2211yescharacteristic, complemented
170#1839C2211yescharacteristic, complemented
171#1832C2211yescharacteristic, complemented
172#1832C2211yescharacteristic, complemented
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1818C2211yescharacteristic
176#1818C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1802C2211yescharacteristic
180#1802C2211yescharacteristic
181#1797C2211yescharacteristic
182#1797C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1776C2211yescharacteristic, complemented
186#1776C2211yescharacteristic, complemented
187C4×#106C2211yescharacteristic, complemented
188C4×#106C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1768C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1745C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121C2311yescharacteristic
215#518—24no—
216#518—24no—
217#518—24no—
218#518—24no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—24no—
221C2×C4×D4—24no—
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42—21no—
253C22×C42—21no—
254C22×C42—21no—
255C22×C42—21no—
256C22×C42C2311yescharacteristic
257#485—24no—
258#482—24no—
259#476—24no—
260#476—24no—
261#463—24no—
262#463—24no—
263#450—24no—
264#447—24no—
265#442—24no—
266#440—24no—
267C4×SD16—24no—
268C4×D8—24no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#393—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#384C2311yescharacteristic
382#383—21no—
383#382C2311yescharacteristic
384#380—21no—
385#380C2311yescharacteristic
386#380C2311yescharacteristic
387C4×C4⋊C4—21no—
388C4×C4⋊C4—21no—
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4D411yescharacteristic
393C4×C4⋊C4D411yescharacteristic
394C4×C4⋊C4D411yescharacteristic
395C4×C4⋊C4D411yescharacteristic
396C4×C4⋊C4C2311yescharacteristic
397C4×C4⋊C4C2311yescharacteristic
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2311yescharacteristic
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2311yescharacteristic
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C22⋊C4—21no—
411C4×C22⋊C4—21no—
412C4×C22⋊C4—21no—
413C4×C22⋊C4—21no—
414C4×C22⋊C4—21no—
415C4×C22⋊C4—21no—
416C4×C22⋊C4—21no—
417C4×C22⋊C4—21no—
418C4×C22⋊C4—21no—
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⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4D411yescharacteristic
442C4×C22⋊C4D411yescharacteristic
443C4×C22⋊C4D411yescharacteristic
444C4×C22⋊C4D411yescharacteristic
445#376—21no—
446#376—21no—
447#376C2311yescharacteristic
448#376C2311yescharacteristic
449C2×#95—21no—
450C2×#95—21no—
451C2×#95—21no—
452C2×#95—21no—
453C43—21no—
454C43C2311yescharacteristic
455C43C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4#4114yes—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—28no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—82no—
526C23×C4—82no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552#126—82no—
553#124—22no—
554#124—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—82no—
558#121—22no—
559#121—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4#4114yes—
591C4×D4#4114yes—
592C4×D4#4114yes—
593C4×D4#4114yes—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—82no—
602#117#4114yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C22⋊C4—28no—
636C2×C22⋊C4—28no—
637C2×C22⋊C4—28no—
638C2×C22⋊C4—28no—
639C2×C22⋊C4—28no—
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⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
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×C42—82no—
694C2×C42—82no—
695C2×C42—82no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#107—22no—
713#107—22no—
714#107—22no—
715#107—22no—
716#106—22no—
717#106—22no—
718#106—22no—
719#106—22no—
720#106—22no—
721#106—22no—
722#106—22no—
723#106—22no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756#97—22no—
757#97—22no—
758C4×C8—22no—
759C4×C8—22no—
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#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—24no—
803C24—24no—
804C24—21no—
805C24—21no—
806C24—24no—
807C24—21no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24C22×D411yescharacteristic
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—24no—
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—21no—
841C2×D4—42no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4C2×#4112yes—
845C2×D4C2×#4112yes—
846C2×D4C2×#4112yes—
847C2×D4C2×#4112yes—
848C2×D4C2×#4112yes—
849C2×D4C2×#4112yes—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—816no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4C2511yescharacteristic
932SD16—44no—
933SD16—44no—
934D8—44no—
935D8—44no—
936C2×C8—21no—
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—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
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—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4C2×#4112yes—
997C4⋊C4C2×#4112yes—
998C4⋊C4C2×#4112yes—
999C4⋊C4C2×#4112yes—
1000C4⋊C4C2×#4112yes—
1001C4⋊C4C2×#4112yes—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C42—24no—
1036C42—22no—
1037C42—22no—
1038C42—24no—
1039C42—22no—
1040C42—22no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—41no—
1050C42—41no—
1051C42—41no—
1052C42—41no—
1053C42—41no—
1054C42—41no—
1055C42—42no—
1056C42—42no—
1057C42—42no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42C2×#4112yes—
1071C42C2×#4112yes—
1072C42C2×#4112yes—
1073C42C2×#4112yes—
1074C23—216no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—21no—
1086C23—21no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23—84no—
1106C23—84no—
1107C23—84no—
1108C23#52512yes—
1109C23C23×D411yescharacteristic
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—162no—
1115D4—216no—
1116D4—22no—
1117D4—22no—
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—22no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—162no—
1127D4#52914yes—
1128D4#52914yes—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—44no—
1173C2×C4—48no—
1174C2×C4—48no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
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—82no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4#52512yes—
1222C2×C4#52512yes—
1223C2×C4#52512yes—
1224C2×C4#52512yes—
1225C2×C4#52512yes—
1226C2×C4#57712yes—
1227C2×C4C22×#4111yescharacteristic
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C22×#4111yescharacteristic
1232C2×C4C22×#4111yescharacteristic
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C22—22no—
1242C22—24no—
1243C22—24no—
1244C22—22no—
1245C22—22no—
1246C22—42no—
1247C22—42no—
1248C22—41no—
1249C22—42no—
1250C22—42no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—42no—
1255C22—41no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—816no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#52511yescharacteristic
1271C22C2×#52511yescharacteristic
1272C22C2×#52511yescharacteristic
1273C22C2×#57711yescharacteristic
1274C22#358411yescharacteristic
1275C22#358511yescharacteristic
1276C22#358511yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—41no—
1284C4—42no—
1285C4—41no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—42no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4C2×#52911yescharacteristic
1304C4C2×#52911yescharacteristic
1305C4#344411yescharacteristic
1306C4#344411yescharacteristic
1307C2—42no—
1308C2—44no—
1309C2—44no—
1310C2—161no—
1311C2#3662111yescharacteristic
1312C2#6057111yescharacteristic
1313C2#6057411yescharacteristic
1314C2#6057911yescharacteristic
1315C2#6058711yescharacteristic
1316C2#6059211yescharacteristic
1317C2#6059711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35299C2semidirect
2. C4×#518C2semidirect
3. #33154C2semidirect
4. #33112C2semidirect
5. #33105C2semidirect
6. #33102C2semidirect
7. #33084C2semidirect
8. #33082C2semidirect
9. #33080C2semidirect
10. #33080C2semidirect
11. #33076C2semidirect
12. #33074C2semidirect
13. #33034C2semidirect
14. #33034C2semidirect
15. #33018C2semidirect
17. #32956C2semidirect
19. #21623C2semidirect
20. #21623C2semidirect
21. #21591C2semidirect
22. #21588C2semidirect
23. #21510C2semidirect
24. #21509C2semidirect
25. #21459C2semidirect
27. #21122C2semidirect
28. #21121C2semidirect
29. #21118C2semidirect
30. #21117C2semidirect
31. #20785C2semidirect
47. #2863C22semidirect
48. #2860C22semidirect
51. #2647C22semidirect
52. #2640C22semidirect
63. #2331C22semidirect
64. #2326C22semidirect
67. #2295C22semidirect
68. #2293C22semidirect
89. #1988C22semidirect
90. #1988C22semidirect
91. #1983C22semidirect
92. #1983C22semidirect
93. #1949C22semidirect
94. #1949C22semidirect
95. #1948C22semidirect
96. #1947C22semidirect
97. #1928C22semidirect
98. #1928C22semidirect
99. #1927C22semidirect
100. #1927C22semidirect
101. #1927C22semidirect
102. #1927C22semidirect
103. #1927C22semidirect
104. #1927C22semidirect
105. #1926C22semidirect
106. #1926C22semidirect
107. #1926C22semidirect
108. #1926C22semidirect
109. #1926C22semidirect
110. #1926C22semidirect
111. #1925C22semidirect
112. #1925C22semidirect
113. #1921C22semidirect
114. #1921C22semidirect
115. #1921C22semidirect
116. #1921C22semidirect
117. #1920C22semidirect
118. #1920C22semidirect
119. #1920C22semidirect
120. #1920C22semidirect
121. #1920C22semidirect
122. #1920C22semidirect
123. #1919C22semidirect
124. #1919C22semidirect
125. #1919C22semidirect
126. #1919C22semidirect
127. #1918C22semidirect
128. #1918C22semidirect
169. #1839C22semidirect
170. #1839C22semidirect
171. #1832C22semidirect
172. #1832C22semidirect
185. #1776C22semidirect
186. #1776C22semidirect
187. C4×#106C22semidirect
188. C4×#106C22semidirect
189. #1768C22semidirect
190. #1768C22semidirect
191. #1763C22semidirect
194. #1762C22semidirect
195. C4×#103C22semidirect
198. C4×#102C22semidirect
201. #1745C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#352992
C4×#5182
#331542
#331122
#331052
#331022
#330842
#330822
#330802
#330762
#330742
#330342
#330182
#330142
#329562
#329082
#216232
#215912
#215882
#215102
#215092
#214592
#214582
#211222
#211212
#211182
#211172
#207852