Finite Group Databasebeta

← #6403864

Subgroups — #6403864

Order 512.

1965 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3307C211yesmaximal, characteristic
2#34323C211yesmaximal, characteristic, complemented
3#34316C211yesmaximal, characteristic, complemented
4#23233C211yesmaximal, characteristic, complemented
5#23141C211yesmaximal, characteristic, complemented
6#23131C211yesmaximal, characteristic, complemented
7#23076C211yesmaximal, characteristic, complemented
8#23012C211yesmaximal, characteristic, complemented
9#22927C211yesmaximal, characteristic, complemented
10#22917C211yesmaximal, characteristic, complemented
11#22877C211yesmaximal, characteristic, complemented
12#22863C211yesmaximal, characteristic, complemented
13#22780C211yesmaximal, characteristic, complemented
14#22712C211yesmaximal, characteristic, complemented
15#22579C211yesmaximal, characteristic, complemented
16#22573C211yesmaximal, characteristic, complemented
17#22498C211yesmaximal, characteristic, complemented
18#22420C211yesmaximal, characteristic, complemented
19#22152C211yesmaximal, characteristic, complemented
20#22120C211yesmaximal, characteristic, complemented
21#22084C211yesmaximal, characteristic, complemented
22#22083C211yesmaximal, characteristic, complemented
23#22051C211yesmaximal, characteristic, complemented
24#22051C211yesmaximal, characteristic, complemented
25C4×#491C211yesmaximal, characteristic, complemented
26C4×#468C211yesmaximal, characteristic, complemented
27#21528C211yesmaximal, characteristic, complemented
28#21286C211yesmaximal, characteristic, complemented
29#21093C211yesmaximal, characteristic, complemented
30#21086C211yesmaximal, characteristic, complemented
31#20491C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#547C2211yescharacteristic
34#3307C4116yescomplemented
35C2×#491C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#461C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#435C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#417C2211yescharacteristic
50C2×#417C2211yescharacteristic
51C2×#416C2211yescharacteristic
52C2×#416C2211yescharacteristic
53C2×C4×M16C2211yescharacteristic
54C22×#97C2211yescharacteristic
55#2374—21no—
56#2374—21no—
57#2373—21no—
58#2370C2211yescharacteristic
59#2365C2211yescharacteristic
60#2363—21no—
61#2363C2211yescharacteristic
62#2362C2211yescharacteristic
63#2362C2211yescharacteristic
64#2361—21no—
65#2361C2211yescharacteristic
66#2359—21no—
67#2354C2211yescharacteristic
68#2354C2211yescharacteristic
69#2352—21no—
70#2352C2211yescharacteristic
71#2349C2211yescharacteristic
72#2346C2211yescharacteristic
73#2345—21no—
74#2345C2211yescharacteristic
75#2341C2211yescharacteristic
76#2341C2211yescharacteristic
77#2335—21no—
78#2335—21no—
79#2335—21no—
80#2334—21no—
81#2325—21no—
82#2324—21no—
83C4×C4⋊Q8C2211yescharacteristic
84C4×#125C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×#121C2211yescharacteristic
88C4×#121C2211yescharacteristic
89#2297C2211yescharacteristic
90#2297C2211yescharacteristic
91#2296C2211yescharacteristic
92#2293C2211yescharacteristic
93#2293C2211yescharacteristic
94C2×#389C2211yescharacteristic
95#2275—21no—
96#2274—21no—
97C42×D4C2211yescharacteristic
98#1992C2211yescharacteristic
99#1989C2211yescharacteristic
100#1981C2211yescharacteristic
101#1973C2211yescharacteristic
102#1973C2211yescharacteristic
103#1972C2211yescharacteristic
104#1970C2211yescharacteristic
105#1960C2211yescharacteristic
106#1949C2211yescharacteristic
107#1947C2211yescharacteristic
108#1944C2211yescharacteristic
109#1944C2211yescharacteristic
110#1943C2211yescharacteristic
111#1941C2211yescharacteristic
112#1936C2211yescharacteristic
113#1936C2211yescharacteristic
114#1936C2211yescharacteristic
115#1936C2211yescharacteristic
116#1936C2211yescharacteristic
117#1936C2211yescharacteristic
118#1935C2211yescharacteristic
119#1935C2211yescharacteristic
120#1935C2211yescharacteristic
121#1935C2211yescharacteristic
122#1935C2211yescharacteristic
123#1935C2211yescharacteristic
124#1935C2211yescharacteristic
125#1935C2211yescharacteristic
126#1934C2211yescharacteristic
127#1934C2211yescharacteristic
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1933C2211yescharacteristic
131#1933C2211yescharacteristic
132#1927C2211yescharacteristic
133#1927C2211yescharacteristic
134#1926C2211yescharacteristic
135#1925C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1921C2211yescharacteristic
139#1920C2211yescharacteristic
140#1920C2211yescharacteristic
141#1919C2211yescharacteristic
142#1919C2211yescharacteristic
143#1918C2211yescharacteristic
144#1895C2211yescharacteristic
145#1894C2211yescharacteristic
146#1893C2211yescharacteristic
147#1892C2211yescharacteristic
148#1880C2211yescharacteristic
149#1880C2211yescharacteristic
150#1879C2211yescharacteristic
151#1879C2211yescharacteristic
152#1877C2211yescharacteristic
153#1877C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1873C2211yescharacteristic
157#1872C2211yescharacteristic
158#1865C2211yescharacteristic
159#1863C2211yescharacteristic
160#1863C2211yescharacteristic
161#1863C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1852C2211yescharacteristic
168#1836C2211yescharacteristic
169#1825C2211yescharacteristic
170#1823C2211yescharacteristic
171#1809C2211yescharacteristic
172#1808C2211yescharacteristic
173#1804C2211yescharacteristic
174#1802C2211yescharacteristic
175#1788C2211yescharacteristic
176#1788C2211yescharacteristic
177#1776C2211yescharacteristic
178#1776C2211yescharacteristic
179C4×#107C2211yescharacteristic
180#1771C2211yescharacteristic
181#1771C2211yescharacteristic
182#1767C2211yescharacteristic
183#1763C2211yescharacteristic
184#1762C2211yescharacteristic
185#1762C2211yescharacteristic
186#1762C2211yescharacteristic
187C4×#103C2211yescharacteristic
188C4×#103C2211yescharacteristic
189C4×#103C2211yescharacteristic
190C4×#103C2211yescharacteristic
191C4×#103C2211yescharacteristic
192C4×#102C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C4×#97C2211yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#553—24no—
214#553C2×C418yes—
215#547—24no—
216#547C2×C418yescomplemented
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4D411yescharacteristic
238C2×C4×D4D411yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4—21no—
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#491C2×C418yescomplemented
258#485C2×C418yescomplemented
259#483C2×C418yescomplemented
260#478C2×C418yescomplemented
261#468C2×C418yescomplemented
262#465C2×C418yescomplemented
263#461C2×C418yescomplemented
264#449C2×C418yescomplemented
265#449C2×C418yescomplemented
266#442C2×C418yescomplemented
267#440—42no—
268C4×SD16—42no—
269#435—24no—
270#435C2×C418yescomplemented
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#417—42no—
283#417C2×C418yescomplemented
284#416—42no—
285#416C2×C418yescomplemented
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C4×M16—42no—
317C2×#97—42no—
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
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#388—21no—
380#388—21no—
381#387—21no—
382#387—21no—
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#387—21no—
393#387—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#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#382—21no—
412#382C2311yescharacteristic
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4D411yescharacteristic
436C4×C4⋊C4D411yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
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⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4D411yescharacteristic
462C4×C22⋊C4D411yescharacteristic
463C4×C22⋊C4D411yescharacteristic
464C4×C22⋊C4D411yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#376—21no—
468C2×#95—21no—
469C2×#95—21no—
470C43C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41C22×C414yes—
514C2×#41C22×C414yes—
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16C22×C414yes—
543C2×SD16C22×C414yes—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8C22×C414yes—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16C22×C414yes—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C22×C414yes—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8C22×C414yes—
569#126—28no—
570#125—22no—
571#125C22×C414yes—
572#123—28no—
573#123—28no—
574#123—28no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8C22×C414yes—
578C22⋊Q8C22×C414yes—
579#121—28no—
580#121—28no—
581#121—22no—
582#121—22no—
583#121C22×C414yes—
584#121C22×C414yes—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×D4—28no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—42no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—42no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—82no—
605C4×D4C22×C414yes—
606C4×D4C22×C414yes—
607C4×D4C22×C414yes—
608C4×D4#4114yes—
609#117—22no—
610#117—44no—
611#117—44no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—82no—
619#117C22×C414yes—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—82no—
649C2×C4⋊C4C22×C414yes—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42—41no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#107C22×C414yes—
737#106—41no—
738#106—41no—
739#106C22×C414yes—
740#106C22×C414yes—
741C4⋊C8—22no—
742C4⋊C8C22×C414yes—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103C22×C414yes—
752#103C22×C414yes—
753#103C22×C414yes—
754#103C22×C414yes—
755#103C22×C414yes—
756#103C22×C414yes—
757#102—22no—
758#102—22no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102C22×C414yes—
766#102C22×C414yes—
767#102C22×C414yes—
768#102C22×C414yes—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8C22×C414yes—
772C22⋊C8C22×C414yes—
773#97—22no—
774#97—22no—
775#97—22no—
776#97—41no—
777#97—41no—
778#97—41no—
779#97—41no—
780#97C22×C414yes—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
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#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823C24—21no—
824C24—21no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827#41—44no—
828#41—44no—
829#41—44no—
830#41—44no—
831#41—82no—
832#41—82no—
833#41—82no—
834#41—82no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8C23×C412yes—
846C2×Q8C23×C412yes—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4C4×D414yes—
872C2×D4C23×C412yes—
873C2×D4C23×C412yes—
874C22×C4—21no—
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—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C23×C412yes—
933C22×C4C23×C412yes—
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2×#4112yes—
947C22×C4C2×#4112yes—
948C22×C4C2511yescharacteristic
949SD16—44no—
950SD16—44no—
951D8—44no—
952M16—44no—
953M16—44no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—44no—
974C2×C8—44no—
975C2×C8C23×C412yes—
976C2×C8C23×C412yes—
977C2×C8C23×C412yes—
978C2×C8C23×C412yes—
979C2×C8H(5,𝔽2)12yes—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4C4×D414yes—
1027C4⋊C4C23×C412yes—
1028C4⋊C4C23×C412yes—
1029C4⋊C4C23×C412yes—
1030C4⋊C4C23×C412yes—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4C4×D414yes—
1064C22⋊C4C4×D414yes—
1065C42—24no—
1066C42—22no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—41no—
1080C42—41no—
1081C42—41no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42C23×C412yes—
1098C42C2×#4112yes—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—22no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23C2×C4×D412yes—
1126C23C2×C4×D412yes—
1127C23C23×D411yescharacteristic
1128Q8—22no—
1129Q8—22no—
1130Q8—22no—
1131Q8—22no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136D4—22no—
1137D4—22no—
1138D4—22no—
1139D4—22no—
1140D4—44no—
1141D4—48no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
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—22no—
1162C2×C4—22no—
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—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
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—48no—
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—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—82no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—82no—
1236C2×C4—82no—
1237C2×C4—82no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4C2×C4×D412yes—
1242C2×C4C2×C4×D412yes—
1243C2×C4C2×C4×D412yes—
1244C2×C4C2×C4×D412yes—
1245C2×C4#57512yes—
1246C2×C4#57512yes—
1247C2×C4C24×C411yescharacteristic
1248C2×C4C22×#4111yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—22no—
1255C8—22no—
1256C8—22no—
1257C8—22no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22C22×C4×D411yescharacteristic
1290C22#349611yescharacteristic
1291C22#350011yescharacteristic
1292C22C2×#57511yescharacteristic
1293C22C2×#57511yescharacteristic
1294C22#358511yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—42no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#342811yescharacteristic
1323C4C4×H(5,𝔽2)11yescharacteristic
1324C4#351311yescharacteristic
1325C4#352111yescharacteristic
1326C2—42no—
1327C2—42no—
1328C2—82no—
1329C2—82no—
1330C2#3430911yescharacteristic
1331C2C4×#57511yescharacteristic
1332C2#6017411yescharacteristic
1333C2#6229711yescharacteristic
1334C2#6230511yescharacteristic
1335C2#6257911yescharacteristic
1336C2#6258611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3307C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34323C2semidirect
3. #34316C2semidirect
4. #23233C2semidirect
5. #23141C2semidirect
6. #23131C2semidirect
7. #23076C2semidirect
8. #23012C2semidirect
9. #22927C2semidirect
10. #22917C2semidirect
11. #22877C2semidirect
12. #22863C2semidirect
13. #22780C2semidirect
14. #22712C2semidirect
15. #22579C2semidirect
16. #22573C2semidirect
17. #22498C2semidirect
18. #22420C2semidirect
19. #22152C2semidirect
20. #22120C2semidirect
21. #22084C2semidirect
22. #22083C2semidirect
23. #22051C2semidirect
24. #22051C2semidirect
25. C4×#491C2semidirect
26. C4×#468C2semidirect
27. #21528C2semidirect
28. #21286C2semidirect
29. #21093C2semidirect
30. #21086C2semidirect
31. #20491C2semidirect
34. #3307C4semidirect
216. #547C2×C4semidirect
257. #491C2×C4semidirect
258. #485C2×C4semidirect
259. #483C2×C4semidirect
260. #478C2×C4semidirect
261. #468C2×C4semidirect
262. #465C2×C4semidirect
263. #461C2×C4semidirect
264. #449C2×C4semidirect
265. #449C2×C4semidirect
266. #442C2×C4semidirect
270. #435C2×C4semidirect
283. #417C2×C4semidirect
285. #416C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33072
#343232
#343162
#232332
#231412
#231312
#230762
#230122
#229272
#229172
#228772
#228632
#227802
#227122
#225792
#225732
#224982
#224202
#221522
#221202
#220842
#220832
#220512
C4×#4912
C4×#4682
#215282
#212862
#210932
#210862
#204912