Finite Group Databasebeta

← #6400208

Subgroups — #6400208

Order 512.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3308C211yesmaximal, characteristic
2#34472C211yesmaximal, characteristic, complemented
3#34298C211yesmaximal, characteristic, complemented
4#23230C211yesmaximal, characteristic, complemented
5#23104C211yesmaximal, characteristic, complemented
6#23069C211yesmaximal, characteristic, complemented
7#23035C211yesmaximal, characteristic, complemented
8#23029C211yesmaximal, characteristic, complemented
9#22932C211yesmaximal, characteristic, complemented
10#22916C211yesmaximal, characteristic, complemented
11#22875C211yesmaximal, characteristic, complemented
12#22860C211yesmaximal, characteristic, complemented
13#22819C211yesmaximal, characteristic, complemented
14#22659C211yesmaximal, characteristic, complemented
15#22578C211yesmaximal, characteristic, complemented
16#22563C211yesmaximal, characteristic, complemented
17#22485C211yesmaximal, characteristic, complemented
18#22416C211yesmaximal, characteristic, complemented
19#22233C211yesmaximal, characteristic, complemented
20#22200C211yesmaximal, characteristic, complemented
21#22181C211yesmaximal, characteristic, complemented
22#22125C211yesmaximal, characteristic, complemented
23#22053C211yesmaximal, characteristic, complemented
24#22047C211yesmaximal, characteristic, complemented
25#21585C211yesmaximal, characteristic, complemented
26#21578C211yesmaximal, characteristic, complemented
27#21510C211yesmaximal, characteristic, complemented
28#21125C211yesmaximal, characteristic, complemented
29#21062C211yesmaximal, characteristic, complemented
30C2×#1927C211yesmaximal, characteristic, complemented
31#20560C211yesmaximal, characteristic, complemented
32C2×#548C2211yescharacteristic
33C2×#547C2211yescharacteristic
34#3308C4116yescomplemented
35C2×#489C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#435C2211yescharacteristic
48C2×C8×D4C2211yescharacteristic
49C2×#428C2211yescharacteristic
50C22×#106C2211yescharacteristic
51C2×#417C2211yescharacteristic
52C2×#416C2211yescharacteristic
53C22×#103C2211yescharacteristic
54C22×#103C2211yescharacteristic
55#2379—21no—
56#2378—21no—
57#2374—21no—
58#2369C2211yescharacteristic
59#2368—21no—
60#2367C2211yescharacteristic
61#2364—21no—
62#2363C2211yescharacteristic
63#2361C2211yescharacteristic
64#2361C2211yescharacteristic
65#2360C2211yescharacteristic
66#2359—21no—
67#2357C2211yescharacteristic
68#2355C2211yescharacteristic
69#2352C2211yescharacteristic
70#2349—21no—
71D4×C4⋊C4C2211yescharacteristic
72#2345C2211yescharacteristic
73#2344C2211yescharacteristic
74Q8×C22⋊C4C2211yescharacteristic
75#2339—21no—
76#2339C2211yescharacteristic
77#2337—21no—
78#2335—21no—
79#2332—21no—
80#2331C2211yescharacteristic
81#2329—21no—
82#2326C2211yescharacteristic
83#2325—21no—
84#2324C2211yescharacteristic
85#2323C2211yescharacteristic
86#2320C2211yescharacteristic
87#2318—21no—
88#2311C2211yescharacteristic
89C4×#123—21no—
90C4×#121C2211yescharacteristic
91C4×#121C2211yescharacteristic
92#2297—21no—
93C2×#391C2211yescharacteristic
94#2290C2211yescharacteristic
95#2275C2211yescharacteristic
96#2274C2211yescharacteristic
97C2×C4×C4⋊C4C2211yescharacteristic
98#1990C2211yescharacteristic
99#1988C2211yescharacteristic
100#1983C2211yescharacteristic
101#1973C2211yescharacteristic
102#1973C2211yescharacteristic
103#1972C2211yescharacteristic
104#1968C2211yescharacteristic
105#1958C2211yescharacteristic
106#1949C2211yescharacteristic
107#1948C2211yescharacteristic
108#1943C2211yescharacteristic
109#1942C2211yescharacteristic
110#1935C2211yescharacteristic
111#1935C2211yescharacteristic
112#1935C2211yescharacteristic
113#1935C2211yescharacteristic
114#1934C2211yescharacteristic
115#1933C2211yescharacteristic
116#1928C2211yescharacteristic
117#1928C2211yescharacteristic
118#1928C2211yescharacteristic
119#1928C2211yescharacteristic
120#1927C2211yescharacteristic
121#1927C2211yescharacteristic
122#1927C2211yescharacteristic
123#1927C2211yescharacteristic
124#1927C2211yescharacteristic
125#1927C2211yescharacteristic
126#1927C2211yescharacteristic
127#1927C2211yescharacteristic
128#1927C2211yescharacteristic
129#1926C2211yescharacteristic
130#1926C2211yescharacteristic
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1925C2211yescharacteristic
134#1925C2211yescharacteristic
135#1925C2211yescharacteristic
136#1921C2211yescharacteristic
137#1921C2211yescharacteristic
138#1918C2211yescharacteristic
139#1918C2211yescharacteristic
140#1918C2211yescharacteristic
141#1918C2211yescharacteristic
142#1893C2211yescharacteristic
143#1893C2211yescharacteristic
144#1893C2211yescharacteristic
145#1892C2211yescharacteristic
146#1880C2211yescharacteristic
147#1879C2211yescharacteristic
148#1879C2211yescharacteristic
149#1877C2211yescharacteristic
150#1877C2211yescharacteristic
151#1877C2211yescharacteristic
152#1874C2211yescharacteristic
153#1874C2211yescharacteristic
154#1874C2211yescharacteristic
155#1873C2211yescharacteristic
156#1865C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1863C2211yescharacteristic
160#1863C2211yescharacteristic
161#1862C2211yescharacteristic
162#1862C2211yescharacteristic
163#1862C2211yescharacteristic
164#1854C2211yescharacteristic
165#1853C2211yescharacteristic
166#1853C2211yescharacteristic
167#1852C2211yescharacteristic
168#1847C2211yescharacteristic
169#1823C2211yescharacteristic
170#1823C2211yescharacteristic
171#1809C2211yescharacteristic
172#1808C2211yescharacteristic
173#1805C2211yescharacteristic
174#1802C2211yescharacteristic
175#1788C2211yescharacteristic
176#1787C2211yescharacteristic
177#1776C2211yescharacteristic
178#1776C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181C4×#107C2211yescharacteristic
182#1771C2211yescharacteristic
183#1770C2211yescharacteristic
184#1768C2211yescharacteristic
185#1763C2211yescharacteristic
186#1763C2211yescharacteristic
187#1762C2211yescharacteristic
188#1762C2211yescharacteristic
189C4×#103C2211yescharacteristic
190C4×#103C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193#1753C2211yescharacteristic
194#1752C2211yescharacteristic
195#1752C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1750C2211yescharacteristic
198#1749C2211yescharacteristic
199#1746C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C2×#336C2211yescharacteristic
204C22×#41—21no—
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#548—24no—
215#548C2×C418yescomplemented
216#547—24no—
217#547C2×C418yescomplemented
218C2×C4⋊Q8C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
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×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C42—21no—
254C22×C42C2311yescharacteristic
255#489C2×C418yescomplemented
256#484C2×C418yescomplemented
257#480C2×C418yescomplemented
258#477C2×C418yescomplemented
259#468C2×C418yescomplemented
260#466C2×C418yescomplemented
261#463C2×C418yescomplemented
262#449C2×C418yescomplemented
263#448C2×C418yescomplemented
264#442—42no—
265#440C2×C418yescomplemented
266C4×SD16—42no—
267#435C2×C418yescomplemented
268C8×D4—24no—
269#428—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106—42no—
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#417C2×C418yescomplemented
287#416—42no—
288C2×#103—42no—
289C2×#103C2×C418yescomplemented
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390—21no—
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
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#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#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388D411yescharacteristic
374#388D411yescharacteristic
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387D411yescharacteristic
389#387D411yescharacteristic
390#386—21no—
391#386—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#386D411yescharacteristic
402#386D411yescharacteristic
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385D411yescharacteristic
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#382—21no—
417#382—21no—
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
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×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⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376C2311yescharacteristic
466C2×#95—21no—
467C2×#95—21no—
468C2×#95—21no—
469C2×#95—21no—
470C2×#95—21no—
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#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503C2×#41—28no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—82no—
510C2×#41—82no—
511C2×#41C22×C414yes—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—22no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8C22×C414yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16C22×C414yes—
550C2×SD16C22×C414yes—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8C22×C414yes—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16C22×C414yes—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8C22×C414yes—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8C22×C414yes—
576#124—28no—
577#124—22no—
578#124C22×C414yes—
579#123—28no—
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—28no—
583C22⋊Q8—28no—
584C22⋊Q8C22×C414yes—
585#121—28no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121C22×C414yes—
590#121C22×C414yes—
591#121C22×C414yes—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8C22×C414yes—
598C4×D4—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—82no—
609C4×D4—82no—
610C4×D4—82no—
611C4×D4—82no—
612C4×D4—82no—
613C4×D4C22×C414yes—
614C4×D4C22×C414yes—
615C4×D4#4114yes—
616#117—22no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—82no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
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—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4C22×C414yes—
648C2×C4⋊C4C22×C414yes—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C42—21no—
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—41no—
715C2×C42—41no—
716C2×C42—82no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107C22×C414yes—
729#107C22×C414yes—
730#107C22×C414yes—
731#106—22no—
732#106—22no—
733#106—22no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8C22×C414yes—
739#103—22no—
740#103—22no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103C22×C414yes—
748#103C22×C414yes—
749#103C22×C414yes—
750#103C22×C414yes—
751#103C22×C414yes—
752#103C22×C414yes—
753#102—22no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102C22×C414yes—
762#102C22×C414yes—
763#102C22×C414yes—
764#102C22×C414yes—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8C22×C414yes—
768C22⋊C8C22×C414yes—
769#97—41no—
770#97—41no—
771#97—41no—
772#97—41no—
773#97C22×C414yes—
774C4×C8—22no—
775C4×C8—41no—
776C4×C8—41no—
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#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#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
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—82no—
830#41—82no—
831#41—816no—
832C2×Q8—24no—
833C2×Q8—24no—
834C2×Q8—21no—
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—44no—
845C2×Q8—44no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—82no—
851C2×Q8—82no—
852C2×Q8C23×C412yes—
853C2×Q8C23×C412yes—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4C4×D414yes—
879C2×D4C23×C412yes—
880C2×D4C23×C412yes—
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—24no—
890C22×C4—22no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
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×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4C23×C412yes—
946C22×C4C23×C412yes—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C2×#4112yes—
960C22×C4C2×#4112yes—
961C22×C4C2511yescharacteristic
962SD16—44no—
963SD16—44no—
964D8—44no—
965M16—44no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—44no—
987C2×C8—82no—
988C2×C8—82no—
989C2×C8C23×C412yes—
990C2×C8C23×C412yes—
991C2×C8C23×C412yes—
992C2×C8C23×C412yes—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
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—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4C4×D414yes—
1035C4⋊C4C23×C412yes—
1036C4⋊C4C23×C412yes—
1037C4⋊C4C23×C412yes—
1038C4⋊C4C23×C412yes—
1039C4⋊C4H(5,𝔽2)12yes—
1040C22⋊C4—24no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4C4×D414yes—
1071C22⋊C4C4×D414yes—
1072C42—24no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—41no—
1082C42—41no—
1083C42—42no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42C23×C412yes—
1099C42C2×#4112yes—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23C2×C4×D412yes—
1125C23C2×C4×D412yes—
1126C23#57612yes—
1127C23#57712yes—
1128C23C23×D411yescharacteristic
1129Q8—22no—
1130Q8—22no—
1131Q8—22no—
1132Q8—22no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—84no—
1138Q8—84no—
1139D4—28no—
1140D4—22no—
1141D4—22no—
1142D4—22no—
1143D4—22no—
1144D4—48no—
1145D4—48no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—84no—
1151D4—84no—
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—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
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—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
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—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—44no—
1200C2×C4—41no—
1201C2×C4—48no—
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—84no—
1237C2×C4—84no—
1238C2×C4—82no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4C2×C4×D412yes—
1249C2×C4C2×C4×D412yes—
1250C2×C4C2×C4×D412yes—
1251C2×C4C2×C4×D412yes—
1252C2×C4C24×C411yescharacteristic
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4#58511yescharacteristic
1256C2×C4#58511yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—22no—
1259C8—22no—
1260C8—22no—
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22#294614yes—
1294C22C22×C4×D411yescharacteristic
1295C22#348511yescharacteristic
1296C22#348811yescharacteristic
1297C22C2×#57611yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358611yescharacteristic
1300C22#358611yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4#342811yescharacteristic
1328C4C4×H(5,𝔽2)11yescharacteristic
1329C4#351411yescharacteristic
1330C4#352111yescharacteristic
1331C2—24no—
1332C2—42no—
1333C2—82no—
1334C2—82no—
1335C2#3429211yescharacteristic
1336C2C2×#294611yescharacteristic
1337C2#6017511yescharacteristic
1338C2#6174511yescharacteristic
1339C2#6175911yescharacteristic
1340C2#6200811yescharacteristic
1341C2#6202211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3308C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34472C2semidirect
3. #34298C2semidirect
4. #23230C2semidirect
5. #23104C2semidirect
6. #23069C2semidirect
7. #23035C2semidirect
8. #23029C2semidirect
9. #22932C2semidirect
10. #22916C2semidirect
11. #22875C2semidirect
12. #22860C2semidirect
13. #22819C2semidirect
14. #22659C2semidirect
15. #22578C2semidirect
16. #22563C2semidirect
17. #22485C2semidirect
18. #22416C2semidirect
19. #22233C2semidirect
20. #22200C2semidirect
21. #22181C2semidirect
22. #22125C2semidirect
23. #22053C2semidirect
24. #22047C2semidirect
25. #21585C2semidirect
26. #21578C2semidirect
27. #21510C2semidirect
28. #21125C2semidirect
29. #21062C2semidirect
30. C2×#1927C2semidirect
31. #20560C2semidirect
34. #3308C4semidirect
215. #548C2×C4semidirect
217. #547C2×C4semidirect
255. #489C2×C4semidirect
256. #484C2×C4semidirect
257. #480C2×C4semidirect
258. #477C2×C4semidirect
259. #468C2×C4semidirect
260. #466C2×C4semidirect
261. #463C2×C4semidirect
262. #449C2×C4semidirect
263. #448C2×C4semidirect
265. #440C2×C4semidirect
267. #435C2×C4semidirect
286. #417C2×C4semidirect
289. C2×#103C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33082
#344722
#342982
#232302
#231042
#230692
#230352
#230292
#229322
#229162
#228752
#228602
#228192
#226592
#225782
#225632
#224852
#224162
#222332
#222002
#221812
#221252
#220532
#220472
#215852
#215782
#215102
#211252
#210622
C2×#19272
#205602