Finite Group Databasebeta

← #6398878

Subgroups — #6398878

Order 512.

2058 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×#3300C211yesmaximal, characteristic
2#34465C211yesmaximal, characteristic, complemented
3#34294C211yesmaximal, characteristic
4#23225C211yesmaximal, characteristic, complemented
5#23028C211yesmaximal, characteristic, complemented
6#23022C211yesmaximal, characteristic, complemented
7#23013C211yesmaximal, characteristic, complemented
8#22976C211yesmaximal, characteristic, complemented
9#22942C211yesmaximal, characteristic, complemented
10#22938C211yesmaximal, characteristic, complemented
11#22867C211yesmaximal, characteristic, complemented
12#22859C211yesmaximal, characteristic, complemented
13#22674C211yesmaximal, characteristic, complemented
14D4×#106C211yesmaximal, characteristic, complemented
15#22571C211yesmaximal, characteristic, complemented
16#22565C211yesmaximal, characteristic, complemented
17#22491C211yesmaximal, characteristic, complemented
18#22421C211yesmaximal, characteristic
19#22227C211yesmaximal, characteristic, complemented
20#22192C211yesmaximal, characteristic, complemented
21#22180C211yesmaximal, characteristic, complemented
22#22159C211yesmaximal, characteristic, complemented
23#22092C211yesmaximal, characteristic, complemented
24#22081C211yesmaximal, characteristic, complemented
25#21622C211yesmaximal, characteristic, complemented
26#21461C211yesmaximal, characteristic, complemented
27#21455C211yesmaximal, characteristic, complemented
28#21132C211yesmaximal, characteristic, complemented
29#20882C211yesmaximal, characteristic, complemented
30C2×#1865C211yesmaximal, characteristic, complemented
31#20560C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#3300C4116yescomplemented
37C2×#488C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#480C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#451C2211yescharacteristic
46C2×#441C2211yescharacteristic
47C2×#441C2211yescharacteristic
48C2×#441C2211yescharacteristic
49C2×C4×Q16C2211yescharacteristic
50C2×C4×SD16C2211yescharacteristic
51C2×#435C2211yescharacteristic
52C2×C8×D4C2211yescharacteristic
53C22×#106C2211yescharacteristic
54C22×#106C2211yescharacteristic
55C2×#417C2211yescharacteristic
56C2×#416C2211yescharacteristic
57C22×#103C2211yescharacteristic
58C22×#103C2211yescharacteristic
59#2383—21no—
60#2382—21no—
61#2370C2211yescharacteristic
62#2367—21no—
63#2367C2211yescharacteristic
64#2361—21no—
65#2361C2211yescharacteristic
66#2360—21no—
67#2360C2211yescharacteristic
68#2360C2211yescharacteristic
69#2360C2211yescharacteristic
70#2359—21no—
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C4⋊C4C2211yescharacteristic
73D4×C4⋊C4—21no—
74D4×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2346C2211yescharacteristic
77#2344C2211yescharacteristic
78#2343—21no—
79#2341C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81#2334—21no—
82#2330—21no—
83#2330C2211yescharacteristic
84#2326—21no—
85#2326C2211yescharacteristic
86#2323—21no—
87#2323C2211yescharacteristic
88#2323C2211yescharacteristic
89#2322—21no—
90#2320C2211yescharacteristic
91#2317—21no—
92#2317C2211yescharacteristic
93C4×C22⋊Q8C2211yescharacteristic
94C4×#121—21no—
95C4×#121C2211yescharacteristic
96C2×#389C2211yescharacteristic
97#2290—21no—
98#2290C2211yescharacteristic
99#2276C2211yescharacteristic
100#1992C2211yescharacteristic
101#1989C2211yescharacteristic
102#1983C2211yescharacteristic
103#1971C2211yescharacteristic
104#1968C2211yescharacteristic
105#1959C2211yescharacteristic
106#1948C2211yescharacteristic
107#1948C2211yescharacteristic
108#1943C2211yescharacteristic
109#1943C2211yescharacteristic
110#1943C2211yescharacteristic
111#1941C2211yescharacteristic
112#1936C2211yescharacteristic
113#1936C2211yescharacteristic
114#1936C2211yescharacteristic
115#1935C2211yescharacteristic
116#1933C2211yescharacteristic
117#1933C2211yescharacteristic
118#1927C2211yescharacteristic
119#1927C2211yescharacteristic
120#1927C2211yescharacteristic
121#1927C2211yescharacteristic
122#1927C2211yescharacteristic
123#1926C2211yescharacteristic
124#1926C2211yescharacteristic
125#1926C2211yescharacteristic
126#1921C2211yescharacteristic
127#1921C2211yescharacteristic
128#1921C2211yescharacteristic
129#1921C2211yescharacteristic
130#1920C2211yescharacteristic
131#1919C2211yescharacteristic
132#1894C2211yescharacteristic
133#1894C2211yescharacteristic
134#1893C2211yescharacteristic
135#1892C2211yescharacteristic
136#1880C2211yescharacteristic
137#1878C2211yescharacteristic
138#1878C2211yescharacteristic
139#1878C2211yescharacteristic
140#1878C2211yescharacteristic
141#1877C2211yescharacteristic
142#1874C2211yescharacteristic
143#1872C2211yescharacteristic
144#1872C2211yescharacteristic
145#1872C2211yescharacteristic
146#1865C2211yescharacteristic
147#1865C2211yescharacteristic
148#1865C2211yescharacteristic
149#1865C2211yescharacteristic
150#1865C2211yescharacteristic
151#1865C2211yescharacteristic
152#1865C2211yescharacteristic
153#1865C2211yescharacteristic
154#1865C2211yescharacteristic
155#1865C2211yescharacteristic
156#1865C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1853C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1844C2211yescharacteristic
171#1825C2211yescharacteristic
172#1823C2211yescharacteristic
173#1807C2211yescharacteristic
174#1807C2211yescharacteristic
175#1803C2211yescharacteristic
176#1803C2211yescharacteristic
177#1788C2211yescharacteristic
178#1787C2211yescharacteristic
179#1776C2211yescharacteristic
180C4×#106C2211yescharacteristic
181C4×#106C2211yescharacteristic
182#1771C2211yescharacteristic
183#1770C2211yescharacteristic
184#1768C2211yescharacteristic
185#1763C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1762C2211yescharacteristic
191C4×#103C2211yescharacteristic
192C4×#103C2211yescharacteristic
193#1753C2211yescharacteristic
194#1752C2211yescharacteristic
195#1752C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1750C2211yescharacteristic
198#1749C2211yescharacteristic
199#1746C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C2×#336C2211yescharacteristic
204C22×#41C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#552—24no—
214#552C2×C418yescomplemented
215#548—24no—
216#548C2×C418yes—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229#520—42no—
230#520—42no—
231C2×C4×Q8—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—42no—
234C2×C4×Q8—42no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117—21no—
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4—21no—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C42—21no—
269C22×C42C2311yescharacteristic
270#488C2×C418yescomplemented
271#485C2×C418yescomplemented
272#480C2×C418yescomplemented
273#479C2×C418yescomplemented
274#467C2×C418yescomplemented
275#465C2×C418yescomplemented
276#464C2×C418yescomplemented
277#452C2×C418yescomplemented
278#451C2×C418yescomplemented
279#441—42no—
280#441—42no—
281#441—42no—
282C4×Q16C2×C418yescomplemented
283C4×SD16—42no—
284#435—24no—
285C8×D4C2×C418yescomplemented
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#106—42no—
289C2×#106—42no—
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303#417—42no—
304#416C2×C418yescomplemented
305C2×#103—42no—
306C2×#103C2×C418yescomplemented
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#386D411yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#384—21no—
432#384—21no—
433#384—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#383—21no—
437#382—21no—
438#382—21no—
439#382—21no—
440#381—21no—
441#380—21no—
442#380—21no—
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376—21no—
474#376—21no—
475#376C2311yescharacteristic
476C2×#95—21no—
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#340C2311yescharacteristic
498#340C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C22×C414yes—
515C22×Q8—21no—
516C22×Q8—22no—
517C22×Q8—22no—
518C22×Q8—22no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8C22×C414yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16C22×C414yes—
547C2×Q16C22×C414yes—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16C22×C414yes—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C22×C414yes—
562C22×C8C22×C414yes—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571#126—28no—
572#125—28no—
573#125—22no—
574#125C22×C414yes—
575#124—28no—
576#124—22no—
577#124C22×C414yes—
578#123—28no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—28no—
583C22⋊Q8C22×C414yes—
584C22⋊Q8C22×C414yes—
585C22⋊Q8C22×C414yes—
586#121—28no—
587#121—22no—
588#121C22×C414yes—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—44no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—44no—
609C4×Q8C22×C414yes—
610C4×Q8C22×C414yes—
611C4×D4—28no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—82no—
619C4×D4—82no—
620C4×D4—82no—
621C4×D4—82no—
622C4×D4C22×C414yes—
623C4×D4#4114yes—
624#117—22no—
625#117—28no—
626#117—41no—
627#117—41no—
628#117—44no—
629#117—82no—
630#117C22×C414yes—
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—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4—44no—
676C2×C4⋊C4—82no—
677C2×C4⋊C4C22×C414yes—
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—41no—
740C2×C42—41no—
741C2×C42—44no—
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749#107C22×C414yes—
750#107C22×C414yes—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758#106—41no—
759#106—41no—
760#106—41no—
761#106C22×C414yes—
762C4⋊C8—22no—
763C4⋊C8C22×C414yes—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103C22×C414yes—
777#103C22×C414yes—
778#103C22×C414yes—
779#103C22×C414yes—
780#103C22×C414yes—
781#103C22×C414yes—
782#103C22×C414yes—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102C22×C414yes—
788#102C22×C414yes—
789#102C22×C414yes—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8C22×C414yes—
793C22⋊C8C22×C414yes—
794#97—22no—
795#97—41no—
796#97—41no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
800C4×C8—41no—
801C4×C8C22×C414yes—
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#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842C24—21no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—28no—
846#41—44no—
847#41—44no—
848#41—44no—
849C2×Q8—24no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—28no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8C23×C412yes—
870C2×Q8C23×C412yes—
871C2×Q8C23×C412yes—
872C2×Q8H(5,𝔽2)12yes—
873C2×Q82−1+412yes—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4C4×D414yes—
888C2×D4C23×C412yes—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—24no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
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
962Q16—28no—
963Q16—44no—
964SD16—44no—
965M16—82no—
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—44no—
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—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
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—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4C4×D414yes—
1051C4⋊C4C23×C412yes—
1052C4⋊C4C23×C412yes—
1053C4⋊C4C23×C412yes—
1054C4⋊C4C23×C412yes—
1055C4⋊C4H(5,𝔽2)12yes—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4C4×D414yes—
1080C22⋊C4C4×D414yes—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—24no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—41no—
1094C42—41no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42C23×C412yes—
1111C42C2×#4112yes—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—22no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23C2×C4×D412yes—
1130C23C2×C4×D412yes—
1131C23#57712yes—
1132C23#57712yes—
1133C23C23×D411yescharacteristic
1134Q8—22no—
1135Q8—22no—
1136Q8—22no—
1137Q8—22no—
1138Q8—22no—
1139Q8—22no—
1140Q8—22no—
1141Q8—48no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8#52014yes—
1147D4—28no—
1148D4—22no—
1149D4—22no—
1150D4—48no—
1151D4—48no—
1152D4—41no—
1153D4—41no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—48no—
1205C2×C4—48no—
1206C2×C4—44no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—48no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—82no—
1244C2×C4—84no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4C2×C4×D412yes—
1251C2×C4C2×C4×D412yes—
1252C2×C4C2×C4×D412yes—
1253C2×C4C2×C4×D412yes—
1254C2×C4C24×C411yescharacteristic
1255C2×C4C22×#4111yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×2−1+411yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—22no—
1261C8—22no—
1262C8—22no—
1263C8—22no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22#295214yes—
1289C22C22×C4×D411yescharacteristic
1290C22#348411yescharacteristic
1291C22#348911yescharacteristic
1292C22C2×#57711yescharacteristic
1293C22C2×#57711yescharacteristic
1294C22#358611yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—24no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—42no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4C2×#52011yescharacteristic
1324C4C4×H(5,𝔽2)11yescharacteristic
1325C4#351311yescharacteristic
1326C4#352011yescharacteristic
1327C2—24no—
1328C2—42no—
1329C2—82no—
1330C2#3428811yescharacteristic
1331C2C2×#295211yescharacteristic
1332C2#6017511yescharacteristic
1333C2#6161111yescharacteristic
1334C2#6161811yescharacteristic
1335C2#6215711yescharacteristic
1336C2#6216911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
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. #34465C2semidirect
4. #23225C2semidirect
5. #23028C2semidirect
6. #23022C2semidirect
7. #23013C2semidirect
8. #22976C2semidirect
9. #22942C2semidirect
10. #22938C2semidirect
11. #22867C2semidirect
12. #22859C2semidirect
13. #22674C2semidirect
14. D4×#106C2semidirect
15. #22571C2semidirect
16. #22565C2semidirect
17. #22491C2semidirect
19. #22227C2semidirect
20. #22192C2semidirect
21. #22180C2semidirect
22. #22159C2semidirect
23. #22092C2semidirect
24. #22081C2semidirect
25. #21622C2semidirect
26. #21461C2semidirect
27. #21455C2semidirect
28. #21132C2semidirect
29. #20882C2semidirect
30. C2×#1865C2semidirect
31. #20560C2semidirect
36. #3300C4semidirect
214. #552C2×C4semidirect
270. #488C2×C4semidirect
271. #485C2×C4semidirect
272. #480C2×C4semidirect
273. #479C2×C4semidirect
274. #467C2×C4semidirect
275. #465C2×C4semidirect
276. #464C2×C4semidirect
277. #452C2×C4semidirect
278. #451C2×C4semidirect
282. C4×Q16C2×C4semidirect
285. C8×D4C2×C4semidirect
304. #416C2×C4semidirect
306. C2×#103C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33002
#344652
#342942
#232252
#230282
#230222
#230132
#229762
#229422
#229382
#228672
#228592
#226742
D4×#1062
#225712
#225652
#224912
#224212
#222272
#221922
#221802
#221592
#220922
#220812
#216222
#214612
#214552
#211322
#208822
C2×#18652
#205602