Finite Group Databasebeta

← #6343406

Subgroups — #6343406

Order 512.

3347 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34190C211yesmaximal, characteristic, complemented
4#17599C214yesmaximal, complemented
5#17597C218yesmaximal, complemented
6#17589C211yesmaximal, characteristic, complemented
7#17587C212yesmaximal, complemented
8#17580C211yesmaximal, characteristic, complemented
9#17577C212yesmaximal, complemented
10#17561C211yesmaximal, characteristic, complemented
11#17559C212yesmaximal, complemented
12#17554C211yesmaximal, characteristic, complemented
13C2×#1510C212yesmaximal, complemented
14#17547C214yesmaximal, complemented
15#3519—21no—
16#3519—22no—
17#3519—21no—
18#3519—21no—
19#3519—22no—
20#3519—21no—
21#3519C412yescomplemented
22#3519C414yescomplemented
23#3519C412yescomplemented
24#3519C2212yes—
25#3519C2214yes—
26#3519C2212yes—
27C2×#555C411yescharacteristic, complemented
28C2×#554C411yescharacteristic, complemented
29C2×#553—21no—
30C2×#553C412yescomplemented
31C2×#550C411yescharacteristic, complemented
32C2×#546—22no—
33C2×#546C412yescomplemented
34C2×D42—21no—
35C2×D42C411yescharacteristic, complemented
36C2×#540—21no—
37C2×#538—22no—
38C2×#532C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×#121C2212yes—
42C2×#518—21no—
43C22×C4×D4C2211yescharacteristic
44#2975—21no—
45#2974C2212yescomplemented
46#2974C2214yescomplemented
47#2974C2212yescomplemented
48#2973—22no—
49#2972—21no—
50D4×M16—21no—
51D4×M16—22no—
52D4×M16—21no—
53#2920C2211yescharacteristic, complemented
54#2920C2211yescharacteristic, complemented
55C2×#407C2212yescomplemented
56C2×#407C2212yescomplemented
57#2357—21no—
58#2353—22no—
59#2349—21no—
60#2344—21no—
61#2342—22no—
62D4×C22⋊C4—21no—
63#2319C2212yescomplemented
64#2318C2214yescomplemented
65#2283C2211yescharacteristic, complemented
66#2283C2211yescharacteristic, complemented
67#2280C2212yescomplemented
68C2×#381C2212yescomplemented
69#2275C2212yescomplemented
70#1521C2214yescomplemented
71#1519C2218yescomplemented
72#1517C2214yescomplemented
73#1516C2218yescomplemented
74#1514C2214yescomplemented
75#1513C2218yescomplemented
76#1512C2214yescomplemented
77#1511C2211yescharacteristic, complemented
78#1511C2211yescharacteristic, complemented
79#1511C2212yescomplemented
80#1510C2211yescharacteristic
81#1510C2212yes—
82#1510C2211yescharacteristic
83#1510C2218yescomplemented
84#1510C2212yescomplemented
85#1510C2212yescomplemented
86#1510C2212yescomplemented
87#1510C2212yescomplemented
88#1509C2214yescomplemented
89#1507C2218yescomplemented
90#1505C2214yescomplemented
91#1504C2218yescomplemented
92#1502C2214yescomplemented
93#1501C2218yescomplemented
94#1500C2214yescomplemented
95C2×#327C2218yescomplemented
96C22×#41—21no—
97C22×#41C2×C412yescomplemented
98C23×D4—22no—
99C23×D4—21no—
100C23×D4C2×C412yescomplemented
101C23×D4D411yescharacteristic
102C24×C4C2312yes—
103C22×M16—22no—
104C22×M16—22no—
105#555—21no—
106#555—21no—
107#555—22no—
108#555C2×C412yes—
109#555C2×C414yescomplemented
110#555C2×C412yescomplemented
111#554—21no—
112#554—22no—
113#554—21no—
114#554C2×C412yes—
115#554C2×C414yescomplemented
116#554C2×C412yescomplemented
117#553—22no—
118#553—22no—
119#553—22no—
120#553—22no—
121#553—22no—
122#553—22no—
123#553—24no—
124#553—22no—
125#553—24no—
126#553—22no—
127#553C2×C414yes—
128#553C2×C414yescomplemented
129#553C2×C414yescomplemented
130#553C2×C414yescomplemented
131#550—21no—
132#550—22no—
133#550—21no—
134#550C2×C412yes—
135#550C2×C412yescomplemented
136#550C2×C414yescomplemented
137#546—22no—
138#546—22no—
139#546—22no—
140#546—22no—
141#546—24no—
142#546—24no—
143#546—24no—
144#546—24no—
145#546—24no—
146#546—24no—
147#546—24no—
148#546—24no—
149#546C2×C414yes—
150#546C2×C414yescomplemented
151#546C2×C414yescomplemented
152#546C2×C414yescomplemented
153D42—22no—
154D42—24no—
155D42—22no—
156D42—22no—
157D42—24no—
158D42—22no—
159D42—22no—
160D42—21no—
161D42—21no—
162D42C2×C412yes—
163D42C2×C412yescomplemented
164D42C2×C414yescomplemented
165#540—22no—
166#540—22no—
167#540—24no—
168#540—22no—
169#540—24no—
170#540—22no—
171#538—24no—
172#538—24no—
173#538—24no—
174#538—24no—
175#538—24no—
176#538—24no—
177#538—24no—
178#538—24no—
179#532—21no—
180#532—21no—
181#532—21no—
182#532—21no—
183#532C2×C412yescomplemented
184#532C2×C412yescomplemented
185#532C2312yes—
186#532C2312yes—
187C2×C4⋊Q8C2×C411yescharacteristic, complemented
188C2×#127—21no—
189C2×#127C2×C411yescharacteristic, complemented
190#529—21no—
191#529—21no—
192#529—21no—
193#529—21no—
194#529C2×C412yescomplemented
195#529C2×C412yescomplemented
196#529C2312yes—
197#529C2312yes—
198C2×#126—22no—
199C2×#126—21no—
200C2×#125—21no—
201C2×#125C2×C411yescharacteristic, complemented
202C2×#124—22no—
203C2×#124—21no—
204C2×#124C2×C411yescharacteristic, complemented
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525C2×C414yescomplemented
210#525C2×C414yescomplemented
211#525C2314yes—
212#525C2314yes—
213C2×#123—22no—
214C2×#123—21no—
215C2×#123—22no—
216C2×#123—22no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8C2×C412yescomplemented
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—22no—
221C2×#121—21no—
222C2×#121—22no—
223C2×#121—22no—
224C2×#121—22no—
225C2×#121—22no—
226C2×#121—22no—
227C2×#121—22no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—22no—
231C2×#121—22no—
232C2×#121C2×C412yescomplemented
233C2×#121C2×C412yescomplemented
234C2×#121C2×C414yescomplemented
235C2×#121C2×C414yescomplemented
236C2×#121C2×C412yescomplemented
237C2×#121C2311yescharacteristic
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#120—22no—
242C2×#120—22no—
243C2×#120—22no—
244#518—24no—
245#518—22no—
246#518—22no—
247#518—22no—
248#518—24no—
249#518—22no—
250C2×C4×Q8C2×C411yescharacteristic, complemented
251C2×C4×D4—21no—
252C2×C4×D4—22no—
253C2×C4×D4—22no—
254C2×C4×D4—21no—
255C2×C4×D4—22no—
256C2×C4×D4—21no—
257C2×C4×D4—22no—
258C2×C4×D4—21no—
259C2×C4×D4C2×C411yescharacteristic
260C2×C4×D4C2×C412yes—
261C2×C4×D4C2×C411yescharacteristic
262C2×C4×D4C2×C411yescharacteristic
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C411yescharacteristic
265C2×C4×D4C2×C411yescharacteristic, complemented
266C2×C4×D4C2×C412yescomplemented
267C2×C4×D4D411yescharacteristic
268C2×C4×D4D412yes—
269C2×C4×D4D411yescharacteristic
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D412yes—
272C2×C4×D4D411yescharacteristic
273C2×C4×D4D411yescharacteristic
274C2×C4×D4D412yes—
275C2×C4×D4D411yescharacteristic
276C2×C4×D4C2312yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×#117—22no—
280C2×#117—21no—
281C2×#117—21no—
282C2×#117C2×C412yescomplemented
283C22×C4⋊C4C2×C412yescomplemented
284C22×C4⋊C4D411yescharacteristic
285C22×C22⋊C4—22no—
286C22×C22⋊C4—22no—
287C22×C22⋊C4—22no—
288C22×C22⋊C4D412yes—
289C22×C42C2311yescharacteristic
290#436—22no—
291#436—24no—
292#436—22no—
293#435—24no—
294#435—24no—
295#435—24no—
296#435—24no—
297C8×D4—22no—
298C8×D4—24no—
299C8×D4—22no—
300#432—21no—
301#432—21no—
302#432C2312yescomplemented
303#432C2312yescomplemented
304#431—21no—
305#431—21no—
306#431C2312yescomplemented
307#431C2312yescomplemented
308#423—21no—
309#423—21no—
310#407—22no—
311#407—22no—
312#407—22no—
313#407—22no—
314#407C2311yescharacteristic
315#407C2312yes—
316#407C2311yescharacteristic
317#407C2314yescomplemented
318#407C2314yescomplemented
319C2×C22⋊C8—22no—
320C2×C22⋊C8—22no—
321C2×C22⋊C8C2314yescomplemented
322C2×C22⋊C8C2314yescomplemented
323C4×M16—21no—
324C4×M16—21no—
325#390—22no—
326#389—22no—
327#388—24no—
328#388—24no—
329#387—24no—
330#386—24no—
331#385—24no—
332#383—21no—
333#383C2312yescomplemented
334#382—21no—
335#382C2312yescomplemented
336#381—22no—
337#381—22no—
338#381C2311yescharacteristic
339#381C2312yes—
340#381C2311yescharacteristic
341#381C2314yescomplemented
342#380—21no—
343#380—21no—
344#380—22no—
345#380C2314yescomplemented
346#379—22no—
347C4×C4⋊C4—22no—
348C4×C4⋊C4—21no—
349C4×C4⋊C4C2312yescomplemented
350C4×C22⋊C4—21no—
351C4×C22⋊C4—21no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4C2314yescomplemented
355#376—21no—
356#376C2312yescomplemented
357C2×#95—22no—
358C2×#95C2314yescomplemented
359#328C2314yescomplemented
360#328C2314yescomplemented
361#328C2318yescomplemented
362#327C2314yes—
363#327C2318yes—
364#327C2314yes—
365#327C2318yescomplemented
366#327C2318yescomplemented
367#327C2318yescomplemented
368#327C2318yescomplemented
369C25—22no—
370C25C2×D412yes—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—84no—
378C2×#41—84no—
379C2×#41C22×C414yes—
380C2×#41C22×C414yes—
381C22×Q8—21no—
382C22×Q8C22×C411yescharacteristic
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—21no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—22no—
394C22×D4—24no—
395C22×D4—22no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—44no—
402C22×D4—48no—
403C22×D4—84no—
404C22×D4—88no—
405C22×D4C22⋊C411yescharacteristic
406C22×D4C22⋊C411yescharacteristic
407C22×D4C22⋊C412yes—
408C22×D4C22⋊C411yescharacteristic
409C22×D4C22⋊C411yescharacteristic
410C22×D4C22⋊C412yes—
411C22×D4C22×C411yescharacteristic
412C22×D4C22×C412yes—
413C22×D4C22×C414yes—
414C22×D4C22×C414yes—
415C22×D4C2×D411yescharacteristic
416C22×D4C2×D412yes—
417C22×D4C2×D411yescharacteristic
418C23×C4—22no—
419C23×C4—21no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—84no—
424C23×C4C22×C412yes—
425C23×C4C22×C412yes—
426C23×C4C22×C412yes—
427C23×C4C22×C412yes—
428C23×C4C2×D411yescharacteristic
429C23×C4C2×D412yes—
430C23×C4C2×D411yescharacteristic
431C23×C4C2×D412yes—
432C23×C4C2×D412yes—
433C23×C4C2×D412yes—
434C23×C4C2×D412yes—
435C23×C4C2×D412yes—
436C23×C4C2×D412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C2×M16—21no—
441C2×M16—22no—
442C2×M16—21no—
443C2×M16—24no—
444C2×M16—24no—
445C2×M16—84no—
446C2×M16—84no—
447C22×C8—24no—
448C22×C8—24no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8C22×C412yes—
452C4⋊Q8C22×C412yes—
453#127—22no—
454#127—22no—
455#127—24no—
456#127—21no—
457#127—21no—
458#127C22×C412yes—
459#127C22×C412yes—
460#126—24no—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—22no—
465#126—22no—
466#126—22no—
467#126—22no—
468#125—22no—
469#125—24no—
470#125—22no—
471#125—21no—
472#125—21no—
473#125C22×C412yes—
474#125C22×C412yes—
475#124—24no—
476#124—24no—
477#124—24no—
478#124—24no—
479#124—22no—
480#124—22no—
481#124—21no—
482#124—21no—
483#124—22no—
484#124—22no—
485#124C22×C412yes—
486#124C22×C412yes—
487#123—24no—
488#123—24no—
489#123—22no—
490#123—22no—
491#123—24no—
492#123—24no—
493#123—22no—
494#123—22no—
495#123—24no—
496#123—24no—
497#123—24no—
498#123—24no—
499#123—24no—
500#123—24no—
501#123—24no—
502#123—24no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8C22×C414yes—
512C22⋊Q8C22×C414yes—
513C22⋊Q8C22×C412yes—
514C22⋊Q8C2412yes—
515#121—24no—
516#121—24no—
517#121—24no—
518#121—24no—
519#121—22no—
520#121—22no—
521#121—24no—
522#121—24no—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—21no—
535#121—21no—
536#121—22no—
537#121—22no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—24no—
546#121—22no—
547#121—24no—
548#121—24no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121—24no—
553#121—24no—
554#121—24no—
555#121C22×C412yes—
556#121C22×C414yes—
557#121C22×C414yes—
558#121C22×C414yes—
559#121C22×C414yes—
560#121C22×C414yes—
561#121C22×C414yes—
562#121C22×C414yes—
563#121C2412yes—
564#121C2414yes—
565#120—24no—
566#120—24no—
567#120—24no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120—24no—
573#120—24no—
574#120—24no—
575#120—24no—
576#120—24no—
577C4×Q8—21no—
578C4×Q8—21no—
579C4×Q8C22×C412yes—
580C4×Q8C22×C412yes—
581C4×D4—22no—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—22no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—48no—
612C4×D4C22⋊C412yes—
613C4×D4C22⋊C411yescharacteristic
614C4×D4C22⋊C411yescharacteristic
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22⋊C412yes—
619C4×D4C22⋊C411yescharacteristic
620C4×D4C22⋊C411yescharacteristic
621C4×D4C22⋊C412yes—
622C4×D4C22⋊C412yes—
623C4×D4C22⋊C411yescharacteristic
624C4×D4C22⋊C411yescharacteristic
625C4×D4C22⋊C412yes—
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C412yes—
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C411yescharacteristic
630C4×D4C22⋊C411yescharacteristic
631C4×D4C22⋊C412yes—
632C4×D4C22×C412yes—
633C4×D4C22×C412yes—
634C4×D4C22×C414yes—
635C4×D4C22×C414yes—
636C4×D4C22×C411yescharacteristic
637C4×D4C22×C412yes—
638C4×D4C22×C411yescharacteristic
639C4×D4C22×C412yes—
640C4×D4C22×C412yes—
641C4×D4C22×C412yes—
642C4×D4C22×C412yes—
643C4×D4C22×C411yescharacteristic
644C4×D4C22×C411yescharacteristic
645C4×D4C22×C412yes—
646C4×D4C2×D411yescharacteristic
647C4×D4C2×D412yes—
648C4×D4C2×D411yescharacteristic
649C4×D4C2×D412yes—
650C4×D4C2×D412yes—
651C4×D4C2×D412yes—
652C4×D4C2×D412yes—
653C4×D4C2×D411yescharacteristic
654C4×D4C2×D412yes—
655C4×D4C2×D411yescharacteristic
656#117—22no—
657#117—22no—
658#117—22no—
659#117—24no—
660#117—22no—
661#117—22no—
662#117—22no—
663#117—22no—
664#117—22no—
665#117—84no—
666#117C22×C414yes—
667#117C22×C414yes—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4C22⋊C411yescharacteristic
681C2×C4⋊C4C22⋊C411yescharacteristic
682C2×C4⋊C4C22⋊C412yes—
683C2×C4⋊C4C22⋊C411yescharacteristic
684C2×C4⋊C4C22⋊C411yescharacteristic
685C2×C4⋊C4C22⋊C412yes—
686C2×C4⋊C4C22×C411yescharacteristic
687C2×C4⋊C4C22×C412yes—
688C2×C4⋊C4C22×C414yes—
689C2×C4⋊C4C22×C414yes—
690C2×C4⋊C4C22×C411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D412yes—
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—24no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—24no—
718C2×C22⋊C4—24no—
719C2×C22⋊C4—24no—
720C2×C22⋊C4—84no—
721C2×C22⋊C4C22⋊C412yes—
722C2×C22⋊C4C22⋊C412yes—
723C2×C22⋊C4C22⋊C412yes—
724C2×C22⋊C4C22⋊C412yes—
725C2×C22⋊C4C22⋊C412yes—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C22⋊C412yes—
728C2×C22⋊C4C22⋊C412yes—
729C2×C22⋊C4C2×D412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C22⋊C4C2×D412yes—
732C2×C22⋊C4C2×D412yes—
733C2×C42—22no—
734C2×C42—21no—
735C2×C42—22no—
736C2×C42—24no—
737C2×C42—22no—
738C2×C42C22×C411yescharacteristic
739C2×C42C22×C411yescharacteristic
740C2×C42C22×C411yescharacteristic
741C2×C42C22×C411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C22⋊C8—21no—
755C22⋊C8—22no—
756C22⋊C8—21no—
757C22⋊C8—24no—
758C22⋊C8—24no—
759C22⋊C8—24no—
760C22⋊C8—24no—
761C22⋊C8C2412yes—
762C22⋊C8C2414yes—
763C22⋊C8C2412yes—
764#97—22no—
765#97—22no—
766C4×C8—22no—
767C4×C8—22no—
768#95—21no—
769#95—22no—
770#95—24no—
771#95—24no—
772#95—22no—
773#95—22no—
774#95—21no—
775#95—22no—
776#95—22no—
777#95C2412yes—
778#95C2414yes—
779#95C2412yes—
780C24—21no—
781C24—22no—
782C24—24no—
783C24—24no—
784C24—44no—
785C24—44no—
786C24—44no—
787C24—48no—
788C24—84no—
789C24—84no—
790C24C2×C22⋊C412yes—
791C24C2×C22⋊C412yes—
792C24C2×C22⋊C412yes—
793C24C2×C22⋊C412yes—
794C24C22×D411yescharacteristic
795C24C22×D412yes—
796C24C22×D412yes—
797#41—84no—
798#41—84no—
799#41—84no—
800#41—84no—
801#41—84no—
802#41—84no—
803#41—84no—
804#41—84no—
805C2×Q8—21no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—42no—
809C2×Q8—82no—
810C2×Q8C23×C412yes—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—22no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—416no—
844C2×D4—48no—
845C2×D4—48no—
846C2×D4—44no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—84no—
850C2×D4—84no—
851C2×D4—84no—
852C2×D4—84no—
853C2×D4—84no—
854C2×D4—84no—
855C2×D4—84no—
856C2×D4—84no—
857C2×D4—82no—
858C2×D4—88no—
859C2×D4—88no—
860C2×D4—88no—
861C2×D4—88no—
862C2×D4C2×C22⋊C412yes—
863C2×D4C2×C22⋊C411yescharacteristic
864C2×D4C2×C22⋊C412yes—
865C2×D4C2×C22⋊C412yes—
866C2×D4C2×C22⋊C411yescharacteristic
867C2×D4C2×C22⋊C411yescharacteristic
868C2×D4C2×C22⋊C412yes—
869C2×D4C2×C22⋊C412yes—
870C2×D4C2×C22⋊C412yes—
871C2×D4C2×C22⋊C411yescharacteristic
872C2×D4C23×C412yes—
873C2×D4C23×C414yes—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—21no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—22no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—42no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—42no—
897C22×C4—44no—
898C22×C4—48no—
899C22×C4—84no—
900C22×C4—82no—
901C22×C4—82no—
902C22×C4—82no—
903C22×C4—82no—
904C22×C4—82no—
905C22×C4—82no—
906C22×C4—82no—
907C22×C4—82no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4C2×C22⋊C411yescharacteristic
913C22×C4C2×C22⋊C412yes—
914C22×C4C2×C22⋊C411yescharacteristic
915C22×C4C2×C22⋊C412yes—
916C22×C4C2×C22⋊C411yescharacteristic
917C22×C4C2×C22⋊C411yescharacteristic
918C22×C4C2×C22⋊C411yescharacteristic
919C22×C4C2×C22⋊C411yescharacteristic
920C22×C4C2×C22⋊C411yescharacteristic
921C22×C4C2×C22⋊C411yescharacteristic
922C22×C4C2×C22⋊C412yes—
923C22×C4C2×C22⋊C412yes—
924C22×C4C2×C22⋊C412yes—
925C22×C4C2×C22⋊C412yes—
926C22×C4C2×C22⋊C412yes—
927C22×C4C2×C22⋊C412yes—
928C22×C4C2×C22⋊C412yes—
929C22×C4C2×C22⋊C412yes—
930C22×C4C2×C22⋊C412yes—
931C22×C4C2×C22⋊C412yes—
932C22×C4C23×C411yescharacteristic
933C22×C4C23×C411yescharacteristic
934C22×C4C23×C412yes—
935C22×C4C23×C412yes—
936C22×C4C23×C412yes—
937C22×C4C23×C412yes—
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D412yes—
945C22×C4C22×D412yes—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C2511yescharacteristic
952M16—42no—
953M16—44no—
954M16—42no—
955M16—84no—
956M16—84no—
957C2×C8—22no—
958C2×C8—22no—
959C2×C8—24no—
960C2×C8—84no—
961C2×C8—84no—
962C4⋊C4—21no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—21no—
978C4⋊C4—22no—
979C4⋊C4—44no—
980C4⋊C4—82no—
981C4⋊C4—84no—
982C4⋊C4C2×C22⋊C412yes—
983C4⋊C4C2×C22⋊C411yescharacteristic
984C4⋊C4C2×C22⋊C411yescharacteristic
985C4⋊C4C2×C22⋊C412yes—
986C4⋊C4C2×C22⋊C411yescharacteristic
987C4⋊C4C2×C22⋊C411yescharacteristic
988C4⋊C4C2×C22⋊C412yes—
989C4⋊C4C2×C22⋊C412yes—
990C4⋊C4C2×C22⋊C412yes—
991C4⋊C4C2×C22⋊C412yes—
992C4⋊C4C23×C412yes—
993C4⋊C4C23×C414yes—
994C4⋊C4C23×C412yes—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—22no—
1018C22⋊C4—24no—
1019C22⋊C4—42no—
1020C22⋊C4—44no—
1021C22⋊C4—42no—
1022C22⋊C4—48no—
1023C22⋊C4—84no—
1024C22⋊C4—84no—
1025C22⋊C4C2×C22⋊C412yes—
1026C22⋊C4C2×C22⋊C412yes—
1027C22⋊C4C2×C22⋊C412yes—
1028C22⋊C4C2×C22⋊C412yes—
1029C22⋊C4C2×C22⋊C412yes—
1030C22⋊C4C2×C22⋊C412yes—
1031C22⋊C4C2×C22⋊C412yes—
1032C22⋊C4C2×C22⋊C412yes—
1033C22⋊C4C2×C22⋊C412yes—
1034C22⋊C4C2×C22⋊C412yes—
1035C22⋊C4C2×C22⋊C412yes—
1036C22⋊C4C2×C22⋊C412yes—
1037C22⋊C4C2×C22⋊C412yes—
1038C22⋊C4C2×C22⋊C412yes—
1039C22⋊C4C2×C22⋊C412yes—
1040C22⋊C4C2×C22⋊C412yes—
1041C42—24no—
1042C42—24no—
1043C42—22no—
1044C42—22no—
1045C42—44no—
1046C42—82no—
1047C42—84no—
1048C42C2×C22⋊C411yescharacteristic
1049C42C2×C22⋊C411yescharacteristic
1050C42C2×C22⋊C411yescharacteristic
1051C42C2×C22⋊C411yescharacteristic
1052C42C2×C22⋊C411yescharacteristic
1053C42C2×C22⋊C411yescharacteristic
1054C42C2×C22⋊C411yescharacteristic
1055C42C2×C22⋊C411yescharacteristic
1056C42C23×C411yescharacteristic
1057C42C23×C411yescharacteristic
1058C42C23×C411yescharacteristic
1059C42C23×C411yescharacteristic
1060C42C22×D411yescharacteristic
1061C42C22×D411yescharacteristic
1062C42C22×D411yescharacteristic
1063C42C22×D411yescharacteristic
1064C23—22no—
1065C23—24no—
1066C23—22no—
1067C23—24no—
1068C23—24no—
1069C23—24no—
1070C23—24no—
1071C23—24no—
1072C23—24no—
1073C23—22no—
1074C23—24no—
1075C23—41no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—44no—
1089C23—44no—
1090C23—42no—
1091C23—48no—
1092C23—44no—
1093C23—42no—
1094C23—48no—
1095C23—84no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—816no—
1100C23—1616no—
1101C23C22×C22⋊C412yes—
1102C23C22×C22⋊C412yes—
1103C23C22×C22⋊C412yes—
1104C23C22×C22⋊C411yescharacteristic
1105C23C22×C22⋊C411yescharacteristic
1106C23C22×C22⋊C412yes—
1107C23C23×D411yescharacteristic
1108Q8—42no—
1109Q8—42no—
1110Q8—82no—
1111Q8—82no—
1112D4—24no—
1113D4—24no—
1114D4—24no—
1115D4—22no—
1116D4—22no—
1117D4—22no—
1118D4—42no—
1119D4—42no—
1120D4—42no—
1121D4—42no—
1122D4—44no—
1123D4—44no—
1124D4—42no—
1125D4—44no—
1126D4—48no—
1127D4—44no—
1128D4—48no—
1129D4—44no—
1130D4—48no—
1131D4—48no—
1132D4—44no—
1133D4—84no—
1134D4—84no—
1135D4—82no—
1136D4—82no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—84no—
1143D4#42114yes—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—44no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—44no—
1192C2×C4—42no—
1193C2×C4—44no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—44no—
1198C2×C4—42no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—168no—
1210C2×C4C22×C22⋊C411yescharacteristic
1211C2×C4C22×C22⋊C412yes—
1212C2×C4C22×C22⋊C412yes—
1213C2×C4C22×C22⋊C411yescharacteristic
1214C2×C4C22×C22⋊C411yescharacteristic
1215C2×C4C22×C22⋊C411yescharacteristic
1216C2×C4C22×C22⋊C411yescharacteristic
1217C2×C4C22×C22⋊C411yescharacteristic
1218C2×C4C22×C22⋊C411yescharacteristic
1219C2×C4C22×C22⋊C411yescharacteristic
1220C2×C4C22×C22⋊C411yescharacteristic
1221C2×C4C22×C22⋊C412yes—
1222C2×C4C22×C22⋊C412yes—
1223C2×C4C22×C22⋊C411yescharacteristic
1224C2×C4C24×C411yescharacteristic
1225C2×C4C23×D411yescharacteristic
1226C8—42no—
1227C8—42no—
1228C8—44no—
1229C22—21no—
1230C22—22no—
1231C22—21no—
1232C22—22no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—21no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—48no—
1248C22—44no—
1249C22—48no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—84no—
1257C22—84no—
1258C22—84no—
1259C22—88no—
1260C22—84no—
1261C22—84no—
1262C22—168no—
1263C22—168no—
1264C22#288312yes—
1265C22C2×#42114yes—
1266C22C23×C22⋊C411yescharacteristic
1267C22#358512yes—
1268C4—21no—
1269C4—21no—
1270C4—21no—
1271C4—21no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—21no—
1277C4—21no—
1278C4—21no—
1279C4—21no—
1280C4—21no—
1281C4—21no—
1282C4—21no—
1283C4—42no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—82no—
1288C4—84no—
1289C4—82no—
1290C4C2×#42112yes—
1291C2—22no—
1292C2—22no—
1293C2—24no—
1294C2—42no—
1295C2—41no—
1296C2—42no—
1297C2—42no—
1298C2—84no—
1299C2—82no—
1300C2C2×#288311yescharacteristic
1301C2#6008711yescharacteristic
1302C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. #34190C2semidirect
4. #17599C2semidirect
5. #17597C2semidirect
6. #17589C2semidirect
7. #17587C2semidirect
8. #17580C2semidirect
9. #17577C2semidirect
10. #17561C2semidirect
11. #17559C2semidirect
12. #17554C2semidirect
13. C2×#1510C2semidirect
14. #17547C2semidirect
21. #3519C4semidirect
22. #3519C4semidirect
23. #3519C4semidirect
27. C2×#555C4semidirect
28. C2×#554C4semidirect
30. C2×#553C4semidirect
31. C2×#550C4semidirect
33. C2×#546C4semidirect
35. C2×D42C4semidirect
45. #2974C22semidirect
46. #2974C22semidirect
47. #2974C22semidirect
53. #2920C22semidirect
54. #2920C22semidirect
55. C2×#407C22semidirect
56. C2×#407C22semidirect
63. #2319C22semidirect
64. #2318C22semidirect
65. #2283C22semidirect
66. #2283C22semidirect
67. #2280C22semidirect
68. C2×#381C22semidirect
69. #2275C22semidirect
70. #1521C22semidirect
71. #1519C22semidirect
72. #1517C22semidirect
73. #1516C22semidirect
74. #1514C22semidirect
75. #1513C22semidirect
76. #1512C22semidirect
77. #1511C22semidirect
78. #1511C22semidirect
79. #1511C22semidirect
83. #1510C22semidirect
84. #1510C22semidirect
85. #1510C22semidirect
86. #1510C22semidirect
87. #1510C22semidirect
88. #1509C22semidirect
89. #1507C22semidirect
90. #1505C22semidirect
91. #1504C22semidirect
92. #1502C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#327C22semidirect
97. C22×#41C2×C4semidirect
100. C23×D4C2×C4semidirect
109. #555C2×C4semidirect
110. #555C2×C4semidirect
115. #554C2×C4semidirect
116. #554C2×C4semidirect
128. #553C2×C4semidirect
129. #553C2×C4semidirect
130. #553C2×C4semidirect
135. #550C2×C4semidirect
136. #550C2×C4semidirect
150. #546C2×C4semidirect
151. #546C2×C4semidirect
152. #546C2×C4semidirect
163. D42C2×C4semidirect
164. D42C2×C4semidirect
183. #532C2×C4semidirect
184. #532C2×C4semidirect
187. C2×C4⋊Q8C2×C4semidirect
189. C2×#127C2×C4semidirect
194. #529C2×C4semidirect
195. #529C2×C4semidirect
201. C2×#125C2×C4semidirect
204. C2×#124C2×C4semidirect
209. #525C2×C4semidirect
210. #525C2×C4semidirect
218. C2×C22⋊Q8C2×C4semidirect
232. C2×#121C2×C4semidirect
233. C2×#121C2×C4semidirect
234. C2×#121C2×C4semidirect
235. C2×#121C2×C4semidirect
236. C2×#121C2×C4semidirect
250. C2×C4×Q8C2×C4semidirect
265. C2×C4×D4C2×C4semidirect
266. C2×C4×D4C2×C4semidirect
282. C2×#117C2×C4semidirect
283. C22×C4⋊C4C2×C4semidirect
302. #432C23semidirect
303. #432C23semidirect
306. #431C23semidirect
307. #431C23semidirect
317. #407C23semidirect
318. #407C23semidirect
321. C2×C22⋊C8C23semidirect
322. C2×C22⋊C8C23semidirect
333. #383C23semidirect
335. #382C23semidirect
341. #381C23semidirect
345. #380C23semidirect
349. C4×C4⋊C4C23semidirect
354. C4×C22⋊C4C23semidirect
356. #376C23semidirect
358. C2×#95C23semidirect
359. #328C23semidirect
360. #328C23semidirect
361. #328C23semidirect
365. #327C23semidirect
366. #327C23semidirect
367. #327C23semidirect
368. #327C23semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
#602302
#341902
#175992
#175972
#175892
#175872
#175802
#175772
#175612
#175592
#175542
C2×#15102
#175472