Finite Group Databasebeta

← #6343604

Subgroups — #6343604

Order 512.

3174 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34190C211yesmaximal, characteristic, complemented
4#17625C214yesmaximal, complemented
5#17623C214yesmaximal, complemented
6#17622C214yesmaximal, complemented
7#17615C214yesmaximal, complemented
8#17587C212yesmaximal, complemented
9#17580C212yesmaximal, complemented
10#17578C211yesmaximal, characteristic, complemented
11#17577C211yesmaximal, characteristic, complemented
12#17559C212yesmaximal, complemented
13#17554C212yesmaximal, complemented
14C2×#1511C211yesmaximal, characteristic, complemented
15C2×#1510C211yesmaximal, characteristic, complemented
16#3505—22no—
17#3505—22no—
18#3505—21no—
19#3505—21no—
20#3505—21no—
21#3505—21no—
22#3505C414yescomplemented
23#3505C414yescomplemented
24#3505C2212yes—
25#3505C2212yes—
26#3505C2212yes—
27#3505C2212yes—
28C2×#553—22no—
29C2×#553C412yescomplemented
30C2×#552C412yescomplemented
31C2×#551—22no—
32C2×#548C412yescomplemented
33C2×#546C412yescomplemented
34C2×#539—21no—
35C2×#538—21no—
36C2×#534—21no—
37C2×#529C2212yes—
38C2×#525C2212yes—
39C22×C22⋊Q8C2211yescharacteristic
40C22×#121C2211yescharacteristic
41C2×#518—21no—
42C22×C4×D4C2211yescharacteristic
43#2975C2212yescomplemented
44#2974—22no—
45#2974—22no—
46#2973C2212yescomplemented
47#2973C2212yescomplemented
48#2972C2212yescomplemented
49D4×M16—22no—
50D4×M16—22no—
51#2920C2212yescomplemented
52C2×#407C2211yescharacteristic
53C2×#407C2211yescharacteristic
54C2×#407C2212yescomplemented
55#2357C2212yescomplemented
56#2353C2212yescomplemented
57#2353C2212yescomplemented
58#2349C2212yescomplemented
59#2344—21no—
60#2342—21no—
61#2342—21no—
62D4×C22⋊C4—21no—
63#2319—21no—
64#2318—21no—
65#2318—21no—
66#2283C2211yescharacteristic, complemented
67#2283C2211yescharacteristic, complemented
68#2280C2211yescharacteristic
69#2280C2211yescharacteristic, complemented
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic, complemented
72#2275—21no—
73#1521C2218yescomplemented
74#1520C2214yescomplemented
75#1519C2214yescomplemented
76#1516C2218yescomplemented
77#1513C2218yescomplemented
78#1512C2218yescomplemented
79#1511C2212yescomplemented
80#1511C2212yescomplemented
81#1511C2214yescomplemented
82#1511C2212yescomplemented
83#1511C2212yescomplemented
84#1510C2212yes—
85#1510C2212yes—
86#1510C2212yes—
87#1510C2212yes—
88#1510C2214yescomplemented
89#1509C2218yescomplemented
90#1508C2214yescomplemented
91#1507C2214yescomplemented
92#1504C2218yescomplemented
93#1501C2218yescomplemented
94#1500C2218yescomplemented
95C2×#328C2214yescomplemented
96C2×#327C2214yescomplemented
97C22×#41C2×C412yescomplemented
98C23×Q8C2×C411yescharacteristic, complemented
99C23×D4—21no—
100C23×D4C2×C411yescharacteristic, complemented
101C23×D4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C22×M16—21no—
105C22×M16—21no—
106C22×M16—22no—
107#553—24no—
108#553—24no—
109#553—24no—
110#553—24no—
111#553—22no—
112#553—22no—
113#553—22no—
114#553—22no—
115#553—24no—
116#553—24no—
117#553—24no—
118#553—24no—
119#553C2×C414yes—
120#553C2×C414yescomplemented
121#553C2×C414yescomplemented
122#553C2×C414yescomplemented
123#552—22no—
124#552—22no—
125#552—22no—
126#552—22no—
127#552C2×C414yes—
128#552C2×C414yescomplemented
129#552C2×C414yescomplemented
130#552C2×C414yescomplemented
131#551—24no—
132#551—24no—
133#551—24no—
134#551—24no—
135#551—24no—
136#551—24no—
137#551—24no—
138#551—24no—
139#548—22no—
140#548—22no—
141#548—22no—
142#548—22no—
143#548C2×C414yes—
144#548C2×C414yescomplemented
145#548C2×C414yescomplemented
146#548C2×C414yescomplemented
147#546—22no—
148#546—22no—
149#546—22no—
150#546—22no—
151#546C2×C414yes—
152#546C2×C414yescomplemented
153#546C2×C414yescomplemented
154#546C2×C414yescomplemented
155#539—24no—
156#539—24no—
157#539—22no—
158#539—22no—
159#539—22no—
160#539—22no—
161#538—24no—
162#538—24no—
163#538—22no—
164#538—22no—
165#538—22no—
166#538—22no—
167#534—24no—
168#534—24no—
169#534—22no—
170#534—22no—
171#534—22no—
172#534—22no—
173#529—22no—
174#529—22no—
175#529—22no—
176#529—22no—
177#529C2×C414yescomplemented
178#529C2×C414yescomplemented
179#529C2314yes—
180#529C2314yes—
181C2×#126—22no—
182C2×#126—22no—
183C2×#126—22no—
184C2×#125—22no—
185C2×#125C2×C412yescomplemented
186C2×#124—22no—
187C2×#124C2×C412yescomplemented
188#525—22no—
189#525—22no—
190#525—22no—
191#525—22no—
192#525C2×C414yescomplemented
193#525C2×C414yescomplemented
194#525C2314yes—
195#525C2314yes—
196C2×#123—22no—
197C2×#123—22no—
198C2×#123—22no—
199C2×#123—22no—
200C2×#123—22no—
201C2×C22⋊Q8—21no—
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8—21no—
204C2×C22⋊Q8—21no—
205C2×C22⋊Q8—21no—
206C2×C22⋊Q8—21no—
207C2×C22⋊Q8—22no—
208C2×C22⋊Q8C2×C412yescomplemented
209C2×C22⋊Q8C2×C412yescomplemented
210C2×C22⋊Q8C2×C412yescomplemented
211C2×C22⋊Q8C2×C412yescomplemented
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×#121—22no—
216C2×#121—22no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—22no—
224C2×#121C2×C412yescomplemented
225C2×#121C2×C412yescomplemented
226C2×#121C2×C412yescomplemented
227C2×#121C2×C412yescomplemented
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#120—22no—
232C2×#120—22no—
233#518—24no—
234#518—24no—
235#518—22no—
236#518—22no—
237#518—22no—
238#518—22no—
239C2×C4×Q8C2×C412yescomplemented
240C2×C4×D4—22no—
241C2×C4×D4—22no—
242C2×C4×D4—22no—
243C2×C4×D4—22no—
244C2×C4×D4—22no—
245C2×C4×D4—22no—
246C2×C4×D4C2×C412yes—
247C2×C4×D4C2×C412yes—
248C2×C4×D4C2×C412yes—
249C2×C4×D4C2×C412yes—
250C2×C4×D4C2×C412yescomplemented
251C2×C4×D4D412yes—
252C2×C4×D4D412yes—
253C2×C4×D4D412yes—
254C2×C4×D4D412yes—
255C2×C4×D4D411yescharacteristic
256C2×C4×D4D411yescharacteristic
257C2×C4×D4D411yescharacteristic
258C2×C4×D4D411yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117—21no—
264C2×#117—21no—
265C2×#117—22no—
266C2×#117—22no—
267C2×#117C2×C412yescomplemented
268C22×C4⋊C4—21no—
269C22×C4⋊C4C2×C411yescharacteristic, complemented
270C22×C4⋊C4C2×C411yescharacteristic, complemented
271C22×C4⋊C4D411yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4—21no—
274C22×C22⋊C4—22no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—21no—
277C22×C22⋊C4D411yescharacteristic
278C22×C22⋊C4D411yescharacteristic
279C22×C42C2311yescharacteristic
280#436—24no—
281#436—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435—24no—
286C8×D4—24no—
287C8×D4—24no—
288#432—22no—
289#432C2314yescomplemented
290#431—22no—
291#431C2314yescomplemented
292#423—22no—
293#407—21no—
294#407—21no—
295#407—21no—
296#407—21no—
297#407—22no—
298#407—22no—
299#407C2312yes—
300#407C2312yes—
301#407C2312yes—
302#407C2312yes—
303#407C2314yescomplemented
304C2×C22⋊C8—21no—
305C2×C22⋊C8—21no—
306C2×C22⋊C8—22no—
307C2×C22⋊C8C2312yes—
308C2×C22⋊C8C2312yes—
309C2×C22⋊C8C2314yescomplemented
310C4×M16—22no—
311#390—22no—
312#389—22no—
313#388—22no—
314#388—22no—
315#388—22no—
316#388—22no—
317#387—22no—
318#387—22no—
319#386—22no—
320#386—22no—
321#385—22no—
322#385—22no—
323#383—21no—
324#383C2312yescomplemented
325#382—21no—
326#382C2312yescomplemented
327#381—21no—
328#381—21no—
329#381—21no—
330#381—21no—
331#381C2312yes—
332#381C2311yescharacteristic
333#381C2311yescharacteristic
334#381C2311yescharacteristic
335#381C2311yescharacteristic
336#381C2312yescomplemented
337#380—21no—
338#380—21no—
339#380—21no—
340#380—21no—
341#380C2312yes—
342#380C2312yescomplemented
343#379—21no—
344#379—21no—
345C4×C4⋊C4—22no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4C2312yescomplemented
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—21no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—22no—
354C4×C22⋊C4C2312yes—
355C4×C22⋊C4C2312yescomplemented
356#376—21no—
357#376C2312yescomplemented
358C2×#95—21no—
359C2×#95—21no—
360C2×#95C2312yes—
361C2×#95C2312yescomplemented
362#328C2318yescomplemented
363#328C2318yescomplemented
364#328C2318yescomplemented
365#328C2318yescomplemented
366#327C2318yes—
367#327C2318yes—
368#327C2318yes—
369#327C2318yes—
370C25—21no—
371C25C2×D411yescharacteristic
372C25C2×D411yescharacteristic
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—84no—
376C2×#41C22×C414yes—
377C2×#41C22×C414yes—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—21no—
381C22×Q8—82no—
382C22×Q8C22×C412yes—
383C22×Q8C22×C412yes—
384C22×Q8C22×C412yes—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—44no—
397C22×D4—48no—
398C22×D4—82no—
399C22×D4C22⋊C412yes—
400C22×D4C22⋊C412yes—
401C22×D4C22⋊C412yes—
402C22×D4C22⋊C412yes—
403C22×D4C22×C412yes—
404C22×D4C22×C412yes—
405C22×D4C22×C412yes—
406C22×D4C2×D411yescharacteristic
407C22×D4C2×D411yescharacteristic
408C22×D4C2×D411yescharacteristic
409C22×D4C2×D411yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—82no—
418C23×C4—82no—
419C23×C4C22×C411yescharacteristic
420C23×C4C22×C411yescharacteristic
421C23×C4C22×C412yes—
422C23×C4C22×C411yescharacteristic
423C23×C4C22×C411yescharacteristic
424C23×C4C22×C412yes—
425C23×C4C2×D411yescharacteristic
426C23×C4C2×D411yescharacteristic
427C23×C4C2×D411yescharacteristic
428C23×C4C2×D411yescharacteristic
429C23×C4C2×D411yescharacteristic
430C23×C4C2×D412yes—
431C23×C4C2×D411yescharacteristic
432C23×C4C2×D411yescharacteristic
433C23×C4C2×D411yescharacteristic
434C23×C4C2×D411yescharacteristic
435C23×C4C2×D411yescharacteristic
436C23×C4C2×D411yescharacteristic
437C23×C4C2×D411yescharacteristic
438C23×C4C2×D412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—24no—
449C2×M16—82no—
450C2×M16—82no—
451C2×M16—84no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—24no—
455#126—24no—
456#126—24no—
457#126—24no—
458#126—24no—
459#126—24no—
460#126—24no—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—24no—
465#126—24no—
466#126—24no—
467#125—24no—
468#125—24no—
469#125—24no—
470#125—24no—
471#125—22no—
472#125—22no—
473#125C22×C414yes—
474#125C22×C414yes—
475#124—24no—
476#124—24no—
477#124—24no—
478#124—24no—
479#124—22no—
480#124—22no—
481#124C22×C414yes—
482#124C22×C414yes—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
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—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8C22×C414yes—
522C22⋊Q8C22×C414yes—
523C22⋊Q8C22×C414yes—
524C22⋊Q8C22×C414yes—
525C22⋊Q8C22×C414yes—
526C22⋊Q8C2414yes—
527#121—24no—
528#121—24no—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121—24no—
553#121C22×C414yes—
554#121C22×C414yes—
555#121C22×C414yes—
556#121C22×C414yes—
557#121C22×C414yes—
558#121C2414yes—
559#120—24no—
560#120—24no—
561#120—24no—
562#120—24no—
563#120—24no—
564#120—24no—
565#120—24no—
566#120—24no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8C22×C414yes—
570C4×Q8C22×C414yes—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—48no—
594C4×D4C22⋊C412yes—
595C4×D4C22⋊C412yes—
596C4×D4C22⋊C412yes—
597C4×D4C22⋊C412yes—
598C4×D4C22⋊C412yes—
599C4×D4C22⋊C412yes—
600C4×D4C22⋊C412yes—
601C4×D4C22⋊C412yes—
602C4×D4C22⋊C412yes—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C412yes—
605C4×D4C22⋊C412yes—
606C4×D4C22⋊C412yes—
607C4×D4C22⋊C412yes—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C412yes—
610C4×D4C22×C414yes—
611C4×D4C22×C414yes—
612C4×D4C22×C412yes—
613C4×D4C22×C412yes—
614C4×D4C22×C412yes—
615C4×D4C22×C412yes—
616C4×D4C22×C412yes—
617C4×D4C22×C412yes—
618C4×D4C22×C412yes—
619C4×D4C22×C412yes—
620C4×D4C2×D412yes—
621C4×D4C2×D412yes—
622C4×D4C2×D412yes—
623C4×D4C2×D412yes—
624C4×D4C2×D412yes—
625C4×D4C2×D412yes—
626C4×D4C2×D412yes—
627C4×D4C2×D412yes—
628#117—22no—
629#117—22no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117—24no—
637#117—24no—
638#117—82no—
639#117—82no—
640#117C22×C414yes—
641#117C22×C414yes—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
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—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4C22⋊C412yes—
663C2×C4⋊C4C22⋊C412yes—
664C2×C4⋊C4C22⋊C412yes—
665C2×C4⋊C4C22⋊C412yes—
666C2×C4⋊C4C22×C412yes—
667C2×C4⋊C4C22×C412yes—
668C2×C4⋊C4C22×C412yes—
669C2×C4⋊C4C22×C412yes—
670C2×C4⋊C4C22×C412yes—
671C2×C4⋊C4C22×C412yes—
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—24no—
695C2×C22⋊C4—24no—
696C2×C22⋊C4—24no—
697C2×C22⋊C4—24no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—82no—
709C2×C22⋊C4—82no—
710C2×C22⋊C4C22⋊C412yes—
711C2×C22⋊C4C22⋊C412yes—
712C2×C22⋊C4C22⋊C412yes—
713C2×C22⋊C4C22⋊C412yes—
714C2×C22⋊C4C22⋊C412yes—
715C2×C22⋊C4C22⋊C412yes—
716C2×C22⋊C4C22⋊C412yes—
717C2×C22⋊C4C22⋊C412yes—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42C22×C412yes—
733C2×C42C22×C412yes—
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D412yes—
737C2×C42C2×D412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C4⋊C8—24no—
741C4⋊C8—24no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—24no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—24no—
750C22⋊C8C2414yes—
751C22⋊C8C2414yes—
752#97—24no—
753C4×C8—24no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—21no—
762#95—22no—
763#95—22no—
764#95—22no—
765#95—22no—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770C24—24no—
771C24—22no—
772C24—22no—
773C24—22no—
774C24—42no—
775C24—42no—
776C24—42no—
777C24—44no—
778C24—82no—
779C24—81no—
780C24—81no—
781C24—82no—
782C24C2×C22⋊C411yescharacteristic
783C24C2×C22⋊C411yescharacteristic
784C24C2×C22⋊C412yes—
785C24C2×C22⋊C411yescharacteristic
786C24C2×C22⋊C411yescharacteristic
787C24C2×C22⋊C412yes—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792C24C22×D411yescharacteristic
793#41—84no—
794#41—84no—
795#41—84no—
796#41—84no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—44no—
801C2×Q8—82no—
802C2×Q8—82no—
803C2×Q8—82no—
804C2×Q8—82no—
805C2×Q8—82no—
806C2×Q8C23×C414yes—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—48no—
833C2×D4—82no—
834C2×D4—82no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—82no—
838C2×D4—84no—
839C2×D4—84no—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C412yes—
842C2×D4C2×C22⋊C412yes—
843C2×D4C2×C22⋊C412yes—
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C412yes—
846C2×D4C2×C22⋊C412yes—
847C2×D4C2×C22⋊C412yes—
848C2×D4C23×C414yes—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—44no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—84no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—82no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—82no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—82no—
896C22×C4—84no—
897C22×C4—82no—
898C22×C4—82no—
899C22×C4—82no—
900C22×C4—82no—
901C22×C4—82no—
902C22×C4C2×C22⋊C412yes—
903C22×C4C2×C22⋊C411yescharacteristic
904C22×C4C2×C22⋊C411yescharacteristic
905C22×C4C2×C22⋊C412yes—
906C22×C4C2×C22⋊C412yes—
907C22×C4C2×C22⋊C412yes—
908C22×C4C2×C22⋊C412yes—
909C22×C4C2×C22⋊C411yescharacteristic
910C22×C4C2×C22⋊C411yescharacteristic
911C22×C4C2×C22⋊C412yes—
912C22×C4C2×C22⋊C411yescharacteristic
913C22×C4C2×C22⋊C411yescharacteristic
914C22×C4C2×C22⋊C411yescharacteristic
915C22×C4C2×C22⋊C411yescharacteristic
916C22×C4C2×C22⋊C411yescharacteristic
917C22×C4C2×C22⋊C411yescharacteristic
918C22×C4C2×C22⋊C411yescharacteristic
919C22×C4C2×C22⋊C411yescharacteristic
920C22×C4C2×C22⋊C412yes—
921C22×C4C2×C22⋊C412yes—
922C22×C4C2×C22⋊C412yes—
923C22×C4C2×C22⋊C412yes—
924C22×C4C23×C411yescharacteristic
925C22×C4C23×C411yescharacteristic
926C22×C4C23×C411yescharacteristic
927C22×C4C23×C411yescharacteristic
928C22×C4C23×C411yescharacteristic
929C22×C4C23×C411yescharacteristic
930C22×C4C23×C412yes—
931C22×C4C23×C412yes—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
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×C4C22×D411yescharacteristic
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C2511yescharacteristic
950M16—44no—
951M16—44no—
952M16—82no—
953M16—82no—
954M16—84no—
955C2×C8—24no—
956C2×C8—24no—
957C2×C8—82no—
958C2×C8—82no—
959C2×C8—84no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—44no—
979C4⋊C4—82no—
980C4⋊C4—82no—
981C4⋊C4—82no—
982C4⋊C4C2×C22⋊C412yes—
983C4⋊C4C2×C22⋊C412yes—
984C4⋊C4C2×C22⋊C412yes—
985C4⋊C4C2×C22⋊C412yes—
986C4⋊C4C2×C22⋊C412yes—
987C4⋊C4C2×C22⋊C412yes—
988C4⋊C4C2×C22⋊C412yes—
989C4⋊C4C2×C22⋊C412yes—
990C4⋊C4C23×C414yes—
991C4⋊C4C23×C414yes—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—24no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—82no—
1019C22⋊C4—82no—
1020C22⋊C4—82no—
1021C22⋊C4—82no—
1022C22⋊C4C2×C22⋊C412yes—
1023C22⋊C4C2×C22⋊C412yes—
1024C22⋊C4C2×C22⋊C412yes—
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—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—44no—
1043C42—82no—
1044C42—82no—
1045C42—82no—
1046C42C2×C22⋊C412yes—
1047C42C2×C22⋊C412yes—
1048C42C2×C22⋊C412yes—
1049C42C2×C22⋊C412yes—
1050C42C23×C412yes—
1051C42C23×C412yes—
1052C42C22×D412yes—
1053C42C22×D412yes—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—24no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—41no—
1085C23—41no—
1086C23—42no—
1087C23—44no—
1088C23—44no—
1089C23—44no—
1090C23—44no—
1091C23—44no—
1092C23—82no—
1093C23—82no—
1094C23—82no—
1095C23—82no—
1096C23—88no—
1097C23—88no—
1098C23—168no—
1099C23C22×C22⋊C411yescharacteristic
1100C23C22×C22⋊C412yes—
1101C23C22×C22⋊C412yes—
1102C23C22×C22⋊C411yescharacteristic
1103C23C22×C22⋊C411yescharacteristic
1104C23C22×C22⋊C411yescharacteristic
1105C23C22×C22⋊C411yescharacteristic
1106C23C22×C22⋊C411yescharacteristic
1107C23#57514yes—
1108C23C23×D411yescharacteristic
1109Q8—44no—
1110Q8—44no—
1111Q8—82no—
1112Q8—82no—
1113D4—24no—
1114D4—24no—
1115D4—24no—
1116D4—24no—
1117D4—42no—
1118D4—42no—
1119D4—42no—
1120D4—42no—
1121D4—44no—
1122D4—44no—
1123D4—48no—
1124D4—48no—
1125D4—48no—
1126D4—48no—
1127D4—82no—
1128D4—82no—
1129D4—84no—
1130D4—84no—
1131D4—84no—
1132D4—84no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—82no—
1206C2×C4—82no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—164no—
1210C2×C4—164no—
1211C2×C4C22×C22⋊C412yes—
1212C2×C4C22×C22⋊C412yes—
1213C2×C4C22×C22⋊C412yes—
1214C2×C4C22×C22⋊C412yes—
1215C2×C4C22×C22⋊C411yescharacteristic
1216C2×C4C22×C22⋊C411yescharacteristic
1217C2×C4C22×C22⋊C412yes—
1218C2×C4C22×C22⋊C412yes—
1219C2×C4C22×C22⋊C411yescharacteristic
1220C2×C4C22×C22⋊C411yescharacteristic
1221C2×C4C22×C22⋊C411yescharacteristic
1222C2×C4C22×C22⋊C411yescharacteristic
1223C2×C4C24×C411yescharacteristic
1224C2×C4C23×D411yescharacteristic
1225C8—44no—
1226C8—44no—
1227C22—21no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—22no—
1238C22—22no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—22no—
1243C22—22no—
1244C22—21no—
1245C22—21no—
1246C22—21no—
1247C22—22no—
1248C22—22no—
1249C22—21no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—82no—
1259C22—82no—
1260C22—84no—
1261C22—82no—
1262C22—82no—
1263C22—88no—
1264C22—84no—
1265C22—164no—
1266C22—164no—
1267C22#288312yes—
1268C22#289612yes—
1269C22#289612yes—
1270C22C23×C22⋊C411yescharacteristic
1271C22C2×#57512yes—
1272C4—21no—
1273C4—21no—
1274C4—21no—
1275C4—21no—
1276C4—22no—
1277C4—22no—
1278C4—21no—
1279C4—21no—
1280C4—21no—
1281C4—21no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—82no—
1290C4—82no—
1291C4—82no—
1292C4—82no—
1293C2—22no—
1294C2—22no—
1295C2—22no—
1296C2—22no—
1297C2—41no—
1298C2—42no—
1299C2—41no—
1300C2—41no—
1301C2—42no—
1302C2—84no—
1303C2C2×#288311yescharacteristic
1304C2C2×#289611yescharacteristic
1305C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
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. #17625C2semidirect
5. #17623C2semidirect
6. #17622C2semidirect
7. #17615C2semidirect
8. #17587C2semidirect
9. #17580C2semidirect
10. #17578C2semidirect
11. #17577C2semidirect
12. #17559C2semidirect
13. #17554C2semidirect
14. C2×#1511C2semidirect
15. C2×#1510C2semidirect
22. #3505C4semidirect
23. #3505C4semidirect
29. C2×#553C4semidirect
30. C2×#552C4semidirect
32. C2×#548C4semidirect
33. C2×#546C4semidirect
43. #2975C22semidirect
46. #2973C22semidirect
47. #2973C22semidirect
48. #2972C22semidirect
51. #2920C22semidirect
54. C2×#407C22semidirect
55. #2357C22semidirect
56. #2353C22semidirect
57. #2353C22semidirect
58. #2349C22semidirect
66. #2283C22semidirect
67. #2283C22semidirect
69. #2280C22semidirect
71. C2×#381C22semidirect
73. #1521C22semidirect
74. #1520C22semidirect
75. #1519C22semidirect
76. #1516C22semidirect
77. #1513C22semidirect
78. #1512C22semidirect
79. #1511C22semidirect
80. #1511C22semidirect
81. #1511C22semidirect
82. #1511C22semidirect
83. #1511C22semidirect
88. #1510C22semidirect
89. #1509C22semidirect
90. #1508C22semidirect
91. #1507C22semidirect
92. #1504C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#328C22semidirect
96. C2×#327C22semidirect
97. C22×#41C2×C4semidirect
98. C23×Q8C2×C4semidirect
100. C23×D4C2×C4semidirect
120. #553C2×C4semidirect
121. #553C2×C4semidirect
122. #553C2×C4semidirect
128. #552C2×C4semidirect
129. #552C2×C4semidirect
130. #552C2×C4semidirect
144. #548C2×C4semidirect
145. #548C2×C4semidirect
146. #548C2×C4semidirect
152. #546C2×C4semidirect
153. #546C2×C4semidirect
154. #546C2×C4semidirect
177. #529C2×C4semidirect
178. #529C2×C4semidirect
185. C2×#125C2×C4semidirect
187. C2×#124C2×C4semidirect
192. #525C2×C4semidirect
193. #525C2×C4semidirect
208. C2×C22⋊Q8C2×C4semidirect
209. C2×C22⋊Q8C2×C4semidirect
210. C2×C22⋊Q8C2×C4semidirect
211. C2×C22⋊Q8C2×C4semidirect
224. C2×#121C2×C4semidirect
225. C2×#121C2×C4semidirect
226. C2×#121C2×C4semidirect
227. C2×#121C2×C4semidirect
239. C2×C4×Q8C2×C4semidirect
250. C2×C4×D4C2×C4semidirect
267. C2×#117C2×C4semidirect
269. C22×C4⋊C4C2×C4semidirect
270. C22×C4⋊C4C2×C4semidirect
289. #432C23semidirect
291. #431C23semidirect
303. #407C23semidirect
309. C2×C22⋊C8C23semidirect
324. #383C23semidirect
326. #382C23semidirect
336. #381C23semidirect
342. #380C23semidirect
347. C4×C4⋊C4C23semidirect
355. C4×C22⋊C4C23semidirect
357. #376C23semidirect
361. C2×#95C23semidirect
362. #328C23semidirect
363. #328C23semidirect
364. #328C23semidirect
365. #328C23semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
#602302
#341902
#176252
#176232
#176222
#176152
#175872
#175802
#175782
#175772
#175592
#175542
C2×#15112
C2×#15102