Finite Group Databasebeta

← #6343487

Subgroups — #6343487

Order 512.

3148 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C211yesmaximal, characteristic
2#60124C211yesmaximal, characteristic, complemented
3#34109C211yesmaximal, characteristic, complemented
4#17610C214yesmaximal, complemented
5#17607C214yesmaximal, complemented
6#17604C218yesmaximal, complemented
7#17583C212yesmaximal, complemented
8#17582C211yesmaximal, characteristic, complemented
9#17579C212yesmaximal, complemented
10#17577C211yesmaximal, characteristic, complemented
11#17544C212yesmaximal, complemented
12#17542C211yesmaximal, characteristic, complemented
13#17537C212yesmaximal, complemented
14C2×#1507C211yesmaximal, characteristic, complemented
15#3494—21no—
16#3494—21no—
17#3494—22no—
18#3494—21no—
19#3494—21no—
20#3494—22no—
21#3494C414yescomplemented
22#3494C412yescomplemented
23#3494C412yescomplemented
24#3494C2214yes—
25#3494C2212yes—
26#3494C2212yes—
27C2×#555—21no—
28C2×#553—21no—
29C2×#553—21no—
30C2×#551—22no—
31C2×#547—21no—
32C2×#546—22no—
33C2×#544C411yescharacteristic, complemented
34C2×#542C412yescomplemented
35C2×#540C412yescomplemented
36C2×#535C411yescharacteristic, complemented
37C2×#532C2212yes—
38C2×#529C2212yes—
39C2×#525C2211yescharacteristic
40C22×#121C2211yescharacteristic
41C2×#520C411yescharacteristic, complemented
42C2×#518C411yescharacteristic, complemented
43C22×#117C2211yescharacteristic
44#2924—22no—
45#2924—21no—
46#2924—21no—
47#2924C2214yescomplemented
48#2924C2212yescomplemented
49#2924C2212yescomplemented
50#2921—22no—
51#2920C2212yescomplemented
52#2920C2212yescomplemented
53#2905—21no—
54C2×#407C2211yescharacteristic
55C2×#407C2211yescharacteristic
56#2873—21no—
57#2347C2212yescomplemented
58#2346C2212yescomplemented
59#2345—21no—
60#2344—21no—
61#2343C2214yescomplemented
62#2342—22no—
63#2298—22no—
64#2296—21no—
65#2283C2212yescomplemented
66#2280C2211yescharacteristic
67C4×#117—21no—
68C4×#117C2212yescomplemented
69C2×C4×C22⋊C4C2211yescharacteristic
70#1521C2218yescomplemented
71#1519C2214yescomplemented
72#1517C2218yescomplemented
73#1516C2214yescomplemented
74#1514C2218yescomplemented
75#1513C2214yescomplemented
76#1512C2218yescomplemented
77#1510C2214yescomplemented
78#1509C2218yescomplemented
79#1508C2211yescharacteristic, complemented
80#1508C2212yescomplemented
81#1508C2211yescharacteristic, complemented
82#1507C2212yes—
83#1507C2212yes—
84#1507C2212yes—
85#1507C2212yes—
86#1507C2214yescomplemented
87#1507C2211yescharacteristic, complemented
88#1507C2211yescharacteristic, complemented
89#1507C2212yescomplemented
90#1505C2218yescomplemented
91#1504C2214yescomplemented
92#1502C2218yescomplemented
93#1501C2214yescomplemented
94#1500C2218yescomplemented
95C2×#327C2214yescomplemented
96C22×#41—22no—
97C22×#41C2×C411yescharacteristic
98C23×D4—21no—
99C23×D4C2×C411yescharacteristic
100C24×C4C2311yescharacteristic
101C22×M16—21no—
102C22×M16—21no—
103#555—24no—
104#555—22no—
105#555—22no—
106#555—24no—
107#555—22no—
108#555—22no—
109#553—24no—
110#553—22no—
111#553—22no—
112#553—24no—
113#553—22no—
114#553—22no—
115#553—24no—
116#553—22no—
117#553—22no—
118#553—22no—
119#553—24no—
120#553—22no—
121#551—24no—
122#551—24no—
123#551—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#551—24no—
128#551—24no—
129#547—24no—
130#547—22no—
131#547—22no—
132#547—24no—
133#547—22no—
134#547—22no—
135#546—24no—
136#546—24no—
137#546—24no—
138#546—24no—
139#546—24no—
140#546—24no—
141#546—24no—
142#546—24no—
143#544—21no—
144#544—21no—
145#544—22no—
146#544C2×C414yes—
147#544C2×C412yescomplemented
148#544C2×C412yescomplemented
149#542—22no—
150#542—22no—
151#542—22no—
152#542—22no—
153#542C2×C414yes—
154#542C2×C414yes—
155#542C2×C414yescomplemented
156#542C2×C414yescomplemented
157#540—22no—
158#540—22no—
159#540—22no—
160#540—22no—
161#540C2×C414yes—
162#540C2×C414yes—
163#540C2×C414yescomplemented
164#540C2×C414yescomplemented
165#535—21no—
166#535—21no—
167#535—22no—
168#535C2×C414yes—
169#535C2×C412yescomplemented
170#535C2×C412yescomplemented
171#532—22no—
172#532—22no—
173#532—22no—
174#532—22no—
175#532C2×C414yescomplemented
176#532C2×C414yescomplemented
177#532C2314yes—
178#532C2314yes—
179C2×C4⋊Q8—21no—
180C2×C4⋊Q8C2×C412yescomplemented
181C2×#127C2×C412yescomplemented
182#529—22no—
183#529—22no—
184#529—22no—
185#529—22no—
186#529C2×C414yescomplemented
187#529C2×C414yescomplemented
188#529C2314yes—
189#529C2314yes—
190C2×#126—22no—
191C2×#126—22no—
192C2×#125—21no—
193C2×#125C2×C412yescomplemented
194C2×#124—22no—
195C2×#124—22no—
196C2×#124C2×C412yescomplemented
197#525—21no—
198#525—21no—
199#525—21no—
200#525—21no—
201#525C2×C412yes—
202#525C2×C412yes—
203#525C2312yes—
204#525C2312yes—
205C2×#123—21no—
206C2×#123—22no—
207C2×#123—22no—
208C2×#123—22no—
209C2×#123—22no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8—22no—
212C2×C22⋊Q8C2×C411yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121—22no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—22no—
224C2×#121—22no—
225C2×#121C2×C412yes—
226C2×#121C2×C412yes—
227C2×#121C2×C412yes—
228C2×#121C2×C411yescharacteristic
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—22no—
235#520—22no—
236#520—21no—
237#520—21no—
238#520C2×C414yes—
239#520C2×C412yescomplemented
240#520C2×C412yescomplemented
241#518—21no—
242#518—21no—
243#518—22no—
244#518C2×C414yes—
245#518C2×C412yescomplemented
246#518C2×C412yescomplemented
247C2×C4×Q8C2×C412yescomplemented
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—22no—
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—22no—
254C2×C4×D4—22no—
255C2×C4×D4C2×C412yescomplemented
256C2×C4×D4C2×C412yescomplemented
257C2×C4×D4C2×C412yescomplemented
258C2×#117—22no—
259C2×#117—21no—
260C2×#117—21no—
261C2×#117—22no—
262C2×#117C2×C411yescharacteristic
263C2×#117C2×C411yescharacteristic
264C2×#117C2×C411yescharacteristic
265C2×#117C2×C412yes—
266C2×#117C2×C412yes—
267C2×#117C2×C411yescharacteristic
268C2×#117C2×C411yescharacteristic
269C2×#117D411yescharacteristic
270C2×#117D411yescharacteristic
271C2×#117D412yes—
272C2×#117D412yes—
273C2×#117D411yescharacteristic
274C2×#117D411yescharacteristic
275C2×#117D411yescharacteristic
276C2×#117D411yescharacteristic
277C2×#117D412yes—
278C2×#117C2312yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×C411yescharacteristic
283C22×C4⋊C4D411yescharacteristic
284C22×C4⋊C4D411yescharacteristic
285C22×C22⋊C4—21no—
286C22×C22⋊C4—22no—
287C22×C22⋊C4—21no—
288C22×C22⋊C4D412yes—
289C22×C42—21no—
290C22×C42C2312yes—
291#433—24no—
292#433—24no—
293#433—24no—
294#433—24no—
295#432—22no—
296#432—22no—
297#432C2314yescomplemented
298#432C2314yescomplemented
299#431—22no—
300#431—22no—
301#431C2314yescomplemented
302#431C2314yescomplemented
303#424—24no—
304#424—22no—
305#424—22no—
306#423—22no—
307#423—22no—
308#407—21no—
309#407—21no—
310#407—21no—
311#407—21no—
312#407C2312yes—
313#407C2311yescharacteristic
314#407C2311yescharacteristic
315#407C2312yes—
316#407C2312yes—
317C2×C22⋊C8—21no—
318C2×C22⋊C8—21no—
319C2×C22⋊C8C2312yes—
320C2×C22⋊C8C2312yes—
321#405—24no—
322#405—22no—
323#405—22no—
324C4×M16—22no—
325C4×M16—22no—
326#389—22no—
327#389—22no—
328#388—24no—
329#388—24no—
330#387—24no—
331#387—24no—
332#385—24no—
333#383C2314yescomplemented
334#382C2314yescomplemented
335#381—22no—
336#381C2312yes—
337#380—22no—
338#380—21no—
339#380C2312yes—
340#379—21no—
341C4×C4⋊C4—22no—
342C4×C4⋊C4—22no—
343C4×C4⋊C4—22no—
344C4×C4⋊C4—22no—
345C4×C4⋊C4C2314yescomplemented
346C4×C22⋊C4—22no—
347C4×C22⋊C4—21no—
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—24no—
351C4×C22⋊C4C2312yes—
352C4×C22⋊C4C2311yescharacteristic
353C4×C22⋊C4C2311yescharacteristic
354C4×C22⋊C4C2312yes—
355#376—22no—
356#376C2314yescomplemented
357C2×#95C2312yes—
358C43—22no—
359#328C2314yescomplemented
360#328C2318yescomplemented
361#328C2314yescomplemented
362#327C2318yes—
363#327C2318yes—
364#327C2318yes—
365#327C2318yes—
366#327C2314yescomplemented
367#327C2314yescomplemented
368#327C2318yescomplemented
369C25—21no—
370C25C2×D411yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—44no—
378C2×#41—88no—
379C2×#41C22×C412yes—
380C2×#41C22×C412yes—
381C22×Q8—22no—
382C22×Q8C22×C411yescharacteristic
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—22no—
386C22×D4—21no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—44no—
398C22×D4—84no—
399C22×D4C22×C412yes—
400C22×D4C22×C411yescharacteristic
401C22×D4C22×C412yes—
402C22×D4C22×C412yes—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4C22×C411yescharacteristic
411C23×C4C22×C411yescharacteristic
412C23×C4C22×C411yescharacteristic
413C23×C4C22×C411yescharacteristic
414C23×C4C2×D411yescharacteristic
415C23×C4C2×D411yescharacteristic
416C23×C4C2×D412yes—
417C23×C4C2×D412yes—
418C23×C4C2×D411yescharacteristic
419C23×C4C2×D411yescharacteristic
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C2×M16—22no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16—44no—
432C2×M16—44no—
433C22×C8—22no—
434C22×C8—22no—
435C4⋊Q8—24no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8—22no—
440C4⋊Q8C22×C414yes—
441C4⋊Q8C22×C414yes—
442#127—22no—
443#127—22no—
444#127C22×C414yes—
445#127C22×C414yes—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—24no—
452#126—24no—
453#126—24no—
454#125—24no—
455#125—22no—
456#125—22no—
457#125—22no—
458#125—22no—
459#125C22×C414yes—
460#125C22×C414yes—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—24no—
467#124—22no—
468#124—22no—
469#124—24no—
470#124—24no—
471#124C22×C414yes—
472#124C22×C414yes—
473#123—22no—
474#123—22no—
475#123—24no—
476#123—24no—
477#123—22no—
478#123—22no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
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—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8C22×C412yes—
506C22⋊Q8C22×C412yes—
507C22⋊Q8C22×C412yes—
508C22⋊Q8C2412yes—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—24no—
516#121—24no—
517#121—21no—
518#121—21no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—24no—
526#121—24no—
527#121—21no—
528#121—21no—
529#121—24no—
530#121—24no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—24no—
536#121—24no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121C22×C414yes—
544#121C22×C414yes—
545#121C22×C414yes—
546#121C22×C412yes—
547#121C22×C412yes—
548#121C22×C412yes—
549#121C2414yes—
550#121C2412yes—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—22no—
555#120—24no—
556#120—24no—
557#120—24no—
558#120—24no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8C22×C414yes—
562C4×Q8C22×C414yes—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4C22×C414yes—
596C4×D4C22×C414yes—
597C4×D4C22×C414yes—
598C4×D4C22×C414yes—
599C4×D4C22×C414yes—
600C4×D4C22×C414yes—
601#117—21no—
602#117—21no—
603#117—24no—
604#117—22no—
605#117—22no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—48no—
611#117—44no—
612#117C22⋊C412yes—
613#117C22⋊C411yescharacteristic
614#117C22⋊C411yescharacteristic
615#117C22⋊C412yes—
616#117C22⋊C411yescharacteristic
617#117C22⋊C411yescharacteristic
618#117C22⋊C412yes—
619#117C22⋊C412yes—
620#117C22⋊C412yes—
621#117C22⋊C412yes—
622#117C22⋊C412yes—
623#117C22⋊C412yes—
624#117C22⋊C412yes—
625#117C22⋊C412yes—
626#117C22⋊C411yescharacteristic
627#117C22⋊C411yescharacteristic
628#117C22⋊C412yes—
629#117C22⋊C411yescharacteristic
630#117C22⋊C411yescharacteristic
631#117C22⋊C412yes—
632#117C22×C412yes—
633#117C22×C412yes—
634#117C22×C412yes—
635#117C22×C411yescharacteristic
636#117C22×C411yescharacteristic
637#117C22×C412yes—
638#117C22×C411yescharacteristic
639#117C22×C411yescharacteristic
640#117C22×C412yes—
641#117C22×C412yes—
642#117C22×C412yes—
643#117C22×C412yes—
644#117C2×D412yes—
645#117C2×D412yes—
646#117C2×D412yes—
647#117C2×D412yes—
648#117C2×D411yescharacteristic
649#117C2×D411yescharacteristic
650#117C2×D412yes—
651#117C2×D411yescharacteristic
652#117C2×D411yescharacteristic
653#117C2×D412yes—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—24no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—24no—
669C2×C4⋊C4C22⋊C411yescharacteristic
670C2×C4⋊C4C22⋊C411yescharacteristic
671C2×C4⋊C4C22⋊C411yescharacteristic
672C2×C4⋊C4C22⋊C411yescharacteristic
673C2×C4⋊C4C22⋊C412yes—
674C2×C4⋊C4C22⋊C412yes—
675C2×C4⋊C4C22⋊C411yescharacteristic
676C2×C4⋊C4C22⋊C411yescharacteristic
677C2×C4⋊C4C22⋊C412yes—
678C2×C4⋊C4C22⋊C411yescharacteristic
679C2×C4⋊C4C22⋊C411yescharacteristic
680C2×C4⋊C4C22⋊C412yes—
681C2×C4⋊C4C22×C412yes—
682C2×C4⋊C4C22×C412yes—
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C22×C411yescharacteristic
685C2×C4⋊C4C22×C411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D412yes—
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D412yes—
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—44no—
719C2×C22⋊C4C22⋊C412yes—
720C2×C22⋊C4C22⋊C412yes—
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⋊C4C2×D412yes—
728C2×C22⋊C4C2×D412yes—
729C2×C22⋊C4C2×D412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C42—22no—
732C2×C42—21no—
733C2×C42—22no—
734C2×C42—24no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—22no—
738C2×C42—24no—
739C2×C42—44no—
740C2×C42C22×C412yes—
741C2×C42C22×C412yes—
742C2×C42C22×C412yes—
743C2×C42C22×C412yes—
744C2×C42C2×D412yes—
745C2×C42C2×D412yes—
746C2×C42C2×D412yes—
747C2×C42C2×D412yes—
748C2×C42C2×D412yes—
749C2×C42C2×D412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C4⋊C8—24no—
753C4⋊C8—24no—
754C4⋊C8—24no—
755C4⋊C8—24no—
756C22⋊C8—22no—
757C22⋊C8—21no—
758C22⋊C8—21no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8C2414yes—
764C22⋊C8C2412yes—
765C22⋊C8C2412yes—
766#97—24no—
767#97—24no—
768C4×C8—24no—
769C4×C8—24no—
770#95—22no—
771#95—24no—
772#95—24no—
773#95—24no—
774#95—22no—
775#95—24no—
776#95C2412yes—
777#95C2412yes—
778#95C2414yes—
779C24—22no—
780C24—21no—
781C24—22no—
782C24—22no—
783C24—42no—
784C24—42no—
785C24—42no—
786C24—44no—
787C24—82no—
788C24—82no—
789C24C2×C22⋊C411yescharacteristic
790C24C2×C22⋊C411yescharacteristic
791C24C2×C22⋊C411yescharacteristic
792C24C2×C22⋊C411yescharacteristic
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C24C22×D411yescharacteristic
796#41—44no—
797#41—44no—
798#41—44no—
799#41—44no—
800#41—88no—
801#41—88no—
802#41—88no—
803#41—88no—
804C2×Q8—21no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—42no—
808C2×Q8—84no—
809C2×Q8C23×C412yes—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—21no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—42no—
834C2×D4—48no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—84no—
839C2×D4—82no—
840C2×D4—84no—
841C2×D4—84no—
842C2×D4—84no—
843C2×D4—84no—
844C2×D4—84no—
845C2×D4—84no—
846C2×D4C23×C414yes—
847C2×D4C23×C412yes—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4C2×C22⋊C412yes—
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C412yes—
892C22×C4C2×C22⋊C411yescharacteristic
893C22×C4C2×C22⋊C411yescharacteristic
894C22×C4C2×C22⋊C411yescharacteristic
895C22×C4C2×C22⋊C411yescharacteristic
896C22×C4C2×C22⋊C411yescharacteristic
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C412yes—
899C22×C4C2×C22⋊C412yes—
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C412yes—
902C22×C4C2×C22⋊C412yes—
903C22×C4C2×C22⋊C412yes—
904C22×C4C2×C22⋊C411yescharacteristic
905C22×C4C2×C22⋊C411yescharacteristic
906C22×C4C2×C22⋊C411yescharacteristic
907C22×C4C2×C22⋊C411yescharacteristic
908C22×C4C2×C22⋊C411yescharacteristic
909C22×C4C23×C411yescharacteristic
910C22×C4C23×C411yescharacteristic
911C22×C4C23×C411yescharacteristic
912C22×C4C23×C411yescharacteristic
913C22×C4C23×C411yescharacteristic
914C22×C4C23×C411yescharacteristic
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2511yescharacteristic
929M16—44no—
930M16—44no—
931M16—44no—
932M16—42no—
933M16—42no—
934C2×C8—22no—
935C2×C8—24no—
936C2×C8—22no—
937C2×C8—44no—
938C2×C8—44no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—22no—
956C4⋊C4—44no—
957C4⋊C4—48no—
958C4⋊C4—84no—
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C411yescharacteristic
961C4⋊C4C2×C22⋊C411yescharacteristic
962C4⋊C4C2×C22⋊C412yes—
963C4⋊C4C2×C22⋊C411yescharacteristic
964C4⋊C4C2×C22⋊C411yescharacteristic
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C411yescharacteristic
967C4⋊C4C2×C22⋊C411yescharacteristic
968C4⋊C4C2×C22⋊C412yes—
969C4⋊C4C2×C22⋊C411yescharacteristic
970C4⋊C4C2×C22⋊C411yescharacteristic
971C4⋊C4C2×C22⋊C412yes—
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C412yes—
974C4⋊C4C2×C22⋊C412yes—
975C4⋊C4C2×C22⋊C412yes—
976C4⋊C4C2×C22⋊C412yes—
977C4⋊C4C2×C22⋊C412yes—
978C4⋊C4C2×C22⋊C412yes—
979C4⋊C4C23×C414yes—
980C4⋊C4C23×C412yes—
981C4⋊C4C23×C412yes—
982C22⋊C4—24no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
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—22no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—24no—
1006C22⋊C4—22no—
1007C22⋊C4—44no—
1008C22⋊C4—42no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—82no—
1012C22⋊C4C2×C22⋊C412yes—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C22⋊C4C2×C22⋊C412yes—
1018C22⋊C4C2×C22⋊C412yes—
1019C22⋊C4C2×C22⋊C412yes—
1020C22⋊C4C2×C22⋊C412yes—
1021C22⋊C4C2×C22⋊C412yes—
1022C22⋊C4C2×C22⋊C412yes—
1023C22⋊C4C2×C22⋊C412yes—
1024C22⋊C4C2×C22⋊C412yes—
1025C22⋊C4C2×C22⋊C412yes—
1026C22⋊C4C2×C22⋊C412yes—
1027C22⋊C4C2×C22⋊C412yes—
1028C42—24no—
1029C42—24no—
1030C42—22no—
1031C42—22no—
1032C42—42no—
1033C42—42no—
1034C42—44no—
1035C42—44no—
1036C42—48no—
1037C42—84no—
1038C42C2×C22⋊C412yes—
1039C42C2×C22⋊C412yes—
1040C42C2×C22⋊C412yes—
1041C42C2×C22⋊C412yes—
1042C42C2×C22⋊C412yes—
1043C42C2×C22⋊C412yes—
1044C42C2×C22⋊C412yes—
1045C42C2×C22⋊C412yes—
1046C42C23×C412yes—
1047C42C23×C412yes—
1048C42C23×C412yes—
1049C42C23×C412yes—
1050C42C22×D412yes—
1051C42C22×D412yes—
1052C42C22×D412yes—
1053C42C22×D412yes—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—44no—
1080C23—44no—
1081C23—44no—
1082C23—44no—
1083C23—42no—
1084C23—44no—
1085C23—82no—
1086C23—82no—
1087C23—82no—
1088C23—82no—
1089C23—88no—
1090C23—168no—
1091C23C22×C22⋊C411yescharacteristic
1092C23C22×C22⋊C411yescharacteristic
1093C23C22×C22⋊C411yescharacteristic
1094C23C22×C22⋊C411yescharacteristic
1095C23C22×C22⋊C411yescharacteristic
1096C23C22×C22⋊C411yescharacteristic
1097C23C23×D411yescharacteristic
1098Q8—42no—
1099Q8—42no—
1100Q8—84no—
1101Q8—84no—
1102D4—44no—
1103D4—42no—
1104D4—44no—
1105D4—48no—
1106D4—44no—
1107D4—44no—
1108D4—48no—
1109D4—44no—
1110D4—44no—
1111D4—44no—
1112D4—44no—
1113D4—42no—
1114D4—84no—
1115D4—84no—
1116D4—84no—
1117D4—84no—
1118D4—82no—
1119D4—82no—
1120D4—84no—
1121D4—84no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—44no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—44no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—44no—
1174C2×C4—42no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—42no—
1178C2×C4—44no—
1179C2×C4—42no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—82no—
1187C2×C4—82no—
1188C2×C4—88no—
1189C2×C4#41014yes—
1190C2×C4C22×C22⋊C412yes—
1191C2×C4C22×C22⋊C412yes—
1192C2×C4C22×C22⋊C411yescharacteristic
1193C2×C4C22×C22⋊C411yescharacteristic
1194C2×C4C22×C22⋊C412yes—
1195C2×C4C22×C22⋊C412yes—
1196C2×C4C22×C22⋊C412yes—
1197C2×C4C22×C22⋊C412yes—
1198C2×C4C22×C22⋊C412yes—
1199C2×C4C22×C22⋊C412yes—
1200C2×C4C22×C22⋊C411yescharacteristic
1201C2×C4C22×C22⋊C411yescharacteristic
1202C2×C4C22×C22⋊C411yescharacteristic
1203C2×C4C22×C22⋊C411yescharacteristic
1204C2×C4C24×C411yescharacteristic
1205C2×C4C23×D411yescharacteristic
1206C8—44no—
1207C8—42no—
1208C8—42no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—21no—
1226C22—21no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—42no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—84no—
1240C22—88no—
1241C22—82no—
1242C22—164no—
1243C22—164no—
1244C22C2×#41012yes—
1245C22#290112yes—
1246C22C23×C22⋊C411yescharacteristic
1247C22#358512yes—
1248C4—21no—
1249C4—21no—
1250C4—21no—
1251C4—21no—
1252C4—21no—
1253C4—21no—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—22no—
1262C4—44no—
1263C4—42no—
1264C4—44no—
1265C4—42no—
1266C4—42no—
1267C4—84no—
1268C4—82no—
1269C4C2×#41012yes—
1270C4C2×#41012yes—
1271C2—22no—
1272C2—22no—
1273C2—22no—
1274C2—41no—
1275C2—41no—
1276C2—41no—
1277C2—41no—
1278C2—82no—
1279C2—84no—
1280C2C22×#41011yescharacteristic
1281C2#6008711yescharacteristic
1282C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3494C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60124C2semidirect
3. #34109C2semidirect
4. #17610C2semidirect
5. #17607C2semidirect
6. #17604C2semidirect
7. #17583C2semidirect
8. #17582C2semidirect
9. #17579C2semidirect
10. #17577C2semidirect
11. #17544C2semidirect
12. #17542C2semidirect
13. #17537C2semidirect
14. C2×#1507C2semidirect
21. #3494C4semidirect
22. #3494C4semidirect
23. #3494C4semidirect
33. C2×#544C4semidirect
34. C2×#542C4semidirect
35. C2×#540C4semidirect
36. C2×#535C4semidirect
41. C2×#520C4semidirect
42. C2×#518C4semidirect
47. #2924C22semidirect
48. #2924C22semidirect
49. #2924C22semidirect
51. #2920C22semidirect
52. #2920C22semidirect
57. #2347C22semidirect
58. #2346C22semidirect
61. #2343C22semidirect
65. #2283C22semidirect
68. C4×#117C22semidirect
70. #1521C22semidirect
71. #1519C22semidirect
72. #1517C22semidirect
73. #1516C22semidirect
74. #1514C22semidirect
75. #1513C22semidirect
76. #1512C22semidirect
77. #1510C22semidirect
78. #1509C22semidirect
79. #1508C22semidirect
80. #1508C22semidirect
81. #1508C22semidirect
86. #1507C22semidirect
87. #1507C22semidirect
88. #1507C22semidirect
89. #1507C22semidirect
90. #1505C22semidirect
91. #1504C22semidirect
92. #1502C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#327C22semidirect
147. #544C2×C4semidirect
148. #544C2×C4semidirect
155. #542C2×C4semidirect
156. #542C2×C4semidirect
163. #540C2×C4semidirect
164. #540C2×C4semidirect
169. #535C2×C4semidirect
170. #535C2×C4semidirect
175. #532C2×C4semidirect
176. #532C2×C4semidirect
180. C2×C4⋊Q8C2×C4semidirect
181. C2×#127C2×C4semidirect
186. #529C2×C4semidirect
187. #529C2×C4semidirect
193. C2×#125C2×C4semidirect
196. C2×#124C2×C4semidirect
239. #520C2×C4semidirect
240. #520C2×C4semidirect
245. #518C2×C4semidirect
246. #518C2×C4semidirect
247. C2×C4×Q8C2×C4semidirect
255. C2×C4×D4C2×C4semidirect
256. C2×C4×D4C2×C4semidirect
257. C2×C4×D4C2×C4semidirect
297. #432C23semidirect
298. #432C23semidirect
301. #431C23semidirect
302. #431C23semidirect
333. #383C23semidirect
334. #382C23semidirect
345. C4×C4⋊C4C23semidirect
356. #376C23semidirect
359. #328C23semidirect
360. #328C23semidirect
361. #328C23semidirect
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×#34942
#601242
#341092
#176102
#176072
#176042
#175832
#175822
#175792
#175772
#175442
#175422
#175372
C2×#15072