Finite Group Databasebeta

← #6343628

Subgroups — #6343628

Order 512.

3134 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×#3494C211yesmaximal, characteristic
2C2×#2924C211yesmaximal, characteristic, complemented
3#34180C211yesmaximal, characteristic, complemented
4#17610C214yesmaximal, complemented
5#17607C214yesmaximal, complemented
6#17604C218yesmaximal, complemented
7#17595C212yesmaximal, complemented
8#17592C211yesmaximal, characteristic, complemented
9#17581C212yesmaximal, complemented
10#17577C211yesmaximal, characteristic, complemented
11#17574C212yesmaximal, complemented
12#17572C211yesmaximal, characteristic, complemented
13#17567C212yesmaximal, complemented
14C2×#1519C211yesmaximal, characteristic, complemented
15#3494—21no—
16#3494—21no—
17#3494—22no—
18#3494—22no—
19#3494—21no—
20#3494—21no—
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
50C2×#433—22no—
51C2×#432C2212yescomplemented
52C2×#431C2212yescomplemented
53C2×#424—21no—
54C2×#407C2211yescharacteristic
55C22×C22⋊C8C2211yescharacteristic
56C2×#405—21no—
57#2347C2212yescomplemented
58#2346C2212yescomplemented
59#2345—21no—
60#2344—21no—
61#2343C2214yescomplemented
62#2342—22no—
63#2317—21no—
64#2314—22no—
65#2285C2212yescomplemented
66#2283C2212yescomplemented
67#2280C2211yescharacteristic
68C2×#380C2211yescharacteristic
69#2274—21no—
70#1521C2218yescomplemented
71#1520C2211yescharacteristic, complemented
72#1520C2212yescomplemented
73#1520C2211yescharacteristic, complemented
74#1519C2212yes—
75#1519C2212yes—
76#1519C2212yes—
77#1519C2212yes—
78#1519C2214yescomplemented
79#1519C2211yescharacteristic, complemented
80#1519C2211yescharacteristic, complemented
81#1519C2212yescomplemented
82#1517C2218yescomplemented
83#1516C2214yescomplemented
84#1514C2218yescomplemented
85#1513C2214yescomplemented
86#1512C2218yescomplemented
87#1510C2214yescomplemented
88#1509C2218yescomplemented
89#1507C2214yescomplemented
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—
102C23×C8—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—21no—
259C2×#117—22no—
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×#117D412yes—
276C2×#117D411yescharacteristic
277C2×#117D411yescharacteristic
278C2×#117C2312yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4—21no—
283C22×C4⋊C4C2×C411yescharacteristic
284C22×C4⋊C4D411yescharacteristic
285C22×C4⋊C4D411yescharacteristic
286C22×C22⋊C4—21no—
287C22×C22⋊C4—22no—
288C22×C22⋊C4—21no—
289C22×C22⋊C4D412yes—
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—
306C2×C4⋊C8—22no—
307C2×C4⋊C8—22no—
308#407—21no—
309#407—21no—
310#407C2312yes—
311#407C2312yes—
312C2×C22⋊C8—21no—
313C2×C22⋊C8—21no—
314C2×C22⋊C8—21no—
315C2×C22⋊C8—21no—
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2312yes—
319C2×C22⋊C8C2312yes—
320C2×C22⋊C8C2312yes—
321#405—24no—
322#405—22no—
323#405—22no—
324C2×#97—22no—
325C2×C4×C8—22no—
326#389—22no—
327#389—22no—
328#388—24no—
329#388—24no—
330#387—24no—
331#387—24no—
332#385—24no—
333#384—22no—
334#383C2314yescomplemented
335#382—22no—
336#382C2314yescomplemented
337#381—22no—
338#381C2312yes—
339#380—21no—
340#380—21no—
341#380—22no—
342#380—21no—
343#380C2312yes—
344#380C2312yes—
345#380C2311yescharacteristic
346#380C2311yescharacteristic
347#379—21no—
348C4×C4⋊C4—22no—
349C4×C4⋊C4—22no—
350C4×C4⋊C4—22no—
351C4×C4⋊C4—22no—
352C4×C4⋊C4C2314yescomplemented
353C4×C22⋊C4—22no—
354C4×C22⋊C4—21no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4C2312yes—
357#376C2314yescomplemented
358C2×#95C2312yes—
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—84no—
379C2×#41—84no—
380C2×#41C22×C412yes—
381C2×#41C22×C412yes—
382C22×Q8—22no—
383C22×Q8C22×C411yescharacteristic
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—22no—
387C22×D4—21no—
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—22no—
397C22×D4—22no—
398C22×D4—44no—
399C22×D4—82no—
400C22×D4—82no—
401C22×D4C22×C412yes—
402C22×D4C22×C411yescharacteristic
403C22×D4C22×C412yes—
404C22×D4C22×C412yes—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—44no—
412C23×C4C22×C411yescharacteristic
413C23×C4C22×C411yescharacteristic
414C23×C4C22×C411yescharacteristic
415C23×C4C22×C411yescharacteristic
416C23×C4C2×D412yes—
417C23×C4C2×D411yescharacteristic
418C23×C4C2×D411yescharacteristic
419C23×C4C2×D411yescharacteristic
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—44no—
431C22×C8—21no—
432C22×C8—21no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—44no—
437C4⋊Q8—24no—
438C4⋊Q8—22no—
439C4⋊Q8—22no—
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C4⋊Q8C22×C414yes—
443C4⋊Q8C22×C414yes—
444#127—22no—
445#127—22no—
446#127C22×C414yes—
447#127C22×C414yes—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—24no—
452#126—24no—
453#126—24no—
454#126—24no—
455#126—24no—
456#125—24no—
457#125—22no—
458#125—22no—
459#125—22no—
460#125—22no—
461#125C22×C414yes—
462#125C22×C414yes—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—24no—
467#124—24no—
468#124—24no—
469#124—22no—
470#124—22no—
471#124—24no—
472#124—24no—
473#124C22×C414yes—
474#124C22×C414yes—
475#123—22no—
476#123—22no—
477#123—24no—
478#123—24no—
479#123—22no—
480#123—22no—
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—
493#123—24no—
494#123—24no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8C22×C412yes—
508C22⋊Q8C22×C412yes—
509C22⋊Q8C22×C412yes—
510C22⋊Q8C2412yes—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—24no—
518#121—24no—
519#121—21no—
520#121—21no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—22no—
527#121—24no—
528#121—24no—
529#121—21no—
530#121—21no—
531#121—24no—
532#121—24no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121C22×C414yes—
546#121C22×C414yes—
547#121C22×C414yes—
548#121C22×C412yes—
549#121C22×C412yes—
550#121C22×C412yes—
551#121C2414yes—
552#121C2412yes—
553#120—22no—
554#120—22no—
555#120—22no—
556#120—22no—
557#120—24no—
558#120—24no—
559#120—24no—
560#120—24no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8C22×C414yes—
564C4×Q8C22×C414yes—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4C22×C414yes—
598C4×D4C22×C414yes—
599C4×D4C22×C414yes—
600C4×D4C22×C414yes—
601C4×D4C22×C414yes—
602C4×D4C22×C414yes—
603#117—21no—
604#117—21no—
605#117—24no—
606#117—22no—
607#117—22no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—44no—
613#117—84no—
614#117C22⋊C412yes—
615#117C22⋊C411yescharacteristic
616#117C22⋊C411yescharacteristic
617#117C22⋊C412yes—
618#117C22⋊C411yescharacteristic
619#117C22⋊C411yescharacteristic
620#117C22⋊C412yes—
621#117C22⋊C412yes—
622#117C22⋊C412yes—
623#117C22⋊C412yes—
624#117C22⋊C412yes—
625#117C22⋊C412yes—
626#117C22⋊C412yes—
627#117C22⋊C412yes—
628#117C22⋊C411yescharacteristic
629#117C22⋊C411yescharacteristic
630#117C22⋊C412yes—
631#117C22⋊C411yescharacteristic
632#117C22⋊C411yescharacteristic
633#117C22⋊C412yes—
634#117C22×C412yes—
635#117C22×C412yes—
636#117C22×C412yes—
637#117C22×C411yescharacteristic
638#117C22×C411yescharacteristic
639#117C22×C412yes—
640#117C22×C411yescharacteristic
641#117C22×C411yescharacteristic
642#117C22×C412yes—
643#117C22×C412yes—
644#117C22×C412yes—
645#117C22×C412yes—
646#117C2×D412yes—
647#117C2×D412yes—
648#117C2×D412yes—
649#117C2×D412yes—
650#117C2×D411yescharacteristic
651#117C2×D411yescharacteristic
652#117C2×D412yes—
653#117C2×D411yescharacteristic
654#117C2×D411yescharacteristic
655#117C2×D412yes—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—24no—
673C2×C4⋊C4—24no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4C22⋊C411yescharacteristic
676C2×C4⋊C4C22⋊C411yescharacteristic
677C2×C4⋊C4C22⋊C411yescharacteristic
678C2×C4⋊C4C22⋊C411yescharacteristic
679C2×C4⋊C4C22⋊C412yes—
680C2×C4⋊C4C22⋊C412yes—
681C2×C4⋊C4C22⋊C411yescharacteristic
682C2×C4⋊C4C22⋊C411yescharacteristic
683C2×C4⋊C4C22⋊C412yes—
684C2×C4⋊C4C22⋊C411yescharacteristic
685C2×C4⋊C4C22⋊C411yescharacteristic
686C2×C4⋊C4C22⋊C412yes—
687C2×C4⋊C4C22×C412yes—
688C2×C4⋊C4C22×C412yes—
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C411yescharacteristic
691C2×C4⋊C4C22×C411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D412yes—
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D412yes—
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—22no—
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—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—24no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—82no—
725C2×C22⋊C4C22⋊C412yes—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C22⋊C412yes—
728C2×C22⋊C4C22⋊C412yes—
729C2×C22⋊C4C22⋊C412yes—
730C2×C22⋊C4C22⋊C412yes—
731C2×C22⋊C4C22⋊C412yes—
732C2×C22⋊C4C22⋊C412yes—
733C2×C22⋊C4C2×D412yes—
734C2×C22⋊C4C2×D412yes—
735C2×C22⋊C4C2×D412yes—
736C2×C22⋊C4C2×D412yes—
737C2×C42—22no—
738C2×C42—21no—
739C2×C42—22no—
740C2×C42—24no—
741C2×C42—24no—
742C2×C42C22×C412yes—
743C2×C42C22×C412yes—
744C2×C42C22×C412yes—
745C2×C42C22×C412yes—
746C2×C42C2×D412yes—
747C2×C42C2×D412yes—
748C2×C42C2×D412yes—
749C2×C42C2×D412yes—
750C2×C42C2×D412yes—
751C2×C42C2×D412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C4⋊C8—24no—
755C4⋊C8—24no—
756C4⋊C8—24no—
757C4⋊C8—24no—
758C22⋊C8—21no—
759C22⋊C8—21no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8C2412yes—
766C22⋊C8C2412yes—
767C22⋊C8C2414yes—
768#97—24no—
769#97—24no—
770C4×C8—24no—
771C4×C8—24no—
772#95—22no—
773#95—24no—
774#95—24no—
775#95—24no—
776#95—22no—
777#95—24no—
778#95C2414yes—
779#95C2412yes—
780#95C2412yes—
781C24—22no—
782C24—22no—
783C24—22no—
784C24—21no—
785C24—22no—
786C24—22no—
787C24—42no—
788C24—44no—
789C24—82no—
790C24—81no—
791C24—82no—
792C24C2×C22⋊C411yescharacteristic
793C24C2×C22⋊C411yescharacteristic
794C24C2×C22⋊C411yescharacteristic
795C24C2×C22⋊C411yescharacteristic
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799#41—44no—
800#41—44no—
801#41—44no—
802#41—44no—
803#41—88no—
804#41—88no—
805#41—84no—
806#41—84no—
807#41—84no—
808#41—84no—
809C2×Q8—21no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—42no—
813C2×Q8—84no—
814C2×Q8C23×C412yes—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—42no—
842C2×D4—44no—
843C2×D4—42no—
844C2×D4—44no—
845C2×D4—84no—
846C2×D4—84no—
847C2×D4—84no—
848C2×D4—82no—
849C2×D4—84no—
850C2×D4—84no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4C23×C414yes—
856C2×D4C23×C412yes—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—82no—
895C22×C4—82no—
896C22×C4—84no—
897C22×C4—82no—
898C22×C4—82no—
899C22×C4C2×C22⋊C411yescharacteristic
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×C4C2×C22⋊C411yescharacteristic
910C22×C4C2×C22⋊C412yes—
911C22×C4C2×C22⋊C412yes—
912C22×C4C2×C22⋊C412yes—
913C22×C4C2×C22⋊C412yes—
914C22×C4C2×C22⋊C411yescharacteristic
915C22×C4C2×C22⋊C411yescharacteristic
916C22×C4C2×C22⋊C411yescharacteristic
917C22×C4C2×C22⋊C411yescharacteristic
918C22×C4C2×C22⋊C411yescharacteristic
919C22×C4C23×C411yescharacteristic
920C22×C4C23×C411yescharacteristic
921C22×C4C23×C411yescharacteristic
922C22×C4C23×C411yescharacteristic
923C22×C4C23×C411yescharacteristic
924C22×C4C23×C411yescharacteristic
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C2511yescharacteristic
939M16—44no—
940M16—44no—
941C2×C8—22no—
942C2×C8—24no—
943C2×C8—22no—
944C2×C8—44no—
945C2×C8—42no—
946C2×C8—42no—
947C2×C8—44no—
948C2×C8—44no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—84no—
971C4⋊C4—84no—
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C411yescharacteristic
974C4⋊C4C2×C22⋊C411yescharacteristic
975C4⋊C4C2×C22⋊C412yes—
976C4⋊C4C2×C22⋊C411yescharacteristic
977C4⋊C4C2×C22⋊C411yescharacteristic
978C4⋊C4C2×C22⋊C412yes—
979C4⋊C4C2×C22⋊C411yescharacteristic
980C4⋊C4C2×C22⋊C411yescharacteristic
981C4⋊C4C2×C22⋊C412yes—
982C4⋊C4C2×C22⋊C411yescharacteristic
983C4⋊C4C2×C22⋊C411yescharacteristic
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⋊C4C2×C22⋊C412yes—
991C4⋊C4C2×C22⋊C412yes—
992C4⋊C4C23×C414yes—
993C4⋊C4C23×C412yes—
994C4⋊C4C23×C412yes—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
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—22no—
1013C22⋊C4—24no—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—82no—
1024C22⋊C4—82no—
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—84no—
1047C42—84no—
1048C42C2×C22⋊C412yes—
1049C42C2×C22⋊C412yes—
1050C42C2×C22⋊C412yes—
1051C42C2×C22⋊C412yes—
1052C42C2×C22⋊C412yes—
1053C42C2×C22⋊C412yes—
1054C42C2×C22⋊C412yes—
1055C42C2×C22⋊C412yes—
1056C42C23×C412yes—
1057C42C23×C412yes—
1058C42C23×C412yes—
1059C42C23×C412yes—
1060C42C22×D412yes—
1061C42C22×D412yes—
1062C42C22×D412yes—
1063C42C22×D412yes—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—24no—
1076C23—22no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—42no—
1089C23—44no—
1090C23—44no—
1091C23—42no—
1092C23—44no—
1093C23—42no—
1094C23—44no—
1095C23—44no—
1096C23—82no—
1097C23—82no—
1098C23—82no—
1099C23—82no—
1100C23—84no—
1101C23—84no—
1102C23—168no—
1103C23C22×C22⋊C411yescharacteristic
1104C23C22×C22⋊C411yescharacteristic
1105C23C22×C22⋊C411yescharacteristic
1106C23C22×C22⋊C411yescharacteristic
1107C23C22×C22⋊C411yescharacteristic
1108C23C22×C22⋊C411yescharacteristic
1109C23#57612yes—
1110C23#57712yes—
1111C23C23×D411yescharacteristic
1112Q8—42no—
1113Q8—42no—
1114Q8—84no—
1115Q8—84no—
1116D4—44no—
1117D4—42no—
1118D4—44no—
1119D4—44no—
1120D4—44no—
1121D4—48no—
1122D4—44no—
1123D4—44no—
1124D4—42no—
1125D4—44no—
1126D4—42no—
1127D4—44no—
1128D4—44no—
1129D4—42no—
1130D4—84no—
1131D4—84no—
1132D4—84no—
1133D4—84no—
1134D4—82no—
1135D4—82no—
1136D4—84no—
1137D4—84no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—44no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—44no—
1187C2×C4—42no—
1188C2×C4—44no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—44no—
1193C2×C4—42no—
1194C2×C4—44no—
1195C2×C4—42no—
1196C2×C4—44no—
1197C2×C4—42no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—82no—
1205C2×C4—82no—
1206C2×C4—164no—
1207C2×C4#41014yes—
1208C2×C4C22×C22⋊C412yes—
1209C2×C4C22×C22⋊C412yes—
1210C2×C4C22×C22⋊C411yescharacteristic
1211C2×C4C22×C22⋊C411yescharacteristic
1212C2×C4C22×C22⋊C412yes—
1213C2×C4C22×C22⋊C412yes—
1214C2×C4C22×C22⋊C412yes—
1215C2×C4C22×C22⋊C412yes—
1216C2×C4C22×C22⋊C412yes—
1217C2×C4C22×C22⋊C412yes—
1218C2×C4C22×C22⋊C411yescharacteristic
1219C2×C4C22×C22⋊C411yescharacteristic
1220C2×C4C22×C22⋊C411yescharacteristic
1221C2×C4C22×C22⋊C411yescharacteristic
1222C2×C4C24×C411yescharacteristic
1223C2×C4C23×D411yescharacteristic
1224C8—42no—
1225C8—42no—
1226C8—44no—
1227C22—21no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—42no—
1256C22—81no—
1257C22—81no—
1258C22—82no—
1259C22—82no—
1260C22—84no—
1261C22—88no—
1262C22—164no—
1263C22—164no—
1264C22C2×#41012yes—
1265C22#289712yes—
1266C22#289712yes—
1267C22C23×C22⋊C411yescharacteristic
1268C22C2×#57611yescharacteristic
1269C22C2×#57711yescharacteristic
1270C4—21no—
1271C4—21no—
1272C4—21no—
1273C4—21no—
1274C4—21no—
1275C4—21no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—42no—
1288C4—82no—
1289C4—82no—
1290C4—84no—
1291C4C2×#41012yes—
1292C4C2×#41012yes—
1293C2—21no—
1294C2—21no—
1295C2—22no—
1296C2—22no—
1297C2—22no—
1298C2—41no—
1299C2—41no—
1300C2—41no—
1301C2—82no—
1302C2—84no—
1303C2C22×#41011yescharacteristic
1304C2C2×#289711yescharacteristic
1305C2#6009311yescharacteristic
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. C2×#2924C2semidirect
3. #34180C2semidirect
4. #17610C2semidirect
5. #17607C2semidirect
6. #17604C2semidirect
7. #17595C2semidirect
8. #17592C2semidirect
9. #17581C2semidirect
10. #17577C2semidirect
11. #17574C2semidirect
12. #17572C2semidirect
13. #17567C2semidirect
14. C2×#1519C2semidirect
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. C2×#432C22semidirect
52. C2×#431C22semidirect
57. #2347C22semidirect
58. #2346C22semidirect
61. #2343C22semidirect
65. #2285C22semidirect
66. #2283C22semidirect
70. #1521C22semidirect
71. #1520C22semidirect
72. #1520C22semidirect
73. #1520C22semidirect
78. #1519C22semidirect
79. #1519C22semidirect
80. #1519C22semidirect
81. #1519C22semidirect
82. #1517C22semidirect
83. #1516C22semidirect
84. #1514C22semidirect
85. #1513C22semidirect
86. #1512C22semidirect
87. #1510C22semidirect
88. #1509C22semidirect
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
334. #383C23semidirect
336. #382C23semidirect
352. C4×C4⋊C4C23semidirect
357. #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
C2×#29242
#341802
#176102
#176072
#176042
#175952
#175922
#175812
#175772
#175742
#175722
#175672
C2×#15192