Finite Group Databasebeta

← #6343484

Subgroups — #6343484

Order 512.

2929 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60277C211yesmaximal, characteristic, complemented
3#34121C211yesmaximal, characteristic, complemented
4#17629C214yesmaximal, complemented
5#17625C214yesmaximal, complemented
6#17624C214yesmaximal, complemented
7#17623C214yesmaximal, complemented
8#17576C212yesmaximal, complemented
9#17563C212yesmaximal, complemented
10#17562C211yesmaximal, characteristic, complemented
11#17561C211yesmaximal, characteristic, complemented
12#17546C212yesmaximal, complemented
13#17545C211yesmaximal, characteristic, complemented
14#17544C211yesmaximal, characteristic, complemented
15#17533C212yesmaximal, complemented
16#3512—22no—
17#3511C412yescomplemented
18#3511C412yescomplemented
19#3510—22no—
20#3509C412yescomplemented
21#3508C412yescomplemented
22#3507—21no—
23#3507C2212yes—
24#3506—21no—
25#3506C2212yes—
26#3505—21no—
27#3505—21no—
28#3505C2212yes—
29#3505C2212yes—
30#3480—22no—
31#3480C414yescomplemented
32#3475—22no—
33#3475C414yescomplemented
34#3455—21no—
35#3455—21no—
36#3449—21no—
37#3444C2212yes—
38#3444C2212yes—
39C2×#533C2211yescharacteristic
40C2×#532C2211yescharacteristic
41#3428—21no—
42C2×C4×#41C2211yescharacteristic
43#2989—22no—
44#2989—22no—
45#2983C2212yescomplemented
46#2975C2212yes—
47#2973C2212yes—
48#2973C2212yescomplemented
49#2965—22no—
50#2965—22no—
51#2920C2211yescharacteristic
52#2920C2211yescharacteristic
53#2920C2212yescomplemented
54C2×#431C2212yescomplemented
55#2357C2212yes—
56#2356C2212yescomplemented
57#2355—21no—
58#2354—21no—
59#2353C2212yes—
60#2353C2212yescomplemented
61#2352—21no—
62#2352—21no—
63#2298—21no—
64#2298—21no—
65#2297—21no—
66#2285C2211yescharacteristic, complemented
67#2283C2211yescharacteristic
68#2283C2211yescharacteristic, complemented
69C4×#117—21no—
70C4×#117C2211yescharacteristic
71C4×#117C2211yescharacteristic, complemented
72C2×C4×C4⋊C4C2211yescharacteristic, complemented
73#1521C2218yescomplemented
74#1516C2218yescomplemented
75#1515C2214yescomplemented
76#1514C2214yes—
77#1513C2218yescomplemented
78#1512C2218yescomplemented
79#1511C2214yes—
80#1510C2214yes—
81#1509C2218yescomplemented
82#1508C2214yes—
83#1507C2214yes—
84#1506C2214yescomplemented
85#1505C2214yes—
86#1504C2218yescomplemented
87#1503C2212yescomplemented
88#1503C2212yescomplemented
89#1503C2212yescomplemented
90#1503C2212yescomplemented
91#1502C2212yes—
92#1502C2212yes—
93#1502C2212yes—
94#1502C2212yes—
95#1501C2218yescomplemented
96#1500C2218yescomplemented
97C22×#41—21no—
98C22×#41D411yescharacteristic
99#559—22no—
100#559—24no—
101#559—24no—
102#559C2×C414yescomplemented
103#557—22no—
104#557C2×C414yescomplemented
105#556—22no—
106#556—24no—
107#556—24no—
108#556—22no—
109#556C2×C414yes—
110#556C2×C414yescomplemented
111#555—22no—
112#555C2×C414yes—
113#554—22no—
114#554C2×C414yescomplemented
115#553—24no—
116#553—22no—
117#553—22no—
118#553—24no—
119#553—24no—
120#553—24no—
121#553—24no—
122#553—24no—
123#553C2×C414yes—
124#553C2×C414yescomplemented
125#552—24no—
126#552—24no—
127#552—22no—
128#552—22no—
129#552C2×C414yes—
130#552C2×C414yescomplemented
131#551—24no—
132#551—24no—
133#551—24no—
134#551—24no—
135#550—22no—
136#550C2×C414yes—
137#548—22no—
138#548—22no—
139#548C2×C414yes—
140#548C2×C414yescomplemented
141#547—22no—
142#547C2×C414yes—
143#546—22no—
144#546—22no—
145#546C2×C414yes—
146#546C2×C414yescomplemented
147#542—22no—
148#542—22no—
149#542—22no—
150#542—22no—
151#541—22no—
152#541—22no—
153#540—22no—
154#540—22no—
155#539—22no—
156#539—22no—
157#539—22no—
158#539—22no—
159#538—22no—
160#538—22no—
161#538—22no—
162#538—22no—
163#537—22no—
164#537—22no—
165#536—22no—
166#536—22no—
167#535—22no—
168#535—22no—
169#534—22no—
170#534—22no—
171#533—21no—
172#533—21no—
173#533—21no—
174#533—21no—
175#533C2×C412yes—
176#533C2×C412yes—
177#533C2×C412yescomplemented
178#533C2×C412yescomplemented
179#533C2×C412yescomplemented
180#533C2×C412yescomplemented
181#533C2312yes—
182#533C2312yes—
183#532—24no—
184#532—21no—
185#532—21no—
186#532—21no—
187#532—21no—
188#532C2×C412yes—
189#532C2×C412yes—
190#532C2×C412yescomplemented
191#532C2×C412yescomplemented
192#532C2×C412yescomplemented
193#532C2×C412yescomplemented
194#532C2312yes—
195#532C2312yes—
196C2×C4⋊Q8C2×C411yescharacteristic, complemented
197C2×C4⋊Q8C2×C411yescharacteristic, complemented
198C2×C4⋊Q8C2×C411yescharacteristic, complemented
199C2×#127C2×C411yescharacteristic, complemented
200#529—24no—
201#529—24no—
202#529—24no—
203#529—24no—
204#529—22no—
205#529—22no—
206#529—22no—
207#529—22no—
208#529—22no—
209#529—22no—
210#529—22no—
211#529—22no—
212#529C2×C414yes—
213#529C2×C414yescomplemented
214#529C2314yes—
215#529C2314yes—
216C2×#125—21no—
217C2×#124—21no—
218#525—24no—
219#525—22no—
220#525—22no—
221#525—22no—
222#525—22no—
223#525C2314yes—
224#525C2314yes—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2312yes—
227C2×#121—21no—
228C2×#121C2312yes—
229#520—22no—
230#520—22no—
231#520—22no—
232#520—22no—
233#519—22no—
234#518—22no—
235#518—22no—
236#518—22no—
237C4×#41—24no—
238C4×#41—22no—
239C4×#41—22no—
240C4×#41—22no—
241C4×#41—22no—
242C4×#41C2×C414yes—
243C4×#41C2×C412yes—
244C4×#41C2×C412yes—
245C4×#41C2×C412yes—
246C4×#41C2×C412yes—
247C4×#41C2×C414yescomplemented
248C4×#41D412yes—
249C4×#41D412yes—
250C4×#41D412yes—
251C4×#41D412yes—
252C2×C4×Q8—21no—
253C2×C4×Q8C2×C412yescomplemented
254C2×C4×Q8D411yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C2×C412yescomplemented
258C2×C4×D4D411yescharacteristic
259C2×C4×D4D411yescharacteristic
260C2×C4×D4D411yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117—21no—
265C2×#117—24no—
266C2×#117—21no—
267C2×#117—21no—
268C2×#117—21no—
269C2×#117D411yescharacteristic
270C2×#117D411yescharacteristic
271C2×#117D411yescharacteristic
272C22×C4⋊C4—21no—
273C22×C42—21no—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277#446—24no—
278#446—24no—
279#436—24no—
280#436—24no—
281#435—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#432—21no—
286#432—21no—
287#432—22no—
288#432C2312yes—
289#432C2312yes—
290#432C2314yes—
291#431—22no—
292#431—22no—
293#431—21no—
294#431—21no—
295#431—22no—
296#431C2312yes—
297#431C2312yes—
298#431C2314yes—
299#423—21no—
300#423—21no—
301#423—22no—
302C2×C4⋊C8—22no—
303#407C2312yes—
304#407C2312yes—
305#407C2314yes—
306C2×C22⋊C8C2314yes—
307C4×M16—21no—
308C4×M16—21no—
309C4×M16—22no—
310C2×C4×C8—22no—
311#391—22no—
312#390—22no—
313#388—22no—
314#388—22no—
315#388—22no—
316#388—22no—
317#387—22no—
318#387—22no—
319#387—22no—
320#387—22no—
321#386—22no—
322#386—22no—
323#384—21no—
324#383C2312yes—
325#383C2312yes—
326#382—21no—
327#382—21no—
328#382C2312yes—
329#381C2312yes—
330#381C2312yes—
331#380—21no—
332#380—21no—
333#380—21no—
334#380C2312yes—
335C4×C4⋊C4—22no—
336C4×C4⋊C4—22no—
337C4×C4⋊C4—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4C2312yes—
343C4×C4⋊C4C2311yescharacteristic
344C4×C4⋊C4C2311yescharacteristic
345C4×C4⋊C4C2311yescharacteristic
346C4×C4⋊C4C2311yescharacteristic
347C4×C22⋊C4—21no—
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—22no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4C2312yes—
354C4×C22⋊C4C2312yes—
355#376—21no—
356#376—21no—
357#376C2312yes—
358#376C2312yes—
359C2×#95C2312yes—
360C43—21no—
361C43—21no—
362#328C2318yes—
363#328C2318yes—
364#328C2318yes—
365#328C2318yes—
366#327C2318yes—
367#327C2318yes—
368#327C2318yes—
369#327C2318yes—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—42no—
377C2×#41—42no—
378C2×#41—44no—
379C2×#41—44no—
380C2×#41C22⋊C412yes—
381C2×#41C22⋊C412yes—
382C2×#41C22⋊C412yes—
383C2×#41C22⋊C412yes—
384C2×#41C22×C414yes—
385C2×#41C22×C414yes—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8C22×C412yes—
389C22×Q8C2×D411yescharacteristic
390C22×D4—22no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4C22×C412yes—
394C22×D4C2×D411yescharacteristic
395C22×D4C2×D411yescharacteristic
396C22×D4C2×D411yescharacteristic
397C23×C4—22no—
398C23×C4—22no—
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D411yescharacteristic
401C23×C4C2×D411yescharacteristic
402C23×C4C2×D411yescharacteristic
403C23×C4C2×D411yescharacteristic
404C23×C4C2×D411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—24no—
411C22×C8—24no—
412C4⋊Q8—24no—
413C4⋊Q8—21no—
414C4⋊Q8—21no—
415C4⋊Q8—21no—
416C4⋊Q8—21no—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8C22×C412yes—
420C4⋊Q8C22×C412yes—
421C4⋊Q8C22×C412yes—
422C4⋊Q8C22×C412yes—
423C4⋊Q8C22×C412yes—
424C4⋊Q8C22×C412yes—
425#127—24no—
426#127—21no—
427#127—21no—
428#127C22×C412yes—
429#127C22×C412yes—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—24no—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#126—24no—
442#125—24no—
443#125—24no—
444#125—24no—
445#125—24no—
446#125—22no—
447#125—22no—
448#125—22no—
449#125—22no—
450#125—22no—
451#125—22no—
452#125C22×C414yes—
453#125C22×C414yes—
454#124—24no—
455#124—24no—
456#124—24no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—22no—
461#124—22no—
462#124—22no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124C22×C414yes—
467#124C22×C414yes—
468#123—24no—
469#123—24no—
470#123—24no—
471#123—24no—
472#123—24no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8C22×C414yes—
503C22⋊Q8C22×C414yes—
504C22⋊Q8C22×C414yes—
505C22⋊Q8C2414yes—
506#121—24no—
507#121—24no—
508#121—24no—
509#121—24no—
510#121—24no—
511#121—24no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121—24no—
528#121C22×C414yes—
529#121C22×C414yes—
530#121C22×C414yes—
531#121C2414yes—
532#120—24no—
533#120—24no—
534#120—24no—
535#120—24no—
536C4×Q8—24no—
537C4×Q8—24no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8C22⋊C412yes—
551C4×Q8C22⋊C412yes—
552C4×Q8C22⋊C412yes—
553C4×Q8C22⋊C412yes—
554C4×Q8C22×C414yes—
555C4×Q8C22×C414yes—
556C4×Q8C22×C414yes—
557C4×Q8C22×C414yes—
558C4×Q8C22×C412yes—
559C4×Q8C22×C412yes—
560C4×Q8C2×D412yes—
561C4×Q8C2×D412yes—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—24no—
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—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4C22⋊C412yes—
593C4×D4C22⋊C412yes—
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×C414yes—
605C4×D4C22×C414yes—
606C4×D4C22×C414yes—
607C4×D4C22×C414yes—
608C4×D4C22×C412yes—
609C4×D4C22×C412yes—
610C4×D4C22×C412yes—
611C4×D4C22×C412yes—
612C4×D4C22×C412yes—
613C4×D4C22×C412yes—
614C4×D4C2×D412yes—
615C4×D4C2×D412yes—
616C4×D4C2×D412yes—
617C4×D4C2×D412yes—
618C4×D4C2×D412yes—
619C4×D4C2×D412yes—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117—44no—
637#117—44no—
638#117—44no—
639#117C22⋊C412yes—
640#117C22⋊C412yes—
641#117C22⋊C412yes—
642#117C22⋊C412yes—
643#117C22⋊C412yes—
644#117C22⋊C412yes—
645#117C22⋊C412yes—
646#117C22⋊C412yes—
647#117C22⋊C412yes—
648#117C22⋊C412yes—
649#117C22⋊C412yes—
650#117C22⋊C412yes—
651#117C22×C414yes—
652#117C22×C414yes—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—24no—
661C2×C4⋊C4—24no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—44no—
669C2×C4⋊C4C22×C412yes—
670C2×C4⋊C4C22×C412yes—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—24no—
681C2×C22⋊C4—24no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C42—22no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—22no—
699C2×C42—22no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—44no—
706C2×C42C22×C411yescharacteristic
707C2×C42C22×C411yescharacteristic
708C2×C42C22×C412yes—
709C2×C42C22×C412yes—
710C2×C42C22×C411yescharacteristic
711C2×C42C22×C411yescharacteristic
712C2×C42C22×C412yes—
713C2×C42C22×C412yes—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D412yes—
723C2×C42C2×D412yes—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D412yes—
727C2×C42C2×D412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C4⋊C8—22no—
733C4⋊C8—22no—
734C4⋊C8—24no—
735C4⋊C8—24no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C22⋊C8—24no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—24no—
742C22⋊C8C2414yes—
743C22⋊C8C2414yes—
744#97—24no—
745#97—22no—
746#97—22no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—24no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95C2412yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764C24—22no—
765C24C22×D411yescharacteristic
766C24C22×D411yescharacteristic
767C24C22×D411yescharacteristic
768#41—44no—
769#41—44no—
770#41—44no—
771#41—44no—
772#41—44no—
773#41—44no—
774#41—48no—
775#41—48no—
776#41—44no—
777#41—44no—
778#41—84no—
779#41—84no—
780#41—84no—
781#41—84no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—41no—
788C2×Q8—41no—
789C2×Q8—44no—
790C2×Q8—82no—
791C2×Q8—82no—
792C2×Q8C2×C22⋊C412yes—
793C2×Q8C2×C22⋊C412yes—
794C2×Q8C23×C414yes—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—41no—
807C2×D4—41no—
808C2×D4—41no—
809C2×D4—41no—
810C2×D4—41no—
811C2×D4—41no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—82no—
816C2×D4—82no—
817C2×D4C2×C22⋊C412yes—
818C2×D4C2×C22⋊C412yes—
819C2×D4C2×C22⋊C412yes—
820C2×D4C2×C22⋊C412yes—
821C2×D4C2×C22⋊C412yes—
822C2×D4C2×C22⋊C412yes—
823C2×D4C23×C414yes—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—82no—
853C22×C4C2×C22⋊C411yescharacteristic
854C22×C4C2×C22⋊C411yescharacteristic
855C22×C4C2×C22⋊C411yescharacteristic
856C22×C4C2×C22⋊C411yescharacteristic
857C22×C4C2×C22⋊C412yes—
858C22×C4C2×C22⋊C412yes—
859C22×C4C2×C22⋊C412yes—
860C22×C4C2×C22⋊C412yes—
861C22×C4C2×C22⋊C411yescharacteristic
862C22×C4C2×C22⋊C411yescharacteristic
863C22×C4C2×C22⋊C412yes—
864C22×C4C2×C22⋊C412yes—
865C22×C4C2×C22⋊C411yescharacteristic
866C22×C4C2×C22⋊C411yescharacteristic
867C22×C4C2×C22⋊C412yes—
868C22×C4C2×C22⋊C412yes—
869C22×C4C23×C411yescharacteristic
870C22×C4C23×C411yescharacteristic
871C22×C4C23×C412yes—
872C22×C4C23×C412yes—
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D411yescharacteristic
888C22×C4C2511yescharacteristic
889M16—84no—
890M16—82no—
891M16—82no—
892C2×C8—24no—
893C2×C8—24no—
894C2×C8—84no—
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—82no—
924C4⋊C4C2×C22⋊C412yes—
925C4⋊C4C2×C22⋊C412yes—
926C4⋊C4C2×C22⋊C412yes—
927C4⋊C4C2×C22⋊C412yes—
928C4⋊C4C2×C22⋊C412yes—
929C4⋊C4C2×C22⋊C412yes—
930C4⋊C4C2×C22⋊C412yes—
931C4⋊C4C2×C22⋊C412yes—
932C4⋊C4C2×C22⋊C412yes—
933C4⋊C4C2×C22⋊C412yes—
934C4⋊C4C2×C22⋊C412yes—
935C4⋊C4C2×C22⋊C412yes—
936C4⋊C4C23×C414yes—
937C4⋊C4C23×C414yes—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—82no—
960C22⋊C4—82no—
961C22⋊C4C2×C22⋊C412yes—
962C22⋊C4C2×C22⋊C412yes—
963C22⋊C4C2×C22⋊C412yes—
964C22⋊C4C2×C22⋊C412yes—
965C22⋊C4C2×C22⋊C412yes—
966C22⋊C4C2×C22⋊C412yes—
967C22⋊C4C2×C22⋊C412yes—
968C22⋊C4C2×C22⋊C412yes—
969C22⋊C4C2×C22⋊C412yes—
970C22⋊C4C2×C22⋊C412yes—
971C22⋊C4C2×C22⋊C412yes—
972C22⋊C4C2×C22⋊C412yes—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—82no—
987C42—82no—
988C42C2×C22⋊C412yes—
989C42C2×C22⋊C412yes—
990C42C2×C22⋊C412yes—
991C42C2×C22⋊C412yes—
992C42C2×C22⋊C411yescharacteristic
993C42C2×C22⋊C411yescharacteristic
994C42C2×C22⋊C411yescharacteristic
995C42C2×C22⋊C411yescharacteristic
996C42C2×C22⋊C412yes—
997C42C2×C22⋊C412yes—
998C42C2×C22⋊C411yescharacteristic
999C42C2×C22⋊C411yescharacteristic
1000C42C2×C22⋊C412yes—
1001C42C2×C22⋊C412yes—
1002C42C2×C22⋊C411yescharacteristic
1003C42C2×C22⋊C411yescharacteristic
1004C42C23×C411yescharacteristic
1005C42C23×C411yescharacteristic
1006C42C23×C412yes—
1007C42C23×C412yes—
1008C42C23×C411yescharacteristic
1009C42C23×C411yescharacteristic
1010C42C22×D412yes—
1011C42C22×D412yes—
1012C42C22×D411yescharacteristic
1013C42C22×D411yescharacteristic
1014C42C22×D411yescharacteristic
1015C42C22×D411yescharacteristic
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—24no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—44no—
1030C23—82no—
1031C23—82no—
1032C23C22×C22⋊C411yescharacteristic
1033C23C22×C22⋊C412yes—
1034C23C22×C22⋊C412yes—
1035C23C22×C22⋊C411yescharacteristic
1036C23C23×D411yescharacteristic
1037Q8—42no—
1038Q8—42no—
1039Q8—44no—
1040Q8—44no—
1041Q8—44no—
1042Q8—44no—
1043Q8—82no—
1044Q8—82no—
1045D4—42no—
1046D4—42no—
1047D4—42no—
1048D4—42no—
1049D4—42no—
1050D4—42no—
1051D4—44no—
1052D4—44no—
1053D4—48no—
1054D4—44no—
1055D4—44no—
1056D4—44no—
1057D4—44no—
1058D4—82no—
1059D4—82no—
1060D4—84no—
1061D4—84no—
1062D4—84no—
1063D4—84no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—48no—
1107C2×C4—42no—
1108C2×C4—44no—
1109C2×C4—42no—
1110C2×C4—48no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—84no—
1123C2×C4—84no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—88no—
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4C22×C22⋊C412yes—
1129C2×C4C22×C22⋊C412yes—
1130C2×C4C22×C22⋊C412yes—
1131C2×C4C22×C22⋊C412yes—
1132C2×C4C22×C22⋊C411yescharacteristic
1133C2×C4C22×C22⋊C411yescharacteristic
1134C2×C4C22×C22⋊C411yescharacteristic
1135C2×C4C22×C22⋊C411yescharacteristic
1136C2×C4C22×C22⋊C412yes—
1137C2×C4C22×C22⋊C412yes—
1138C2×C4C22×C22⋊C411yescharacteristic
1139C2×C4C22×C22⋊C411yescharacteristic
1140C2×C4C22×C22⋊C411yescharacteristic
1141C2×C4C22×C22⋊C411yescharacteristic
1142C2×C4C22×C22⋊C411yescharacteristic
1143C2×C4#57512yes—
1144C2×C4#57512yes—
1145C2×C4C24×C411yescharacteristic
1146C2×C4C23×D411yescharacteristic
1147C8—44no—
1148C8—44no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—22no—
1153C22—22no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—22no—
1158C22—22no—
1159C22—21no—
1160C22—22no—
1161C22—22no—
1162C22—21no—
1163C22—42no—
1164C22—42no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—164no—
1173C22C23×C22⋊C411yescharacteristic
1174C22C2×#57511yescharacteristic
1175C22C2×#57511yescharacteristic
1176C4—21no—
1177C4—21no—
1178C4—22no—
1179C4—22no—
1180C4—21no—
1181C4—21no—
1182C4—21no—
1183C4—21no—
1184C4—22no—
1185C4—22no—
1186C4—21no—
1187C4—22no—
1188C4—22no—
1189C4—21no—
1190C4—21no—
1191C4—44no—
1192C4—44no—
1193C4—44no—
1194C4—44no—
1195C4—82no—
1196C4—82no—
1197C4—82no—
1198C4#289612yes—
1199C4#289612yes—
1200C4#290112yes—
1201C2—21no—
1202C2—21no—
1203C2—42no—
1204C2—41no—
1205C2—42no—
1206C2—41no—
1207C2—84no—
1208C2#6007011yescharacteristic
1209C2C2×#289611yescharacteristic
1210C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62815C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60277C2semidirect
3. #34121C2semidirect
4. #17629C2semidirect
5. #17625C2semidirect
6. #17624C2semidirect
7. #17623C2semidirect
8. #17576C2semidirect
9. #17563C2semidirect
10. #17562C2semidirect
11. #17561C2semidirect
12. #17546C2semidirect
13. #17545C2semidirect
14. #17544C2semidirect
15. #17533C2semidirect
17. #3511C4semidirect
18. #3511C4semidirect
20. #3509C4semidirect
21. #3508C4semidirect
31. #3480C4semidirect
33. #3475C4semidirect
45. #2983C22semidirect
48. #2973C22semidirect
53. #2920C22semidirect
54. C2×#431C22semidirect
56. #2356C22semidirect
60. #2353C22semidirect
66. #2285C22semidirect
68. #2283C22semidirect
71. C4×#117C22semidirect
72. C2×C4×C4⋊C4C22semidirect
73. #1521C22semidirect
74. #1516C22semidirect
75. #1515C22semidirect
77. #1513C22semidirect
78. #1512C22semidirect
81. #1509C22semidirect
84. #1506C22semidirect
86. #1504C22semidirect
87. #1503C22semidirect
88. #1503C22semidirect
89. #1503C22semidirect
90. #1503C22semidirect
95. #1501C22semidirect
96. #1500C22semidirect
102. #559C2×C4semidirect
104. #557C2×C4semidirect
110. #556C2×C4semidirect
114. #554C2×C4semidirect
124. #553C2×C4semidirect
130. #552C2×C4semidirect
140. #548C2×C4semidirect
146. #546C2×C4semidirect
177. #533C2×C4semidirect
178. #533C2×C4semidirect
179. #533C2×C4semidirect
180. #533C2×C4semidirect
190. #532C2×C4semidirect
191. #532C2×C4semidirect
192. #532C2×C4semidirect
193. #532C2×C4semidirect
196. C2×C4⋊Q8C2×C4semidirect
197. C2×C4⋊Q8C2×C4semidirect
198. C2×C4⋊Q8C2×C4semidirect
199. C2×#127C2×C4semidirect
213. #529C2×C4semidirect
247. C4×#41C2×C4semidirect
253. C2×C4×Q8C2×C4semidirect
257. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628152
#602772
#341212
#176292
#176252
#176242
#176232
#175762
#175632
#175622
#175612
#175462
#175452
#175442
#175332