Finite Group Databasebeta

← #6343578

Subgroups — #6343578

Order 512.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1215 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62819C211yesmaximal, characteristic
2#60234C211yesmaximal, characteristic, complemented
3#34228C211yesmaximal, characteristic, complemented
4#17627C212yesmaximal, complemented
5#17625C212yesmaximal, complemented
6#17623C212yesmaximal, complemented
7#17621C212yesmaximal, complemented
8#17609C214yesmaximal, complemented
9#17608C214yesmaximal, complemented
10#17598C214yesmaximal, complemented
11#17587C211yesmaximal, characteristic, complemented
12C2×#1511C211yesmaximal, characteristic, complemented
13#17548C214yesmaximal, complemented
14#17542C211yesmaximal, characteristic, complemented
15C2×#1508C211yesmaximal, characteristic, complemented
16#3541—22no—
17#3541C414yescomplemented
18#3538—21no—
19#3538C412yescomplemented
20#3536—21no—
21#3536C412yescomplemented
22#3535—22no—
23#3535—22no—
24#3520—22no—
25#3520C2214yes—
26#3505—21no—
27#3505C2212yes—
28#3501—21no—
29#3501C2212yes—
30#3495C412yescomplemented
31#3495C2212yes—
32#3492—22no—
33#3492C412yescomplemented
34#3490—22no—
35#3489C412yescomplemented
36#3489C2212yes—
37#3486C412yescomplemented
38C2×#525C2211yescharacteristic
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41#2978—22no—
42#2976—22no—
43#2975C2212yes—
44#2974C2214yescomplemented
45#2973C2212yes—
46#2933—22no—
47#2930—22no—
48#2924C2212yescomplemented
49#2880C2212yescomplemented
50C2×#407C2211yescharacteristic
51C2×#407C2211yescharacteristic
52#2368—21no—
53#2364—21no—
54#2358—22no—
55#2357C2212yes—
56#2353C2212yes—
57#2343C2212yescomplemented
58#2339C2212yescomplemented
59#2333—21no—
60#2332—21no—
61#2318C2212yescomplemented
62C4×#123—22no—
63C2×#381C2211yescharacteristic
64#2275C2212yescomplemented
65C2×C4×C22⋊C4C2211yescharacteristic
66#1521C2214yescomplemented
67#1520C2214yescomplemented
68#1518C2214yescomplemented
69#1516C2214yes—
70#1516C2214yescomplemented
71#1515C2214yescomplemented
72#1513C2214yescomplemented
73#1512C2214yescomplemented
74#1511C2212yes—
75#1511C2212yes—
76#1511C2211yescharacteristic
77#1511C2211yescharacteristic
78#1511C2214yescomplemented
79#1511C2214yescomplemented
80#1510C2211yescharacteristic
81#1510C2211yescharacteristic
82#1509C2214yescomplemented
83#1508C2212yes—
84#1508C2212yes—
85#1508C2212yes—
86#1508C2212yescomplemented
87#1508C2212yescomplemented
88#1508C2214yescomplemented
89#1507C2212yes—
90#1506C2214yescomplemented
91#1504C2214yes—
92#1504C2214yes—
93#1504C2214yescomplemented
94#1503C2214yescomplemented
95#1501C2212yes—
96#1501C2212yes—
97#1501C2214yescomplemented
98#1500C2214yescomplemented
99C2×#328C2214yescomplemented
100C2×#328C2214yescomplemented
101C2×#328C2214yescomplemented
102C2×2−1+4C2×C412yescomplemented
103C22×#41C2×C411yescharacteristic, complemented
104C22×#41C2311yescharacteristic
105C23×Q8C2×C411yescharacteristic, complemented
106C24×C4C2311yescharacteristic
107C2×#131—22no—
108C22×M16—21no—
109C22×M16—21no—
110#563—24no—
111#563—24no—
112#562—24no—
113#562—24no—
114#556—22no—
115#556C2×C414yescomplemented
116#554—24no—
117#554—22no—
118#554—24no—
119#554—24no—
120#554—22no—
121#554—24no—
122#554C2×C414yescomplemented
123#554C2×C414yescomplemented
124#553—24no—
125#553—22no—
126#553—24no—
127#553C2×C414yescomplemented
128#552—24no—
129#552—22no—
130#552—24no—
131#552—22no—
132#552—22no—
133#552C2×C414yescomplemented
134#552C2×C414yescomplemented
135#552C2×C414yescomplemented
136#551—24no—
137#551—24no—
138#551—24no—
139#551—24no—
140#551—24no—
141#551—24no—
142D4×Q8—22no—
143D4×Q8—22no—
144D4×Q8—22no—
145D4×Q8C2×C414yescomplemented
146D4×Q8C2×C414yescomplemented
147D4×Q8C2×C414yescomplemented
148#548—22no—
149#548—22no—
150#548—22no—
151#548C2×C414yescomplemented
152#548C2×C414yescomplemented
153#548C2×C414yescomplemented
154#547—24no—
155#547—22no—
156#547—24no—
157#547—22no—
158#547C2×C414yescomplemented
159#547C2×C414yescomplemented
160#546—24no—
161#546—22no—
162#546—24no—
163#546—24no—
164#546—24no—
165#546C2×C414yescomplemented
166#544—22no—
167#544—22no—
168#544—22no—
169#544C2×C412yescomplemented
170#543—22no—
171#543—22no—
172#543—22no—
173#542—24no—
174#542—22no—
175#542—24no—
176#542C2×C414yescomplemented
177#541—22no—
178#541C2×C414yescomplemented
179#539—24no—
180#539—24no—
181#539—22no—
182#539—22no—
183#539—22no—
184#539—24no—
185#539—24no—
186#539—22no—
187#538—22no—
188#538—24no—
189#538—24no—
190#538—22no—
191#537—22no—
192#537—22no—
193#537C2×C412yescomplemented
194#537C2×C414yescomplemented
195#536—24no—
196#536—22no—
197#536C2×C412yescomplemented
198#536C2×C412yescomplemented
199#536C2×C414yescomplemented
200#534—22no—
201#533—22no—
202#533C2314yes—
203#529—22no—
204#529C2314yes—
205#525—21no—
206#525—21no—
207#525—21no—
208#525—21no—
209#525—22no—
210#525—24no—
211#525—24no—
212#525C2×C412yes—
213#525C2×C412yes—
214#525C2×C412yes—
215#525C2×C412yes—
216#525C2×C412yescomplemented
217#525C2×C412yescomplemented
218#525D412yes—
219#525D412yes—
220#525D412yes—
221#525D412yes—
222#525C2312yes—
223#525C2312yes—
224#525C2314yes—
225C2×#123—21no—
226C2×#123D412yes—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—22no—
234C2×C22⋊Q8C2×C412yescomplemented
235C2×C22⋊Q8C2×C412yescomplemented
236C2×C22⋊Q8C2×C412yescomplemented
237C2×C22⋊Q8C2×C411yescharacteristic, complemented
238C2×C22⋊Q8D411yescharacteristic
239C2×C22⋊Q8D411yescharacteristic
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2314yes—
245C2×#121C2×C411yescharacteristic, complemented
246C2×#121D411yescharacteristic
247C2×#121D411yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120D412yes—
251#520—24no—
252#520C2×C412yescomplemented
253#520C2×C412yescomplemented
254#519C2×C412yescomplemented
255#518—22no—
256#518—22no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4—22no—
260C2×C4×D4—22no—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×#117C2×C411yescharacteristic, complemented
264C2×#117C2311yescharacteristic
265C22×C4⋊C4—21no—
266C22×C4⋊C4C2×C411yescharacteristic, complemented
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C22⋊C4—21no—
270C22×C42—21no—
271#436—24no—
272#436—24no—
273#436—24no—
274#435—24no—
275#435—24no—
276#435—24no—
277#435—24no—
278C8×D4—24no—
279#433—24no—
280#432C2314yes—
281#431C2314yes—
282#424—22no—
283#408—22no—
284#408—24no—
285#407—21no—
286#407—21no—
287#407—21no—
288#407—21no—
289#407C2312yes—
290#407C2311yescharacteristic
291#407C2312yes—
292#407C2312yes—
293#407C2311yescharacteristic
294#407C2314yes—
295C2×C22⋊C8—21no—
296C2×C22⋊C8—21no—
297C2×C22⋊C8C2312yes—
298C2×C22⋊C8C2312yes—
299C2×C22⋊C8C2314yes—
300#405—22no—
301#391—22no—
302#390—22no—
303#388—22no—
304#388—22no—
305#388—22no—
306#388—22no—
307#387—22no—
308#387—22no—
309#387—22no—
310#387—22no—
311#386—22no—
312#386—22no—
313#386—22no—
314#386—22no—
315#385—22no—
316#385—22no—
317#383C2312yes—
318#382C2312yes—
319#381—21no—
320#381—21no—
321#381C2312yes—
322#381C2312yes—
323#381C2311yescharacteristic
324#381C2311yescharacteristic
325#380C2312yes—
326C4×C4⋊C4—22no—
327C4×C4⋊C4—22no—
328C4×C4⋊C4C2312yes—
329C4×C22⋊C4—21no—
330C4×C22⋊C4—21no—
331C4×C22⋊C4—22no—
332C4×C22⋊C4—22no—
333C4×C22⋊C4—22no—
334C4×C22⋊C4—22no—
335C4×C22⋊C4C2311yescharacteristic
336C4×C22⋊C4C2312yes—
337C4×C22⋊C4C2312yes—
338C4×C22⋊C4C2311yescharacteristic
339#376C2312yes—
340C2×#95—21no—
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344#328C2314yes—
345#328C2314yes—
346#328C2314yes—
347#328C2314yes—
348#328C2314yes—
349#328C2314yes—
350#328C2314yes—
351#328C2314yes—
352#328C2314yes—
353#328C2314yes—
354#328C2314yes—
355#328C2314yes—
356#327C2314yes—
357#327C2314yes—
358#327C2314yes—
359#327C2314yes—
360C25C2×D411yescharacteristic
3612−1+4—84no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—22no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—82no—
368C2×#41—82no—
369C2×#41C22×C412yes—
370C2×#41C22×C412yes—
371C2×#41C22×C414yes—
372C2×#41C22×C412yes—
373C2×#41C22×C412yes—
374C2×#41C2×D412yes—
375C2×#41C2×D412yes—
376C22×Q8—22no—
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—82no—
381C22×Q8C22×C412yes—
382C22×Q8C22×C412yes—
383C22×Q8C22×C412yes—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C414yes—
386C22×Q8C2×D411yescharacteristic
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—21no—
390C22×D4C22×C411yescharacteristic
391C22×D4C2×D412yes—
392C22×D4C2×D412yes—
393C22×D4C2×D412yes—
394C22×D4C2×D411yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—82no—
402C23×C4C22×C411yescharacteristic
403C23×C4C22×C411yescharacteristic
404C23×C4C22×C411yescharacteristic
405C23×C4C22×C411yescharacteristic
406C23×C4C2×D411yescharacteristic
407C23×C4C2×D411yescharacteristic
408C23×C4C2×D411yescharacteristic
409C23×C4C2×D411yescharacteristic
410C23×C4C2×D411yescharacteristic
411C23×C4C2×D411yescharacteristic
412C23×C4C2×D411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417#131—84no—
418C2×M16—22no—
419C2×M16—21no—
420C2×M16—22no—
421C2×M16—22no—
422C2×M16—21no—
423C2×M16—24no—
424C2×M16—82no—
425C2×M16—82no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—24no—
429C4⋊Q8—22no—
430C4⋊Q8—24no—
431C4⋊Q8—22no—
432C4⋊Q8—24no—
433C4⋊Q8—24no—
434C4⋊Q8—24no—
435C4⋊Q8C22×C414yes—
436C4⋊Q8C22×C414yes—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#126—24no—
442#126—24no—
443#126—24no—
444#126—24no—
445#126—24no—
446#126—24no—
447#125—22no—
448#125—24no—
449#125—24no—
450#125—24no—
451#125—24no—
452#125—24no—
453#125—24no—
454#125—24no—
455#125—24no—
456#125C22×C414yes—
457#124—22no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124C22×C414yes—
465#123—24no—
466#123—24no—
467#123—24no—
468#123—24no—
469#123—24no—
470#123—24no—
471#123—22no—
472#123—22no—
473#123—22no—
474#123—22no—
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—
484#123—24no—
485#123C22⋊C414yes—
486#123C22⋊C414yes—
487#123C22⋊C414yes—
488#123C22⋊C414yes—
489C22⋊Q8—22no—
490C22⋊Q8—24no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—22no—
511C22⋊Q8—24no—
512C22⋊Q8—22no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—24no—
528C22⋊Q8C22⋊C412yes—
529C22⋊Q8C22⋊C412yes—
530C22⋊Q8C22⋊C412yes—
531C22⋊Q8C22⋊C412yes—
532C22⋊Q8C22⋊C412yes—
533C22⋊Q8C22⋊C412yes—
534C22⋊Q8C22⋊C412yes—
535C22⋊Q8C22⋊C412yes—
536C22⋊Q8C22×C414yes—
537C22⋊Q8C22×C414yes—
538C22⋊Q8C22×C414yes—
539C22⋊Q8C22×C412yes—
540C22⋊Q8C22×C412yes—
541C22⋊Q8C22×C412yes—
542C22⋊Q8C22×C414yes—
543C22⋊Q8C22×C414yes—
544C22⋊Q8C22×C414yes—
545C22⋊Q8C2414yes—
546C22⋊Q8C2412yes—
547#121—24no—
548#121—24no—
549#121—22no—
550#121—24no—
551#121—24no—
552#121—24no—
553#121—24no—
554#121—24no—
555#121—24no—
556#121—24no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121—24no—
562#121C22⋊C412yes—
563#121C22⋊C412yes—
564#121C22⋊C412yes—
565#121C22⋊C412yes—
566#121C22⋊C412yes—
567#121C22⋊C412yes—
568#121C22⋊C412yes—
569#121C22⋊C412yes—
570#121C22×C412yes—
571#121C22×C412yes—
572#121C22×C412yes—
573#121C22×C414yes—
574#121C2412yes—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—24no—
580#120—24no—
581#120C22⋊C414yes—
582#120C22⋊C414yes—
583#120C22⋊C414yes—
584#120C22⋊C414yes—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—24no—
589C4×Q8—24no—
590C4×Q8C22×C414yes—
591C4×Q8C22×C414yes—
592C4×Q8C22×C414yes—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—24no—
616C4×D4—48no—
617C4×D4—84no—
618C4×D4C22×C414yes—
619C4×D4C22×C414yes—
620C4×D4C22×C414yes—
621C4×D4C22×C414yes—
622C4×D4C22×C414yes—
623C4×D4C2×D414yes—
624C4×D4C2×D414yes—
625C4×D4C2×D414yes—
626C4×D4C2×D414yes—
627#117—21no—
628#117—21no—
629#117—24no—
630#117—22no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117C22×C412yes—
637#117C22×C412yes—
638#117C22×C414yes—
639#117C22×C412yes—
640#117C22×C412yes—
641#117C2×D412yes—
642#117C2×D412yes—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—24no—
655C2×C4⋊C4—24no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4C22×C412yes—
661C2×C4⋊C4C22×C412yes—
662C2×C4⋊C4C22×C412yes—
663C2×C4⋊C4C22×C411yescharacteristic
664C2×C4⋊C4C22×C411yescharacteristic
665C2×C4⋊C4C22×C414yes—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D412yes—
669C2×C4⋊C4C2×D412yes—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—24no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—24no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—44no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4C2×D412yes—
695C2×C22⋊C4C2×D412yes—
696C2×C22⋊C4C2×D412yes—
697C2×C22⋊C4C2×D412yes—
698C2×C22⋊C4C2×D412yes—
699C2×C42—21no—
700C2×C42—22no—
701C2×C42—22no—
702C2×C42—21no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—21no—
706C2×C42—82no—
707C2×C42C2412yes—
708C4⋊C8—24no—
709C4⋊C8—24no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—21no—
713C22⋊C8—22no—
714C22⋊C8—21no—
715C22⋊C8—22no—
716C22⋊C8—22no—
717C22⋊C8—24no—
718C22⋊C8—24no—
719C22⋊C8C2412yes—
720C22⋊C8C2414yes—
721C22⋊C8C2412yes—
722#97—24no—
723C4×C8—24no—
724#95—21no—
725#95—21no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739C24—21no—
740C24—42no—
741C24—42no—
742C24—42no—
743C24C2×C22⋊C411yescharacteristic
744C24C2×C22⋊C411yescharacteristic
745C24C2×C22⋊C411yescharacteristic
746C24C2×C22⋊C411yescharacteristic
747C24C22×D411yescharacteristic
748C24C22×D411yescharacteristic
749C24C22×D411yescharacteristic
750C24C22×D412yes—
751#41—44no—
752#41—44no—
753#41—44no—
754#41—82no—
755#41—82no—
756#41—82no—
757#41—82no—
758#41—88no—
759#41—88no—
760#41—84no—
761#41—82no—
762#41—84no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—21no—
768C2×Q8—24no—
769C2×Q8—44no—
770C2×Q8—82no—
771C2×Q8—81no—
772C2×Q8—82no—
773C2×Q8—82no—
774C2×Q8—84no—
775C2×Q8—82no—
776C2×Q8—82no—
777C2×Q8—81no—
778C2×Q8—84no—
779C2×Q8C2×C22⋊C412yes—
780C2×Q8C2×C22⋊C412yes—
781C2×Q8C23×C414yes—
782C2×Q8C23×C412yes—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—82no—
800C2×D4—82no—
801C2×D4C2×C22⋊C414yes—
802C2×D4C2×C22⋊C414yes—
803C2×D4C2×C22⋊C414yes—
804C2×D4C2×C22⋊C414yes—
805C2×D4C2×C22⋊C412yes—
806C2×D4C2×C22⋊C414yes—
807C2×D4C2×C22⋊C414yes—
808C2×D4C2×C22⋊C412yes—
809C2×D4C23×C412yes—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—82no—
848C22×C4—82no—
849C22×C4—82no—
850C22×C4—82no—
851C22×C4—82no—
852C22×C4—82no—
853C22×C4—82no—
854C22×C4—82no—
855C22×C4—82no—
856C22×C4C2×C22⋊C411yescharacteristic
857C22×C4C2×C22⋊C411yescharacteristic
858C22×C4C2×C22⋊C411yescharacteristic
859C22×C4C2×C22⋊C411yescharacteristic
860C22×C4C2×C22⋊C411yescharacteristic
861C22×C4C2×C22⋊C411yescharacteristic
862C22×C4C2×C22⋊C411yescharacteristic
863C22×C4C2×C22⋊C411yescharacteristic
864C22×C4C2×C22⋊C411yescharacteristic
865C22×C4C2×C22⋊C411yescharacteristic
866C22×C4C2×C22⋊C411yescharacteristic
867C22×C4C2×C22⋊C411yescharacteristic
868C22×C4C23×C411yescharacteristic
869C22×C4C23×C411yescharacteristic
870C22×C4C23×C411yescharacteristic
871C22×C4C23×C411yescharacteristic
872C22×C4C23×C414yes—
873C22×C4C23×C411yescharacteristic
874C22×C4C23×C411yescharacteristic
875C22×C4C22×D412yes—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D414yes—
887C22×C4C22×D411yescharacteristic
888C22×C4C2511yescharacteristic
889M16—44no—
890M16—81no—
891M16—82no—
892M16—81no—
893M16—82no—
894M16—84no—
895C2×C8—22no—
896C2×C8—24no—
897C2×C8—22no—
898C2×C8—44no—
899C2×C8—82no—
900C2×C8—84no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—22no—
926C4⋊C4—44no—
927C4⋊C4—82no—
928C4⋊C4—82no—
929C4⋊C4C2×C22⋊C412yes—
930C4⋊C4C2×C22⋊C414yes—
931C4⋊C4C2×C22⋊C412yes—
932C4⋊C4C2×C22⋊C412yes—
933C4⋊C4C2×C22⋊C412yes—
934C4⋊C4C2×C22⋊C414yes—
935C4⋊C4C2×C22⋊C414yes—
936C4⋊C4C2×C22⋊C414yes—
937C4⋊C4C23×C414yes—
938C4⋊C4C23×C412yes—
939C4⋊C4C23×C412yes—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—22no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—42no—
966C22⋊C4—44no—
967C22⋊C4—82no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—82no—
971C22⋊C4C2×C22⋊C414yes—
972C22⋊C4C2×C22⋊C414yes—
973C22⋊C4C2×C22⋊C414yes—
974C22⋊C4C2×C22⋊C414yes—
975C22⋊C4C2×C22⋊C414yes—
976C22⋊C4C2×C22⋊C414yes—
977C22⋊C4C2×C22⋊C414yes—
978C22⋊C4C2×C22⋊C414yes—
979C22⋊C4C2×C22⋊C414yes—
980C22⋊C4C2×C22⋊C414yes—
981C42—22no—
982C42—22no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—24no—
987C42—44no—
988C42—82no—
989C42—81no—
990C42—82no—
991C42—81no—
992C42—82no—
993C42C23×C414yes—
994C42C22×D414yes—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—42no—
1012C23—41no—
1013C23—42no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—81no—
1023C23—81no—
1024C23—88no—
1025C23C22×C22⋊C411yescharacteristic
1026C23C22×C22⋊C411yescharacteristic
1027C23C22×C22⋊C411yescharacteristic
1028C23C22×C22⋊C414yes—
1029C23C22×C22⋊C411yescharacteristic
1030C23C22×C22⋊C411yescharacteristic
1031C23C22×C22⋊C411yescharacteristic
1032C23C23×D411yescharacteristic
1033Q8—42no—
1034Q8—42no—
1035Q8—44no—
1036Q8—42no—
1037Q8—44no—
1038Q8—82no—
1039Q8—82no—
1040Q8—84no—
1041Q8—81no—
1042Q8—84no—
1043D4—28no—
1044D4—28no—
1045D4—44no—
1046D4—44no—
1047D4—44no—
1048D4—44no—
1049D4—42no—
1050D4—42no—
1051D4—42no—
1052D4—44no—
1053D4—44no—
1054D4—44no—
1055D4—44no—
1056D4—81no—
1057D4—82no—
1058D4—82no—
1059D4—84no—
1060D4—84no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—42no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—42no—
1077C2×C4—41no—
1078C2×C4—44no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—82no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—81no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—81no—
1125C2×C4—84no—
1126C2×C4—84no—
1127C2×C4—88no—
1128C2×C4—164no—
1129C2×C4—164no—
1130C2×C4C22×C22⋊C414yes—
1131C2×C4C22×C22⋊C411yescharacteristic
1132C2×C4C22×C22⋊C411yescharacteristic
1133C2×C4C22×C22⋊C414yes—
1134C2×C4C22×C22⋊C414yes—
1135C2×C4C22×C22⋊C411yescharacteristic
1136C2×C4C22×C22⋊C411yescharacteristic
1137C2×C4C22×C22⋊C411yescharacteristic
1138C2×C4C22×C22⋊C411yescharacteristic
1139C2×C4C24×C411yescharacteristic
1140C2×C4C23×D411yescharacteristic
1141C8—42no—
1142C8—42no—
1143C8—44no—
1144C22—21no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—24no—
1155C22—21no—
1156C22—21no—
1157C22—24no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—24no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—82no—
1172C22—82no—
1173C22—82no—
1174C22—82no—
1175C22—82no—
1176C22—82no—
1177C22—162no—
1178C22#288312yes—
1179C22#290112yes—
1180C22C23×C22⋊C411yescharacteristic
1181C22#358612yes—
1182C4—21no—
1183C4—21no—
1184C4—21no—
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—21no—
1190C4—24no—
1191C4—24no—
1192C4—24no—
1193C4—44no—
1194C4—42no—
1195C4—44no—
1196C4—42no—
1197C4—44no—
1198C4—42no—
1199C4—82no—
1200C4—82no—
1201C4—82no—
1202C2—22no—
1203C2—22no—
1204C2—22no—
1205C2—41no—
1206C2—41no—
1207C2—41no—
1208C2—44no—
1209C2—41no—
1210C2—82no—
1211C2C2×#288311yescharacteristic
1212C2#6008811yescharacteristic
1213C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62819C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60234C2semidirect
3. #34228C2semidirect
4. #17627C2semidirect
5. #17625C2semidirect
6. #17623C2semidirect
7. #17621C2semidirect
8. #17609C2semidirect
9. #17608C2semidirect
10. #17598C2semidirect
11. #17587C2semidirect
12. C2×#1511C2semidirect
13. #17548C2semidirect
14. #17542C2semidirect
15. C2×#1508C2semidirect
17. #3541C4semidirect
19. #3538C4semidirect
21. #3536C4semidirect
30. #3495C4semidirect
33. #3492C4semidirect
35. #3489C4semidirect
37. #3486C4semidirect
44. #2974C22semidirect
48. #2924C22semidirect
49. #2880C22semidirect
57. #2343C22semidirect
58. #2339C22semidirect
61. #2318C22semidirect
64. #2275C22semidirect
66. #1521C22semidirect
67. #1520C22semidirect
68. #1518C22semidirect
70. #1516C22semidirect
71. #1515C22semidirect
72. #1513C22semidirect
73. #1512C22semidirect
78. #1511C22semidirect
79. #1511C22semidirect
82. #1509C22semidirect
86. #1508C22semidirect
87. #1508C22semidirect
88. #1508C22semidirect
90. #1506C22semidirect
93. #1504C22semidirect
94. #1503C22semidirect
97. #1501C22semidirect
98. #1500C22semidirect
99. C2×#328C22semidirect
100. C2×#328C22semidirect
101. C2×#328C22semidirect
102. C2×2−1+4C2×C4semidirect
103. C22×#41C2×C4semidirect
105. C23×Q8C2×C4semidirect
115. #556C2×C4semidirect
122. #554C2×C4semidirect
123. #554C2×C4semidirect
127. #553C2×C4semidirect
133. #552C2×C4semidirect
134. #552C2×C4semidirect
135. #552C2×C4semidirect
145. D4×Q8C2×C4semidirect
146. D4×Q8C2×C4semidirect
147. D4×Q8C2×C4semidirect
151. #548C2×C4semidirect
152. #548C2×C4semidirect
153. #548C2×C4semidirect
158. #547C2×C4semidirect
159. #547C2×C4semidirect
165. #546C2×C4semidirect
169. #544C2×C4semidirect
176. #542C2×C4semidirect
178. #541C2×C4semidirect
193. #537C2×C4semidirect
194. #537C2×C4semidirect
197. #536C2×C4semidirect
198. #536C2×C4semidirect
199. #536C2×C4semidirect
216. #525C2×C4semidirect
217. #525C2×C4semidirect
234. C2×C22⋊Q8C2×C4semidirect
235. C2×C22⋊Q8C2×C4semidirect
236. C2×C22⋊Q8C2×C4semidirect
237. C2×C22⋊Q8C2×C4semidirect
245. C2×#121C2×C4semidirect
252. #520C2×C4semidirect
253. #520C2×C4semidirect
254. #519C2×C4semidirect
263. C2×#117C2×C4semidirect
266. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628192
#602342
#342282
#176272
#176252
#176232
#176212
#176092
#176082
#175982
#175872
C2×#15112
#175482
#175422
C2×#15082