Finite Group Databasebeta

← #6343583

Subgroups — #6343583

Order 512.

2725 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62823C211yesmaximal, characteristic
2#60289C211yesmaximal, characteristic, complemented
3#34237C211yesmaximal, characteristic, complemented
4#17627C212yesmaximal, complemented
5#17625C212yesmaximal, complemented
6#17623C212yesmaximal, complemented
7#17621C212yesmaximal, complemented
8#17609C214yesmaximal, complemented
9#17605C214yesmaximal, complemented
10#17601C212yesmaximal, complemented
11#17600C212yesmaximal, complemented
12#17590C211yesmaximal, characteristic, complemented
13#17554C211yesmaximal, characteristic, complemented
14#17549C212yesmaximal, complemented
15#17548C212yesmaximal, complemented
16#17545C211yesmaximal, characteristic, complemented
17#17537C211yesmaximal, characteristic, complemented
18#3564—22no—
19#3564—22no—
20#3563—21no—
21#3563C412yescomplemented
22#3561—21no—
23#3561C412yescomplemented
24#3553—22no—
25#3552C412yescomplemented
26#3552C412yescomplemented
27#3523C412yescomplemented
28#3523C2212yes—
29#3520C412yescomplemented
30#3520C2212yes—
31#3516—22no—
32#3516C414yescomplemented
33#3505—21no—
34#3505C2212yes—
35#3501—21no—
36#3501C2212yes—
37#3495—22no—
38#3495C2214yes—
39#3491—22no—
40C2×#533C2211yescharacteristic
41C2×#529C2211yescharacteristic
42C2×#529C2211yescharacteristic
43#2995—22no—
44#2993—22no—
45#2984C2212yescomplemented
46#2975C2212yes—
47#2974C2212yescomplemented
48#2973C2212yes—
49#2969—22no—
50#2967—22no—
51#2924C2214yescomplemented
52#2920C2211yescharacteristic
53#2920C2211yescharacteristic
54#2370—21no—
55#2367—21no—
56#2363—21no—
57#2362—21no—
58#2357C2212yes—
59#2353C2212yes—
60#2346C2212yescomplemented
61#2343C2212yescomplemented
62#2335—22no—
63#2320C2211yescharacteristic, complemented
64#2319C2211yescharacteristic, complemented
65C4×#126—22no—
66#2283C2211yescharacteristic
67#2276C2211yescharacteristic, complemented
68#2275C2211yescharacteristic, complemented
69C4×#117C2211yescharacteristic
70#1521C2214yes—
71#1520C2214yescomplemented
72#1518C2212yescomplemented
73#1518C2212yescomplemented
74#1518C2214yescomplemented
75#1516C2214yes—
76#1515C2214yescomplemented
77#1513C2214yes—
78#1512C2212yes—
79#1512C2212yes—
80#1512C2214yes—
81#1511C2211yescharacteristic
82#1511C2211yescharacteristic
83#1511C2212yes—
84#1511C2212yes—
85#1511C2214yescomplemented
86#1510C2211yescharacteristic
87#1510C2211yescharacteristic
88#1509C2212yes—
89#1509C2212yes—
90#1509C2214yes—
91#1508C2212yes—
92#1508C2212yes—
93#1508C2212yes—
94#1508C2214yescomplemented
95#1507C2212yes—
96#1506C2214yescomplemented
97#1506C2212yescomplemented
98#1506C2212yescomplemented
99#1506C2214yescomplemented
100#1504C2214yes—
101#1503C2212yescomplemented
102#1503C2212yescomplemented
103#1503C2214yescomplemented
104#1501C2214yes—
105#1500C2214yes—
106#1500C2212yes—
107#1500C2212yes—
108#1500C2214yes—
109C2×#328C2214yescomplemented
110#564—22no—
111#563—24no—
112#563—24no—
113#563—22no—
114#563—22no—
115#562—22no—
116#557—22no—
117#557C2×C412yescomplemented
118#557C2×C414yescomplemented
119#557C2×C412yescomplemented
120#556—24no—
121#556—22no—
122#556—24no—
123#556C2×C412yes—
124#556C2×C414yescomplemented
125#556C2×C412yescomplemented
126#554—22no—
127#554—24no—
128#554—24no—
129#554—24no—
130#554—24no—
131#554—22no—
132#554C2×C414yescomplemented
133#554C2×C414yescomplemented
134#553—22no—
135#553—24no—
136#553—24no—
137#553C2×C414yescomplemented
138#552—24no—
139#552—22no—
140#552—24no—
141#552—24no—
142#552—24no—
143#552—24no—
144#552—24no—
145#552—24no—
146#552—24no—
147#552—22no—
148#552C2×C414yes—
149#552C2×C414yescomplemented
150#551—24no—
151#551—24no—
152#551—24no—
153#551—24no—
154#551—24no—
155#551—24no—
156D4×Q8—22no—
157D4×Q8—22no—
158D4×Q8C2×C412yes—
159D4×Q8C2×C414yescomplemented
160D4×Q8C2×C414yescomplemented
161D4×Q8C2×C412yescomplemented
162#548—22no—
163#548—22no—
164#548C2×C414yes—
165#548C2×C414yescomplemented
166#547C2×C412yes—
167#547C2×C412yes—
168#546—22no—
169#546C2×C414yescomplemented
170#544—22no—
171#544—22no—
172#544—22no—
173#544C2×C414yescomplemented
174#543—22no—
175#543—22no—
176#543—22no—
177#542—24no—
178#542—22no—
179#542—24no—
180#542—22no—
181#542C2×C414yescomplemented
182#542C2×C414yescomplemented
183#541—24no—
184#541—24no—
185#541—22no—
186#541—24no—
187#541—22no—
188#541—24no—
189#541C2×C414yescomplemented
190#541C2×C414yescomplemented
191#539—24no—
192#539—24no—
193#539—24no—
194#539—22no—
195#539—24no—
196#539—22no—
197#538—22no—
198#538—22no—
199#536—22no—
200#536C2×C414yescomplemented
201#534—22no—
202#533—22no—
203#533—21no—
204#533—21no—
205#533—21no—
206#533—21no—
207#533C2×C412yescomplemented
208#533C2×C412yescomplemented
209#533C2312yes—
210#533C2312yes—
211#533C2314yes—
212C2×C4⋊Q8C2×C411yescharacteristic, complemented
213C2×C4⋊Q8C2×C411yescharacteristic, complemented
214#529—24no—
215#529—24no—
216#529—22no—
217#529—21no—
218#529—21no—
219#529—21no—
220#529—21no—
221#529C2×C412yes—
222#529C2×C412yes—
223#529C2×C412yes—
224#529C2×C412yes—
225#529C2×C412yescomplemented
226#529C2×C412yescomplemented
227#529D412yes—
228#529D412yes—
229#529D412yes—
230#529D412yes—
231#529C2312yes—
232#529C2312yes—
233#529C2314yes—
234C2×#126—21no—
235C2×#126D412yes—
236C2×#125—21no—
237C2×#125C2×C411yescharacteristic, complemented
238C2×#125D411yescharacteristic
239C2×#124C2×C411yescharacteristic, complemented
240C2×#124D411yescharacteristic
241#525—22no—
242#525C2314yes—
243C2×#123—21no—
244C2×#123D412yes—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8D411yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×#121D411yescharacteristic
252C2×#121C2311yescharacteristic
253#520—22no—
254#520C2×C414yescomplemented
255#519—22no—
256#519C2×C414yescomplemented
257#518—22no—
258#518—22no—
259C2×C4×Q8—21no—
260C2×C4×Q8—21no—
261C2×C4×Q8C2×C411yescharacteristic, complemented
262C2×C4×Q8C2×C412yescomplemented
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4C2×C411yescharacteristic, complemented
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2312yes—
269C2×#117—21no—
270C2×#117—21no—
271C2×#117—21no—
272C2×#117C2312yes—
273C22×C42C2311yescharacteristic
274#446—24no—
275#446—22no—
276C8×Q8—22no—
277#436—24no—
278#436—22no—
279#436—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283C8×D4—22no—
284#433—24no—
285#433—24no—
286#432—21no—
287#432—21no—
288#432C2312yes—
289#432C2312yes—
290#432C2314yes—
291#431—21no—
292#431—21no—
293#431C2312yes—
294#431C2312yes—
295#431C2314yes—
296#424—24no—
297#423—21no—
298#423—21no—
299#407C2311yescharacteristic
300#407C2312yes—
301#407C2311yescharacteristic
302#407C2314yes—
303C2×C22⋊C8C2314yes—
304#405—24no—
305C4×M16—21no—
306C4×M16—21no—
307#391—21no—
308#390—21no—
309#390—22no—
310#389—21no—
311#389—21no—
312#389—22no—
313#388—22no—
314#388—22no—
315#388—22no—
316#388—22no—
317#388—22no—
318#388—22no—
319#387—22no—
320#387—22no—
321#387—22no—
322#387—22no—
323#386—22no—
324#385—22no—
325#383—21no—
326#383C2312yes—
327#382C2312yes—
328#382C2311yescharacteristic
329#382C2311yescharacteristic
330#381C2312yes—
331#381C2311yescharacteristic
332#381C2311yescharacteristic
333#380—21no—
334#380C2312yes—
335C4×C4⋊C4—22no—
336C4×C4⋊C4—22no—
337C4×C4⋊C4—22no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4C2311yescharacteristic
343C4×C4⋊C4C2312yes—
344C4×C4⋊C4C2311yescharacteristic
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347C4×C22⋊C4—22no—
348C4×C22⋊C4—22no—
349C4×C22⋊C4—22no—
350C4×C22⋊C4C2312yes—
351C4×C22⋊C4C2312yes—
352#376C2311yescharacteristic
353#376C2311yescharacteristic
354#376C2312yes—
355#376C2312yes—
356C2×#95C2312yes—
357C43—21no—
358#328C2312yes—
359#328C2314yes—
360#328C2314yes—
361#328C2314yes—
362#328C2314yes—
363#328C2312yes—
364#328C2312yes—
365#328C2314yes—
366#328C2314yes—
367#328C2312yes—
368#328C2314yes—
369#328C2314yes—
370#328C2314yes—
371#328C2314yes—
372#327C2312yes—
373#327C2314yes—
374#327C2312yes—
375#327C2312yes—
376#327C2314yes—
377#327C2312yes—
378C2×#41—22no—
379C2×#41C22×C414yes—
380C22×Q8—22no—
381C22×Q8—21no—
382C22×Q8C22×C411yescharacteristic
383C22×Q8C22×C412yes—
384C22×Q8C22×C414yes—
385C22×Q8C2×D411yescharacteristic
386C22×D4—21no—
387C22×D4C22×C411yescharacteristic
388C22×D4C2×D411yescharacteristic
389C22×D4C2×D412yes—
390C23×C4—21no—
391C23×C4—22no—
392C23×C4C2×D411yescharacteristic
393C23×C4C2×D411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C2×M16—21no—
397C2×M16—22no—
398C2×M16—21no—
399C2×M16—24no—
400C22×C8—24no—
401C4⋊Q8—22no—
402C4⋊Q8—24no—
403C4⋊Q8—22no—
404C4⋊Q8—24no—
405C4⋊Q8—24no—
406C4⋊Q8—24no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411C4⋊Q8C22×C412yes—
412C4⋊Q8C22×C412yes—
413C4⋊Q8C22×C414yes—
414C4⋊Q8C22×C412yes—
415C4⋊Q8C22×C412yes—
416C4⋊Q8C22×C414yes—
417#126—24no—
418#126—24no—
419#126—24no—
420#126—24no—
421#126—24no—
422#126—24no—
423#126—24no—
424#126—24no—
425#126—24no—
426#126—24no—
427#126—24no—
428#126—24no—
429#126—24no—
430#126—22no—
431#126—22no—
432#126—22no—
433#126—22no—
434#126—24no—
435#126C22⋊C414yes—
436#126C22⋊C414yes—
437#126C22⋊C414yes—
438#126C22⋊C414yes—
439#125—24no—
440#125—24no—
441#125—22no—
442#125—24no—
443#125—24no—
444#125—24no—
445#125—24no—
446#125—24no—
447#125—24no—
448#125—24no—
449#125—24no—
450#125—24no—
451#125—24no—
452#125—24no—
453#125—22no—
454#125—22no—
455#125—21no—
456#125—21no—
457#125—22no—
458#125—22no—
459#125—24no—
460#125C22⋊C412yes—
461#125C22⋊C412yes—
462#125C22⋊C412yes—
463#125C22⋊C412yes—
464#125C22×C412yes—
465#125C22×C412yes—
466#125C22×C414yes—
467#124—22no—
468#124—24no—
469#124—24no—
470#124—24no—
471#124—24no—
472#124—21no—
473#124—21no—
474#124C22⋊C412yes—
475#124C22⋊C412yes—
476#124C22⋊C412yes—
477#124C22⋊C412yes—
478#124C22×C412yes—
479#124C22×C412yes—
480#124C22×C414yes—
481#123—24no—
482#123—24no—
483#123—22no—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496#123—24no—
497#123C22⋊C414yes—
498#123C22⋊C414yes—
499#123C22⋊C414yes—
500#123C22⋊C414yes—
501C22⋊Q8—22no—
502C22⋊Q8—24no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
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⋊Q8—24no—
529C22⋊Q8—24no—
530C22⋊Q8—24no—
531C22⋊Q8—24no—
532C22⋊Q8—24no—
533C22⋊Q8—24no—
534C22⋊Q8C22⋊C412yes—
535C22⋊Q8C22⋊C412yes—
536C22⋊Q8C22⋊C412yes—
537C22⋊Q8C22⋊C412yes—
538C22⋊Q8C22×C412yes—
539C22⋊Q8C22×C414yes—
540C22⋊Q8C22×C414yes—
541C22⋊Q8C22×C414yes—
542C22⋊Q8C22×C414yes—
543C22⋊Q8C2412yes—
544C22⋊Q8C2414yes—
545#121—22no—
546#121—24no—
547#121—24no—
548#121—24no—
549#121—21no—
550#121—21no—
551#121—24no—
552#121C22⋊C412yes—
553#121C22⋊C412yes—
554#121C22⋊C412yes—
555#121C22⋊C412yes—
556#121C22×C412yes—
557#121C22×C414yes—
558#121C2412yes—
559#120—24no—
560#120—24no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—24no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—24no—
576C4×Q8—44no—
577C4×Q8C22×C412yes—
578C4×Q8C22×C414yes—
579C4×Q8C22×C412yes—
580C4×Q8C22×C414yes—
581C4×Q8C22×C414yes—
582C4×Q8C22×C414yes—
583C4×Q8C22×C414yes—
584C4×Q8C22×C412yes—
585C4×Q8C22×C412yes—
586C4×Q8C2×D412yes—
587C4×Q8C2×D412yes—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—44no—
608C4×D4C22×C412yes—
609C4×D4C22×C412yes—
610C4×D4C22×C414yes—
611C4×D4C22×C414yes—
612C4×D4C22×C412yes—
613C4×D4C22×C412yes—
614C4×D4C22×C414yes—
615C4×D4C2×D412yes—
616C4×D4C2×D412yes—
617C4×D4C2×D414yes—
618C4×D4C2×D414yes—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—24no—
624#117—22no—
625#117—24no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—24no—
636#117—44no—
637#117C22×C414yes—
638#117C22×C414yes—
639#117C22×C414yes—
640#117C2×D414yes—
641#117C2×D414yes—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—24no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4C22×C411yescharacteristic
662C2×C4⋊C4C22×C411yescharacteristic
663C2×C4⋊C4C22×C412yes—
664C2×C4⋊C4C22×C414yes—
665C2×C4⋊C4C2×D412yes—
666C2×C4⋊C4C2×D412yes—
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D412yes—
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D412yes—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—24no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4C2×D412yes—
686C2×C22⋊C4C2×D412yes—
687C2×C22⋊C4C2×D412yes—
688C2×C22⋊C4C2×D412yes—
689C2×C22⋊C4C2×D412yes—
690C2×C42—21no—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—21no—
694C2×C42—22no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—22no—
700C2×C42—22no—
701C2×C42C22×C411yescharacteristic
702C2×C42C22×C411yescharacteristic
703C2×C42C22×C411yescharacteristic
704C2×C42C22×C411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—24no—
719C4⋊C8—24no—
720C22⋊C8—24no—
721C22⋊C8—21no—
722C22⋊C8—22no—
723C22⋊C8—21no—
724C22⋊C8—24no—
725C22⋊C8C2412yes—
726C22⋊C8C2414yes—
727C22⋊C8C2412yes—
728#97—22no—
729#97—22no—
730#97—24no—
731C4×C8—22no—
732C4×C8—22no—
733C4×C8—24no—
734#95—22no—
735#95—21no—
736#95—22no—
737#95—21no—
738#95—22no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—22no—
743#95—22no—
744#95—21no—
745#95—22no—
746#95—22no—
747#95C2411yescharacteristic
748#95C2412yes—
749#95C2411yescharacteristic
750#95C2411yescharacteristic
751#95C2412yes—
752#95C2411yescharacteristic
753C24—21no—
754C24C22×D411yescharacteristic
755C24C22×D412yes—
756#41—84no—
757#41—84no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—21no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—42no—
765C2×Q8—82no—
766C2×Q8—84no—
767C2×Q8—81no—
768C2×Q8—82no—
769C2×Q8—84no—
770C2×Q8C2×C22⋊C412yes—
771C2×Q8C2×C22⋊C412yes—
772C2×Q8C23×C412yes—
773C2×Q8C23×C414yes—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—21no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—81no—
785C2×D4C2×C22⋊C412yes—
786C2×D4C2×C22⋊C414yes—
787C2×D4C2×C22⋊C414yes—
788C2×D4C2×C22⋊C412yes—
789C2×D4C23×C412yes—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—42no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—44no—
811C22×C4—82no—
812C22×C4—81no—
813C22×C4—82no—
814C22×C4—82no—
815C22×C4—82no—
816C22×C4C2×C22⋊C411yescharacteristic
817C22×C4C2×C22⋊C411yescharacteristic
818C22×C4C2×C22⋊C411yescharacteristic
819C22×C4C2×C22⋊C411yescharacteristic
820C22×C4C2×C22⋊C411yescharacteristic
821C22×C4C2×C22⋊C411yescharacteristic
822C22×C4C2×C22⋊C411yescharacteristic
823C22×C4C2×C22⋊C411yescharacteristic
824C22×C4C23×C411yescharacteristic
825C22×C4C23×C411yescharacteristic
826C22×C4C23×C414yes—
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D412yes—
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D412yes—
834C22×C4C22×D412yes—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D414yes—
838C22×C4C2511yescharacteristic
839M16—81no—
840M16—82no—
841M16—84no—
842M16—81no—
843C2×C8—22no—
844C2×C8—24no—
845C2×C8—22no—
846C2×C8—84no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—82no—
886C4⋊C4—82no—
887C4⋊C4C2×C22⋊C414yes—
888C4⋊C4C2×C22⋊C412yes—
889C4⋊C4C2×C22⋊C414yes—
890C4⋊C4C2×C22⋊C412yes—
891C4⋊C4C2×C22⋊C414yes—
892C4⋊C4C2×C22⋊C414yes—
893C4⋊C4C2×C22⋊C414yes—
894C4⋊C4C2×C22⋊C412yes—
895C4⋊C4C2×C22⋊C414yes—
896C4⋊C4C2×C22⋊C414yes—
897C4⋊C4C2×C22⋊C412yes—
898C4⋊C4C2×C22⋊C414yes—
899C4⋊C4C23×C412yes—
900C4⋊C4C23×C414yes—
901C4⋊C4C23×C412yes—
902C22⋊C4—24no—
903C22⋊C4—22no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—22no—
909C22⋊C4—24no—
910C22⋊C4—22no—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—22no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—82no—
925C22⋊C4—81no—
926C22⋊C4—82no—
927C22⋊C4—81no—
928C22⋊C4C2×C22⋊C414yes—
929C22⋊C4C2×C22⋊C414yes—
930C22⋊C4C2×C22⋊C414yes—
931C22⋊C4C2×C22⋊C414yes—
932C22⋊C4C2×C22⋊C414yes—
933C22⋊C4C2×C22⋊C414yes—
934C22⋊C4C2×C22⋊C414yes—
935C22⋊C4C2×C22⋊C414yes—
936C22⋊C4C2×C22⋊C414yes—
937C22⋊C4C2×C22⋊C414yes—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—44no—
947C42—42no—
948C42—42no—
949C42—44no—
950C42—81no—
951C42—81no—
952C42—82no—
953C42—82no—
954C42—82no—
955C42C2×C22⋊C411yescharacteristic
956C42C2×C22⋊C411yescharacteristic
957C42C2×C22⋊C411yescharacteristic
958C42C2×C22⋊C411yescharacteristic
959C42C2×C22⋊C411yescharacteristic
960C42C2×C22⋊C411yescharacteristic
961C42C2×C22⋊C411yescharacteristic
962C42C2×C22⋊C411yescharacteristic
963C42C23×C411yescharacteristic
964C42C23×C411yescharacteristic
965C42C23×C411yescharacteristic
966C42C23×C411yescharacteristic
967C42C23×C414yes—
968C42C22×D411yescharacteristic
969C42C22×D411yescharacteristic
970C42C22×D414yes—
971C42C22×D411yescharacteristic
972C42C22×D411yescharacteristic
973C23—22no—
974C23—21no—
975C23—21no—
976C23—22no—
977C23—22no—
978C23—41no—
979C23—42no—
980C23—41no—
981C23—42no—
982C23—42no—
983C23—81no—
984C23—81no—
985C23C22×C22⋊C414yes—
986C23C22×C22⋊C411yescharacteristic
987C23C22×C22⋊C411yescharacteristic
988C23C23×D411yescharacteristic
989Q8—24no—
990Q8—42no—
991Q8—42no—
992Q8—44no—
993Q8—44no—
994Q8—84no—
995Q8—81no—
996Q8—82no—
997Q8—82no—
998Q8—84no—
999D4—24no—
1000D4—44no—
1001D4—44no—
1002D4—42no—
1003D4—42no—
1004D4—44no—
1005D4—42no—
1006D4—42no—
1007D4—81no—
1008D4—84no—
1009D4—84no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—42no—
1027C2×C4—41no—
1028C2×C4—42no—
1029C2×C4—44no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—44no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—44no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—42no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—42no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—42no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—82no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—81no—
1065C2×C4—82no—
1066C2×C4—84no—
1067C2×C4—81no—
1068C2×C4—82no—
1069C2×C4—84no—
1070C2×C4—164no—
1071C2×C4C22×C22⋊C411yescharacteristic
1072C2×C4C22×C22⋊C411yescharacteristic
1073C2×C4C22×C22⋊C411yescharacteristic
1074C2×C4C22×C22⋊C414yes—
1075C2×C4C22×C22⋊C414yes—
1076C2×C4C22×C22⋊C414yes—
1077C2×C4C22×C22⋊C411yescharacteristic
1078C2×C4C22×C22⋊C411yescharacteristic
1079C2×C4C22×C22⋊C411yescharacteristic
1080C2×C4C22×C22⋊C411yescharacteristic
1081C2×C4C22×C22⋊C411yescharacteristic
1082C2×C4C22×C22⋊C411yescharacteristic
1083C2×C4C22×C22⋊C411yescharacteristic
1084C2×C4C24×C411yescharacteristic
1085C2×C4C23×D411yescharacteristic
1086C8—42no—
1087C8—44no—
1088C8—42no—
1089C22—21no—
1090C22—21no—
1091C22—21no—
1092C22—24no—
1093C22—21no—
1094C22—21no—
1095C22—21no—
1096C22—24no—
1097C22—21no—
1098C22—21no—
1099C22—24no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—82no—
1104C22—81no—
1105C22—82no—
1106C22—81no—
1107C22—162no—
1108C22C23×C22⋊C411yescharacteristic
1109C22#358611yescharacteristic
1110C22#358611yescharacteristic
1111C4—21no—
1112C4—21no—
1113C4—24no—
1114C4—21no—
1115C4—21no—
1116C4—21no—
1117C4—21no—
1118C4—21no—
1119C4—21no—
1120C4—24no—
1121C4—21no—
1122C4—21no—
1123C4—21no—
1124C4—24no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—44no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—82no—
1135C4—81no—
1136C4#290112yes—
1137C2—21no—
1138C2—21no—
1139C2—41no—
1140C2—44no—
1141C2—41no—
1142C2—82no—
1143C2#6007011yescharacteristic
1144C2#6008811yescharacteristic
1145C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62823C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60289C2semidirect
3. #34237C2semidirect
4. #17627C2semidirect
5. #17625C2semidirect
6. #17623C2semidirect
7. #17621C2semidirect
8. #17609C2semidirect
9. #17605C2semidirect
10. #17601C2semidirect
11. #17600C2semidirect
12. #17590C2semidirect
13. #17554C2semidirect
14. #17549C2semidirect
15. #17548C2semidirect
16. #17545C2semidirect
17. #17537C2semidirect
21. #3563C4semidirect
23. #3561C4semidirect
25. #3552C4semidirect
26. #3552C4semidirect
27. #3523C4semidirect
29. #3520C4semidirect
32. #3516C4semidirect
45. #2984C22semidirect
47. #2974C22semidirect
51. #2924C22semidirect
60. #2346C22semidirect
61. #2343C22semidirect
63. #2320C22semidirect
64. #2319C22semidirect
67. #2276C22semidirect
68. #2275C22semidirect
71. #1520C22semidirect
72. #1518C22semidirect
73. #1518C22semidirect
74. #1518C22semidirect
76. #1515C22semidirect
85. #1511C22semidirect
94. #1508C22semidirect
96. #1506C22semidirect
97. #1506C22semidirect
98. #1506C22semidirect
99. #1506C22semidirect
101. #1503C22semidirect
102. #1503C22semidirect
103. #1503C22semidirect
109. C2×#328C22semidirect
117. #557C2×C4semidirect
118. #557C2×C4semidirect
119. #557C2×C4semidirect
124. #556C2×C4semidirect
125. #556C2×C4semidirect
132. #554C2×C4semidirect
133. #554C2×C4semidirect
137. #553C2×C4semidirect
149. #552C2×C4semidirect
159. D4×Q8C2×C4semidirect
160. D4×Q8C2×C4semidirect
161. D4×Q8C2×C4semidirect
165. #548C2×C4semidirect
169. #546C2×C4semidirect
173. #544C2×C4semidirect
181. #542C2×C4semidirect
182. #542C2×C4semidirect
189. #541C2×C4semidirect
190. #541C2×C4semidirect
200. #536C2×C4semidirect
207. #533C2×C4semidirect
208. #533C2×C4semidirect
212. C2×C4⋊Q8C2×C4semidirect
213. C2×C4⋊Q8C2×C4semidirect
225. #529C2×C4semidirect
226. #529C2×C4semidirect
237. C2×#125C2×C4semidirect
239. C2×#124C2×C4semidirect
254. #520C2×C4semidirect
256. #519C2×C4semidirect
261. C2×C4×Q8C2×C4semidirect
262. C2×C4×Q8C2×C4semidirect
266. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628232
#602892
#342372
#176272
#176252
#176232
#176212
#176092
#176052
#176012
#176002
#175902
#175542
#175492
#175482
#175452
#175372