Finite Group Databasebeta

← #6393861

Subgroups — #6393861

Order 512.

3183 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#60263C211yesmaximal, characteristic, complemented
3M16×#41C211yesmaximal, characteristic, complemented
4#22537C214yesmaximal, complemented
5#22411C214yesmaximal, complemented
6#22410C218yesmaximal, complemented
7#21879C212yesmaximal, complemented
8#21878C211yesmaximal, characteristic, complemented
9#21800C212yesmaximal, complemented
10#21799C211yesmaximal, characteristic, complemented
11#21425C212yesmaximal, complemented
12#21424C211yesmaximal, characteristic, complemented
13#21218C212yesmaximal, complemented
14C2×#1966C211yesmaximal, characteristic, complemented
15#3511—21no—
16#3511—21no—
17#3511—22no—
18#3511—22no—
19#3511—21no—
20#3511—21no—
21#3511—21no—
22#3511—21no—
23#3511—22no—
24#3511—22no—
25#3511—21no—
26#3511—21no—
27C2×#556C2212yes—
28C2×#555C412yes—
29C2×#554C412yes—
30C2×#553C414yes—
31C2×#548C2214yes—
32C2×#547C2212yes—
33C2×#542C414yes—
34C2×#537C412yes—
35C2×#533C2212yes—
36C2×#532C2212yes—
37C2×#532C2211yescharacteristic
38C22×C4⋊Q8C2211yescharacteristic
39C2×#520C412yes—
40C2×C4×#41C2211yescharacteristic
41#2991—21no—
42#2990—22no—
43#2990—21no—
44#2989—21no—
45#2989—22no—
46#2988—21no—
47#2971—21no—
48#2970—22no—
49#2970—21no—
50#2965—21no—
51#2965—22no—
52C8×#41—21no—
53Q8×M16C2212yes—
54Q8×M16C2212yes—
55D4×M16C2214yes—
56D4×M16C2212yes—
57D4×M16C2214yes—
58D4×M16C2212yes—
59#2920C2211yescharacteristic
60#2920C2211yescharacteristic
61#2920C2212yes—
62#2920C2212yes—
63C2×#423C2211yescharacteristic
64C2×#423C2212yes—
65C2×#413C2218yes—
66C22×#101C2214yes—
67C2×C4×M16C2211yescharacteristic
68C2×C4×M16C2212yes—
69#1997C2212yes—
70#1997C2211yescharacteristic
71#1997C2211yescharacteristic
72#1967C2218yes—
73#1967C2218yes—
74#1966C2214yes—
75#1966C2214yes—
76#1966C2212yes—
77#1966C2212yes—
78#1966C2212yes—
79#1966C2212yes—
80#1965C2211yescharacteristic
81#1965C2212yes—
82#1965C2211yescharacteristic
83#1901C2218yes—
84#1901C2218yes—
85#1900C2214yes—
86#1900C2214yes—
87#1801C2218yes—
88#1800C2214yes—
89#1785C2218yes—
90#1784C2214yes—
91C4×#101C2218yes—
92C4×#100C2214yes—
93C22×#41C2×C412yes—
94C22×#41C2×C411yescharacteristic
95C22×#41C2314yes—
96C23×Q8C2312yes—
97C22×M16C2312yes—
98C22×M16C2314yes—
99C22×M16C2312yes—
100C22×M16C2314yes—
101#556—22no—
102#556—22no—
103#556—22no—
104#556—22no—
105#556—24no—
106#556—24no—
107#555—22no—
108#555—22no—
109#555—24no—
110#555—22no—
111#555—22no—
112#555—24no—
113#554—22no—
114#554—22no—
115#554—22no—
116#554—22no—
117#554—24no—
118#554—24no—
119#553—24no—
120#553—24no—
121#553—24no—
122#553—24no—
123#553—24no—
124#553—24no—
125#553—24no—
126#553—24no—
127#548—24no—
128#548—24no—
129#548—24no—
130#548—24no—
131#548—24no—
132#548—24no—
133#548—24no—
134#548—24no—
135#547—22no—
136#547—22no—
137#547—24no—
138#547—24no—
139#547—22no—
140#547—22no—
141#542—24no—
142#542—24no—
143#542—24no—
144#542—24no—
145#542—24no—
146#542—24no—
147#542—24no—
148#542—24no—
149#537—22no—
150#537—22no—
151#537—22no—
152#537—22no—
153#537—24no—
154#537—24no—
155#533—22no—
156#533—22no—
157#533—22no—
158#533—22no—
159#533—22no—
160#533—22no—
161#533—22no—
162#533—22no—
163#532—21no—
164#532—21no—
165#532—21no—
166#532—21no—
167#532—21no—
168#532—21no—
169#532—21no—
170#532—21no—
171#532—22no—
172#532—22no—
173#532—22no—
174#532—22no—
175#532—22no—
176#532—22no—
177#532—22no—
178#532—22no—
179C2×C4⋊Q8—21no—
180C2×C4⋊Q8—21no—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8—21no—
183C2×C4⋊Q8—21no—
184C2×C4⋊Q8—21no—
185C2×C4⋊Q8—21no—
186C2×C4⋊Q8—21no—
187C2×C4⋊Q8C2×C412yes—
188C2×C4⋊Q8C2×C412yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×#127C2311yescharacteristic
193C2×#126C2×C418yes—
194C2×#125C2×C414yes—
195C2×#124C2×C412yes—
196C2×#124C2×C418yes—
197C2×#124C2314yes—
198C2×#123C2×C418yes—
199C2×C22⋊Q8C2×C414yes—
200C2×C22⋊Q8C2×C414yes—
201C2×C22⋊Q8C2×C418yes—
202C2×C22⋊Q8C2314yes—
203C2×#121C2×C414yes—
204C2×#121C2×C412yes—
205C2×#121C2×C414yes—
206C2×#121C2×C414yes—
207C2×#121C2×C418yes—
208C2×#121C2312yes—
209#520—24no—
210#520—24no—
211#520—22no—
212#520—22no—
213#520—22no—
214#520—22no—
215C4×#41D411yescharacteristic
216C4×#41D411yescharacteristic
217C4×#41D412yes—
218C4×#41D412yes—
219C4×#41D411yescharacteristic
220C4×#41D411yescharacteristic
221C4×#41D411yescharacteristic
222C4×#41D411yescharacteristic
223C4×#41D412yes—
224C4×#41D412yes—
225C4×#41D411yescharacteristic
226C4×#41D411yescharacteristic
227C2×C4×Q8C2×C414yes—
228C2×C4×Q8C2×C411yescharacteristic
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4C2×C414yes—
232C2×C4×D4C2×C418yes—
233C2×C4×D4C2×C414yes—
234C2×C4×D4C2×C412yes—
235C2×C4×D4C2×C412yes—
236C2×C4×D4C2×C411yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×#117C2×C414yes—
241C2×#117C2×C414yes—
242C2×#117C2×C411yescharacteristic
243C2×#117C2×C412yes—
244C22×C4⋊C4C2×C412yes—
245C22×C4⋊C4C2×C414yes—
246C22×C4⋊C4C2×C412yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249#446—22no—
250#446—24no—
251#446—22no—
252#446—24no—
253C8×Q8—22no—
254C8×Q8—22no—
255#436—22no—
256#436—24no—
257#436—22no—
258#436—24no—
259#435—24no—
260#435—24no—
261#435—24no—
262#435—24no—
263#435—24no—
264#435—24no—
265C8×D4—22no—
266C8×D4—24no—
267C8×D4—22no—
268C8×D4—24no—
269#432—21no—
270#432—22no—
271#432—21no—
272#432—22no—
273#432—21no—
274#432—22no—
275#432—21no—
276#432—22no—
277#431—21no—
278#431—22no—
279#431—21no—
280#431—22no—
281#431—21no—
282#431—22no—
283#431—21no—
284#431—22no—
285#423—21no—
286#423—22no—
287#423—21no—
288#423—22no—
289#423C2312yes—
290#423C2312yes—
291#423C2314yes—
292#423C2314yes—
293#423C2312yes—
294#423C2311yescharacteristic
295#423C2311yescharacteristic
296C2×C4⋊C8—21no—
297C2×C4⋊C8—22no—
298C2×C4⋊C8—21no—
299C2×C4⋊C8—22no—
300#413—416no—
301C2×#101—48no—
302C2×#101C2318yes—
303C2×#101C2318yes—
304C2×#101C2318yes—
305C2×#101C2318yes—
306C2×#100C2314yes—
307C2×#100C2318yes—
308C2×#100C2314yes—
309#407C2312yes—
310#407C2312yes—
311#407C2314yes—
312#407C2314yes—
313C4×M16—21no—
314C4×M16—22no—
315C4×M16—21no—
316C4×M16—22no—
317C4×M16C2311yescharacteristic
318C4×M16C2311yescharacteristic
319C4×M16C2312yes—
320C4×M16C2312yes—
321C4×M16C2314yes—
322C4×M16C2312yes—
323C4×M16C2314yes—
324C2×#97—21no—
325C2×#97—22no—
326C2×C4×C8—21no—
327C2×C4×C8—22no—
328#343C2318yes—
329#343C2314yes—
330#343C2314yes—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—48no—
340C2×#41—48no—
341C2×#41—44no—
342C2×#41—48no—
343C2×#41C22⋊C411yescharacteristic
344C2×#41C22⋊C411yescharacteristic
345C2×#41C22⋊C412yes—
346C2×#41C22⋊C412yes—
347C2×#41C22⋊C411yescharacteristic
348C2×#41C22⋊C411yescharacteristic
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—44no—
354C22×Q8—44no—
355C22×Q8C22×C412yes—
356C22×Q8C22×C414yes—
357C22×Q8C22×C411yescharacteristic
358C22×Q8C2414yes—
359C22×D4C22×C412yes—
360C22×D4C22×C414yes—
361C22×D4C22×C412yes—
362C22×D4C22×C418yes—
363C22×D4C22×C411yescharacteristic
364C22×D4C22×C412yes—
365C22×D4C2412yes—
366C23×C4C22×C411yescharacteristic
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C22×C418yes—
370C23×C4C22×C411yescharacteristic
371C23×C4C22×C412yes—
372C23×C4C22×C412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C2×M16—22no—
376C2×M16—24no—
377C2×M16—22no—
378C2×M16—24no—
379C2×M16—24no—
380C2×M16—28no—
381C2×M16—42no—
382C2×M16—44no—
383C2×M16—44no—
384C2×M16—48no—
385C2×M16C2412yes—
386C2×M16C2414yes—
387C2×M16C2414yes—
388C2×M16C2412yes—
389C2×M16C2412yes—
390C2×M16C2412yes—
391C22×C8—22no—
392C22×C8—24no—
393C22×C8—22no—
394C22×C8—24no—
395C4⋊Q8—22no—
396C4⋊Q8—22no—
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—22no—
401C4⋊Q8—22no—
402C4⋊Q8—22no—
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405C4⋊Q8—22no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410C4⋊Q8—22no—
411C4⋊Q8—21no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8—21no—
415#127—21no—
416#127—21no—
417#127—21no—
418#127—21no—
419#126—28no—
420#126—28no—
421#126—28no—
422#126—28no—
423#125—24no—
424#125—24no—
425#125—24no—
426#125—24no—
427#124—28no—
428#124—28no—
429#124—28no—
430#124—28no—
431#124—22no—
432#124—22no—
433#124—22no—
434#124—22no—
435#124—24no—
436#124—24no—
437#124—24no—
438#124—24no—
439#123—28no—
440#123—28no—
441#123—28no—
442#123—28no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—28no—
446C22⋊Q8—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—24no—
451C22⋊Q8—24no—
452C22⋊Q8—24no—
453C22⋊Q8—24no—
454C22⋊Q8—28no—
455C22⋊Q8—28no—
456C22⋊Q8—28no—
457C22⋊Q8—28no—
458#121—24no—
459#121—24no—
460#121—28no—
461#121—28no—
462#121—28no—
463#121—28no—
464#121—28no—
465#121—24no—
466#121—24no—
467#121—24no—
468#121—24no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—24no—
474#121—24no—
475#121—24no—
476#121—24no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481C4×Q8—24no—
482C4×Q8—24no—
483C4×Q8—24no—
484C4×Q8—24no—
485C4×Q8—24no—
486C4×Q8—24no—
487C4×Q8—24no—
488C4×Q8—24no—
489C4×Q8C22⋊C411yescharacteristic
490C4×Q8C22⋊C411yescharacteristic
491C4×Q8C22⋊C411yescharacteristic
492C4×Q8C22⋊C411yescharacteristic
493C4×Q8C22⋊C412yes—
494C4×Q8C22⋊C412yes—
495C4×Q8C2×D411yescharacteristic
496C4×Q8C2×D411yescharacteristic
497C4×Q8C2×D411yescharacteristic
498C4×Q8C2×D411yescharacteristic
499C4×Q8C2×D412yes—
500C4×Q8C2×D412yes—
501C4×D4—28no—
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—24no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4C22⋊C412yes—
522C4×D4C22⋊C412yes—
523C4×D4C22⋊C412yes—
524C4×D4C22⋊C412yes—
525C4×D4C22⋊C412yes—
526C4×D4C22⋊C412yes—
527C4×D4C22⋊C412yes—
528C4×D4C22⋊C412yes—
529C4×D4C22⋊C411yescharacteristic
530C4×D4C22⋊C411yescharacteristic
531C4×D4C22⋊C412yes—
532C4×D4C22⋊C411yescharacteristic
533C4×D4C22⋊C411yescharacteristic
534C4×D4C22⋊C412yes—
535C4×D4C2×D411yescharacteristic
536C4×D4C2×D411yescharacteristic
537C4×D4C2×D412yes—
538C4×D4C2×D412yes—
539C4×D4C2×D411yescharacteristic
540C4×D4C2×D411yescharacteristic
541C4×D4C2×D412yes—
542C4×D4C2×D412yes—
543C4×D4C2×D412yes—
544C4×D4C2×D412yes—
545C4×D4C2×D412yes—
546C4×D4C2×D412yes—
547C4×D4C2×D412yes—
548C4×D4C2×D412yes—
549#117—24no—
550#117—24no—
551#117—24no—
552#117—24no—
553#117—28no—
554#117—24no—
555#117—24no—
556#117C22⋊C412yes—
557#117C22⋊C411yescharacteristic
558#117C22⋊C412yes—
559#117C22⋊C411yescharacteristic
560#117C22⋊C411yescharacteristic
561#117C22⋊C411yescharacteristic
562#117C22⋊C412yes—
563#117C22⋊C412yes—
564#117C22⋊C412yes—
565#117C22⋊C412yes—
566#117C22⋊C412yes—
567#117C22⋊C412yes—
568#117C22⋊C412yes—
569#117C22⋊C412yes—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—28no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4C22×C414yes—
582C2×C4⋊C4C22×C414yes—
583C2×C4⋊C4C22×C414yes—
584C2×C4⋊C4C22×C418yes—
585C2×C4⋊C4C22×C414yes—
586C2×C4⋊C4C22×C412yes—
587C2×C4⋊C4C22×C418yes—
588C2×C4⋊C4C22×C411yescharacteristic
589C2×C4⋊C4C22×C411yescharacteristic
590C2×C4⋊C4C22×C412yes—
591C2×C4⋊C4C22×C412yes—
592C2×C4⋊C4C2412yes—
593C2×C22⋊C4C22×C418yes—
594C2×C22⋊C4C22×C418yes—
595C2×C22⋊C4C22×C418yes—
596C2×C22⋊C4C22×C414yes—
597C2×C22⋊C4C22×C414yes—
598C2×C22⋊C4C22×C412yes—
599C2×C22⋊C4C22×C412yes—
600C2×C22⋊C4C22×C412yes—
601C2×C42C22×C418yes—
602C2×C42C22×C412yes—
603C2×C42C22×C411yescharacteristic
604C2×C42C22×C412yes—
605C2×C42C22×C411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D412yes—
615C2×C42C2×D412yes—
616C2×C42C2×D412yes—
617C2×C42C2×D412yes—
618C2×C42C2×D412yes—
619C2×C42C2×D412yes—
620C2×C42C2×D412yes—
621C2×C42C2×D412yes—
622C2×C42C2411yescharacteristic
623C2×C42C2412yes—
624C2×C42C2411yescharacteristic
625C4⋊C8—22no—
626C4⋊C8—21no—
627C4⋊C8—22no—
628C4⋊C8—21no—
629C4⋊C8—22no—
630C4⋊C8—24no—
631C4⋊C8—22no—
632C4⋊C8—24no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635C4⋊C8—22no—
636C4⋊C8—24no—
637C4⋊C8—22no—
638C4⋊C8—24no—
639#101—216no—
640#101—48no—
641#101—48no—
642#101—48no—
643#100—28no—
644#100—44no—
645#100—48no—
646C22⋊C8—22no—
647C22⋊C8—24no—
648C22⋊C8—22no—
649C22⋊C8—24no—
650C22⋊C8—22no—
651C22⋊C8—24no—
652C22⋊C8—22no—
653C22⋊C8—24no—
654#97—21no—
655#97—21no—
656#97—22no—
657#97—22no—
658#97—24no—
659#97—22no—
660#97—24no—
661C4×C8—21no—
662C4×C8—21no—
663C4×C8—22no—
664C4×C8—22no—
665C4×C8—24no—
666C4×C8—22no—
667C4×C8—24no—
668C24C23×C411yescharacteristic
669C24C23×C414yes—
670C24C23×C412yes—
671#41—24no—
672#41—24no—
673#41—44no—
674#41—44no—
675#41—42no—
676#41—42no—
677#41—48no—
678#41—48no—
679#41—48no—
680#41—48no—
681#41—88no—
682#41—88no—
683#41—84no—
684#41—84no—
685#41—84no—
686#41—84no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—24no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—48no—
696C2×Q8—42no—
697C2×Q8—44no—
698C2×Q8—84no—
699C2×Q8—84no—
700C2×Q8—82no—
701C2×Q8—82no—
702C2×Q8—82no—
703C2×Q8—82no—
704C2×Q8C2×C22⋊C411yescharacteristic
705C2×Q8C2×C22⋊C411yescharacteristic
706C2×Q8C2×C22⋊C412yes—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—416no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4C2×C22⋊C412yes—
726C2×D4C2×C22⋊C412yes—
727C2×D4C2×C22⋊C411yescharacteristic
728C2×D4C2×C22⋊C411yescharacteristic
729C2×D4C2×C22⋊C412yes—
730C2×D4C2×C22⋊C412yes—
731C2×D4C2×C22⋊C412yes—
732C22×C4—22no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—416no—
748C22×C4—48no—
749C22×C4C2×C22⋊C411yescharacteristic
750C22×C4C2×C22⋊C411yescharacteristic
751C22×C4C2×C22⋊C411yescharacteristic
752C22×C4C2×C22⋊C411yescharacteristic
753C22×C4C2×C22⋊C411yescharacteristic
754C22×C4C2×C22⋊C412yes—
755C22×C4C2×C22⋊C412yes—
756C22×C4C2×C22⋊C412yes—
757C22×C4C2×C22⋊C412yes—
758C22×C4C2×C22⋊C411yescharacteristic
759C22×C4C2×C22⋊C411yescharacteristic
760C22×C4C2×C22⋊C412yes—
761C22×C4C2×C22⋊C412yes—
762C22×C4C2×C22⋊C412yes—
763C22×C4C2×C22⋊C412yes—
764C22×C4C2×C22⋊C411yescharacteristic
765C22×C4C23×C418yes—
766C22×C4C23×C411yescharacteristic
767C22×C4C23×C411yescharacteristic
768C22×C4C23×C411yescharacteristic
769C22×C4C23×C412yes—
770C22×C4C23×C411yescharacteristic
771C22×C4C23×C414yes—
772C22×C4C23×C412yes—
773C22×C4C23×C411yescharacteristic
774C22×C4C23×C412yes—
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D412yes—
780C22×C4C22×D412yes—
781C22×C4C22×D412yes—
782C22×C4C22×D412yes—
783C22×C4C2511yescharacteristic
784M16—22no—
785M16—24no—
786M16—24no—
787M16—28no—
788M16—22no—
789M16—22no—
790M16—24no—
791M16—24no—
792M16—44no—
793M16—48no—
794M16—82no—
795M16—84no—
796M16H(5,𝔽2)14yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—24no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8—24no—
803C2×C8—44no—
804C2×C8—48no—
805C2×C8—82no—
806C2×C8—84no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4C2×C22⋊C412yes—
824C4⋊C4C2×C22⋊C411yescharacteristic
825C4⋊C4C2×C22⋊C411yescharacteristic
826C4⋊C4C2×C22⋊C412yes—
827C4⋊C4C2×C22⋊C411yescharacteristic
828C4⋊C4C2×C22⋊C411yescharacteristic
829C4⋊C4C2×C22⋊C412yes—
830C4⋊C4C2×C22⋊C412yes—
831C4⋊C4C2×C22⋊C412yes—
832C4⋊C4C2×C22⋊C412yes—
833C4⋊C4C2×C22⋊C412yes—
834C4⋊C4C2×C22⋊C412yes—
835C4⋊C4C2×C22⋊C412yes—
836C4⋊C4C2×C22⋊C412yes—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4C2×C22⋊C412yes—
848C22⋊C4C2×C22⋊C412yes—
849C22⋊C4C2×C22⋊C412yes—
850C22⋊C4C2×C22⋊C412yes—
851C22⋊C4C2×C22⋊C412yes—
852C22⋊C4C2×C22⋊C412yes—
853C22⋊C4C2×C22⋊C412yes—
854C22⋊C4C2×C22⋊C412yes—
855C22⋊C4C2×C22⋊C412yes—
856C22⋊C4C2×C22⋊C412yes—
857C22⋊C4C2×C22⋊C412yes—
858C22⋊C4C2×C22⋊C412yes—
859C42—28no—
860C42—28no—
861C42C2×C22⋊C412yes—
862C42C2×C22⋊C412yes—
863C42C2×C22⋊C412yes—
864C42C2×C22⋊C412yes—
865C42C2×C22⋊C411yescharacteristic
866C42C2×C22⋊C411yescharacteristic
867C42C2×C22⋊C411yescharacteristic
868C42C2×C22⋊C411yescharacteristic
869C42C2×C22⋊C412yes—
870C42C2×C22⋊C412yes—
871C42C2×C22⋊C412yes—
872C42C2×C22⋊C412yes—
873C42C2×C22⋊C411yescharacteristic
874C42C2×C22⋊C411yescharacteristic
875C42C2×C22⋊C411yescharacteristic
876C42C2×C22⋊C411yescharacteristic
877C42C22×D411yescharacteristic
878C42C22×D411yescharacteristic
879C42C22×D411yescharacteristic
880C42C22×D412yes—
881C42C22×D412yes—
882C42C22×D411yescharacteristic
883C42C22×D411yescharacteristic
884C42C22×D411yescharacteristic
885C42C22×D412yes—
886C42C22×D412yes—
887C42C22×D411yescharacteristic
888C42C22×D411yescharacteristic
889C23—22no—
890C23—22no—
891C23—24no—
892C23—24no—
893C23—28no—
894C23—41no—
895C23—42no—
896C23—42no—
897C23—44no—
898C23—44no—
899C23C22×C22⋊C412yes—
900C23C22×C22⋊C412yes—
901C23C22×C22⋊C411yescharacteristic
902C23C22×C22⋊C411yescharacteristic
903C23C24×C411yescharacteristic
904Q8—22no—
905Q8—22no—
906Q8—42no—
907Q8—44no—
908Q8—44no—
909Q8—48no—
910Q8—44no—
911Q8—44no—
912Q8—84no—
913Q8—84no—
914D4—24no—
915D4—24no—
916D4—22no—
917D4—22no—
918D4—42no—
919D4—42no—
920D4—42no—
921D4—44no—
922D4—44no—
923D4—48no—
924D4—48no—
925D4—44no—
926D4—44no—
927D4—44no—
928D4—42no—
929D4—42no—
930D4—88no—
931D4—88no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—28no—
960C2×C4—216no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—48no—
971C2×C4—48no—
972C2×C4—44no—
973C2×C4—88no—
974C2×C4—88no—
975C2×C4—84no—
976C2×C4—84no—
977C2×C4#41314yescomplemented
978C2×C4C22×C22⋊C412yes—
979C2×C4C22×C22⋊C412yes—
980C2×C4C22×C22⋊C411yescharacteristic
981C2×C4C22×C22⋊C411yescharacteristic
982C2×C4C22×C22⋊C411yescharacteristic
983C2×C4C22×C22⋊C411yescharacteristic
984C2×C4C22×C22⋊C412yes—
985C2×C4C22×C22⋊C412yes—
986C2×C4C22×C22⋊C411yescharacteristic
987C2×C4C22×C22⋊C411yescharacteristic
988C2×C4C22×C22⋊C412yes—
989C2×C4C22×C22⋊C412yes—
990C2×C4C22×C22⋊C411yescharacteristic
991C2×C4C22×C22⋊C411yescharacteristic
992C2×C4C22×C22⋊C411yescharacteristic
993C2×C4C22×C22⋊C411yescharacteristic
994C2×C4C23×D411yescharacteristic
995C2×C4C23×D411yescharacteristic
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4#58512yes—
998C8—24no—
999C8—44no—
1000C8—42no—
1001C8—42no—
1002C8—44no—
1003C8—42no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—22no—
1010C22—22no—
1011C22—21no—
1012C22—22no—
1013C22—22no—
1014C22—21no—
1015C22—22no—
1016C22—22no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—84no—
1022C22—88no—
1023C22C2×#41312yes—
1024C22C23×C22⋊C411yescharacteristic
1025C22C4×H(5,𝔽2)12yes—
1026C4—21no—
1027C4—21no—
1028C4—22no—
1029C4—22no—
1030C4—21no—
1031C4—22no—
1032C4—22no—
1033C4—21no—
1034C4—21no—
1035C4—22no—
1036C4—22no—
1037C4—21no—
1038C4—21no—
1039C4—44no—
1040C4—48no—
1041C4C2×#41312yes—
1042C4C2×#41312yes—
1043C4#288912yes—
1044C4#348812yes—
1045C4#349811yescharacteristic
1046C4#350011yescharacteristic
1047C2—22no—
1048C2—22no—
1049C2—41no—
1050C2—42no—
1051C2—42no—
1052C2—84no—
1053C2#3425811yescharacteristic
1054C2C22×#41311yescharacteristic
1055C2C2×#288911yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3511C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60263C2semidirect
3. M16×#41C2semidirect
4. #22537C2semidirect
5. #22411C2semidirect
6. #22410C2semidirect
7. #21879C2semidirect
8. #21878C2semidirect
9. #21800C2semidirect
10. #21799C2semidirect
11. #21425C2semidirect
12. #21424C2semidirect
13. #21218C2semidirect
14. C2×#1966C2semidirect
977. C2×C4#413semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#602632
M16×#412
#225372
#224112
#224102
#218792
#218782
#218002
#217992
#214252
#214242
#212182
C2×#19662