Finite Group Databasebeta

← #6394052

Subgroups — #6394052

Order 512.

3067 conjugacy classes of subgroups.

The subgroup lattice has 1043 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#22515C214yesmaximal, complemented
5#22483C214yesmaximal, complemented
6#22482C218yesmaximal, complemented
7#21878C212yesmaximal, complemented
8#21878C211yesmaximal, characteristic, complemented
9#21831C212yesmaximal, complemented
10#21829C211yesmaximal, characteristic, complemented
11#21424C211yesmaximal, characteristic, complemented
12#21424C212yesmaximal, complemented
13#21337C212yesmaximal, complemented
14C2×#1997C211yesmaximal, 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×#556C412yes—
28C2×#555C2212yes—
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#548C414yes—
32C2×#547C412yes—
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#2920C2212yes—
61#2920C2211yescharacteristic
62#2920C2212yes—
63C2×#423C2211yescharacteristic
64C2×#423C2212yes—
65C2×C4×M16C2211yescharacteristic
66C2×C4×M16C2212yes—
67#1998C2218yes—
68#1998C2218yes—
69#1997C2212yes—
70#1997C2212yes—
71#1997C2214yes—
72#1997C2211yescharacteristic
73#1997C2212yes—
74#1997C2212yes—
75#1997C2212yes—
76#1997C2214yes—
77#1997C2211yescharacteristic
78#1965C2211yescharacteristic
79#1965C2212yes—
80#1965C2211yescharacteristic
81#1900C2214yes—
82#1900C2218yes—
83#1900C2214yes—
84#1900C2218yes—
85#1822C2218yes—
86#1821C2214yes—
87#1800C2218yes—
88#1800C2214yes—
89C4×#100C2218yes—
90C4×#100C2214yes—
91#1742C2218yes—
92C2×#343C2214yes—
93C22×#41C2×C412yes—
94C22×#41C2×C414yes—
95C22×#41C2×C411yescharacteristic
96C23×Q8C2×C412yes—
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—24no—
111#555—22no—
112#555—22no—
113#554—22no—
114#554—22no—
115#554—24no—
116#554—24no—
117#554—22no—
118#554—22no—
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—22no—
139#547—22no—
140#547—24no—
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×#125C2314yes—
195C2×#124C2×C412yes—
196C2×#124C2×C414yes—
197C2×#124C2×C418yes—
198C2×#123C2×C418yes—
199C2×C22⋊Q8C2×C414yes—
200C2×C22⋊Q8C2×C414yes—
201C2×C22⋊Q8C2×C414yes—
202C2×C22⋊Q8C2×C418yes—
203C2×#121C2×C414yes—
204C2×#121C2×C412yes—
205C2×#121C2×C414yes—
206C2×#121C2×C418yes—
207C2×#121C2312yes—
208C2×#121C2314yes—
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×C414yes—
229C2×C4×Q8C2×C411yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4C2×C414yes—
232C2×C4×D4C2×C418yes—
233C2×C4×D4C2×C412yes—
234C2×C4×D4C2×C411yescharacteristic
235C2×C4×D4C2×C412yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×#117C2×C414yes—
241C2×#117C2×C411yescharacteristic
242C2×#117C2×C412yes—
243C2×#117C2314yes—
244C22×C4⋊C4C2×C412yes—
245C22×C4⋊C4C2×C414yes—
246C22×C4⋊C4C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249#446—24no—
250#446—22no—
251#446—24no—
252#446—22no—
253C8×Q8—22no—
254C8×Q8—22no—
255#436—24no—
256#436—22no—
257#436—24no—
258#436—22no—
259#435—24no—
260#435—24no—
261#435—24no—
262#435—24no—
263#435—24no—
264#435—24no—
265C8×D4—24no—
266C8×D4—22no—
267C8×D4—24no—
268C8×D4—22no—
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#423C2314yes—
291#423C2312yes—
292#423C2314yes—
293#423C2312yes—
294#423C2311yescharacteristic
295#423C2311yescharacteristic
296C2×C4⋊C8—21no—
297C2×C4⋊C8—22no—
298C2×C4⋊C8—21no—
299C2×C4⋊C8—22no—
300C2×#100C2314yes—
301C2×#100C2314yes—
302C2×#100C2318yes—
303#407C2312yes—
304#407C2312yes—
305#407C2314yes—
306#407C2314yes—
307C4×M16—21no—
308C4×M16—22no—
309C4×M16—21no—
310C4×M16—22no—
311C4×M16C2311yescharacteristic
312C4×M16C2311yescharacteristic
313C4×M16C2312yes—
314C4×M16C2312yes—
315C4×M16C2314yes—
316C4×M16C2312yes—
317C4×M16C2314yes—
318C2×#97—21no—
319C2×#97—22no—
320C2×C4×C8—21no—
321C2×C4×C8—22no—
322#343C2318yes—
323#343C2318yes—
324#343C2318yes—
325#343C2318yes—
326#343C2314yes—
327#343C2318yes—
328#343C2314yes—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—44no—
338C2×#41—48no—
339C2×#41—88no—
340C2×#41C22⋊C411yescharacteristic
341C2×#41C22⋊C411yescharacteristic
342C2×#41C22⋊C412yes—
343C2×#41C22⋊C412yes—
344C2×#41C22⋊C411yescharacteristic
345C2×#41C22⋊C411yescharacteristic
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—84no—
351C22×Q8C22×C412yes—
352C22×Q8C22×C414yes—
353C22×Q8C22×C414yes—
354C22×Q8C22×C411yescharacteristic
355C22×D4C22×C414yes—
356C22×D4C22×C412yes—
357C22×D4C22×C412yes—
358C22×D4C22×C418yes—
359C22×D4C22×C411yescharacteristic
360C22×D4C22×C412yes—
361C22×D4C2412yes—
362C23×C4C22×C411yescharacteristic
363C23×C4C22×C414yes—
364C23×C4C22×C414yes—
365C23×C4C22×C418yes—
366C23×C4C22×C412yes—
367C23×C4C22×C411yescharacteristic
368C23×C4C22×C412yes—
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C2×M16—22no—
372C2×M16—24no—
373C2×M16—22no—
374C2×M16—24no—
375C2×M16—24no—
376C2×M16—28no—
377C2×M16—42no—
378C2×M16—44no—
379C2×M16—44no—
380C2×M16—48no—
381C2×M16C2414yes—
382C2×M16C2412yes—
383C2×M16C2412yes—
384C2×M16C2414yes—
385C2×M16C2412yes—
386C2×M16C2412yes—
387C22×C8—22no—
388C22×C8—24no—
389C22×C8—22no—
390C22×C8—24no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394C4⋊Q8—22no—
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—21no—
408C4⋊Q8—21no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411#127—21no—
412#127—21no—
413#127—21no—
414#127—21no—
415#126—28no—
416#126—28no—
417#126—28no—
418#126—28no—
419#125—24no—
420#125—24no—
421#125—24no—
422#125—24no—
423#124—28no—
424#124—28no—
425#124—28no—
426#124—28no—
427#124—22no—
428#124—22no—
429#124—22no—
430#124—22no—
431#124—24no—
432#124—24no—
433#124—24no—
434#124—24no—
435#123—28no—
436#123—28no—
437#123—28no—
438#123—28no—
439C22⋊Q8—24no—
440C22⋊Q8—24no—
441C22⋊Q8—28no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—24no—
446C22⋊Q8—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—28no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454#121—24no—
455#121—24no—
456#121—28no—
457#121—28no—
458#121—28no—
459#121—28no—
460#121—28no—
461#121—24no—
462#121—24no—
463#121—24no—
464#121—24no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—24no—
474#121—24no—
475#121—24no—
476#121—24no—
477C4×Q8—24no—
478C4×Q8—24no—
479C4×Q8—24no—
480C4×Q8—24no—
481C4×Q8—24no—
482C4×Q8—24no—
483C4×Q8—24no—
484C4×Q8—24no—
485C4×Q8C22⋊C411yescharacteristic
486C4×Q8C22⋊C411yescharacteristic
487C4×Q8C22⋊C411yescharacteristic
488C4×Q8C22⋊C411yescharacteristic
489C4×Q8C22⋊C412yes—
490C4×Q8C22⋊C412yes—
491C4×Q8C2×D411yescharacteristic
492C4×Q8C2×D411yescharacteristic
493C4×Q8C2×D412yes—
494C4×Q8C2×D412yes—
495C4×Q8C2×D411yescharacteristic
496C4×Q8C2×D411yescharacteristic
497C4×D4—28no—
498C4×D4—28no—
499C4×D4—28no—
500C4×D4—28no—
501C4×D4—24no—
502C4×D4—24no—
503C4×D4—24no—
504C4×D4—24no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
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×D4C22⋊C411yescharacteristic
518C4×D4C22⋊C411yescharacteristic
519C4×D4C22⋊C412yes—
520C4×D4C22⋊C411yescharacteristic
521C4×D4C22⋊C411yescharacteristic
522C4×D4C22⋊C412yes—
523C4×D4C22⋊C412yes—
524C4×D4C22⋊C412yes—
525C4×D4C22⋊C412yes—
526C4×D4C22⋊C412yes—
527C4×D4C22⋊C412yes—
528C4×D4C22⋊C412yes—
529C4×D4C22⋊C412yes—
530C4×D4C22⋊C412yes—
531C4×D4C2×D412yes—
532C4×D4C2×D412yes—
533C4×D4C2×D412yes—
534C4×D4C2×D412yes—
535C4×D4C2×D412yes—
536C4×D4C2×D412yes—
537C4×D4C2×D412yes—
538C4×D4C2×D412yes—
539C4×D4C2×D411yescharacteristic
540C4×D4C2×D411yescharacteristic
541C4×D4C2×D412yes—
542C4×D4C2×D412yes—
543C4×D4C2×D411yescharacteristic
544C4×D4C2×D411yescharacteristic
545#117—24no—
546#117—24no—
547#117—24no—
548#117—24no—
549#117—28no—
550#117—24no—
551#117—24no—
552#117C22⋊C412yes—
553#117C22⋊C411yescharacteristic
554#117C22⋊C412yes—
555#117C22⋊C411yescharacteristic
556#117C22⋊C411yescharacteristic
557#117C22⋊C411yescharacteristic
558#117C22⋊C412yes—
559#117C22⋊C412yes—
560#117C22⋊C412yes—
561#117C22⋊C412yes—
562#117C22⋊C412yes—
563#117C22⋊C412yes—
564#117C22⋊C412yes—
565#117C22⋊C412yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4C22×C414yes—
578C2×C4⋊C4C22×C414yes—
579C2×C4⋊C4C22×C418yes—
580C2×C4⋊C4C22×C414yes—
581C2×C4⋊C4C22×C412yes—
582C2×C4⋊C4C22×C418yes—
583C2×C4⋊C4C22×C411yescharacteristic
584C2×C4⋊C4C22×C411yescharacteristic
585C2×C4⋊C4C22×C412yes—
586C2×C4⋊C4C22×C412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C22⋊C4C22×C418yes—
590C2×C22⋊C4C22×C418yes—
591C2×C22⋊C4C22×C414yes—
592C2×C22⋊C4C22×C418yes—
593C2×C22⋊C4C22×C414yes—
594C2×C22⋊C4C22×C412yes—
595C2×C22⋊C4C22×C412yes—
596C2×C22⋊C4C22×C412yes—
597C2×C42C22×C418yes—
598C2×C42C22×C412yes—
599C2×C42C22×C411yescharacteristic
600C2×C42C22×C411yescharacteristic
601C2×C42C22×C412yes—
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D412yes—
611C2×C42C2×D412yes—
612C2×C42C2×D412yes—
613C2×C42C2×D412yes—
614C2×C42C2×D412yes—
615C2×C42C2×D412yes—
616C2×C42C2×D412yes—
617C2×C42C2×D412yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C4⋊C8—22no—
622C4⋊C8—21no—
623C4⋊C8—22no—
624C4⋊C8—21no—
625C4⋊C8—24no—
626C4⋊C8—22no—
627C4⋊C8—24no—
628C4⋊C8—22no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—24no—
632C4⋊C8—22no—
633C4⋊C8—24no—
634C4⋊C8—22no—
635#100—28no—
636#100—44no—
637#100—48no—
638C22⋊C8—22no—
639C22⋊C8—24no—
640C22⋊C8—22no—
641C22⋊C8—24no—
642C22⋊C8—22no—
643C22⋊C8—24no—
644C22⋊C8—22no—
645C22⋊C8—24no—
646#97—21no—
647#97—21no—
648#97—22no—
649#97—24no—
650#97—22no—
651#97—24no—
652#97—22no—
653C4×C8—21no—
654C4×C8—21no—
655C4×C8—22no—
656C4×C8—24no—
657C4×C8—22no—
658C4×C8—24no—
659C4×C8—22no—
660C24C23×C411yescharacteristic
661C24C23×C414yes—
662C24C23×C412yes—
663#41—24no—
664#41—24no—
665#41—44no—
666#41—44no—
667#41—42no—
668#41—42no—
669#41—48no—
670#41—48no—
671#41—48no—
672#41—48no—
673#41—88no—
674#41—88no—
675#41—88no—
676#41—88no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—24no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—42no—
684C2×Q8—48no—
685C2×Q8—44no—
686C2×Q8—84no—
687C2×Q8—84no—
688C2×Q8—84no—
689C2×Q8—84no—
690C2×Q8—84no—
691C2×Q8C2×C22⋊C411yescharacteristic
692C2×Q8C2×C22⋊C411yescharacteristic
693C2×Q8C2×C22⋊C412yes—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—42no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—48no—
711C2×D4—88no—
712C2×D4C2×C22⋊C412yes—
713C2×D4C2×C22⋊C412yes—
714C2×D4C2×C22⋊C411yescharacteristic
715C2×D4C2×C22⋊C411yescharacteristic
716C2×D4C2×C22⋊C412yes—
717C2×D4C2×C22⋊C412yes—
718C2×D4C2×C22⋊C412yes—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—48no—
734C22×C4—84no—
735C22×C4—88no—
736C22×C4C2×C22⋊C411yescharacteristic
737C22×C4C2×C22⋊C411yescharacteristic
738C22×C4C2×C22⋊C411yescharacteristic
739C22×C4C2×C22⋊C412yes—
740C22×C4C2×C22⋊C412yes—
741C22×C4C2×C22⋊C411yescharacteristic
742C22×C4C2×C22⋊C411yescharacteristic
743C22×C4C2×C22⋊C412yes—
744C22×C4C2×C22⋊C412yes—
745C22×C4C2×C22⋊C412yes—
746C22×C4C2×C22⋊C412yes—
747C22×C4C2×C22⋊C411yescharacteristic
748C22×C4C2×C22⋊C411yescharacteristic
749C22×C4C2×C22⋊C412yes—
750C22×C4C2×C22⋊C412yes—
751C22×C4C2×C22⋊C411yescharacteristic
752C22×C4C23×C412yes—
753C22×C4C23×C411yescharacteristic
754C22×C4C23×C411yescharacteristic
755C22×C4C23×C411yescharacteristic
756C22×C4C23×C411yescharacteristic
757C22×C4C23×C414yes—
758C22×C4C23×C418yes—
759C22×C4C23×C411yescharacteristic
760C22×C4C23×C412yes—
761C22×C4C23×C412yes—
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D412yes—
767C22×C4C22×D412yes—
768C22×C4C22×D412yes—
769C22×C4C22×D412yes—
770C22×C4C2511yescharacteristic
771M16—22no—
772M16—24no—
773M16—22no—
774M16—24no—
775M16—22no—
776M16—24no—
777M16—28no—
778M16—24no—
779M16—44no—
780M16—48no—
781M16—82no—
782M16—84no—
783M162−1+414yes—
784C2×C8—22no—
785C2×C8—22no—
786C2×C8—24no—
787C2×C8—22no—
788C2×C8—24no—
789C2×C8—22no—
790C2×C8—44no—
791C2×C8—48no—
792C2×C8—82no—
793C2×C8—84no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4C2×C22⋊C412yes—
811C4⋊C4C2×C22⋊C411yescharacteristic
812C4⋊C4C2×C22⋊C411yescharacteristic
813C4⋊C4C2×C22⋊C412yes—
814C4⋊C4C2×C22⋊C411yescharacteristic
815C4⋊C4C2×C22⋊C411yescharacteristic
816C4⋊C4C2×C22⋊C412yes—
817C4⋊C4C2×C22⋊C412yes—
818C4⋊C4C2×C22⋊C412yes—
819C4⋊C4C2×C22⋊C412yes—
820C4⋊C4C2×C22⋊C412yes—
821C4⋊C4C2×C22⋊C412yes—
822C4⋊C4C2×C22⋊C412yes—
823C4⋊C4C2×C22⋊C412yes—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4C2×C22⋊C412yes—
835C22⋊C4C2×C22⋊C412yes—
836C22⋊C4C2×C22⋊C412yes—
837C22⋊C4C2×C22⋊C412yes—
838C22⋊C4C2×C22⋊C412yes—
839C22⋊C4C2×C22⋊C412yes—
840C22⋊C4C2×C22⋊C412yes—
841C22⋊C4C2×C22⋊C412yes—
842C22⋊C4C2×C22⋊C412yes—
843C22⋊C4C2×C22⋊C412yes—
844C22⋊C4C2×C22⋊C412yes—
845C22⋊C4C2×C22⋊C412yes—
846C42—28no—
847C42—28no—
848C42C2×C22⋊C412yes—
849C42C2×C22⋊C412yes—
850C42C2×C22⋊C412yes—
851C42C2×C22⋊C412yes—
852C42C2×C22⋊C411yescharacteristic
853C42C2×C22⋊C411yescharacteristic
854C42C2×C22⋊C411yescharacteristic
855C42C2×C22⋊C411yescharacteristic
856C42C2×C22⋊C411yescharacteristic
857C42C2×C22⋊C411yescharacteristic
858C42C2×C22⋊C411yescharacteristic
859C42C2×C22⋊C411yescharacteristic
860C42C2×C22⋊C412yes—
861C42C2×C22⋊C412yes—
862C42C2×C22⋊C412yes—
863C42C2×C22⋊C412yes—
864C42C22×D411yescharacteristic
865C42C22×D412yes—
866C42C22×D412yes—
867C42C22×D411yescharacteristic
868C42C22×D411yescharacteristic
869C42C22×D411yescharacteristic
870C42C22×D412yes—
871C42C22×D412yes—
872C42C22×D411yescharacteristic
873C42C22×D411yescharacteristic
874C42C22×D411yescharacteristic
875C42C22×D411yescharacteristic
876C23—22no—
877C23—22no—
878C23—24no—
879C23—24no—
880C23—28no—
881C23—41no—
882C23—42no—
883C23—42no—
884C23—44no—
885C23—44no—
886C23C22×C22⋊C412yes—
887C23C22×C22⋊C412yes—
888C23C22×C22⋊C411yescharacteristic
889C23C22×C22⋊C411yescharacteristic
890C23C24×C411yescharacteristic
891Q8—22no—
892Q8—22no—
893Q8—42no—
894Q8—48no—
895Q8—44no—
896Q8—44no—
897Q8—48no—
898Q8—84no—
899Q8—84no—
900D4—24no—
901D4—24no—
902D4—22no—
903D4—22no—
904D4—42no—
905D4—42no—
906D4—42no—
907D4—44no—
908D4—44no—
909D4—48no—
910D4—48no—
911D4—44no—
912D4—44no—
913D4—44no—
914D4—42no—
915D4—42no—
916D4—88no—
917D4—88no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—44no—
958C2×C4—48no—
959C2×C4—88no—
960C2×C4—88no—
961C2×C4—84no—
962C2×C4—84no—
963C2×C4#41314yes—
964C2×C4C22×C22⋊C412yes—
965C2×C4C22×C22⋊C412yes—
966C2×C4C22×C22⋊C411yescharacteristic
967C2×C4C22×C22⋊C411yescharacteristic
968C2×C4C22×C22⋊C411yescharacteristic
969C2×C4C22×C22⋊C411yescharacteristic
970C2×C4C22×C22⋊C411yescharacteristic
971C2×C4C22×C22⋊C411yescharacteristic
972C2×C4C22×C22⋊C412yes—
973C2×C4C22×C22⋊C412yes—
974C2×C4C22×C22⋊C412yes—
975C2×C4C22×C22⋊C412yes—
976C2×C4C22×C22⋊C411yescharacteristic
977C2×C4C22×C22⋊C411yescharacteristic
978C2×C4C22×C22⋊C411yescharacteristic
979C2×C4C22×C22⋊C411yescharacteristic
980C2×C4C23×D411yescharacteristic
981C2×C4C23×D411yescharacteristic
982C2×C4C2×2−1+412yes—
983C2×C4#58512yes—
984C8—24no—
985C8—44no—
986C8—42no—
987C8—42no—
988C8—44no—
989C8—42no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—22no—
996C22—22no—
997C22—21no—
998C22—22no—
999C22—22no—
1000C22—21no—
1001C22—22no—
1002C22—22no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—84no—
1008C22—88no—
1009C22C2×#41312yes—
1010C22C23×C22⋊C411yescharacteristic
1011C22C4×2−1+412yes—
1012C4—21no—
1013C4—21no—
1014C4—22no—
1015C4—22no—
1016C4—21no—
1017C4—22no—
1018C4—22no—
1019C4—21no—
1020C4—21no—
1021C4—22no—
1022C4—21no—
1023C4—21no—
1024C4—22no—
1025C4—44no—
1026C4—48no—
1027C4C2×#41312yes—
1028C4C2×#41312yes—
1029C4#288812yes—
1030C4#348912yes—
1031C4#349911yescharacteristic
1032C4#350011yescharacteristic
1033C2—22no—
1034C2—22no—
1035C2—41no—
1036C2—42no—
1037C2—42no—
1038C2—84no—
1039C2#3425911yescharacteristic
1040C2C22×#41311yescharacteristic
1041C2C2×#288811yescharacteristic
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. #22515C2semidirect
5. #22483C2semidirect
6. #22482C2semidirect
7. #21878C2semidirect
8. #21878C2semidirect
9. #21831C2semidirect
10. #21829C2semidirect
11. #21424C2semidirect
12. #21424C2semidirect
13. #21337C2semidirect
14. C2×#1997C2semidirect

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
#225152
#224832
#224822
#218782
#218312
#218292
#214242
#213372
C2×#19972