Finite Group Databasebeta

← C2×#20865 #6371297

Subgroups — C2×#20865 #6371297

Order 512.

4782 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3428C211yesmaximal, characteristic
2C22×#428C211yesmaximal, characteristic, complemented
3C22×#421C211yesmaximal, characteristic
4C22×#417C211yesmaximal, characteristic
5C2×#2317C211yesmaximal, characteristic, complemented
6#20865C2116yesmaximal, direct product factor
7C2×#1860C214yesmaximal, complemented
8C2×#1859C214yesmaximal, complemented
9C2×#1742C211yesmaximal, characteristic, complemented
10C2×#1733C211yesmaximal, characteristic, complemented
11C23×#41C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14#3428—24no—
15#3428—24no—
16#3428—24no—
17#3428C2218yes—
18C2×#520—21no—
19C2×#520—21no—
20C2×#520C2212yes—
21C2×#520C2212yes—
22C2×#519—21no—
23C2×#518—21no—
24C2×#518—22no—
25C2×C4×#41—22no—
26C2×C4×#41—22no—
27C22×#117—22no—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C2×#428—22no—
33C2×#428—24no—
34C2×#428C2214yescomplemented
35C2×#428C2218yescomplemented
36C22×#107—21no—
37C22×#106—21no—
38C2×#421C4116yescomplemented
39C2×#421C2218yes—
40C22×#104C2214yes—
41C2×#417—22no—
42C2×#417—24no—
43C2×#417C2214yes—
44C2×#417C2218yes—
45C22×#103—21no—
46C22×#102—21no—
47#2317—24no—
48#2317C2218yescomplemented
49C2×#389—22no—
50C2×#385—22no—
51C2×#384C2212yescomplemented
52C2×#382C2212yescomplemented
53#1860C22132yescomplemented
54#1859C22132yescomplemented
55#1742C2218yescomplemented
56C2×#343C2212yescomplemented
57C2×#343C2212yescomplemented
58#1733C2218yescomplemented
59C2×#339C2214yescomplemented
60C22×#41—21no—
61C22×#41—21no—
62C22×#41—22no—
63C22×#41—22no—
64C22×#41—24no—
65C22×#41—24no—
66C22×#41C2×C418yes—
67C22×#41D412yes—
68C22×#41D414yes—
69C22×#41Q818yes—
70C22×#41C2312yes—
71C22×#41C2314yes—
72C23×Q8D411yescharacteristic
73C23×D4—21no—
74C23×D4D411yescharacteristic
75C24×C4—21no—
76C24×C4—21no—
77C24×C4C2311yescharacteristic
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—24no—
81C22×M16—22no—
82C22×M16—21no—
83C22×M16—24no—
84C22×M16—24no—
85C22×M16C2×C418yescomplemented
86C22×M16C2312yes—
87C22×M16C2314yes—
88C22×M16C2312yes—
89C22×M16C2314yes—
90C23×C8—21no—
91C23×C8—21no—
92#520—28no—
93#520—28no—
94#520—24no—
95#520—24no—
96#520—24no—
97#520—24no—
98#520—28no—
99#520—28no—
100#520—24no—
101#520—24no—
102#520C2318yes—
103#520C2318yes—
104#519—28no—
105#519—28no—
106#518—28no—
107#518—216no—
108#518—28no—
109#518—216no—
110C4×#41—216no—
111C4×#41—216no—
112C4×#41—216no—
113C4×#41—216no—
114C2×C4×Q8—22no—
115C2×C4×Q8—22no—
116C2×C4×Q8—22no—
117C2×C4×Q8—22no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—216no—
129C2×#117—22no—
130C2×#117—21no—
131C2×#117—21no—
132C2×#117—21no—
133C2×#117—21no—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—22no—
137C2×#117—22no—
138C2×#117—22no—
139C2×#117—22no—
140C2×#117—24no—
141C2×#117—216no—
142C2×#117—22no—
143C2×#117—22no—
144C2×#117C2×C418yescomplemented
145C2×#117D412yes—
146C2×#117D414yes—
147C2×#117D414yes—
148C2×#117C2312yes—
149C2×#117C2314yes—
150C2×#117C2314yes—
151C2×#117C2314yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—22no—
154C22×C4⋊C4—22no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—22no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—22no—
161C22×C4⋊C4—22no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4D411yescharacteristic
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4C2314yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C22⋊C4—24no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4D412yes—
174C22×C42—24no—
175C22×C42—21no—
176C22×C42D412yes—
177C22×C42C2312yes—
178#428—216no—
179#428—28no—
180#428C23116yescomplemented
181C2×#107—24no—
182C2×#107—28no—
183C2×#106—24no—
184C2×#106—28no—
185#421C2×C4164yescomplemented
186C2×#104C2×C4132yescomplemented
187C2×#104C23116yes—
188#417—28no—
189#417—216no—
190#417C23116yes—
191C2×#103—24no—
192C2×#103—28no—
193C2×#102—24no—
194C2×#102—28no—
195#389—216no—
196#385—216no—
197#384—24no—
198#384C2318yescomplemented
199#382—24no—
200#382C2318yescomplemented
201C2×#95—24no—
202#343C2318yescomplemented
203#343C2318yescomplemented
204#339C23116yescomplemented
205C25—21no—
206C25C2×D411yescharacteristic
207C2×#41—28no—
208C2×#41—216no—
209C2×#41—28no—
210C2×#41—216no—
211C2×#41—24no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—28no—
215C2×#41—216no—
216C2×#41—28no—
217C2×#41—216no—
218C2×#41—28no—
219C2×#41—216no—
220C2×#41—24no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—24no—
224C2×#41—24no—
225C2×#41—28no—
226C2×#41—24no—
227C2×#41—28no—
228C2×#41C4⋊C4116yescomplemented
229C2×#41C4⋊C4132yescomplemented
230C2×#41C22×C418yes—
231C2×#41C22×C4116yes—
232C2×#41C2×D414yes—
233C2×#41C2×D418yes—
234C2×#41C2×Q818yes—
235C2×#41C2×Q8116yes—
236C2×#41C2414yes—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8C4⋊C418yescomplemented
241C22×Q8C2×D412yes—
242C22×Q8C2×D414yes—
243C22×D4—28no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—28no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4C4⋊C418yescomplemented
253C22×D4C2×D412yes—
254C22×D4C2×D414yes—
255C23×C4—21no—
256C23×C4—28no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—28no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—41no—
271C23×C4—41no—
272C23×C4—84no—
273C23×C4C22×C414yes—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D412yes—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D412yes—
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×Q814yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C2×M16—28no—
290C2×M16—216no—
291C2×M16—22no—
292C2×M16—24no—
293C2×M16—24no—
294C2×M16—28no—
295C2×M16—24no—
296C2×M16—22no—
297C2×M16—24no—
298C2×M16—28no—
299C2×M16—24no—
300C2×M16—28no—
301C2×M16—44no—
302C2×M16—48no—
303C2×M16C22×C418yes—
304C2×M16C22×C4116yescomplemented
305C2×M16C2414yes—
306C2×M16C2414yes—
307C22×C8—28no—
308C22×C8—22no—
309C22×C8—24no—
310C22×C8—24no—
311C22×C8—22no—
312C22×C8—44no—
313C4×Q8—28no—
314C4×Q8—28no—
315C4×Q8—216no—
316C4×Q8—216no—
317C4×Q8—28no—
318C4×Q8—28no—
319C4×D4—216no—
320C4×D4—216no—
321C4×D4—232no—
322C4×D4—232no—
323C4×D4—28no—
324C4×D4—28no—
325C4×D4—216no—
326C4×D4—216no—
327C4×D4—28no—
328C4×D4—28no—
329C4×D4—216no—
330C4×D4—216no—
331#117—232no—
332#117—232no—
333#117—28no—
334#117—28no—
335#117—216no—
336#117—24no—
337#117—24no—
338#117—24no—
339#117—24no—
340#117—24no—
341#117—24no—
342#117—24no—
343#117—24no—
344#117—24no—
345#117—24no—
346#117—24no—
347#117—24no—
348#117—22no—
349#117—24no—
350#117—22no—
351#117—28no—
352#117—28no—
353#117—28no—
354#117C22×C4116yescomplemented
355#117C2×D418yes—
356#117C2×D414yes—
357#117C2414yes—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—216no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—88no—
397C2×C4⋊C4C2×D412yes—
398C2×C4⋊C4C2×D412yes—
399C2×C4⋊C4C2×D412yes—
400C2×C4⋊C4C2×D412yes—
401C2×C4⋊C4C2×D414yes—
402C2×C4⋊C4C2×D414yes—
403C2×C4⋊C4C2414yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—232no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4C2×D418yes—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—232no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42C22×C418yes—
432C2×C42C2×D418yes—
433C2×C42C2414yes—
434#107—216no—
435#106—216no—
436#104C22×C4164yescomplemented
437#103—216no—
438#102—216no—
439#95—216no—
440C24—22no—
441C24—24no—
442C24—28no—
443C24—42no—
444C24—42no—
445C24—82no—
446C24—82no—
447C24C4×D414yes—
448C24#12011yescharacteristic
449C24#12011yescharacteristic
450C24#12012yes—
451C24C22⋊Q814yes—
452C24C22×D411yescharacteristic
453C24C22×D412yes—
454#41—216no—
455#41—28no—
456#41—28no—
457#41—216no—
458#41—28no—
459#41—216no—
460#41—28no—
461#41—216no—
462#41—28no—
463#41—216no—
464#41—24no—
465#41—24no—
466#41—232no—
467#41—232no—
468#41—232no—
469#41C2×C4⋊C4116yes—
470#41C2×C4⋊C4132yescomplemented
471#41C23×C418yes—
472#41C22×Q818yes—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—216no—
479C2×Q8C2×C4⋊C418yes—
480C2×Q8C2×C4⋊C4116yescomplemented
481C2×Q8C22×D414yes—
482C2×D4—28no—
483C2×D4—216no—
484C2×D4—24no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—216no—
488C2×D4—24no—
489C2×D4—216no—
490C2×D4—232no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—28no—
495C2×D4—216no—
496C2×D4—28no—
497C2×D4C2×C4⋊C418yes—
498C2×D4C2×C4⋊C4116yescomplemented
499C2×D4C22×D414yes—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—28no—
506C22×C4—24no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—24no—
510C22×C4—216no—
511C22×C4—232no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—88no—
537C22×C4—88no—
538C22×C4—88no—
539C22×C4—84no—
540C22×C4—84no—
541C22×C4—88no—
542C22×C4C2×C4⋊C414yes—
543C22×C4C2×C4⋊C414yes—
544C22×C4C2×C4⋊C418yes—
545C22×C4C4×D414yes—
546C22×C4C4×D414yes—
547C22×C4C4×D418yes—
548C22×C4C4×D414yes—
549C22×C4C4×D418yes—
550C22×C4#12012yes—
551C22×C4#12012yes—
552C22×C4#12012yes—
553C22×C4#12012yes—
554C22×C4#12012yes—
555C22×C4#12011yescharacteristic
556C22×C4#12011yescharacteristic
557C22×C4C22⋊Q814yes—
558C22×C4C22⋊Q814yes—
559C22×C4C22⋊Q818yes—
560C22×C4C22⋊Q814yes—
561C22×C4C22⋊Q818yes—
562C22×C4#12314yes—
563C22×C4#12314yes—
564C22×C4#12318yes—
565C22×C4C23×C412yes—
566C22×C4C23×C414yes—
567C22×C4C22×D414yes—
568C22×C4C22×D414yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D412yes—
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D411yescharacteristic
579C22×C4C22×Q812yes—
580C22×C4C22×Q814yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4114yes—
585C22×C4C2511yescharacteristic
586M16—28no—
587M16—216no—
588M16—24no—
589M16—24no—
590M16—24no—
591M16—48no—
592M16—44no—
593M16C23×C418yes—
594C2×C8—28no—
595C2×C8—216no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—48no—
599C2×C8—44no—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—816no—
622C4⋊C4C22×D414yes—
623C4⋊C4C22×D414yes—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—24no—
630C22⋊C4—28no—
631C22⋊C4—24no—
632C42—216no—
633C42—216no—
634C42—28no—
635C42—28no—
636C42—28no—
637C42—24no—
638C42—28no—
639C42—24no—
640C42—24no—
641C42C23×C418yes—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—28no—
650C23—216no—
651C23—42no—
652C23—42no—
653C23—48no—
654C23—42no—
655C23—48no—
656C23—42no—
657C23—44no—
658C23—44no—
659C23—816no—
660C23—84no—
661C23—84no—
662C23#38514yes—
663C23#38514yes—
664C23#38518yes—
665C23C2×C4×D412yes—
666C23C2×C4×D414yes—
667C23C2×#12012yes—
668C23C2×#12011yescharacteristic
669C23C2×#12012yes—
670C23C2×#12011yescharacteristic
671C23C2×C22⋊Q812yes—
672C23C2×C22⋊Q814yes—
673C23C23×D411yescharacteristic
674Q8—24no—
675Q8—28no—
676Q8—216no—
677Q8C22×C4⋊C418yes—
678D4—28no—
679D4—28no—
680D4—216no—
681D4—232no—
682D4—24no—
683D4—28no—
684D4—216no—
685D4C22×C4⋊C418yes—
686C2×C4—24no—
687C2×C4—28no—
688C2×C4—216no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—216no—
692C2×C4—232no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—416no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—48no—
708C2×C4—44no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4—816no—
714C2×C4—816no—
715C2×C4—84no—
716C2×C4—88no—
717C2×C4—88no—
718C2×C4—84no—
719C2×C4#38518yes—
720C2×C4#38514yes—
721C2×C4#38518yes—
722C2×C4#38514yes—
723C2×C4#38518yes—
724C2×C4#38518yes—
725C2×C4#38518yes—
726C2×C4C22×C4⋊C412yes—
727C2×C4C22×C4⋊C414yes—
728C2×C4C22×C4⋊C412yes—
729C2×C4C22×C4⋊C414yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D414yes—
732C2×C4C2×C4×D414yes—
733C2×C4C2×C4×D412yes—
734C2×C4C2×C4×D412yes—
735C2×C4C2×C4×D414yes—
736C2×C4C2×#12012yes—
737C2×C4C2×#12011yescharacteristic
738C2×C4C2×#12012yes—
739C2×C4C2×#12011yescharacteristic
740C2×C4C2×C22⋊Q814yes—
741C2×C4C2×C22⋊Q812yes—
742C2×C4C2×C22⋊Q812yes—
743C2×C4C2×C22⋊Q814yes—
744C2×C4C2×C22⋊Q812yes—
745C2×C4C2×C22⋊Q814yes—
746C2×C4C2×#12314yes—
747C2×C4C2×#12312yes—
748C2×C4C2×#12314yes—
749C2×C4C2×#12312yes—
750C2×C4C24×C411yescharacteristic
751C2×C4C23×D411yescharacteristic
752C2×C4C23×D411yescharacteristic
753C2×C4C23×Q811yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C8—28no—
757C8—44no—
758C22—24no—
759C22—28no—
760C22—24no—
761C22—28no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—22no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—22no—
770C22—28no—
771C22—44no—
772C22—44no—
773C22—48no—
774C22—416no—
775C22—44no—
776C22—44no—
777C22—816no—
778C22C2×#38514yes—
779C22C2×#38512yes—
780C22C2×#38514yes—
781C22C2×#38512yes—
782C22#302112yes—
783C22#302212yes—
784C22C22×C4×D411yescharacteristic
785C22C22×#12011yescharacteristic
786C22C22×C22⋊Q811yescharacteristic
787C4—28no—
788C4—48no—
789C4—44no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4—84no—
794C4C2×#38512yes—
795C4C2×#38514yes—
796C4C2×#38512yes—
797C4C2×#38514yes—
798C4C23×C4⋊C411yescharacteristic
799C4C22×C4×D411yescharacteristic
800C4C22×C22⋊Q811yescharacteristic
801C4C22×#12311yescharacteristic
802C2—21no—
803C2—24no—
804C2—21no—
805C2—22no—
806C2—24no—
807C2—48no—
808C2#2086514yesdirect product factor
809C2C22×#38511yescharacteristic
810C2C2×#302111yescharacteristic
811C2C2×#302211yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#428C2semidirect
5. C2×#2317C2semidirect
6. #20865C2direct (N × H)
7. C2×#1860C2semidirect
8. C2×#1859C2semidirect
9. C2×#1742C2semidirect
10. C2×#1733C2semidirect
34. C2×#428C22semidirect
35. C2×#428C22semidirect
38. C2×#421C4semidirect
48. #2317C22semidirect
51. C2×#384C22semidirect
52. C2×#382C22semidirect
53. #1860C22semidirect
54. #1859C22semidirect
55. #1742C22semidirect
56. C2×#343C22semidirect
57. C2×#343C22semidirect
58. #1733C22semidirect
59. C2×#339C22semidirect
85. C22×M16C2×C4semidirect
144. C2×#117C2×C4semidirect
180. #428C23semidirect
185. #421C2×C4semidirect
186. C2×#104C2×C4semidirect
198. #384C23semidirect
200. #382C23semidirect
202. #343C23semidirect
203. #343C23semidirect
204. #339C23semidirect
228. C2×#41C4⋊C4semidirect
229. C2×#41C4⋊C4semidirect
240. C22×Q8C4⋊C4semidirect
252. C22×D4C4⋊C4semidirect
304. C2×M16C22×C4semidirect
354. #117C22×C4semidirect
436. #104C22×C4semidirect
470. #41C2×C4⋊C4semidirect
480. C2×Q8C2×C4⋊C4semidirect
498. C2×D4C2×C4⋊C4semidirect
808. C2#20865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34282
C22×#4282
C22×#4212
C22×#4172
C2×#23172
#208652
C2×#18602
C2×#18592
C2×#17422
C2×#17332