Finite Group Databasebeta

← C2×#19493 #6354564

Subgroups — C2×#19493 #6354564

Order 512.

1736 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic, complemented
2C2×#3115C211yesmaximal, characteristic
3C2×#3076C211yesmaximal, characteristic, complemented
4C2×#2991C211yesmaximal, characteristic, complemented
5#19493C2116yesmaximal, direct product factor
6C2×#1703C211yesmaximal, characteristic, complemented
7C2×#1697C211yesmaximal, characteristic, complemented
8C2×#1689C211yesmaximal, characteristic, complemented
9C2×#1685C211yesmaximal, characteristic, complemented
10C2×#1684C211yesmaximal, characteristic, complemented
11C2×#1678C211yesmaximal, characteristic, complemented
12C2×#1670C211yesmaximal, characteristic, complemented
13C2×#1666C211yesmaximal, characteristic, complemented
14C2×#1573C211yesmaximal, characteristic, complemented
15C2×#1559C211yesmaximal, characteristic, complemented
16C2×#1547C211yesmaximal, characteristic, complemented
17C2×#533C2211yescharacteristic
18C2×#532C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20#3210—24no—
21#3210C2218yescomplemented
22C2×#494C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#486C2211yescharacteristic
26#3115—24no—
27#3115C2218yes—
28C2×#482—21no—
29#3076—24no—
30#3076C2218yescomplemented
31C2×#479—21no—
32C2×#477C2211yescharacteristic
33C2×#475C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#478—21no—
36C2×#476C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#464—21no—
40C2×#464—21no—
41C2×#460C2211yescharacteristic
42C2×#459C2211yescharacteristic
43C2×#452—21no—
44C2×#452—21no—
45C2×#449—21no—
46#2991—24no—
47#2991C2218yescomplemented
48C2×C8×Q8C2211yescharacteristic
49C2×C8×Q8C2211yescharacteristic
50C2×#442—21no—
51C2×#440—21no—
52C2×#436—21no—
53C2×#436—21no—
54C2×#436C2211yescharacteristic
55C2×#436C2211yescharacteristic
56C2×#432C2211yescharacteristic
57C2×#431—21no—
58C2×#431C2211yescharacteristic
59C2×#427—21no—
60C2×#423—21no—
61C2×#423C2211yescharacteristic
62C22×C4⋊C8C2211yescharacteristic
63C2×#416—21no—
64#1703C2218yescomplemented
65#1697C2218yescomplemented
66#1689C2218yescomplemented
67#1685C2218yescomplemented
68#1684C2218yescomplemented
69#1678C2218yescomplemented
70#1670C2218yescomplemented
71#1666C2218yescomplemented
72#1573C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1559C2218yescomplemented
78#1547C2218yescomplemented
79C2×#333C2211yescharacteristic
80C2×#333C2211yescharacteristic
81C2×#332C2211yescharacteristic
82C2×#332C2211yescharacteristic
83C2×#332C2211yescharacteristic
84C2×#332C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C22×#41D411yescharacteristic
89C22×Q16—21no—
90C22×Q16—21no—
91C22×SD16—21no—
92C22×SD16—21no—
93C22×SD16—21no—
94C22×D8—21no—
95C22×M16—21no—
96C22×M16—21no—
97C22×M16—21no—
98C23×C8—21no—
99#533—22no—
100#533—22no—
101#533—22no—
102#533C2314yes—
103#532—22no—
104#532—22no—
105#532—22no—
106#532C2314yes—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#125—21no—
112C2×#124—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×#121—21no—
116C2×#121—21no—
117C4×#41—22no—
118C4×#41—22no—
119C4×#41D414yes—
120C4×#41C2314yes—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8D411yescharacteristic
124C2×C4×Q8C2311yescharacteristic
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4D411yescharacteristic
130C2×C4×D4C2311yescharacteristic
131C2×#117—21no—
132C2×#117—21no—
133C2×#117D411yescharacteristic
134C22×C42—21no—
135C22×C42C2311yescharacteristic
136#494—22no—
137#494C2314yes—
138#492—22no—
139#492C2314yes—
140#487—22no—
141#487C2314yes—
142#486—22no—
143#486C2314yes—
144#482—28no—
145#479—28no—
146#478—28no—
147#477—22no—
148#477C2314yes—
149#476—22no—
150#476C2314yes—
151#475—22no—
152#475—22no—
153#475C2314yes—
154#475C2314yes—
155#474—22no—
156#474—22no—
157#474C2314yes—
158#474C2314yes—
159#464—28no—
160#464—28no—
161#460—22no—
162#460C2314yes—
163#459—22no—
164#459C2314yes—
165#452—28no—
166#452—28no—
167#449—28no—
168C8×Q8—22no—
169C8×Q8—22no—
170C8×Q8C2314yes—
171C8×Q8C2314yes—
172#442—28no—
173#440—28no—
174#436—28no—
175#436—28no—
176#436—22no—
177#436—22no—
178#436C2314yes—
179#436C2314yes—
180#432—22no—
181#432C2314yes—
182#431—28no—
183#431D414yes—
184#431C2314yes—
185#427—28no—
186C2×#107—21no—
187C2×#107—21no—
188C2×#107—21no—
189C2×#106—21no—
190C2×#106—21no—
191C2×#106—21no—
192#423—22no—
193#423—28no—
194#423C2314yes—
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—22no—
199C2×C4⋊C8—21no—
200C2×C4⋊C8D411yescharacteristic
201C2×C4⋊C8D411yescharacteristic
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208C2×C4⋊C8C2314yes—
209#416—28no—
210C2×#103—21no—
211C2×#103—21no—
212C2×#103—21no—
213C2×#103—21no—
214C2×#103—21no—
215C2×#102—21no—
216C2×#102—21no—
217C2×#102—21no—
218C2×#102—21no—
219C2×#102—21no—
220C2×#102—21no—
221C2×#102—21no—
222C2×C22⋊C8—21no—
223C2×C22⋊C8—21no—
224C2×C22⋊C8—21no—
225C2×C22⋊C8D411yescharacteristic
226C2×C22⋊C8D411yescharacteristic
227C2×#97—21no—
228C2×C4×C8—21no—
229C2×C4×C8—21no—
230C2×C4×C8C2311yescharacteristic
231C2×C4×C8C2311yescharacteristic
232#335C2314yes—
233#335C2314yes—
234#334C2314yes—
235#334C2314yes—
236#333C2314yes—
237#333C2314yes—
238#332C2314yes—
239#332C2314yes—
240#332C2314yes—
241#332C2314yes—
242#331C2314yes—
243#331C2314yes—
244C2×#41—22no—
245C2×#41—24no—
246C2×#41—24no—
247C2×#41—42no—
248C2×#41—42no—
249C2×#41—82no—
250C2×#41—82no—
251C2×#41C2×D414yes—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8C2×D411yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—41no—
261C22×D4C2×D411yescharacteristic
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—41no—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4#4111yescharacteristic
269C2×Q16—24no—
270C2×Q16—24no—
271C2×Q16—82no—
272C2×Q16—82no—
273C2×SD16—24no—
274C2×SD16—24no—
275C2×SD16—24no—
276C2×SD16—44no—
277C2×SD16—82no—
278C2×SD16—82no—
279C2×D8—24no—
280C2×D8—44no—
281C2×M16—24no—
282C2×M16—24no—
283C2×M16—24no—
284C2×M16—82no—
285C2×M16—82no—
286C2×M16—82no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—24no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—44no—
295C22×C8C2×D411yescharacteristic
296C22×C8C2×D411yescharacteristic
297C22×C8C2×D411yescharacteristic
298C22×C8C2×D411yescharacteristic
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C2412yes—
309C4⋊Q8C2412yes—
310C4⋊Q8C2412yes—
311#127—21no—
312#127—21no—
313#127—21no—
314#127C2412yes—
315#125—24no—
316#125—42no—
317#124—24no—
318#124—42no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323#121—24no—
324#121—24no—
325#121—42no—
326#121—42no—
327C4×Q8—22no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—42no—
333C4×Q8—42no—
334C4×Q8C2×D414yes—
335C4×Q8C2×D412yes—
336C4×Q8C2412yes—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—21no—
343C4×D4—24no—
344C4×D4—21no—
345C4×D4—24no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4C2×D414yes—
349C4×D4C2×D412yes—
350C4×D4C2412yes—
351#117—22no—
352#117—24no—
353#117—24no—
354#117—24no—
355#117—42no—
356#117C2×D414yes—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4C2×D411yescharacteristic
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—41no—
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D412yes—
384C2×C42C2×D412yes—
385C2×C42#4111yescharacteristic
386C2×C42#4112yes—
387C2×C42C2411yescharacteristic
388C2×C42C2412yes—
389#107—24no—
390#107—24no—
391#107—24no—
392#106—24no—
393#106—24no—
394#106—24no—
395C4⋊C8—24no—
396C4⋊C8—24no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—24no—
400C4⋊C8—24no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C2×D414yes—
406C4⋊C8C2×D414yes—
407C4⋊C8C2412yes—
408C4⋊C8C2412yes—
409C4⋊C8C2412yes—
410C4⋊C8C2412yes—
411C4⋊C8C2412yes—
412C4⋊C8C2412yes—
413#103—24no—
414#103—24no—
415#103—24no—
416#103—24no—
417#103—24no—
418#102—24no—
419#102—24no—
420#102—24no—
421#102—24no—
422#102—24no—
423#102—24no—
424#102—24no—
425C22⋊C8—24no—
426C22⋊C8—24no—
427C22⋊C8—24no—
428C22⋊C8C2×D414yes—
429C22⋊C8C2×D414yes—
430#97—24no—
431C4×C8—24no—
432C4×C8—24no—
433C4×C8C2×D412yes—
434C4×C8C2×D412yes—
435C4×C8C2412yes—
436C4×C8C2412yes—
437C24—21no—
438C24—41no—
439C24#12111yescharacteristic
440#41—28no—
441#41—44no—
442#41—48no—
443#41—84no—
444#41—84no—
445#41—88no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—82no—
459C2×Q8#13714yes—
460C2×Q8C22×D412yes—
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—82no—
478C2×D4—84no—
479C2×D4C22×D412yes—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—44no—
500C22×C4—84no—
501C22×C4#12112yes—
502C22×C4#12112yes—
503C22×C4#12111yescharacteristic
504C22×C4#12111yescharacteristic
505C22×C4#12111yescharacteristic
506C22×C4#12112yes—
507C22×C4C22×D412yes—
508C22×C4C22×D412yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4112yes—
513Q16—84no—
514Q16—84no—
515SD16—48no—
516SD16—84no—
517SD16—84no—
518D8—48no—
519M16—84no—
520M16—84no—
521M16—84no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—48no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—42no—
537C2×C8—42no—
538C2×C8—42no—
539C2×C8C22×D412yes—
540C2×C8C22×D412yes—
541C2×C8C22×D412yes—
542C2×C8C22×D412yes—
543C4⋊C4—22no—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4C22×D412yes—
563C4⋊C4C22×D412yes—
564C22⋊C4—24no—
565C22⋊C4—22no—
566C22⋊C4—24no—
567C22⋊C4—22no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C42—24no—
572C42—24no—
573C42—22no—
574C42—22no—
575C42—44no—
576C42#12112yes—
577C42#12112yes—
578C42#12112yes—
579C42C22×D411yescharacteristic
580C42C22×D412yes—
581C42C22×D411yescharacteristic
582C42C22×D412yes—
583C42C2×#4112yes—
584C42C2×#4111yescharacteristic
585C42C2511yescharacteristic
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—82no—
595C23—82no—
596C23—82no—
597C23C2×#12112yes—
598C23C2×#12111yescharacteristic
599Q8—24no—
600Q8—22no—
601Q8—42no—
602Q8—42no—
603Q8—42no—
604Q8—42no—
605Q8—82no—
606Q8—82no—
607Q8—82no—
608Q8—82no—
609Q8C2×#13714yes—
610D4—22no—
611D4—22no—
612D4—48no—
613D4—42no—
614D4—42no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—82no—
619D4—82no—
620D4—88no—
621D4—82no—
622D4—82no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—48no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—44no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—88no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—82no—
653C2×C4C2×#12112yes—
654C2×C4C2×#12112yes—
655C2×C4C2×#12111yescharacteristic
656C2×C4C2×#12112yes—
657C2×C4C2×#12111yescharacteristic
658C2×C4C2×#12111yescharacteristic
659C2×C4C2×#13712yes—
660C2×C4#57512yes—
661C2×C4#57612yes—
662C2×C4#57712yes—
663C2×C4C23×D411yescharacteristic
664C2×C4C23×D411yescharacteristic
665C2×C4C22×#4111yescharacteristic
666C8—22no—
667C8—22no—
668C8—22no—
669C8—22no—
670C8—42no—
671C8—42no—
672C8—42no—
673C8—42no—
674C8—42no—
675C8—42no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—44no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—84no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—164no—
688C22#304512yes—
689C22#305612yes—
690C22#306712yes—
691C22C22×#12111yescharacteristic
692C4—22no—
693C4—22no—
694C4—24no—
695C4—22no—
696C4—21no—
697C4—21no—
698C4—42no—
699C4—42no—
700C4—82no—
701C4—82no—
702C4—82no—
703C4#304512yes—
704C4#305612yes—
705C4C22×#13711yescharacteristic
706C4C2×#57511yescharacteristic
707C4C2×#57611yescharacteristic
708C4C2×#57711yescharacteristic
709C2—42no—
710C2—82no—
711C2—162no—
712C2#1949314yesdirect product factor
713C2C2×#304511yescharacteristic
714C2C2×#305611yescharacteristic
715C2C2×#306711yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3210C2semidirect
3. C2×#3076C2semidirect
4. C2×#2991C2semidirect
5. #19493C2direct (N × H)
6. C2×#1703C2semidirect
7. C2×#1697C2semidirect
8. C2×#1689C2semidirect
9. C2×#1685C2semidirect
10. C2×#1684C2semidirect
11. C2×#1678C2semidirect
12. C2×#1670C2semidirect
13. C2×#1666C2semidirect
14. C2×#1573C2semidirect
15. C2×#1559C2semidirect
16. C2×#1547C2semidirect
21. #3210C22semidirect
30. #3076C22semidirect
47. #2991C22semidirect
64. #1703C22semidirect
65. #1697C22semidirect
66. #1689C22semidirect
67. #1685C22semidirect
68. #1684C22semidirect
69. #1678C22semidirect
70. #1670C22semidirect
71. #1666C22semidirect
72. #1573C22semidirect
77. #1559C22semidirect
78. #1547C22semidirect
712. C2#19493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32102
C2×#31152
C2×#30762
C2×#29912
#194932
C2×#17032
C2×#16972
C2×#16892
C2×#16852
C2×#16842
C2×#16782
C2×#16702
C2×#16662
C2×#15732
C2×#15592
C2×#15472