Finite Group Databasebeta

← C2×#19303 #6353949

Subgroups — C2×#19303 #6353949

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 713 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3131C211yesmaximal, characteristic, complemented
2C2×#3116C211yesmaximal, characteristic, complemented
3C2×#3115C211yesmaximal, characteristic
4C2×#2965C211yesmaximal, characteristic, complemented
5#19303C2116yesmaximal, direct product factor
6C2×#1704C211yesmaximal, characteristic, complemented
7C2×#1702C211yesmaximal, characteristic, complemented
8C2×#1700C211yesmaximal, characteristic, complemented
9C2×#1698C211yesmaximal, characteristic, complemented
10C2×#1703C211yesmaximal, characteristic, complemented
11C2×#1701C211yesmaximal, characteristic, complemented
12C2×#1699C211yesmaximal, characteristic, complemented
13C2×#1697C211yesmaximal, characteristic, complemented
14C2×#1568C211yesmaximal, characteristic, complemented
15C2×#1554C211yesmaximal, characteristic, complemented
16C2×#1553C211yesmaximal, characteristic, complemented
17C2×#533C2211yescharacteristic
18C2×#532C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20#3131—24no—
21#3131C2218yescomplemented
22C2×#488—21no—
23C2×#488—21no—
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#486C2211yescharacteristic
28#3116—24no—
29#3116C2218yescomplemented
30#3115—24no—
31#3115C2218yes—
32C2×#485—21no—
33C2×#482—21no—
34C2×#477C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#462C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#452—21no—
43C2×#449—21no—
44#2965—24no—
45#2965C2218yescomplemented
46C2×#446C2211yescharacteristic
47C2×#446C2211yescharacteristic
48C2×#442—21no—
49C2×#441—21no—
50C2×#440—21no—
51C2×#440—21no—
52C2×#436C2211yescharacteristic
53C2×#436C2211yescharacteristic
54C2×#435—21no—
55C2×#435—21no—
56C2×#432C2211yescharacteristic
57C2×#432C2211yescharacteristic
58C2×#431—21no—
59C2×#431C2211yescharacteristic
60C2×#416—21no—
61C2×#416—21no—
62C2×C4×M16—21no—
63C22×C4×C8C2211yescharacteristic
64#1704C2218yescomplemented
65#1703C2218yescomplemented
66#1702C2218yescomplemented
67#1701C2218yescomplemented
68#1700C2218yescomplemented
69#1699C2218yescomplemented
70#1698C2218yescomplemented
71#1697C2218yescomplemented
72#1568C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1554C2218yescomplemented
78#1553C2218yescomplemented
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×SD16—21no—
91C22×SD16—21no—
92C22×D8—21no—
93C22×M16—21no—
94C22×M16—21no—
95C23×C8D411yescharacteristic
96C23×C8D411yescharacteristic
97#533—22no—
98#533—22no—
99#533—22no—
100#533C2314yes—
101#532—22no—
102#532—22no—
103#532—22no—
104#532C2314yes—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#125—21no—
110C2×#124—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×#121—21no—
114C2×#121—21no—
115C4×#41—22no—
116C4×#41—22no—
117C4×#41D414yes—
118C4×#41C2314yes—
119C2×C4×Q8—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8D411yescharacteristic
122C2×C4×Q8C2311yescharacteristic
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4D411yescharacteristic
128C2×C4×D4C2311yescharacteristic
129C2×#117—21no—
130C2×#117—21no—
131C2×#117D411yescharacteristic
132C22×C42—21no—
133C22×C42C2311yescharacteristic
134#488—28no—
135#488—28no—
136#487—22no—
137#487—22no—
138#487C2314yes—
139#487C2314yes—
140#486—22no—
141#486—22no—
142#486C2314yes—
143#486C2314yes—
144#485—28no—
145#482—28no—
146#477—22no—
147#477C2314yes—
148#476—22no—
149#476C2314yes—
150#475—22no—
151#475C2314yes—
152#474—22no—
153#474C2314yes—
154#462—22no—
155#462C2314yes—
156#461—22no—
157#461C2314yes—
158#460—22no—
159#460C2314yes—
160#459—22no—
161#459C2314yes—
162#452—28no—
163#449—28no—
164#446—22no—
165#446—22no—
166#446C2314yes—
167#446C2314yes—
168#442—28no—
169#441—28no—
170#440—28no—
171#440—28no—
172#436—22no—
173#436—22no—
174#436C2314yes—
175#436C2314yes—
176#435—28no—
177#435—28no—
178#432—22no—
179#432—22no—
180#432C2314yes—
181#432C2314yes—
182#431—22no—
183#431—28no—
184#431C2314yes—
185C2×#107—21no—
186C2×#107—21no—
187C2×#106—21no—
188C2×#106—21no—
189C2×C4⋊C8—21no—
190C2×C4⋊C8—21no—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197#416—28no—
198#416—28no—
199C2×#103—21no—
200C2×#103—21no—
201C2×#103—21no—
202C2×#103—21no—
203C2×#103—21no—
204C2×#103—21no—
205C2×#103—21no—
206C2×#103—21no—
207C2×#102—21no—
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—21no—
211C2×#102—21no—
212C2×#102—21no—
213C2×#102—21no—
214C2×#102—21no—
215C2×C22⋊C8—21no—
216C2×C22⋊C8—21no—
217C2×C22⋊C8—21no—
218C2×C22⋊C8—21no—
219C2×C22⋊C8—21no—
220C4×M16—28no—
221C2×#97—21no—
222C2×#97—21no—
223C2×#97—21no—
224C2×#97—21no—
225C2×C4×C8—21no—
226C2×C4×C8D411yescharacteristic
227C2×C4×C8D411yescharacteristic
228C2×C4×C8D414yes—
229C2×C4×C8C2311yescharacteristic
230C2×C4×C8C2311yescharacteristic
231C2×C4×C8C2314yes—
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—42no—
247C2×#41—42no—
248C2×#41—44no—
249C2×#41—44no—
250C2×#41—42no—
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—44no—
271C2×SD16—24no—
272C2×SD16—24no—
273C2×SD16—44no—
274C2×SD16—44no—
275C2×D8—24no—
276C2×D8—44no—
277C2×M16—24no—
278C2×M16—24no—
279C2×M16—44no—
280C2×M16—44no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—42no—
288C22×C8—42no—
289C22×C8C2×D411yescharacteristic
290C22×C8C2×D411yescharacteristic
291C22×C8C2×D411yescharacteristic
292C22×C8C2×D411yescharacteristic
293C22×C8C2×D414yes—
294C22×C8C2×D414yes—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C2412yes—
305C4⋊Q8C2412yes—
306C4⋊Q8C2412yes—
307#127—21no—
308#127—21no—
309#127—21no—
310#127C2412yes—
311#125—24no—
312#125—42no—
313#124—24no—
314#124—42no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—42no—
318C22⋊Q8—42no—
319#121—24no—
320#121—24no—
321#121—42no—
322#121—42no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—24no—
327C4×Q8—24no—
328C4×Q8—42no—
329C4×Q8—42no—
330C4×Q8C2×D414yes—
331C4×Q8C2×D412yes—
332C4×Q8C2412yes—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—24no—
340C4×D4—21no—
341C4×D4—24no—
342C4×D4—42no—
343C4×D4—42no—
344C4×D4C2×D414yes—
345C4×D4C2×D412yes—
346C4×D4C2412yes—
347#117—22no—
348#117—24no—
349#117—24no—
350#117—24no—
351#117—42no—
352#117C2×D414yes—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4C2×D411yescharacteristic
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—41no—
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D412yes—
379C2×C42C2×D412yes—
380C2×C42C2×D411yescharacteristic
381C2×C42#4111yescharacteristic
382C2×C42#4112yes—
383C2×C42C2411yescharacteristic
384C2×C42C2412yes—
385#107—24no—
386#107—24no—
387#106—24no—
388#106—24no—
389C4⋊C8—24no—
390C4⋊C8—24no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C2412yes—
398C4⋊C8C2412yes—
399C4⋊C8C2412yes—
400C4⋊C8C2412yes—
401C4⋊C8C2412yes—
402C4⋊C8C2412yes—
403#103—24no—
404#103—24no—
405#103—24no—
406#103—24no—
407#103—24no—
408#103—24no—
409#103—24no—
410#103—24no—
411#102—24no—
412#102—24no—
413#102—24no—
414#102—24no—
415#102—24no—
416#102—24no—
417#102—24no—
418#102—24no—
419C22⋊C8—24no—
420C22⋊C8—24no—
421C22⋊C8—24no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424#97—24no—
425#97—24no—
426#97—24no—
427#97—24no—
428C4×C8—24no—
429C4×C8C2×D414yes—
430C4×C8C2×D414yes—
431C4×C8C2×D412yes—
432C4×C8C2×D412yes—
433C4×C8C2412yes—
434C4×C8C2412yes—
435C24—21no—
436C24—41no—
437C24#12111yescharacteristic
438#41—44no—
439#41—44no—
440#41—48no—
441#41—48no—
442#41—48no—
443#41—88no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—82no—
458C2×Q8C22×D412yes—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—82no—
476C2×D4—84no—
477C2×D4C22×D412yes—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—44no—
498C22×C4—84no—
499C22×C4#12112yes—
500C22×C4#12112yes—
501C22×C4#12111yescharacteristic
502C22×C4#12111yescharacteristic
503C22×C4#12111yescharacteristic
504C22×C4#12112yes—
505C22×C4C22×D412yes—
506C22×C4C22×D412yes—
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4112yes—
511Q16—48no—
512SD16—48no—
513SD16—48no—
514D8—48no—
515M16—48no—
516M16—48no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—44no—
528C2×C8—44no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8—42no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8C22×D412yes—
536C2×C8C22×D412yes—
537C2×C8C22×D412yes—
538C2×C8C22×D412yes—
539C4⋊C4—24no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4C22×D412yes—
559C4⋊C4C22×D412yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C42—24no—
568C42—24no—
569C42—22no—
570C42—22no—
571C42—44no—
572C42#12112yes—
573C42#12112yes—
574C42#12112yes—
575C42C22×D412yes—
576C42C22×D411yescharacteristic
577C42C22×D412yes—
578C42C22×D411yescharacteristic
579C42C2×#4112yes—
580C42C2×#4111yescharacteristic
581C42C2511yescharacteristic
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—82no—
591C23—82no—
592C23—82no—
593C23C2×#12112yes—
594C23C2×#12111yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—42no—
598Q8—42no—
599Q8—42no—
600Q8—42no—
601Q8—42no—
602Q8—82no—
603Q8—82no—
604Q8—82no—
605Q8—82no—
606D4—22no—
607D4—22no—
608D4—48no—
609D4—42no—
610D4—42no—
611D4—42no—
612D4—42no—
613D4—42no—
614D4—82no—
615D4—82no—
616D4—88no—
617D4—82no—
618D4—82no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—48no—
635C2×C4—48no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—88no—
646C2×C4—82no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4C2×#12112yes—
650C2×C4C2×#12112yes—
651C2×C4C2×#12112yes—
652C2×C4C2×#12111yescharacteristic
653C2×C4C2×#12111yescharacteristic
654C2×C4C2×#12111yescharacteristic
655C2×C4#57512yes—
656C2×C4#57512yes—
657C2×C4#57512yes—
658C2×C4#57512yes—
659C2×C4C23×D411yescharacteristic
660C2×C4C23×D411yescharacteristic
661C2×C4C22×#4111yescharacteristic
662C8—22no—
663C8—22no—
664C8—22no—
665C8—22no—
666C8—42no—
667C8—42no—
668C8—42no—
669C8—42no—
670C8—42no—
671C8—42no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—44no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—84no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—164no—
684C22#304012yes—
685C22#305412yes—
686C22#306712yes—
687C22C22×#12111yescharacteristic
688C4—22no—
689C4—22no—
690C4—21no—
691C4—21no—
692C4—22no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—82no—
697C4—82no—
698C4—82no—
699C4#304012yes—
700C4#305412yes—
701C4C2×#57511yescharacteristic
702C4C2×#57511yescharacteristic
703C4C2×#57511yescharacteristic
704C4C2×#57511yescharacteristic
705C2—42no—
706C2—82no—
707C2—162no—
708C2#1930314yesdirect product factor
709C2C2×#304011yescharacteristic
710C2C2×#305411yescharacteristic
711C2C2×#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×#3131C2semidirect
2. C2×#3116C2semidirect
4. C2×#2965C2semidirect
5. #19303C2direct (N × H)
6. C2×#1704C2semidirect
7. C2×#1702C2semidirect
8. C2×#1700C2semidirect
9. C2×#1698C2semidirect
10. C2×#1703C2semidirect
11. C2×#1701C2semidirect
12. C2×#1699C2semidirect
13. C2×#1697C2semidirect
14. C2×#1568C2semidirect
15. C2×#1554C2semidirect
16. C2×#1553C2semidirect
21. #3131C22semidirect
29. #3116C22semidirect
45. #2965C22semidirect
64. #1704C22semidirect
65. #1703C22semidirect
66. #1702C22semidirect
67. #1701C22semidirect
68. #1700C22semidirect
69. #1699C22semidirect
70. #1698C22semidirect
71. #1697C22semidirect
72. #1568C22semidirect
77. #1554C22semidirect
78. #1553C22semidirect
708. C2#19303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31312
C2×#31162
C2×#31152
C2×#29652
#193032
C2×#17042
C2×#17022
C2×#17002
C2×#16982
C2×#17032
C2×#17012
C2×#16992
C2×#16972
C2×#15682
C2×#15542
C2×#15532