Finite Group Databasebeta

← C2×#19247 #6353752

Subgroups — C2×#19247 #6353752

Order 512.

1676 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3247C211yesmaximal, characteristic
2C2×#3233C211yesmaximal, characteristic, complemented
3C2×#3182C211yesmaximal, characteristic, complemented
4C2×#2969C211yesmaximal, characteristic, complemented
5#19247C2116yesmaximal, direct product factor
6C2×#1696C211yesmaximal, characteristic, complemented
7C2×#1686C211yesmaximal, characteristic, complemented
8C2×#1703C211yesmaximal, characteristic, complemented
9C2×#1697C211yesmaximal, characteristic, complemented
10C2×#1684C211yesmaximal, characteristic, complemented
11C2×#1678C211yesmaximal, characteristic, complemented
12C2×#1675C211yesmaximal, characteristic, complemented
13C2×#1665C211yesmaximal, characteristic, complemented
14C2×#1565C211yesmaximal, characteristic, complemented
15C2×#1543C211yesmaximal, characteristic, complemented
16C2×#1542C211yesmaximal, characteristic, complemented
17C2×#533C2211yescharacteristic
18C2×#532C2211yescharacteristic
19C2×#529C2211yescharacteristic
20#3247—24no—
21#3247C2218yes—
22#3233—24no—
23#3233C2218yescomplemented
24#3182—24no—
25#3182C2218yescomplemented
26C2×#500C2211yescharacteristic
27C2×#499—21no—
28C2×#492C2211yescharacteristic
29C2×#488—21no—
30C2×#487C2211yescharacteristic
31C2×#486C2211yescharacteristic
32C2×#485—21no—
33C2×#482—21no—
34C2×#477C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#478—21no—
38C2×#476C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#468—21no—
42C2×#468—21no—
43C2×#466—21no—
44C2×#465—21no—
45C2×#460C2211yescharacteristic
46C2×#463—21no—
47C2×#459C2211yescharacteristic
48#2969—24no—
49#2969C2218yescomplemented
50C2×#446C2211yescharacteristic
51C2×C8×Q8C2211yescharacteristic
52C2×#440—21no—
53C2×#440—21no—
54C2×#436—21no—
55C2×#436C2211yescharacteristic
56C2×#435—21no—
57C2×C8×D4C2211yescharacteristic
58C2×#433—21no—
59C2×#431C2211yescharacteristic
60C2×#431C2211yescharacteristic
61C22×C4⋊C8C2211yescharacteristic
62C2×#405—21no—
63C2×C4×M16C2211yescharacteristic
64#1703C2218yescomplemented
65#1697C2218yescomplemented
66#1696C2218yescomplemented
67#1686C2218yescomplemented
68#1684C2218yescomplemented
69#1678C2218yescomplemented
70#1675C2218yescomplemented
71#1665C2218yescomplemented
72#1565C2218yescomplemented
73C2×#335C2211yescharacteristic
74C2×#335C2211yescharacteristic
75C2×#334C2211yescharacteristic
76C2×#334C2211yescharacteristic
77#1543C2218yescomplemented
78#1542C2218yescomplemented
79C2×#333C2211yescharacteristic
80C2×#333C2211yescharacteristic
81C2×#333C2211yescharacteristic
82C2×#333C2211yescharacteristic
83C2×#332C2211yescharacteristic
84C2×#332C2211yescharacteristic
85C2×#331C2211yescharacteristic
86C2×#331C2211yescharacteristic
87C22×#41—21no—
88C22×SD16—21no—
89C22×SD16—21no—
90C22×SD16—21no—
91C22×D8—21no—
92C22×M16—21no—
93C22×M16D411yescharacteristic
94C22×M16D411yescharacteristic
95C23×C8—21no—
96C23×C8—21no—
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
109#529—22no—
110#529—22no—
111#529D414yes—
112#529C2314yes—
113C2×#126—21no—
114C2×#125—21no—
115C2×#125D411yescharacteristic
116C2×#124—21no—
117C2×#124D411yescharacteristic
118C2×#123—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8D411yescharacteristic
122C2×#121—21no—
123C2×#121—21no—
124C2×#121D411yescharacteristic
125C2×C4×Q8—21no—
126C2×C4×Q8—21no—
127C2×C4×Q8C2311yescharacteristic
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4C2311yescharacteristic
132C2×#117—21no—
133C2×#117—21no—
134C22×C42C2311yescharacteristic
135#500—22no—
136#500C2314yes—
137#499—28no—
138#492—22no—
139#492C2314yes—
140#488—28no—
141#487—22no—
142#487C2314yes—
143#486—22no—
144#486C2314yes—
145#485—28no—
146#482—28no—
147#478—28no—
148#477—22no—
149#477—22no—
150#477C2314yes—
151#477C2314yes—
152#476—22no—
153#476—22no—
154#476C2314yes—
155#476C2314yes—
156#475—22no—
157#475C2314yes—
158#474—22no—
159#474C2314yes—
160#468—28no—
161#468—28no—
162#466—28no—
163#465—28no—
164#463—28no—
165#460—22no—
166#460C2314yes—
167#459—22no—
168#459C2314yes—
169#446—22no—
170#446C2314yes—
171C8×Q8—22no—
172C8×Q8C2314yes—
173#440—28no—
174#440—28no—
175#436—28no—
176#436—22no—
177#436C2314yes—
178#435—28no—
179C8×D4—22no—
180C8×D4C2314yes—
181#433—28no—
182#431—22no—
183#431—22no—
184#431C2314yes—
185#431C2314yes—
186C2×#107—21no—
187C2×#107—21no—
188C2×#107—21no—
189C2×#107—21no—
190C2×#107—21no—
191C2×#106—21no—
192C2×#106—21no—
193C2×#106—21no—
194C2×C4⋊C8—21no—
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—22no—
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×C4⋊C8C2311yescharacteristic
201C2×C4⋊C8C2311yescharacteristic
202C2×C4⋊C8C2311yescharacteristic
203C2×C4⋊C8C2311yescharacteristic
204C2×C4⋊C8C2314yes—
205C2×#103—21no—
206C2×#103—21no—
207C2×#103—21no—
208C2×#103—21no—
209C2×#103—21no—
210C2×#102—21no—
211C2×#102—21no—
212C2×#102—21no—
213C2×#102—21no—
214C2×#102—21no—
215C2×#102—21no—
216C2×#102—21no—
217C2×C22⋊C8—21no—
218C2×C22⋊C8—21no—
219C2×C22⋊C8—21no—
220C2×C22⋊C8—21no—
221#405—28no—
222C4×M16D414yes—
223C4×M16C2314yes—
224C2×#97—21no—
225C2×#97D411yescharacteristic
226C2×#97D411yescharacteristic
227C2×C4×C8—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#333C2314yes—
239#333C2314yes—
240#332C2314yes—
241#332C2314yes—
242#331C2314yes—
243#331C2314yes—
244C2×#41—24no—
245C2×#41—42no—
246C2×#41—84no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8C2×D411yescharacteristic
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—41no—
256C22×D4C2×D411yescharacteristic
257C23×C4—21no—
258C23×C4—41no—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4#4111yescharacteristic
262C2×SD16—24no—
263C2×SD16—24no—
264C2×SD16—24no—
265C2×SD16—44no—
266C2×SD16—44no—
267C2×SD16—82no—
268C2×D8—24no—
269C2×D8—82no—
270C2×M16—24no—
271C2×M16—24no—
272C2×M16—42no—
273C2×M16—44no—
274C2×M16C2×D414yes—
275C2×M16C2×D414yes—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—24no—
283C22×C8—24no—
284C22×C8—44no—
285C22×C8—82no—
286C22×C8C2×D411yescharacteristic
287C22×C8C2×D411yescharacteristic
288C22×C8C2×D411yescharacteristic
289C22×C8C2×D411yescharacteristic
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8C2412yes—
300C4⋊Q8C2412yes—
301C4⋊Q8C2412yes—
302#127—21no—
303#127—21no—
304#127—21no—
305#127C2412yes—
306#126—24no—
307#126—24no—
308#125—22no—
309#125—24no—
310#125—42no—
311#125C2×D414yes—
312#124—22no—
313#124—24no—
314#124—42no—
315#124C2×D414yes—
316#123—24no—
317#123—24no—
318C22⋊Q8—22no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323C22⋊Q8C2×D414yes—
324#121—22no—
325#121—24no—
326#121—24no—
327#121—42no—
328#121—42no—
329#121C2×D414yes—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—24no—
333C4×Q8—24no—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8C2×D412yes—
337C4×Q8C2412yes—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—21no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—21no—
344C4×D4—42no—
345C4×D4—42no—
346C4×D4C2×D412yes—
347C4×D4C2412yes—
348#117—24no—
349#117—24no—
350#117—24no—
351#117—42no—
352C2×C4⋊C4—21no—
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—21no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C4⋊C4C2×D411yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C42—21no—
375C2×C42—41no—
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D412yes—
379C2×C42C2×D412yes—
380C2×C42#4111yescharacteristic
381C2×C42#4112yes—
382C2×C42C2411yescharacteristic
383C2×C42C2412yes—
384#107—24no—
385#107—24no—
386#107—24no—
387#107—24no—
388#107—24no—
389#106—24no—
390#106—24no—
391#106—24no—
392C4⋊C8—24no—
393C4⋊C8—24no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—24no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C2412yes—
402C4⋊C8C2412yes—
403C4⋊C8C2412yes—
404C4⋊C8C2412yes—
405C4⋊C8C2412yes—
406C4⋊C8C2412yes—
407#103—24no—
408#103—24no—
409#103—24no—
410#103—24no—
411#103—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—
423#97—24no—
424#97C2×D414yes—
425#97C2×D414yes—
426C4×C8—24no—
427C4×C8—24no—
428C4×C8—24no—
429C4×C8C2×D412yes—
430C4×C8C2×D412yes—
431C4×C8C2412yes—
432C4×C8C2412yes—
433C24—21no—
434C24—41no—
435C24#12111yescharacteristic
436#41—88no—
437#41—88no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—82no—
450C2×Q8—82no—
451C2×Q8C22×D412yes—
452C2×D4—24no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—44no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—82no—
468C2×D4—82no—
469C2×D4—84no—
470C2×D4C22×D412yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—44no—
487C22×C4—84no—
488C22×C4#12112yes—
489C22×C4#12112yes—
490C22×C4#12111yescharacteristic
491C22×C4#12111yescharacteristic
492C22×C4#12111yescharacteristic
493C22×C4#12112yes—
494C22×C4C22×D412yes—
495C22×C4C22×D412yes—
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4112yes—
500SD16—48no—
501SD16—48no—
502SD16—84no—
503D8—84no—
504M16—28no—
505M16—44no—
506M16—48no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—42no—
517C2×C8—42no—
518C2×C8—42no—
519C2×C8—42no—
520C2×C8—42no—
521C2×C8—42no—
522C2×C8—48no—
523C2×C8—84no—
524C2×C8#13514yes—
525C2×C8C22×D412yes—
526C2×C8C22×D412yes—
527C2×C8C22×D412yes—
528C2×C8C22×D412yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C4⋊C4C22×D412yes—
551C4⋊C4C22×D412yes—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C42—22no—
562C42—22no—
563C42—44no—
564C42#12112yes—
565C42#12112yes—
566C42#12112yes—
567C42C22×D412yes—
568C42C22×D412yes—
569C42C22×D411yescharacteristic
570C42C22×D411yescharacteristic
571C42C2×#4111yescharacteristic
572C42C2×#4112yes—
573C42C2511yescharacteristic
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—82no—
583C23—82no—
584C23—82no—
585C23C2×#12112yes—
586C23C2×#12111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—82no—
593Q8—82no—
594Q8—82no—
595Q8—82no—
596Q8—82no—
597D4—22no—
598D4—22no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—82no—
605D4—82no—
606D4—84no—
607D4—88no—
608D4—82no—
609D4—82no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—88no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4C2×#12112yes—
639C2×C4C2×#12112yes—
640C2×C4C2×#12111yescharacteristic
641C2×C4C2×#12112yes—
642C2×C4C2×#12111yescharacteristic
643C2×C4C2×#12111yescharacteristic
644C2×C4C2×#13512yes—
645C2×C4#57512yes—
646C2×C4#57712yes—
647C2×C4#57812yes—
648C2×C4C23×D411yescharacteristic
649C2×C4C23×D411yescharacteristic
650C2×C4C22×#4111yescharacteristic
651C8—22no—
652C8—22no—
653C8—22no—
654C8—42no—
655C8—42no—
656C8—42no—
657C8—42no—
658C8—42no—
659C8—42no—
660C8C2×#13514yes—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—84no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—164no—
673C22#303512yes—
674C22#306312yes—
675C22#306812yes—
676C22C22×#12111yescharacteristic
677C4—22no—
678C4—22no—
679C4—21no—
680C4—21no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—82no—
686C4—82no—
687C4—82no—
688C4#303512yes—
689C4#306312yes—
690C4C22×#13511yescharacteristic
691C4C2×#57511yescharacteristic
692C4C2×#57711yescharacteristic
693C4C2×#57811yescharacteristic
694C2—42no—
695C2—82no—
696C2—162no—
697C2#1924714yesdirect product factor
698C2C2×#303511yescharacteristic
699C2C2×#306311yescharacteristic
700C2C2×#306811yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3247C2
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
2. C2×#3233C2semidirect
3. C2×#3182C2semidirect
4. C2×#2969C2semidirect
5. #19247C2direct (N × H)
6. C2×#1696C2semidirect
7. C2×#1686C2semidirect
8. C2×#1703C2semidirect
9. C2×#1697C2semidirect
10. C2×#1684C2semidirect
11. C2×#1678C2semidirect
12. C2×#1675C2semidirect
13. C2×#1665C2semidirect
14. C2×#1565C2semidirect
15. C2×#1543C2semidirect
16. C2×#1542C2semidirect
23. #3233C22semidirect
25. #3182C22semidirect
49. #2969C22semidirect
64. #1703C22semidirect
65. #1697C22semidirect
66. #1696C22semidirect
67. #1686C22semidirect
68. #1684C22semidirect
69. #1678C22semidirect
70. #1675C22semidirect
71. #1665C22semidirect
72. #1565C22semidirect
77. #1543C22semidirect
78. #1542C22semidirect
697. C2#19247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32472
C2×#32332
C2×#31822
C2×#29692
#192472
C2×#16962
C2×#16862
C2×#17032
C2×#16972
C2×#16842
C2×#16782
C2×#16752
C2×#16652
C2×#15652
C2×#15432
C2×#15422