Finite Group Databasebeta

← C2×#19707 #6357290

Subgroups — C2×#19707 #6357290

Order 512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3231C211yesmaximal, characteristic, complemented
3C2×#3228C211yesmaximal, characteristic
4C2×#3210C211yesmaximal, characteristic
5C2×#3170C211yesmaximal, characteristic, complemented
6C2×#3167C211yesmaximal, characteristic
7#19707C2116yesmaximal, direct product factor
8C2×#1723C211yesmaximal, characteristic, complemented
9C2×#1723C211yesmaximal, characteristic, complemented
10C2×#1720C211yesmaximal, characteristic, complemented
11C2×#1719C211yesmaximal, characteristic, complemented
12C2×#1719C211yesmaximal, characteristic, complemented
13C2×#1718C211yesmaximal, characteristic, complemented
14C2×#1716C211yesmaximal, characteristic, complemented
15C2×#1714C211yesmaximal, characteristic, complemented
16C2×#1452C211yesmaximal, characteristic, complemented
17C2×#533C2211yescharacteristic
18C2×#533C2211yescharacteristic
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21#3231—24no—
22#3231—24no—
23#3231C2218yescomplemented
24#3231C2218yescomplemented
25#3228—24no—
26#3228C2218yes—
27#3210—24no—
28#3210C2218yes—
29#3170—24no—
30#3170C2218yescomplemented
31#3167—24no—
32#3167C2218yes—
33C2×#500C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#500C2211yescharacteristic
37C2×#498C2211yescharacteristic
38C2×#498C2211yescharacteristic
39C2×#498C2211yescharacteristic
40C2×#498C2211yescharacteristic
41C2×#494C2211yescharacteristic
42C2×#494C2211yescharacteristic
43C2×#492C2211yescharacteristic
44C2×#492C2211yescharacteristic
45C2×#487C2211yescharacteristic
46C2×#487C2211yescharacteristic
47C2×#487C2211yescharacteristic
48C2×#487C2211yescharacteristic
49C2×#487C2211yescharacteristic
50C2×#487C2211yescharacteristic
51C2×#487C2211yescharacteristic
52C2×#487C2211yescharacteristic
53C2×#486C2211yescharacteristic
54C2×#486C2211yescharacteristic
55C2×#486C2211yescharacteristic
56C2×#486C2211yescharacteristic
57C2×#485—22no—
58C2×#485—22no—
59C2×#482—22no—
60C2×#479—22no—
61C2×#479—22no—
62C2×#478—22no—
63C2×#467—22no—
64C2×#465—22no—
65C2×#464—22no—
66C2×#452—22no—
67C2×C4×Q16—22no—
68C2×C4×SD16—22no—
69C2×#431C2211yescharacteristic
70C2×#431C2211yescharacteristic
71C22×C4×C8C2211yescharacteristic
72#1723C2218yescomplemented
73#1723C2218yescomplemented
74#1720C2218yescomplemented
75#1719C2218yescomplemented
76#1719C2218yescomplemented
77#1718C2218yescomplemented
78#1716C2218yescomplemented
79#1714C2218yescomplemented
80#1452C2218yescomplemented
81C2×#322C2211yescharacteristic
82C2×#322C2211yescharacteristic
83C2×#322C2211yescharacteristic
84C2×#322C2211yescharacteristic
85C22×#41—21no—
86C22×Q16—22no—
87C22×Q16—22no—
88C22×SD16—22no—
89C22×SD16—22no—
90C23×C8D412yes—
91#533—22no—
92#533—22no—
93#533—22no—
94#533—22no—
95#533—22no—
96#533—22no—
97#533—22no—
98#533—22no—
99#533—22no—
100#533C2314yes—
101#533C2314yes—
102#533C2314yes—
103#532—22no—
104#532—22no—
105#532—22no—
106#532C2314yes—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127C2311yescharacteristic
115C2×#125—21no—
116C2×#125—21no—
117C2×#125—21no—
118C2×#124—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×Q8—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—21no—
138C22×C42C2311yescharacteristic
139#500—22no—
140#500—22no—
141#500—22no—
142#500—22no—
143#500C2314yes—
144#500C2314yes—
145#500C2314yes—
146#500C2314yes—
147#498—22no—
148#498—22no—
149#498—22no—
150#498—22no—
151#498C2314yes—
152#498C2314yes—
153#498C2314yes—
154#498C2314yes—
155#494—22no—
156#494—22no—
157#494C2314yes—
158#494C2314yes—
159#492—22no—
160#492—22no—
161#492C2314yes—
162#492C2314yes—
163#487—22no—
164#487—22no—
165#487—22no—
166#487—22no—
167#487—22no—
168#487—22no—
169#487—22no—
170#487—22no—
171#487C2314yes—
172#487C2314yes—
173#487C2314yes—
174#487C2314yes—
175#487C2314yes—
176#487C2314yes—
177#487C2314yes—
178#487C2314yes—
179#486—22no—
180#486—22no—
181#486—22no—
182#486—22no—
183#486C2314yes—
184#486C2314yes—
185#486C2314yes—
186#486C2314yes—
187#485—216no—
188#485—216no—
189#482—216no—
190#479—216no—
191#479—216no—
192#478—216no—
193#467—216no—
194#465—216no—
195#464—216no—
196#452—216no—
197C4×Q16—216no—
198C4×SD16—216no—
199#431D414yes—
200#431D414yes—
201#431C2314yes—
202#431C2314yes—
203C2×#107—22no—
204C2×#107—22no—
205C2×#107—22no—
206C2×#107—22no—
207C2×#106—22no—
208C2×#106—22no—
209C2×#106—22no—
210C2×#106—22no—
211C2×C4⋊C8D412yes—
212C2×C4⋊C8D412yes—
213C2×#103—22no—
214C2×#103—22no—
215C2×#103—22no—
216C2×#103—22no—
217C2×#103—22no—
218C2×#103—22no—
219C2×#103—22no—
220C2×#103—22no—
221C2×#102—22no—
222C2×#102—22no—
223C2×#102—22no—
224C2×#102—22no—
225C2×C22⋊C8D412yes—
226C2×C22⋊C8D412yes—
227C2×C4×C8D414yes—
228C2×C4×C8D412yes—
229C2×C4×C8C2311yescharacteristic
230C2×C4×C8C2311yescharacteristic
231C2×C4×C8C2314yes—
232C2×C4×C8C2311yescharacteristic
233C2×C4×C8C2311yescharacteristic
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2311yescharacteristic
236#322C2314yes—
237#322C2314yes—
238#322C2314yes—
239#322C2314yes—
240C2×#41—24no—
241C2×#41—42no—
242C2×#41—84no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—41no—
254C23×C4—41no—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C2×Q16—28no—
259C2×Q16—28no—
260C2×Q16—48no—
261C2×Q16—84no—
262C2×SD16—28no—
263C2×SD16—28no—
264C2×SD16—48no—
265C2×SD16—84no—
266C22×C8—44no—
267C22×C8C2×D412yes—
268C22×C8C2×D412yes—
269C22×C8C2×D412yes—
270C22×C8C2×D412yes—
271C22×C8C2×D412yes—
272C22×C8C2×D412yes—
273C22×C8C2×D418yes—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C2412yes—
296C4⋊Q8C2412yes—
297C4⋊Q8C2412yes—
298C4⋊Q8C2412yes—
299C4⋊Q8C2412yes—
300C4⋊Q8C2412yes—
301C4⋊Q8C2412yes—
302#127—21no—
303#127—21no—
304#127—21no—
305#127C2412yes—
306#125—24no—
307#125—24no—
308#125—24no—
309#125—42no—
310#125—42no—
311#125—42no—
312#124—24no—
313#124—42no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—42no—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323C22⋊Q8—42no—
324C22⋊Q8—42no—
325C22⋊Q8—42no—
326#121—24no—
327#121—24no—
328#121—42no—
329#121—42no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—24no—
333C4×Q8—24no—
334C4×Q8—24no—
335C4×Q8—24no—
336C4×Q8—42no—
337C4×Q8—42no—
338C4×Q8—42no—
339C4×Q8—42no—
340C4×Q8—42no—
341C4×Q8—42no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—42no—
345C4×D4—42no—
346#117—24no—
347#117—24no—
348#117—24no—
349#117—42no—
350#117—42no—
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—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C42—41no—
378C2×C42—41no—
379C2×C42—41no—
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D412yes—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C2×C42C2411yescharacteristic
387C2×C42C2412yes—
388#107—28no—
389#107—28no—
390#107—28no—
391#107—28no—
392#106—28no—
393#106—28no—
394#106—28no—
395#106—28no—
396C4⋊C8C2×D418yes—
397C4⋊C8C2×D418yes—
398#103—28no—
399#103—28no—
400#103—28no—
401#103—28no—
402#103—28no—
403#103—28no—
404#103—28no—
405#103—28no—
406#102—28no—
407#102—28no—
408#102—28no—
409#102—28no—
410C22⋊C8C2×D418yes—
411C22⋊C8C2×D418yes—
412C4×C8C2×D418yes—
413C4×C8C2×D412yes—
414C4×C8C2×D412yes—
415C4×C8C2×D412yes—
416C4×C8C2×D412yes—
417C4×C8C2×D412yes—
418C4×C8C2×D412yes—
419C4×C8C2412yes—
420C4×C8C2412yes—
421C4×C8C2412yes—
422C4×C8C2412yes—
423C4×C8C2412yes—
424C4×C8C2412yes—
425C24—41no—
426C24#12711yescharacteristic
427#41—88no—
428#41—88no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—44no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—84no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—44no—
472C22×C4—84no—
473C22×C4#12712yes—
474C22×C4#12712yes—
475C22×C4#12712yes—
476C22×C4#12711yescharacteristic
477C22×C4#12711yescharacteristic
478C22×C4#12711yescharacteristic
479C22×C4C22×D412yes—
480C22×C4C22×D412yes—
481C22×C4C22×D412yes—
482C22×C4C22×D411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×D411yescharacteristic
485Q16—416no—
486Q16—88no—
487SD16—416no—
488SD16—88no—
489C2×C8—24no—
490C2×C8—24no—
491C2×C8—24no—
492C2×C8—24no—
493C2×C8—24no—
494C2×C8—24no—
495C2×C8—48no—
496C2×C8C22×D414yes—
497C2×C8C22×D414yes—
498C2×C8C22×D414yes—
499C2×C8C22×D414yes—
500C2×C8C22×D414yes—
501C2×C8C22×D414yes—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—44no—
535C4⋊C4—44no—
536C22⋊C4—44no—
537C22⋊C4—44no—
538C22⋊C4—44no—
539C22⋊C4—44no—
540C22⋊C4—44no—
541C42—44no—
542C42—44no—
543C42—44no—
544C42#12712yes—
545C42#12712yes—
546C42#12712yes—
547C42C22×D412yes—
548C42C22×D411yescharacteristic
549C42C22×D411yescharacteristic
550C42C22×D411yescharacteristic
551C42C22×D412yes—
552C42C22×D412yes—
553C42C2511yescharacteristic
554C23—22no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—82no—
559C23—82no—
560C23—82no—
561C23C2×#12712yes—
562C23C2×#12711yescharacteristic
563Q8—44no—
564Q8—44no—
565Q8—44no—
566Q8—44no—
567Q8—44no—
568Q8—44no—
569Q8—44no—
570Q8—82no—
571Q8—82no—
572Q8—82no—
573Q8—82no—
574Q8—82no—
575Q8—82no—
576Q8—82no—
577D4—44no—
578D4—44no—
579D4—44no—
580D4—88no—
581D4—82no—
582D4—82no—
583D4—82no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—88no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4C2×#12712yes—
609C2×C4C2×#12712yes—
610C2×C4C2×#12712yes—
611C2×C4C2×#12711yescharacteristic
612C2×C4C2×#12711yescharacteristic
613C2×C4C2×#12711yescharacteristic
614C2×C4#57514yes—
615C2×C4#57714yes—
616C2×C4#57814yes—
617C2×C4C23×D411yescharacteristic
618C2×C4C23×D411yescharacteristic
619C2×C4C23×D411yescharacteristic
620C8—24no—
621C8—24no—
622C8—24no—
623C8—24no—
624C8—24no—
625C8—24no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—44no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22—164no—
634C22#315012yes—
635C22#315412yes—
636C22#315612yes—
637C22C22×#12711yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—82no—
642C4—82no—
643C4—82no—
644C4—82no—
645C4—82no—
646C4—82no—
647C4—82no—
648C4#315012yes—
649C4#315412yes—
650C4#315612yes—
651C4C2×#57512yes—
652C4C2×#57712yes—
653C4C2×#57812yes—
654C2—42no—
655C2—162no—
656C2#1970714yesdirect product factor
657C2C2×#315011yescharacteristic
658C2C2×#315411yescharacteristic
659C2C2×#315611yescharacteristic
subgroupG/H
center, socleC23C2×#127
commutator, Frattini, cosocleC42C25
prime radicalC2×#532C22
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×#3231C2semidirect
2. C2×#3231C2semidirect
5. C2×#3170C2semidirect
7. #19707C2direct (N × H)
8. C2×#1723C2semidirect
9. C2×#1723C2semidirect
10. C2×#1720C2semidirect
11. C2×#1719C2semidirect
12. C2×#1719C2semidirect
13. C2×#1718C2semidirect
14. C2×#1716C2semidirect
15. C2×#1714C2semidirect
16. C2×#1452C2semidirect
23. #3231C22semidirect
24. #3231C22semidirect
30. #3170C22semidirect
72. #1723C22semidirect
73. #1723C22semidirect
74. #1720C22semidirect
75. #1719C22semidirect
76. #1719C22semidirect
77. #1718C22semidirect
78. #1716C22semidirect
79. #1714C22semidirect
80. #1452C22semidirect
656. C2#19707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32282
C2×#32102
C2×#31702
C2×#31672
#197072
C2×#17232
C2×#17202
C2×#17192
C2×#17182
C2×#17162
C2×#17142
C2×#14522