Finite Group Databasebeta

← C2×#11290 #358304

Subgroups — C2×#11290 #358304

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C22×#343C211yesmaximal, characteristic
3C22×#343C211yesmaximal, characteristic
4C22×#341C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C22×#340C211yesmaximal, characteristic
7C2×#1729C211yesmaximal, characteristic
8#11290C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C24×C8C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#428—24no—
17C2×#428—22no—
18C2×#428—24no—
19C2×#428C2214yes—
20C22×#107—21no—
21C22×#106—21no—
22C2×#343—24no—
23C2×#343C418yescomplemented
24C2×#343C2214yes—
25C2×#343C2214yes—
26C2×#341—24no—
27C2×#341C2214yes—
28#1736—22no—
29#1736C2214yes—
30C2×#340—22no—
31C2×#340—22no—
32C2×#340—21no—
33C2×#340—21no—
34C2×#340C2214yes—
35#1729—22no—
36#1729C2214yes—
37C2×#336—22no—
38C24×C4—21no—
39C24×C4—21no—
40C24×C4C2311yescharacteristic
41C22×M16—22no—
42C22×M16—21no—
43C22×M16—22no—
44C22×M16—22no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—22no—
48C22×M16—22no—
49C22×M16—22no—
50C22×M16—22no—
51C22×M16—22no—
52C22×M16—22no—
53C22×M16—22no—
54C22×M16—22no—
55C22×M16—22no—
56C22×M16—22no—
57C22×M16C2×C414yes—
58C22×M16C2×C414yes—
59C22×M16D414yes—
60C22×M16Q814yes—
61C22×M16Q814yes—
62C22×M16C2312yes—
63C22×M16C2312yes—
64C22×M16C2312yes—
65C23×C8—21no—
66C23×C8—21no—
67C23×C8—21no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8D412yes—
75C23×C8D412yes—
76C23×C8C2312yes—
77C2×#117—21no—
78C2×#117—21no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117D412yes—
84C2×#117C2312yes—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4C2×C414yes—
102C22×C4⋊C4D411yescharacteristic
103C22×C4⋊C4D411yescharacteristic
104C22×C4⋊C4D414yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C22⋊C4—21no—
108C22×C42—21no—
109#428—216no—
110#428—28no—
111#428—28no—
112C2×#107—28no—
113C2×#107—24no—
114C2×#106—28no—
115C2×#106—24no—
116#343—28no—
117#343C2×C4116yescomplemented
118#341—28no—
119#340—28no—
120#340—24no—
121#340—24no—
122#336—28no—
123C25#4111yescharacteristic
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—24no—
127C23×C4—24no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—41no—
131C23×C4—41no—
132C23×C4—41no—
133C23×C4—41no—
134C23×C4—42no—
135C23×C4—42no—
136C23×C4—82no—
137C23×C4—82no—
138C23×C4—82no—
139C23×C4—82no—
140C23×C4C22×C412yes—
141C23×C4C2×D412yes—
142C23×C4C2×D412yes—
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×Q812yes—
148C23×C4C2×Q812yes—
149C23×C4#4111yescharacteristic
150C23×C4#4112yes—
151C23×C4#4112yes—
152C23×C4#4112yes—
153C23×C4#4112yes—
154C23×C4#4112yes—
155C23×C4#4112yes—
156C23×C4#4112yes—
157C23×C4C2411yescharacteristic
158C2×M16—24no—
159C2×M16—28no—
160C2×M16—24no—
161C2×M16—24no—
162C2×M16—28no—
163C2×M16—28no—
164C2×M16—22no—
165C2×M16—22no—
166C2×M16—22no—
167C2×M16—24no—
168C2×M16—24no—
169C2×M16—22no—
170C2×M16—22no—
171C2×M16—28no—
172C2×M16—28no—
173C2×M16—28no—
174C2×M16—28no—
175C2×M16—22no—
176C2×M16—22no—
177C2×M16—22no—
178C2×M16—22no—
179C2×M16—22no—
180C2×M16—22no—
181C2×M16—22no—
182C2×M16—22no—
183C2×M16—42no—
184C2×M16—42no—
185C2×M16—42no—
186C2×M16—42no—
187C2×M16—44no—
188C2×M16—44no—
189C2×M16—44no—
190C2×M16—44no—
191C2×M16C4⋊C4116yes—
192C2×M16C22×C414yes—
193C2×M16C22×C414yes—
194C2×M16C2×D414yes—
195C2×M16C2×Q814yes—
196C2×M16C2×Q814yes—
197C22×C8—24no—
198C22×C8—24no—
199C22×C8—24no—
200C22×C8—22no—
201C22×C8—24no—
202C22×C8—24no—
203C22×C8—24no—
204C22×C8—24no—
205C22×C8—24no—
206C22×C8—24no—
207C22×C8—24no—
208C22×C8—24no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—42no—
218C22×C8—42no—
219C22×C8—44no—
220C22×C8—42no—
221C22×C8—44no—
222C22×C8—42no—
223C22×C8—44no—
224C22×C8—44no—
225C22×C8C2×D414yes—
226#117—24no—
227#117—24no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—22no—
232#117—42no—
233#117—42no—
234#117—42no—
235#117—42no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—41no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4C22×C414yes—
277C2×C4⋊C4C2×D414yes—
278C2×C4⋊C4C2×D412yes—
279C2×C4⋊C4C2×D412yes—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42—42no—
287C2×C42—42no—
288#107—216no—
289#106—216no—
290C24—22no—
291C24—22no—
292C24—22no—
293C24—22no—
294C24#11712yes—
295C24#12111yescharacteristic
296C24#12111yescharacteristic
297C24#12312yes—
298C24#12412yes—
299C24#12512yes—
300C24#12512yes—
301C24#12612yes—
302C24C2×#4111yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—44no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—88no—
322C22×C4—88no—
323C22×C4—82no—
324C22×C4—82no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4—82no—
328C22×C4—82no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4—88no—
332C22×C4—88no—
333C22×C4—82no—
334C22×C4—82no—
335C22×C4—82no—
336C22×C4—82no—
337C22×C4C2×C4⋊C414yes—
338C22×C4#11714yes—
339C22×C4#11712yes—
340C22×C4C4×D412yes—
341C22×C4C4×D412yes—
342C22×C4C4×D414yes—
343C22×C4C4×D412yes—
344C22×C4C4×D412yes—
345C22×C4C4×Q814yes—
346C22×C4#12012yes—
347C22×C4#12012yes—
348C22×C4#12112yes—
349C22×C4#12112yes—
350C22×C4#12112yes—
351C22×C4#12112yes—
352C22×C4#12111yescharacteristic
353C22×C4#12111yescharacteristic
354C22×C4C22⋊Q814yes—
355C22×C4C22⋊Q812yes—
356C22×C4C22⋊Q812yes—
357C22×C4C22⋊Q812yes—
358C22×C4C22⋊Q812yes—
359C22×C4C22⋊Q814yes—
360C22×C4C22⋊Q814yes—
361C22×C4#12314yes—
362C22×C4#12312yes—
363C22×C4#12312yes—
364C22×C4#12312yes—
365C22×C4#12312yes—
366C22×C4#12312yes—
367C22×C4#12312yes—
368C22×C4#12312yes—
369C22×C4#12414yes—
370C22×C4#12414yes—
371C22×C4#12412yes—
372C22×C4#12412yes—
373C22×C4#12412yes—
374C22×C4#12514yes—
375C22×C4#12514yes—
376C22×C4#12514yes—
377C22×C4#12512yes—
378C22×C4#12512yes—
379C22×C4#12614yes—
380C22×C4#12614yes—
381C22×C4#12614yes—
382C22×C4#12612yes—
383C22×C4C4⋊Q812yes—
384C22×C4C4⋊Q812yes—
385C22×C4C23×C411yescharacteristic
386C22×C4C22×D411yescharacteristic
387C22×C4C22×D411yescharacteristic
388C22×C4C22×D411yescharacteristic
389C22×C4C22×D411yescharacteristic
390C22×C4C22×Q811yescharacteristic
391C22×C4C22×Q811yescharacteristic
392C22×C4C2×#4111yescharacteristic
393C22×C4C2×#4111yescharacteristic
394C22×C4C2×#4111yescharacteristic
395C22×C4C2×#4111yescharacteristic
396C22×C4C2×#4111yescharacteristic
397C22×C4C2×#4111yescharacteristic
398C22×C4C2×#4111yescharacteristic
399M16—24no—
400M16—24no—
401M16—24no—
402M16—216no—
403M16—24no—
404M16—24no—
405M16—24no—
406M16—24no—
407M16—42no—
408M16—42no—
409M16—42no—
410M16—42no—
411M16—48no—
412M16—48no—
413M16C2×C4⋊C418yes—
414C2×C8—24no—
415C2×C8—24no—
416C2×C8—24no—
417C2×C8—216no—
418C2×C8—24no—
419C2×C8—24no—
420C2×C8—24no—
421C2×C8—24no—
422C2×C8—24no—
423C2×C8—42no—
424C2×C8—42no—
425C2×C8—42no—
426C2×C8—42no—
427C2×C8—42no—
428C2×C8—42no—
429C2×C8—42no—
430C2×C8—42no—
431C2×C8—48no—
432C2×C8—48no—
433C2×C8—48no—
434C2×C8—48no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—44no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—44no—
456C42—42no—
457C42—42no—
458C42—44no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23#38214yes—
480C23#38714yes—
481C23#38812yes—
482C23#38812yes—
483C23#39412yes—
484C23#39412yes—
485C23#39812yes—
486C23#39812yes—
487C23#40014yes—
488C23#40014yes—
489C23#47112yes—
490C23#47112yes—
491C23#47212yes—
492C23#47312yes—
493C23C2×#11711yescharacteristic
494C23C2×#12111yescharacteristic
495C23C2×#12311yescharacteristic
496C23C2×#12411yescharacteristic
497C23C2×#12511yescharacteristic
498C23C2×#12511yescharacteristic
499C23C2×#12611yescharacteristic
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—88no—
510C2×C4—84no—
511C2×C4—88no—
512C2×C4—84no—
513C2×C4—88no—
514C2×C4—84no—
515C2×C4—88no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—84no—
521C2×C4—84no—
522C2×C4#38214yes—
523C2×C4#38514yes—
524C2×C4#38514yes—
525C2×C4#38714yes—
526C2×C4#38714yes—
527C2×C4#38714yes—
528C2×C4#38812yes—
529C2×C4#38812yes—
530C2×C4#38814yes—
531C2×C4#38814yes—
532C2×C4#38914yes—
533C2×C4#38914yes—
534C2×C4#39314yes—
535C2×C4#39314yes—
536C2×C4#39412yes—
537C2×C4#39412yes—
538C2×C4#39714yes—
539C2×C4#39714yes—
540C2×C4#39814yes—
541C2×C4#39814yes—
542C2×C4#39812yes—
543C2×C4#39812yes—
544C2×C4#40014yes—
545C2×C4#40014yes—
546C2×C4#40014yes—
547C2×C4#40014yes—
548C2×C4C22×C4⋊C411yescharacteristic
549C2×C4C2×#11711yescharacteristic
550C2×C4C2×C4×D411yescharacteristic
551C2×C4C2×C4×D411yescharacteristic
552C2×C4C2×C4×D411yescharacteristic
553C2×C4C2×C4×Q811yescharacteristic
554C2×C4C2×#12011yescharacteristic
555C2×C4C2×#12111yescharacteristic
556C2×C4C2×#12111yescharacteristic
557C2×C4C2×C22⋊Q811yescharacteristic
558C2×C4C2×C22⋊Q811yescharacteristic
559C2×C4C2×C22⋊Q811yescharacteristic
560C2×C4C2×C22⋊Q811yescharacteristic
561C2×C4C2×C22⋊Q811yescharacteristic
562C2×C4C2×#12311yescharacteristic
563C2×C4C2×#12311yescharacteristic
564C2×C4C2×#12311yescharacteristic
565C2×C4C2×#12311yescharacteristic
566C2×C4C2×#12411yescharacteristic
567C2×C4C2×#12411yescharacteristic
568C2×C4C2×#12411yescharacteristic
569C2×C4C2×#12511yescharacteristic
570C2×C4C2×#12511yescharacteristic
571C2×C4C2×#12511yescharacteristic
572C2×C4C2×#12611yescharacteristic
573C2×C4C2×#12611yescharacteristic
574C2×C4C2×#12611yescharacteristic
575C2×C4C2×C4⋊Q811yescharacteristic
576C8—28no—
577C8—44no—
578C8—44no—
579C8—44no—
580C22—28no—
581C22—28no—
582C22—28no—
583C22—28no—
584C22—21no—
585C22—21no—
586C22—22no—
587C22—21no—
588C22—21no—
589C22—22no—
590C22—21no—
591C22—21no—
592C22—22no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—21no—
598C22—22no—
599C22—21no—
600C22—21no—
601C22—22no—
602C22#144214yes—
603C22#144214yes—
604C22#193014yes—
605C22#193114yes—
606C22#205114yes—
607C22#205214yes—
608C22#208914yes—
609C22#209014yes—
610C22C2×#38211yescharacteristic
611C22C2×#38711yescharacteristic
612C22C2×#38811yescharacteristic
613C22C2×#39411yescharacteristic
614C22C2×#39811yescharacteristic
615C22C2×#40011yescharacteristic
616C22C2×#40011yescharacteristic
617C22C2×#47111yescharacteristic
618C22C2×#47111yescharacteristic
619C22C2×#47211yescharacteristic
620C22C2×#47311yescharacteristic
621C4—84no—
622C4—82no—
623C4—84no—
624C4—82no—
625C4#144214yes—
626C4#144214yes—
627C4C2×#38511yescharacteristic
628C4C2×#38711yescharacteristic
629C4C2×#38811yescharacteristic
630C4C2×#38911yescharacteristic
631C4C2×#39311yescharacteristic
632C4C2×#39711yescharacteristic
633C4C2×#39811yescharacteristic
634C4C2×#40011yescharacteristic
635C2—21no—
636C2—21no—
637C2—24no—
638C2—21no—
639C2—21no—
640C2#1129018yesdirect product factor
641C2C2×#144211yescharacteristic
642C2C2×#193011yescharacteristic
643C2C2×#193111yescharacteristic
644C2C2×#205111yescharacteristic
645C2C2×#205211yescharacteristic
646C2C2×#208911yescharacteristic
647C2C2×#209011yescharacteristic
subgroupG/H
center, socleC24#121
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11290C2direct (N × H)
23. C2×#343C4semidirect
117. #343C2×C4semidirect
640. C2#11290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4282
C22×#3432
C22×#3412
C2×#17362
C22×#3402
C2×#17292
#112902