Finite Group Databasebeta

← C2×#11292 #358312

Subgroups — C2×#11292 #358312

Order 512.

2458 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#340C211yesmaximal, characteristic
3C22×#340C211yesmaximal, characteristic
4C22×#340C211yesmaximal, characteristic
5C22×#340C211yesmaximal, characteristic
6C22×#336C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8#11292C218yesmaximal, direct product factor
9C24×C8C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C23×C4⋊C4—21no—
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#389—22no—
18C2×#389—24no—
19C2×#389—24no—
20C2×#389C2214yes—
21C22×#95—21no—
22C22×#95—21no—
23C22×#95—21no—
24C2×#340—24no—
25C2×#340—24no—
26C2×#340—24no—
27C2×#340C418yescomplemented
28C2×#340C2214yes—
29C2×#340C2214yes—
30C2×#340C2214yes—
31C2×#340C2214yes—
32C2×#336—24no—
33C2×#336C2214yes—
34C4⋊#95—22no—
35C4⋊#95C2214yes—
36C24×C4—21no—
37C24×C4—21no—
38C24×C4—21no—
39C24×C4—21no—
40C24×C4D411yescharacteristic
41C24×C4D411yescharacteristic
42C24×C4C2311yescharacteristic
43C23×C8—22no—
44C23×C8—22no—
45C23×C8—22no—
46C23×C8—22no—
47C23×C8—22no—
48C23×C8—22no—
49C23×C8—22no—
50C23×C8—22no—
51C23×C8—22no—
52C23×C8—22no—
53C23×C8—22no—
54C23×C8—22no—
55C23×C8C2×C414yes—
56C23×C8D414yes—
57C23×C8C2312yes—
58C23×C8C2312yes—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—28no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—44no—
84C22×C4⋊C4—44no—
85C22×C4⋊C4C2×C414yes—
86C22×C4⋊C4C2×C414yes—
87C22×C4⋊C4D414yes—
88C22×C4⋊C4D414yes—
89C22×C4⋊C4Q814yes—
90C22×C4⋊C4Q814yes—
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2312yes—
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42D412yes—
102C22×C42C2312yes—
103#389—216no—
104#389—28no—
105#389—28no—
106C2×#95—28no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—44no—
111C2×#95—44no—
112#340—28no—
113#340—28no—
114#340—28no—
115#340C2×C4116yescomplemented
116#336—28no—
117C25C2×D411yescharacteristic
118C23×C4—24no—
119C23×C4—22no—
120C23×C4—24no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—24no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—24no—
135C23×C4—24no—
136C23×C4—24no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—42no—
157C23×C4—42no—
158C23×C4—42no—
159C23×C4—42no—
160C23×C4—42no—
161C23×C4—42no—
162C23×C4D814yes—
163C23×C4SD1614yes—
164C23×C4C22×C412yes—
165C23×C4C2×D412yes—
166C23×C4C2×D412yes—
167C23×C4C2×D412yes—
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D412yes—
170C23×C4C2×D412yes—
171C23×C4C2×Q812yes—
172C23×C4C2×Q812yes—
173C23×C4#4112yes—
174C23×C4#4112yes—
175C23×C4#4112yes—
176C23×C4#4112yes—
177C23×C4#4112yes—
178C23×C4#4112yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4C2411yescharacteristic
182C22×C8—28no—
183C22×C8—28no—
184C22×C8—28no—
185C22×C8—28no—
186C22×C8—28no—
187C22×C8—28no—
188C22×C8—22no—
189C22×C8—22no—
190C22×C8—22no—
191C22×C8—22no—
192C22×C8—22no—
193C22×C8—22no—
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—44no—
201C22×C8—44no—
202C22×C8—44no—
203C22×C8—44no—
204C22×C8—44no—
205C22×C8—44no—
206C22×C8—44no—
207C22×C8—44no—
208C22×C8C22×C414yes—
209C22×C8C2×D414yes—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—28no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—216no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—48no—
245C2×C4⋊C4—432no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—44no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4C4⋊C4116yes—
260C2×C4⋊C4C22×C414yes—
261C2×C4⋊C4C22×C414yes—
262C2×C4⋊C4C2×D414yes—
263C2×C4⋊C4C2×D414yes—
264C2×C4⋊C4C2×Q814yes—
265C2×C4⋊C4C2×Q814yes—
266C2×C42—24no—
267C2×C42—24no—
268C2×C42—24no—
269C2×C42—22no—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—44no—
276C2×C42—44no—
277C2×C42—44no—
278C2×C42—44no—
279#95—216no—
280#95—48no—
281#95—48no—
282C24C4×D412yes—
283C24#12012yes—
284C24#12112yes—
285C24C22⋊Q812yes—
286C24C22⋊Q812yes—
287C24#12312yes—
288C24#12412yes—
289C24C2×D812yes—
290C24C2×SD1612yes—
291C24#13512yes—
292C24#13512yes—
293C24AGL(1,ℤ/8)12yes—
294C24#13712yes—
295C24#13712yes—
296C24#13712yes—
297C24C22×D411yescharacteristic
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—216no—
314C22×C4—28no—
315C22×C4—28no—
316C22×C4—28no—
317C22×C4—28no—
318C22×C4—28no—
319C22×C4—28no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—44no—
328C22×C4—44no—
329C22×C4—48no—
330C22×C4—48no—
331C22×C4—48no—
332C22×C4—44no—
333C22×C4—44no—
334C22×C4—48no—
335C22×C4—44no—
336C22×C4—44no—
337C22×C4—48no—
338C22×C4—48no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—48no—
360C22×C4—48no—
361C22×C4—48no—
362C22×C4—48no—
363C22×C4—48no—
364C22×C4—48no—
365C22×C4—48no—
366C22×C4—48no—
367C22×C4—48no—
368C22×C4—84no—
369C22×C4—84no—
370C22×C4—84no—
371C22×C4—84no—
372C22×C4—84no—
373C22×C4—84no—
374C22×C4—84no—
375C22×C4—84no—
376C22×C4—84no—
377C22×C4—84no—
378C22×C4—84no—
379C22×C4—84no—
380C22×C4C2×C4⋊C414yes—
381C22×C4#11714yes—
382C22×C4#11714yes—
383C22×C4C4×D414yes—
384C22×C4C4×D414yes—
385C22×C4C4×D412yes—
386C22×C4C4×Q814yes—
387C22×C4#12012yes—
388C22×C4#12114yes—
389C22×C4#12114yes—
390C22×C4#12112yes—
391C22×C4C22⋊Q814yes—
392C22×C4C22⋊Q814yes—
393C22×C4C22⋊Q814yes—
394C22×C4C22⋊Q812yes—
395C22×C4C22⋊Q812yes—
396C22×C4#12314yes—
397C22×C4#12314yes—
398C22×C4#12314yes—
399C22×C4#12314yes—
400C22×C4#12312yes—
401C22×C4#12414yes—
402C22×C4#12414yes—
403C22×C4#12414yes—
404C22×C4#12412yes—
405C22×C4#12514yes—
406C22×C4#12514yes—
407C22×C4#12514yes—
408C22×C4#12514yes—
409C22×C4#12514yes—
410C22×C4#12614yes—
411C22×C4#12614yes—
412C22×C4#12614yes—
413C22×C4#12614yes—
414C22×C4C4⋊Q814yes—
415C22×C4C2×D814yes—
416C22×C4C2×SD1614yes—
417C22×C4C23×C411yescharacteristic
418C22×C4C22×D411yescharacteristic
419C22×C4C22×D411yescharacteristic
420C22×C4C22×D411yescharacteristic
421C22×C4C22×Q811yescharacteristic
422C22×C4C22×Q811yescharacteristic
423C22×C4C2×#4111yescharacteristic
424C22×C4C2×#4111yescharacteristic
425C22×C4C2×#4111yescharacteristic
426C22×C4C2×#4111yescharacteristic
427C22×C4C2×#4111yescharacteristic
428C22×C4C2×#4111yescharacteristic
429C22×C4C2×#4111yescharacteristic
430C22×C4C2×#4111yescharacteristic
431C2×C8—24no—
432C2×C8—24no—
433C2×C8—24no—
434C2×C8—24no—
435C2×C8—24no—
436C2×C8—24no—
437C2×C8—42no—
438C2×C8—42no—
439C2×C8—42no—
440C2×C8—42no—
441C2×C8—42no—
442C2×C8—42no—
443C2×C8—42no—
444C2×C8—42no—
445C2×C8—416no—
446C2×C8—416no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—216no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—432no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—48no—
465C4⋊C4—48no—
466C4⋊C4—48no—
467C4⋊C4C2×C4⋊C418yes—
468C42—42no—
469C42—42no—
470C42—42no—
471C42—42no—
472C42—48no—
473C23#38514yes—
474C23#38714yes—
475C23#38814yes—
476C23#39314yes—
477C23#39414yes—
478C23#39814yes—
479C23#40014yes—
480C23C4×D814yes—
481C23C4×SD1614yes—
482C23#44014yes—
483C23#44114yes—
484C23#44714yes—
485C23#44814yes—
486C23#45214yes—
487C23#45214yes—
488C23#46514yes—
489C23#46614yes—
490C23#46814yes—
491C23#47014yes—
492C23#47414yes—
493C23#47414yes—
494C23#47514yes—
495C23#47614yes—
496C23#47814yes—
497C23#47914yes—
498C23#47914yes—
499C23#47914yes—
500C23#48014yes—
501C23#48214yes—
502C23#48314yes—
503C23#48514yes—
504C23#48614yes—
505C23#48814yes—
506C23#48914yes—
507C23#49114yes—
508C23C2×C4×D411yescharacteristic
509C23C2×#12011yescharacteristic
510C23C2×#12111yescharacteristic
511C23C2×C22⋊Q811yescharacteristic
512C23C2×C22⋊Q811yescharacteristic
513C23C2×#12311yescharacteristic
514C23C2×#12411yescharacteristic
515C23C22×D811yescharacteristic
516C23C22×SD1611yescharacteristic
517C23C2×#13511yescharacteristic
518C23C2×#13511yescharacteristic
519C23C2×AGL(1,ℤ/8)11yescharacteristic
520C23C2×#13711yescharacteristic
521C23C2×#13711yescharacteristic
522C23C2×#13711yescharacteristic
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—432no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—416no—
545C2×C4—416no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—816no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—816no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—816no—
571C2×C4#38218yes—
572C2×C4#38514yes—
573C2×C4#38714yes—
574C2×C4#38718yes—
575C2×C4#38814yes—
576C2×C4#38818yes—
577C2×C4#38918yes—
578C2×C4#39314yes—
579C2×C4#39414yes—
580C2×C4#39718yes—
581C2×C4#39818yes—
582C2×C4#39814yes—
583C2×C4#40018yes—
584C2×C4#40018yes—
585C2×C4#40014yes—
586C2×C4C22×C4⋊C411yescharacteristic
587C2×C4C2×#11711yescharacteristic
588C2×C4C2×#11711yescharacteristic
589C2×C4C2×C4×D411yescharacteristic
590C2×C4C2×C4×D411yescharacteristic
591C2×C4C2×C4×Q811yescharacteristic
592C2×C4C2×#12111yescharacteristic
593C2×C4C2×#12111yescharacteristic
594C2×C4C2×C22⋊Q811yescharacteristic
595C2×C4C2×C22⋊Q811yescharacteristic
596C2×C4C2×C22⋊Q811yescharacteristic
597C2×C4C2×#12311yescharacteristic
598C2×C4C2×#12311yescharacteristic
599C2×C4C2×#12311yescharacteristic
600C2×C4C2×#12311yescharacteristic
601C2×C4C2×#12411yescharacteristic
602C2×C4C2×#12411yescharacteristic
603C2×C4C2×#12411yescharacteristic
604C2×C4C2×#12511yescharacteristic
605C2×C4C2×#12511yescharacteristic
606C2×C4C2×#12511yescharacteristic
607C2×C4C2×#12511yescharacteristic
608C2×C4C2×#12511yescharacteristic
609C2×C4C2×#12611yescharacteristic
610C2×C4C2×#12611yescharacteristic
611C2×C4C2×#12611yescharacteristic
612C2×C4C2×#12611yescharacteristic
613C2×C4C2×C4⋊Q811yescharacteristic
614C8—44no—
615C8—44no—
616C22#144218yes—
617C22#186218yes—
618C22#186518yes—
619C22#191818yes—
620C22#192018yes—
621C22#193418yes—
622C22#193518yes—
623C22#202318yes—
624C22#202618yes—
625C22#203318yes—
626C22#203518yes—
627C22#208618yes—
628C22#208818yes—
629C22#209918yes—
630C22#210118yes—
631C22C2×#38511yescharacteristic
632C22C2×#38711yescharacteristic
633C22C2×#38811yescharacteristic
634C22C2×#39311yescharacteristic
635C22C2×#39411yescharacteristic
636C22C2×#39811yescharacteristic
637C22C2×#40011yescharacteristic
638C22C2×C4×D811yescharacteristic
639C22C2×C4×SD1611yescharacteristic
640C22C2×#44011yescharacteristic
641C22C2×#44111yescharacteristic
642C22C2×#44711yescharacteristic
643C22C2×#44811yescharacteristic
644C22C2×#45211yescharacteristic
645C22C2×#45211yescharacteristic
646C22C2×#46511yescharacteristic
647C22C2×#46611yescharacteristic
648C22C2×#46811yescharacteristic
649C22C2×#47011yescharacteristic
650C22C2×#47411yescharacteristic
651C22C2×#47411yescharacteristic
652C22C2×#47611yescharacteristic
653C22C2×#47811yescharacteristic
654C22C2×#47511yescharacteristic
655C22C2×#47911yescharacteristic
656C22C2×#47911yescharacteristic
657C22C2×#47911yescharacteristic
658C22C2×#48011yescharacteristic
659C22C2×#48311yescharacteristic
660C22C2×#48211yescharacteristic
661C22C2×#48511yescharacteristic
662C22C2×#48611yescharacteristic
663C22C2×#48811yescharacteristic
664C22C2×#48911yescharacteristic
665C22C2×#49111yescharacteristic
666C4—48no—
667C4—44no—
668C4—44no—
669C4—84no—
670C4—84no—
671C4—84no—
672C4#144218yes—
673C4C2×#38211yescharacteristic
674C4C2×#38711yescharacteristic
675C4C2×#38811yescharacteristic
676C4C2×#38911yescharacteristic
677C4C2×#39711yescharacteristic
678C4C2×#39811yescharacteristic
679C4C2×#40011yescharacteristic
680C4C2×#40011yescharacteristic
681C2#11292116yesdirect product factor
682C2C2×#144211yescharacteristic
683C2C2×#186211yescharacteristic
684C2C2×#186511yescharacteristic
685C2C2×#191811yescharacteristic
686C2C2×#192011yescharacteristic
687C2C2×#193411yescharacteristic
688C2C2×#193511yescharacteristic
689C2C2×#202311yescharacteristic
690C2C2×#202611yescharacteristic
691C2C2×#203311yescharacteristic
692C2C2×#203511yescharacteristic
693C2C2×#208611yescharacteristic
694C2C2×#208811yescharacteristic
695C2C2×#209911yescharacteristic
696C2C2×#210111yescharacteristic
subgroupG/H
center, socle, prime radicalC25C2×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11292C2direct (N × H)
27. C2×#340C4semidirect
115. #340C2×C4semidirect
681. C2#11292direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3402
C22×#3362
C2×C4⋊#952
#112922