Finite Group Databasebeta

← C2×#11339 #358483

Subgroups — C2×#11339 #358483

Order 512.

2350 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic
3C22×#382C211yesmaximal, characteristic
4C22×#343C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C22×#339C211yesmaximal, characteristic
8#11339C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#428—24no—
17C2×#428—22no—
18C2×#428—24no—
19C2×#428C2214yes—
20C22×#107—21no—
21C22×#106—21no—
22#2317—22no—
23#2317—22no—
24#2317—22no—
25#2317C2214yes—
26C2×#389—22no—
27C2×#385—22no—
28C2×#384—21no—
29C2×#382—24no—
30C2×#382—21no—
31C2×#382—22no—
32C2×#382—24no—
33C2×#382C2214yes—
34C22×#95—22no—
35C2×#343—24no—
36C2×#343C2214yes—
37#1736—22no—
38#1736C2214yes—
39C2×#340—22no—
40C2×#339—24no—
41C2×#339C418yescomplemented
42C2×#339C2214yes—
43C2×#339C2214yes—
44C24×C4—21no—
45C24×C4—21no—
46C24×C4D412yes—
47C24×C4C2311yescharacteristic
48C22×M16—22no—
49C22×M16—21no—
50C22×M16—22no—
51C22×M16—22no—
52C22×M16—21no—
53C22×M16—22no—
54C22×M16—22no—
55C22×M16—22no—
56C22×M16—22no—
57C22×M16—22no—
58C22×M16C2×C414yes—
59C22×M16D414yes—
60C22×M16Q814yes—
61C22×M16Q814yes—
62C22×M16C2312yes—
63C22×M16C2312yes—
64C23×C8—21no—
65C23×C8—21no—
66C2×#117—21no—
67C2×#117—21no—
68C2×#117—22no—
69C2×#117—22no—
70C2×#117—21no—
71C2×#117—21no—
72C2×#117—22no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—22no—
76C2×#117C2×C414yes—
77C2×#117D412yes—
78C2×#117D412yes—
79C2×#117Q814yes—
80C2×#117C2312yes—
81C2×#117C2312yes—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4D412yes—
100C22×C4⋊C4D411yescharacteristic
101C22×C4⋊C4D411yescharacteristic
102C22×C4⋊C4D414yes—
103C22×C4⋊C4D412yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C42—21no—
109C22×C42—22no—
110C22×C42—21no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—21no—
114C22×C42C2×C414yes—
115C22×C42D414yes—
116C22×C42Q814yes—
117C22×C42C2312yes—
118#428—216no—
119#428—28no—
120#428—28no—
121C2×#107—28no—
122C2×#107—24no—
123C2×#106—28no—
124C2×#106—24no—
125#389—28no—
126#389—28no—
127#385—28no—
128#385—28no—
129#384—24no—
130#384—24no—
131#382—24no—
132#382—216no—
133#382—24no—
134#382—28no—
135#382—28no—
136C2×#95—216no—
137C2×#95—24no—
138C2×#95—28no—
139#343—28no—
140#340—28no—
141#339—28no—
142#339C2×C4116yescomplemented
143C25C2×D411yescharacteristic
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—22no—
147C23×C4—24no—
148C23×C4—22no—
149C23×C4—24no—
150C23×C4—24no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—24no—
157C23×C4—44no—
158C23×C4—44no—
159C23×C4—48no—
160C23×C4—48no—
161C23×C4—41no—
162C23×C4—41no—
163C23×C4—42no—
164C23×C4C22×C412yes—
165C23×C4C2×D414yes—
166C23×C4C2×D412yes—
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D412yes—
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D412yes—
173C23×C4C2×D411yescharacteristic
174C23×C4C2×Q812yes—
175C23×C4C2×Q812yes—
176C23×C4C2×Q812yes—
177C23×C4C2×Q812yes—
178C23×C4#4112yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4#4112yes—
182C23×C4C2411yescharacteristic
183C2×M16—24no—
184C2×M16—28no—
185C2×M16—24no—
186C2×M16—24no—
187C2×M16—28no—
188C2×M16—28no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—24no—
193C2×M16—22no—
194C2×M16—28no—
195C2×M16—28no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—42no—
201C2×M16—44no—
202C2×M16—44no—
203C2×M16—42no—
204C2×M16C4⋊C4116yescomplemented
205C2×M16C22×C414yes—
206C2×M16C2×D414yes—
207C2×M16C2×Q814yes—
208C2×M16C2×Q814yes—
209C22×C8—24no—
210C22×C8—24no—
211C22×C8—24no—
212C22×C8—22no—
213C22×C8—24no—
214C22×C8—22no—
215C22×C8—42no—
216C22×C8—42no—
217#117—24no—
218#117—24no—
219#117—24no—
220#117—24no—
221#117—24no—
222#117—22no—
223#117—22no—
224#117—24no—
225#117—24no—
226#117—22no—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—42no—
231#117—42no—
232#117—42no—
233#117—42no—
234#117C4⋊C418yes—
235#117C22×C414yes—
236#117C2×Q814yes—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—216no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
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⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—88no—
282C2×C4⋊C4C4⋊C418yes—
283C2×C4⋊C4C2×D414yes—
284C2×C4⋊C4C2×D412yes—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4C2×D414yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C42—24no—
296C2×C42—28no—
297C2×C42—24no—
298C2×C42—22no—
299C2×C42—24no—
300C2×C42—24no—
301C2×C42—28no—
302C2×C42—24no—
303C2×C42—28no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—42no—
311C2×C42—42no—
312C2×C42C4⋊C4116yescomplemented
313C2×C42C22×C414yes—
314C2×C42C2×D414yes—
315C2×C42C2×Q814yes—
316#107—216no—
317#106—216no—
318#95—232no—
319#95—216no—
320C24—24no—
321C24—24no—
322C24C4×D412yes—
323C24#12011yescharacteristic
324C24#12012yes—
325C24#12011yescharacteristic
326C24#12112yes—
327C24C22⋊Q812yes—
328C24C22⋊Q812yes—
329C24C4⋊Q812yes—
330C24C22×D411yescharacteristic
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—216no—
336C22×C4—28no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—416no—
344C22×C4—416no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—48no—
348C22×C4—48no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—48no—
352C22×C4—48no—
353C22×C4—416no—
354C22×C4—416no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—48no—
366C22×C4—84no—
367C22×C4—84no—
368C22×C4—88no—
369C22×C4—84no—
370C22×C4—88no—
371C22×C4C2×C4⋊C414yes—
372C22×C4C2×C4⋊C414yes—
373C22×C4C2×C4⋊C412yes—
374C22×C4C2×C4⋊C412yes—
375C22×C4C4×D412yes—
376C22×C4C4×D414yes—
377C22×C4C4×D412yes—
378C22×C4C4×D412yes—
379C22×C4C4×Q814yes—
380C22×C4#12012yes—
381C22×C4#12012yes—
382C22×C4#12011yescharacteristic
383C22×C4#12011yescharacteristic
384C22×C4#12012yes—
385C22×C4#12112yes—
386C22×C4#12112yes—
387C22×C4#12112yes—
388C22×C4#12112yes—
389C22×C4#12112yes—
390C22×C4C22⋊Q812yes—
391C22×C4C22⋊Q812yes—
392C22×C4C22⋊Q814yes—
393C22×C4C22⋊Q814yes—
394C22×C4C22⋊Q812yes—
395C22×C4C22⋊Q812yes—
396C22×C4C22⋊Q812yes—
397C22×C4C22⋊Q812yes—
398C22×C4C22⋊Q814yes—
399C22×C4C22⋊Q814yes—
400C22×C4C22⋊Q812yes—
401C22×C4C22⋊Q812yes—
402C22×C4#12314yes—
403C22×C4#12314yes—
404C22×C4#12312yes—
405C22×C4#12312yes—
406C22×C4#12514yes—
407C22×C4#12514yes—
408C22×C4#12514yes—
409C22×C4#12712yes—
410C22×C4#12712yes—
411C22×C4C4⋊Q814yes—
412C22×C4C4⋊Q812yes—
413C22×C4C4⋊Q814yes—
414C22×C4C4⋊Q812yes—
415C22×C4C4⋊Q812yes—
416C22×C4C4⋊Q814yes—
417C22×C4C4⋊Q812yes—
418C22×C4C4⋊Q812yes—
419C22×C4C23×C411yescharacteristic
420C22×C4C22×D411yescharacteristic
421C22×C4C22×D411yescharacteristic
422C22×C4C22×D411yescharacteristic
423C22×C4C22×D411yescharacteristic
424C22×C4C22×D411yescharacteristic
425C22×C4C22×Q811yescharacteristic
426C22×C4C22×Q811yescharacteristic
427C22×C4C22×Q811yescharacteristic
428C22×C4C22×Q811yescharacteristic
429C22×C4C2×#4111yescharacteristic
430C22×C4C2×#4111yescharacteristic
431C22×C4C2×#4111yescharacteristic
432C22×C4C2×#4111yescharacteristic
433M16—24no—
434M16—24no—
435M16—24no—
436M16—216no—
437M16—24no—
438M16—24no—
439M16—42no—
440M16—42no—
441M16—48no—
442M16C2×C4⋊C418yescomplemented
443C2×C8—24no—
444C2×C8—24no—
445C2×C8—24no—
446C2×C8—216no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—48no—
451C4⋊C4—24no—
452C4⋊C4—28no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—44no—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C4⋊C4—44no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—816no—
472C4⋊C4C2×C4⋊C418yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—28no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—44no—
479C42—24no—
480C42—24no—
481C42—24no—
482C42—24no—
483C42—24no—
484C42—216no—
485C42—28no—
486C42—42no—
487C42—42no—
488C42—44no—
489C42C2×C4⋊C418yescomplemented
490C23—28no—
491C23—28no—
492C23—28no—
493C23—28no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23#38512yes—
503C23#38514yes—
504C23#38512yes—
505C23#38914yes—
506C23#39212yes—
507C23#39212yes—
508C23#39512yes—
509C23#39514yes—
510C23#39512yes—
511C23#39814yes—
512C23#45414yes—
513C23#45514yes—
514C23C2×C4×D411yescharacteristic
515C23C2×#12011yescharacteristic
516C23C2×#12011yescharacteristic
517C23C2×#12111yescharacteristic
518C23C2×C22⋊Q811yescharacteristic
519C23C2×C22⋊Q811yescharacteristic
520C23C2×C4⋊Q811yescharacteristic
521C2×C4—28no—
522C2×C4—28no—
523C2×C4—48no—
524C2×C4—432no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4—416no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—48no—
532C2×C4—48no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—88no—
541C2×C4—84no—
542C2×C4—88no—
543C2×C4—84no—
544C2×C4—84no—
545C2×C4—88no—
546C2×C4—84no—
547C2×C4—88no—
548C2×C4—84no—
549C2×C4#38414yes—
550C2×C4#38414yes—
551C2×C4#38514yes—
552C2×C4#38512yes—
553C2×C4#38512yes—
554C2×C4#38514yes—
555C2×C4#38514yes—
556C2×C4#38914yes—
557C2×C4#38914yes—
558C2×C4#38914yes—
559C2×C4#38914yes—
560C2×C4#38914yes—
561C2×C4#39212yes—
562C2×C4#39212yes—
563C2×C4#39514yes—
564C2×C4#39514yes—
565C2×C4#39514yes—
566C2×C4#39512yes—
567C2×C4#39512yes—
568C2×C4#39814yes—
569C2×C4#39814yes—
570C2×C4#39814yes—
571C2×C4#39814yes—
572C2×C4#39814yes—
573C2×C4#39914yes—
574C2×C4#39914yes—
575C2×C4C22×C4⋊C411yescharacteristic
576C2×C4C22×C4⋊C411yescharacteristic
577C2×C4C22×C4⋊C411yescharacteristic
578C2×C4C2×C4×D411yescharacteristic
579C2×C4C2×C4×D411yescharacteristic
580C2×C4C2×C4×Q811yescharacteristic
581C2×C4C2×#12011yescharacteristic
582C2×C4C2×#12111yescharacteristic
583C2×C4C2×#12111yescharacteristic
584C2×C4C2×C22⋊Q811yescharacteristic
585C2×C4C2×C22⋊Q811yescharacteristic
586C2×C4C2×C22⋊Q811yescharacteristic
587C2×C4C2×C22⋊Q811yescharacteristic
588C2×C4C2×C22⋊Q811yescharacteristic
589C2×C4C2×C22⋊Q811yescharacteristic
590C2×C4C2×C22⋊Q811yescharacteristic
591C2×C4C2×#12311yescharacteristic
592C2×C4C2×#12311yescharacteristic
593C2×C4C2×#12311yescharacteristic
594C2×C4C2×#12511yescharacteristic
595C2×C4C2×#12511yescharacteristic
596C2×C4C2×#12511yescharacteristic
597C2×C4C2×#12711yescharacteristic
598C2×C4C2×C4⋊Q811yescharacteristic
599C2×C4C2×C4⋊Q811yescharacteristic
600C2×C4C2×C4⋊Q811yescharacteristic
601C2×C4C2×C4⋊Q811yescharacteristic
602C2×C4C2×C4⋊Q811yescharacteristic
603C8—28no—
604C8—44no—
605C22—22no—
606C22—22no—
607C22—24no—
608C22—28no—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—24no—
621C22#144414yes—
622C22#144414yes—
623C22#186018yes—
624C22#200314yes—
625C22#200414yes—
626C22#206118yes—
627C22C2×#38511yescharacteristic
628C22C2×#38511yescharacteristic
629C22C2×#38911yescharacteristic
630C22C2×#39211yescharacteristic
631C22C2×#39511yescharacteristic
632C22C2×#39511yescharacteristic
633C22C2×#39811yescharacteristic
634C22C2×#45512yes—
635C22C2×#45412yes—
636C4—48no—
637C4—48no—
638C4—84no—
639C4—82no—
640C4—82no—
641C4—84no—
642C4#144414yes—
643C4#144414yes—
644C4C2×#38411yescharacteristic
645C4C2×#38511yescharacteristic
646C4C2×#38911yescharacteristic
647C4C2×#38911yescharacteristic
648C4C2×#39511yescharacteristic
649C4C2×#39811yescharacteristic
650C4C2×#39811yescharacteristic
651C4C2×#39911yescharacteristic
652C2—21no—
653C2—21no—
654C2—21no—
655C2—24no—
656C2—21no—
657C2#1133918yesdirect product factor
658C2C2×#144411yescharacteristic
659C2C2×#186012yes—
660C2C2×#200411yescharacteristic
661C2C2×#200311yescharacteristic
662C2C2×#206112yes—
subgroupG/H
center, socleC24#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
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. #11339C2direct (N × H)
41. C2×#339C4semidirect
142. #339C2×C4semidirect
204. C2×M16C4⋊C4semidirect
312. C2×C42C4⋊C4semidirect
442. M16C2×C4⋊C4semidirect
489. C42C2×C4⋊C4semidirect
657. C2#11339direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#23172
C22×#3822
C22×#3432
C2×#17362
C22×#3392
#113392