Finite Group Databasebeta

← C2×#11276 #358286

Subgroups — C2×#11276 #358286

Order 512.

2090 conjugacy classes of subgroups.

The subgroup lattice has 725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2317C211yesmaximal, characteristic
2C22×#343C211yesmaximal, characteristic
3C2×#1736C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8#11276C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16#2317—22no—
17#2317—22no—
18#2317—22no—
19#2317C2214yes—
20C2×#389—21no—
21C2×#389—21no—
22C2×#385—22no—
23C2×#384—21no—
24C2×#382—21no—
25C22×#95—22no—
26C2×#343—24no—
27C2×#343C2214yes—
28#1736—22no—
29#1736—22no—
30#1736C2214yes—
31#1736C2214yes—
32C2×#340—21no—
33C2×#340—21no—
34C2×#340—21no—
35C2×#340—21no—
36C2×#339—24no—
37C2×#339C418yescomplemented
38C2×#339C2214yes—
39C2×#339C2214yes—
40C4⋊#95—22no—
41C4⋊#95C2214yes—
42C24×C4—21no—
43C24×C4—21no—
44C24×C4D412yes—
45C24×C4C2311yescharacteristic
46C22×M16—21no—
47C22×M16—21no—
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×M16—22no—
58C22×M16C2×C414yes—
59C22×M16D414yes—
60C22×M16C2312yes—
61C22×M16C2312yes—
62C23×C8—21no—
63C23×C8—21no—
64C2×#117—21no—
65C2×#117—21no—
66C2×#117—22no—
67C2×#117—22no—
68C2×#117—21no—
69C2×#117—21no—
70C2×#117—22no—
71C2×#117—22no—
72C2×#117—22no—
73C2×#117—22no—
74C2×#117C2×C414yes—
75C2×#117D412yes—
76C2×#117D412yes—
77C2×#117Q814yes—
78C2×#117C2312yes—
79C2×#117C2312yes—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4D412yes—
99C22×C4⋊C4D411yescharacteristic
100C22×C4⋊C4D411yescharacteristic
101C22×C4⋊C4D411yescharacteristic
102C22×C4⋊C4D411yescharacteristic
103C22×C4⋊C4Q814yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C42—21no—
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42—22no—
116C22×C42C2×C414yes—
117C22×C42C2312yes—
118#389—24no—
119#389—24no—
120#389—24no—
121#389—24no—
122#385—28no—
123#385—28no—
124#384—24no—
125#384—24no—
126#382—24no—
127#382—24no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—28no—
131C2×#95—48no—
132#343—28no—
133#340—24no—
134#340—24no—
135#340—24no—
136#340—24no—
137#339—28no—
138#339C2×C4116yescomplemented
139C25C2×D411yescharacteristic
140C23×C4—24no—
141C23×C4—24no—
142C23×C4—24no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—24no—
150C23×C4—24no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—24no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—42no—
157C23×C4—42no—
158C23×C4—44no—
159C23×C4—44no—
160C23×C4—44no—
161C23×C4—44no—
162C23×C4—41no—
163C23×C4—41no—
164C23×C4—42no—
165C23×C4C22×C412yes—
166C23×C4C2×D414yes—
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D412yes—
173C23×C4C2×Q812yes—
174C23×C4C2×Q812yes—
175C23×C4#4112yes—
176C23×C4#4112yes—
177C23×C4#4112yes—
178C23×C4#4112yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4#4112yes—
182C23×C4#4112yes—
183C23×C4C2411yescharacteristic
184C2×M16—24no—
185C2×M16—24no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—28no—
189C2×M16—28no—
190C2×M16—28no—
191C2×M16—28no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—42no—
201C2×M16—42no—
202C2×M16—44no—
203C2×M16—42no—
204C2×M16—42no—
205C2×M16—44no—
206C2×M16—44no—
207C2×M16—44no—
208C2×M16C22×C414yes—
209C2×M16C2×D414yes—
210C22×C8—24no—
211C22×C8—24no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—42no—
215C22×C8—42no—
216C22×C8—42no—
217C22×C8—42no—
218#117—24no—
219#117—24no—
220#117—24no—
221#117—24no—
222#117—24no—
223#117—22no—
224#117—22no—
225#117—24no—
226#117—24no—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—42no—
232#117—42no—
233#117—42no—
234#117—42no—
235#117C4⋊C418yes—
236#117C22×C414yes—
237#117C2×Q814yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
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—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4—41no—
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—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—84no—
286C2×C4⋊C4—84no—
287C2×C4⋊C4C4⋊C414yes—
288C2×C4⋊C4C4⋊C414yes—
289C2×C4⋊C4C2×D412yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4C2×Q814yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C42—24no—
303C2×C42—22no—
304C2×C42—24no—
305C2×C42—22no—
306C2×C42—28no—
307C2×C42—28no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—24no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—44no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—44no—
322C2×C42C22×C414yes—
323#95—28no—
324#95—28no—
325#95—416no—
326C24—22no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24C4×D412yes—
331C24#12011yescharacteristic
332C24#12011yescharacteristic
333C24#12112yes—
334C24C22⋊Q812yes—
335C24C22⋊Q812yes—
336C24#12312yes—
337C24#12412yes—
338C24C22×D411yescharacteristic
339C22×C4—24no—
340C22×C4—216no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—48no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—48no—
357C22×C4—48no—
358C22×C4—48no—
359C22×C4—48no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—48no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—416no—
372C22×C4—416no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—44no—
376C22×C4—44no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—42no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—44no—
386C22×C4—42no—
387C22×C4—82no—
388C22×C4—82no—
389C22×C4—82no—
390C22×C4—82no—
391C22×C4—88no—
392C22×C4—82no—
393C22×C4—82no—
394C22×C4—88no—
395C22×C4C2×C4⋊C412yes—
396C22×C4C2×C4⋊C412yes—
397C22×C4#11714yes—
398C22×C4#11714yes—
399C22×C4C4×D412yes—
400C22×C4C4×D412yes—
401C22×C4C4×D414yes—
402C22×C4C4×D412yes—
403C22×C4C4×Q814yes—
404C22×C4#12011yescharacteristic
405C22×C4#12011yescharacteristic
406C22×C4#12112yes—
407C22×C4#12112yes—
408C22×C4#12112yes—
409C22×C4#12112yes—
410C22×C4#12112yes—
411C22×C4C22⋊Q812yes—
412C22×C4C22⋊Q812yes—
413C22×C4C22⋊Q812yes—
414C22×C4C22⋊Q812yes—
415C22×C4C22⋊Q812yes—
416C22×C4C22⋊Q812yes—
417C22×C4C22⋊Q812yes—
418C22×C4C22⋊Q812yes—
419C22×C4#12312yes—
420C22×C4#12312yes—
421C22×C4#12312yes—
422C22×C4#12312yes—
423C22×C4#12314yes—
424C22×C4#12314yes—
425C22×C4#12312yes—
426C22×C4#12412yes—
427C22×C4#12412yes—
428C22×C4#12412yes—
429C22×C4#12412yes—
430C22×C4#12412yes—
431C22×C4#12412yes—
432C22×C4#12412yes—
433C22×C4#12514yes—
434C22×C4#12514yes—
435C22×C4#12514yes—
436C22×C4#12514yes—
437C22×C4#12514yes—
438C22×C4#12614yes—
439C22×C4#12614yes—
440C22×C4#12614yes—
441C22×C4#12614yes—
442C22×C4C4⋊Q814yes—
443C22×C4C23×C411yescharacteristic
444C22×C4C22×D411yescharacteristic
445C22×C4C22×D411yescharacteristic
446C22×C4C22×D411yescharacteristic
447C22×C4C22×Q811yescharacteristic
448C22×C4C22×Q811yescharacteristic
449C22×C4C2×#4111yescharacteristic
450C22×C4C2×#4111yescharacteristic
451C22×C4C2×#4111yescharacteristic
452C22×C4C2×#4111yescharacteristic
453C22×C4C2×#4111yescharacteristic
454C22×C4C2×#4111yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4111yescharacteristic
457M16—24no—
458M16—24no—
459M16—24no—
460M16—24no—
461M16—42no—
462M16—42no—
463M16—42no—
464M16—42no—
465M16—48no—
466M16—48no—
467C2×C8—24no—
468C2×C8—24no—
469C2×C8—42no—
470C2×C8—42no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—48no—
474C2×C8—48no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—44no—
492C4⋊C4—44no—
493C4⋊C4—44no—
494C4⋊C4—44no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—88no—
498C4⋊C4—88no—
499C4⋊C4C2×C4⋊C414yes—
500C4⋊C4C2×C4⋊C414yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—28no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—44no—
507C42—24no—
508C42—24no—
509C42—28no—
510C42—24no—
511C42—24no—
512C42—42no—
513C42—42no—
514C42—42no—
515C42—42no—
516C42—48no—
517C42—44no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23#38512yes—
539C23#38512yes—
540C23#38714yes—
541C23#38814yes—
542C23#39312yes—
543C23#39312yes—
544C23#39412yes—
545C23#39412yes—
546C23#39814yes—
547C23#40014yes—
548C23#45312yes—
549C23#45412yes—
550C23#45512yes—
551C23#45612yes—
552C23C2×C4×D411yescharacteristic
553C23C2×#12011yescharacteristic
554C23C2×#12111yescharacteristic
555C23C2×C22⋊Q811yescharacteristic
556C23C2×C22⋊Q811yescharacteristic
557C23C2×#12311yescharacteristic
558C23C2×#12411yescharacteristic
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—432no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—48no—
569C2×C4—48no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—48no—
576C2×C4—48no—
577C2×C4—44no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—84no—
588C2×C4—88no—
589C2×C4—88no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4—88no—
593C2×C4—84no—
594C2×C4—88no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4#38214yes—
598C2×C4#38214yes—
599C2×C4#38512yes—
600C2×C4#38512yes—
601C2×C4#38714yes—
602C2×C4#38714yes—
603C2×C4#38714yes—
604C2×C4#38814yes—
605C2×C4#38814yes—
606C2×C4#38814yes—
607C2×C4#38914yes—
608C2×C4#38914yes—
609C2×C4#39312yes—
610C2×C4#39312yes—
611C2×C4#39412yes—
612C2×C4#39412yes—
613C2×C4#39714yes—
614C2×C4#39714yes—
615C2×C4#39814yes—
616C2×C4#39814yes—
617C2×C4#39814yes—
618C2×C4#40014yes—
619C2×C4#40014yes—
620C2×C4#40014yes—
621C2×C4#40014yes—
622C2×C4#40014yes—
623C2×C4C22×C4⋊C411yescharacteristic
624C2×C4C2×#11711yescharacteristic
625C2×C4C2×#11711yescharacteristic
626C2×C4C2×C4×D411yescharacteristic
627C2×C4C2×C4×D411yescharacteristic
628C2×C4C2×C4×Q811yescharacteristic
629C2×C4C2×#12111yescharacteristic
630C2×C4C2×#12111yescharacteristic
631C2×C4C2×C22⋊Q811yescharacteristic
632C2×C4C2×C22⋊Q811yescharacteristic
633C2×C4C2×C22⋊Q811yescharacteristic
634C2×C4C2×#12311yescharacteristic
635C2×C4C2×#12311yescharacteristic
636C2×C4C2×#12311yescharacteristic
637C2×C4C2×#12311yescharacteristic
638C2×C4C2×#12411yescharacteristic
639C2×C4C2×#12411yescharacteristic
640C2×C4C2×#12411yescharacteristic
641C2×C4C2×#12511yescharacteristic
642C2×C4C2×#12511yescharacteristic
643C2×C4C2×#12511yescharacteristic
644C2×C4C2×#12511yescharacteristic
645C2×C4C2×#12511yescharacteristic
646C2×C4C2×#12611yescharacteristic
647C2×C4C2×#12611yescharacteristic
648C2×C4C2×#12611yescharacteristic
649C2×C4C2×#12611yescharacteristic
650C2×C4C2×C4⋊Q811yescharacteristic
651C8—44no—
652C8—44no—
653C22—28no—
654C22—28no—
655C22—28no—
656C22—28no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—21no—
661C22—21no—
662C22—22no—
663C22—21no—
664C22—21no—
665C22—22no—
666C22—21no—
667C22—21no—
668C22—22no—
669C22—21no—
670C22—21no—
671C22—22no—
672C22—21no—
673C22—21no—
674C22—22no—
675C22#144214yes—
676C22#144214yes—
677C22#185914yes—
678C22#186014yes—
679C22#202714yes—
680C22#202814yes—
681C22#203714yes—
682C22#203814yes—
683C22C2×#38511yescharacteristic
684C22C2×#38711yescharacteristic
685C22C2×#38811yescharacteristic
686C22C2×#39311yescharacteristic
687C22C2×#39411yescharacteristic
688C22C2×#39811yescharacteristic
689C22C2×#40011yescharacteristic
690C22C2×#45311yescharacteristic
691C22C2×#45511yescharacteristic
692C22C2×#45411yescharacteristic
693C22C2×#45611yescharacteristic
694C4—48no—
695C4—44no—
696C4—44no—
697C4—84no—
698C4—84no—
699C4—82no—
700C4—82no—
701C4#144214yes—
702C4#144214yes—
703C4C2×#38211yescharacteristic
704C4C2×#38711yescharacteristic
705C4C2×#38811yescharacteristic
706C4C2×#38911yescharacteristic
707C4C2×#39711yescharacteristic
708C4C2×#39811yescharacteristic
709C4C2×#40011yescharacteristic
710C4C2×#40011yescharacteristic
711C2—21no—
712C2—21no—
713C2—21no—
714C2—24no—
715C2—21no—
716C2#1127618yesdirect product factor
717C2C2×#144211yescharacteristic
718C2C2×#185911yescharacteristic
719C2C2×#186011yescharacteristic
720C2C2×#202711yescharacteristic
721C2C2×#202811yescharacteristic
722C2C2×#203711yescharacteristic
723C2C2×#203811yescharacteristic
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. #11276C2direct (N × H)
37. C2×#339C4semidirect
138. #339C2×C4semidirect
716. C2#11276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23172
C22×#3432
C2×#17362
C22×#3392
C2×C4⋊#952
#112762