Finite Group Databasebeta

← C2×#11262 #358273

Subgroups — C2×#11262 #358273

Order 512.

1878 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2285C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11262C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C42C2211yescharacteristic
16#2285—22no—
17#2285—22no—
18#2285—22no—
19#2285C2214yes—
20C2×#384—21no—
21C2×#382—21no—
22C2×#380—22no—
23C2×C4×C4⋊C4—22no—
24C2×#344—24no—
25C2×#344C2214yes—
26#1740—22no—
27#1740C2214yes—
28C2×#342—22no—
29#1733—22no—
30#1733C2214yes—
31C2×#339—21no—
32C2×#339—21no—
33C2×#339—22no—
34C2×#339—22no—
35C2×#339C418yescomplemented
36C2×#339C2214yes—
37C2×#339C2214yes—
38C2×H(3,ℤ/4)—24no—
39C2×H(3,ℤ/4)C2214yes—
40C24×C4—21no—
41C24×C4C2311yescharacteristic
42C22×M16—22no—
43C22×M16—22no—
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
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—21no—
67C2×#117—21no—
68C2×#117—21no—
69C2×#117—21no—
70C2×#117—22no—
71C2×#117—22no—
72C2×#117—22no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—21no—
76C2×#117—21no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—21no—
90C2×#117—21no—
91C2×#117—22no—
92C2×#117C2×C414yes—
93C2×#117D412yes—
94C2×#117D412yes—
95C2×#117Q812yes—
96C2×#117C2312yes—
97C2×#117C2312yes—
98C2×#117C2312yes—
99C2×#117C2312yes—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4Q812yes—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4D412yes—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42—21no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—21no—
115C22×C42—21no—
116C22×C42—21no—
117C22×C42C2×C414yes—
118C22×C42D412yes—
119C22×C42D411yescharacteristic
120C22×C42D411yescharacteristic
121C22×C42D412yes—
122C22×C42Q814yes—
123C22×C42C2312yes—
124#384—24no—
125#384—24no—
126#382—24no—
127#382—24no—
128#380—28no—
129#380—28no—
130C4×C4⋊C4—28no—
131C4×C4⋊C4—28no—
132C2×#95—24no—
133#344—28no—
134#342—28no—
135#339—24no—
136#339—24no—
137#339—28no—
138#339C2×C4116yescomplemented
139H(3,ℤ/4)—28no—
140C25C2×D411yescharacteristic
141C23×C4—21no—
142C23×C4—24no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—24no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—48no—
151C23×C4—41no—
152C23×C4C22×C412yes—
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4C2×D412yes—
159C23×C4C2×Q812yes—
160C23×C4C2×Q811yescharacteristic
161C23×C4C2×Q811yescharacteristic
162C23×C4#4112yes—
163C23×C4#4112yes—
164C23×C4#4111yescharacteristic
165C23×C4#4111yescharacteristic
166C23×C4#4111yescharacteristic
167C23×C4#4111yescharacteristic
168C23×C4#4111yescharacteristic
169C23×C4#4111yescharacteristic
170C23×C4#4112yes—
171C23×C4#4112yes—
172C23×C4#4112yes—
173C23×C4C2411yescharacteristic
174C2×M16—24no—
175C2×M16—24no—
176C2×M16—22no—
177C2×M16—22no—
178C2×M16—24no—
179C2×M16—24no—
180C2×M16—24no—
181C2×M16—24no—
182C2×M16—24no—
183C2×M16—24no—
184C2×M16—24no—
185C2×M16—24no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—42no—
195C2×M16—42no—
196C2×M16—42no—
197C2×M16—42no—
198C2×M16—42no—
199C2×M16—42no—
200C2×M16—41no—
201C2×M16—41no—
202C2×M16—41no—
203C2×M16—41no—
204C2×M16—42no—
205C2×M16—42no—
206C2×M16—42no—
207C2×M16—42no—
208C2×M16C22×C414yes—
209C2×M16C2×D414yes—
210C22×C8—24no—
211C22×C8—24no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—41no—
215C22×C8—41no—
216C22×C8—41no—
217C22×C8—41no—
218C22×C8—42no—
219C22×C8—42no—
220#117—24no—
221#117—24no—
222#117—24no—
223#117—22no—
224#117—22no—
225#117—22no—
226#117—22no—
227#117—22no—
228#117—24no—
229#117—24no—
230#117—24no—
231#117—22no—
232#117—22no—
233#117—22no—
234#117—22no—
235#117—22no—
236#117—24no—
237#117—22no—
238#117—22no—
239#117—22no—
240#117—22no—
241#117—22no—
242#117—22no—
243#117—22no—
244#117—22no—
245#117—22no—
246#117—41no—
247#117—41no—
248#117—42no—
249#117—42no—
250#117—42no—
251#117—42no—
252#117—42no—
253#117—42no—
254#117—42no—
255#117—42no—
256#117—41no—
257#117—41no—
258#117—41no—
259#117—41no—
260#117—41no—
261#117—41no—
262#117—42no—
263#117—42no—
264#117—42no—
265#117C22×C414yes—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—216no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—416no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4C2×Q814yes—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4—41no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—41no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4C2×D414yes—
304C2×C42—24no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—22no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—24no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—24no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—24no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—41no—
331C2×C42—41no—
332C2×C42—41no—
333C2×C42—41no—
334C2×C42—41no—
335C2×C42—42no—
336C2×C42C4⋊C414yes—
337C2×C42C4⋊C414yes—
338C2×C42C4⋊C418yes—
339C2×C42C22×C414yes—
340C2×C42C2×D414yes—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C2×C42C2×Q814yes—
344#95—216no—
345C24—44no—
346C24C4×D412yes—
347C24#12011yescharacteristic
348C24#12011yescharacteristic
349C24#12112yes—
350C24C22⋊Q811yescharacteristic
351C24C22⋊Q812yes—
352C24C22⋊Q811yescharacteristic
353C24#12312yes—
354C24#12411yescharacteristic
355C24#12411yescharacteristic
356C24C22×D411yescharacteristic
357C22×C4—28no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—48no—
369C22×C4—48no—
370C22×C4—416no—
371C22×C4—416no—
372C22×C4—44no—
373C22×C4—48no—
374C22×C4—48no—
375C22×C4—42no—
376C22×C4—44no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—84no—
382C22×C4—84no—
383C22×C4C2×C4⋊C412yes—
384C22×C4C2×C4⋊C412yes—
385C22×C4#11712yes—
386C22×C4#11712yes—
387C22×C4#11712yes—
388C22×C4#11712yes—
389C22×C4C4×D412yes—
390C22×C4C4×D412yes—
391C22×C4C4×D412yes—
392C22×C4C4×D412yes—
393C22×C4C4×D412yes—
394C22×C4C4×Q812yes—
395C22×C4C4×Q812yes—
396C22×C4#12011yescharacteristic
397C22×C4#12011yescharacteristic
398C22×C4#12112yes—
399C22×C4#12112yes—
400C22×C4#12112yes—
401C22×C4#12112yes—
402C22×C4#12112yes—
403C22×C4C22⋊Q812yes—
404C22×C4C22⋊Q812yes—
405C22×C4C22⋊Q811yescharacteristic
406C22×C4C22⋊Q811yescharacteristic
407C22×C4C22⋊Q811yescharacteristic
408C22×C4C22⋊Q811yescharacteristic
409C22×C4C22⋊Q811yescharacteristic
410C22×C4C22⋊Q811yescharacteristic
411C22×C4C22⋊Q811yescharacteristic
412C22×C4C22⋊Q811yescharacteristic
413C22×C4C22⋊Q812yes—
414C22×C4C22⋊Q811yescharacteristic
415C22×C4C22⋊Q811yescharacteristic
416C22×C4#12312yes—
417C22×C4#12312yes—
418C22×C4#12312yes—
419C22×C4#12312yes—
420C22×C4#12312yes—
421C22×C4#12312yes—
422C22×C4#12312yes—
423C22×C4#12312yes—
424C22×C4#12312yes—
425C22×C4#12411yescharacteristic
426C22×C4#12411yescharacteristic
427C22×C4#12411yescharacteristic
428C22×C4#12411yescharacteristic
429C22×C4#12412yes—
430C22×C4#12412yes—
431C22×C4#12411yescharacteristic
432C22×C4#12411yescharacteristic
433C22×C4#12411yescharacteristic
434C22×C4#12411yescharacteristic
435C22×C4#12411yescharacteristic
436C22×C4#12411yescharacteristic
437C22×C4#12512yes—
438C22×C4#12512yes—
439C22×C4#12512yes—
440C22×C4#12512yes—
441C22×C4#12512yes—
442C22×C4#12512yes—
443C22×C4#12512yes—
444C22×C4#12512yes—
445C22×C4#12512yes—
446C22×C4#12512yes—
447C22×C4#12612yes—
448C22×C4#12612yes—
449C22×C4#12612yes—
450C22×C4#12612yes—
451C22×C4#12612yes—
452C22×C4#12612yes—
453C22×C4#12612yes—
454C22×C4#12612yes—
455C22×C4C4⋊Q812yes—
456C22×C4C4⋊Q812yes—
457C22×C4C23×C411yescharacteristic
458C22×C4C22×D411yescharacteristic
459C22×C4C22×D411yescharacteristic
460C22×C4C22×D411yescharacteristic
461C22×C4C22×Q811yescharacteristic
462C22×C4C22×Q811yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471M16—24no—
472M16—24no—
473M16—24no—
474M16—24no—
475M16—42no—
476M16—42no—
477M16—42no—
478M16—42no—
479M16—44no—
480M16—44no—
481M16—44no—
482M16—44no—
483C2×C8—24no—
484C2×C8—24no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—44no—
490C2×C8—44no—
491C2×C8—44no—
492C2×C8—44no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—432no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—44no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—44no—
506C4⋊C4—44no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—44no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—44no—
519C22⋊C4—44no—
520C42—24no—
521C42—24no—
522C42—22no—
523C42—22no—
524C42—24no—
525C42—28no—
526C42—24no—
527C42—24no—
528C42—24no—
529C42—24no—
530C42—42no—
531C42—42no—
532C42—42no—
533C42—42no—
534C42—42no—
535C42—44no—
536C42—42no—
537C42—42no—
538C42—44no—
539C42—44no—
540C42C2×C4⋊C414yes—
541C42C2×C4⋊C414yes—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—44no—
546C23—42no—
547C23—44no—
548C23—42no—
549C23—44no—
550C23—42no—
551C23—44no—
552C23—42no—
553C23#38512yes—
554C23#38512yes—
555C23#38712yes—
556C23#38712yes—
557C23#38812yes—
558C23#38812yes—
559C23#39311yescharacteristic
560C23#39311yescharacteristic
561C23#39311yescharacteristic
562C23#39311yescharacteristic
563C23#39412yes—
564C23#39412yes—
565C23#39812yes—
566C23#39812yes—
567C23#40012yes—
568C23#40012yes—
569C23C2×C4×D411yescharacteristic
570C23C2×#12011yescharacteristic
571C23C2×#12111yescharacteristic
572C23C2×C22⋊Q811yescharacteristic
573C23C2×C22⋊Q811yescharacteristic
574C23C2×#12311yescharacteristic
575C23C2×#12411yescharacteristic
576C2×C4—28no—
577C2×C4—216no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—48no—
581C2×C4—48no—
582C2×C4—416no—
583C2×C4—44no—
584C2×C4—48no—
585C2×C4—48no—
586C2×C4—48no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—88no—
592C2×C4—88no—
593C2×C4—84no—
594C2×C4—88no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4—84no—
598C2×C4#38212yes—
599C2×C4#38212yes—
600C2×C4#38212yes—
601C2×C4#38212yes—
602C2×C4#38512yes—
603C2×C4#38512yes—
604C2×C4#38712yes—
605C2×C4#38712yes—
606C2×C4#38712yes—
607C2×C4#38712yes—
608C2×C4#38712yes—
609C2×C4#38712yes—
610C2×C4#38812yes—
611C2×C4#38812yes—
612C2×C4#38812yes—
613C2×C4#38812yes—
614C2×C4#38812yes—
615C2×C4#38812yes—
616C2×C4#38912yes—
617C2×C4#38912yes—
618C2×C4#38912yes—
619C2×C4#38912yes—
620C2×C4#39311yescharacteristic
621C2×C4#39311yescharacteristic
622C2×C4#39311yescharacteristic
623C2×C4#39311yescharacteristic
624C2×C4#39412yes—
625C2×C4#39412yes—
626C2×C4#39712yes—
627C2×C4#39712yes—
628C2×C4#39712yes—
629C2×C4#39712yes—
630C2×C4#39812yes—
631C2×C4#39812yes—
632C2×C4#39812yes—
633C2×C4#39812yes—
634C2×C4#39812yes—
635C2×C4#39812yes—
636C2×C4#40012yes—
637C2×C4#40012yes—
638C2×C4#40012yes—
639C2×C4#40012yes—
640C2×C4#40012yes—
641C2×C4#40012yes—
642C2×C4#40012yes—
643C2×C4#40012yes—
644C2×C4#40012yes—
645C2×C4#40012yes—
646C2×C4C22×C4⋊C411yescharacteristic
647C2×C4C2×#11711yescharacteristic
648C2×C4C2×#11711yescharacteristic
649C2×C4C2×C4×D411yescharacteristic
650C2×C4C2×C4×D411yescharacteristic
651C2×C4C2×C4×Q811yescharacteristic
652C2×C4C2×#12111yescharacteristic
653C2×C4C2×#12111yescharacteristic
654C2×C4C2×C22⋊Q811yescharacteristic
655C2×C4C2×C22⋊Q811yescharacteristic
656C2×C4C2×C22⋊Q811yescharacteristic
657C2×C4C2×#12311yescharacteristic
658C2×C4C2×#12311yescharacteristic
659C2×C4C2×#12311yescharacteristic
660C2×C4C2×#12311yescharacteristic
661C2×C4C2×#12411yescharacteristic
662C2×C4C2×#12411yescharacteristic
663C2×C4C2×#12411yescharacteristic
664C2×C4C2×#12511yescharacteristic
665C2×C4C2×#12511yescharacteristic
666C2×C4C2×#12511yescharacteristic
667C2×C4C2×#12511yescharacteristic
668C2×C4C2×#12511yescharacteristic
669C2×C4C2×#12611yescharacteristic
670C2×C4C2×#12611yescharacteristic
671C2×C4C2×#12611yescharacteristic
672C2×C4C2×#12611yescharacteristic
673C2×C4C2×C4⋊Q811yescharacteristic
674C8—44no—
675C8—44no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—41no—
689C22—41no—
690C22—42no—
691C22—41no—
692C22—41no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22#144212yes—
699C22#144212yes—
700C22#144212yes—
701C22#144212yes—
702C22#203114yes—
703C22C2×#38511yescharacteristic
704C22C2×#38711yescharacteristic
705C22C2×#38811yescharacteristic
706C22C2×#39311yescharacteristic
707C22C2×#39411yescharacteristic
708C22C2×#39811yescharacteristic
709C22C2×#40011yescharacteristic
710C4—28no—
711C4—44no—
712C4—84no—
713C4—84no—
714C4—84no—
715C4—84no—
716C4#144212yes—
717C4#144212yes—
718C4#144212yes—
719C4#144212yes—
720C4C2×#38211yescharacteristic
721C4C2×#38711yescharacteristic
722C4C2×#38811yescharacteristic
723C4C2×#38911yescharacteristic
724C4C2×#39711yescharacteristic
725C4C2×#39811yescharacteristic
726C4C2×#40011yescharacteristic
727C4C2×#40011yescharacteristic
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—21no—
733C2—22no—
734C2—22no—
735C2—22no—
736C2—21no—
737C2#1126214yesdirect product factor
738C2C2×#144211yescharacteristic
739C2C2×#203112yes—
subgroupG/H
centerC22×C4#124
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#393
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11262C2direct (N × H)
35. C2×#339C4semidirect
138. #339C2×C4semidirect
737. C2#11262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#22852
C22×#3442
C2×#17402
C2×#17332
C22×#3392
C22×H(3,ℤ/4)2
#112622