Finite Group Databasebeta

← C2×#11282 #358297

Subgroups — C2×#11282 #358297

Order 512.

1878 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2296C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11282C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C42C2211yescharacteristic
16#2296—22no—
17#2296—22no—
18#2296—22no—
19#2296C2214yes—
20C2×#389—22no—
21C2×#385—22no—
22C2×C4×C4⋊C4—22no—
23C2×#344—24no—
24C2×#344C2214yes—
25#1740—22no—
26#1740C2214yes—
27C2×#342—22no—
28#1733—22no—
29#1733C2214yes—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339—24no—
34C2×#339C2214yes—
35C2×#339C2214yes—
36C2×H(3,ℤ/4)C418yescomplemented
37C2×H(3,ℤ/4)C2214yes—
38C24×C4—21no—
39C24×C4C2311yescharacteristic
40C22×M16—22no—
41C22×M16—22no—
42C22×M16—21no—
43C22×M16—21no—
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—22no—
49C22×M16—22no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—22no—
55C22×M16—22no—
56C22×M16C2×C414yes—
57C22×M16D414yes—
58C22×M16C2312yes—
59C22×M16C2312yes—
60C23×C8—21no—
61C23×C8—21no—
62C2×#117—21no—
63C2×#117—21no—
64C2×#117—22no—
65C2×#117—22no—
66C2×#117—21no—
67C2×#117—21no—
68C2×#117—21no—
69C2×#117—21no—
70C2×#117—22no—
71C2×#117—21no—
72C2×#117—21no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—21no—
80C2×#117—21no—
81C2×#117—21no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117C2×C414yes—
89C2×#117C2×C414yes—
90C2×#117D412yes—
91C2×#117D412yes—
92C2×#117Q812yes—
93C2×#117Q814yes—
94C2×#117C2312yes—
95C2×#117C2312yes—
96C2×#117C2312yes—
97C2×#117C2312yes—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4Q812yes—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4D412yes—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—21no—
112C22×C42—21no—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42—21no—
116C22×C42—21no—
117C22×C42D412yes—
118C22×C42D412yes—
119C22×C42D412yes—
120C22×C42C2312yes—
121#389—28no—
122#389—28no—
123#385—28no—
124#385—28no—
125C4×C4⋊C4—28no—
126C4×C4⋊C4—28no—
127C2×#95—24no—
128#344—28no—
129#342—28no—
130#339—28no—
131#339—28no—
132#339—28no—
133H(3,ℤ/4)C2×C4116yescomplemented
134C25C2×D411yescharacteristic
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—48no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—41no—
145C23×C4C22×C412yes—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D412yes—
152C23×C4C2×Q812yes—
153C23×C4C2×Q811yescharacteristic
154C23×C4C2×Q811yescharacteristic
155C23×C4#4112yes—
156C23×C4#4112yes—
157C23×C4#4111yescharacteristic
158C23×C4#4111yescharacteristic
159C23×C4#4111yescharacteristic
160C23×C4#4111yescharacteristic
161C23×C4#4111yescharacteristic
162C23×C4#4111yescharacteristic
163C23×C4#4112yes—
164C23×C4#4112yes—
165C23×C4#4112yes—
166C23×C4C2411yescharacteristic
167C2×M16—24no—
168C2×M16—24no—
169C2×M16—22no—
170C2×M16—22no—
171C2×M16—24no—
172C2×M16—24no—
173C2×M16—24no—
174C2×M16—24no—
175C2×M16—24no—
176C2×M16—24no—
177C2×M16—24no—
178C2×M16—24no—
179C2×M16—22no—
180C2×M16—22no—
181C2×M16—22no—
182C2×M16—22no—
183C2×M16—22no—
184C2×M16—22no—
185C2×M16—22no—
186C2×M16—22no—
187C2×M16—42no—
188C2×M16—42no—
189C2×M16—42no—
190C2×M16—42no—
191C2×M16—42no—
192C2×M16—41no—
193C2×M16—41no—
194C2×M16—41no—
195C2×M16—41no—
196C2×M16—42no—
197C2×M16—42no—
198C2×M16—42no—
199C2×M16—42no—
200C2×M16—42no—
201C2×M16C22×C414yes—
202C2×M16C2×D414yes—
203C22×C8—24no—
204C22×C8—24no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—42no—
208C22×C8—41no—
209C22×C8—41no—
210C22×C8—41no—
211C22×C8—41no—
212C22×C8—42no—
213#117—24no—
214#117—24no—
215#117—24no—
216#117—24no—
217#117—24no—
218#117—22no—
219#117—22no—
220#117—24no—
221#117—22no—
222#117—24no—
223#117—24no—
224#117—24no—
225#117—22no—
226#117—22no—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—24no—
231#117—22no—
232#117—22no—
233#117—22no—
234#117—22no—
235#117—22no—
236#117—22no—
237#117—22no—
238#117—22no—
239#117—22no—
240#117—41no—
241#117—41no—
242#117—42no—
243#117—42no—
244#117—42no—
245#117—42no—
246#117—42no—
247#117—41no—
248#117—41no—
249#117—41no—
250#117—41no—
251#117—42no—
252#117—41no—
253#117—41no—
254#117—42no—
255#117C4⋊C418yes—
256#117C22×C414yes—
257#117C22×C414yes—
258#117C2×Q814yes—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—216no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—416no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4C2×Q814yes—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4—41no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—41no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4C2×D414yes—
297C2×C42—22no—
298C2×C42—24no—
299C2×C42—24no—
300C2×C42—24no—
301C2×C42—24no—
302C2×C42—24no—
303C2×C42—24no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—41no—
325C2×C42—42no—
326C2×C42—41no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—41no—
330C2×C42C4⋊C418yes—
331C2×C42C2×D414yes—
332C2×C42C2×D414yes—
333#95—216no—
334C24—44no—
335C24C4×D412yes—
336C24#12011yescharacteristic
337C24#12011yescharacteristic
338C24#12112yes—
339C24C22⋊Q811yescharacteristic
340C24C22⋊Q812yes—
341C24C22⋊Q811yescharacteristic
342C24#12312yes—
343C24#12411yescharacteristic
344C24#12411yescharacteristic
345C24C22×D411yescharacteristic
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—28no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—48no—
353C22×C4—48no—
354C22×C4—48no—
355C22×C4—44no—
356C22×C4—416no—
357C22×C4—416no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—48no—
363C22×C4—42no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—44no—
368C22×C4—84no—
369C22×C4—84no—
370C22×C4C2×C4⋊C412yes—
371C22×C4C2×C4⋊C412yes—
372C22×C4#11712yes—
373C22×C4#11712yes—
374C22×C4#11712yes—
375C22×C4#11712yes—
376C22×C4C4×D412yes—
377C22×C4C4×D412yes—
378C22×C4C4×D412yes—
379C22×C4C4×D412yes—
380C22×C4C4×D412yes—
381C22×C4C4×Q812yes—
382C22×C4C4×Q812yes—
383C22×C4#12011yescharacteristic
384C22×C4#12011yescharacteristic
385C22×C4#12112yes—
386C22×C4#12112yes—
387C22×C4#12112yes—
388C22×C4#12112yes—
389C22×C4#12112yes—
390C22×C4C22⋊Q812yes—
391C22×C4C22⋊Q812yes—
392C22×C4C22⋊Q811yescharacteristic
393C22×C4C22⋊Q811yescharacteristic
394C22×C4C22⋊Q811yescharacteristic
395C22×C4C22⋊Q811yescharacteristic
396C22×C4C22⋊Q811yescharacteristic
397C22×C4C22⋊Q811yescharacteristic
398C22×C4C22⋊Q811yescharacteristic
399C22×C4C22⋊Q811yescharacteristic
400C22×C4C22⋊Q812yes—
401C22×C4C22⋊Q811yescharacteristic
402C22×C4C22⋊Q811yescharacteristic
403C22×C4#12312yes—
404C22×C4#12312yes—
405C22×C4#12312yes—
406C22×C4#12312yes—
407C22×C4#12312yes—
408C22×C4#12312yes—
409C22×C4#12312yes—
410C22×C4#12312yes—
411C22×C4#12312yes—
412C22×C4#12411yescharacteristic
413C22×C4#12411yescharacteristic
414C22×C4#12411yescharacteristic
415C22×C4#12412yes—
416C22×C4#12412yes—
417C22×C4#12411yescharacteristic
418C22×C4#12411yescharacteristic
419C22×C4#12411yescharacteristic
420C22×C4#12411yescharacteristic
421C22×C4#12411yescharacteristic
422C22×C4#12411yescharacteristic
423C22×C4#12411yescharacteristic
424C22×C4#12512yes—
425C22×C4#12512yes—
426C22×C4#12512yes—
427C22×C4#12512yes—
428C22×C4#12512yes—
429C22×C4#12512yes—
430C22×C4#12512yes—
431C22×C4#12512yes—
432C22×C4#12512yes—
433C22×C4#12512yes—
434C22×C4#12612yes—
435C22×C4#12612yes—
436C22×C4#12612yes—
437C22×C4#12612yes—
438C22×C4#12612yes—
439C22×C4#12612yes—
440C22×C4#12612yes—
441C22×C4#12612yes—
442C22×C4C4⋊Q812yes—
443C22×C4C4⋊Q812yes—
444C22×C4C23×C411yescharacteristic
445C22×C4C22×D411yescharacteristic
446C22×C4C22×D411yescharacteristic
447C22×C4C22×D411yescharacteristic
448C22×C4C22×Q811yescharacteristic
449C22×C4C22×Q811yescharacteristic
450C22×C4C2×#4111yescharacteristic
451C22×C4C2×#4111yescharacteristic
452C22×C4C2×#4111yescharacteristic
453C22×C4C2×#4111yescharacteristic
454C22×C4C2×#4111yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458M16—24no—
459M16—24no—
460M16—24no—
461M16—24no—
462M16—42no—
463M16—42no—
464M16—42no—
465M16—42no—
466M16—44no—
467M16—44no—
468M16—44no—
469M16—44no—
470C2×C8—24no—
471C2×C8—24no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8—44no—
477C2×C8—44no—
478C2×C8—44no—
479C2×C8—44no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—28no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—432no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—44no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—44no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—28no—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—44no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—44no—
507C42—24no—
508C42—28no—
509C42—24no—
510C42—24no—
511C42—24no—
512C42—42no—
513C42—42no—
514C42—42no—
515C42—42no—
516C42—42no—
517C42—42no—
518C42—42no—
519C42—44no—
520C42—42no—
521C42—42no—
522C42—44no—
523C42—44no—
524C42—44no—
525C42C2×C4⋊C418yes—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—42no—
530C23—44no—
531C23—44no—
532C23—42no—
533C23—44no—
534C23—44no—
535C23—42no—
536C23—42no—
537C23#38512yes—
538C23#38512yes—
539C23#38712yes—
540C23#38712yes—
541C23#38812yes—
542C23#38812yes—
543C23#39311yescharacteristic
544C23#39311yescharacteristic
545C23#39311yescharacteristic
546C23#39311yescharacteristic
547C23#39412yes—
548C23#39412yes—
549C23#39812yes—
550C23#39812yes—
551C23#40012yes—
552C23#40012yes—
553C23C2×C4×D411yescharacteristic
554C23C2×#12011yescharacteristic
555C23C2×#12111yescharacteristic
556C23C2×C22⋊Q811yescharacteristic
557C23C2×C22⋊Q811yescharacteristic
558C23C2×#12311yescharacteristic
559C23C2×#12411yescharacteristic
560C2×C4—28no—
561C2×C4—28no—
562C2×C4—48no—
563C2×C4—416no—
564C2×C4—416no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—416no—
569C2×C4—44no—
570C2×C4—48no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—88no—
575C2×C4—88no—
576C2×C4—84no—
577C2×C4—84no—
578C2×C4—84no—
579C2×C4—84no—
580C2×C4#38212yes—
581C2×C4#38212yes—
582C2×C4#38212yes—
583C2×C4#38212yes—
584C2×C4#38512yes—
585C2×C4#38512yes—
586C2×C4#38712yes—
587C2×C4#38712yes—
588C2×C4#38712yes—
589C2×C4#38712yes—
590C2×C4#38712yes—
591C2×C4#38712yes—
592C2×C4#38812yes—
593C2×C4#38812yes—
594C2×C4#38812yes—
595C2×C4#38812yes—
596C2×C4#38812yes—
597C2×C4#38812yes—
598C2×C4#38912yes—
599C2×C4#38912yes—
600C2×C4#38912yes—
601C2×C4#38912yes—
602C2×C4#39311yescharacteristic
603C2×C4#39311yescharacteristic
604C2×C4#39311yescharacteristic
605C2×C4#39311yescharacteristic
606C2×C4#39412yes—
607C2×C4#39412yes—
608C2×C4#39712yes—
609C2×C4#39712yes—
610C2×C4#39712yes—
611C2×C4#39712yes—
612C2×C4#39812yes—
613C2×C4#39812yes—
614C2×C4#39812yes—
615C2×C4#39812yes—
616C2×C4#39812yes—
617C2×C4#39812yes—
618C2×C4#40012yes—
619C2×C4#40012yes—
620C2×C4#40012yes—
621C2×C4#40012yes—
622C2×C4#40012yes—
623C2×C4#40012yes—
624C2×C4#40012yes—
625C2×C4#40012yes—
626C2×C4#40012yes—
627C2×C4#40012yes—
628C2×C4C22×C4⋊C411yescharacteristic
629C2×C4C2×#11711yescharacteristic
630C2×C4C2×#11711yescharacteristic
631C2×C4C2×C4×D411yescharacteristic
632C2×C4C2×C4×D411yescharacteristic
633C2×C4C2×C4×Q811yescharacteristic
634C2×C4C2×#12111yescharacteristic
635C2×C4C2×#12111yescharacteristic
636C2×C4C2×C22⋊Q811yescharacteristic
637C2×C4C2×C22⋊Q811yescharacteristic
638C2×C4C2×C22⋊Q811yescharacteristic
639C2×C4C2×#12311yescharacteristic
640C2×C4C2×#12311yescharacteristic
641C2×C4C2×#12311yescharacteristic
642C2×C4C2×#12311yescharacteristic
643C2×C4C2×#12411yescharacteristic
644C2×C4C2×#12411yescharacteristic
645C2×C4C2×#12411yescharacteristic
646C2×C4C2×#12511yescharacteristic
647C2×C4C2×#12511yescharacteristic
648C2×C4C2×#12511yescharacteristic
649C2×C4C2×#12511yescharacteristic
650C2×C4C2×#12511yescharacteristic
651C2×C4C2×#12611yescharacteristic
652C2×C4C2×#12611yescharacteristic
653C2×C4C2×#12611yescharacteristic
654C2×C4C2×#12611yescharacteristic
655C2×C4C2×C4⋊Q811yescharacteristic
656C8—44no—
657C8—44no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22#144212yes—
681C22#144212yes—
682C22#144212yes—
683C22#144212yes—
684C22#203114yes—
685C22C2×#38511yescharacteristic
686C22C2×#38711yescharacteristic
687C22C2×#38811yescharacteristic
688C22C2×#39311yescharacteristic
689C22C2×#39411yescharacteristic
690C22C2×#39811yescharacteristic
691C22C2×#40011yescharacteristic
692C4—48no—
693C4—48no—
694C4—84no—
695C4—84no—
696C4—84no—
697C4#144212yes—
698C4#144212yes—
699C4#144212yes—
700C4#144212yes—
701C4C2×#38211yescharacteristic
702C4C2×#38711yescharacteristic
703C4C2×#38811yescharacteristic
704C4C2×#38911yescharacteristic
705C4C2×#39711yescharacteristic
706C4C2×#39811yescharacteristic
707C4C2×#40011yescharacteristic
708C4C2×#40011yescharacteristic
709C2—21no—
710C2—21no—
711C2—21no—
712C2—21no—
713C2—21no—
714C2—22no—
715C2—22no—
716C2—22no—
717C2—21no—
718C2#1128214yesdirect product factor
719C2C2×#144211yescharacteristic
720C2C2×#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. #11282C2direct (N × H)
36. C2×H(3,ℤ/4)C4semidirect
133. H(3,ℤ/4)C2×C4semidirect
718. C2#11282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#22962
C22×#3442
C2×#17402
C2×#17332
C22×#3392
C22×H(3,ℤ/4)2
#112822