Finite Group Databasebeta

← C2×#11362 #358612

Subgroups — C2×#11362 #358612

Order 512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 727 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C22×#344C211yesmaximal, characteristic
4C22×#343C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C2×#1736C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11362C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#430—24no—
17C2×#430—22no—
18C2×#430C418yescomplemented
19C2×#430C2214yes—
20C22×#108—22no—
21C2×#344—24no—
22C2×#344—24no—
23C2×#344C2214yes—
24C2×#344C2214yes—
25C2×#343—22no—
26C2×#343—22no—
27C2×#343C2214yes—
28#1736—22no—
29#1736—22no—
30#1736C2214yes—
31#1736C2214yes—
32C2×#340—22no—
33C2×#340—22no—
34C2×H(3,ℤ/4)—24no—
35C2×H(3,ℤ/4)C2214yes—
36C24×C4—21no—
37C24×C4C2311yescharacteristic
38C22×M16—21no—
39C22×M16—21no—
40C22×M16—22no—
41C22×M16—21no—
42C22×M16—21no—
43C22×M16—22no—
44C22×M16—22no—
45C22×M16—21no—
46C22×M16—22no—
47C22×M16—22no—
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—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—21no—
60C22×M16—22no—
61C22×M16—22no—
62C22×M16—21no—
63C22×M16—21no—
64C22×M16—22no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—22no—
68C22×M16C2×C414yes—
69C22×M16C2×C414yes—
70C22×M16C2×C414yes—
71C22×M16D414yes—
72C22×M16D412yes—
73C22×M16Q814yes—
74C22×M16C2312yes—
75C22×M16C2312yes—
76C22×M16C2312yes—
77C22×M16C2312yes—
78C23×C8—21no—
79C23×C8—21no—
80C23×C8—21no—
81C23×C8D412yes—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—22no—
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—22no—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117D414yes—
95C2×#117Q814yes—
96C2×#117C2312yes—
97C2×#117C2312yes—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4D412yes—
112C22×C4⋊C4D412yes—
113C22×C4⋊C4C2312yes—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C42—21no—
117C22×C42—21no—
118#430—216no—
119#430—28no—
120#430C2×C4116yescomplemented
121C2×#108—216no—
122C2×#108—28no—
123#344—28no—
124#344—28no—
125#343—28no—
126#340—28no—
127#340—28no—
128H(3,ℤ/4)—28no—
129C25#4111yescharacteristic
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—41no—
134C23×C4—41no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—41no—
138C23×C4—41no—
139C23×C4—84no—
140C23×C4C22×C412yes—
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D412yes—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D412yes—
147C23×C4C2×Q812yes—
148C23×C4C2×Q812yes—
149C23×C4#4111yescharacteristic
150C23×C4#4111yescharacteristic
151C23×C4#4112yes—
152C23×C4#4111yescharacteristic
153C23×C4#4111yescharacteristic
154C23×C4#4112yes—
155C23×C4#4111yescharacteristic
156C23×C4#4111yescharacteristic
157C23×C4#4112yes—
158C23×C4#4111yescharacteristic
159C23×C4#4111yescharacteristic
160C23×C4#4111yescharacteristic
161C23×C4C2411yescharacteristic
162C2×M16—24no—
163C2×M16—24no—
164C2×M16—24no—
165C2×M16—24no—
166C2×M16—22no—
167C2×M16—22no—
168C2×M16—24no—
169C2×M16—24no—
170C2×M16—24no—
171C2×M16—24no—
172C2×M16—24no—
173C2×M16—22no—
174C2×M16—22no—
175C2×M16—22no—
176C2×M16—22no—
177C2×M16—24no—
178C2×M16—24no—
179C2×M16—24no—
180C2×M16—22no—
181C2×M16—22no—
182C2×M16—22no—
183C2×M16—24no—
184C2×M16—24no—
185C2×M16—24no—
186C2×M16—24no—
187C2×M16—24no—
188C2×M16—24no—
189C2×M16—24no—
190C2×M16—24no—
191C2×M16—24no—
192C2×M16—24no—
193C2×M16—24no—
194C2×M16—24no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16—41no—
208C2×M16—41no—
209C2×M16—41no—
210C2×M16—41no—
211C2×M16—42no—
212C2×M16—42no—
213C2×M16—42no—
214C2×M16—42no—
215C2×M16—42no—
216C2×M16—41no—
217C2×M16—41no—
218C2×M16—42no—
219C2×M16—42no—
220C2×M16—42no—
221C2×M16—42no—
222C2×M16—42no—
223C2×M16—42no—
224C2×M16—42no—
225C2×M16—42no—
226C2×M16—42no—
227C2×M16—42no—
228C2×M16C22⋊C418yes—
229C2×M16C22×C414yes—
230C2×M16C22×C414yes—
231C2×M16C22×C414yes—
232C2×M16C2×D414yes—
233C2×M16C2×Q814yes—
234C22×C8—22no—
235C22×C8—24no—
236C22×C8—22no—
237C22×C8—24no—
238C22×C8—24no—
239C22×C8—24no—
240C22×C8—22no—
241C22×C8—22no—
242C22×C8—22no—
243C22×C8—41no—
244C22×C8—41no—
245C22×C8—41no—
246C22×C8—41no—
247C22×C8—42no—
248C22×C8—41no—
249C22×C8—41no—
250C22×C8—42no—
251C22×C8—42no—
252C22×C8C22⋊C418yes—
253C22×C8C2×D414yes—
254#117—24no—
255#117—24no—
256#117—22no—
257#117—22no—
258#117—24no—
259#117—24no—
260#117—22no—
261#117—22no—
262#117—24no—
263#117—24no—
264#117—22no—
265#117—22no—
266#117—42no—
267#117—42no—
268#117—42no—
269#117—42no—
270#117—42no—
271#117—42no—
272#117C2×D414yes—
273#117C2×Q814yes—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4C2×D414yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—42no—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—42no—
323C2×C42—41no—
324C2×C42—41no—
325C2×C42—42no—
326#108—232no—
327C24—42no—
328C24—42no—
329C24C4×Q812yes—
330C24C22⋊Q812yes—
331C24#12311yescharacteristic
332C24#12312yes—
333C24#12311yescharacteristic
334C24#12411yescharacteristic
335C24#12411yescharacteristic
336C24#12611yescharacteristic
337C24#12612yes—
338C24#12611yescharacteristic
339C24C2×#4111yescharacteristic
340C22×C4—24no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—44no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—82no—
352C22×C4—82no—
353C22×C4—82no—
354C22×C4—82no—
355C22×C4—84no—
356C22×C4—84no—
357C22×C4—84no—
358C22×C4—84no—
359C22×C4—84no—
360C22×C4—84no—
361C22×C4—84no—
362C22×C4C2×C22⋊C412yes—
363C22×C4C2×C22⋊C412yes—
364C22×C4#11712yes—
365C22×C4#11712yes—
366C22×C4#11712yes—
367C22×C4#11712yes—
368C22×C4C4×D412yes—
369C22×C4C4×D412yes—
370C22×C4C4×D412yes—
371C22×C4C4×D412yes—
372C22×C4C4×Q812yes—
373C22×C4C4×Q812yes—
374C22×C4C4×Q812yes—
375C22×C4#12111yescharacteristic
376C22×C4#12111yescharacteristic
377C22×C4#12111yescharacteristic
378C22×C4#12112yes—
379C22×C4#12112yes—
380C22×C4#12111yescharacteristic
381C22×C4C22⋊Q812yes—
382C22×C4C22⋊Q812yes—
383C22×C4C22⋊Q812yes—
384C22×C4C22⋊Q812yes—
385C22×C4C22⋊Q812yes—
386C22×C4C22⋊Q812yes—
387C22×C4C22⋊Q812yes—
388C22×C4C22⋊Q812yes—
389C22×C4C22⋊Q812yes—
390C22×C4C22⋊Q812yes—
391C22×C4C22⋊Q812yes—
392C22×C4#12311yescharacteristic
393C22×C4#12312yes—
394C22×C4#12311yescharacteristic
395C22×C4#12311yescharacteristic
396C22×C4#12312yes—
397C22×C4#12311yescharacteristic
398C22×C4#12312yes—
399C22×C4#12312yes—
400C22×C4#12312yes—
401C22×C4#12312yes—
402C22×C4#12312yes—
403C22×C4#12311yescharacteristic
404C22×C4#12311yescharacteristic
405C22×C4#12311yescharacteristic
406C22×C4#12312yes—
407C22×C4#12311yescharacteristic
408C22×C4#12311yescharacteristic
409C22×C4#12311yescharacteristic
410C22×C4#12312yes—
411C22×C4#12412yes—
412C22×C4#12412yes—
413C22×C4#12411yescharacteristic
414C22×C4#12411yescharacteristic
415C22×C4#12512yes—
416C22×C4#12512yes—
417C22×C4#12512yes—
418C22×C4#12512yes—
419C22×C4#12512yes—
420C22×C4#12512yes—
421C22×C4#12512yes—
422C22×C4#12512yes—
423C22×C4#12612yes—
424C22×C4#12611yescharacteristic
425C22×C4#12611yescharacteristic
426C22×C4#12611yescharacteristic
427C22×C4#12612yes—
428C22×C4#12611yescharacteristic
429C22×C4#12611yescharacteristic
430C22×C4#12611yescharacteristic
431C22×C4#12612yes—
432C22×C4#12712yes—
433C22×C4#12712yes—
434C22×C4C4⋊Q812yes—
435C22×C4C4⋊Q812yes—
436C22×C4C23×C411yescharacteristic
437C22×C4C22×D411yescharacteristic
438C22×C4C22×D411yescharacteristic
439C22×C4C22×D411yescharacteristic
440C22×C4C22×D411yescharacteristic
441C22×C4C22×Q811yescharacteristic
442C22×C4C22×Q811yescharacteristic
443C22×C4C2×#4111yescharacteristic
444C22×C4C2×#4111yescharacteristic
445C22×C4C2×#4111yescharacteristic
446C22×C4C2×#4111yescharacteristic
447C22×C4C2×#4111yescharacteristic
448C22×C4C2×#4111yescharacteristic
449C22×C4C2×#4111yescharacteristic
450M16—24no—
451M16—24no—
452M16—24no—
453M16—24no—
454M16—28no—
455M16—28no—
456M16—24no—
457M16—24no—
458M16—24no—
459M16—24no—
460M16—24no—
461M16—24no—
462M16—42no—
463M16—42no—
464M16—42no—
465M16—42no—
466M16—42no—
467M16—42no—
468M16—44no—
469M16—44no—
470M16—44no—
471M16—44no—
472M16—44no—
473M16—44no—
474C2×C8—24no—
475C2×C8—24no—
476C2×C8—28no—
477C2×C8—28no—
478C2×C8—24no—
479C2×C8—24no—
480C2×C8—24no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8—44no—
488C2×C8—44no—
489C2×C8—44no—
490C2×C8—44no—
491C2×C8—44no—
492C2×C8—44no—
493C2×C8C2×C22⋊C418yes—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—44no—
507C4⋊C4—44no—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—44no—
513C22⋊C4—44no—
514C42—24no—
515C42—24no—
516C42—42no—
517C42—42no—
518C42—44no—
519C42—44no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—41no—
534C23—41no—
535C23—44no—
536C23—41no—
537C23—41no—
538C23#38712yes—
539C23#38712yes—
540C23#38712yes—
541C23#38712yes—
542C23#39112yes—
543C23#39112yes—
544C23#39712yes—
545C23#39711yescharacteristic
546C23#39711yescharacteristic
547C23#39711yescharacteristic
548C23#39712yes—
549C23#39711yescharacteristic
550C23#39912yes—
551C23#39912yes—
552C23#40012yes—
553C23#40012yes—
554C23C2×C4×Q811yescharacteristic
555C23C2×C22⋊Q811yescharacteristic
556C23C2×#12311yescharacteristic
557C23C2×#12311yescharacteristic
558C23C2×#12411yescharacteristic
559C23C2×#12611yescharacteristic
560C23C2×#12611yescharacteristic
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—88no—
565C2×C4—88no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—84no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—84no—
574C2×C4—84no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4#38112yes—
578C2×C4#38112yes—
579C2×C4#38112yes—
580C2×C4#38112yes—
581C2×C4#38712yes—
582C2×C4#38712yes—
583C2×C4#38712yes—
584C2×C4#38712yes—
585C2×C4#38712yes—
586C2×C4#38712yes—
587C2×C4#38712yes—
588C2×C4#38712yes—
589C2×C4#38712yes—
590C2×C4#38712yes—
591C2×C4#38712yes—
592C2×C4#38712yes—
593C2×C4#39012yes—
594C2×C4#39012yes—
595C2×C4#39012yes—
596C2×C4#39012yes—
597C2×C4#39112yes—
598C2×C4#39112yes—
599C2×C4#39712yes—
600C2×C4#39712yes—
601C2×C4#39711yescharacteristic
602C2×C4#39711yescharacteristic
603C2×C4#39711yescharacteristic
604C2×C4#39711yescharacteristic
605C2×C4#39812yes—
606C2×C4#39812yes—
607C2×C4#39812yes—
608C2×C4#39812yes—
609C2×C4#39812yes—
610C2×C4#39812yes—
611C2×C4#39812yes—
612C2×C4#39812yes—
613C2×C4#39912yes—
614C2×C4#39912yes—
615C2×C4#39912yes—
616C2×C4#39912yes—
617C2×C4#39912yes—
618C2×C4#39912yes—
619C2×C4#40012yes—
620C2×C4#40012yes—
621C2×C4#40012yes—
622C2×C4#40012yes—
623C2×C4#40012yes—
624C2×C4#40012yes—
625C2×C4C22×C22⋊C411yescharacteristic
626C2×C4C2×#11711yescharacteristic
627C2×C4C2×#11711yescharacteristic
628C2×C4C2×C4×D411yescharacteristic
629C2×C4C2×C4×D411yescharacteristic
630C2×C4C2×C4×Q811yescharacteristic
631C2×C4C2×#12111yescharacteristic
632C2×C4C2×#12111yescharacteristic
633C2×C4C2×C22⋊Q811yescharacteristic
634C2×C4C2×C22⋊Q811yescharacteristic
635C2×C4C2×C22⋊Q811yescharacteristic
636C2×C4C2×C22⋊Q811yescharacteristic
637C2×C4C2×C22⋊Q811yescharacteristic
638C2×C4C2×#12311yescharacteristic
639C2×C4C2×#12311yescharacteristic
640C2×C4C2×#12311yescharacteristic
641C2×C4C2×#12311yescharacteristic
642C2×C4C2×#12311yescharacteristic
643C2×C4C2×#12311yescharacteristic
644C2×C4C2×#12411yescharacteristic
645C2×C4C2×#12511yescharacteristic
646C2×C4C2×#12511yescharacteristic
647C2×C4C2×#12511yescharacteristic
648C2×C4C2×#12511yescharacteristic
649C2×C4C2×#12611yescharacteristic
650C2×C4C2×#12611yescharacteristic
651C2×C4C2×#12711yescharacteristic
652C2×C4C2×C4⋊Q811yescharacteristic
653C8—28no—
654C8—44no—
655C8—44no—
656C8—44no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22#144512yes—
686C22#144512yes—
687C22#144512yes—
688C22#144512yes—
689C22#208112yes—
690C22#208212yes—
691C22C2×#38711yescharacteristic
692C22C2×#38711yescharacteristic
693C22C2×#39111yescharacteristic
694C22C2×#39711yescharacteristic
695C22C2×#39711yescharacteristic
696C22C2×#39911yescharacteristic
697C22C2×#40011yescharacteristic
698C4—84no—
699C4—84no—
700C4—84no—
701C4#144512yes—
702C4#144512yes—
703C4#144512yes—
704C4#144512yes—
705C4C2×#38111yescharacteristic
706C4C2×#38711yescharacteristic
707C4C2×#38711yescharacteristic
708C4C2×#39011yescharacteristic
709C4C2×#39811yescharacteristic
710C4C2×#39811yescharacteristic
711C4C2×#39911yescharacteristic
712C4C2×#40011yescharacteristic
713C2—21no—
714C2—21no—
715C2—21no—
716C2—22no—
717C2—22no—
718C2—22no—
719C2—21no—
720C2—21no—
721C2—21no—
722C2#1136214yesdirect product factor
723C2C2×#144511yescharacteristic
724C2C2×#208111yescharacteristic
725C2C2×#208211yescharacteristic
subgroupG/H
center, socleC23#397
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11362C2direct (N × H)
18. C2×#430C4semidirect
120. #430C2×C4semidirect
722. C2#11362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4302
C22×#3442
C22×#3432
C2×#17362
C22×H(3,ℤ/4)2
#113622