Finite Group Databasebeta

← C2×#11203 #357980

Subgroups — C2×#11203 #357980

Order 512.

3854 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#385C211yesmaximal, characteristic
2C22×#380C211yesmaximal, characteristic
3C22×#342C212yesmaximal
4C22×#342C212yesmaximal
5C2×C22⋊#95C211yesmaximal, characteristic
6#11203C218yesmaximal, direct product factor
7C25×C4C2211yescharacteristic
8C23×C4⋊C4—21no—
9C23×C4⋊C4C412yescomplemented
10C23×C22⋊C4C2211yescharacteristic
11C23×C22⋊C4C2212yes—
12C23×C22⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C2×#385—21no—
15C2×#385—22no—
16C2×#385—22no—
17C2×#385—21no—
18C2×#385—22no—
19C2×#385C414yescomplemented
20C2×#385C2214yes—
21C2×#380—22no—
22C2×#380—28no—
23C2×#380C2214yes—
24C22×#95—21no—
25C22×#95—22no—
26C22×#95C412yescomplemented
27C2×#342—28no—
28C2×#342—28no—
29C2×#342C2218yes—
30C2×#342C2218yes—
31C22⋊#95—22no—
32C22⋊#95C2214yes—
33C26C2311yescharacteristic
34C24×C4—24no—
35C24×C4—24no—
36C24×C4—22no—
37C24×C4—22no—
38C24×C4—48no—
39C24×C4C2×C412yes—
40C24×C4C2×C411yescharacteristic
41C24×C4C2×C411yescharacteristic
42C24×C4C2×C412yes—
43C24×C4C2×C412yes—
44C24×C4D411yescharacteristic
45C24×C4D412yes—
46C24×C4D412yes—
47C24×C4D411yescharacteristic
48C24×C4D412yes—
49C24×C4C2312yes—
50C22×C4⋊C4—28no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—48no—
56C22×C4⋊C4—48no—
57C22×C4⋊C4C2×C418yescomplemented
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—24no—
65C22×C22⋊C4—24no—
66C22×C22⋊C4—24no—
67C22×C22⋊C4—24no—
68C22×C22⋊C4—24no—
69C22×C22⋊C4—24no—
70C22×C22⋊C4—24no—
71C22×C22⋊C4—24no—
72C22×C22⋊C4—22no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—21no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4—24no—
81C22×C22⋊C4—24no—
82C22×C22⋊C4C2×C412yes—
83C22×C22⋊C4C2×C412yes—
84C22×C22⋊C4D418yes—
85C22×C22⋊C4D414yes—
86C22×C22⋊C4Q818yes—
87C22×C22⋊C4Q814yes—
88C22×C22⋊C4C2312yes—
89C22×C22⋊C4C2314yes—
90C22×C22⋊C4C2314yes—
91C22×C22⋊C4C2312yes—
92#385—24no—
93#385—28no—
94#385—24no—
95#385—24no—
96#385—28no—
97#385—24no—
98#380—216no—
99#380—216no—
100C2×#95—28no—
101C2×#95—24no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—24no—
105C2×#95—28no—
106C2×#95—48no—
107C2×#95C2×C418yescomplemented
108#342—216no—
109#342—216no—
110C25—44no—
111C25—44no—
112C25C22×C411yescharacteristic
113C25C22×C411yescharacteristic
114C25C2×D411yescharacteristic
115C25C2×D411yescharacteristic
116C25C2×D411yescharacteristic
117C25C2×D411yescharacteristic
118C25C2×D412yes—
119C25C2×D414yes—
120C25C2×Q812yes—
121C25C2×Q814yes—
122C25#4112yes—
123C25#4112yes—
124C25#4114yes—
125C25#4114yes—
126C25C2411yescharacteristic
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—28no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—24no—
133C23×C4—28no—
134C23×C4—28no—
135C23×C4—22no—
136C23×C4—24no—
137C23×C4—28no—
138C23×C4—28no—
139C23×C4—24no—
140C23×C4—22no—
141C23×C4—24no—
142C23×C4—24no—
143C23×C4—28no—
144C23×C4—28no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—28no—
150C23×C4—28no—
151C23×C4—24no—
152C23×C4—24no—
153C23×C4—24no—
154C23×C4—24no—
155C23×C4—48no—
156C23×C4—48no—
157C23×C4—48no—
158C23×C4—48no—
159C23×C4—44no—
160C23×C4—44no—
161C23×C4—44no—
162C23×C4—432no—
163C23×C4—432no—
164C23×C4—44no—
165C23×C4—44no—
166C23×C4—48no—
167C23×C4—48no—
168C23×C4—48no—
169C23×C4—48no—
170C23×C4—44no—
171C23×C4—44no—
172C23×C4—44no—
173C23×C4—44no—
174C23×C4—44no—
175C23×C4—44no—
176C23×C4C22⋊C412yes—
177C23×C4C22⋊C412yes—
178C23×C4C22⋊C414yes—
179C23×C4C22⋊C414yes—
180C23×C4C22⋊C412yes—
181C23×C4C22⋊C412yes—
182C23×C4C4⋊C418yescomplemented
183C23×C4C22×C414yes—
184C23×C4C22×C412yes—
185C23×C4C22×C412yes—
186C23×C4C22×C414yes—
187C23×C4C2×D412yes—
188C23×C4C2×D414yes—
189C23×C4C2×D412yes—
190C2×C4⋊C4—216no—
191C2×C4⋊C4—28no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4—432no—
194C2×C4⋊C4—416no—
195C2×C4⋊C4—48no—
196C2×C4⋊C4—416no—
197C2×C4⋊C4—48no—
198C2×C4⋊C4—416no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—24no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—216no—
215C2×C22⋊C4—216no—
216C2×C22⋊C4—216no—
217C2×C22⋊C4—216no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—24no—
220C2×C22⋊C4—24no—
221C2×C22⋊C4—24no—
222C2×C22⋊C4—24no—
223C2×C22⋊C4—24no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—28no—
229C2×C22⋊C4—28no—
230C2×C22⋊C4—28no—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—42no—
238C2×C22⋊C4—42no—
239C2×C22⋊C4—44no—
240C2×C22⋊C4—44no—
241C2×C22⋊C4—48no—
242C2×C22⋊C4—48no—
243C2×C22⋊C4—44no—
244C2×C22⋊C4—44no—
245C2×C22⋊C4—44no—
246C2×C22⋊C4—42no—
247C2×C22⋊C4—42no—
248C2×C22⋊C4—48no—
249C2×C22⋊C4—44no—
250C2×C22⋊C4—48no—
251C2×C22⋊C4C4⋊C418yescomplemented
252C2×C22⋊C4C2×D418yes—
253C2×C22⋊C4C2×D414yes—
254C2×C22⋊C4C2×Q818yes—
255C2×C22⋊C4C2×Q814yes—
256#95—216no—
257#95—28no—
258#95—28no—
259#95—416no—
260C24—24no—
261C24—24no—
262C24—24no—
263C24—24no—
264C24—24no—
265C24—24no—
266C24—42no—
267C24—42no—
268C24—42no—
269C24—48no—
270C24—48no—
271C24—42no—
272C24—42no—
273C24—48no—
274C24—42no—
275C24—42no—
276C24—48no—
277C24—48no—
278C24—416no—
279C24—48no—
280C24—48no—
281C24—48no—
282C24—416no—
283C24—42no—
284C24C2×C22⋊C411yescharacteristic
285C24C2×C22⋊C411yescharacteristic
286C24C2×C22⋊C411yescharacteristic
287C24C2×C22⋊C411yescharacteristic
288C24C2×C4⋊C412yes—
289C24C2×C4⋊C412yes—
290C24#11712yes—
291C24#11712yes—
292C24C4×D414yes—
293C24C4×D414yes—
294C24C4×Q814yes—
295C24C4×Q814yes—
296C24#12012yes—
297C24#12012yes—
298C24#12112yes—
299C24#12112yes—
300C24#12114yes—
301C24#12112yes—
302C24#12112yes—
303C24#12114yes—
304C24#12118yes—
305C24C22⋊Q812yes—
306C24C22⋊Q812yes—
307C24C22⋊Q814yes—
308C24C22⋊Q812yes—
309C24C22⋊Q812yes—
310C24C22⋊Q818yes—
311C24C22⋊Q818yes—
312C24C22⋊Q814yes—
313C24#12312yes—
314C24#12312yes—
315C24#12318yes—
316C24#12412yes—
317C24#12412yes—
318C24#12518yes—
319C24#12518yes—
320C24#12618yes—
321C24C4⋊Q812yes—
322C24C4⋊Q818yes—
323C24C4⋊Q812yes—
324C24C23×C411yescharacteristic
325C24C22×D411yescharacteristic
326C24C22×D411yescharacteristic
327C24C22×D411yescharacteristic
328C24C22×D412yes—
329C24C22×Q811yescharacteristic
330C24C22×Q812yes—
331C24C2×#4111yescharacteristic
332C24C2×#4111yescharacteristic
333C24C2×#4112yes—
334C24C2×#4112yes—
335C22×C4—216no—
336C22×C4—216no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—28no—
343C22×C4—28no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—28no—
347C22×C4—22no—
348C22×C4—28no—
349C22×C4—22no—
350C22×C4—28no—
351C22×C4—28no—
352C22×C4—28no—
353C22×C4—28no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—28no—
365C22×C4—28no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—44no—
374C22×C4—432no—
375C22×C4—432no—
376C22×C4—416no—
377C22×C4—416no—
378C22×C4—432no—
379C22×C4—432no—
380C22×C4—416no—
381C22×C4—416no—
382C22×C4—44no—
383C22×C4—416no—
384C22×C4—44no—
385C22×C4—48no—
386C22×C4—48no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—416no—
391C22×C4—44no—
392C22×C4—48no—
393C22×C4—48no—
394C22×C4—416no—
395C22×C4—44no—
396C22×C4—48no—
397C22×C4—48no—
398C22×C4—416no—
399C22×C4—432no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—416no—
410C22×C4—416no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—816no—
416C22×C4—816no—
417C22×C4—88no—
418C22×C4—88no—
419C22×C4—816no—
420C22×C4—88no—
421C22×C4—88no—
422C22×C4#9918yes—
423C22×C4C2×C22⋊C414yes—
424C22×C4C2×C22⋊C414yes—
425C22×C4C2×C4⋊C418yescomplemented
426C4⋊C4—432no—
427C4⋊C4—416no—
428C4⋊C4—416no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—28no—
437C22⋊C4—28no—
438C22⋊C4—28no—
439C22⋊C4—42no—
440C22⋊C4—44no—
441C22⋊C4—44no—
442C22⋊C4—44no—
443C22⋊C4—44no—
444C22⋊C4—42no—
445C22⋊C4—44no—
446C22⋊C4—44no—
447C22⋊C4—44no—
448C22⋊C4—416no—
449C22⋊C4—416no—
450C23—28no—
451C23—28no—
452C23—28no—
453C23—28no—
454C23—28no—
455C23—28no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—28no—
471C23—28no—
472C23—24no—
473C23—28no—
474C23—28no—
475C23—24no—
476C23—216no—
477C23—28no—
478C23—216no—
479C23—28no—
480C23—44no—
481C23—42no—
482C23—44no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—48no—
490C23—42no—
491C23—44no—
492C23—44no—
493C23—416no—
494C23—44no—
495C23—48no—
496C23—44no—
497C23—44no—
498C23—416no—
499C23—416no—
500C23—416no—
501C23—42no—
502C23—44no—
503C23—416no—
504C23—416no—
505C23—416no—
506C23—44no—
507C23—416no—
508C23—42no—
509C23—42no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23#38012yes—
517C23#38012yes—
518C23#38012yes—
519C23#38012yes—
520C23#38612yes—
521C23#38612yes—
522C23#38612yes—
523C23#38612yes—
524C23#38718yes—
525C23#38718yes—
526C23#38918yes—
527C23#38918yes—
528C23#39112yes—
529C23#39112yes—
530C23#39112yes—
531C23#39112yes—
532C23#39414yes—
533C23#39414yes—
534C23#39514yes—
535C23#39514yes—
536C23#39618yes—
537C23#39618yes—
538C23#39814yes—
539C23#39818yes—
540C23#39814yes—
541C23#39818yes—
542C23#40014yes—
543C23#40014yes—
544C23C2×#9914yes—
545C23#41014yes—
546C23C22×C22⋊C411yescharacteristic
547C23C22×C4⋊C411yescharacteristic
548C23C2×#11711yescharacteristic
549C23C2×C4×D412yes—
550C23C2×C4×Q812yes—
551C23C2×#12011yescharacteristic
552C23C2×#12111yescharacteristic
553C23C2×#12111yescharacteristic
554C23C2×#12112yes—
555C23C2×#12112yes—
556C23C2×C22⋊Q811yescharacteristic
557C23C2×C22⋊Q812yes—
558C23C2×C22⋊Q811yescharacteristic
559C23C2×C22⋊Q812yes—
560C23C2×C22⋊Q812yes—
561C23C2×#12311yescharacteristic
562C23C2×#12312yes—
563C23C2×#12411yescharacteristic
564C23C2×#12512yes—
565C23C2×#12512yes—
566C23C2×#12612yes—
567C23C2×C4⋊Q811yescharacteristic
568C23C2×C4⋊Q812yes—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—216no—
572C2×C4—24no—
573C2×C4—216no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—28no—
578C2×C4—24no—
579C2×C4—416no—
580C2×C4—416no—
581C2×C4—416no—
582C2×C4—416no—
583C2×C4—48no—
584C2×C4—416no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—48no—
588C2×C4—416no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—48no—
592C2×C4—48no—
593C2×C4—48no—
594C2×C4—416no—
595C2×C4—48no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—48no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—88no—
603C2×C4—88no—
604C2×C4—88no—
605C2×C4—832no—
606C2×C4—832no—
607C2×C4—84no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4—84no—
613C2×C4—84no—
614C2×C4—84no—
615C2×C4C2×#9918yes—
616C22—24no—
617C22—22no—
618C22—24no—
619C22—22no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—22no—
624C22—22no—
625C22—24no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—24no—
631C22—24no—
632C22—28no—
633C22—216no—
634C22—216no—
635C22—216no—
636C22—28no—
637C22—28no—
638C22—216no—
639C22—28no—
640C22—21no—
641C22—21no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—21no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—21no—
652C22—22no—
653C22—22no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—48no—
663C22—48no—
664C22—44no—
665C22—44no—
666C22—48no—
667C22—48no—
668C22—44no—
669C22—44no—
670C22#144114yes—
671C22#144114yes—
672C22#144114yes—
673C22#144114yes—
674C22#179918yes—
675C22#189814yes—
676C22#189914yes—
677C22#199618yes—
678C22C2×#38011yescharacteristic
679C22C2×#38611yescharacteristic
680C22C2×#38712yes—
681C22C2×#38912yes—
682C22C2×#39111yescharacteristic
683C22C2×#39411yescharacteristic
684C22C2×#39511yescharacteristic
685C22C2×#39612yes—
686C22C2×#39811yescharacteristic
687C22C2×#39812yes—
688C22C2×#40011yescharacteristic
689C22C22×#9912yes—
690C22C2×#41012yes—
691C4—28no—
692C4—48no—
693C4—44no—
694C4—88no—
695C4—88no—
696C4—82no—
697C4—82no—
698C2—21no—
699C2—22no—
700C2—21no—
701C2—22no—
702C2—21no—
703C2—21no—
704C2—24no—
705C2—24no—
706C2—24no—
707C2—22no—
708C2—22no—
709C2#1120318yesdirect product factor
710C2C2×#144111yescharacteristic
711C2C2×#179912yes—
712C2C2×#189811yescharacteristic
713C2C2×#189911yescharacteristic
714C2C2×#199612yes—
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC25C24
prime radicalC26C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #11203C2direct (N × H)
9. C23×C4⋊C4C4semidirect
19. C2×#385C4semidirect
26. C22×#95C4semidirect
57. C22×C4⋊C4C2×C4semidirect
107. C2×#95C2×C4semidirect
182. C23×C4C4⋊C4semidirect
251. C2×C22⋊C4C4⋊C4semidirect
425. C22×C4C2×C4⋊C4semidirect
709. C2#11203direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3852
C22×#3802
C22×#3422
C2×C22⋊#952
#112032