Finite Group Databasebeta

← C2×#11315 #358352

Subgroups — C2×#11315 #358352

Order 512.

2198 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#340C211yesmaximal, characteristic
2C22×#340C211yesmaximal, characteristic
3C22×#340C211yesmaximal, characteristic
4C22×#340C211yesmaximal, characteristic
5C22×#336C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8#11315C218yesmaximal, direct product factor
9C24×C8C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C22×#95—21no—
17C22×#95—21no—
18C22×#95—21no—
19C22×#95—21no—
20C2×#340—24no—
21C2×#340—24no—
22C2×#340—24no—
23C2×#340C418yescomplemented
24C2×#340C2214yes—
25C2×#340C2214yes—
26C2×#340C2214yes—
27C2×#340C2214yes—
28C2×#336—24no—
29C2×#336C2214yes—
30C4⋊#95—22no—
31C4⋊#95—22no—
32C4⋊#95C2214yes—
33C4⋊#95C2214yes—
34C24×C4—21no—
35C24×C4—21no—
36C24×C4—21no—
37C24×C4—21no—
38C24×C4D411yescharacteristic
39C24×C4D411yescharacteristic
40C24×C4C2311yescharacteristic
41C23×C8—22no—
42C23×C8—22no—
43C23×C8—22no—
44C23×C8—22no—
45C23×C8—22no—
46C23×C8—22no—
47C23×C8—22no—
48C23×C8—22no—
49C23×C8—22no—
50C23×C8—22no—
51C23×C8—22no—
52C23×C8—22no—
53C23×C8C2×C414yes—
54C23×C8D414yes—
55C23×C8C2312yes—
56C23×C8C2312yes—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4C2×C414yes—
82C22×C4⋊C4C2×C414yes—
83C22×C4⋊C4D414yes—
84C22×C4⋊C4Q814yes—
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2312yes—
88C22×C4⋊C4C2312yes—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42D412yes—
96C22×C42C2312yes—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—44no—
102C2×#95—44no—
103C2×#95—44no—
104C2×#95—44no—
105#340—28no—
106#340—28no—
107#340—28no—
108#340C2×C4116yescomplemented
109#336—28no—
110C25C2×D411yescharacteristic
111C23×C4—22no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—24no—
124C23×C4—24no—
125C23×C4—24no—
126C23×C4—24no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—42no—
132C23×C4—42no—
133C23×C4—42no—
134C23×C4—42no—
135C23×C4—42no—
136C23×C4—42no—
137C23×C4—42no—
138C23×C4—42no—
139C23×C4—42no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4D814yes—
156C23×C4SD1614yes—
157C23×C4C22×C412yes—
158C23×C4C2×D412yes—
159C23×C4C2×D412yes—
160C23×C4C2×D411yescharacteristic
161C23×C4C2×D412yes—
162C23×C4C2×D412yes—
163C23×C4C2×Q812yes—
164C23×C4#4112yes—
165C23×C4#4112yes—
166C23×C4#4112yes—
167C23×C4#4112yes—
168C23×C4#4112yes—
169C23×C4#4112yes—
170C23×C4#4112yes—
171C23×C4#4112yes—
172C23×C4#4112yes—
173C23×C4#4112yes—
174C23×C4C2411yescharacteristic
175C22×C8—28no—
176C22×C8—28no—
177C22×C8—28no—
178C22×C8—28no—
179C22×C8—28no—
180C22×C8—28no—
181C22×C8—22no—
182C22×C8—22no—
183C22×C8—22no—
184C22×C8—22no—
185C22×C8—22no—
186C22×C8—22no—
187C22×C8—22no—
188C22×C8—22no—
189C22×C8—22no—
190C22×C8—22no—
191C22×C8—22no—
192C22×C8—22no—
193C22×C8—44no—
194C22×C8—44no—
195C22×C8—44no—
196C22×C8—44no—
197C22×C8—44no—
198C22×C8—44no—
199C22×C8—44no—
200C22×C8—44no—
201C22×C8C22×C414yes—
202C22×C8C2×D414yes—
203C2×C4⋊C4—28no—
204C2×C4⋊C4—28no—
205C2×C4⋊C4—28no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—28no—
208C2×C4⋊C4—28no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—44no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—44no—
241C2×C4⋊C4—42no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4C22×C414yes—
252C2×C4⋊C4C22×C414yes—
253C2×C4⋊C4C2×D414yes—
254C2×C4⋊C4C2×Q814yes—
255C2×C42—24no—
256C2×C42—24no—
257C2×C42—24no—
258C2×C42—22no—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42—22no—
264C2×C42—44no—
265C2×C42—44no—
266C2×C42—44no—
267C2×C42—44no—
268#95—48no—
269#95—48no—
270#95—48no—
271#95—48no—
272C24C4×D412yes—
273C24#12112yes—
274C24#12112yes—
275C24C22⋊Q812yes—
276C24#12312yes—
277C24#12312yes—
278C24#12412yes—
279C24C2×D812yes—
280C24C2×SD1612yes—
281C24#13512yes—
282C24#13512yes—
283C24AGL(1,ℤ/8)12yes—
284C24#13712yes—
285C24#13712yes—
286C24#13712yes—
287C24C22×D411yescharacteristic
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—28no—
303C22×C4—28no—
304C22×C4—28no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—44no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—48no—
343C22×C4—48no—
344C22×C4—48no—
345C22×C4—48no—
346C22×C4—48no—
347C22×C4—48no—
348C22×C4—48no—
349C22×C4—48no—
350C22×C4—48no—
351C22×C4—48no—
352C22×C4—48no—
353C22×C4—48no—
354C22×C4—84no—
355C22×C4—84no—
356C22×C4—84no—
357C22×C4—84no—
358C22×C4—84no—
359C22×C4—84no—
360C22×C4—84no—
361C22×C4—84no—
362C22×C4—84no—
363C22×C4—84no—
364C22×C4—84no—
365C22×C4—84no—
366C22×C4—84no—
367C22×C4—84no—
368C22×C4—84no—
369C22×C4—84no—
370C22×C4#11714yes—
371C22×C4#11714yes—
372C22×C4#11714yes—
373C22×C4C4×D414yes—
374C22×C4C4×D414yes—
375C22×C4C4×D412yes—
376C22×C4C4×Q814yes—
377C22×C4#12114yes—
378C22×C4#12112yes—
379C22×C4#12112yes—
380C22×C4C22⋊Q814yes—
381C22×C4C22⋊Q814yes—
382C22×C4C22⋊Q812yes—
383C22×C4#12314yes—
384C22×C4#12314yes—
385C22×C4#12314yes—
386C22×C4#12314yes—
387C22×C4#12312yes—
388C22×C4#12312yes—
389C22×C4#12414yes—
390C22×C4#12414yes—
391C22×C4#12412yes—
392C22×C4#12514yes—
393C22×C4#12514yes—
394C22×C4#12514yes—
395C22×C4#12614yes—
396C22×C4#12614yes—
397C22×C4#12614yes—
398C22×C4#12614yes—
399C22×C4#12614yes—
400C22×C4#12614yes—
401C22×C4#12614yes—
402C22×C4#12614yes—
403C22×C4#12614yes—
404C22×C4#12614yes—
405C22×C4C2×D814yes—
406C22×C4C2×SD1614yes—
407C22×C4C23×C411yescharacteristic
408C22×C4C22×D411yescharacteristic
409C22×C4C22×D411yescharacteristic
410C22×C4C22×Q811yescharacteristic
411C22×C4C2×#4111yescharacteristic
412C22×C4C2×#4111yescharacteristic
413C22×C4C2×#4111yescharacteristic
414C22×C4C2×#4111yescharacteristic
415C22×C4C2×#4111yescharacteristic
416C22×C4C2×#4111yescharacteristic
417C22×C4C2×#4111yescharacteristic
418C22×C4C2×#4111yescharacteristic
419C22×C4C2×#4111yescharacteristic
420C22×C4C2×#4111yescharacteristic
421C2×C8—24no—
422C2×C8—24no—
423C2×C8—24no—
424C2×C8—24no—
425C2×C8—24no—
426C2×C8—24no—
427C2×C8—42no—
428C2×C8—42no—
429C2×C8—42no—
430C2×C8—42no—
431C2×C8—42no—
432C2×C8—42no—
433C2×C8—42no—
434C2×C8—42no—
435C2×C8—416no—
436C2×C8—416no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—48no—
454C4⋊C4—48no—
455C4⋊C4—48no—
456C4⋊C4—48no—
457C42—42no—
458C42—42no—
459C42—42no—
460C42—42no—
461C42—48no—
462C23#38714yes—
463C23#38814yes—
464C23#38814yes—
465C23#39614yes—
466C23#39714yes—
467C23#39714yes—
468C23#40014yes—
469C23C4×D814yes—
470C23C4×SD1614yes—
471C23#44014yes—
472C23#44114yes—
473C23#45914yes—
474C23#46114yes—
475C23#46414yes—
476C23#46414yes—
477C23#46514yes—
478C23#46614yes—
479C23#46814yes—
480C23#47014yes—
481C23#47414yes—
482C23#47514yes—
483C23#47814yes—
484C23#47914yes—
485C23#48014yes—
486C23#48014yes—
487C23#48114yes—
488C23#48214yes—
489C23#48314yes—
490C23#48514yes—
491C23#48514yes—
492C23#48514yes—
493C23#48614yes—
494C23#48814yes—
495C23#48914yes—
496C23#49114yes—
497C23C2×C4×D411yescharacteristic
498C23C2×#12111yescharacteristic
499C23C2×#12111yescharacteristic
500C23C2×C22⋊Q811yescharacteristic
501C23C2×#12311yescharacteristic
502C23C2×#12311yescharacteristic
503C23C2×#12411yescharacteristic
504C23C22×D811yescharacteristic
505C23C22×SD1611yescharacteristic
506C23C2×#13511yescharacteristic
507C23C2×#13511yescharacteristic
508C23C2×AGL(1,ℤ/8)11yescharacteristic
509C23C2×#13711yescharacteristic
510C23C2×#13711yescharacteristic
511C23C2×#13711yescharacteristic
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—416no—
523C2×C4—416no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—816no—
545C2×C4—816no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—816no—
551C2×C4—816no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4#38318yes—
561C2×C4#38714yes—
562C2×C4#38718yes—
563C2×C4#38718yes—
564C2×C4#38814yes—
565C2×C4#38814yes—
566C2×C4#38818yes—
567C2×C4#39614yes—
568C2×C4#39718yes—
569C2×C4#39714yes—
570C2×C4#39714yes—
571C2×C4#40018yes—
572C2×C4#40018yes—
573C2×C4#40014yes—
574C2×C4#40118yes—
575C2×C4C2×#11711yescharacteristic
576C2×C4C2×#11711yescharacteristic
577C2×C4C2×#11711yescharacteristic
578C2×C4C2×C4×D411yescharacteristic
579C2×C4C2×C4×D411yescharacteristic
580C2×C4C2×C4×Q811yescharacteristic
581C2×C4C2×#12111yescharacteristic
582C2×C4C2×C22⋊Q811yescharacteristic
583C2×C4C2×C22⋊Q811yescharacteristic
584C2×C4C2×#12311yescharacteristic
585C2×C4C2×#12311yescharacteristic
586C2×C4C2×#12311yescharacteristic
587C2×C4C2×#12311yescharacteristic
588C2×C4C2×#12411yescharacteristic
589C2×C4C2×#12411yescharacteristic
590C2×C4C2×#12511yescharacteristic
591C2×C4C2×#12511yescharacteristic
592C2×C4C2×#12511yescharacteristic
593C2×C4C2×#12611yescharacteristic
594C2×C4C2×#12611yescharacteristic
595C2×C4C2×#12611yescharacteristic
596C2×C4C2×#12611yescharacteristic
597C2×C4C2×#12611yescharacteristic
598C2×C4C2×#12611yescharacteristic
599C2×C4C2×#12611yescharacteristic
600C2×C4C2×#12611yescharacteristic
601C2×C4C2×#12611yescharacteristic
602C2×C4C2×#12611yescharacteristic
603C8—44no—
604C8—44no—
605C22#144318yes—
606C22#191818yes—
607C22#191918yes—
608C22#192518yes—
609C22#192718yes—
610C22#193418yes—
611C22#193518yes—
612C22#206618yes—
613C22#206718yes—
614C22#207118yes—
615C22#207418yes—
616C22#207518yes—
617C22#207718yes—
618C22#209918yes—
619C22#210118yes—
620C22C2×#38711yescharacteristic
621C22C2×#38811yescharacteristic
622C22C2×#38811yescharacteristic
623C22C2×#39611yescharacteristic
624C22C2×#39711yescharacteristic
625C22C2×#39711yescharacteristic
626C22C2×#40011yescharacteristic
627C22C2×C4×D811yescharacteristic
628C22C2×C4×SD1611yescharacteristic
629C22C2×#44011yescharacteristic
630C22C2×#44111yescharacteristic
631C22C2×#45911yescharacteristic
632C22C2×#46111yescharacteristic
633C22C2×#46411yescharacteristic
634C22C2×#46411yescharacteristic
635C22C2×#46511yescharacteristic
636C22C2×#46611yescharacteristic
637C22C2×#46811yescharacteristic
638C22C2×#47011yescharacteristic
639C22C2×#47411yescharacteristic
640C22C2×#47811yescharacteristic
641C22C2×#47511yescharacteristic
642C22C2×#47911yescharacteristic
643C22C2×#48011yescharacteristic
644C22C2×#48011yescharacteristic
645C22C2×#48311yescharacteristic
646C22C2×#48211yescharacteristic
647C22C2×#48511yescharacteristic
648C22C2×#48511yescharacteristic
649C22C2×#48511yescharacteristic
650C22C2×#48111yescharacteristic
651C22C2×#48611yescharacteristic
652C22C2×#48811yescharacteristic
653C22C2×#48911yescharacteristic
654C22C2×#49111yescharacteristic
655C4—44no—
656C4—44no—
657C4—84no—
658C4—84no—
659C4—84no—
660C4—84no—
661C4#144318yes—
662C4C2×#38311yescharacteristic
663C4C2×#38711yescharacteristic
664C4C2×#38711yescharacteristic
665C4C2×#38811yescharacteristic
666C4C2×#39711yescharacteristic
667C4C2×#40011yescharacteristic
668C4C2×#40011yescharacteristic
669C4C2×#40111yescharacteristic
670C2#11315116yesdirect product factor
671C2C2×#144311yescharacteristic
672C2C2×#191811yescharacteristic
673C2C2×#191911yescharacteristic
674C2C2×#192511yescharacteristic
675C2C2×#192711yescharacteristic
676C2C2×#193411yescharacteristic
677C2C2×#193511yescharacteristic
678C2C2×#206711yescharacteristic
679C2C2×#206611yescharacteristic
680C2C2×#207111yescharacteristic
681C2C2×#207411yescharacteristic
682C2C2×#207511yescharacteristic
683C2C2×#207711yescharacteristic
684C2C2×#209911yescharacteristic
685C2C2×#210111yescharacteristic
subgroupG/H
center, socle, prime radicalC25C2×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11315C2direct (N × H)
23. C2×#340C4semidirect
108. #340C2×C4semidirect
670. C2#11315direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3402
C22×#3362
C2×C4⋊#952
#113152