Finite Group Databasebeta

← C2×#11473 #480091

Subgroups — C2×#11473 #480091

Order 512.

1612 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2321C211yesmaximal, characteristic
2C2×#1460C211yesmaximal, characteristic, complemented
3C2×#1459C211yesmaximal, characteristic, complemented
4#11473C218yesmaximal, direct product factor
5C2×#1326C212yesmaximal, complemented
6C2×#1316C212yesmaximal, complemented
7C22×#120C411yescharacteristic
8C22×C4×D4C2211yescharacteristic
9C23×C22⋊C4C411yescharacteristic
10C2×#431—21no—
11C22×C22⋊C8—21no—
12#2321—22no—
13#2321—22no—
14#2321C414yes—
15#2321C2214yes—
16C2×#390—21no—
17C2×#388—21no—
18C2×#388—21no—
19C2×#386—21no—
20C2×#386C411yescharacteristic
21C2×#385C2211yescharacteristic
22C2×#379C2211yescharacteristic
23C2×C4×C22⋊C4C411yescharacteristic
24#1460—22no—
25#1460C2214yescomplemented
26#1459—22no—
27#1459C2214yescomplemented
28C2×#324—21no—
29C2×#323—21no—
30C2×#323C2212yes—
31C2×#323C2212yes—
32#1326C2218yescomplemented
33#1316C2218yescomplemented
34C26C2×C411yescharacteristic
35C23×D4—21no—
36C23×D4C2×C411yescharacteristic
37C24×C4C2×C411yescharacteristic
38C24×C4C2×C411yescharacteristic
39C24×C4D411yescharacteristic
40C23×C8—41no—
41C2×#120—22no—
42C2×#120—24no—
43C2×#120C818yescomplemented
44C2×#120C2×C414yes—
45C2×C4×D4—41no—
46C2×C4×D4—41no—
47C2×C4×D4—42no—
48C2×C4×D4C2×C412yes—
49C2×C4×D4D412yes—
50C2×C4×D4D412yes—
51C2×C4×D4C2312yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4D411yescharacteristic
54C22×C22⋊C4—21no—
55C22×C22⋊C4—22no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—42no—
62C22×C22⋊C4—41no—
63C22×C22⋊C4—41no—
64C22×C22⋊C4C2×C411yescharacteristic
65C22×C22⋊C4C2×C414yes—
66C22×C22⋊C4C2×C411yescharacteristic
67C22×C22⋊C4D411yescharacteristic
68C22×C22⋊C4C2311yescharacteristic
69C22×C42—21no—
70C22×C42D411yescharacteristic
71#431—24no—
72#431—42no—
73C2×C4⋊C8—41no—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—24no—
76C2×C22⋊C8—22no—
77C2×C22⋊C8—42no—
78C2×C22⋊C8—41no—
79C2×C4×C8—41no—
80#390—24no—
81#390—24no—
82#388—24no—
83#388—24no—
84#388—24no—
85#388—24no—
86#386—22no—
87#386—24no—
88#386—24no—
89#386C2×C414yes—
90#385—21no—
91#385—21no—
92#385C2×C412yes—
93#385C2312yes—
94#379—21no—
95#379—21no—
96#379C2×C412yes—
97#379C2312yes—
98C4×C22⋊C4—22no—
99C4×C22⋊C4C2×C414yes—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103#324—24no—
104#323—24no—
105#323—22no—
106#323—22no—
107#323C2314yes—
108#323C2314yes—
109C25—21no—
110C25—21no—
111C25—22no—
112C25—41no—
113C25—41no—
114C25—42no—
115C25—82no—
116C25—82no—
117C25C22⋊C411yescharacteristic
118C25C2×C814yescomplemented
119C25C22×C411yescharacteristic
120C25C22×C412yes—
121C22×D4—28no—
122C22×D4—24no—
123C22×D4—41no—
124C22×D4—41no—
125C22×D4—42no—
126C22×D4—82no—
127C22×D4—82no—
128C22×D4C22⋊C412yes—
129C22×D4C2×C814yes—
130C22×D4M1614yes—
131C22×D4C22×C412yes—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—41no—
143C23×C4—41no—
144C23×C4—82no—
145C23×C4—82no—
146C23×C4—82no—
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22⋊C411yescharacteristic
149C23×C4C22⋊C412yes—
150C23×C4C22⋊C412yes—
151C23×C4C22⋊C411yescharacteristic
152C23×C4C22×C412yes—
153C23×C4C22×C412yes—
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D412yes—
157C22×C8—42no—
158C22×C8—44no—
159C22×C8—42no—
160C22×C8—84no—
161#120—216no—
162#120—28no—
163#120C2×C8116yescomplemented
164C4×D4—42no—
165C4×D4—42no—
166C4×D4—42no—
167C4×D4—42no—
168C4×D4—42no—
169C4×D4—42no—
170C4×D4—42no—
171C4×D4—42no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C2×D412yes—
179C2×C22⋊C4—21no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—28no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—42no—
197C2×C22⋊C4—44no—
198C2×C22⋊C4—44no—
199C2×C22⋊C4—42no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4—44no—
205C2×C22⋊C4—82no—
206C2×C22⋊C4—82no—
207C2×C22⋊C4—82no—
208C2×C22⋊C4C22⋊C412yes—
209C2×C22⋊C4C2×C814yescomplemented
210C2×C22⋊C4C22×C412yes—
211C2×C22⋊C4C22×C412yes—
212C2×C22⋊C4C22×C411yescharacteristic
213C2×C22⋊C4C2×D412yes—
214C2×C22⋊C4C2×D411yescharacteristic
215C2×C22⋊C4C2×D411yescharacteristic
216C2×C22⋊C4C2411yescharacteristic
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—22no—
220C2×C42—24no—
221C2×C42—82no—
222C2×C42C22⋊C412yes—
223C2×C42C2×D412yes—
224C4⋊C8—44no—
225C22⋊C8—24no—
226C22⋊C8—24no—
227C22⋊C8—42no—
228C22⋊C8—44no—
229C22⋊C8—42no—
230C4×C8—44no—
231#95—24no—
232#95—22no—
233#95—24no—
234#95—22no—
235C24—21no—
236C24—21no—
237C24—21no—
238C24—22no—
239C24—21no—
240C24—22no—
241C24—22no—
242C24—24no—
243C24—22no—
244C24—24no—
245C24—42no—
246C24—42no—
247C24—42no—
248C24—42no—
249C24—42no—
250C24—42no—
251C24—42no—
252C24—42no—
253C24—42no—
254C24—42no—
255C24—44no—
256C24—44no—
257C24—42no—
258C24—44no—
259C24—44no—
260C24—42no—
261C24—41no—
262C24—41no—
263C24—42no—
264C24—88no—
265C24—82no—
266C24—82no—
267C24—82no—
268C24—82no—
269C24—88no—
270C24—84no—
271C24—84no—
272C24—84no—
273C24—84no—
274C24—816no—
275C24C22⋊C814yes—
276C24C2×C22⋊C411yescharacteristic
277C24C2×C22⋊C412yes—
278C24C2×C22⋊C411yescharacteristic
279C24C22×C812yes—
280C24C22×C814yescomplemented
281C24C2×M1612yes—
282C24C23×C411yescharacteristic
283C2×D4—216no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—44no—
288C2×D4—44no—
289C2×D4—44no—
290C2×D4—44no—
291C2×D4—42no—
292C2×D4—84no—
293C2×D4—84no—
294C2×D4—816no—
295C2×D4C22⋊C818yes—
296C2×D4C22×C814yes—
297C2×D4C2×M1614yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—44no—
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—41no—
332C22×C4—41no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—82no—
336C22×C4—82no—
337C22×C4—82no—
338C22×C4—82no—
339C22×C4—82no—
340C22×C4—84no—
341C22×C4—84no—
342C22×C4—82no—
343C22×C4—82no—
344C22×C4—82no—
345C22×C4—82no—
346C22×C4—84no—
347C22×C4—84no—
348C22×C4C22⋊C814yes—
349C22×C4#9911yescharacteristic
350C22×C4#9911yescharacteristic
351C22×C4#9912yes—
352C22×C4C2×C22⋊C412yes—
353C22×C4C2×C22⋊C411yescharacteristic
354C22×C4C2×C22⋊C412yes—
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C412yes—
357C22×C4C22×D411yescharacteristic
358C22×C4C22×D411yescharacteristic
359C2×C8—44no—
360C2×C8—44no—
361C2×C8—84no—
362C2×C8—88no—
363C2×C8—84no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—82no—
367C4⋊C4—82no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—216no—
371C22⋊C4—42no—
372C22⋊C4—41no—
373C22⋊C4—42no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—48no—
378C22⋊C4—42no—
379C22⋊C4—44no—
380C22⋊C4—44no—
381C22⋊C4—42no—
382C22⋊C4—82no—
383C22⋊C4—82no—
384C22⋊C4—82no—
385C22⋊C4—82no—
386C22⋊C4—84no—
387C22⋊C4C22×C814yescomplemented
388C42—22no—
389C42—22no—
390C42—22no—
391C42—22no—
392C42—84no—
393C23—22no—
394C23—22no—
395C23—21no—
396C23—21no—
397C23—22no—
398C23—21no—
399C23—21no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—22no—
406C23—24no—
407C23—24no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—44no—
413C23—44no—
414C23—42no—
415C23—42no—
416C23—48no—
417C23—42no—
418C23—42no—
419C23—48no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—48no—
425C23—44no—
426C23—48no—
427C23—48no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—44no—
436C23—44no—
437C23—81no—
438C23—81no—
439C23—84no—
440C23—82no—
441C23—82no—
442C23—84no—
443C23—84no—
444C23—84no—
445C23—84no—
446C23—88no—
447C23—84no—
448C23—84no—
449C23—816no—
450C23—816no—
451C23—88no—
452C23—88no—
453C23—816no—
454C23—84no—
455C23—84no—
456C23—816no—
457C23—82no—
458C23—82no—
459C23C2×C22⋊C812yes—
460C23C2×C22⋊C812yes—
461C23C2×C22⋊C814yes—
462C23C2×#9911yescharacteristic
463C23C2×#9911yescharacteristic
464C23#41312yes—
465C23C22×C22⋊C411yescharacteristic
466C23C23×C811yescharacteristic
467C23C22×M1611yescharacteristic
468D4—48no—
469D4—44no—
470D4—44no—
471D4—816no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4—84no—
515C2×C4—82no—
516C2×C4—84no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4C2×C22⋊C814yes—
520C2×C4C2×#9912yes—
521C2×C4C2×#9912yes—
522C8—84no—
523C8—84no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—24no—
529C22—24no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—24no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—42no—
550C22—44no—
551C22—44no—
552C22—48no—
553C22—44no—
554C22—82no—
555C22—84no—
556C22—82no—
557C22—82no—
558C22—88no—
559C22—88no—
560C22—88no—
561C22—816no—
562C22—82no—
563C22—82no—
564C22—88no—
565C22#145912yes—
566C22#145912yes—
567C22#212112yes—
568C22#212212yes—
569C22C22×C22⋊C811yescharacteristic
570C22C22×#9911yescharacteristic
571C22C2×#41311yescharacteristic
572C4—22no—
573C4—22no—
574C4—24no—
575C4—44no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—82no—
582C4—82no—
583C2—21no—
584C2—21no—
585C2—22no—
586C2—41no—
587C2—41no—
588C2—42no—
589C2—44no—
590C2—84no—
591C2#1147314yesdirect product factor
592C2C2×#145911yescharacteristic
593C2C2×#212111yescharacteristic
594C2C2×#212211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23C23×C8
Frattini, cosocleC2×C22⋊C4C24
prime radicalC22×#120C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1460C2semidirect
3. C2×#1459C2semidirect
4. #11473C2direct (N × H)
5. C2×#1326C2semidirect
6. C2×#1316C2semidirect
25. #1460C22semidirect
27. #1459C22semidirect
32. #1326C22semidirect
33. #1316C22semidirect
43. C2×#120C8semidirect
118. C25C2×C8semidirect
163. #120C2×C8semidirect
209. C2×C22⋊C4C2×C8semidirect
280. C24C22×C8semidirect
387. C22⋊C4C22×C8semidirect
591. C2#11473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23212
C2×#14602
C2×#14592
#114732
C2×#13262
C2×#13162