Finite Group Databasebeta

← C2×#9529 #202061

Subgroups — C2×#9529 #202061

Order 512.

1286 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3109C211yesmaximal, characteristic
2C2×#2981C211yesmaximal, characteristic, complemented
3C2×#1557C211yesmaximal, characteristic, complemented
4C2×#1486C211yesmaximal, characteristic, complemented
5C2×#1466C211yesmaximal, characteristic, complemented
6#9529C218yesmaximal, direct product factor
7C2×#1307C211yesmaximal, characteristic, complemented
8C2×#1287C211yesmaximal, characteristic, complemented
9C2×#532C2211yescharacteristic
10C22×C4×D4C2211yescharacteristic
11#3109—22no—
12#3109—22no—
13#3109C414yes—
14#3109C2214yes—
15C2×#481C412yes—
16C2×#476—21no—
17C2×#459—21no—
18C2×#447C412yes—
19#2981—22no—
20#2981—22no—
21#2981—22no—
22#2981C2214yescomplemented
23C2×#442—22no—
24C2×#436—21no—
25C2×#435—22no—
26C2×C8×D4—21no—
27C2×#432C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#432C2211yescharacteristic
30C2×#431C2211yescharacteristic
31C2×#423C2211yescharacteristic
32C2×#408—22no—
33#1557—22no—
34#1557C2214yescomplemented
35C2×#332—21no—
36C2×#331—21no—
37#1486—22no—
38#1486C2214yescomplemented
39C2×D4⋊C8—21no—
40C2×D4⋊C8—21no—
41#1466—22no—
42#1466C2214yescomplemented
43C2×#323—22no—
44#1307C2214yescomplemented
45#1287C2214yescomplemented
46C22×#41—21no—
47C23×D4C2×C411yescharacteristic
48C24×C4—21no—
49C22×D8—22no—
50C22×M16—22no—
51C22×M16—21no—
52C23×C8—22no—
53#532—21no—
54#532—21no—
55#532—21no—
56#532—21no—
57#532C2×C412yes—
58#532D412yes—
59#532D412yes—
60#532C2312yes—
61C2×C4⋊Q8D411yescharacteristic
62C2×#127D411yescharacteristic
63C2×#124—21no—
64C2×#121—21no—
65C2×#121C2×C412yes—
66C2×C4×D4—21no—
67C2×C4×D4—21no—
68C2×C4×D4—21no—
69C2×C4×D4—21no—
70C2×C4×D4—21no—
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—21no—
75C2×C4×D4—21no—
76C2×C4×D4—21no—
77C2×C4×D4C2×C412yes—
78C2×C4×D4D412yes—
79C2×C4×D4C2312yes—
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C22⋊C4—21no—
82C22×C42C2311yescharacteristic
83#481—24no—
84#481C2×C418yes—
85#476—24no—
86#476—24no—
87#459—24no—
88#459—24no—
89#447—24no—
90#447C2×C418yes—
91#442—28no—
92#442—28no—
93#436—24no—
94#436—24no—
95#435—28no—
96#435—28no—
97C8×D4—24no—
98C8×D4—24no—
99#432—21no—
100#432—21no—
101#432—21no—
102#432—21no—
103#432—21no—
104#432—21no—
105#432—21no—
106#432C2×C412yes—
107#432D412yes—
108#432C2312yes—
109#432C2312yes—
110#432C2312yes—
111#431—21no—
112#431—21no—
113#431D412yes—
114#431C2312yes—
115C2×#106—22no—
116#423—21no—
117#423—21no—
118#423—21no—
119#423C2312yes—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×#102—22no—
127C2×#102—22no—
128#408—28no—
129#408—28no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8C2×C412yes—
135C2×C22⋊C8D412yes—
136C2×#97—21no—
137C2×#97—21no—
138C2×#97—21no—
139C2×C4×C8D411yescharacteristic
140C2×C4×C8D411yescharacteristic
141#332—24no—
142#331—24no—
143D4⋊C8—24no—
144D4⋊C8—24no—
145#323—28no—
146C25—21no—
147C2×#41—22no—
148C2×#41—22no—
149C2×#41—22no—
150C2×#41—22no—
151C2×#41—84no—
152C22×Q8—21no—
153C22×D4—22no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—44no—
162C22×D4C22⋊C412yes—
163C22×D4C22×C412yes—
164C23×C4—22no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—41no—
169C23×C4—41no—
170C23×C4—41no—
171C23×C4—41no—
172C23×C4—82no—
173C23×C4—82no—
174C23×C4C22×C411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4#4111yescharacteristic
177C2×D8—28no—
178C2×D8—48no—
179C2×M16—28no—
180C2×M16—22no—
181C2×M16—41no—
182C2×M16—84no—
183C2×M16—82no—
184C22×C8—22no—
185C22×C8—21no—
186C22×C8—22no—
187C22×C8—21no—
188C22×C8—28no—
189C22×C8—41no—
190C22×C8—41no—
191C22×C8—84no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8C22⋊C412yes—
195C4⋊Q8C2×D412yes—
196#127—21no—
197#127—21no—
198#127C22⋊C412yes—
199#127C2×D412yes—
200#124—22no—
201#124—22no—
202#124—22no—
203#124—22no—
204#121—22no—
205#121—22no—
206#121—22no—
207#121—22no—
208#121—22no—
209#121—22no—
210#121C22⋊C414yes—
211#121C22×C414yes—
212C4×D4—22no—
213C4×D4—22no—
214C4×D4—22no—
215C4×D4—22no—
216C4×D4—22no—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—22no—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—41no—
227C4×D4—41no—
228C4×D4—41no—
229C4×D4—41no—
230C4×D4—41no—
231C4×D4—41no—
232C4×D4—41no—
233C4×D4—41no—
234C4×D4C22⋊C414yes—
235C4×D4C2×D414yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C22⋊C412yes—
243C2×C4⋊C4C22×C412yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—41no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—41no—
252C2×C42C22×C411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42C2×D411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42#4111yescharacteristic
261C2×C42#4111yescharacteristic
262C2×C42#4111yescharacteristic
263C2×C42C2411yescharacteristic
264#106—28no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—22no—
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274C4⋊C8—41no—
275C4⋊C8—41no—
276C4⋊C8—41no—
277#102—28no—
278#102—28no—
279C22⋊C8—28no—
280C22⋊C8—28no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8—22no—
284C22⋊C8—22no—
285C22⋊C8—22no—
286C22⋊C8—41no—
287C22⋊C8C22×C414yes—
288C22⋊C8C2×D414yes—
289#97—22no—
290#97—22no—
291#97—22no—
292#97—22no—
293#97—22no—
294#97—41no—
295C4×C8—21no—
296C4×C8—21no—
297C4×C8C2×D412yes—
298C4×C8C2×D412yes—
299C24—24no—
300C24—22no—
301C24—22no—
302C24—42no—
303C24—41no—
304C24—41no—
305C24—82no—
306C24—82no—
307C24C4×D411yescharacteristic
308#41—84no—
309#41—84no—
310#41—84no—
311#41—84no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—82no—
315C2×D4—24no—
316C2×D4—24no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—44no—
329C2×D4—44no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—44no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—82no—
338C2×D4—84no—
339C2×D4C2×C22⋊C414yes—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—84no—
357C22×C4—84no—
358C22×C4—82no—
359C22×C4—82no—
360C22×C4—84no—
361C22×C4—82no—
362C22×C4—82no—
363C22×C4—82no—
364C22×C4—82no—
365C22×C4—82no—
366C22×C4C2×C22⋊C411yescharacteristic
367C22×C4C2×C22⋊C411yescharacteristic
368C22×C4C4×D411yescharacteristic
369C22×C4C4×D411yescharacteristic
370C22×C4C4×D411yescharacteristic
371C22×C4C4×D411yescharacteristic
372C22×C4C4×D411yescharacteristic
373C22×C4#12011yescharacteristic
374C22×C4#12011yescharacteristic
375C22×C4#12111yescharacteristic
376C22×C4#12111yescharacteristic
377C22×C4#12111yescharacteristic
378C22×C4#12111yescharacteristic
379C22×C4#12311yescharacteristic
380C22×C4#12311yescharacteristic
381C22×C4C23×C411yescharacteristic
382C22×C4C22×D411yescharacteristic
383C22×C4C2×#4111yescharacteristic
384D8—416no—
385M16—88no—
386M16—82no—
387M16—82no—
388C2×C8—24no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—24no—
392C2×C8—42no—
393C2×C8—44no—
394C2×C8—42no—
395C2×C8—44no—
396C2×C8—42no—
397C2×C8—42no—
398C2×C8—88no—
399C2×C8—82no—
400C2×C8—82no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4C2×C22⋊C414yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C42C2×C22⋊C411yescharacteristic
418C42C2×C22⋊C411yescharacteristic
419C42C4×D411yescharacteristic
420C42C4×D411yescharacteristic
421C42#12011yescharacteristic
422C42#12011yescharacteristic
423C42#12111yescharacteristic
424C42#12111yescharacteristic
425C42#12111yescharacteristic
426C42#12111yescharacteristic
427C42#12311yescharacteristic
428C42#12311yescharacteristic
429C42C22×D411yescharacteristic
430C42C22×D411yescharacteristic
431C42C22×D411yescharacteristic
432C42C2×#4111yescharacteristic
433C23—22no—
434C23—22no—
435C23—22no—
436C23—24no—
437C23—24no—
438C23—42no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—44no—
444C23—42no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—88no—
450C23—88no—
451C23—82no—
452C23—82no—
453C23#38611yescharacteristic
454C23#38611yescharacteristic
455C23C2×C4×D411yescharacteristic
456Q8—82no—
457Q8—82no—
458D4—24no—
459D4—24no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—44no—
464D4—44no—
465D4—44no—
466D4—42no—
467D4—42no—
468D4—82no—
469D4—82no—
470D4—82no—
471D4—84no—
472D4—84no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—48no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—84no—
503C2×C4—82no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4#38611yescharacteristic
507C2×C4#38611yescharacteristic
508C2×C4#38611yescharacteristic
509C2×C4#38611yescharacteristic
510C2×C4#38611yescharacteristic
511C2×C4#38611yescharacteristic
512C2×C4#47112yes—
513C2×C4#47212yes—
514C2×C4C22×C22⋊C411yescharacteristic
515C2×C4C2×C4×D411yescharacteristic
516C2×C4C2×#12011yescharacteristic
517C2×C4C2×#12111yescharacteristic
518C2×C4C2×#12111yescharacteristic
519C2×C4C2×#12311yescharacteristic
520C8—42no—
521C8—44no—
522C8—42no—
523C8—44no—
524C8—82no—
525C8—82no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—44no—
533C22—44no—
534C22—44no—
535C22—44no—
536C22—44no—
537C22—84no—
538C22—84no—
539C22—88no—
540C22—82no—
541C22—82no—
542C22—88no—
543C22—88no—
544C22#189112yes—
545C22#190412yes—
546C22#190712yes—
547C22C2×#38611yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—44no—
559C4—82no—
560C4#190712yes—
561C4C2×#47111yescharacteristic
562C4C2×#47211yescharacteristic
563C2—41no—
564C2—41no—
565C2—84no—
566C2—84no—
567C2#952914yesdirect product factor
568C2C2×#189111yescharacteristic
569C2C2×#190411yescharacteristic
570C2C2×#190711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#3109C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2981C2semidirect
3. C2×#1557C2semidirect
4. C2×#1486C2semidirect
5. C2×#1466C2semidirect
6. #9529C2direct (N × H)
7. C2×#1307C2semidirect
8. C2×#1287C2semidirect
22. #2981C22semidirect
34. #1557C22semidirect
38. #1486C22semidirect
42. #1466C22semidirect
44. #1307C22semidirect
45. #1287C22semidirect
567. C2#9529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31092
C2×#29812
C2×#15572
C2×#14862
C2×#14662
#95292
C2×#13072
C2×#12872