Finite Group Databasebeta

← C2×#9480 #201454

Subgroups — C2×#9480 #201454

Order 512.

2190 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic
2C2×#2313C211yesmaximal, characteristic, complemented
3C2×#1789C212yesmaximal
4C2×#1463C211yesmaximal, characteristic, complemented
5#9480C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal, complemented
7C23×#41C2211yescharacteristic
8C22×#123—21no—
9C23×C4⋊C4C2211yescharacteristic
10C22×#104—24no—
11C2×#407C2212yes—
12#2406—22no—
13#2406—22no—
14#2406C414yescomplemented
15#2406C2214yes—
16C2×#395C412yescomplemented
17C2×#394C412yescomplemented
18#2313—24no—
19#2313—22no—
20#2313C2214yescomplemented
21C2×#387—24no—
22C2×#386—21no—
23C2×#385—22no—
24C2×#381—21no—
25C2×#381C2211yescharacteristic
26C2×#380—21no—
27C2×C4×C22⋊C4C2212yes—
28#1789—24no—
29#1789C2218yes—
30#1463—22no—
31#1463C2214yescomplemented
32C2×#324—22no—
33#1284C2218yescomplemented
34C22×#41—21no—
35C22×#41—21no—
36C22×#41—22no—
37C22×#41—22no—
38C22×#41—22no—
39C22×#41—22no—
40C22×#41—48no—
41C22×#41C2×C412yes—
42C22×#41C2312yes—
43C23×Q8C2×C411yescharacteristic
44C23×D4—21no—
45C23×D4C2×C411yescharacteristic
46C24×C4—21no—
47C24×C4D411yescharacteristic
48C24×C4D411yescharacteristic
49C24×C4C2311yescharacteristic
50C22×M16—22no—
51C2×#123—24no—
52C2×#123—24no—
53C2×#123—48no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4C2×C412yes—
61C22×C4⋊C4C2×C412yes—
62C22×C4⋊C4D412yes—
63C22×C4⋊C4D412yes—
64C22×C4⋊C4D412yes—
65C22×C4⋊C4C2312yes—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—22no—
68C22×C22⋊C4—22no—
69C22×C22⋊C4—22no—
70C22×C42D414yes—
71C2×#104—216no—
72C2×#104—416no—
73#407—22no—
74#407—22no—
75#407—22no—
76#407C2314yes—
77C2×C22⋊C8—22no—
78C2×C22⋊C8—22no—
79#395—24no—
80#395C2×C418yescomplemented
81#394—24no—
82#394C2×C418yescomplemented
83#387—216no—
84#387—216no—
85#386—24no—
86#386—24no—
87#385—28no—
88#385—28no—
89#381—24no—
90#381—24no—
91#381—21no—
92#381—21no—
93#381C2×C412yes—
94#381C2312yes—
95#380—24no—
96#380—24no—
97C4×C22⋊C4—22no—
98C4×C22⋊C4—22no—
99C4×C22⋊C4D414yes—
100C4×C22⋊C4C2314yes—
101C2×#95—22no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—21no—
106C2×#95C2×C412yes—
107#324—28no—
108C25—21no—
109C25C2×D411yescharacteristic
110C2×#41—216no—
111C2×#41—24no—
112C2×#41—24no—
113C2×#41—24no—
114C2×#41—24no—
115C2×#41—48no—
116C2×#41—48no—
117C2×#41—48no—
118C2×#41—48no—
119C2×#41—48no—
120C2×#41—48no—
121C2×#41—48no—
122C2×#41—416no—
123C2×#41—416no—
124C2×#41—42no—
125C2×#41—42no—
126C2×#41—42no—
127C2×#41—42no—
128C22×Q8—21no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—44no—
132C22×Q8C22×C412yes—
133C22×D4—28no—
134C22×D4—22no—
135C22×D4—22no—
136C22×D4—21no—
137C22×D4—22no—
138C22×D4—22no—
139C22×D4—44no—
140C22×D4—44no—
141C22×D4—41no—
142C22×D4—41no—
143C22×D4—41no—
144C22×D4—41no—
145C22×D4C22×C412yes—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—22no—
156C23×C4—24no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—44no—
160C23×C4—44no—
161C23×C4—44no—
162C23×C4—44no—
163C23×C4—42no—
164C23×C4—42no—
165C23×C4—44no—
166C23×C4C22⋊C412yes—
167C23×C4C22⋊C412yes—
168C23×C4C22⋊C412yes—
169C23×C4C22⋊C412yes—
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C2×D412yes—
173C23×C4C2×D412yes—
174C23×C4C2×D412yes—
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D412yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4C2411yescharacteristic
182C2×M16—24no—
183C2×M16—42no—
184C2×M16—48no—
185C22×C8—42no—
186#123—416no—
187#123—416no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—28no—
201C2×C4⋊C4—28no—
202C2×C4⋊C4—48no—
203C2×C4⋊C4—84no—
204C2×C4⋊C4C22⋊C414yes—
205C2×C4⋊C4C22⋊C414yes—
206C2×C4⋊C4C22×C414yes—
207C2×C4⋊C4C2×D414yes—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—24no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—28no—
213C2×C22⋊C4—28no—
214C2×C22⋊C4—48no—
215C2×C22⋊C4—48no—
216C2×C22⋊C4—48no—
217C2×C22⋊C4—44no—
218C2×C42—24no—
219C2×C42—48no—
220C2×C42C2×D418yes—
221#104—432no—
222C22⋊C8—24no—
223C22⋊C8—24no—
224C22⋊C8—42no—
225C22⋊C8—42no—
226#95—28no—
227#95—216no—
228#95—22no—
229#95—28no—
230#95—22no—
231#95—24no—
232#95—24no—
233#95—22no—
234#95C22×C414yes—
235C24—24no—
236C24—24no—
237C24—24no—
238C24—22no—
239C24—42no—
240C24—42no—
241C24—44no—
242C24—41no—
243C24—41no—
244C24—44no—
245C24C2×C22⋊C411yescharacteristic
246C24C2×C22⋊C411yescharacteristic
247C24#12011yescharacteristic
248C24#12011yescharacteristic
249C24#12311yescharacteristic
250C24#12311yescharacteristic
251C24C22×D411yescharacteristic
252#41—216no—
253#41—216no—
254#41—416no—
255#41—48no—
256#41—48no—
257#41—416no—
258#41—48no—
259#41—48no—
260#41—48no—
261#41—48no—
262#41—416no—
263#41—416no—
264C2×Q8—28no—
265C2×Q8—24no—
266C2×Q8—44no—
267C2×Q8—44no—
268C2×Q8—44no—
269C2×Q8—48no—
270C2×Q8—42no—
271C2×D4—28no—
272C2×D4—28no—
273C2×D4—28no—
274C2×D4—24no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—48no—
278C2×D4—44no—
279C2×D4—44no—
280C2×D4—48no—
281C2×D4—44no—
282C2×D4—48no—
283C2×D4—48no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—48no—
289C2×D4—42no—
290C22×C4—28no—
291C22×C4—24no—
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—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—28no—
309C22×C4—42no—
310C22×C4—44no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—42no—
317C22×C4—44no—
318C22×C4—44no—
319C22×C4—42no—
320C22×C4—44no—
321C22×C4—44no—
322C22×C4—416no—
323C22×C4—44no—
324C22×C4—44no—
325C22×C4—44no—
326C22×C4—44no—
327C22×C4—42no—
328C22×C4—44no—
329C22×C4—44no—
330C22×C4—416no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—44no—
334C22×C4—44no—
335C22×C4—44no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—48no—
341C22×C4—48no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—48no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4C2×C22⋊C414yes—
349C22×C4C2×C22⋊C414yes—
350C22×C4C2×C22⋊C411yescharacteristic
351C22×C4C2×C22⋊C411yescharacteristic
352C22×C4C4×D412yes—
353C22×C4C4×D412yes—
354C22×C4C4×D412yes—
355C22×C4C4×D412yes—
356C22×C4#12012yes—
357C22×C4#12112yes—
358C22×C4#12112yes—
359C22×C4#12112yes—
360C22×C4#12112yes—
361C22×C4#12312yes—
362C22×C4C23×C411yescharacteristic
363C22×C4C22×D412yes—
364C22×C4C22×D411yescharacteristic
365C22×C4C2×#4112yes—
366M16—48no—
367M16—84no—
368C2×C8—44no—
369C2×C8—84no—
370C4⋊C4—28no—
371C4⋊C4—28no—
372C4⋊C4—28no—
373C4⋊C4—28no—
374C4⋊C4—416no—
375C4⋊C4—88no—
376C22⋊C4—416no—
377C22⋊C4—48no—
378C22⋊C4—48no—
379C22⋊C4—416no—
380C22⋊C4—44no—
381C22⋊C4—44no—
382C42—48no—
383C42—84no—
384C23—22no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—24no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—416no—
405C23—42no—
406C23—44no—
407C23—416no—
408C23—44no—
409C23—44no—
410C23—44no—
411C23—42no—
412C23—88no—
413C23—82no—
414C23—82no—
415C23—82no—
416C23—82no—
417C23#38611yescharacteristic
418C23#38611yescharacteristic
419C23#38611yescharacteristic
420C23#38611yescharacteristic
421C23#42114yes—
422C23B(4,𝔽2)14yes—
423C23C22×C22⋊C411yescharacteristic
424C23C2×#12011yescharacteristic
425C23C2×#12311yescharacteristic
426Q8—28no—
427Q8—44no—
428Q8—48no—
429D4—28no—
430D4—44no—
431D4—48no—
432D4—48no—
433D4—48no—
434D4—48no—
435D4—48no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—416no—
458C2×C4—416no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—816no—
483C2×C4—88no—
484C2×C4#38612yes—
485C2×C4#38612yes—
486C2×C4C2×C4×D412yes—
487C2×C4C2×#12112yes—
488C8—84no—
489C22—28no—
490C22—28no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—44no—
509C22—48no—
510C22—44no—
511C22—44no—
512C22—84no—
513C22—88no—
514C22—88no—
515C22—82no—
516C22—82no—
517C22#188912yes—
518C22#188912yes—
519C22#189712yes—
520C22#189712yes—
521C22#191212yes—
522C22C2×#38611yescharacteristic
523C22C2×#42112yes—
524C22C2×B(4,𝔽2)12yes—
525C4—22no—
526C4—22no—
527C4—22no—
528C4—22no—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—88no—
533C4—84no—
534C2—22no—
535C2—22no—
536C2—22no—
537C2—22no—
538C2—41no—
539C2—41no—
540C2—84no—
541C2#948014yesdirect product factor
542C2C2×#188911yescharacteristic
543C2C2×#189711yescharacteristic
544C2C2×#191211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2313C2semidirect
4. C2×#1463C2semidirect
5. #9480C2direct (N × H)
6. C2×#1284C2semidirect
14. #2406C4semidirect
16. C2×#395C4semidirect
17. C2×#394C4semidirect
20. #2313C22semidirect
31. #1463C22semidirect
33. #1284C22semidirect
80. #395C2×C4semidirect
82. #394C2×C4semidirect
541. C2#9480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24062
C2×#23132
C2×#17892
C2×#14632
#94802
C2×#12842