Finite Group Databasebeta

← C2×#9466 #201284

Subgroups — C2×#9466 #201284

Order 512.

2220 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2436C211yesmaximal, characteristic
2C2×#2310C211yesmaximal, characteristic, complemented
3C2×#1784C211yesmaximal, characteristic, complemented
4C2×#1510C212yesmaximal
5#9466C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal, complemented
7C24×Q8C2211yescharacteristic
8C22×#124C412yescomplemented
9C22×#121C2211yescharacteristic
10C22×#117—21no—
11C22×#101—22no—
12C2×#407C2212yes—
13#2436—22no—
14#2436—22no—
15#2436C414yescomplemented
16#2436C2214yes—
17C2×#393—22no—
18#2310—24no—
19#2310—22no—
20#2310C2214yescomplemented
21C2×#391—24no—
22C2×#391C412yescomplemented
23C2×#386—21no—
24C2×#386—21no—
25C2×#381—21no—
26C2×#381C2212yes—
27C2×C4×C22⋊C4C2211yescharacteristic
28#1784—22no—
29#1784C2214yescomplemented
30#1510—24no—
31#1510C2218yes—
32C2×#327—24no—
33#1284C2218yescomplemented
34C23×Q8—22no—
35C23×Q8—22no—
36C23×Q8—22no—
37C23×Q8—22no—
38C23×Q8—48no—
39C23×Q8C2×C412yes—
40C23×Q8C2×C412yes—
41C23×Q8D412yes—
42C23×Q8D412yes—
43C23×Q8D412yes—
44C23×Q8C2312yes—
45C23×D4—21no—
46C23×D4C2×C411yescharacteristic
47C24×C4D411yescharacteristic
48C24×C4D411yescharacteristic
49C24×C4C2311yescharacteristic
50C22×M16—22no—
51C2×#124—24no—
52C2×#124—48no—
53C2×#124C2×C418yescomplemented
54C2×#121—21no—
55C2×#121—21no—
56C2×#121—22no—
57C2×#121—22no—
58C2×#121—22no—
59C2×#121—22no—
60C2×#121C2×C412yes—
61C2×#121C2312yes—
62C2×#117—24no—
63C2×#117—24no—
64C2×#117—48no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4C2×C411yescharacteristic
67C22×C22⋊C4—22no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—21no—
72C22×C42—22no—
73C22×C42C2×C412yes—
74C2×#101—28no—
75C2×#101—48no—
76#407—22no—
77#407—22no—
78#407—22no—
79#407C2314yes—
80C2×C22⋊C8—22no—
81C2×C22⋊C8—22no—
82#393—28no—
83#393—28no—
84#391—216no—
85#391—24no—
86#391—216no—
87#391C2×C418yescomplemented
88#386—24no—
89#386—24no—
90#386—24no—
91#386—24no—
92#381—24no—
93#381—22no—
94#381—22no—
95#381—24no—
96#381D414yes—
97#381C2314yes—
98C4×C22⋊C4—21no—
99C4×C22⋊C4—21no—
100C4×C22⋊C4C2×C412yes—
101C4×C22⋊C4C2312yes—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—21no—
106C2×#95—22no—
107C2×#95D414yes—
108#327—216no—
109C25—21no—
110C25C2×D411yescharacteristic
111C22×Q8—28no—
112C22×Q8—28no—
113C22×Q8—24no—
114C22×Q8—24no—
115C22×Q8—24no—
116C22×Q8—24no—
117C22×Q8—24no—
118C22×Q8—24no—
119C22×Q8—24no—
120C22×Q8—24no—
121C22×Q8—24no—
122C22×Q8—24no—
123C22×Q8—24no—
124C22×Q8—24no—
125C22×Q8—44no—
126C22×Q8—44no—
127C22×Q8—48no—
128C22×Q8—48no—
129C22×Q8—48no—
130C22×Q8—48no—
131C22×Q8—48no—
132C22×Q8—48no—
133C22×Q8—416no—
134C22×Q8—416no—
135C22×Q8—416no—
136C22×Q8C22⋊C414yes—
137C22×Q8C22⋊C414yes—
138C22×Q8C22×C414yes—
139C22×Q8C2×D414yes—
140C22×D4—22no—
141C22×D4—22no—
142C22×D4—21no—
143C22×D4—22no—
144C22×D4—22no—
145C22×D4—44no—
146C22×D4—48no—
147C22×D4—41no—
148C22×D4—41no—
149C22×D4—41no—
150C22×D4—41no—
151C22×D4C22×C412yes—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—28no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—24no—
164C23×C4—44no—
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×D411yescharacteristic
174C23×C4C2×D412yes—
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D412yes—
178C23×C4C2×D412yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4C2411yescharacteristic
182C2×M16—24no—
183C2×M16—42no—
184C2×M16—48no—
185C22×C8—42no—
186#124—416no—
187#124—416no—
188#121—24no—
189#121—24no—
190#121—24no—
191#121—24no—
192#121—42no—
193#121—42no—
194#121—42no—
195#121—42no—
196#117—416no—
197#117—416no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—28no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—48no—
203C2×C4⋊C4C22×C412yes—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—28no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—48no—
213C2×C22⋊C4—44no—
214C2×C22⋊C4—48no—
215C2×C22⋊C4—48no—
216C2×C22⋊C4—42no—
217C2×C22⋊C4—42no—
218C2×C42—28no—
219C2×C42—22no—
220C2×C42—44no—
221C2×C42—48no—
222C2×C42C22×C414yes—
223#101—416no—
224C22⋊C8—24no—
225C22⋊C8—24no—
226C22⋊C8—42no—
227C22⋊C8—42no—
228#95—216no—
229#95—22no—
230#95—28no—
231#95—28no—
232#95—24no—
233#95—24no—
234#95—22no—
235#95—24no—
236#95C2×D418yes—
237C24—24no—
238C24—24no—
239C24—22no—
240C24—42no—
241C24—44no—
242C24—44no—
243C24—41no—
244C24—41no—
245C24—44no—
246C24C2×C22⋊C411yescharacteristic
247C24C2×C22⋊C411yescharacteristic
248C24#12011yescharacteristic
249C24#12011yescharacteristic
250C24#12311yescharacteristic
251C24#12311yescharacteristic
252C24C22×D411yescharacteristic
253C2×Q8—28no—
254C2×Q8—28no—
255C2×Q8—28no—
256C2×Q8—28no—
257C2×Q8—28no—
258C2×Q8—28no—
259C2×Q8—28no—
260C2×Q8—28no—
261C2×Q8—44no—
262C2×Q8—44no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8—416no—
266C2×Q8—416no—
267C2×Q8—416no—
268C2×Q8—416no—
269C2×Q8—48no—
270C2×Q8—48no—
271C2×Q8—48no—
272C2×Q8—48no—
273C2×Q8—416no—
274C2×Q8—416no—
275C2×Q8—416no—
276C2×Q8—416no—
277C2×Q8—416no—
278C2×Q8—416no—
279C2×D4—24no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4—48no—
283C2×D4—48no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—84no—
290C2×D4—84no—
291C2×D4—84no—
292C2×D4—84no—
293C2×D4—84no—
294C2×D4—84no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—28no—
298C22×C4—28no—
299C22×C4—28no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—28no—
322C22×C4—44no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—44no—
327C22×C4—44no—
328C22×C4—44no—
329C22×C4—44no—
330C22×C4—44no—
331C22×C4—42no—
332C22×C4—44no—
333C22×C4—44no—
334C22×C4—44no—
335C22×C4—44no—
336C22×C4—48no—
337C22×C4—44no—
338C22×C4—48no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—44no—
344C22×C4—48no—
345C22×C4#9918yes—
346C22×C4C2×C22⋊C414yes—
347C22×C4C2×C22⋊C411yescharacteristic
348C22×C4C2×C22⋊C411yescharacteristic
349C22×C4C2×C22⋊C414yes—
350C22×C4C4×D412yes—
351C22×C4C4×D412yes—
352C22×C4C4×D412yes—
353C22×C4C4×D412yes—
354C22×C4#12012yes—
355C22×C4#12112yes—
356C22×C4#12112yes—
357C22×C4#12112yes—
358C22×C4#12112yes—
359C22×C4#12312yes—
360C22×C4C23×C411yescharacteristic
361C22×C4C22×D411yescharacteristic
362C22×C4C22×D412yes—
363C22×C4C2×#4112yes—
364M16—48no—
365M16—84no—
366C2×C8—44no—
367C2×C8—84no—
368C4⋊C4—24no—
369C4⋊C4—416no—
370C4⋊C4—42no—
371C22⋊C4—416no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—48no—
375C22⋊C4—48no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—416no—
379C42—44no—
380C42—416no—
381C42—44no—
382C23—22no—
383C23—22no—
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—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—416no—
402C23—44no—
403C23—44no—
404C23—44no—
405C23—42no—
406C23—82no—
407C23—82no—
408C23—816no—
409C23—82no—
410C23—82no—
411C23—82no—
412C23—82no—
413C23#38611yescharacteristic
414C23#38611yescharacteristic
415C23#38611yescharacteristic
416C23#38611yescharacteristic
417C23C2×#9914yes—
418C23#45414yes—
419C23C22×C22⋊C411yescharacteristic
420C23C2×#12011yescharacteristic
421C23C2×#12311yescharacteristic
422Q8—416no—
423Q8—416no—
424Q8—416no—
425Q8—416no—
426D4—84no—
427D4—84no—
428D4—84no—
429D4—84no—
430D4—84no—
431D4—84no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—28no—
445C2×C4—28no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—48no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—816no—
475C2×C4—88no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4#38612yes—
479C2×C4#38612yes—
480C2×C4C2×#9918yes—
481C2×C4C2×C4×D412yes—
482C2×C4C2×#12112yes—
483C8—84no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—28no—
493C22—28no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—44no—
501C22—44no—
502C22—44no—
503C22—44no—
504C22—44no—
505C22—88no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22—164no—
510C22—164no—
511C22#188812yes—
512C22#188812yes—
513C22#189812yes—
514C22#189812yes—
515C22#191212yes—
516C22C2×#38611yescharacteristic
517C22C22×#9912yes—
518C22C2×#45412yes—
519C4—22no—
520C4—28no—
521C4—22no—
522C4—22no—
523C4—22no—
524C4—44no—
525C4—88no—
526C4—84no—
527C4—82no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2—22no—
532C2—41no—
533C2—41no—
534C2—162no—
535C2#946614yesdirect product factor
536C2C2×#188811yescharacteristic
537C2C2×#189811yescharacteristic
538C2C2×#191211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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×#2310C2semidirect
3. C2×#1784C2semidirect
5. #9466C2direct (N × H)
6. C2×#1284C2semidirect
8. C22×#124C4semidirect
15. #2436C4semidirect
20. #2310C22semidirect
22. C2×#391C4semidirect
29. #1784C22semidirect
33. #1284C22semidirect
53. C2×#124C2×C4semidirect
87. #391C2×C4semidirect
535. C2#9466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24362
C2×#23102
C2×#17842
C2×#15102
#94662
C2×#12842