Finite Group Databasebeta

← C2×#10433 #238658

Subgroups — C2×#10433 #238658

Order 512.

1434 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#1834C211yesmaximal, characteristic, complemented
3C2×#1803C211yesmaximal, characteristic, complemented
4C2×#1802C211yesmaximal, characteristic
5C22×Q8⋊C8C211yesmaximal, characteristic, complemented
6C22×D4⋊C8C211yesmaximal, characteristic
7#10433C218yesmaximal, direct product factor
8C2×#1296C211yesmaximal, characteristic, complemented
9C22×C22⋊Q8—21no—
10C22×C4×Q8C2211yescharacteristic
11C22×C4×D4C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×#103—21no—
15C22×#102—21no—
16C22×C4×C8C2211yescharacteristic
17#2538—22no—
18#2538—22no—
19#2538—22no—
20#2538C2214yes—
21C2×#396—22no—
22C2×#390—21no—
23C2×#389—21no—
24C2×#384C2211yescharacteristic
25C2×#384C2211yescharacteristic
26C2×#380—21no—
27#1834—22no—
28#1834C2214yescomplemented
29#1803—22no—
30#1803C2214yescomplemented
31#1802—22no—
32#1802C2214yes—
33C2×#340—22no—
34C2×#340—21no—
35C2×#340—21no—
36C2×Q8⋊C8—24no—
37C2×Q8⋊C8C2214yescomplemented
38C2×D4⋊C8—24no—
39C2×D4⋊C8C2214yes—
40#1296C2214yescomplemented
41C23×Q8D411yescharacteristic
42C23×D4D411yescharacteristic
43C24×C4—21no—
44C23×C8—21no—
45C23×C8—21no—
46C23×C8—21no—
47C2×C22⋊Q8—24no—
48C2×C22⋊Q8—24no—
49C2×C22⋊Q8—44no—
50C2×C22⋊Q8—44no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×C4×Q8—22no—
54C2×C4×Q8—22no—
55C2×C4×Q8—22no—
56C2×C4×Q8—22no—
57C2×C4×Q8D412yes—
58C2×C4×Q8C2312yes—
59C2×C4×D4—21no—
60C2×C4×D4—21no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4—22no—
64C2×C4×D4—22no—
65C2×C4×D4D412yes—
66C2×C4×D4C2312yes—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4D411yescharacteristic
75C22×C4⋊C4D411yescharacteristic
76C22×C4⋊C4D412yes—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—22no—
80C22×C42—21no—
81C22×C42C2311yescharacteristic
82C2×C4⋊C8—22no—
83C2×C4⋊C8—22no—
84C2×C4⋊C8—22no—
85C2×C4⋊C8—22no—
86C2×C4⋊C8—21no—
87C2×C4⋊C8—21no—
88C2×C4⋊C8C2312yes—
89C2×C4⋊C8C2312yes—
90C2×#103—24no—
91C2×#103—44no—
92C2×#102—24no—
93C2×#102—44no—
94C2×C4×C8—21no—
95C2×C4×C8—22no—
96C2×C4×C8D414yes—
97C2×C4×C8C2312yes—
98#396—28no—
99#396—28no—
100#390—24no—
101#390—24no—
102#389—24no—
103#389—24no—
104#384—21no—
105#384—21no—
106#384—21no—
107#384—21no—
108#384—21no—
109#384D412yes—
110#384C2312yes—
111#384C2312yes—
112#380—24no—
113#380—24no—
114C2×#95—22no—
115#340—24no—
116#340—24no—
117#340—28no—
118Q8⋊C8—28no—
119D4⋊C8—28no—
120C25—21no—
121C22×Q8—21no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8D814yes—
128C22×Q8C2×D412yes—
129C22×D4—21no—
130C22×D4—22no—
131C22×D4—22no—
132C22×D4—22no—
133C22×D4—22no—
134C22×D4—22no—
135C22×D4SD1614yes—
136C22×D4C2×D412yes—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—41no—
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C22×C8—24no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—42no—
158C22×C8—42no—
159C22×C8—42no—
160C22×C8—42no—
161C22×C8—42no—
162C22×C8—42no—
163C22×C8—42no—
164C22×C8—42no—
165C22⋊Q8—48no—
166C22⋊Q8—416no—
167C22⋊Q8—48no—
168C4×Q8—24no—
169C4×Q8—24no—
170C4×Q8—22no—
171C4×Q8—22no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×Q8—42no—
175C4×Q8—42no—
176C4×Q8—42no—
177C4×Q8—42no—
178C4×D4—24no—
179C4×D4—24no—
180C4×D4—22no—
181C4×D4—22no—
182C4×D4—22no—
183C4×D4—22no—
184C4×D4—42no—
185C4×D4—42no—
186C4×D4—42no—
187C4×D4—42no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—48no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—44no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4—42no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4C2×D412yes—
222C2×C4⋊C4C2×D412yes—
223C2×C4⋊C4C2×D414yes—
224C2×C22⋊C4—28no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—28no—
228C2×C22⋊C4—48no—
229C2×C22⋊C4—42no—
230C2×C22⋊C4—42no—
231C2×C22⋊C4—84no—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42—42no—
235C2×C42—42no—
236C2×C42C2×D412yes—
237C2×C42C2×D411yescharacteristic
238C2×C42C2×D411yescharacteristic
239C2×C42C2×D411yescharacteristic
240C2×C42#4112yes—
241C2×C42#4112yes—
242C2×C42#4112yes—
243C2×C42C2411yescharacteristic
244C4⋊C8—22no—
245C4⋊C8—22no—
246C4⋊C8—22no—
247C4⋊C8—22no—
248C4⋊C8—42no—
249C4⋊C8—42no—
250#103—48no—
251#102—48no—
252C4×C8—24no—
253C4×C8—22no—
254C4×C8C2×D414yes—
255#95—28no—
256C24—22no—
257C24—24no—
258C24—42no—
259C24—42no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24#12011yescharacteristic
265C2×Q8—22no—
266C2×Q8—24no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—28no—
272C2×Q8—28no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—44no—
276C2×Q8—44no—
277C2×Q8C2×D814yes—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—24no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—44no—
289C2×D4—44no—
290C2×D4C2×SD1614yes—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—44no—
303C22×C4—42no—
304C22×C4—44no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—44no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—44no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—42no—
319C22×C4—84no—
320C22×C4—84no—
321C22×C4—84no—
322C22×C4—84no—
323C22×C4—82no—
324C22×C4—82no—
325C22×C4—82no—
326C22×C4#12011yescharacteristic
327C22×C4#12011yescharacteristic
328C22×C4#12011yescharacteristic
329C22×C4#12112yes—
330C22×C4#12112yes—
331C22×C4#12112yes—
332C22×C4#12312yes—
333C22×C4#12312yes—
334C22×C4#12412yes—
335C22×C4C2×D812yes—
336C22×C4C2×SD1612yes—
337C22×C4#13512yes—
338C22×C4#13512yes—
339C22×C4AGL(1,ℤ/8)12yes—
340C22×C4#13712yes—
341C22×C4#13712yes—
342C22×C4#13712yes—
343C22×C4C22×D411yescharacteristic
344C22×C4C22×D411yescharacteristic
345C22×C4C22×D411yescharacteristic
346C2×C8—24no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—48no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—42no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—84no—
357C2×C8—84no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—44no—
363C4⋊C4—416no—
364C4⋊C4—44no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—44no—
374C4⋊C4—44no—
375C4⋊C4—44no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—82no—
381C4⋊C4—82no—
382C4⋊C4—82no—
383C4⋊C4—82no—
384C22⋊C4—416no—
385C22⋊C4—42no—
386C22⋊C4—42no—
387C22⋊C4—44no—
388C22⋊C4—88no—
389C42—42no—
390C42—42no—
391C42—44no—
392C42#12112yes—
393C42#12112yes—
394C42#12112yes—
395C42#12312yes—
396C42#12312yes—
397C42#12412yes—
398C42C22×D411yescharacteristic
399C42C2×#4111yescharacteristic
400C42C2×#4111yescharacteristic
401C42C2×#4111yescharacteristic
402C23—24no—
403C23—42no—
404C23—48no—
405C23—48no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—48no—
412C23—84no—
413C23—84no—
414C23—84no—
415C23—84no—
416C23#39412yes—
417C23#44712yes—
418C23#44812yes—
419C23#45212yes—
420C23#45212yes—
421C23#45412yes—
422C23#45512yes—
423C23C2×#12011yescharacteristic
424Q8—24no—
425Q8—24no—
426Q8—42no—
427Q8—42no—
428Q8—48no—
429D4—24no—
430D4—24no—
431D4—42no—
432D4—42no—
433D4—48no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—48no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—88no—
454C2×C4—84no—
455C2×C4—84no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—88no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—164no—
465C2×C4#39412yes—
466C2×C4#39412yes—
467C2×C4#39412yes—
468C2×C4#44712yes—
469C2×C4#44812yes—
470C2×C4#45212yes—
471C2×C4#45212yes—
472C2×C4#46514yes—
473C2×C4#46614yes—
474C2×C4#46814yes—
475C2×C4#47014yes—
476C2×C4#48014yes—
477C2×C4#48214yes—
478C2×C4#48314yes—
479C2×C4#48514yes—
480C2×C4C2×#12111yescharacteristic
481C2×C4C2×#12111yescharacteristic
482C2×C4C2×#12111yescharacteristic
483C2×C4C2×#12311yescharacteristic
484C2×C4C2×#12311yescharacteristic
485C2×C4C2×#12411yescharacteristic
486C2×C4C22×D811yescharacteristic
487C2×C4C22×SD1611yescharacteristic
488C2×C4C2×#13511yescharacteristic
489C2×C4C2×#13511yescharacteristic
490C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
491C2×C4C2×#13711yescharacteristic
492C2×C4C2×#13711yescharacteristic
493C2×C4C2×#13711yescharacteristic
494C8—44no—
495C8—82no—
496C8—82no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—816no—
504C22—82no—
505C22#162714yes—
506C22#163814yes—
507C22#164114yes—
508C22#164314yes—
509C22#203314yes—
510C22#203514yes—
511C22#204014yes—
512C22C2×#39411yescharacteristic
513C22C2×#44711yescharacteristic
514C22C2×#44811yescharacteristic
515C22C2×#45211yescharacteristic
516C22C2×#45211yescharacteristic
517C22C2×#45511yescharacteristic
518C22C2×#45411yescharacteristic
519C4—21no—
520C4—21no—
521C4—22no—
522C4—44no—
523C4—84no—
524C4—82no—
525C4—82no—
526C4—162no—
527C4#203314yes—
528C4#203514yes—
529C4C2×#46511yescharacteristic
530C4C2×#46611yescharacteristic
531C4C2×#46811yescharacteristic
532C4C2×#47011yescharacteristic
533C4C2×#48011yescharacteristic
534C4C2×#48311yescharacteristic
535C4C2×#48211yescharacteristic
536C4C2×#48511yescharacteristic
537C2—84no—
538C2#1043318yesdirect product factor
539C2C2×#164311yescharacteristic
540C2C2×#162711yescharacteristic
541C2C2×#163811yescharacteristic
542C2C2×#164111yescharacteristic
543C2C2×#203311yescharacteristic
544C2C2×#203511yescharacteristic
545C2C2×#204011yescharacteristic
subgroupG/H
center, socleC24#120
commutator, Frattini, cosocleC2×C42C24
prime radicalC23×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1834C2semidirect
3. C2×#1803C2semidirect
5. C22×Q8⋊C8C2semidirect
7. #10433C2direct (N × H)
8. C2×#1296C2semidirect
28. #1834C22semidirect
30. #1803C22semidirect
37. C2×Q8⋊C8C22semidirect
40. #1296C22semidirect
538. C2#10433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#18342
C2×#18032
C2×#18022
C22×Q8⋊C82
C22×D4⋊C82
#104332
C2×#12962