Finite Group Databasebeta

← C2×#9464 #201278

Subgroups — C2×#9464 #201278

Order 512.

1716 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic
2C2×#2313C211yesmaximal, characteristic, complemented
3C2×#1821C211yesmaximal, characteristic, complemented
4C2×#1510C212yesmaximal
5#9464C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal, complemented
7C22×#123—21no—
8C22×#123—21no—
9C22×#121C2211yescharacteristic
10C23×C4⋊C4C2211yescharacteristic
11C2×#407C2212yes—
12#2501—22no—
13#2501—22no—
14#2501C414yescomplemented
15#2501C2214yes—
16C2×#399—22no—
17#2313—24no—
18#2313—22no—
19#2313C2214yescomplemented
20C2×#390C412yescomplemented
21C2×#387—24no—
22C2×#384C412yescomplemented
23C2×#381C2212yes—
24C2×#380—21no—
25C2×C4×C22⋊C4—21no—
26C2×C4×C22⋊C4C2211yescharacteristic
27#1821—22no—
28#1821C2214yescomplemented
29C2×#343—22no—
30#1510—24no—
31#1510C2218yes—
32C2×#327—24no—
33#1284C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4D411yescharacteristic
38C24×C4C2311yescharacteristic
39C22×M16—22no—
40C2×#123—24no—
41C2×#123—24no—
42C2×#123—24no—
43C2×#123—24no—
44C2×#123—48no—
45C2×#123—48no—
46C2×#121—21no—
47C2×#121—21no—
48C2×#121—22no—
49C2×#121—22no—
50C2×#121—22no—
51C2×#121—22no—
52C2×#121C2×C412yes—
53C2×#121C2312yes—
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⋊C4—22no—
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C412yes—
63C22×C4⋊C4C2×C412yes—
64C22×C4⋊C4D412yes—
65C22×C4⋊C4D412yes—
66C22×C4⋊C4D412yes—
67C22×C4⋊C4C2312yes—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—21no—
73C22×C42—22no—
74C22×C42C2×C412yes—
75#407—22no—
76#407—22no—
77#407—22no—
78#407C2314yes—
79C2×C22⋊C8—22no—
80C2×C22⋊C8—22no—
81#399—28no—
82#399—28no—
83#390—24no—
84#390C2×C418yescomplemented
85#387—216no—
86#387—216no—
87#384—24no—
88#384C2×C418yescomplemented
89#381—22no—
90#381—22no—
91#381D414yes—
92#381C2314yes—
93#380—24no—
94#380—24no—
95C4×C22⋊C4—24no—
96C4×C22⋊C4—24no—
97C4×C22⋊C4—21no—
98C4×C22⋊C4—21no—
99C4×C22⋊C4C2×C412yes—
100C4×C22⋊C4C2312yes—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95—22no—
105C2×#95D414yes—
106#343—28no—
107#327—216no—
108C25—21no—
109C25C2×D411yescharacteristic
110C22×D4—22no—
111C22×D4—22no—
112C22×D4—21no—
113C22×D4—22no—
114C22×D4—22no—
115C22×D4—44no—
116C22×D4—44no—
117C22×D4—44no—
118C22×D4—41no—
119C22×D4—41no—
120C22×D4—41no—
121C22×D4—41no—
122C22×D4C22×C412yes—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—24no—
134C23×C4—44no—
135C23×C4—44no—
136C23×C4—44no—
137C23×C4C22⋊C412yes—
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C412yes—
140C23×C4C22⋊C412yes—
141C23×C4C22×C411yescharacteristic
142C23×C4C22×C411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D412yes—
145C23×C4C2×D412yes—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D412yes—
149C23×C4C2×D412yes—
150C23×C4#4112yes—
151C23×C4#4112yes—
152C23×C4C2411yescharacteristic
153C2×M16—24no—
154C2×M16—42no—
155C2×M16—48no—
156C22×C8—42no—
157#123—416no—
158#123—416no—
159#123—416no—
160#123—416no—
161#121—24no—
162#121—24no—
163#121—24no—
164#121—24no—
165#121—42no—
166#121—42no—
167#121—42no—
168#121—42no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—28no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—28no—
187C2×C4⋊C4—48no—
188C2×C4⋊C4—48no—
189C2×C4⋊C4—84no—
190C2×C4⋊C4C22⋊C414yes—
191C2×C4⋊C4C22⋊C414yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C22×C414yes—
194C2×C4⋊C4C2×D414yes—
195C2×C22⋊C4—28no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—28no—
202C2×C22⋊C4—28no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—48no—
205C2×C22⋊C4—48no—
206C2×C22⋊C4—48no—
207C2×C22⋊C4—42no—
208C2×C22⋊C4—42no—
209C2×C42—22no—
210C2×C42—28no—
211C2×C42—44no—
212C2×C42—84no—
213C2×C42C22×C414yes—
214C22⋊C8—24no—
215C22⋊C8—24no—
216C22⋊C8—42no—
217C22⋊C8—42no—
218#95—28no—
219#95—28no—
220#95—22no—
221#95—24no—
222#95—24no—
223#95—22no—
224#95—24no—
225#95C2×D418yes—
226C24—24no—
227C24—24no—
228C24—22no—
229C24—42no—
230C24—42no—
231C24—42no—
232C24—44no—
233C24—41no—
234C24—41no—
235C24—44no—
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C411yescharacteristic
238C24#12011yescharacteristic
239C24#12011yescharacteristic
240C24#12311yescharacteristic
241C24#12311yescharacteristic
242C24C22×D411yescharacteristic
243C2×D4—24no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—84no—
256C2×D4—84no—
257C2×D4—84no—
258C2×D4—84no—
259C2×D4—84no—
260C2×D4—84no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—28no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—44no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—42no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—48no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—48no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—48no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4—82no—
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C2×C22⋊C411yescharacteristic
312C22×C4C2×C22⋊C414yes—
313C22×C4C2×C22⋊C414yes—
314C22×C4C4×D412yes—
315C22×C4C4×D412yes—
316C22×C4C4×D412yes—
317C22×C4C4×D412yes—
318C22×C4#12012yes—
319C22×C4#12112yes—
320C22×C4#12112yes—
321C22×C4#12112yes—
322C22×C4#12112yes—
323C22×C4#12312yes—
324C22×C4C23×C411yescharacteristic
325C22×C4C22×D411yescharacteristic
326C22×C4C22×D412yes—
327C22×C4C2×#4112yes—
328M16—48no—
329M16—84no—
330C2×C8—44no—
331C2×C8—84no—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C4⋊C4—28no—
336C4⋊C4—24no—
337C4⋊C4—416no—
338C4⋊C4—416no—
339C4⋊C4—42no—
340C4⋊C4—88no—
341C22⋊C4—28no—
342C22⋊C4—28no—
343C22⋊C4—416no—
344C22⋊C4—416no—
345C22⋊C4—48no—
346C22⋊C4—48no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C42—44no—
350C42—44no—
351C42—88no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—416no—
372C23—42no—
373C23—42no—
374C23—44no—
375C23—44no—
376C23—42no—
377C23—82no—
378C23—82no—
379C23—88no—
380C23—88no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23#38611yescharacteristic
386C23#38611yescharacteristic
387C23#38611yescharacteristic
388C23#38611yescharacteristic
389C23#41014yes—
390C23#45314yes—
391C23C22×C22⋊C411yescharacteristic
392C23C2×#12011yescharacteristic
393C23C2×#12311yescharacteristic
394D4—84no—
395D4—84no—
396D4—84no—
397D4—84no—
398D4—84no—
399D4—84no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—28no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—416no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—48no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—816no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4#38612yes—
446C2×C4#38612yes—
447C2×C4C2×C4×D412yes—
448C2×C4C2×#12112yes—
449C8—84no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—28no—
459C22—28no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—84no—
472C22—84no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—164no—
477C22—164no—
478C22#188712yes—
479C22#188712yes—
480C22#189912yes—
481C22#189912yes—
482C22#191212yes—
483C22C2×#38611yescharacteristic
484C22C2×#41012yes—
485C22C2×#45312yes—
486C4—22no—
487C4—22no—
488C4—22no—
489C4—22no—
490C4—48no—
491C4—44no—
492C4—44no—
493C4—88no—
494C4—82no—
495C2—22no—
496C2—22no—
497C2—22no—
498C2—22no—
499C2—41no—
500C2—41no—
501C2—162no—
502C2#946414yesdirect product factor
503C2C2×#188711yescharacteristic
504C2C2×#189911yescharacteristic
505C2C2×#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×#2313C2semidirect
3. C2×#1821C2semidirect
5. #9464C2direct (N × H)
6. C2×#1284C2semidirect
14. #2501C4semidirect
19. #2313C22semidirect
20. C2×#390C4semidirect
22. C2×#384C4semidirect
28. #1821C22semidirect
33. #1284C22semidirect
84. #390C2×C4semidirect
88. #384C2×C4semidirect
502. C2#9464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#23132
C2×#18212
C2×#15102
#94642
C2×#12842