Finite Group Databasebeta

← C2×#9427 #200842

Subgroups — C2×#9427 #200842

Order 512.

1126 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic
2C2×#2381C211yesmaximal, characteristic
3C2×#1556C211yesmaximal, characteristic
4C2×#1515C211yesmaximal, characteristic
5C2×#1515C211yesmaximal, characteristic
6#9427C218yesmaximal, direct product factor
7C2×#1288C211yesmaximal, characteristic
8C2×#1288C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11#3165—22no—
12#3165—22no—
13#3165C414yescomplemented
14#3165C2214yes—
15C2×#501—22no—
16C2×#500C412yescomplemented
17C2×#498C412yescomplemented
18C2×#432C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#428—22no—
21C2×C4×M16C2211yescharacteristic
22#2381—22no—
23#2381—22no—
24#2381—22no—
25#2381C2214yes—
26C2×#391—22no—
27C2×#387—22no—
28C2×#387—22no—
29C2×#383C2211yescharacteristic
30C2×#383C2211yescharacteristic
31#1556—22no—
32#1556C2214yes—
33C2×#332—22no—
34#1515—22no—
35#1515—22no—
36#1515C2214yes—
37#1515C2214yes—
38C2×#328—22no—
39C2×#328—22no—
40#1288C2214yes—
41#1288C2214yes—
42C23×Q8—21no—
43C22×M16—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533C2×C412yes—
51#533C2312yes—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8C2×C411yescharacteristic
59C2×C4⋊Q8C2×C411yescharacteristic
60C2×C4⋊Q8C2×C412yes—
61C2×C4⋊Q8C2×C412yes—
62C2×C4⋊Q8D412yes—
63C2×C4⋊Q8D412yes—
64C2×C4⋊Q8D412yes—
65C2×C4⋊Q8C2312yes—
66C2×#125—21no—
67C2×C22⋊Q8—21no—
68C2×C22⋊Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8—21no—
71C2×#117—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4D412yes—
75C22×C42—22no—
76C22×C42C2311yescharacteristic
77#501—28no—
78#501—28no—
79#500—24no—
80#500C2×C418yescomplemented
81#498—24no—
82#498C2×C418yescomplemented
83#432—21no—
84#432—21no—
85#432—21no—
86#432—21no—
87#432—21no—
88#432—21no—
89#432C2312yes—
90#432C2312yes—
91#428—28no—
92#428—28no—
93C2×#107—24no—
94C2×#106—24no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C22⋊C8—21no—
98C2×C22⋊C8—21no—
99C4×M16—21no—
100C4×M16—21no—
101C4×M16C2×C412yes—
102C4×M16C2312yes—
103C2×#97—21no—
104C2×#97—21no—
105C2×#97—21no—
106C2×C4×C8C2×C412yes—
107#391—28no—
108#391—28no—
109#387—28no—
110#387—28no—
111#387—28no—
112#387—28no—
113#383—21no—
114#383—21no—
115#383—21no—
116#383—21no—
117#383D412yes—
118#383D412yes—
119#383C2312yes—
120#383C2312yes—
121C2×#95—24no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95D412yes—
127C2×#95D412yes—
128#332—28no—
129#328—28no—
130#328—28no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—22no—
137C22×Q8—21no—
138C22×Q8—21no—
139C22×Q8—82no—
140C22×Q8—82no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C2×M16—28no—
148C2×M16—22no—
149C2×M16—22no—
150C22×C8—22no—
151C22×C8—41no—
152C22×C8—41no—
153C4⋊Q8—21no—
154C4⋊Q8—21no—
155C4⋊Q8—22no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4⋊Q8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4⋊Q8—22no—
170C4⋊Q8—22no—
171C4⋊Q8C22⋊C414yes—
172C4⋊Q8C22⋊C414yes—
173C4⋊Q8C22×C412yes—
174C4⋊Q8C22×C412yes—
175C4⋊Q8C22×C414yes—
176C4⋊Q8C2×D414yes—
177#125—22no—
178#125—22no—
179#125—41no—
180#125—41no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—41no—
186C22⋊Q8—41no—
187C22⋊Q8—41no—
188C22⋊Q8—41no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×Q8—41no—
194C4×Q8—41no—
195C4×Q8—41no—
196C4×Q8—41no—
197#117—22no—
198#117—22no—
199#117—41no—
200#117—41no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—84no—
218C2×C4⋊C4C22⋊C414yes—
219C2×C4⋊C4C22⋊C414yes—
220C2×C4⋊C4C2×D414yes—
221C2×C22⋊C4—41no—
222C2×C42—28no—
223C2×C42—41no—
224C2×C42—84no—
225C2×C42C22×C411yescharacteristic
226C2×C42C22×C411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42#4111yescharacteristic
233C2×C42#4111yescharacteristic
234C2×C42#4111yescharacteristic
235C2×C42#4111yescharacteristic
236C2×C42C2411yescharacteristic
237#107—216no—
238#106—216no—
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—41no—
242C4⋊C8—41no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—41no—
246C22⋊C8—41no—
247#97—22no—
248#97—22no—
249#97—22no—
250#97—22no—
251#97—41no—
252#97—41no—
253C4×C8—22no—
254C4×C8C22×C414yes—
255#95—216no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95C2×D414yes—
267#95C2×D414yes—
268C24#12011yescharacteristic
269C2×Q8—24no—
270C2×Q8—24no—
271C2×Q8—24no—
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—84no—
278C2×Q8—84no—
279C2×Q8—82no—
280C2×Q8—82no—
281C2×Q8—84no—
282C2×Q8—82no—
283C2×Q8—82no—
284C2×Q8—84no—
285C2×Q8—82no—
286C2×Q8—82no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—44no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4C2×C22⋊C411yescharacteristic
306C22×C4C2×C22⋊C411yescharacteristic
307C22×C4C4×D411yescharacteristic
308C22×C4C4×D411yescharacteristic
309C22×C4C4×D411yescharacteristic
310C22×C4C4×D411yescharacteristic
311C22×C4#12011yescharacteristic
312C22×C4#12011yescharacteristic
313C22×C4#12011yescharacteristic
314C22×C4#12111yescharacteristic
315C22×C4#12111yescharacteristic
316C22×C4#12111yescharacteristic
317C22×C4#12111yescharacteristic
318C22×C4#12311yescharacteristic
319C22×C4#12311yescharacteristic
320C22×C4C22×D411yescharacteristic
321C22×C4C22×D411yescharacteristic
322C22×C4C22×D411yescharacteristic
323M16—28no—
324M16—28no—
325C2×C8—28no—
326C2×C8—24no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—82no—
330C2×C8—82no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—88no—
351C4⋊C4C2×C22⋊C418yes—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C42—42no—
355C42—42no—
356C42—88no—
357C42C2×C22⋊C411yescharacteristic
358C42C2×C22⋊C411yescharacteristic
359C42C4×D411yescharacteristic
360C42C4×D411yescharacteristic
361C42C4×D411yescharacteristic
362C42C4×D411yescharacteristic
363C42#12111yescharacteristic
364C42#12111yescharacteristic
365C42#12111yescharacteristic
366C42#12111yescharacteristic
367C42#12311yescharacteristic
368C42#12311yescharacteristic
369C42C23×C411yescharacteristic
370C42C22×D411yescharacteristic
371C42C2×#4111yescharacteristic
372C42C2×#4111yescharacteristic
373C23—22no—
374C23—22no—
375C23#38611yescharacteristic
376C23#38611yescharacteristic
377C23#45614yes—
378C23C2×#12011yescharacteristic
379Q8—84no—
380Q8—84no—
381Q8—84no—
382Q8—84no—
383Q8—82no—
384Q8—82no—
385Q8—82no—
386Q8—82no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—28no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—48no—
409C2×C4—48no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—88no—
419C2×C4—88no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4#38611yescharacteristic
423C2×C4#38611yescharacteristic
424C2×C4#38611yescharacteristic
425C2×C4#38611yescharacteristic
426C2×C4#38611yescharacteristic
427C2×C4#38611yescharacteristic
428C2×C4C22×C22⋊C411yescharacteristic
429C2×C4C2×C4×D411yescharacteristic
430C2×C4C2×C4×D411yescharacteristic
431C2×C4C2×#12111yescharacteristic
432C2×C4C2×#12111yescharacteristic
433C2×C4C2×#12311yescharacteristic
434C8—28no—
435C8—82no—
436C8—82no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—28no—
442C22#188612yes—
443C22#188612yes—
444C22#190412yes—
445C22#190512yes—
446C22C2×#38611yescharacteristic
447C22C2×#45612yes—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—48no—
461C4—84no—
462C4—84no—
463C4—82no—
464C4—82no—
465C2—22no—
466C2—22no—
467C2#942714yesdirect product factor
468C2C2×#188611yescharacteristic
469C2C2×#190411yescharacteristic
470C2C2×#190511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24#120
LCSG ▷ C42 ▷ 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
6. #9427C2direct (N × H)
13. #3165C4semidirect
16. C2×#500C4semidirect
17. C2×#498C4semidirect
80. #500C2×C4semidirect
82. #498C2×C4semidirect
467. C2#9427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#23812
C2×#15562
C2×#15152
#94272
C2×#12882