Finite Group Databasebeta

← C2×#10163 #236902

Subgroups — C2×#10163 #236902

Order 512.

1334 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×#3209C211yesmaximal, characteristic
2C2×#3165C211yesmaximal, characteristic
3C22×#487C211yesmaximal, characteristic
4C2×#1997C211yesmaximal, characteristic
5C2×#1548C211yesmaximal, characteristic
6C2×#1493C211yesmaximal, characteristic
7#10163C218yesmaximal, direct product factor
8C2×#1278C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4⋊Q8C2211yescharacteristic
12#3209—22no—
13#3209—22no—
14#3209—22no—
15#3209C2214yes—
16#3165—22no—
17#3165—22no—
18#3165—22no—
19#3165C2214yes—
20C2×#501—22no—
21C2×#500—21no—
22C2×#498—21no—
23C2×#494—21no—
24C2×#487—22no—
25C2×#487—22no—
26C2×#487—21no—
27C2×#487—22no—
28C2×#487—22no—
29C2×#487—22no—
30C2×#487C2214yes—
31C2×#462—22no—
32C2×#451—22no—
33C2×#431C2211yescharacteristic
34C2×#428—22no—
35C2×#423C2211yescharacteristic
36C22×#103—22no—
37C2×C4×M16C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic
39#1997—22no—
40#1997C2214yes—
41C2×#343—22no—
42#1548—22no—
43#1548C2214yes—
44C2×#333—22no—
45#1493—22no—
46#1493C2214yes—
47C2×Q8⋊C8—22no—
48#1278C2214yes—
49C23×Q8—21no—
50C23×Q8D412yes—
51C22×Q16—24no—
52C22×M16—21no—
53C22×M16D412yes—
54C23×C8—21no—
55#533—21no—
56#533—21no—
57#533—21no—
58#533—21no—
59#533—21no—
60#533—21no—
61#533D412yes—
62#533C2312yes—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8—21no—
65C2×C4⋊Q8—21no—
66C2×C4⋊Q8—21no—
67C2×C4⋊Q8—21no—
68C2×C4⋊Q8—21no—
69C2×C4⋊Q8—21no—
70C2×C4⋊Q8—21no—
71C2×C4⋊Q8—21no—
72C2×C4⋊Q8—21no—
73C2×C4⋊Q8—21no—
74C2×C4⋊Q8—21no—
75C2×C4⋊Q8—21no—
76C2×C4⋊Q8—21no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8—21no—
79C2×C4⋊Q8—21no—
80C2×C4⋊Q8—21no—
81C2×C4⋊Q8—21no—
82C2×C4⋊Q8D412yes—
83C2×C4⋊Q8D411yescharacteristic
84C2×C4⋊Q8D412yes—
85C2×C4⋊Q8D412yes—
86C2×C4⋊Q8D411yescharacteristic
87C2×C4⋊Q8C2312yes—
88C2×C4⋊Q8C2312yes—
89C2×#125—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C2×C4×Q8—21no—
93C2×C4×Q8—21no—
94C2×#117—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C42C2311yescharacteristic
100#501—28no—
101#501—28no—
102#500—24no—
103#500—24no—
104#498—24no—
105#498—24no—
106#494—24no—
107#494—24no—
108#487—28no—
109#487—28no—
110#487—24no—
111#487—28no—
112#487—24no—
113#487—28no—
114#462—28no—
115#462—28no—
116#451—28no—
117#451—28no—
118#431—21no—
119#431—21no—
120#431D412yes—
121#431C2312yes—
122#428—28no—
123#428—28no—
124C2×#107—24no—
125C2×#106—24no—
126#423—21no—
127#423—21no—
128#423—21no—
129#423C2312yes—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8D412yes—
133C2×#103—28no—
134C2×#103—28no—
135C2×#103—24no—
136C2×#103—28no—
137C2×C22⋊C8—21no—
138C4×M16—21no—
139C4×M16—21no—
140C4×M16D412yes—
141C4×M16C2312yes—
142C2×#97—21no—
143C2×C4×C8—21no—
144C2×C4×C8—21no—
145C2×C4×C8—21no—
146C2×C4×C8—21no—
147C2×C4×C8—21no—
148C2×C4×C8D412yes—
149C2×C4×C8D412yes—
150C2×C4×C8C2312yes—
151#343—28no—
152#333—28no—
153Q8⋊C8—28no—
154C22×Q8—22no—
155C22×Q8—21no—
156C22×Q8—22no—
157C22×Q8—22no—
158C22×Q8—22no—
159C22×Q8—22no—
160C22×Q8—21no—
161C22×Q8—22no—
162C22×Q8—22no—
163C22×Q8—22no—
164C22×Q8—48no—
165C22×Q8—41no—
166C22×Q8—41no—
167C22×Q8—41no—
168C22×Q8—84no—
169C22×Q8C2×D414yes—
170C23×C4—22no—
171C23×C4—41no—
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4#4111yescharacteristic
175C2×Q16—216no—
176C2×Q16—88no—
177C2×M16—22no—
178C2×M16—24no—
179C2×M16—22no—
180C2×M16—41no—
181C2×M16—44no—
182C2×M16Q1618yescomplemented
183C2×M16C2×D414yes—
184C22×C8—22no—
185C22×C8—22no—
186C22×C8—22no—
187C22×C8—22no—
188C22×C8—22no—
189C22×C8—44no—
190C22×C8—41no—
191C4⋊Q8—22no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—22no—
199C4⋊Q8—22no—
200C4⋊Q8—22no—
201C4⋊Q8—22no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—22no—
205C4⋊Q8—22no—
206C4⋊Q8—21no—
207C4⋊Q8—22no—
208C4⋊Q8—22no—
209C4⋊Q8—22no—
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214C4⋊Q8—41no—
215C4⋊Q8—41no—
216C4⋊Q8—41no—
217C4⋊Q8—41no—
218C4⋊Q8—41no—
219C4⋊Q8—41no—
220C4⋊Q8—41no—
221C4⋊Q8—41no—
222C4⋊Q8—41no—
223C4⋊Q8—41no—
224C4⋊Q8—41no—
225C4⋊Q8—41no—
226C4⋊Q8—41no—
227C4⋊Q8—41no—
228C4⋊Q8C2×D414yes—
229C4⋊Q8C2×D412yes—
230C4⋊Q8C2×D412yes—
231#125—22no—
232#125—22no—
233#125—41no—
234#125—41no—
235C22⋊Q8—22no—
236C22⋊Q8—22no—
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—41no—
240C22⋊Q8—41no—
241C22⋊Q8—41no—
242C22⋊Q8—41no—
243C4×Q8—22no—
244C4×Q8—22no—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×Q8—41no—
248C4×Q8—41no—
249C4×Q8—41no—
250C4×Q8—41no—
251#117—22no—
252#117—22no—
253#117—41no—
254#117—41no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C22⋊C4—41no—
286C2×C42—41no—
287C2×C42C2×D411yescharacteristic
288C2×C42C2×D411yescharacteristic
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42C2×D411yescharacteristic
292C2×C42C2×D411yescharacteristic
293C2×C42C2×D411yescharacteristic
294C2×C42C2×D411yescharacteristic
295C2×C42C2×D411yescharacteristic
296C2×C42C2×D411yescharacteristic
297C2×C42#4111yescharacteristic
298C2×C42C2411yescharacteristic
299#107—216no—
300#106—216no—
301C4⋊C8—22no—
302C4⋊C8—22no—
303C4⋊C8—22no—
304C4⋊C8—41no—
305C4⋊C8—41no—
306C4⋊C8C2×D414yes—
307#103—232no—
308#103—216no—
309C22⋊C8—22no—
310C22⋊C8—22no—
311#97—22no—
312#97—22no—
313C4×C8—22no—
314C4×C8—22no—
315C4×C8—22no—
316C4×C8—22no—
317C4×C8—22no—
318C4×C8—22no—
319C4×C8—22no—
320C4×C8C2×D414yes—
321C24#12111yescharacteristic
322C2×Q8—24no—
323C2×Q8—24no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—24no—
327C2×Q8—48no—
328C2×Q8—48no—
329C2×Q8—48no—
330C2×Q8—42no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—44no—
338C2×Q8—48no—
339C2×Q8—44no—
340C2×Q8—84no—
341C2×Q8—84no—
342C2×Q8—84no—
343C2×Q8—84no—
344C2×Q8—84no—
345C2×Q8—84no—
346C2×Q8—84no—
347C2×Q8—84no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—84no—
359C22×C4—84no—
360C22×C4#12011yescharacteristic
361C22×C4#12011yescharacteristic
362C22×C4#12011yescharacteristic
363C22×C4#12011yescharacteristic
364C22×C4#12011yescharacteristic
365C22×C4#12011yescharacteristic
366C22×C4#12111yescharacteristic
367C22×C4#12111yescharacteristic
368C22×C4#12111yescharacteristic
369C22×C4#12111yescharacteristic
370C22×C4#12111yescharacteristic
371C22×C4#12111yescharacteristic
372C22×C4#12111yescharacteristic
373C22×C4#12711yescharacteristic
374C22×C4#12711yescharacteristic
375C22×C4C2×Q1614yes—
376C22×C4#13714yes—
377C22×C4C22×D411yescharacteristic
378C22×C4C22×D411yescharacteristic
379C22×C4C2×#4111yescharacteristic
380Q16—816no—
381M16—24no—
382M16—28no—
383M16—44no—
384M16—82no—
385M16C2×Q1618yescomplemented
386C2×C8—24no—
387C2×C8—28no—
388C2×C8—24no—
389C2×C8—24no—
390C2×C8—44no—
391C2×C8—44no—
392C2×C8—44no—
393C2×C8—44no—
394C2×C8—42no—
395C2×C8—82no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C42—42no—
427C42—42no—
428C42#12011yescharacteristic
429C42#12011yescharacteristic
430C42#12011yescharacteristic
431C42#12011yescharacteristic
432C42#12011yescharacteristic
433C42#12011yescharacteristic
434C42#12111yescharacteristic
435C42#12111yescharacteristic
436C42#12111yescharacteristic
437C42#12111yescharacteristic
438C42#12711yescharacteristic
439C42#12711yescharacteristic
440C42C22×D411yescharacteristic
441C42C22×D411yescharacteristic
442C42C22×D411yescharacteristic
443C42C22×D411yescharacteristic
444C23—22no—
445C23—22no—
446C23#39211yescharacteristic
447C23#39211yescharacteristic
448C23#46214yes—
449C23C2×#12111yescharacteristic
450Q8—48no—
451Q8—44no—
452Q8—48no—
453Q8—44no—
454Q8—84no—
455Q8—84no—
456Q8—84no—
457Q8—82no—
458Q8—84no—
459Q8—82no—
460Q8—84no—
461Q8—84no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—84no—
477C2×C4—84no—
478C2×C4—84no—
479C2×C4—84no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4#39211yescharacteristic
485C2×C4#39211yescharacteristic
486C2×C4#39211yescharacteristic
487C2×C4#39211yescharacteristic
488C2×C4#39211yescharacteristic
489C2×C4#39211yescharacteristic
490C2×C4#45114yes—
491C2×C4#45114yes—
492C2×C4#45514yes—
493C2×C4#46214yes—
494C2×C4#47114yes—
495C2×C4#49412yes—
496C2×C4#49412yes—
497C2×C4#49712yes—
498C2×C4#49712yes—
499C2×C4C2×#12011yescharacteristic
500C2×C4C2×#12011yescharacteristic
501C2×C4C2×#12011yescharacteristic
502C2×C4C2×#12111yescharacteristic
503C2×C4C2×#12111yescharacteristic
504C2×C4C2×#12711yescharacteristic
505C2×C4C22×Q1612yes—
506C2×C4C2×#13712yes—
507C8—28no—
508C8—44no—
509C8—44no—
510C8—82no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—28no—
516C22#200412yes—
517C22#201612yes—
518C22#201612yes—
519C22#201912yes—
520C22C2×#39211yescharacteristic
521C22C2×#46212yes—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—84no—
527C4—82no—
528C4—84no—
529C4—82no—
530C4#200412yes—
531C4#201612yes—
532C4#201612yes—
533C4#201912yes—
534C4C2×#45112yes—
535C4C2×#45512yes—
536C4C2×#47112yes—
537C4C2×#49411yescharacteristic
538C4C2×#49711yescharacteristic
539C2—22no—
540C2—22no—
541C2#1016314yesdirect product factor
542C2C2×#200411yescharacteristic
543C2C2×#201611yescharacteristic
544C2C2×#201911yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC2×C42C24
prime radicalC24#121
LCSG ▷ C2×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
7. #10163C2direct (N × H)
182. C2×M16Q16semidirect
385. M16C2×Q16semidirect
541. C2#10163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32092
C2×#31652
C22×#4872
C2×#19972
C2×#15482
C2×#14932
#101632
C2×#12782