Finite Group Databasebeta

← C2×#81894 #11667229

Subgroups — C2×#81894 #11667229

Order 768.

2286 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5725C211yesmaximal, characteristic
3C2×C3×#498C211yesmaximal, characteristic, complemented
4C2×#5080C211yesmaximal, characteristic, complemented
5C2×#5088C211yesmaximal, characteristic, complemented
6#81894C2116yesmaximal, direct product factor
7C2×#4870C214yesmaximal, complemented
8C2×#4863C214yesmaximal, complemented
9C2×#4694C211yesmaximal, characteristic, complemented
10C2×#4685C211yesmaximal, characteristic, complemented
11C2×#3227—31nomaximal, Sylow
12C22×#239—21no—
13C22×D3×Q8—21no—
14C2×C3×C4⋊Q8C2211yescharacteristic
15C2×C3×C4⋊Q8C2211yescharacteristic
16C2×#947—21no—
17C2×#944—21no—
18#5725—24no—
19#5725C2218yes—
20D3×C4⋊Q8—24no—
21D3×C4⋊Q8C2218yescomplemented
22C2×#895—21no—
23C2×#895C2212yes—
24C2×#893—21no—
25C2×#893C2212yes—
26C2×D3×C4⋊C4—21no—
27C2×D3×C4⋊C4C2212yes—
28C2×#888—21no—
29C2×#888C2212yes—
30C2×#874C2211yescharacteristic
31C2×C42×D3C2211yescharacteristic
32C2×#869C2211yescharacteristic
33C3×#498C2218yescomplemented
34C2×C3×#106C2214yes—
35C2×C3×C4×C8C2211yescharacteristic
36C2×#821C2214yes—
37C2×(C2×D3)⋊C8C2212yes—
38C2×Dic3⋊C8C2212yes—
39#5088C2218yescomplemented
40#5080C2218yescomplemented
41C2×#809C2214yes—
42C2×#808C2214yes—
43C2×C4×C3⋊C8C2211yescharacteristic
44#4870C22132yescomplemented
45#4863C22132yescomplemented
46#4694C2218yescomplemented
47#4685C2218yescomplemented
48C2×#532—31no—
49C22×C4⋊Q8—31no—
50#3227—316no—
51C2×#498—31no—
52C2×#498D311yescharacteristic, complemented
53C2×#486—31no—
54C2×#486—31no—
55C2×#481—34no—
56C2×#476—34no—
57C2×#431—31no—
58C22×C3×Q8—21no—
59C22×C3×Q8—21no—
60C2×#239—28no—
61C2×#239—48no—
62C2×D3×Q8—28no—
63C2×D3×Q8—48no—
64C22×D12—22no—
65C22×D12—21no—
66C22×D12—21no—
67C22×D12C2312yes—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3D411yescharacteristic
71C22×C4×D3D411yescharacteristic
72C22×C4×D3C2311yescharacteristic
73C22×Dic6—21no—
74C22×Dic6—22no—
75C22×C3×C8C2312yes—
76C3×C4⋊Q8—22no—
77C3×C4⋊Q8—22no—
78C3×C4⋊Q8C2314yes—
79C3×C4⋊Q8C2314yes—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4C2312yes—
83C2×C3×C4⋊C4C2312yes—
84C2×C3×C42C2311yescharacteristic
85#947—28no—
86#944—28no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—22no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3C2312yes—
91C2×Dic3⋊C4—22no—
92C2×Dic3⋊C4—22no—
93C2×C4×Dic3D411yescharacteristic
94C2×C4×Dic3D411yescharacteristic
95C2×C4×Dic3C2311yescharacteristic
96C22×C3⋊C8C2312yes—
97#895—24no—
98#895—28no—
99#895C2318yes—
100#893—24no—
101#893—28no—
102#893C2318yes—
103D3×C4⋊C4—24no—
104D3×C4⋊C4—28no—
105D3×C4⋊C4C2318yes—
106#888—24no—
107#888—28no—
108#888C2318yes—
109#874—22no—
110#874C2314yes—
111C42×D3D414yes—
112C42×D3C2314yes—
113#869—22no—
114#869C2314yes—
115C3×#106C23116yes—
116C3×C4×C8C2314yes—
117#821C23116yes—
118(C2×D3)⋊C8C2318yes—
119Dic3⋊C8C2318yes—
120#809C23116yes—
121#808C23116yes—
122C4×C3⋊C8C2314yes—
123C22×#41—61no—
124C23×Q8—61no—
125#532—38no—
126#532—64no—
127C2×C4⋊Q8—38no—
128C2×C4⋊Q8—32no—
129C2×C4⋊Q8—31no—
130C2×C4⋊Q8—61no—
131C2×C4⋊Q8—64no—
132C2×C4⋊Q8—61no—
133C2×C4⋊Q8C2×D311yescharacteristic
134C2×C4⋊Q8C2×D311yescharacteristic
135C2×#127—31no—
136C2×#124—61no—
137C2×#121—32no—
138C2×#121—61no—
139C2×C4×D4—32no—
140C2×C4×D4—61no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4—61no—
143C22×C42—31no—
144#498—38no—
145#498C2×D318yescomplemented
146#486—38no—
147#486—38no—
148#481—332no—
149#476—332no—
150#431—38no—
151C2×#106—34no—
152C2×#106C2×D314yes—
153C2×C4⋊C8—32no—
154C2×#102—34no—
155C2×#102—34no—
156C2×C22⋊C8—32no—
157C2×C4×C8—31no—
158C2×C4×C8C2×D311yescharacteristic
159C23×D3—22no—
160C23×D3C2×D411yescharacteristic
161C2×C3×Q8—24no—
162C2×C3×Q8—24no—
163C2×C3×Q8—44no—
164C2×C3×Q8—44no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2411yescharacteristic
170C22×Dic3—22no—
171C22×Dic3C2×D411yescharacteristic
172C22×Dic3C2×D411yescharacteristic
173C22×Dic3C2×D411yescharacteristic
174#239—432no—
175D3×Q8—432no—
176C2×D12—28no—
177C2×D12—28no—
178C2×D12—22no—
179C2×D12—24no—
180C2×D12—24no—
181C2×D12—48no—
182C2×D12—44no—
183C2×D12—44no—
184C2×D12C2414yes—
185C2×C4×D3—24no—
186C2×C4×D3—24no—
187C2×C4×D3—28no—
188C2×C4×D3—28no—
189C2×C4×D3—48no—
190C2×C4×D3—48no—
191C2×C4×D3SD1618yes—
192C2×C4×D3C2×D412yes—
193C2×C4×D3C2×D414yes—
194C2×C4×D3C2×D414yes—
195C2×C4×D3C2412yes—
196C2×Dic6—24no—
197C2×Dic6—28no—
198C2×Dic6—48no—
199C2×Dic6—44no—
200C2×C3×C8—24no—
201C2×C3×C8C2414yes—
202C3×C4⋊C4—24no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—24no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4C2414yes—
207C3×C4⋊C4C2414yes—
208C3×C42C2×D412yes—
209C3×C42C2412yes—
210(C2×D3)⋊C4—28no—
211(C2×D3)⋊C4—28no—
212C4⋊Dic3—22no—
213C4⋊Dic3—24no—
214C4⋊Dic3C2414yes—
215Dic3⋊C4—28no—
216Dic3⋊C4—28no—
217C4×Dic3C2×D412yes—
218C4×Dic3C2×D414yes—
219C4×Dic3C2×D414yes—
220C4×Dic3C2412yes—
221C2×C3⋊C8—24no—
222C2×C3⋊C8C2414yes—
223C2×#41—68no—
224C2×#41—128no—
225C22×Q8—21no—
226C22×Q8—21no—
227C22×Q8—62no—
228C22×Q8—68no—
229C22×Q8—61no—
230C22×Q8—128no—
231C22×D4—32no—
232C22×D4—62no—
233C22×D4—61no—
234C22×D4—61no—
235C23×C4—31no—
236C23×C4—31no—
237C23×C4—31no—
238C23×C4—62no—
239C23×C4—62no—
240C22×C8—32no—
241C22×C8C22×D312yes—
242C4⋊Q8—22no—
243C4⋊Q8—22no—
244C4⋊Q8—38no—
245C4⋊Q8—34no—
246C4⋊Q8—64no—
247C4⋊Q8—68no—
248C4⋊Q8—68no—
249C4⋊Q8—62no—
250C4⋊Q8C22×D314yes—
251C4⋊Q8C22×D314yes—
252#127—34no—
253#127—62no—
254#124—68no—
255#121—38no—
256#121—64no—
257#121—68no—
258C4×D4—38no—
259C4×D4—64no—
260C4×D4—68no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—32no—
264C2×C4⋊C4—38no—
265C2×C4⋊C4—64no—
266C2×C4⋊C4—68no—
267C2×C4⋊C4—62no—
268C2×C4⋊C4—62no—
269C2×C4⋊C4—61no—
270C2×C4⋊C4C22×D312yes—
271C2×C4⋊C4C22×D312yes—
272C2×C22⋊C4—62no—
273C2×C22⋊C4—62no—
274C2×C42—31no—
275C2×C42—31no—
276C2×C42—31no—
277C2×C42—34no—
278C2×C42—34no—
279C2×C42C22×D311yescharacteristic
280#106—316no—
281#106C22×D3116yes—
282C4⋊C8—38no—
283#102—316no—
284#102—316no—
285C22⋊C8—38no—
286C4×C8—34no—
287C4×C8C22×D314yes—
288C23×C3C22×D411yescharacteristic
289C22×D3—22no—
290C22×D3—22no—
291C22×D3—24no—
292C22×D3—44no—
293C22×D3—44no—
294C22×D3—44no—
295C22×D3C2×SD1614yes—
296C22×D3C22×D412yes—
297C3×Q8—48no—
298C3×Q8—48no—
299C2×C3×C4—24no—
300C2×C3×C4—24no—
301C2×C3×C4—44no—
302C2×C3×C4—44no—
303C2×C3×C4C2×SD1614yes—
304C2×C3×C4AGL(1,ℤ/8)14yes—
305C2×C3×C4C22×D411yescharacteristic
306C2×C3×C4C22×D412yes—
307C2×C3×C4C22×D412yes—
308C2×C3×C42−1+414yes—
309C2×C3×C4C2511yescharacteristic
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—24no—
313C2×Dic3—44no—
314C2×Dic3C2×SD1614yes—
315C2×Dic3C22×D412yes—
316C2×Dic3C22×D412yes—
317C2×Dic3C22×D412yes—
318D12—28no—
319D12—416no—
320D12—44no—
321D12—48no—
322D12—48no—
323C4×D3—24no—
324C4×D3—28no—
325C4×D3—24no—
326C4×D3—416no—
327C4×D3—416no—
328C4×D3C2×SD16116yes—
329Dic6—416no—
330Dic6—48no—
331C3×C8—24no—
332C3⋊C8—24no—
333C24—31no—
334C24—62no—
335#41—1232no—
336C2×Q8—24no—
337C2×Q8—24no—
338C2×Q8—44no—
339C2×Q8—44no—
340C2×Q8—68no—
341C2×Q8—64no—
342C2×Q8—128no—
343C2×Q8—1232no—
344C2×Q8—124no—
345C2×D4—34no—
346C2×D4—68no—
347C2×D4—64no—
348C2×D4—62no—
349C2×D4—64no—
350C2×D4—68no—
351C2×D4—128no—
352C2×D4—124no—
353C2×D4—124no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—31no—
357C22×C4—38no—
358C22×C4—34no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—32no—
362C22×C4—34no—
363C22×C4—32no—
364C22×C4—68no—
365C22×C4—68no—
366C22×C4—64no—
367C22×C4—64no—
368C22×C4—62no—
369C22×C4—128no—
370C22×C4—128no—
371C22×C4D3×D411yescharacteristic
372C22×C4D3×D411yescharacteristic
373C22×C4C23×D311yescharacteristic
374C2×C8—24no—
375C2×C8—34no—
376C2×C8—64no—
377C2×C8C23×D314yes—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—34no—
383C4⋊C4—68no—
384C4⋊C4—68no—
385C4⋊C4—62no—
386C4⋊C4—64no—
387C4⋊C4C23×D314yes—
388C4⋊C4C23×D314yes—
389C22⋊C4—68no—
390C22⋊C4—68no—
391C42—34no—
392C42—32no—
393C42—34no—
394C42—32no—
395C42D3×D412yes—
396C42C23×D312yes—
397C22×C3#53612yes—
398C22×C3C22×SD1612yes—
399C22×C3C2×AGL(1,ℤ/8)12yes—
400C22×C3C23×D411yescharacteristic
401C2×D3—22no—
402C2×D3—28no—
403C2×D3—22no—
404C2×D3—44no—
405C2×D3—44no—
406C2×D3—44no—
407C2×D3—88no—
408C2×D3C22×SD1614yes—
409C3×C4—44no—
410C3×C4—44no—
411C3×C4#53612yes—
412C3×C4C22×SD1614yes—
413C3×C4C2×AGL(1,ℤ/8)14yes—
414C3×C4C2×2−1+412yes—
415Dic3—22no—
416Dic3—22no—
417Dic3—44no—
418Dic3C22×SD1614yes—
419C23—32no—
420C23—34no—
421C23—62no—
422C23—62no—
423C23—64no—
424C23—124no—
425C23—124no—
426C23—124no—
427C23C2×D3×D411yescharacteristic
428Q8—48no—
429Q8—48no—
430Q8—1216no—
431Q8—128no—
432D4—68no—
433D4—1216no—
434D4—124no—
435D4—128no—
436D4—128no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—32no—
440C2×C4—34no—
441C2×C4—316no—
442C2×C4—32no—
443C2×C4—32no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—64no—
449C2×C4—64no—
450C2×C4—68no—
451C2×C4—64no—
452C2×C4—1216no—
453C2×C4—1216no—
454C2×C4—124no—
455C2×C4D3×SD1614yes—
456C2×C4#91414yes—
457C2×C4C2×D3×D411yescharacteristic
458C2×C4C2×D3×D412yes—
459C2×C4C2×D3×D412yes—
460C2×C4#100714yes—
461C2×C4C24×D311yescharacteristic
462C8—24no—
463C8—64no—
464C2×C3#322714yescomplemented
465C2×C3C2×#53611yescharacteristic
466C2×C3C23×SD1611yescharacteristic
467C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
468D3—24no—
469D3—84no—
470C22—34no—
471C22—62no—
472C22—62no—
473C22—68no—
474C22—124no—
475C22—124no—
476C22—124no—
477C22—248no—
478C22#572412yes—
479C22C2×D3×SD1612yes—
480C22C2×#91412yes—
481C22C22×D3×D411yescharacteristic
482C4—34no—
483C4—44no—
484C4—44no—
485C4—62no—
486C4—62no—
487C4—124no—
488C4#572412yes—
489C4C2×D3×SD1614yes—
490C4C2×#91414yes—
491C4C2×#100712yes—
492C3C2×#322711yescharacteristic, complemented, Sylow
493C2—64no—
494C2—244no—
495C2#8189414yesdirect product factor
496C2C2×#572411yescharacteristic
497C2C22×D3×SD1611yescharacteristic
498C2C22×#91411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#498C2
socleC23×C3C22×D4
prime radicalC2×#5725C2
hypercenterC2×#498D3
hypocenterC3C2×#3227
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊Q8C2semidirect
3. C2×C3×#498C2semidirect
4. C2×#5080C2semidirect
5. C2×#5088C2semidirect
6. #81894C2direct (N × H)
7. C2×#4870C2semidirect
8. C2×#4863C2semidirect
9. C2×#4694C2semidirect
10. C2×#4685C2semidirect
21. D3×C4⋊Q8C22semidirect
33. C3×#498C22semidirect
39. #5088C22semidirect
40. #5080C22semidirect
44. #4870C22semidirect
45. #4863C22semidirect
46. #4694C22semidirect
47. #4685C22semidirect
52. C2×#498D3semidirect
145. #498C2×D3semidirect
464. C2×C3#3227semidirect
492. C3C2×#3227semidirect
495. C2#81894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Q82
C2×#57252
C2×C3×#4982
C2×#50802
C2×#50882
#818942
C2×#48702
C2×#48632
C2×#46942
C2×#46852
C2×#32273