Finite Group Databasebeta

← C2×#81908 #11664999

Subgroups — C2×#81908 #11664999

Order 768.

1970 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5698C211yesmaximal, characteristic, complemented
2C2×#5697C211yesmaximal, characteristic
3C2×C3×#499C211yesmaximal, characteristic, complemented
4C2×#5069C211yesmaximal, characteristic, complemented
5C2×#5067C211yesmaximal, characteristic, complemented
6#81908C2116yesmaximal, direct product factor
7C2×#4886C212yesmaximal, complemented
8C2×#4889C212yesmaximal, complemented
9C2×#4864C212yesmaximal, complemented
10C2×#4852C212yesmaximal, complemented
11C2×#4693C211yesmaximal, characteristic, complemented
12C2×#4689C211yesmaximal, characteristic, complemented
13C2×#3174—31nomaximal, Sylow
14C2×C3×#125C2211yescharacteristic
15C2×C3×#125C2211yescharacteristic
16C22×#204C2212yes—
17C22×#204C2212yes—
18C22×ΓL(1,𝔽25)C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20#5698—24no—
21#5698C2218yescomplemented
22#5697—24no—
23#5697C2218yes—
24C2×#898—22no—
25C2×#897C2212yes—
26C2×#895—22no—
27C2×#895C2212yes—
28C2×#894—22no—
29C2×#893C2212yes—
30C2×#890—22no—
31C2×#887C2212yes—
32C2×#874C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×#869C2211yescharacteristic
35C3×#499C2218yescomplemented
36C2×C3×#107C2212yes—
37C2×C3×#106C2212yes—
38C2×C3×C4×C8C2211yescharacteristic
39C2×#815C2211yescharacteristic
40C2×C8×Dic3C2211yescharacteristic
41#5069C2218yescomplemented
42#5067C2218yescomplemented
43C2×#810C2212yes—
44C2×#810C2212yes—
45C2×#809C2212yes—
46C2×#809C2212yes—
47C2×#803C2211yescharacteristic
48#4889C22116yescomplemented
49#4886C22116yescomplemented
50#4864C22116yescomplemented
51#4852C22116yescomplemented
52#4693C2218yescomplemented
53#4689C2218yescomplemented
54C2×#541—31no—
55C2×#540—31no—
56#3174—316no—
57C2×#499D311yescharacteristic, complemented
58C2×#492—31no—
59C2×#491—31no—
60C2×#490—31no—
61C2×#468—32no—
62C2×#465—32no—
63C2×#440—32no—
64C2×C4×SD16—32no—
65C2×#405—31no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12C2312yes—
69C22×C4×D3—22no—
70C22×C4×D3C2311yescharacteristic
71C22×Dic6C2312yes—
72C22×C3×C8C2311yescharacteristic
73C22×C3×C8C2311yescharacteristic
74C3×#125—22no—
75C3×#125—22no—
76C3×#125C2314yes—
77C3×#125C2314yes—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4C2312yes—
81C2×C3×C4⋊C4C2312yes—
82C2×C3×C42C2311yescharacteristic
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4D412yes—
87C2×C4⋊Dic3—22no—
88C2×C4⋊Dic3—22no—
89C2×Dic3⋊C4—22no—
90C2×Dic3⋊C4D412yes—
91C2×C4×Dic3—22no—
92C2×C4×Dic3C2311yescharacteristic
93C22×C3⋊C8C2311yescharacteristic
94C22×C3⋊C8C2311yescharacteristic
95C2×#204—28no—
96C2×#204—28no—
97C2×#204C2318yes—
98C2×#204C2318yes—
99C2×ΓL(1,𝔽25)—24no—
100C2×ΓL(1,𝔽25)C2314yes—
101C2×D3×C8—24no—
102C2×D3×C8C2314yes—
103#898—216no—
104#897—24no—
105#897C2318yes—
106#895—24no—
107#895—216no—
108#895C2318yes—
109#894—216no—
110#893—24no—
111#893C2318yes—
112#890—216no—
113#887—24no—
114#887C2318yes—
115#874—22no—
116#874C2314yes—
117#872D414yes—
118#872C2314yes—
119#869—22no—
120#869C2314yes—
121C3×#107C2318yes—
122C3×#106C2318yes—
123C3×C4×C8C2314yes—
124#815C2314yes—
125C8×Dic3C2314yes—
126#810C2318yes—
127#810C2318yes—
128#809C2318yes—
129#809C2318yes—
130#803C2314yes—
131C22×SD16—32no—
132C22×SD16—32no—
133C22×M16—31no—
134C23×C8—31no—
135#541—38no—
136#541—64no—
137#540—38no—
138#540—64no—
139C2×C4⋊Q8—31no—
140C2×#127—31no—
141C2×#126—62no—
142C2×#125—62no—
143C2×#125C2×D311yescharacteristic
144C2×#125C2×D311yescharacteristic
145C2×#123—62no—
146C2×C22⋊Q8—32no—
147C2×#121—32no—
148C2×#121—62no—
149C2×C4×Q8—32no—
150C2×C4×D4—32no—
151C2×#117—31no—
152#499C2×D318yescomplemented
153#492—38no—
154#491—38no—
155#490—38no—
156#468—316no—
157#465—316no—
158#440—316no—
159C4×SD16—316no—
160C2×#107C2×D312yes—
161C2×#106C2×D312yes—
162C2×#103—32no—
163C2×#103—32no—
164C2×#102—32no—
165C2×#102—32no—
166#405—38no—
167C2×#97—31no—
168C2×#97—31no—
169C2×C4×C8—31no—
170C2×C4×C8C2×D311yescharacteristic
171C23×D3—22no—
172C23×D3C2×D411yescharacteristic
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4C2×D412yes—
176C22×C3×C4C2411yescharacteristic
177C22×Dic3—22no—
178C22×Dic3C2×D412yes—
179C22×Dic3C2×D411yescharacteristic
180C2×D12—24no—
181C2×D12—24no—
182C2×D12—22no—
183C2×D12—28no—
184C2×D12—28no—
185C2×D12—84no—
186C2×D12—84no—
187C2×D12C2414yes—
188C2×C4×D3—22no—
189C2×C4×D3—22no—
190C2×C4×D3—28no—
191C2×C4×D3—84no—
192C2×C4×D3C2×D412yes—
193C2×C4×D3C2412yes—
194C2×Dic6—24no—
195C2×Dic6—24no—
196C2×Dic6—22no—
197C2×Dic6C2414yes—
198C2×C3×C8#4114yes—
199C2×C3×C8#4114yes—
200C2×C3×C8C2412yes—
201C2×C3×C8C2412yes—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—28no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—28no—
206C3×C4⋊C4C2414yes—
207C3×C4⋊C4C2414yes—
208C3×C42C2×D412yes—
209C3×C42C2412yes—
210(C2×D3)⋊C4—28no—
211(C2×D3)⋊C4—28no—
212(C2×D3)⋊C4—28no—
213(C2×D3)⋊C4C2×D418yes—
214C4⋊Dic3—28no—
215C4⋊Dic3—28no—
216Dic3⋊C4—28no—
217Dic3⋊C4C2×D418yes—
218C4×Dic3—28no—
219C4×Dic3C2×D412yes—
220C4×Dic3C2412yes—
221C2×C3⋊C8—22no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8C2412yes—
224C2×C3⋊C8C2412yes—
225#204—216no—
226#204—216no—
227ΓL(1,𝔽25)—28no—
228D3×C8—28no—
229C22×Q8—32no—
230C22×D4—32no—
231C22×D4—62no—
232C22×D4—62no—
233C23×C4—31no—
234C23×C4—62no—
235C2×SD16—38no—
236C2×SD16—38no—
237C2×SD16—68no—
238C2×SD16—68no—
239C2×M16—34no—
240C2×M16—64no—
241C22×C8—31no—
242C22×C8—31no—
243C22×C8—34no—
244C22×C8—64no—
245C22×C8C22×D311yescharacteristic
246C22×C8C22×D311yescharacteristic
247C4⋊Q8—34no—
248C4⋊Q8—62no—
249#127—34no—
250#127—62no—
251#126—616no—
252#125—22no—
253#125—22no—
254#125—616no—
255#125C22×D314yes—
256#125C22×D314yes—
257#123—616no—
258C22⋊Q8—38no—
259C22⋊Q8—64no—
260#121—38no—
261#121—616no—
262#121—64no—
263C4×Q8—38no—
264C4×Q8—64no—
265C4×D4—38no—
266C4×D4—64no—
267#117—34no—
268#117—34no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—62no—
273C2×C4⋊C4—62no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4C22×D312yes—
276C2×C4⋊C4C22×D312yes—
277C2×C22⋊C4—32no—
278C2×C22⋊C4—62no—
279C2×C22⋊C4—62no—
280C2×C22⋊C4—62no—
281C2×C42—31no—
282C2×C42—62no—
283C2×C42C22×D311yescharacteristic
284#107C22×D318yes—
285#106C22×D318yes—
286#103—38no—
287#103—38no—
288#102—38no—
289#102—38no—
290#97—34no—
291#97—34no—
292C4×C8—34no—
293C4×C8C22×D314yes—
294C23×C3C22×D411yescharacteristic
295C22×D3—22no—
296C22×D3—24no—
297C22×D3—24no—
298C22×D3—44no—
299C22×D3—44no—
300C22×D3—44no—
301C22×D3C22×D412yes—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—24no—
305C2×C3×C4—44no—
306C2×C3×C4—44no—
307C2×C3×C4C22×D414yes—
308C2×C3×C4C22×D411yescharacteristic
309C2×C3×C4C2×#4112yes—
310C2×C3×C4C2×#4112yes—
311C2×C3×C4C2511yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—24no—
314C2×Dic3—24no—
315C2×Dic3—44no—
316C2×Dic3C22×D414yes—
317C2×Dic3C22×D412yes—
318D12—24no—
319D12—24no—
320D12—44no—
321D12—88no—
322D12—88no—
323C4×D3—24no—
324C4×D3—22no—
325C4×D3—22no—
326C4×D3—88no—
327Dic6—24no—
328Dic6—24no—
329Dic6—44no—
330C3×C8C2×#4114yes—
331C3×C8C2×#4114yes—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C24—31no—
335C24—62no—
336C2×Q8—34no—
337C2×Q8—62no—
338C2×Q8—64no—
339C2×Q8—64no—
340C2×D4—34no—
341C2×D4—68no—
342C2×D4—62no—
343C2×D4—68no—
344C2×D4—64no—
345C2×D4—64no—
346C2×D4—244no—
347C2×D4—244no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—32no—
351C22×C4—31no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—68no—
355C22×C4—62no—
356C22×C4—62no—
357C22×C4—62no—
358C22×C4—244no—
359C22×C4D3×D412yes—
360C22×C4C23×D311yescharacteristic
361SD16—616no—
362SD16—616no—
363M16—68no—
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—62no—
367C2×C8—62no—
368C2×C8—68no—
369C2×C8#23914yes—
370C2×C8#23914yes—
371C2×C8C23×D312yes—
372C2×C8C23×D312yes—
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—38no—
378C4⋊C4—68no—
379C4⋊C4—68no—
380C4⋊C4—68no—
381C4⋊C4C23×D314yes—
382C4⋊C4C23×D314yes—
383C22⋊C4—38no—
384C22⋊C4—68no—
385C22⋊C4—68no—
386C22⋊C4—68no—
387C42—32no—
388C42—32no—
389C42—68no—
390C42D3×D412yes—
391C42C23×D312yes—
392C22×C3#53212yes—
393C22×C3#57714yes—
394C22×C3C23×D411yescharacteristic
395C2×D3—22no—
396C2×D3—24no—
397C2×D3—44no—
398C2×D3—44no—
399C2×D3—44no—
400C2×D3—44no—
401C2×D3—88no—
402C3×C4—24no—
403C3×C4—44no—
404C3×C4—44no—
405C3×C4#53212yes—
406C3×C4C22×#4111yescharacteristic
407C3×C4C22×#4111yescharacteristic
408Dic3—22no—
409Dic3—24no—
410Dic3—44no—
411C23—32no—
412C23—62no—
413C23—64no—
414C23—64no—
415C23—124no—
416C23—124no—
417C23—124no—
418C23C2×D3×D411yescharacteristic
419Q8—64no—
420Q8—64no—
421Q8—124no—
422D4—64no—
423D4—64no—
424D4—124no—
425D4—248no—
426D4—248no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—34no—
431C2×C4—32no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—62no—
435C2×C4—64no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—64no—
439C2×C4—64no—
440C2×C4—124no—
441C2×C4—248no—
442C2×C4C2×D3×D414yes—
443C2×C4C2×D3×D411yescharacteristic
444C2×C4C2×#23912yes—
445C2×C4C2×#23912yes—
446C2×C4C24×D311yescharacteristic
447C8—62no—
448C8—62no—
449C8C2×#23914yes—
450C8C2×#23914yes—
451C2×C3#317414yescomplemented
452C2×C3C2×#53211yescharacteristic
453C2×C3C2×#57712yes—
454D3—42no—
455D3—84no—
456C22—64no—
457C22—62no—
458C22—124no—
459C22—124no—
460C22—124no—
461C22—124no—
462C22—248no—
463C22#572512yes—
464C22#577014yes—
465C22C22×D3×D411yescharacteristic
466C4—24no—
467C4—44no—
468C4—44no—
469C4—64no—
470C4—62no—
471C4—124no—
472C4#572512yes—
473C4C22×#23911yescharacteristic
474C4C22×#23911yescharacteristic
475C3C2×#317411yescharacteristic, complemented, Sylow
476C2—122no—
477C2—244no—
478C2#8190814yesdirect product factor
479C2C2×#572511yescharacteristic
480C2C2×#577012yes—
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#499C2
socleC23×C3C22×D4
prime radicalC2×#5697C2
hypercenterC2×#499D3
hypocenterC3C2×#3174
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
1. C2×#5698C2semidirect
3. C2×C3×#499C2semidirect
4. C2×#5069C2semidirect
5. C2×#5067C2semidirect
6. #81908C2direct (N × H)
7. C2×#4886C2semidirect
8. C2×#4889C2semidirect
9. C2×#4864C2semidirect
10. C2×#4852C2semidirect
11. C2×#4693C2semidirect
12. C2×#4689C2semidirect
21. #5698C22semidirect
35. C3×#499C22semidirect
41. #5069C22semidirect
42. #5067C22semidirect
48. #4889C22semidirect
49. #4886C22semidirect
50. #4864C22semidirect
51. #4852C22semidirect
52. #4693C22semidirect
53. #4689C22semidirect
57. C2×#499D3semidirect
152. #499C2×D3semidirect
451. C2×C3#3174semidirect
475. C3C2×#3174semidirect
478. C2#81908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56982
C2×#56972
C2×C3×#4992
C2×#50692
C2×#50672
#819082
C2×#48862
C2×#48892
C2×#48642
C2×#48522
C2×#46932
C2×#46892
C2×#31743