Finite Group Databasebeta

← C2×#81907 #11664915

Subgroups — C2×#81907 #11664915

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5691C212yesmaximal, complemented
2C2×C3×#499C211yesmaximal, characteristic, complemented
3C2×#5068C212yesmaximal, complemented
4#81907C2116yesmaximal, direct product factor
5C2×#4887C211yesmaximal, characteristic, complemented
6C2×#4883C211yesmaximal, characteristic
7C2×#4873C211yesmaximal, characteristic, complemented
8C2×#4872C211yesmaximal, characteristic, complemented
9C2×#4864C212yesmaximal, complemented
10C2×#4852C212yesmaximal, complemented
11C2×#4696C211yesmaximal, characteristic, complemented
12C2×C4×D3×C8C211yesmaximal, characteristic, complemented
13C2×#3168—31nomaximal, Sylow
14C2×C3×#125C2212yes—
15C22×Dic12C2211yescharacteristic
16C22×D24C2211yescharacteristic
17C22×#204C2212yes—
18C22×D3×C8C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20#5691—28no—
21#5691C22116yescomplemented
22C2×#898—22no—
23C2×#897C2212yes—
24C2×#895C2212yes—
25C2×#894—22no—
26C2×#893—22no—
27C2×#893C2212yes—
28C2×#892—22no—
29C2×#887C2212yes—
30C2×#875C2212yes—
31C2×C42×D3C2211yescharacteristic
32C3×#499C2218yescomplemented
33C2×C3×#107C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2212yes—
36C2×C3×C4×C8C2211yescharacteristic
37C2×C8×Dic3C2211yescharacteristic
38C2×C8×Dic3C2211yescharacteristic
39#5068C22116yescomplemented
40C2×#810C2212yes—
41C2×#810C2212yes—
42C2×#809C2212yes—
43C2×#809C2212yes—
44C2×C4×C3⋊C8C2211yescharacteristic
45#4887C2218yescomplemented
46#4883C2218yes—
47#4873C2218yescomplemented
48#4872C2218yescomplemented
49#4864C22116yescomplemented
50#4852C22116yescomplemented
51#4696C2218yescomplemented
52C4×D3×C8C2218yescomplemented
53C2×#529—32no—
54#3168—316no—
55C2×#499D311yescharacteristic, complemented
56C2×#495—31no—
57C2×#488—32no—
58C2×#467—31no—
59C2×#466—31no—
60C2×#465—32no—
61C2×C4×Q16—31no—
62C2×C4×SD16—32no—
63C2×C4×D8—31no—
64C22×C4×C8—31no—
65C22×D12—22no—
66C22×D12C2312yes—
67C22×C4×D3—22no—
68C22×C4×D3D411yescharacteristic
69C22×C4×D3D411yescharacteristic
70C22×C4×D3C2311yescharacteristic
71C22×Dic6C2312yes—
72C22×C3×C8C2311yescharacteristic
73C22×C3×C8C2311yescharacteristic
74C3×#125—24no—
75C3×#125C2318yes—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4C2312yes—
79C2×C3×C4⋊C4C2312yes—
80C2×C3×C42C2311yescharacteristic
81C2×(C2×D3)⋊C4—22no—
82C2×(C2×D3)⋊C4—22no—
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×C4⋊Dic3—22no—
87C2×Dic3⋊C4—22no—
88C2×C4×Dic3—22no—
89C2×C4×Dic3D411yescharacteristic
90C2×C4×Dic3D411yescharacteristic
91C2×C4×Dic3C2311yescharacteristic
92C22×C3⋊C8C2311yescharacteristic
93C22×C3⋊C8C2311yescharacteristic
94C2×Dic12—24no—
95C2×Dic12C2314yes—
96C2×D24—24no—
97C2×D24C2314yes—
98C2×#204—28no—
99C2×#204C2318yes—
100C2×D3×C8—24no—
101C2×D3×C8—24no—
102C2×D3×C8C2314yes—
103C2×D3×C8C2314yes—
104#898—216no—
105#897—24no—
106#897C2318yes—
107#895—24no—
108#895C2318yes—
109#894—216no—
110#893—216no—
111#893—24no—
112#893C2318yes—
113#892—216no—
114#887—24no—
115#887C2318yes—
116#875—24no—
117#875C2318yes—
118C42×D3D414yes—
119C42×D3C2314yes—
120C3×#107C2314yes—
121C3×#107C2314yes—
122C3×#106C2318yes—
123C3×C4×C8C2314yes—
124C8×Dic3C2314yes—
125C8×Dic3C2314yes—
126#810C2318yes—
127#810C2318yes—
128#809C2318yes—
129#809C2318yes—
130C4×C3⋊C8C2314yes—
131C22×Q16—31no—
132C22×SD16—32no—
133C22×D8—31no—
134C23×C8—31no—
135C23×C8—31no—
136#529—316no—
137#529—68no—
138C2×#126—62no—
139C2×#125C2×D312yes—
140C2×#124—32no—
141C2×#123—62no—
142C2×C22⋊Q8—32no—
143C2×#121—32no—
144C2×C4×Q8—32no—
145C2×C4×D4—32no—
146C2×C4×D4—62no—
147C2×#117—62no—
148C22×C42—31no—
149#499C2×D318yescomplemented
150#495—38no—
151#488—316no—
152#467—38no—
153#466—38no—
154#465—316no—
155C4×Q16—38no—
156C4×SD16—316no—
157C4×D8—38no—
158C2×#107C2×D311yescharacteristic
159C2×#107C2×D311yescharacteristic
160C2×#106C2×D312yes—
161C2×#103—32no—
162C2×#103—32no—
163C2×#102—32no—
164C2×#102—32no—
165C2×C4×C8—31no—
166C2×C4×C8—31no—
167C2×C4×C8—31no—
168C2×C4×C8—38no—
169C2×C4×C8C2×D311yescharacteristic
170C23×D3—22no—
171C23×D3C2×D411yescharacteristic
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2411yescharacteristic
177C22×Dic3—22no—
178C22×Dic3C2×D411yescharacteristic
179C22×Dic3C2×D411yescharacteristic
180C22×Dic3C2×D411yescharacteristic
181C2×D12—24no—
182C2×D12—24no—
183C2×D12—28no—
184C2×D12—22no—
185C2×D12—48no—
186C2×D12C2414yes—
187C2×C4×D3—24no—
188C2×C4×D3—22no—
189C2×C4×D3—22no—
190C2×C4×D3—24no—
191C2×C4×D3—28no—
192C2×C4×D3—48no—
193C2×C4×D3C2×D412yes—
194C2×C4×D3C2×D414yes—
195C2×C4×D3C2×D414yes—
196C2×C4×D3C2412yes—
197C2×Dic6—24no—
198C2×Dic6—24no—
199C2×Dic6—22no—
200C2×Dic6C2414yes—
201C2×C3×C8#4114yes—
202C2×C3×C8#4114yes—
203C2×C3×C8C2412yes—
204C2×C3×C8C2412yes—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—28no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—28no—
209C3×C4⋊C4C2414yes—
210C3×C4⋊C4C2414yes—
211C3×C42C2×D412yes—
212C3×C42C2412yes—
213(C2×D3)⋊C4—28no—
214(C2×D3)⋊C4—28no—
215(C2×D3)⋊C4—28no—
216(C2×D3)⋊C4—28no—
217(C2×D3)⋊C4—28no—
218C4⋊Dic3—28no—
219Dic3⋊C4—28no—
220C4×Dic3—28no—
221C4×Dic3C2×D412yes—
222C4×Dic3C2×D414yes—
223C4×Dic3C2×D414yes—
224C4×Dic3C2412yes—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8C2412yes—
228C2×C3⋊C8C2412yes—
229Dic12—28no—
230D24—28no—
231#204—216no—
232D3×C8—28no—
233D3×C8—28no—
234C22×Q8—32no—
235C22×D4—32no—
236C22×D4—62no—
237C23×C4—31no—
238C23×C4—31no—
239C23×C4—31no—
240C23×C4—62no—
241C2×Q16—34no—
242C2×Q16—64no—
243C2×SD16—38no—
244C2×SD16—68no—
245C2×D8—34no—
246C2×D8—64no—
247C22×C8—31no—
248C22×C8—31no—
249C22×C8—34no—
250C22×C8—34no—
251C22×C8—64no—
252C22×C8—64no—
253C22×C8C22×D311yescharacteristic
254C22×C8C22×D311yescharacteristic
255#126—616no—
256#125—24no—
257#125C22×D318yes—
258#124—38no—
259#124—64no—
260#123—616no—
261C22⋊Q8—38no—
262C22⋊Q8—64no—
263#121—38no—
264#121—64no—
265C4×Q8—38no—
266C4×Q8—64no—
267C4×D4—38no—
268C4×D4—64no—
269C4×D4—616no—
270#117—616no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—62no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4C22×D312yes—
276C2×C4⋊C4C22×D312yes—
277C2×C22⋊C4—62no—
278C2×C22⋊C4—62no—
279C2×C22⋊C4—62no—
280C2×C22⋊C4—62no—
281C2×C22⋊C4—62no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—31no—
285C2×C42—34no—
286C2×C42—34no—
287C2×C42—62no—
288C2×C42C22×D311yescharacteristic
289#107C22×D314yes—
290#107C22×D314yes—
291#106C22×D318yes—
292#103—38no—
293#103—38no—
294#102—38no—
295#102—38no—
296C4×C8—34no—
297C4×C8—34no—
298C4×C8—34no—
299C4×C8C22×D314yes—
300C23×C3C22×D411yescharacteristic
301C22×D3—22no—
302C22×D3—22no—
303C22×D3—24no—
304C22×D3—44no—
305C22×D3—44no—
306C22×D3—44no—
307C22×D3#13514yes—
308C22×D3C22×D412yes—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—44no—
314C2×C3×C4—44no—
315C2×C3×C4C22×D412yes—
316C2×C3×C4C22×D412yes—
317C2×C3×C4C22×D411yescharacteristic
318C2×C3×C4C2×#4112yes—
319C2×C3×C4C2×#4112yes—
320C2×C3×C4C2511yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—24no—
324C2×Dic3—44no—
325C2×Dic3#13514yes—
326C2×Dic3C22×D412yes—
327C2×Dic3C22×D412yes—
328C2×Dic3C22×D412yes—
329D12—24no—
330D12—24no—
331D12—416no—
332D12—44no—
333C4×D3—28no—
334C4×D3—24no—
335C4×D3—22no—
336C4×D3—22no—
337C4×D3—28no—
338C4×D3—416no—
339Dic6—24no—
340Dic6—24no—
341Dic6—44no—
342C3×C8C2×#4114yes—
343C3×C8C2×#4114yes—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C24—31no—
347C24—62no—
348C2×Q8—34no—
349C2×Q8—62no—
350C2×Q8—64no—
351C2×Q8—64no—
352C2×D4—34no—
353C2×D4—68no—
354C2×D4—62no—
355C2×D4—64no—
356C2×D4—64no—
357C2×D4—128no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—34no—
364C22×C4—32no—
365C22×C4—34no—
366C22×C4—32no—
367C22×C4—64no—
368C22×C4—68no—
369C22×C4—64no—
370C22×C4—62no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—128no—
374C22×C4D3×D411yescharacteristic
375C22×C4D3×D411yescharacteristic
376C22×C4C23×D311yescharacteristic
377Q16—68no—
378SD16—616no—
379D8—68no—
380C2×C8—32no—
381C2×C8—32no—
382C2×C8—62no—
383C2×C8—62no—
384C2×C8—68no—
385C2×C8—68no—
386C2×C8#23914yes—
387C2×C8#23914yes—
388C2×C8C23×D312yes—
389C2×C8C23×D312yes—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—68no—
395C4⋊C4—68no—
396C4⋊C4C23×D314yes—
397C4⋊C4C23×D314yes—
398C22⋊C4—68no—
399C22⋊C4—68no—
400C22⋊C4—68no—
401C22⋊C4—68no—
402C22⋊C4—68no—
403C42—34no—
404C42—32no—
405C42—34no—
406C42—32no—
407C42—68no—
408C42D3×D412yes—
409C42C23×D312yes—
410C22×C3#53212yes—
411C22×C3C2×#13512yes—
412C22×C3C2×#13512yes—
413C22×C3C23×D411yescharacteristic
414C2×D3—28no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—44no—
418C2×D3—44no—
419C2×D3—44no—
420C2×D3—88no—
421C2×D3C2×#13514yes—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—44no—
425C3×C4—44no—
426C3×C4#53212yes—
427C3×C4C22×#4111yescharacteristic
428C3×C4C22×#4111yescharacteristic
429Dic3—22no—
430Dic3—22no—
431Dic3—44no—
432Dic3C2×#13514yes—
433C23—32no—
434C23—34no—
435C23—62no—
436C23—62no—
437C23—64no—
438C23—124no—
439C23—124no—
440C23—124no—
441C23C2×D3×D411yescharacteristic
442Q8—64no—
443Q8—64no—
444Q8—124no—
445D4—64no—
446D4—64no—
447D4—1216no—
448D4—124no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—32no—
454C2×C4—34no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—68no—
460C2×C4—68no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—64no—
466C2×C4—64no—
467C2×C4—1216no—
468C2×C4—124no—
469C2×C4C2×D3×D412yes—
470C2×C4C2×D3×D412yes—
471C2×C4C2×D3×D411yescharacteristic
472C2×C4C2×#23912yes—
473C2×C4C2×#23912yes—
474C2×C4C24×D311yescharacteristic
475C8—62no—
476C8—62no—
477C8C2×#23914yes—
478C8C2×#23914yes—
479C2×C3#316814yescomplemented
480C2×C3C2×#53211yescharacteristic
481C2×C3C22×#13511yescharacteristic
482C2×C3C22×#13511yescharacteristic
483D3—24no—
484D3—84no—
485C22—34no—
486C22—62no—
487C22—62no—
488C22—68no—
489C22—124no—
490C22—124no—
491C22—124no—
492C22—248no—
493C22#572512yes—
494C22D3×#13512yes—
495C22D3×#13512yes—
496C22C22×D3×D411yescharacteristic
497C4—22no—
498C4—22no—
499C4—34no—
500C4—44no—
501C4—44no—
502C4—62no—
503C4—62no—
504C4—124no—
505C4#572512yes—
506C4C22×#23911yescharacteristic
507C4C22×#23911yescharacteristic
508C3C2×#316811yescharacteristic, complemented, Sylow
509C2—64no—
510C2—244no—
511C2#8190714yesdirect product factor
512C2C2×#572511yescharacteristic
513C2C2×D3×#13511yescharacteristic
514C2C2×D3×#13511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#499C2
socleC23×C3C22×D4
prime radicalC2×#4883C2
hypercenterC2×#499D3
hypocenterC3C2×#3168
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×#5691C2semidirect
2. C2×C3×#499C2semidirect
3. C2×#5068C2semidirect
4. #81907C2direct (N × H)
5. C2×#4887C2semidirect
7. C2×#4873C2semidirect
8. C2×#4872C2semidirect
9. C2×#4864C2semidirect
10. C2×#4852C2semidirect
11. C2×#4696C2semidirect
12. C2×C4×D3×C8C2semidirect
21. #5691C22semidirect
32. C3×#499C22semidirect
39. #5068C22semidirect
45. #4887C22semidirect
47. #4873C22semidirect
48. #4872C22semidirect
49. #4864C22semidirect
50. #4852C22semidirect
51. #4696C22semidirect
52. C4×D3×C8C22semidirect
55. C2×#499D3semidirect
149. #499C2×D3semidirect
479. C2×C3#3168semidirect
508. C3C2×#3168semidirect
511. C2#81907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56912
C2×C3×#4992
C2×#50682
#819072
C2×#48872
C2×#48832
C2×#48732
C2×#48722
C2×#48642
C2×#48522
C2×#46962
C2×C4×D3×C82
C2×#31683