Finite Group Databasebeta

← C2×#13081045 #15632275

Subgroups — C2×#13081045 #15632275

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic
2C2×#10623115C211yesmaximal, characteristic
3#13081045C2116yesmaximal, direct product factor
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622480C212yesmaximal, complemented
6C2×#10622428C212yesmaximal, complemented
7C2×#10622464C211yesmaximal, characteristic, complemented
8C2×#10622426C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic
11C2×#10622473C212yesmaximal, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000—21no—
16C2×#66999C2212yes—
17C2×Q8×Dic11—21no—
18C22×#4326C2211yescharacteristic
19C22×C8×D11C2212yes—
20#10623263—24no—
21#10623263C2218yes—
22#10623115—24no—
23#10623115C2218yes—
24C2×#66951—22no—
25C2×#66951—22no—
26C2×#66950C2212yes—
27C2×#66945C2212yes—
28C2×#66945C2212yes—
29C2×#66928—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C11×#475C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66881C2212yes—
41C2×#66880C2212yes—
42#10622691C2218yescomplemented
43C4×#4326C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66871C2212yes—
46C2×#66871C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622480C22116yescomplemented
50#10622473C22116yescomplemented
51#10622464C2218yescomplemented
52#10622447C2218yes—
53#10622428C22116yescomplemented
54#10622426C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D44D411yescharacteristic
58C22×C4×D11C2312yes—
59C22×Dic22—21no—
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C4×Q8×C11—22no—
65C4×Q8×C11C2314yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#67000—28no—
73#66999—24no—
74#66999C2318yes—
75Q8×Dic11—28no—
76C2×#4326—24no—
77C2×#4326C2314yes—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4D412yes—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—22no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×C8×D11—28no—
96C2×C8×D11C2318yes—
97#66951—216no—
98#66951—216no—
99#66950—24no—
100#66950C2318yes—
101#66945—24no—
102#66945—24no—
103#66945C2318yes—
104#66945C2318yes—
105#66928—28no—
106C4×D44D414yes—
107C4×D44C2314yes—
108#66922—22no—
109#66922C2314yes—
110C4×Dic22—22no—
111C4×Dic22—28no—
112C4×Dic22C2314yes—
113C11×#106C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#103C2318yes—
116#66899C2314yes—
117(C2×D11)⋊C8C2318yes—
118#66881C2318yes—
119#66880C2318yes—
120#66874C2314yes—
121#66871C2314yes—
122#66871C2318yes—
123#66871C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3342—111nomaximal, Sylow
126C23×D11C2×D412yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11C2412yes—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11C2×D412yes—
143C2×D44—24no—
144C2×D44C2×D414yes—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11C2×D414yes—
148C2×C4×D11C2414yes—
149C2×Dic22—24no—
150C2×Dic22—21no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—44no—
154C2×Dic22C2412yes—
155C2×C8×C11—24no—
156C2×C8×C11C2414yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4C2414yes—
162C11×C4⋊C4C2412yes—
163C42×C11—24no—
164C42×C11C2×D412yes—
165C42×C11C2412yes—
166#4326—28no—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4C2×D418yes—
172C4⋊Dic11—28no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—24no—
176C4⋊Dic11C2×D414yes—
177C4⋊Dic11C2414yes—
178C4⋊Dic11C2412yes—
179Dic11⋊C4—28no—
180Dic11⋊C4—24no—
181C4×Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8#4114yes—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2412yes—
188C8×D11—216no—
189C2×#556—111no—
190C2×#556—111no—
191#3342—1116no—
192C2×#500—111no—
193C2×#485—112no—
194C2×#485—112no—
195C2×#475—111no—
196C2×#475D1111yescharacteristic, complemented
197C2×#467—112no—
198C2×C4×Q16—111no—
199C2×C8×D4—111no—
200C2×#427—112no—
201C23×C11C22×D411yescharacteristic
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11C22×D414yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—48no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11#13514yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C2×#4112yes—
222C2×C4×C112−1+412yes—
223C2×C4×C11C2511yescharacteristic
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230C2×Dic11—42no—
231C2×Dic11C22×D414yes—
232D44—28no—
233C4×D11—28no—
234C4×D11—24no—
235C4×D11—24no—
236Dic22—22no—
237Dic22—22no—
238Dic22—42no—
239Dic22—48no—
240C8×C11—24no—
241C11⋊C8—22no—
242C11⋊C8C2×#4114yes—
243C22×Q16—111no—
244C23×C8—112no—
245#556—118no—
246#556—118no—
247#556—224no—
248#556—224no—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×#126—222no—
252C2×#126—222no—
253C2×#124—221no—
254C2×#124—221no—
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8—112no—
257C2×C4×Q8—111no—
258C2×C4×Q8—221no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×D4—111no—
262C2×#117—112no—
263C2×#117—112no—
264#500—118no—
265#485—1116no—
266#485—1116no—
267#475—118no—
268#475C2×D1118yescomplemented
269#467—1116no—
270C4×Q16—118no—
271C8×D4—118no—
272#427—1116no—
273C2×#107—112no—
274C2×#107—112no—
275C2×#107—111no—
276C2×#106—112no—
277C2×#106C2×D1112yes—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—111no—
280C2×#103—112no—
281C2×#103—111no—
282C2×#103C2×D1112yes—
283C2×C22⋊C8—112no—
284C2×C4×C8—111no—
285C22×C11#54712yes—
286C22×C11C2×#13512yes—
287C22×C11#57812yes—
288C22×C11C23×D411yescharacteristic
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—48no—
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—44no—
296C4×C11—42no—
297C4×C11#54712yes—
298C4×C11C2×#13514yes—
299C4×C11C22×#4111yescharacteristic
300C4×C11C2×2−1+411yescharacteristic
301Dic11—24no—
302Dic11—42no—
303Dic11—44no—
304Dic11—42no—
305C22×Q8—21no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8C22×D1111yescharacteristic
309C22×D4—111no—
310C23×C4—112no—
311C2×Q16—114no—
312C2×Q16—224no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—118no—
316C22×C8—228no—
317C22×C8C22×D1112yes—
318C4⋊Q8—22no—
319C4⋊Q8—114no—
320C4⋊Q8—222no—
321C4⋊Q8C22×D1114yes—
322#126—2216no—
323#126—2216no—
324#124—228no—
325#124—228no—
326C22⋊Q8—118no—
327C22⋊Q8—118no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330C4×Q8—22no—
331C4×Q8—114no—
332C4×Q8—228no—
333C4×Q8—228no—
334C4×Q8—222no—
335C4×Q8C22×D1114yes—
336C4×D4—114no—
337C4×D4—114no—
338#117—118no—
339#117—118no—
340#117—224no—
341#117—224no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—112no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C42—21no—
359C2×C42—222no—
360C2×C42—222no—
361C2×C42—221no—
362C2×C42C22×D1111yescharacteristic
363#107—114no—
364#107—118no—
365#107—118no—
366#106—118no—
367#106C22×D1118yes—
368C4⋊C8C22×D1114yes—
369#103—114no—
370#103—118no—
371#103—114no—
372#103C22×D1118yes—
373C22⋊C8—118no—
374C4×C8—114no—
375C2×C11#334214yescomplemented
376C2×C11C2×#54711yescharacteristic
377C2×C11C22×#13511yescharacteristic
378C2×C11C2×#57811yescharacteristic
379D11—44no—
380C24—112no—
381C2×Q8—21no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—44no—
386C2×Q8—112no—
387C2×Q8—221no—
388C2×Q8—224no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—444no—
392C2×Q8C23×D1112yes—
393C2×D4—114no—
394C2×D4—224no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—112no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—24no—
411C2×C8—114no—
412C2×C8—112no—
413C2×C8—112no—
414C2×C8—2216no—
415C2×C8—222no—
416C2×C8C23×D1114yes—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—114no—
422C4⋊C4—112no—
423C4⋊C4—114no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—221no—
427C4⋊C4—222no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4C23×D1112yes—
431C4⋊C4C23×D1114yes—
432C22⋊C4—118no—
433C22⋊C4—228no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C42—24no—
438C42—228no—
439C42—228no—
440C42—224no—
441C42D4×D1112yes—
442C42C23×D1112yes—
443C11C2×#334211yescharacteristic, complemented, Sylow
444C23—114no—
445C23—224no—
446C23—224no—
447C23—224no—
448C23C2×D4×D1111yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—48no—
452Q8—42no—
453Q8—222no—
454Q8—222no—
455Q8—448no—
456Q8—442no—
457D4—228no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—114no—
466C2×C4—224no—
467C2×C4—228no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—444no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4#6696914yes—
477C2×C4C2×D4×D1112yes—
478C2×C4C2×D4×D1112yes—
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4#6704012yes—
481C2×C4#41×D1112yes—
482C2×C4C24×D1111yescharacteristic
483C8—24no—
484C8—114no—
485C8—222no—
486C22—224no—
487C22—224no—
488C22—224no—
489C22—448no—
490C22#1062316212yes—
491C22C2×#6696912yes—
492C22#1062331012yes—
493C22C22×D4×D1111yescharacteristic
494C4—22no—
495C4—44no—
496C4—42no—
497C4—42no—
498C4—224no—
499C4—444no—
500C4—442no—
501C4—442no—
502C4#1062316212yes—
503C4C2×#6696914yes—
504C4C2×#6704011yescharacteristic
505C4C2×#41×D1111yescharacteristic
506C2—444no—
507C2#1308104514yesdirect product factor
508C2C2×#1062316211yescharacteristic
509C2C22×#6696911yescharacteristic
510C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#475D11
hypocenterC11C2×#3342
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13081045C2direct (N × H)
4. C2×#10622691C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622464C2semidirect
8. C2×#10622426C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×#10622473C2semidirect
12. C2×C11×#475C2semidirect
34. C11×#475C22semidirect
42. #10622691C22semidirect
43. C4×#4326C22semidirect
49. #10622480C22semidirect
50. #10622473C22semidirect
51. #10622464C22semidirect
53. #10622428C22semidirect
54. #10622426C22semidirect
196. C2×#475D11semidirect
268. #475C2×D11semidirect
375. C2×C11#3342semidirect
443. C11C2×#3342semidirect
507. C2#13081045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106231152
#130810452
C2×#106226912
C2×#106224802
C2×#106224282
C2×#106224642
C2×#106224262
C2×C4×#43262
C2×#106224472
C2×#106224732
C2×C11×#4752
C2×#334211