Finite Group Databasebeta

← C2×#13079745 #15625815

Subgroups — C2×#13079745 #15625815

Order 2816.

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×#10623256C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079745C2116yesmaximal, direct product factor
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622307C211yesmaximal, characteristic, complemented
7C2×#10622476C214yesmaximal, complemented
8C2×#10622483C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic, complemented
10C2×C11×#498C211yesmaximal, characteristic, complemented
11C22×#4343—21no—
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000—21no—
16C2×#66997—21no—
17#10623256—24no—
18#10623256C2218yes—
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8C2218yescomplemented
21C2×#66948—21no—
22C2×#66948C2212yes—
23C2×#66946—21no—
24C2×#66946C2212yes—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2212yes—
27C2×#66941—21no—
28C2×#66941C2212yes—
29C2×#66927C2211yescharacteristic
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#498C2218yescomplemented
33C2×C11×#106C2214yes—
34C2×C4×C8×C11C2211yescharacteristic
35C2×#66885C2214yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×Dic11⋊C8C2212yes—
38#10622701C2218yescomplemented
39#10622692C2218yescomplemented
40C2×#66873C2214yes—
41C2×#66872C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622483C22132yescomplemented
44#10622476C22132yescomplemented
45#10622307C2218yescomplemented
46#10622298C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C2×#4343—28no—
50C2×#4343—48no—
51C2×Q8×D11—28no—
52C2×Q8×D11—48no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2312yes—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C11×C4⋊Q8C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C42×C11C2311yescharacteristic
74#67000—28no—
75#66997—28no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66948—24no—
87#66948—28no—
88#66948C2318yes—
89#66946—24no—
90#66946—28no—
91#66946C2318yes—
92C4⋊C4×D11—24no—
93C4⋊C4×D11—28no—
94C4⋊C4×D11C2318yes—
95#66941—24no—
96#66941—28no—
97#66941C2318yes—
98#66927—22no—
99#66927C2314yes—
100C42×D11D414yes—
101C42×D11C2314yes—
102#66922—22no—
103#66922C2314yes—
104C11×#106C23116yes—
105C4×C8×C11C2314yes—
106#66885C23116yes—
107(C2×D11)⋊C8C2318yes—
108Dic11⋊C8C2318yes—
109#66873C23116yes—
110#66872C23116yes—
111C4×C11⋊C8C2314yes—
112C2×#3227—111nomaximal, Sylow
113C23×D11—22no—
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—24no—
116C2×Q8×C11—24no—
117C2×Q8×C11—44no—
118C2×Q8×C11—44no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128#4343—432no—
129Q8×D11—432no—
130C2×D44—28no—
131C2×D44—22no—
132C2×D44—24no—
133C2×D44—24no—
134C2×D44—28no—
135C2×D44—48no—
136C2×D44—44no—
137C2×D44—44no—
138C2×D44C2414yes—
139C2×C4×D11—28no—
140C2×C4×D11—28no—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—48no—
144C2×C4×D11—48no—
145C2×C4×D11SD1618yes—
146C2×C4×D11C2×D412yes—
147C2×C4×D11C2×D414yes—
148C2×C4×D11C2×D414yes—
149C2×C4×D11C2412yes—
150C2×Dic22—28no—
151C2×Dic22—24no—
152C2×Dic22—48no—
153C2×Dic22—44no—
154C2×C8×C11—24no—
155C2×C8×C11C2414yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2414yes—
161C11×C4⋊C4C2414yes—
162C42×C11C2×D412yes—
163C42×C11C2412yes—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166C4⋊Dic11—22no—
167C4⋊Dic11—24no—
168C4⋊Dic11C2414yes—
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171C4×Dic11C2×D412yes—
172C4×Dic11C2×D414yes—
173C4×Dic11C2×D414yes—
174C4×Dic11C2412yes—
175C2×C11⋊C8—24no—
176C2×C11⋊C8C2414yes—
177C2×#532—111no—
178C22×C4⋊Q8—111no—
179#3227—1116no—
180C2×#498—111no—
181C2×#498D1111yescharacteristic, complemented
182C2×#486—111no—
183C2×#486—111no—
184C2×#481—114no—
185C2×#476—114no—
186C2×#431—111no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—44no—
192C22×D11—44no—
193C22×D11—44no—
194C22×D11C2×SD1614yes—
195C22×D11C22×D412yes—
196Q8×C11—48no—
197Q8×C11—48no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11C2×SD1614yes—
203C2×C4×C11AGL(1,ℤ/8)14yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D412yes—
206C2×C4×C11C22×D412yes—
207C2×C4×C112−1+414yes—
208C2×C4×C11C2511yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—44no—
213C2×Dic11C2×SD1614yes—
214C2×Dic11C22×D412yes—
215C2×Dic11C22×D412yes—
216C2×Dic11C22×D412yes—
217D44—28no—
218D44—416no—
219D44—44no—
220D44—48no—
221D44—48no—
222C4×D11—24no—
223C4×D11—28no—
224C4×D11—24no—
225C4×D11—416no—
226C4×D11—416no—
227C4×D11C2×SD16116yes—
228Dic22—416no—
229Dic22—48no—
230C8×C11—24no—
231C11⋊C8—24no—
232C22×#41—221no—
233C23×Q8—221no—
234#532—118no—
235#532—224no—
236C2×C4⋊Q8—118no—
237C2×C4⋊Q8—112no—
238C2×C4⋊Q8—111no—
239C2×C4⋊Q8—221no—
240C2×C4⋊Q8—224no—
241C2×C4⋊Q8—221no—
242C2×C4⋊Q8C2×D1111yescharacteristic
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#127—111no—
245C2×#124—221no—
246C2×#121—112no—
247C2×#121—221no—
248C2×C4×D4—112no—
249C2×C4×D4—221no—
250C22×C4⋊C4—112no—
251C22×C4⋊C4—221no—
252C22×C42—111no—
253#498—118no—
254#498C2×D1118yescomplemented
255#486—118no—
256#486—118no—
257#481—1132no—
258#476—1132no—
259#431—118no—
260C2×#106—114no—
261C2×#106C2×D1114yes—
262C2×C4⋊C8—112no—
263C2×#102—114no—
264C2×#102—114no—
265C2×C22⋊C8—112no—
266C2×C4×C8—111no—
267C2×C4×C8C2×D1111yescharacteristic
268C22×C11#53612yes—
269C22×C11C22×SD1612yes—
270C22×C11C2×AGL(1,ℤ/8)12yes—
271C22×C11C23×D411yescharacteristic
272C2×D11—22no—
273C2×D11—28no—
274C2×D11—22no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—88no—
279C2×D11C22×SD1614yes—
280C4×C11—44no—
281C4×C11—44no—
282C4×C11#53612yes—
283C4×C11C22×SD1614yes—
284C4×C11C2×AGL(1,ℤ/8)14yes—
285C4×C11C2×2−1+412yes—
286Dic11—22no—
287Dic11—22no—
288Dic11—44no—
289Dic11C22×SD1614yes—
290C2×#41—228no—
291C2×#41—448no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—222no—
295C22×Q8—228no—
296C22×Q8—221no—
297C22×Q8—448no—
298C22×D4—112no—
299C22×D4—222no—
300C22×D4—221no—
301C22×D4—221no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—222no—
306C23×C4—222no—
307C22×C8—112no—
308C22×C8C22×D1112yes—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—118no—
312C4⋊Q8—114no—
313C4⋊Q8—224no—
314C4⋊Q8—228no—
315C4⋊Q8—228no—
316C4⋊Q8—222no—
317C4⋊Q8C22×D1114yes—
318C4⋊Q8C22×D1114yes—
319#127—114no—
320#127—222no—
321#124—228no—
322#121—118no—
323#121—224no—
324#121—228no—
325C4×D4—118no—
326C4×D4—224no—
327C4×D4—228no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—228no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4C22×D1112yes—
338C2×C4⋊C4C22×D1112yes—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C42—111no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—114no—
345C2×C42—114no—
346C2×C42C22×D1111yescharacteristic
347#106—1116no—
348#106C22×D11116yes—
349C4⋊C8—118no—
350#102—1116no—
351#102—1116no—
352C22⋊C8—118no—
353C4×C8—114no—
354C4×C8C22×D1114yes—
355C2×C11#322714yescomplemented
356C2×C11C2×#53611yescharacteristic
357C2×C11C23×SD1611yescharacteristic
358C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
359D11—24no—
360D11—84no—
361C24—111no—
362C24—222no—
363#41—4432no—
364C2×Q8—24no—
365C2×Q8—24no—
366C2×Q8—44no—
367C2×Q8—44no—
368C2×Q8—228no—
369C2×Q8—224no—
370C2×Q8—448no—
371C2×Q8—4432no—
372C2×Q8—444no—
373C2×D4—114no—
374C2×D4—228no—
375C2×D4—224no—
376C2×D4—222no—
377C2×D4—224no—
378C2×D4—228no—
379C2×D4—448no—
380C2×D4—444no—
381C2×D4—444no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—111no—
385C22×C4—118no—
386C22×C4—114no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—112no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—228no—
393C22×C4—228no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—222no—
397C22×C4—448no—
398C22×C4—448no—
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4C23×D1111yescharacteristic
402C2×C8—24no—
403C2×C8—114no—
404C2×C8—224no—
405C2×C8C23×D1114yes—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—114no—
411C4⋊C4—228no—
412C4⋊C4—228no—
413C4⋊C4—222no—
414C4⋊C4—224no—
415C4⋊C4C23×D1114yes—
416C4⋊C4C23×D1114yes—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C42—114no—
420C42—112no—
421C42—114no—
422C42—112no—
423C42D4×D1112yes—
424C42C23×D1112yes—
425C11C2×#322711yescharacteristic, complemented, Sylow
426C23—114no—
427C23—112no—
428C23—222no—
429C23—222no—
430C23—224no—
431C23—444no—
432C23—444no—
433C23—444no—
434C23C2×D4×D1111yescharacteristic
435Q8—48no—
436Q8—48no—
437Q8—4416no—
438Q8—448no—
439D4—228no—
440D4—4416no—
441D4—444no—
442D4—448no—
443D4—448no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—114no—
449C2×C4—112no—
450C2×C4—1116no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—228no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—4416no—
460C2×C4—4416no—
461C2×C4—444no—
462C2×C4SD16×D1114yes—
463C2×C4#6696714yes—
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4C2×D4×D1112yes—
466C2×C4C2×D4×D1112yes—
467C2×C4#6704014yes—
468C2×C4C24×D1111yescharacteristic
469C8—24no—
470C8—224no—
471C22—114no—
472C22—222no—
473C22—228no—
474C22—222no—
475C22—444no—
476C22—444no—
477C22—444no—
478C22—888no—
479C22#1062325512yes—
480C22C2×SD16×D1112yes—
481C22C2×#6696712yes—
482C22C22×D4×D1111yescharacteristic
483C4—44no—
484C4—44no—
485C4—114no—
486C4—222no—
487C4—222no—
488C4—444no—
489C4#1062325512yes—
490C4C2×SD16×D1114yes—
491C4C2×#6696714yes—
492C4C2×#6704012yes—
493C2—224no—
494C2—884no—
495C2#1307974514yesdirect product factor
496C2C2×#1062325511yescharacteristic
497C2C22×SD16×D1111yescharacteristic
498C2C22×#6696711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#498D11
hypocenterC11C2×#3227
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079745C2direct (N × H)
4. C2×#10622692C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622307C2semidirect
7. C2×#10622476C2semidirect
8. C2×#10622483C2semidirect
9. C2×#10622298C2semidirect
10. C2×C11×#498C2semidirect
20. D11×C4⋊Q8C22semidirect
32. C11×#498C22semidirect
38. #10622701C22semidirect
39. #10622692C22semidirect
43. #10622483C22semidirect
44. #10622476C22semidirect
45. #10622307C22semidirect
46. #10622298C22semidirect
181. C2×#498D11semidirect
254. #498C2×D11semidirect
355. C2×C11#3227semidirect
425. C11C2×#3227semidirect
495. C2#13079745direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×D11×C4⋊Q82
#130797452
C2×#106226922
C2×#106227012
C2×#106223072
C2×#106224762
C2×#106224832
C2×#106222982
C2×C11×#4982
C2×#322711