Finite Group Databasebeta

← C2×#13081017 #15632244

Subgroups — C2×#13081017 #15632244

Order 2816.

1994 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623226C212yesmaximal, complemented
2#13081017C2116yesmaximal, direct product factor
3C2×#10622476C212yesmaximal, complemented
4C2×#10622479C212yesmaximal, complemented
5C2×#10622679C212yesmaximal, complemented
6C2×#10622496C211yesmaximal, characteristic, complemented
7C2×#10622496C211yesmaximal, characteristic, complemented
8C2×C4×D88C211yesmaximal, characteristic, complemented
9C2×C8×D44C211yesmaximal, characteristic, complemented
10C2×#10622493C211yesmaximal, characteristic, complemented
11C2×D11×#107C211yesmaximal, characteristic, complemented
12C2×C11×#499C211yesmaximal, characteristic, complemented
13C2×C11×#125C2212yes—
14C22×D88C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17#10623226—28no—
18#10623226C22116yescomplemented
19C2×#66951—22no—
20C2×#66948—22no—
21C2×#66948C2212yes—
22C2×#66948C2212yes—
23C2×#66947—22no—
24C2×#66946—22no—
25C2×#66945C2212yes—
26C2×C4⋊C4×D11C2212yes—
27C2×C4×D44C2212yes—
28C2×C4×D44C2211yescharacteristic
29C11×#499C2218yescomplemented
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2212yes—
33C2×C4×C8×C11C2211yescharacteristic
34C2×#66885C2212yes—
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38#10622679C22116yescomplemented
39C2×#66873C2212yes—
40C2×#66873C2212yes—
41C2×#66872C2212yes—
42C2×#66871C2212yes—
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622496C2218yescomplemented
45#10622496C2218yescomplemented
46#10622493C2218yescomplemented
47D11×#107C2218yescomplemented
48#10622479C22116yescomplemented
49#10622476C22116yescomplemented
50C4×D88C2218yescomplemented
51C8×D44C2218yescomplemented
52C22×D44—22no—
53C22×D44—22no—
54C22×D44D411yescharacteristic
55C22×D44C2312yes—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2311yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#125—24no—
63C11×#125C2318yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D411yescharacteristic
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×D88—24no—
82C2×D88C2314yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11C2314yes—
86C2×C8×D11C2314yes—
87#66951—216no—
88#66948—216no—
89#66948—24no—
90#66948—24no—
91#66948C2318yes—
92#66948C2318yes—
93#66947—216no—
94#66946—216no—
95#66945—24no—
96#66945C2318yes—
97C4⋊C4×D11—24no—
98C4⋊C4×D11C2318yes—
99C4×D44—24no—
100C4×D44D414yes—
101C4×D44C2314yes—
102C4×D44C2318yes—
103C11×#107C2314yes—
104C11×#107C2314yes—
105C11×#106C2318yes—
106C4×C8×C11C2314yes—
107#66885C2318yes—
108(C2×D11)⋊C8C2314yes—
109(C2×D11)⋊C8C2314yes—
110#66882C2314yes—
111#66873C2318yes—
112#66873C2318yes—
113#66872C2318yes—
114#66871C2318yes—
115C4⋊(C11⋊C8)C2314yes—
116C2×#3339—111nomaximal, Sylow
117C23×D11—22no—
118C23×D11C2×D411yescharacteristic
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×D44—24no—
129C2×D44—28no—
130C2×D44—28no—
131C2×D44—22no—
132C2×D44—24no—
133C2×D44—24no—
134C2×D44—48no—
135C2×D44—84no—
136C2×D44C2×D414yes—
137C2×D44C2414yes—
138C2×C4×D11—28no—
139C2×C4×D11—28no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—84no—
145C2×C4×D11—84no—
146C2×C4×D11C2×D412yes—
147C2×C4×D11C2×D412yes—
148C2×C4×D11C2412yes—
149C2×C4×D11C2412yes—
150C2×C8×C11—22no—
151C2×C8×C11#4114yes—
152C2×C8×C11C2412yes—
153C2×C8×C11C2412yes—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4C2414yes—
159C11×C4⋊C4C2414yes—
160C42×C11C2×D412yes—
161C42×C11C2412yes—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4C2×D414yes—
167(C2×D11)⋊C4C2×D414yes—
168C4⋊Dic11—22no—
169C4⋊Dic11C2×D414yes—
170C4⋊Dic11C2414yes—
171Dic11⋊C4—28no—
172C4×Dic11—28no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C2412yes—
176C2×C11⋊C8C2412yes—
177D88—28no—
178C8×D11—28no—
179C8×D11—28no—
180C2×#553—112no—
181#3339—1116no—
182C2×#499D1111yescharacteristic, complemented
183C2×#481—112no—
184C2×#482—112no—
185C2×#478—112no—
186C2×#466—111no—
187C2×#466—111no—
188C2×C4×D8—111no—
189C2×C8×D4—111no—
190C2×#427—111no—
191C22×#107—111no—
192C23×C11C22×D411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—24no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11#13514yes—
203C22×D11C22×D412yes—
204C22×D11C22×D412yes—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11C22×D412yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4112yes—
215C2×C4×C112−1+412yes—
216C2×C4×C11C2511yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—44no—
221C2×Dic11C22×D412yes—
222C2×Dic11C22×D412yes—
223D44—28no—
224D44—24no—
225D44—24no—
226D44—416no—
227D44—44no—
228D44—88no—
229C4×D11—24no—
230C4×D11—24no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—88no—
236C4×D11—88no—
237C8×C11—22no—
238C8×C11C2×#4114yes—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C22×D8—111no—
242C23×C8—111no—
243C23×C8—111no—
244#553—1116no—
245#553—228no—
246C2×#126—222no—
247C2×#125C2×D1112yes—
248C2×#123—222no—
249C2×#121—112no—
250C2×#121—112no—
251C2×#121—222no—
252C2×C4×D4—111no—
253C2×C4×D4—112no—
254C2×C4×D4—222no—
255C2×#117—112no—
256C22×C4⋊C4—112no—
257#499C2×D1118yescomplemented
258#482—1116no—
259#481—1116no—
260#478—1116no—
261#466—118no—
262#466—118no—
263C4×D8—118no—
264C8×D4—118no—
265#427—118no—
266C2×#107—111no—
267C2×#107—112no—
268C2×#107—118no—
269C2×#107C2×D1111yescharacteristic
270C2×#107C2×D1111yescharacteristic
271C2×#106—112no—
272C2×#106C2×D1112yes—
273C2×C4⋊C8—111no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102—112no—
277C2×C22⋊C8—111no—
278C2×C22⋊C8—111no—
279C2×C4×C8C2×D1111yescharacteristic
280C22×C11#54712yes—
281C22×C11C2×#13512yes—
282C22×C11#57612yes—
283C22×C11C23×D411yescharacteristic
284C2×D11—28no—
285C2×D11—22no—
286C2×D11—22no—
287C2×D11—22no—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—88no—
295C2×D11C2×#13514yes—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—44no—
299C4×C11—44no—
300C4×C11#54712yes—
301C4×C11C22×#4111yescharacteristic
302C4×C11C2×2−1+411yescharacteristic
303Dic11—22no—
304Dic11—22no—
305Dic11—44no—
306C22×D4—111no—
307C22×D4—112no—
308C22×D4—222no—
309C22×D4—222no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—222no—
313C23×C4—222no—
314C2×D8—114no—
315C2×D8—224no—
316C22×C8—111no—
317C22×C8—111no—
318C22×C8—114no—
319C22×C8—114no—
320C22×C8—224no—
321C22×C8—224no—
322C22×C8C22×D1111yescharacteristic
323C22×C8C22×D1111yescharacteristic
324#126—2216no—
325#125—24no—
326#125C22×D1118yes—
327#123—2216no—
328#121—118no—
329#121—118no—
330#121—224no—
331#121—224no—
332#121—2216no—
333C4×D4—114no—
334C4×D4—114no—
335C4×D4—118no—
336C4×D4—2216no—
337C4×D4—224no—
338#117—118no—
339#117—224no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4C22×D1112yes—
348C2×C4⋊C4C22×D1112yes—
349C2×C22⋊C4—111no—
350C2×C22⋊C4—111no—
351C2×C22⋊C4—222no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—222no—
356C2×C42C22×D1111yescharacteristic
357#107—114no—
358#107—118no—
359#107C22×D1114yes—
360#107C22×D1114yes—
361#106—118no—
362#106C22×D1118yes—
363C4⋊C8—114no—
364#102—118no—
365#102—118no—
366#102—118no—
367C22⋊C8—114no—
368C22⋊C8—114no—
369C4×C8C22×D1114yes—
370C2×C11#333914yescomplemented
371C2×C11C2×#54711yescharacteristic
372C2×C11C22×#13511yescharacteristic
373C2×C11C2×#57611yescharacteristic
374D11—24no—
375D11—42no—
376D11—84no—
377C24—111no—
378C24—111no—
379C24—222no—
380C2×D4—114no—
381C2×D4—114no—
382C2×D4—224no—
383C2×D4—228no—
384C2×D4—228no—
385C2×D4—222no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—448no—
389C2×D4—884no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—228no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—228no—
405C22×C4—884no—
406C22×C4—884no—
407C22×C4D4×D1111yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4C23×D1111yescharacteristic
410D8—228no—
411C2×C8—22no—
412C2×C8—112no—
413C2×C8—112no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—228no—
417C2×C8—228no—
418C2×C8#434314yes—
419C2×C8C23×D1112yes—
420C2×C8C23×D1112yes—
421C4⋊C4—28no—
422C4⋊C4—28no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—114no—
426C4⋊C4—114no—
427C4⋊C4—228no—
428C4⋊C4—222no—
429C4⋊C4C23×D1114yes—
430C4⋊C4C23×D1114yes—
431C22⋊C4—114no—
432C22⋊C4—114no—
433C22⋊C4—228no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C42—228no—
438C42D4×D1112yes—
439C42C23×D1112yes—
440C11C2×#333911yescharacteristic, complemented, Sylow
441C23—114no—
442C23—112no—
443C23—112no—
444C23—222no—
445C23—222no—
446C23—222no—
447C23—222no—
448C23—222no—
449C23—224no—
450C23—444no—
451C23—444no—
452C23—444no—
453C23C2×D4×D1111yescharacteristic
454D4—228no—
455D4—224no—
456D4—224no—
457D4—4416no—
458D4—444no—
459D4—888no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—224no—
477C2×C4—444no—
478C2×C4—888no—
479C2×C4—888no—
480C2×C4C2×D4×D1112yes—
481C2×C4C2×D4×D1112yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434312yes—
484C2×C4#6704012yes—
485C2×C4C24×D1111yescharacteristic
486C8—22no—
487C8—222no—
488C8—222no—
489C8C2×#434314yes—
490C22—114no—
491C22—228no—
492C22—222no—
493C22—222no—
494C22—222no—
495C22—222no—
496C22—222no—
497C22—444no—
498C22—444no—
499C22—444no—
500C22—444no—
501C22—888no—
502C22#1062325712yes—
503C22D11×#13512yes—
504C22#1062330012yes—
505C22C22×D4×D1111yescharacteristic
506C4—22no—
507C4—22no—
508C4—44no—
509C4—44no—
510C4—222no—
511C4—222no—
512C4—444no—
513C4#1062325712yes—
514C4C22×#434311yescharacteristic
515C4C2×#6704011yescharacteristic
516C2—224no—
517C2—442no—
518C2—884no—
519C2#1308101714yesdirect product factor
520C2C2×#1062325711yescharacteristic
521C2C2×D11×#13511yescharacteristic
522C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#499C2
socleC23×C11C22×D4
hypercenterC2×#499D11
hypocenterC11C2×#3339
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. #13081017C2direct (N × H)
3. C2×#10622476C2semidirect
4. C2×#10622479C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622496C2semidirect
7. C2×#10622496C2semidirect
8. C2×C4×D88C2semidirect
9. C2×C8×D44C2semidirect
10. C2×#10622493C2semidirect
11. C2×D11×#107C2semidirect
12. C2×C11×#499C2semidirect
18. #10623226C22semidirect
29. C11×#499C22semidirect
38. #10622679C22semidirect
44. #10622496C22semidirect
45. #10622496C22semidirect
46. #10622493C22semidirect
47. D11×#107C22semidirect
48. #10622479C22semidirect
49. #10622476C22semidirect
50. C4×D88C22semidirect
51. C8×D44C22semidirect
182. C2×#499D11semidirect
257. #499C2×D11semidirect
370. C2×C11#3339semidirect
440. C11C2×#3339semidirect
519. C2#13081017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232262
#130810172
C2×#106224762
C2×#106224792
C2×#106226792
C2×#106224962
C2×C4×D882
C2×C8×D442
C2×#106224932
C2×D11×#1072
C2×C11×#4992
C2×#333911