Finite Group Databasebeta

← C2×#13081014 #15632241

Subgroups — C2×#13081014 #15632241

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×#10623045C212yesmaximal, complemented
2#13081014C2116yesmaximal, direct product factor
3C2×#10622491C211yesmaximal, characteristic, complemented
4C2×#10622581C212yesmaximal, complemented
5C2×#10622498C212yesmaximal, complemented
6C2×#10622504C212yesmaximal, complemented
7C2×#10622496C211yesmaximal, characteristic, complemented
8C2×#10622728C211yesmaximal, characteristic, complemented
9C2×#10622485C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
11C2×#10622493C211yesmaximal, characteristic, complemented
12C22×C11×#107C211yesmaximal, characteristic, complemented
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66983—22no—
16C2×#66983C2212yes—
17C2×C4×C22⋊D11—22no—
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623045—28no—
22#10623045C22116yescomplemented
23C2×#66951—22no—
24C2×#66948C2212yes—
25C2×#66947—22no—
26C2×#66946C2212yes—
27C2×#66945C2212yes—
28C2×#66943C2212yes—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2212yes—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#107C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622728C2218yescomplemented
35C2×#66885C2212yes—
36C8×C22⋊D11C2218yescomplemented
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622581C22116yescomplemented
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66872C2212yes—
45C2×#66872C2212yes—
46#10622504C22116yescomplemented
47#10622498C22116yescomplemented
48#10622496C2218yescomplemented
49#10622493C2218yescomplemented
50#10622491C2218yescomplemented
51#10622485C2218yescomplemented
52C23×C4×C11—22no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—22no—
55C22×C22⋊D11D411yescharacteristic
56C22×D44—22no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11—24no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2314yes—
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2318yes—
69C2×C22⋊Dic11D411yescharacteristic
70#66983—24no—
71#66983—216no—
72#66983C2318yes—
73C4×C22⋊D11—216no—
74C4×C22⋊D11D414yes—
75C4×C22⋊D11C2314yes—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C2×D88—24no—
90C2×D88C2314yes—
91C2×C8×D11—24no—
92C2×C8×D11C2314yes—
93#66951—216no—
94#66948—24no—
95#66948C2318yes—
96#66947—216no—
97#66946—24no—
98#66946C2318yes—
99#66945—24no—
100#66945C2318yes—
101#66943—24no—
102#66943C2318yes—
103C11×#107C2314yes—
104C11×#107C2314yes—
105C11×#107C2318yes—
106C22⋊(C11⋊C8)C2314yes—
107#66885C2318yes—
108(C2×D11)⋊C8C2314yes—
109#66882C2314yes—
110Dic11⋊C8C2314yes—
111C8×Dic11C2314yes—
112#66873C2318yes—
113#66873C2318yes—
114#66872C2318yes—
115#66872C2318yes—
116C2×#3339—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—84no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—28no—
132C2×C22⋊D11—48no—
133C2×C22⋊D11C2×D414yes—
134C22×Dic11—22no—
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C2×D44—28no—
139C2×D44—22no—
140C2×D44—24no—
141C2×D44—24no—
142C2×D44—84no—
143C2×D44C2414yes—
144C2×C4×D11—28no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—84no—
148C2×C4×D11C2×D412yes—
149C2×C4×D11C2412yes—
150C2×C8×C11—28no—
151C2×C8×C11—22no—
152C2×C8×C11#4114yes—
153C2×C8×C11C2412yes—
154C2×C8×C11C2412yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4C2414yes—
159C11×C4⋊C4C2414yes—
160C22⋊Dic11C2×D414yes—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4C2×D414yes—
166C4⋊Dic11—28no—
167C4⋊Dic11—22no—
168C4⋊Dic11C2414yes—
169Dic11⋊C4—28no—
170Dic11⋊C4C2×D414yes—
171C4×Dic11—28no—
172C4×Dic11C2×D412yes—
173C4×Dic11C2412yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8C2412yes—
177C2×C11⋊C8C2412yes—
178D88—28no—
179C8×D11—28no—
180C2×#553—112no—
181#3339—1116no—
182C2×#499—111no—
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×#107D1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11#13514yes—
195C23×C11C22×D412yes—
196C23×C11C22×D411yescharacteristic
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—24no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11C22×D412yes—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—88no—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4112yes—
217C2×C4×C112−1+412yes—
218C2×C4×C11C2511yescharacteristic
219C22⋊D11—28no—
220C22⋊D11—416no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—44no—
226C2×Dic11C22×D412yes—
227C2×Dic11C22×D412yes—
228C2×Dic11C22×D412yes—
229D44—24no—
230D44—24no—
231D44—44no—
232D44—88no—
233C4×D11—24no—
234C4×D11—22no—
235C4×D11—22no—
236C4×D11—88no—
237C8×C11—22no—
238C8×C11C2×#4114yes—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C22×D8—111no—
242C23×C8—111no—
243C23×C8C2×D1111yescharacteristic
244#553—1116no—
245#553—228no—
246C2×#126—222no—
247C2×#125—112no—
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⋊C4C2×D1112yes—
257#499—118no—
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×#107C2×D1112yes—
268C2×#107C2×D1111yescharacteristic
269C2×#107C2×D1111yescharacteristic
270C2×#107C2×D1118yescomplemented
271C2×#106—112no—
272C2×#106—112no—
273C2×C4⋊C8—111no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102—112no—
277C2×C22⋊C8—111no—
278C2×C22⋊C8—111no—
279C2×C4×C8—111no—
280C22×C11—28no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11#54712yes—
284C22×C11C2×#13514yes—
285C22×C11C2×#13512yes—
286C22×C11#57612yes—
287C22×C11C23×D411yescharacteristic
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—88no—
296C4×C11—22no—
297C4×C11—44no—
298C4×C11—44no—
299C4×C11#54712yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—22no—
303Dic11—22no—
304Dic11—22no—
305Dic11—44no—
306C22×D4—111no—
307C22×D4—112no—
308C22×D4—222no—
309C22×D4—222no—
310C23×C4—22no—
311C23×C4—111no—
312C23×C4—222no—
313C23×C4C22×D1111yescharacteristic
314C2×D8—114no—
315C2×D8—224no—
316C22×C8—24no—
317C22×C8—111no—
318C22×C8—111no—
319C22×C8—114no—
320C22×C8—224no—
321C22×C8C22×D1111yescharacteristic
322C22×C8C22×D1114yes—
323C22×C8C22×D1111yescharacteristic
324#126—2216no—
325#125—118no—
326#125—224no—
327#123—2216no—
328#121—118no—
329#121—118no—
330#121—224no—
331#121—2216no—
332#121—224no—
333C4×D4—114no—
334C4×D4—114no—
335C4×D4—118no—
336C4×D4—224no—
337C4×D4—2216no—
338#117—118no—
339#117—224no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4C22×D1112yes—
347C2×C4⋊C4C22×D1112yes—
348C2×C4⋊C4C22×D1118yes—
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—111no—
356C2×C42—222no—
357#107—114no—
358#107C22×D1114yes—
359#107C22×D1114yes—
360#107C22×D1118yes—
361#106—118no—
362#106—118no—
363C4⋊C8—114no—
364#102—118no—
365#102—118no—
366#102—118no—
367C22⋊C8—114no—
368C22⋊C8—114no—
369C4×C8—114no—
370C2×C11—24no—
371C2×C11#333914yescomplemented
372C2×C11C2×#54711yescharacteristic
373C2×C11C22×#13511yescharacteristic
374C2×C11C2×#57611yescharacteristic
375D11—42no—
376D11—84no—
377C24—111no—
378C24—222no—
379C24D4×D1111yescharacteristic
380C2×D4—114no—
381C2×D4—114no—
382C2×D4—228no—
383C2×D4—224no—
384C2×D4—228no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—224no—
388C2×D4—448no—
389C2×D4—884no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—28no—
395C22×C4—84no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—228no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—884no—
406C22×C4D4×D1112yes—
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1112yes—
409C22×C4C23×D1111yescharacteristic
410D8—228no—
411C2×C8—22no—
412C2×C8—28no—
413C2×C8—112no—
414C2×C8—112no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—228no—
418C2×C8#433914yes—
419C2×C8C23×D1112yes—
420C2×C8C23×D1112yes—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—28no—
424C4⋊C4—114no—
425C4⋊C4—114no—
426C4⋊C4—228no—
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—112no—
438C42—112no—
439C42—228no—
440C11C2×#333911yescharacteristic, complemented, Sylow
441C23—22no—
442C23—22no—
443C23—112no—
444C23—222no—
445C23—222no—
446C23—222no—
447C23—224no—
448C23—444no—
449C23—444no—
450C23—444no—
451C23#6697214yes—
452C23C2×D4×D1112yes—
453C23C2×D4×D1111yescharacteristic
454D4—228no—
455D4—224no—
456D4—224no—
457D4—4416no—
458D4—444no—
459D4—888no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—88no—
469C2×C4—112no—
470C2×C4—112no—
471C2×C4—112no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—224no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—444no—
480C2×C4—888no—
481C2×C4C2×#433912yes—
482C2×C4C2×D4×D1112yes—
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4#6704012yes—
485C2×C4C24×D1111yescharacteristic
486C8—22no—
487C8—222no—
488C8—222no—
489C8C2×#433914yes—
490C22—28no—
491C22—22no—
492C22—22no—
493C22—222no—
494C22—222no—
495C22—222no—
496C22—444no—
497C22—444no—
498C22—444no—
499C22—444no—
500C22—888no—
501C22#1062303812yes—
502C22#1062328812yes—
503C22C2×#6697214yes—
504C22C2×#6697212yes—
505C22C22×D4×D1111yescharacteristic
506C4—22no—
507C4—44no—
508C4—44no—
509C4—222no—
510C4—222no—
511C4—222no—
512C4—444no—
513C4#1062303812yes—
514C4C22×#433911yescharacteristic
515C4C2×#6704011yescharacteristic
516C2—24no—
517C2—442no—
518C2—884no—
519C2#1308101414yesdirect product factor
520C2C2×#1062303811yescharacteristic
521C2C22×#6697211yescharacteristic
522C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
hypercenterC22×#107D11
hypocenterC11C2×#3339
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#10623045C2semidirect
2. #13081014C2direct (N × H)
3. C2×#10622491C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622496C2semidirect
8. C2×#10622728C2semidirect
9. C2×#10622485C2semidirect
10. C2×C8×C22⋊D11C2semidirect
11. C2×#10622493C2semidirect
12. C22×C11×#107C2semidirect
22. #10623045C22semidirect
32. C2×C11×#107C22semidirect
34. #10622728C22semidirect
36. C8×C22⋊D11C22semidirect
41. #10622581C22semidirect
46. #10622504C22semidirect
47. #10622498C22semidirect
48. #10622496C22semidirect
49. #10622493C22semidirect
50. #10622491C22semidirect
51. #10622485C22semidirect
191. C22×#107D11semidirect
270. C2×#107C2×D11semidirect
371. C2×C11#3339semidirect
440. C11C2×#3339semidirect
519. C2#13081014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230452
#130810142
C2×#106224912
C2×#106225812
C2×#106224982
C2×#106225042
C2×#106224962
C2×#106227282
C2×#106224852
C2×C8×C22⋊D112
C2×#106224932
C22×C11×#1072
C2×#333911