Finite Group Databasebeta

← C2×#13073089 #14922950

Subgroups — C2×#13073089 #14922950

Order 2816.

3094 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
1C22×#66949C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3#13073089C2116yesmaximal, direct product factor
4C2×#10622274C211yesmaximal, characteristic, complemented
5C2×#10622593C211yesmaximal, characteristic, complemented
6C2×#10622596C211yesmaximal, characteristic, complemented
7C2×#10622259C212yesmaximal, complemented
8C2×#10622281C212yesmaximal
9C2×#10622602C212yesmaximal
10C2×#10622589C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C2×#66949—28no—
31C2×#66949C2218yes—
32C2×C4⋊C4×D11—28no—
33C2×C4⋊C4×D11C2218yes—
34C11×#398C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622602C22116yes—
42#10622596C2218yescomplemented
43#10622593C2218yescomplemented
44#10622589C22116yescomplemented
45#10622281C22116yes—
46#10622279C2218yes—
47#10622274C2218yescomplemented
48#10622259C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—28no—
61C22×C4×D11—28no—
62C22×C4×D11—44no—
63C22×C4×D11—44no—
64C22×C4×D11D418yes—
65C22×C4×D11C2314yes—
66C22×C4×D11C2318yes—
67C22×Dic22—24no—
68C22×Dic22—28no—
69C22×Dic22C2314yes—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—44no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2318yes—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4Q8116yescomplemented
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—44no—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2318yes—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—44no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×C4×Dic11—28no—
97C2×C4×Dic11C2318yes—
98#66949—232no—
99C4⋊C4×D11—232no—
100C11×#95C2318yes—
101C11×#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C2×#2502—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—24no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11C2×D414yes—
112C23×D11C2×Q818yes—
113C23×D11C2412yes—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×Q818yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2414yes—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11C2×D414yes—
143C22×Dic11C2×Q818yes—
144C22×Dic11#4118yes—
145C22×Dic11C2412yes—
146C22×Dic11C2414yes—
147C22×Dic11C2412yes—
148C22×Dic11C2414yes—
149C22×Dic11C2412yes—
150C2×C4×D11—232no—
151C2×C4×D11—216no—
152C2×C4×D11—216no—
153C2×C4×D11—48no—
154C2×C4×D11—48no—
155C2×C4×D11—432no—
156C2×C4×D11C2×D4116yes—
157C2×Dic22—28no—
158C2×Dic22—216no—
159C2×Dic22—416no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—48no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4C2×Q8132yescomplemented
166C4⋊Dic11—28no—
167C4⋊Dic11—48no—
168Dic11⋊C4—216no—
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—48no—
172Dic11⋊C4—48no—
173C4×Dic11—216no—
174C22×C22⋊Q8—111no—
175C23×C4⋊C4—111no—
176#2502—1116no—
177C2×#398—111no—
178C2×#398—111no—
179C2×#398—111no—
180C2×#398D1111yescharacteristic, complemented
181C2×#391—112no—
182C2×#385—112no—
183C2×#385—112no—
184C2×#384—112no—
185C2×C4×C22⋊C4—111no—
186C23×C11C22×D412yes—
187C23×C11C22×Q814yes—
188C23×C11C2×#4114yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C11C2511yescharacteristic
192C22×D11—28no—
193C22×D11—28no—
194C22×D11—216no—
195C22×D11—216no—
196C22×D11—24no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11C4⋊Q8116yes—
200C22×D11C22×D414yes—
201C22×D11C22×Q818yes—
202C2×C4×C11—28no—
203C2×C4×C11—216no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—44no—
216C2×C4×C11—48no—
217C2×C4×C11—44no—
218C2×C4×C11C22×D414yes—
219C2×C4×C11C22×Q818yes—
220C2×Dic11—216no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—44no—
232C2×Dic11—48no—
233C2×Dic11—44no—
234C2×Dic11#123116yes—
235C2×Dic11C22×D414yes—
236C2×Dic11C22×Q818yes—
237C2×Dic11C2×#4118yes—
238C4×D11—232no—
239C4×D11—432no—
240Dic22—416no—
241C23×Q8—111no—
242C24×C4—111no—
243C24×C4—112no—
244C2×C22⋊Q8—118no—
245C2×C22⋊Q8—228no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—111no—
249C22×C4⋊C4—111no—
250C22×C4⋊C4—112no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—118no—
254C22×C4⋊C4—228no—
255C22×C4⋊C4C2×D1111yescharacteristic
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C4⋊C4C2×D1112yes—
258C22×C22⋊C4—112no—
259C22×C22⋊C4—111no—
260C22×C22⋊C4—111no—
261C22×C42—112no—
262#398—118no—
263#398—118no—
264#398—118no—
265#398C2×D1118yescomplemented
266#391—1116no—
267#385—1116no—
268#385—1116no—
269#384—1116no—
270C4×C22⋊C4—118no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95C2×D1111yescharacteristic
276C2×#95C2×D1112yes—
277C22×C11C2×#12314yes—
278C22×C11C2×C4⋊Q814yes—
279C22×C11#53514yes—
280C22×C11#55418yes—
281C22×C11#55418yes—
282C22×C11C23×D411yescharacteristic
283C22×C11C23×Q812yes—
284C22×C11C22×#4112yes—
285C22×C11C2×H(5,𝔽2)11yescharacteristic
286C22×C11C2×H(5,𝔽2)11yescharacteristic
287C2×D11—24no—
288C2×D11—24no—
289C2×D11—28no—
290C2×D11—28no—
291C2×D11—232no—
292C2×D11C2×C4⋊Q818yes—
293C4×C11—24no—
294C4×C11—28no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—44no—
298Dic11—28no—
299Dic11—42no—
300Dic11—44no—
301Dic11—42no—
302Dic11C2×#12318yes—
303C25—111no—
304C22×Q8—114no—
305C22×Q8—224no—
306C22×Q8—228no—
307C23×C4—111no—
308C23×C4—112no—
309C23×C4—118no—
310C23×C4—114no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—112no—
314C23×C4—118no—
315C23×C4—228no—
316C23×C4—228no—
317C23×C4—444no—
318C23×C4—444no—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1112yes—
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1112yes—
324C22⋊Q8—2232no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—2232no—
336C2×C4⋊C4—228no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—444no—
341C2×C4⋊C4—444no—
342C2×C4⋊C4—444no—
343C2×C4⋊C4C22×D1114yes—
344C2×C4⋊C4C22×D1114yes—
345C2×C4⋊C4C22×D1118yes—
346C2×C22⋊C4—1116no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—114no—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—224no—
351C2×C22⋊C4—224no—
352C2×C42—118no—
353C2×C42—228no—
354#95—114no—
355#95—118no—
356#95—118no—
357#95—118no—
358#95C22×D1114yes—
359#95C22×D1118yes—
360C2×C11#250218yescomplemented
361C2×C11C22×#12311yescharacteristic
362C2×C11C22×C4⋊Q811yescharacteristic
363C2×C11C2×#53511yescharacteristic
364C2×C11C2×#55412yes—
365C2×C11C2×#55412yes—
366D11—28no—
367C24—114no—
368C24—118no—
369C24—112no—
370C24—222no—
371C24—224no—
372C24—222no—
373C24C23×D1111yescharacteristic
374C2×Q8—228no—
375C2×Q8—2216no—
376C2×Q8—4416no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—114no—
389C22×C4—118no—
390C22×C4—112no—
391C22×C4—118no—
392C22×C4—114no—
393C22×C4—1116no—
394C22×C4—112no—
395C22×C4—114no—
396C22×C4—112no—
397C22×C4—2232no—
398C22×C4—2216no—
399C22×C4—2216no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—224no—
405C22×C4—222no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—222no—
409C22×C4—224no—
410C22×C4—448no—
411C22×C4—448no—
412C22×C4—4432no—
413C22×C4D4×D1114yes—
414C22×C4Q8×D1118yes—
415C22×C4C23×D1112yes—
416C22×C4C23×D1114yes—
417C22×C4C23×D1112yes—
418C22×C4C23×D1112yes—
419C22×C4C23×D1114yes—
420C4⋊C4—28no—
421C4⋊C4—28no—
422C4⋊C4—48no—
423C4⋊C4—2216no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—228no—
427C4⋊C4—448no—
428C4⋊C4—448no—
429C4⋊C4—448no—
430C22⋊C4—1132no—
431C22⋊C4—228no—
432C22⋊C4—228no—
433C42—2216no—
434C11C2×#250211yescharacteristic, complemented, Sylow
435C23—1116no—
436C23—114no—
437C23—118no—
438C23—228no—
439C23—2216no—
440C23—228no—
441C23—222no—
442C23—224no—
443C23—222no—
444C23—2216no—
445C23C2×D4×D1112yes—
446C23#6703712yes—
447C23C2×Q8×D1114yes—
448C23#41×D1114yes—
449C23#6704212yes—
450C23C24×D1111yescharacteristic
451Q8—4416no—
452C2×C4—216no—
453C2×C4—28no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—1116no—
469C2×C4—114no—
470C2×C4—118no—
471C2×C4—118no—
472C2×C4—2232no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—2216no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—4432no—
485C2×C4—448no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4C2×D4×D1114yes—
489C2×C4C2×Q8×D1118yes—
490C22—118no—
491C22—228no—
492C22—228no—
493C22—224no—
494C22—2232no—
495C22—224no—
496C22#1062313814yes—
497C22#1062316718yes—
498C22D11×#12314yes—
499C22#1062322118yes—
500C22D11×C4⋊Q814yes—
501C22C22×D4×D1111yescharacteristic
502C22C2×#6703711yescharacteristic
503C22C22×Q8×D1112yes—
504C22C2×#41×D1112yes—
505C22C2×#6704211yescharacteristic
506C4—28no—
507C4—24no—
508C4—44no—
509C4—42no—
510C4—42no—
511C4—118no—
512C4—228no—
513C4—444no—
514C4—442no—
515C4—442no—
516C2—228no—
517C2#1307308918yesdirect product factor
518C2C2×D11×#12311yescharacteristic
519C2C2×D11×C4⋊Q811yescharacteristic
520C2C2×#1062313811yescharacteristic
521C2C2×#1062316712yes—
522C2C2×#1062322112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#398D11
hypocenterC11C2×#2502
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13073089C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622593C2semidirect
6. C2×#10622596C2semidirect
7. C2×#10622259C2semidirect
10. C2×#10622589C2semidirect
12. C2×C11×#398C2semidirect
34. C11×#398C22semidirect
42. #10622596C22semidirect
43. #10622593C22semidirect
44. #10622589C22semidirect
47. #10622274C22semidirect
48. #10622259C22semidirect
78. C2×(C2×D11)⋊C4Q8semidirect
165. (C2×D11)⋊C4C2×Q8semidirect
180. C2×#398D11semidirect
265. #398C2×D11semidirect
360. C2×C11#2502semidirect
434. C11C2×#2502semidirect
517. C2#13073089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C4⋊C4×D112
#130730892
C2×#106222742
C2×#106225932
C2×#106225962
C2×#106222592
C2×#106222812
C2×#106226022
C2×#106225892
C2×#106222792
C2×C11×#3982
C2×#250211