Finite Group Databasebeta

← C2×#13079560 #15624960

Subgroups — C2×#13079560 #15624960

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079560C2116yesmaximal, direct product factor
4C2×#10622705C211yesmaximal, characteristic, complemented
5C2×#10622294C211yesmaximal, characteristic, complemented
6C2×#10622694C211yesmaximal, characteristic, complemented
7C2×#10622795C214yesmaximal, complemented
8C2×#10622799C214yesmaximal
9C2×#10622298C211yesmaximal, characteristic
10C2×C11×#494C211yesmaximal, characteristic, complemented
11C22×Q8×D11C2212yes—
12C22×C11×Q16C2214yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#66999C2212yes—
16C2×Q8×Dic11C2212yes—
17C2×#66997C2212yes—
18C22×#4326C2214yes—
19#10623259—24no—
20#10623259C2218yes—
21D11×C4⋊Q8—24no—
22D11×C4⋊Q8C2218yes—
23C2×#66950—21no—
24C2×#66945—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11—21no—
27C2×#66943—21no—
28C2×#66941—21no—
29C2×#66941—21no—
30C2×#66940—21no—
31C2×C42×D11C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C11×#494C2218yescomplemented
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66899C2214yes—
37#10622799C22132yes—
38#10622795C22132yescomplemented
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66880C2214yes—
41C2×Dic11⋊C8C2212yes—
42#10622705C2218yescomplemented
43#10622694C2218yescomplemented
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622298C2218yes—
46#10622294C2218yescomplemented
47C22×Q8×C11C2312yes—
48C22×Q8×C11C2312yes—
49C2×Q8×D11—24no—
50C2×Q8×D11—48no—
51C2×Q8×D11C2318yes—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22C2312yes—
59C2×C11×Q16—48no—
60C2×C11×Q16C23116yes—
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C11×C4⋊Q8C2314yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71#66999—24no—
72#66999C2318yes—
73Q8×Dic11—24no—
74Q8×Dic11C2318yes—
75#66997—24no—
76#66997C2318yes—
77C2×#4326—48no—
78C2×#4326C23116yes—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93#66950—28no—
94#66945—28no—
95C4⋊C4×D11—28no—
96C4⋊C4×D11—28no—
97#66943—28no—
98#66941—28no—
99#66941—28no—
100#66940—28no—
101C42×D11D414yes—
102C42×D11C2314yes—
103#66922—22no—
104#66922—22no—
105#66922C2314yes—
106#66922C2314yes—
107C4×C8×C11C2314yes—
108#66899C23116yes—
109(C2×D11)⋊C8C2318yes—
110#66880C23116yes—
111Dic11⋊C8C2318yes—
112C4×C11⋊C8C2314yes—
113C2×#3209—111nomaximal, Sylow
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—28no—
119C2×Q8×C11C2414yes—
120C2×Q8×C11C2414yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131Q8×D11—416no—
132Q8×D11—416no—
133C2×C4×D11—28no—
134C2×C4×D11—24no—
135C2×C4×D11—24no—
136C2×C4×D11—48no—
137C2×C4×D11Q1618yescomplemented
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×D414yes—
140C2×C4×D11C2×D414yes—
141C2×C4×D11C2412yes—
142C2×Dic22—28no—
143C2×Dic22—22no—
144C2×Dic22—24no—
145C2×Dic22—28no—
146C2×Dic22—48no—
147C2×Dic22—44no—
148C2×Dic22C2414yes—
149C11×Q16—416no—
150C2×C8×C11—24no—
151C2×C8×C11C2414yes—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C42×C11C2×D412yes—
157C42×C11C2412yes—
158#4326—416no—
159(C2×D11)⋊C4—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—22no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11C2414yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169C4×Dic11—28no—
170C4×Dic11C2×D412yes—
171C4×Dic11C2×D414yes—
172C4×Dic11C2×D414yes—
173C4×Dic11C2412yes—
174C2×C11⋊C8—24no—
175C2×C11⋊C8C2414yes—
176C2×#533—111no—
177C22×C4⋊Q8—111no—
178#3209—1116no—
179C2×#494—111no—
180C2×#494D1111yescharacteristic, complemented
181C2×#487—111no—
182C2×#487—111no—
183C2×#462—114no—
184C2×#451—114no—
185C2×#431—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—22no—
189C22×D11C2×Q1614yes—
190C22×D11C22×D412yes—
191Q8×C11—28no—
192Q8×C11—28no—
193Q8×C11—44no—
194Q8×C11—44no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11C2×Q1614yes—
200C2×C4×C11#13714yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11H(5,𝔽2)14yes—
205C2×C4×C11C2511yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11C2×Q1614yes—
213C2×Dic11C22×D412yes—
214C2×Dic11C22×D412yes—
215C2×Dic11C22×D412yes—
216C4×D11—24no—
217C4×D11—28no—
218C4×D11—24no—
219C4×D11—416no—
220C4×D11C2×Q16116yescomplemented
221Dic22—28no—
222Dic22—416no—
223Dic22—44no—
224Dic22—48no—
225C8×C11—24no—
226C11⋊C8—24no—
227C23×Q8—112no—
228C22×Q16—114no—
229C22×Q16C2×D1114yes—
230#533—118no—
231#533—224no—
232C2×C4⋊Q8—112no—
233C2×C4⋊Q8—118no—
234C2×C4⋊Q8—111no—
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8—221no—
237C2×C4⋊Q8—221no—
238C2×C4⋊Q8—224no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#125—221no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—221no—
244C2×C4×Q8—112no—
245C2×C4×Q8—221no—
246C2×#117—221no—
247C22×C4⋊C4—221no—
248C22×C4⋊C4—221no—
249C22×C42—111no—
250#494—118no—
251#494C2×D1118yescomplemented
252#487—118no—
253#487—118no—
254#462—1132no—
255#451—1132no—
256#431—118no—
257C2×C4⋊C8—112no—
258C2×#103—114no—
259C2×#103—114no—
260C2×C22⋊C8—112no—
261C2×C4×C8—111no—
262C2×C4×C8C2×D1111yescharacteristic
263C22×C11#53512yes—
264C22×C11C22×Q1612yes—
265C22×C11C2×#13712yes—
266C22×C11C23×D411yescharacteristic
267C2×D11—22no—
268C2×D11—28no—
269C2×D11—22no—
270C2×D11C22×Q1614yes—
271C4×C11—44no—
272C4×C11—44no—
273C4×C11#53512yes—
274C4×C11C22×Q1614yes—
275C4×C11C2×#13714yes—
276C4×C11C2×H(5,𝔽2)12yes—
277Dic11—22no—
278Dic11—22no—
279Dic11—44no—
280Dic11—44no—
281Dic11C22×Q1614yes—
282C22×Q8—118no—
283C22×Q8—112no—
284C22×Q8—222no—
285C22×Q8—224no—
286C22×Q8—221no—
287C22×Q8—448no—
288C22×Q8C22×D1112yes—
289C22×Q8C22×D1112yes—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—222no—
294C2×Q16—48no—
295C2×Q16—1116no—
296C2×Q16—448no—
297C2×Q16C22×D11116yes—
298C22×C8—112no—
299C22×C8C22×D1112yes—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—118no—
303C4⋊Q8—114no—
304C4⋊Q8—114no—
305C4⋊Q8—228no—
306C4⋊Q8—228no—
307C4⋊Q8—224no—
308C4⋊Q8—222no—
309C4⋊Q8—222no—
310C4⋊Q8C22×D1114yes—
311C4⋊Q8C22×D1114yes—
312#125—228no—
313C22⋊Q8—118no—
314C22⋊Q8—228no—
315C22⋊Q8—224no—
316C4×Q8—118no—
317C4×Q8—228no—
318C4×Q8—224no—
319#117—228no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—228no—
326C2×C4⋊C4—228no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C22⋊C4—222no—
335C2×C42—111no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—114no—
339C2×C42—114no—
340C2×C42—222no—
341C2×C42C22×D1111yescharacteristic
342C4⋊C8—118no—
343#103—1116no—
344#103—1116no—
345C22⋊C8—118no—
346C4×C8—114no—
347C4×C8C22×D1114yes—
348C2×C11#320914yescomplemented
349C2×C11C2×#53511yescharacteristic
350C2×C11C23×Q1611yescharacteristic
351C2×C11C22×#13711yescharacteristic
352D11—24no—
353C24—111no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—28no—
357C2×Q8—28no—
358C2×Q8—114no—
359C2×Q8—228no—
360C2×Q8—224no—
361C2×Q8—222no—
362C2×Q8—228no—
363C2×Q8—448no—
364C2×Q8—4416no—
365C2×Q8—4416no—
366C2×Q8—444no—
367C2×Q8C23×D1114yes—
368C2×Q8C23×D1114yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—111no—
372C22×C4—118no—
373C22×C4—114no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—114no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—228no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—448no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388Q16—416no—
389Q16—4416no—
390C2×C8—24no—
391C2×C8—114no—
392C2×C8—224no—
393C2×C8C23×D1114yes—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—114no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—228no—
402C4⋊C4—228no—
403C4⋊C4—222no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C22⋊C4—228no—
408C42—112no—
409C42—114no—
410C42—114no—
411C42—112no—
412C42—228no—
413C42D4×D1112yes—
414C42C23×D1112yes—
415C11C2×#320911yescharacteristic, complemented, Sylow
416C23—114no—
417C23—112no—
418C23—222no—
419C23—222no—
420C23C2×D4×D1111yescharacteristic
421Q8—28no—
422Q8—28no—
423Q8—44no—
424Q8—44no—
425Q8—228no—
426Q8—4416no—
427Q8—444no—
428Q8—448no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—114no—
434C2×C4—112no—
435C2×C4—1116no—
436C2×C4—112no—
437C2×C4—112no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—224no—
441C2×C4—228no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—4416no—
446C2×C4—444no—
447C2×C4—444no—
448C2×C4Q16×D1114yes—
449C2×C4#6697114yes—
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C2×D4×D1112yes—
452C2×C4C2×D4×D1112yes—
453C2×C4#6703714yes—
454C2×C4C24×D1111yescharacteristic
455C8—24no—
456C8—224no—
457C22—114no—
458C22—228no—
459C22—222no—
460C22—222no—
461C22#1062324612yes—
462C22C2×Q16×D1112yes—
463C22C2×#6697112yes—
464C22C22×D4×D1111yescharacteristic
465C4—44no—
466C4—44no—
467C4—114no—
468C4—222no—
469C4—222no—
470C4—444no—
471C4—444no—
472C4#1062324612yes—
473C4C2×Q16×D1114yes—
474C4C2×#6697114yes—
475C4C2×#6703712yes—
476C2—224no—
477C2#1307956014yesdirect product factor
478C2C2×#1062324611yescharacteristic
479C2C22×Q16×D1111yescharacteristic
480C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#494C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#494D11
hypocenterC11C2×#3209
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
3. #13079560C2direct (N × H)
4. C2×#10622705C2semidirect
5. C2×#10622294C2semidirect
6. C2×#10622694C2semidirect
7. C2×#10622795C2semidirect
10. C2×C11×#494C2semidirect
34. C11×#494C22semidirect
38. #10622795C22semidirect
42. #10622705C22semidirect
43. #10622694C22semidirect
46. #10622294C22semidirect
137. C2×C4×D11Q16semidirect
180. C2×#494D11semidirect
220. C4×D11C2×Q16semidirect
251. #494C2×D11semidirect
348. C2×C11#3209semidirect
415. C11C2×#3209semidirect
477. C2#13079560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×D11×C4⋊Q82
#130795602
C2×#106227052
C2×#106222942
C2×#106226942
C2×#106227952
C2×#106227992
C2×#106222982
C2×C11×#4942
C2×#320911