Finite Group Databasebeta

← C2×#13079569 #15624980

Subgroups — C2×#13079569 #15624980

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623256C211yesmaximal, characteristic
3#13079569C2116yesmaximal, direct product factor
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622307C211yesmaximal, characteristic, complemented
7C2×#10622798C214yesmaximal, complemented
8C2×#10622800C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic, complemented
10C2×C11×#494C211yesmaximal, characteristic, complemented
11C22×#4343C2212yes—
12C22×C11×Q16C2214yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000C2212yes—
16C2×#66999C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4325C2214yes—
19#10623259—24no—
20#10623259C2218yescomplemented
21#10623256—24no—
22#10623256C2218yes—
23C2×#66950—21no—
24C2×#66948—21no—
25C2×#66948—21no—
26C2×#66946—21no—
27C2×#66946—21no—
28C2×#66945—21no—
29C2×#66943—21no—
30C2×#66940—21no—
31C2×#66927C2211yescharacteristic
32C2×C42×D11C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C11×#494C2218yescomplemented
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66899C2214yes—
37#10622800C22132yescomplemented
38#10622798C22132yescomplemented
39C2×#66885C2214yes—
40C2×(C2×D11)⋊C8C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622698C2218yescomplemented
43#10622694C2218yescomplemented
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622307C2218yescomplemented
46#10622298C2218yescomplemented
47C22×Q8×C11C2312yes—
48C22×Q8×C11C2312yes—
49C2×#4343—24no—
50C2×#4343—48no—
51C2×#4343C2318yes—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—21no—
55C22×D44C2312yes—
56C22×C4×D11—22no—
57C22×C4×D11D411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22—21no—
61C2×C11×Q16—48no—
62C2×C11×Q16C23116yes—
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73#67000—24no—
74#67000C2318yes—
75#66999—24no—
76#66999C2318yes—
77Q8×Dic11—24no—
78Q8×Dic11C2318yes—
79C2×#4325—48no—
80C2×#4325C23116yes—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93#66950—28no—
94#66948—28no—
95#66948—28no—
96#66946—28no—
97#66946—28no—
98#66945—28no—
99#66943—28no—
100#66940—28no—
101#66927—22no—
102#66927C2314yes—
103C42×D11D414yes—
104C42×D11C2314yes—
105#66922—22no—
106#66922C2314yes—
107C4×C8×C11C2314yes—
108#66899C23116yes—
109#66885C23116yes—
110(C2×D11)⋊C8C2318yes—
111Dic11⋊C8C2318yes—
112C4×C11⋊C8C2314yes—
113C2×#3210—111nomaximal, Sylow
114C23×D11—22no—
115C23×D11C2×D411yescharacteristic
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—28no—
120C2×Q8×C11C2414yes—
121C2×Q8×C11C2414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131#4343—416no—
132#4343—416no—
133C2×D44—28no—
134C2×D44—22no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—28no—
138C2×D44—48no—
139C2×D44—44no—
140C2×D44—44no—
141C2×D44C2414yes—
142C2×C4×D11—28no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—48no—
147C2×C4×D11C2×D412yes—
148C2×C4×D11C2×D414yes—
149C2×C4×D11C2×D414yes—
150C2×C4×D11C2412yes—
151C2×Dic22—24no—
152C2×Dic22—44no—
153C11×Q16—416no—
154C2×C8×C11—24no—
155C2×C8×C11C2414yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C42×C11C2×D412yes—
161C42×C11C2412yes—
162#4325—416no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166C4⋊Dic11—28no—
167C4⋊Dic11—22no—
168C4⋊Dic11—24no—
169C4⋊Dic11C2414yes—
170Dic11⋊C4—28no—
171C4×Dic11—28no—
172C4×Dic11C2×D412yes—
173C4×Dic11C2×D414yes—
174C4×Dic11C2×D414yes—
175C4×Dic11C2412yes—
176C2×C11⋊C8—24no—
177C2×C11⋊C8C2414yes—
178C2×#533—111no—
179C2×#532—111no—
180#3210—1116no—
181C2×#494D1111yescharacteristic, complemented
182C2×#492—111no—
183C2×#487—111no—
184C2×#486—111no—
185C2×#464—114no—
186C2×#452—114no—
187C2×#431—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—24no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11C22×D412yes—
197Q8×C11—28no—
198Q8×C11—28no—
199Q8×C11—44no—
200Q8×C11—44no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11#13514yes—
206C2×C4×C11#13714yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D412yes—
209C2×C4×C11C22×D412yes—
210C2×C4×C11H(5,𝔽2)14yes—
211C2×C4×C11C2511yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—44no—
217C2×Dic11C22×D412yes—
218C2×Dic11C22×D412yes—
219C2×Dic11C22×D412yes—
220D44—28no—
221D44—416no—
222D44—44no—
223D44—48no—
224D44—48no—
225C4×D11—24no—
226C4×D11—28no—
227C4×D11—28no—
228C4×D11—24no—
229C4×D11—416no—
230Dic22—48no—
231C8×C11—24no—
232C11⋊C8—24no—
233C22×#41—112no—
234C22×Q16C2×D1114yes—
235C22×SD16—114no—
236#533—118no—
237#533—224no—
238#532—118no—
239#532—224no—
240C2×C4⋊Q8—111no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×C4⋊Q8C2×D1111yescharacteristic
243C2×#127—111no—
244C2×#125—221no—
245C2×#124—112no—
246C2×C22⋊Q8—112no—
247C2×C22⋊Q8—221no—
248C2×#121—221no—
249C2×#121—221no—
250C2×C4×Q8—112no—
251C2×C4×Q8—221no—
252C2×C4×D4—221no—
253C2×C4×D4—221no—
254C2×#117—221no—
255C22×C42—111no—
256#494C2×D1118yescomplemented
257#492—118no—
258#487—118no—
259#486—118no—
260#464—1132no—
261#452—1132no—
262#431—118no—
263C2×C4⋊C8—112no—
264C2×#103—114no—
265C2×#102—114no—
266C2×C22⋊C8—112no—
267C2×C4×C8—111no—
268C2×C4×C8C2×D1111yescharacteristic
269C22×C11#53512yes—
270C22×C11C2×#13512yes—
271C22×C11C2×#13712yes—
272C22×C11C23×D411yescharacteristic
273C2×D11—22no—
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—88no—
281C4×C11—44no—
282C4×C11—44no—
283C4×C11#53512yes—
284C4×C11C2×#13514yes—
285C4×C11C2×#13714yes—
286C4×C11C2×H(5,𝔽2)12yes—
287Dic11—22no—
288Dic11—22no—
289Dic11—22no—
290Dic11—44no—
291C2×#41—118no—
292C2×#41—224no—
293C2×#41—448no—
294C22×Q8—221no—
295C22×Q8C22×D1112yes—
296C22×Q8C22×D1112yes—
297C22×D4—112no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—221no—
301C23×C4—111no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—222no—
305C2×Q16—48no—
306C2×Q16C22×D11116yes—
307C2×SD16—1116no—
308C2×SD16—448no—
309C22×C8—112no—
310C22×C8C22×D1112yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—114no—
314C4⋊Q8—222no—
315C4⋊Q8C22×D1114yes—
316C4⋊Q8C22×D1114yes—
317#127—114no—
318#127—222no—
319#125—228no—
320#124—118no—
321#124—224no—
322C22⋊Q8—118no—
323C22⋊Q8—228no—
324C22⋊Q8—224no—
325#121—228no—
326#121—228no—
327C4×Q8—118no—
328C4×Q8—228no—
329C4×Q8—224no—
330C4×D4—228no—
331C4×D4—228no—
332#117—228no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—222no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—114no—
348C2×C42—114no—
349C2×C42—222no—
350C2×C42C22×D1111yescharacteristic
351C4⋊C8—118no—
352#103—1116no—
353#102—1116no—
354C22⋊C8—118no—
355C4×C8—114no—
356C4×C8C22×D1114yes—
357C2×C11#321014yescomplemented
358C2×C11C2×#53511yescharacteristic
359C2×C11C22×#13511yescharacteristic
360C2×C11C22×#13711yescharacteristic
361D11—42no—
362D11—84no—
363C24—111no—
364C24—222no—
365#41—4416no—
366#41—4416no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—28no—
370C2×Q8—28no—
371C2×Q8—224no—
372C2×Q8—444no—
373C2×Q8C23×D1114yes—
374C2×Q8C23×D1114yes—
375C2×D4—114no—
376C2×D4—228no—
377C2×D4—224no—
378C2×D4—224no—
379C2×D4—222no—
380C2×D4—228no—
381C2×D4—448no—
382C2×D4—444no—
383C2×D4—444no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—228no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—222no—
398C22×C4—448no—
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4C23×D1111yescharacteristic
402Q16—416no—
403SD16—4416no—
404C2×C8—24no—
405C2×C8—114no—
406C2×C8—224no—
407C2×C8C23×D1114yes—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—114no—
413C4⋊C4—228no—
414C4⋊C4—228no—
415C4⋊C4—222no—
416C4⋊C4—224no—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C42—114no—
421C42—114no—
422C42—112no—
423C42—112no—
424C42—228no—
425C42D4×D1112yes—
426C42C23×D1112yes—
427C11C2×#321011yescharacteristic, complemented, Sylow
428C23—112no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23—224no—
433C23—444no—
434C23—444no—
435C23—444no—
436C23C2×D4×D1111yescharacteristic
437Q8—28no—
438Q8—28no—
439Q8—44no—
440Q8—44no—
441Q8—448no—
442D4—228no—
443D4—4416no—
444D4—444no—
445D4—448no—
446D4—448no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—112no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—224no—
458C2×C4—228no—
459C2×C4—228no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—4416no—
463C2×C4—444no—
464C2×C4#6697114yes—
465C2×C4#6697214yes—
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×D4×D1112yes—
468C2×C4C2×D4×D1112yes—
469C2×C4#6703714yes—
470C2×C4C24×D1111yescharacteristic
471C8—24no—
472C8—224no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—444no—
477C22—444no—
478C22—444no—
479C22—444no—
480C22—888no—
481C22#1062324612yes—
482C22C2×#6697112yes—
483C22C2×#6697212yes—
484C22C22×D4×D1111yescharacteristic
485C4—44no—
486C4—44no—
487C4—222no—
488C4—222no—
489C4—222no—
490C4—444no—
491C4#1062324612yes—
492C4C2×#6697114yes—
493C4C2×#6697214yes—
494C4C2×#6703712yes—
495C2—442no—
496C2—884no—
497C2#1307956914yesdirect product factor
498C2C2×#1062324611yescharacteristic
499C2C22×#6697211yescharacteristic
500C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#494C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#494D11
hypocenterC11C2×#3210
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
1. C2×#10623259C2semidirect
3. #13079569C2direct (N × H)
4. C2×#10622698C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622307C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622800C2semidirect
9. C2×#10622298C2semidirect
10. C2×C11×#494C2semidirect
20. #10623259C22semidirect
34. C11×#494C22semidirect
37. #10622800C22semidirect
38. #10622798C22semidirect
42. #10622698C22semidirect
43. #10622694C22semidirect
45. #10622307C22semidirect
46. #10622298C22semidirect
181. C2×#494D11semidirect
256. #494C2×D11semidirect
357. C2×C11#3210semidirect
427. C11C2×#3210semidirect
497. C2#13079569direct (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×#106232562
#130795692
C2×#106226982
C2×#106226942
C2×#106223072
C2×#106227982
C2×#106228002
C2×#106222982
C2×C11×#4942
C2×#321011