Finite Group Databasebeta

← C2×#13080552 #15630233

Subgroups — C2×#13080552 #15630233

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic
3#13080552C2116yesmaximal, direct product factor
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622479C212yesmaximal, complemented
6C2×#10622477C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622423C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×#10622417C212yesmaximal, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000—21no—
17C2×Q8×Dic11—21no—
18C22×#4326C2211yescharacteristic
19C22×#4314C2212yes—
20C22×C8×D11C2212yes—
21#10623263—24no—
22#10623263C2218yescomplemented
23#10623108—24no—
24#10623108C2218yes—
25C2×#66951—22no—
26C2×#66950C2212yes—
27C2×#66948—22no—
28C2×#66948C2212yes—
29C2×#66945C2212yes—
30C2×#66927—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#475C2218yescomplemented
36C2×C11×#106C2212yes—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2212yes—
39C2×#66899C2211yescharacteristic
40C2×#66885C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42#10622701C2218yescomplemented
43C4×#4326C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622479C22116yescomplemented
50#10622477C22116yescomplemented
51#10622461C2218yescomplemented
52#10622447C2218yescomplemented
53#10622423C22116yescomplemented
54#10622417C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C2×#4343—24no—
58C2×#4343—28no—
59C2×#4343—44no—
60C2×#4343C2318yes—
61C22×D44—22no—
62C22×D44—21no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44D411yescharacteristic
66C22×D44C2312yes—
67C22×C4×D11—22no—
68C22×C4×D11C2312yes—
69C22×Dic22C2311yescharacteristic
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81#67000—28no—
82Q8×Dic11—28no—
83C2×#4326—24no—
84C2×#4326C2314yes—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4D412yes—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—22no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4314—44no—
98C2×#4314C2318yes—
99C2×C8×D11—44no—
100C2×C8×D11C2318yes—
101#66951—216no—
102#66950—24no—
103#66950C2318yes—
104#66948—24no—
105#66948—216no—
106#66948C2318yes—
107#66945—24no—
108#66945C2318yes—
109#66927—28no—
110#66927—22no—
111#66927C2314yes—
112C4×D44—28no—
113C4×D44D414yes—
114C4×D44C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117C11×#106C2318yes—
118C11×C4⋊C8C2314yes—
119C11×#103C2318yes—
120#66899C2314yes—
121#66885C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66874C2314yes—
124#66873C2318yes—
125#66873C2318yes—
126#66871C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3304—111nomaximal, Sylow
129C23×D11—22no—
130C23×D11C2×D412yes—
131C2×Q8×C11—21no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—44no—
135C2×Q8×C11#4114yes—
136C2×Q8×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D412yes—
146#4343—216no—
147#4343—48no—
148#4343—416no—
149C2×D44—28no—
150C2×D44—28no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—48no—
158C2×D44—44no—
159C2×D44—82no—
160C2×D44—84no—
161C2×D44C2×D414yes—
162C2×D44C2414yes—
163C2×C4×D11—28no—
164C2×C4×D11—24no—
165C2×C4×D11—24no—
166C2×C4×D11—48no—
167C2×C4×D11C2×D414yes—
168C2×C4×D11C2414yes—
169C2×Dic22—21no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22C2412yes—
173C2×C8×C11—24no—
174C2×C8×C11C2414yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4C2412yes—
180C11×C4⋊C4C2414yes—
181C42×C11—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184#4326—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4C2×D418yes—
189C4⋊Dic11—28no—
190C4⋊Dic11—21no—
191C4⋊Dic11C2×D414yes—
192C4⋊Dic11C2412yes—
193Dic11⋊C4—24no—
194C4×Dic11—28no—
195C4×Dic11—24no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4314—48no—
201C8×D11—48no—
202C2×#556—111no—
203C2×#550—111no—
204#3304—1116no—
205C2×#486—111no—
206C2×#482—112no—
207C2×#475D1111yescharacteristic, complemented
208C2×#465—112no—
209C2×#460—111no—
210C2×#452—112no—
211C2×C4×Q16—111no—
212C2×C8×D4—111no—
213C2×#416—112no—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11C22×D414yes—
223Q8×C11—24no—
224Q8×C11—22no—
225Q8×C11—48no—
226Q8×C11C2×#4114yes—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11#13514yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11H(5,𝔽2)12yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11C22×D414yes—
247D44—28no—
248D44—24no—
249D44—24no—
250D44—416no—
251D44—44no—
252D44—48no—
253D44—84no—
254D44—88no—
255C4×D11—28no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—416no—
259Dic22—22no—
260Dic22—22no—
261Dic22—42no—
262C8×C11—24no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C22×#41—112no—
266C22×Q16—111no—
267C22×SD16—112no—
268C23×C8—112no—
269#556—118no—
270#556—224no—
271#550—118no—
272#550—224no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C2×#127—111no—
275C2×#127—221no—
276C2×#126—222no—
277C2×#124—221no—
278C2×C22⋊Q8—112no—
279C2×#121—112no—
280C2×#121—222no—
281C2×C4×Q8—111no—
282C2×C4×Q8—221no—
283C2×C4×Q8C2×D1111yescharacteristic
284C2×C4×D4—111no—
285C2×C4×D4—221no—
286C2×#117—112no—
287#486—118no—
288#482—1116no—
289#475C2×D1118yescomplemented
290#465—1116no—
291#460—118no—
292#452—1116no—
293C4×Q16—118no—
294C8×D4—118no—
295C2×#107—111no—
296C2×#106C2×D1112yes—
297C2×C4⋊C8C2×D1111yescharacteristic
298#416—1116no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103C2×D1112yes—
302C2×#102—112no—
303C2×#102—112no—
304C2×#102—112no—
305C2×C22⋊C8—112no—
306C2×C4×C8—111no—
307C22×C11#54612yes—
308C22×C11C2×#13512yes—
309C22×C11#57712yes—
310C22×C11C23×D411yescharacteristic
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—48no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—88no—
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—44no—
322C4×C11—42no—
323C4×C11#54612yes—
324C4×C11C2×#13514yes—
325C4×C11C22×#4111yescharacteristic
326C4×C11C2×H(5,𝔽2)11yescharacteristic
327Dic11—24no—
328Dic11—42no—
329Dic11—42no—
330C2×#41—118no—
331C2×#41—224no—
332C2×#41—228no—
333C2×#41—444no—
334C22×Q8—21no—
335C22×Q8—111no—
336C22×Q8C22×D1111yescharacteristic
337C22×D4—111no—
338C22×D4—112no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—221no—
342C22×D4—221no—
343C23×C4—112no—
344C23×C4—222no—
345C2×Q16—114no—
346C2×Q16—224no—
347C2×SD16—118no—
348C2×SD16—444no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—118no—
352C22×C8—444no—
353C22×C8C22×D1112yes—
354C4⋊Q8—22no—
355C4⋊Q8C22×D1114yes—
356#127—114no—
357#127—228no—
358#127—222no—
359#126—2216no—
360#124—228no—
361C22⋊Q8—118no—
362C22⋊Q8—224no—
363#121—118no—
364#121—2216no—
365#121—224no—
366C4×Q8—22no—
367C4×Q8—114no—
368C4×Q8—228no—
369C4×Q8—222no—
370C4×Q8C22×D1114yes—
371C4×D4—114no—
372C4×D4—114no—
373C4×D4—228no—
374#117—118no—
375#117—224no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1112yes—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—112no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C42—21no—
389C2×C42—222no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—114no—
393#106C22×D1118yes—
394C4⋊C8C22×D1114yes—
395#103—114no—
396#103—114no—
397#103C22×D1118yes—
398#102—118no—
399#102—118no—
400#102—118no—
401C22⋊C8—118no—
402C4×C8—114no—
403C2×C11#330414yescomplemented
404C2×C11C2×#54611yescharacteristic
405C2×C11C22×#13511yescharacteristic
406C2×C11C2×#57711yescharacteristic
407D11—44no—
408D11—84no—
409C24—112no—
410C24—222no—
411#41—2216no—
412#41—448no—
413#41—4416no—
414C2×Q8—21no—
415C2×Q8—24no—
416C2×Q8—22no—
417C2×Q8—44no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8#434314yes—
423C2×Q8C23×D1112yes—
424C2×D4—114no—
425C2×D4—114no—
426C2×D4—228no—
427C2×D4—228no—
428C2×D4—224no—
429C2×D4—224no—
430C2×D4—222no—
431C2×D4—224no—
432C2×D4—224no—
433C2×D4—224no—
434C2×D4—448no—
435C2×D4—444no—
436C2×D4—882no—
437C2×D4—884no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—112no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—228no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—448no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453Q16—228no—
454SD16—448no—
455C2×C8—24no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—448no—
461C2×C8C23×D1114yes—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—114no—
467C4⋊C4—112no—
468C4⋊C4—228no—
469C4⋊C4—221no—
470C4⋊C4—224no—
471C4⋊C4C23×D1114yes—
472C4⋊C4C23×D1112yes—
473C22⋊C4—118no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C22⋊C4—228no—
477C42—24no—
478C42—228no—
479C42—224no—
480C42D4×D1112yes—
481C42C23×D1112yes—
482C11C2×#330411yescharacteristic, complemented, Sylow
483C23—114no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—444no—
489C23—444no—
490C23—444no—
491C23C2×D4×D1111yescharacteristic
492Q8—24no—
493Q8—22no—
494Q8—48no—
495Q8—222no—
496Q8—222no—
497Q8—442no—
498Q8C2×#434314yes—
499D4—228no—
500D4—224no—
501D4—224no—
502D4—4416no—
503D4—448no—
504D4—444no—
505D4—884no—
506D4—888no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—114no—
515C2×C4—224no—
516C2×C4—228no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—4416no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4#6696914yes—
525C2×C4C2×D4×D1112yes—
526C2×C4C2×D4×D1112yes—
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434312yes—
529C2×C4#6704212yes—
530C2×C4C24×D1111yescharacteristic
531C8—24no—
532C8—222no—
533C8—222no—
534C22—224no—
535C22—224no—
536C22—224no—
537C22—448no—
538C22—444no—
539C22—444no—
540C22—444no—
541C22—888no—
542C22#1062316112yes—
543C22C2×#6696912yes—
544C22#1062330912yes—
545C22C22×D4×D1111yescharacteristic
546C4—24no—
547C4—22no—
548C4—44no—
549C4—42no—
550C4—224no—
551C4—442no—
552C4—442no—
553C4#1062316112yes—
554C4C2×#6696914yes—
555C4C22×#434311yescharacteristic
556C4C2×#6704211yescharacteristic
557C2—444no—
558C2—884no—
559C2#1308055214yesdirect product factor
560C2C2×#1062316111yescharacteristic
561C2C22×#6696911yescharacteristic
562C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×#475D11
hypocenterC11C2×#3304
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
3. #13080552C2direct (N × H)
4. C2×#10622701C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622477C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622423C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×#10622447C2semidirect
11. C2×#10622417C2semidirect
12. C2×C11×#475C2semidirect
22. #10623263C22semidirect
35. C11×#475C22semidirect
42. #10622701C22semidirect
43. C4×#4326C22semidirect
49. #10622479C22semidirect
50. #10622477C22semidirect
51. #10622461C22semidirect
52. #10622447C22semidirect
53. #10622423C22semidirect
54. #10622417C22semidirect
207. C2×#475D11semidirect
289. #475C2×D11semidirect
403. C2×C11#3304semidirect
482. C11C2×#3304semidirect
559. C2#13080552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106231082
#130805522
C2×#106227012
C2×#106224792
C2×#106224772
C2×#106224612
C2×#106224232
C2×C4×#43262
C2×#106224472
C2×#106224172
C2×C11×#4752
C2×#330411