Finite Group Databasebeta

← C2×#13081652 #15634746

Subgroups — C2×#13081652 #15634746

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623263C211yesmaximal, characteristic
3#13081652C2116yesmaximal, direct product factor
4C2×#10622803C212yesmaximal
5C2×#10622798C212yesmaximal
6C2×#10622795C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622696C211yesmaximal, characteristic
9C2×#10622292C211yesmaximal, characteristic, complemented
10C2×#10622797C212yesmaximal, complemented
11C2×C4×#4314C211yesmaximal, characteristic
12C2×C11×#494C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2212yes—
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#67000C2212yes—
18C2×Q8×Dic11C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×#66997C2212yes—
21C22×#4326C2212yes—
22C22×#4325C2212yes—
23C22×#4314C2211yescharacteristic
24#10623263—24no—
25#10623263C2218yes—
26#10623252—24no—
27#10623252C2218yescomplemented
28C2×#66951—22no—
29C2×#66950—21no—
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66942—22no—
33C2×#66940—21no—
34C2×C4×D44C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#494C2218yescomplemented
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41#10622803C22116yes—
42#10622798C22116yes—
43#10622797C22116yescomplemented
44#10622795C22116yescomplemented
45C2×#66885C2211yescharacteristic
46C2×#66881C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66879C2212yes—
49C2×Dic11⋊C8C2212yes—
50#10622703C2218yescomplemented
51#10622696C2218yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C4×#4314C2218yes—
54#10622292C2218yescomplemented
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2312yes—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×Dic22D411yescharacteristic
60C22×Dic22C2311yescharacteristic
61C2×C11×Q16—28no—
62C2×C11×Q16—44no—
63C2×C11×Q16C2318yes—
64C2×C11×Q16C2318yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C11×C4⋊Q8C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76#67000—24no—
77#67000C2318yes—
78Q8×Dic11—24no—
79Q8×Dic11—24no—
80Q8×Dic11C2318yes—
81Q8×Dic11C2318yes—
82#66997—24no—
83#66997C2318yes—
84C2×#4326—44no—
85C2×#4326C2318yes—
86C2×#4325—44no—
87C2×#4325C2318yes—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4D412yes—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2312yes—
104C22×C11⋊C8C2312yes—
105C2×#4314—24no—
106C2×#4314C2314yes—
107#66951—216no—
108#66950—28no—
109#66945—28no—
110#66943—28no—
111#66942—216no—
112#66940—28no—
113C4×D44—22no—
114C4×D44C2314yes—
115C4×Dic22—22no—
116C4×Dic22D414yes—
117C4×Dic22C2314yes—
118C4×Dic22C2314yes—
119C4×C8×C11C2314yes—
120#66899C2318yes—
121#66899C2318yes—
122#66885C2314yes—
123#66881C2314yes—
124#66880C2314yes—
125#66879C2318yes—
126Dic11⋊C8C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3398—111nomaximal, Sylow
129C23×D11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—24no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11C2414yes—
137C2×Q8×C11C2414yes—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×D44—21no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44C2412yes—
152C2×C4×D11—24no—
153C2×C4×D11—44no—
154C2×Dic22—24no—
155C2×Dic22—21no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22C2×D414yes—
159C2×Dic22C2412yes—
160C11×Q16—216no—
161C11×Q16—48no—
162C2×C8×C11—22no—
163C2×C8×C11#4114yes—
164C2×C8×C11C2412yes—
165C2×C8×C11C2412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172#4326—48no—
173#4325—48no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—24no—
177C4⋊Dic11—28no—
178C4⋊Dic11—28no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2412yes—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—24no—
187Dic11⋊C4C2×D418yes—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C4×Dic11—24no—
191C4×Dic11C2×D414yes—
192C4×Dic11C2414yes—
193C2×C11⋊C8—24no—
194C2×C11⋊C8C2414yes—
195#4314—28no—
196C2×#557—111no—
197C2×#556—111no—
198#3398—1116no—
199C2×#497—112no—
200C2×#494D1111yescharacteristic, complemented
201C2×#464—112no—
202C2×#462—112no—
203C2×#462—111no—
204C2×#461—111no—
205C2×#446—111no—
206C2×#441—112no—
207C2×C4×SD16—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—44no—
218Q8×C11—44no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11#13714yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D412yes—
228C2×C4×C11C2×#4112yes—
229C2×C4×C11H(5,𝔽2)12yes—
230C2×C4×C11C2511yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11C22×D414yes—
240C2×Dic11C22×D414yes—
241D44—22no—
242D44—22no—
243D44—42no—
244C4×D11—48no—
245Dic22—28no—
246Dic22—22no—
247Dic22—22no—
248Dic22—42no—
249C8×C11—22no—
250C8×C11C2×#4114yes—
251C11⋊C8—24no—
252C22×Q16—112no—
253C22×Q16C2×D1112yes—
254C22×Q16C2×D1112yes—
255C22×SD16—112no—
256C22×SD16—111no—
257#557—118no—
258#557—224no—
259#556—118no—
260#556—224no—
261C2×C4⋊Q8—112no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#126—222no—
265C2×#125—222no—
266C2×#125—221no—
267C2×#124—112no—
268C2×C22⋊Q8—221no—
269C2×C4×Q8—111no—
270C2×C4×Q8—112no—
271C2×C4×Q8—112no—
272C2×C4×Q8—111no—
273C2×C4×Q8—221no—
274C2×C4×D4—111no—
275C2×#117—221no—
276#497—1116no—
277#494C2×D1118yescomplemented
278#464—1116no—
279#462—1116no—
280#462—118no—
281#461—118no—
282#446—118no—
283#441—1116no—
284C4×SD16—118no—
285C2×#106—111no—
286C2×C4⋊C8—112no—
287C2×C4⋊C8—111no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#103—111no—
291C2×#102—111no—
292C2×#97—112no—
293C2×C4×C8C2×D1111yescharacteristic
294C22×C11#55012yes—
295C22×C11C2×#13712yes—
296C22×C11#57812yes—
297C22×C11C23×D411yescharacteristic
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—84no—
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—44no—
305C4×C11#55012yes—
306C4×C11C2×#13714yes—
307C4×C11C22×#4111yescharacteristic
308C4×C11C2×H(5,𝔽2)11yescharacteristic
309Dic11—24no—
310Dic11—24no—
311Dic11—42no—
312Dic11—42no—
313Dic11—42no—
314C22×Q8—111no—
315C22×Q8—111no—
316C22×Q8C22×D1112yes—
317C22×Q8C22×D1112yes—
318C22×D4—111no—
319C23×C4—221no—
320C2×Q16—28no—
321C2×Q16—44no—
322C2×Q16—118no—
323C2×Q16—444no—
324C2×Q16C22×D1118yes—
325C2×Q16C22×D1118yes—
326C2×SD16—118no—
327C2×SD16—114no—
328C2×SD16—224no—
329C2×SD16—444no—
330C22×C8—112no—
331C22×C8C22×D1111yescharacteristic
332C22×C8C22×D1111yescharacteristic
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—118no—
336C4⋊Q8—224no—
337C4⋊Q8C22×D1114yes—
338C4⋊Q8C22×D1114yes—
339#126—2216no—
340#125—2216no—
341#125—228no—
342#124—118no—
343#124—224no—
344C22⋊Q8—228no—
345C4×Q8—114no—
346C4×Q8—114no—
347C4×Q8—118no—
348C4×Q8—118no—
349C4×Q8—114no—
350C4×Q8—224no—
351C4×Q8—224no—
352C4×Q8—228no—
353C4×Q8—222no—
354C4×D4—114no—
355C4×D4—222no—
356#117—228no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—221no—
373C2×C42—112no—
374C2×C42—222no—
375C2×C42—222no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378#106—114no—
379C4⋊C8—118no—
380C4⋊C8—114no—
381#103—118no—
382#103—118no—
383#103—114no—
384#102—114no—
385#97—118no—
386C4×C8C22×D1114yes—
387C2×C11#339814yescomplemented
388C2×C11C2×#55011yescharacteristic
389C2×C11C22×#13711yescharacteristic
390C2×C11C2×#57811yescharacteristic
391D11—82no—
392C24—221no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—114no—
400C2×Q8—112no—
401C2×Q8—224no—
402C2×Q8—221no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×Q8C23×D1114yes—
406C2×Q8C23×D1114yes—
407C2×D4—112no—
408C2×D4—221no—
409C2×D4—222no—
410C2×D4—222no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—224no—
419C22×C4—444no—
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423Q16—216no—
424Q16—48no—
425Q16—448no—
426SD16—228no—
427SD16—448no—
428C2×C8—22no—
429C2×C8—114no—
430C2×C8—224no—
431C2×C8#434114yes—
432C2×C8C23×D1112yes—
433C2×C8C23×D1112yes—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—114no—
439C4⋊C4—118no—
440C4⋊C4—112no—
441C4⋊C4—112no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—224no—
449C22⋊C4—228no—
450C22⋊C4—228no—
451C22⋊C4—224no—
452C42—114no—
453C42—114no—
454C42—228no—
455C42—228no—
456C42—224no—
457C42D4×D1112yes—
458C42C23×D1112yes—
459C11C2×#339811yescharacteristic, complemented, Sylow
460C23—222no—
461C23—442no—
462C23—442no—
463C23—442no—
464C23C2×D4×D1111yescharacteristic
465Q8—24no—
466Q8—24no—
467Q8—24no—
468Q8—24no—
469Q8—44no—
470Q8—44no—
471Q8—228no—
472Q8—222no—
473Q8—222no—
474Q8—442no—
475D4—222no—
476D4—222no—
477D4—442no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—448no—
494C2×C4#6697114yes—
495C2×C4C2×D4×D1112yes—
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4C2×D4×D1112yes—
498C2×C4C2×#434112yes—
499C2×C4#6703712yes—
500C2×C4C24×D1111yescharacteristic
501C8—22no—
502C8—224no—
503C8C2×#434114yes—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—884no—
508C22#1062324912yes—
509C22C2×#6697112yes—
510C22#1062329712yes—
511C22C22×D4×D1111yescharacteristic
512C4—22no—
513C4—44no—
514C4—44no—
515C4—224no—
516C4—224no—
517C4—442no—
518C4—442no—
519C4—442no—
520C4#1062324912yes—
521C4C2×#6697114yes—
522C4C22×#434111yescharacteristic
523C4C2×#6703711yescharacteristic
524C2—882no—
525C2#1308165214yesdirect product factor
526C2C2×#1062324911yescharacteristic
527C2C22×#6697111yescharacteristic
528C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#494C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#494D11
hypocenterC11C2×#3398
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×#10623252C2semidirect
3. #13081652C2direct (N × H)
6. C2×#10622795C2semidirect
7. C2×#10622703C2semidirect
9. C2×#10622292C2semidirect
10. C2×#10622797C2semidirect
12. C2×C11×#494C2semidirect
27. #10623252C22semidirect
37. C11×#494C22semidirect
43. #10622797C22semidirect
44. #10622795C22semidirect
50. #10622703C22semidirect
54. #10622292C22semidirect
200. C2×#494D11semidirect
277. #494C2×D11semidirect
387. C2×C11#3398semidirect
459. C11C2×#3398semidirect
525. C2#13081652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106232632
#130816522
C2×#106228032
C2×#106227982
C2×#106227952
C2×#106227032
C2×#106226962
C2×#106222922
C2×#106227972
C2×C4×#43142
C2×C11×#4942
C2×#339811