Finite Group Databasebeta

← C2×#13081300 #15633384

Subgroups — C2×#13081300 #15633384

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic
3#13081300C2116yesmaximal, direct product factor
4C2×#10622381C212yesmaximal
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622490C212yesmaximal, complemented
7C2×#10622380C212yesmaximal
8C2×#10622462C211yesmaximal, characteristic, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622486C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#474C211yesmaximal, characteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11—21no—
16C2×#66997—21no—
17C2×#66989C2212yes—
18C22×#4324C2211yescharacteristic
19C2×#66979—21no—
20C2×#66977—21no—
21C22×Dic44C2212yes—
22#10623252—24no—
23#10623252C2218yescomplemented
24#10623073—24no—
25#10623073C2218yes—
26C2×#66943C2212yes—
27C2×#66942—22no—
28C2×#66940C2212yes—
29C2×#66940C2212yes—
30C2×#66932—22no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#474C2218yes—
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66880C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622706C2218yescomplemented
43C4×#4324C2218yes—
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46C2×#66874C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622490C22116yescomplemented
50#10622486C22116yescomplemented
51#10622462C2218yescomplemented
52#10622443C2218yescomplemented
53#10622381C22116yes—
54#10622380C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×Dic22D411yescharacteristic
59C22×Dic22C2312yes—
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C4×D4×C11—22no—
65C4×D4×C11C2314yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73Q8×Dic11—28no—
74#66997—28no—
75#66989—24no—
76#66989C2318yes—
77C2×#4324—24no—
78C2×#4324C2314yes—
79#66979—28no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85#66977—28no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4D412yes—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×Dic44—28no—
98C2×Dic44C2318yes—
99#66943—24no—
100#66943C2318yes—
101#66942—216no—
102#66940—24no—
103#66940—24no—
104#66940C2318yes—
105#66940C2318yes—
106#66932—216no—
107#66922—22no—
108#66922C2314yes—
109C4×Dic22—22no—
110C4×Dic22D414yes—
111C4×Dic22C2314yes—
112C4×Dic22C2314yes—
113C11×#107C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#102C2318yes—
116#66896C2314yes—
117#66880C2318yes—
118Dic11⋊C8C2318yes—
119C8×Dic11C2318yes—
120#66874C2314yes—
121#66874C2318yes—
122#66874C2318yes—
123#66872C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3364—111nomaximal, Sylow
126C24×C11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—44no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11C2412yes—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—44no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C2×Dic22—24no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22—24no—
149C2×Dic22—22no—
150C2×Dic22—24no—
151C2×Dic22C2×D414yes—
152C2×Dic22#4114yes—
153C2×Dic22C2414yes—
154C2×Dic22C2412yes—
155C2×C8×C11—24no—
156C2×C8×C11C2414yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4C2412yes—
161C11×C4⋊C4C2414yes—
162C11×C22⋊C4—24no—
163C42×C11C2×D412yes—
164C42×C11C2412yes—
165C22⋊Dic11—28no—
166C22⋊Dic11—28no—
167#4324—28no—
168C4⋊Dic11—28no—
169C4⋊Dic11—21no—
170C4⋊Dic11—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11C2×D414yes—
173C4⋊Dic11C2412yes—
174Dic11⋊C4—28no—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177Dic11⋊C4—24no—
178Dic11⋊C4C2×D418yes—
179C4×Dic11—28no—
180C4×Dic11—28no—
181C4×Dic11—24no—
182C4×Dic11C2×D414yes—
183C4×Dic11C2414yes—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2412yes—
188Dic44—216no—
189C2×#557—111no—
190C2×#556—111no—
191#3364—1116no—
192C2×#488—112no—
193C2×#487—111no—
194C2×#479—112no—
195C2×#474D1111yescharacteristic
196C2×#464—112no—
197C2×#462—111no—
198C2×C8×Q8—111no—
199C2×C4×Q16—112no—
200C2×C4×SD16—111no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206Q8×C11—48no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—42no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—48no—
216C2×C4×C11#13514yes—
217C2×C4×C11C22×D412yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D412yes—
220C2×C4×C11C2×#4112yes—
221C2×C4×C112−1+412yes—
222C2×C4×C11C2511yescharacteristic
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—44no—
230C2×Dic11—42no—
231C2×Dic11C22×D414yes—
232C2×Dic11C22×D414yes—
233Dic22—24no—
234Dic22—28no—
235Dic22—22no—
236Dic22—24no—
237Dic22—24no—
238Dic22—44no—
239Dic22C2×#4114yes—
240C8×C11—24no—
241C11⋊C8—22no—
242C11⋊C8—22no—
243C22×Q16—112no—
244C22×SD16—111no—
245#557—118no—
246#557—224no—
247#556—118no—
248#556—224no—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8—221no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#126—222no—
253C2×#125—112no—
254C2×#125—222no—
255C2×#124—112no—
256C2×C22⋊Q8—221no—
257C2×C4×Q8—111no—
258C2×C4×Q8—112no—
259C2×C4×Q8—112no—
260C2×C4×Q8—111no—
261C2×C4×Q8—221no—
262C2×C4×D4C2×D1111yescharacteristic
263C2×#117—221no—
264#488—1116no—
265#487—118no—
266#479—1116no—
267#474C2×D1118yes—
268#464—1116no—
269#462—118no—
270C8×Q8—118no—
271C4×Q16—1116no—
272C4×SD16—118no—
273C2×#107C2×D1112yes—
274C2×#106—111no—
275C2×C4⋊C8—112no—
276C2×C4⋊C8C2×D1111yescharacteristic
277C2×#103—112no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#103—111no—
281C2×#102—111no—
282C2×#102C2×D1112yes—
283C2×C4×C8—112no—
284C2×C4×C8—111no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—84no—
289C22×C11#54812yes—
290C22×C11C2×#13512yes—
291C22×C11#57812yes—
292C22×C11C23×D411yescharacteristic
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—44no—
296C4×C11#54812yes—
297C4×C11C2×#13514yes—
298C4×C11C22×#4111yescharacteristic
299C4×C11C2×2−1+411yescharacteristic
300Dic11—24no—
301Dic11—24no—
302Dic11—24no—
303Dic11—44no—
304Dic11—42no—
305C22×Q8—21no—
306C22×Q8—111no—
307C22×Q8—111no—
308C22×Q8—112no—
309C22×D4C22×D1111yescharacteristic
310C23×C4—21no—
311C2×Q16—118no—
312C2×Q16—228no—
313C2×SD16—114no—
314C2×SD16—224no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8C22×D1112yes—
318C4⋊Q8—22no—
319C4⋊Q8—114no—
320C4⋊Q8—228no—
321C4⋊Q8—222no—
322C4⋊Q8C22×D1114yes—
323#126—2216no—
324#125—118no—
325#125—224no—
326#125—2216no—
327#124—118no—
328#124—224no—
329C22⋊Q8—228no—
330C4×Q8—114no—
331C4×Q8—114no—
332C4×Q8—118no—
333C4×Q8—118no—
334C4×Q8—114no—
335C4×Q8—224no—
336C4×Q8—224no—
337C4×Q8—228no—
338C4×Q8—222no—
339C4×D4—22no—
340C4×D4C22×D1114yes—
341#117—228no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C42—112no—
359C2×C42—222no—
360C2×C42—222no—
361C2×C42—221no—
362C2×C42C22×D1111yescharacteristic
363#107C22×D1118yes—
364#106—114no—
365C4⋊C8—118no—
366C4⋊C8C22×D1114yes—
367#103—118no—
368#103—114no—
369#103—118no—
370#103—118no—
371#102—114no—
372#102C22×D1118yes—
373C4×C8—118no—
374C4×C8—114no—
375C2×C11—82no—
376C2×C11#336414yescomplemented
377C2×C11C2×#54811yescharacteristic
378C2×C11C22×#13511yescharacteristic
379C2×C11C2×#57811yescharacteristic
380C24—21no—
381C2×Q8—24no—
382C2×Q8—44no—
383C2×Q8—114no—
384C2×Q8—114no—
385C2×Q8—112no—
386C2×Q8—114no—
387C2×Q8—224no—
388C2×Q8—221no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—224no—
392C2×Q8—224no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4C23×D1112yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—44no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—2216no—
410SD16—228no—
411C2×C8—24no—
412C2×C8—112no—
413C2×C8—112no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8C23×D1114yes—
417C4⋊C4—24no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—114no—
421C4⋊C4—118no—
422C4⋊C4—112no—
423C4⋊C4—228no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—228no—
427C4⋊C4—221no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4C23×D1114yes—
432C4⋊C4C23×D1112yes—
433C22⋊C4—24no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C42—114no—
437C42—114no—
438C42—228no—
439C42—228no—
440C42—224no—
441C42D4×D1112yes—
442C42C23×D1112yes—
443C11C2×#336411yescharacteristic, complemented, Sylow
444C23—22no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23C2×D4×D1111yescharacteristic
449Q8—48no—
450Q8—114no—
451Q8—228no—
452Q8—224no—
453Q8—222no—
454Q8—224no—
455Q8—224no—
456Q8—444no—
457D4—22no—
458D4—22no—
459D4—42no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—48no—
466C2×C4—114no—
467C2×C4—114no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—222no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—442no—
475C2×C4—444no—
476C2×C4#6696514yes—
477C2×C4C2×D4×D1112yes—
478C2×C4C2×D4×D1112yes—
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4#6704012yes—
481C2×C4#41×D1112yes—
482C2×C4C24×D1111yescharacteristic
483C8—24no—
484C8—222no—
485C8—222no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—84no—
490C22#1062316412yes—
491C22C2×#6696512yes—
492C22#1062331012yes—
493C22C22×D4×D1111yescharacteristic
494C4—22no—
495C4—42no—
496C4—44no—
497C4—224no—
498C4—224no—
499C4—224no—
500C4—444no—
501C4—442no—
502C4#1062316412yes—
503C4C2×#6696514yes—
504C4C2×#6704011yescharacteristic
505C4C2×#41×D1111yescharacteristic
506C2—82no—
507C2#1308130014yesdirect product factor
508C2C2×#1062316411yescharacteristic
509C2C22×#6696511yescharacteristic
510C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11C2×#3364
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081300C2direct (N × H)
5. C2×#10622706C2semidirect
6. C2×#10622490C2semidirect
8. C2×#10622462C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622486C2semidirect
23. #10623252C22semidirect
42. #10622706C22semidirect
49. #10622490C22semidirect
50. #10622486C22semidirect
51. #10622462C22semidirect
52. #10622443C22semidirect
376. C2×C11#3364semidirect
443. C11C2×#3364semidirect
507. C2#13081300direct (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×#106230732
#130813002
C2×#106223812
C2×#106227062
C2×#106224902
C2×#106223802
C2×#106224622
C2×#106224432
C2×#106224862
C2×C4×#43242
C2×C11×#4742
C2×#336411