Finite Group Databasebeta

← C2×#13081355 #15633495

Subgroups — C2×#13081355 #15633495

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623253C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic
3#13081355C2116yesmaximal, direct product factor
4C2×#10622378C212yesmaximal
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622467C212yesmaximal, complemented
7C2×#10622380C212yesmaximal
8C2×#10622462C211yesmaximal, characteristic, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622466C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66997—22no—
16C2×#66989C2212yes—
17C22×#4324C2211yescharacteristic
18C2×#66979—21no—
19C2×#66977—21no—
20C22×Dic44C2212yes—
21#10623253—24no—
22#10623253C2218yescomplemented
23#10623073—24no—
24#10623073C2218yes—
25C2×#66941—21no—
26C2×#66941C2212yes—
27C2×#66940—21no—
28C2×#66940C2212yes—
29C2×#66940C2212yes—
30C2×#66932—22no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#476C2218yes—
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66880C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622706C2218yescomplemented
43C4×#4324C2218yes—
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46C2×#66874C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622467C22116yescomplemented
50#10622466C22116yescomplemented
51#10622462C2218yescomplemented
52#10622444C2218yescomplemented
53#10622380C22116yes—
54#10622378C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×Dic22—22no—
59C22×Dic22D411yescharacteristic
60C22×Dic22C2312yes—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2312yes—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C4×D4×C11—22no—
66C4×D4×C11C2314yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74#66997—216no—
75#66989—24no—
76#66989C2318yes—
77C2×#4324—24no—
78C2×#4324C2314yes—
79#66979—28no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84#66977—28no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4D412yes—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×Dic44—28no—
97C2×Dic44C2318yes—
98#66941—28no—
99#66941—24no—
100#66941C2318yes—
101#66940—28no—
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×#106C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#102C2318yes—
116#66896C2314yes—
117#66880C2318yes—
118#66879C2318yes—
119Dic11⋊C8C2318yes—
120#66874C2314yes—
121#66874C2318yes—
122#66874C2318yes—
123#66872C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3369—111nomaximal, Sylow
126C24×C11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—82no—
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—28no—
146C2×Dic22—24no—
147C2×Dic22—21no—
148C2×Dic22—22no—
149C2×Dic22—24no—
150C2×Dic22—22no—
151C2×Dic22—24no—
152C2×Dic22—84no—
153C2×Dic22C2×D414yes—
154C2×Dic22#4114yes—
155C2×Dic22C2414yes—
156C2×Dic22C2412yes—
157C2×C8×C11—24no—
158C2×C8×C11C2414yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2412yes—
163C11×C4⋊C4C2414yes—
164C11×C22⋊C4—24no—
165C42×C11C2×D412yes—
166C42×C11C2412yes—
167C22⋊Dic11—28no—
168C22⋊Dic11—28no—
169#4324—28no—
170C4⋊Dic11—21no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11C2×D414yes—
174C4⋊Dic11C2412yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—24no—
179Dic11⋊C4C2×D418yes—
180C4×Dic11—28no—
181C4×Dic11—28no—
182C4×Dic11—24no—
183C4×Dic11C2×D414yes—
184C4×Dic11C2414yes—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2412yes—
188C2×C11⋊C8C2412yes—
189Dic44—216no—
190C2×Q82—111no—
191C2×#556—111no—
192#3369—1116no—
193C2×#489—112no—
194C2×#487—111no—
195C2×#475—112no—
196C2×#476D1111yescharacteristic
197C2×#464—112no—
198C2×#462—111no—
199C2×#446—111no—
200C2×#441—112no—
201C2×C4×SD16—111no—
202C23×C11—22no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C22×D411yescharacteristic
207Q8×C11—84no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—42no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—48no—
217C2×C4×C11#13714yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C2×C4×C11C2×#4112yes—
222C2×C4×C112−1+412yes—
223C2×C4×C11C2511yescharacteristic
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—44no—
231C2×Dic11—42no—
232C2×Dic11C22×D414yes—
233C2×Dic11C22×D414yes—
234Dic22—24no—
235Dic22—28no—
236Dic22—22no—
237Dic22—24no—
238Dic22—24no—
239Dic22—44no—
240Dic22—88no—
241Dic22C2×#4114yes—
242C8×C11—24no—
243C11⋊C8—22no—
244C11⋊C8—22no—
245C22×Q16—112no—
246C22×SD16—111no—
247Q82—118no—
248Q82—224no—
249#556—118no—
250#556—224no—
251C2×C4⋊Q8—112no—
252C2×C4⋊Q8—111no—
253C2×C4⋊Q8—221no—
254C2×C4⋊Q8—222no—
255C2×C4⋊Q8C2×D1111yescharacteristic
256C2×#126—222no—
257C2×#124—112no—
258C2×C22⋊Q8—221no—
259C2×C4×Q8—111no—
260C2×C4×Q8—112no—
261C2×C4×Q8—112no—
262C2×C4×Q8—111no—
263C2×C4×Q8—221no—
264C2×C4×D4C2×D1111yescharacteristic
265C2×#117—221no—
266#489—1116no—
267#487—118no—
268#476C2×D1118yes—
269#475—1116no—
270#464—1116no—
271#462—118no—
272#446—118no—
273#441—1116no—
274C4×SD16—118no—
275C2×#106—111no—
276C2×#106C2×D1112yes—
277C2×C4⋊C8—112no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—112no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103—111no—
283C2×#102—111no—
284C2×#102C2×D1112yes—
285C2×#97—112no—
286C2×C4×C8—111no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—84no—
291C22×C11#54812yes—
292C22×C11C2×#13712yes—
293C22×C11#57712yes—
294C22×C11C23×D411yescharacteristic
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11#54812yes—
299C4×C11C2×#13714yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—24no—
303Dic11—24no—
304Dic11—24no—
305Dic11—44no—
306Dic11—42no—
307C22×Q8—21no—
308C22×Q8—111no—
309C22×Q8—111no—
310C22×Q8—112no—
311C22×Q8—222no—
312C22×D4C22×D1111yescharacteristic
313C23×C4—21no—
314C2×Q16—118no—
315C2×Q16—228no—
316C2×SD16—114no—
317C2×SD16—224no—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8C22×D1112yes—
321C4⋊Q8—22no—
322C4⋊Q8—118no—
323C4⋊Q8—114no—
324C4⋊Q8—224no—
325C4⋊Q8—228no—
326C4⋊Q8—2216no—
327C4⋊Q8—222no—
328C4⋊Q8C22×D1114yes—
329#126—2216no—
330#124—118no—
331#124—224no—
332C22⋊Q8—228no—
333C4×Q8—114no—
334C4×Q8—114no—
335C4×Q8—118no—
336C4×Q8—118no—
337C4×Q8—114no—
338C4×Q8—224no—
339C4×Q8—224no—
340C4×Q8—228no—
341C4×Q8—222no—
342C4×D4—22no—
343C4×D4C22×D1114yes—
344#117—228no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—112no—
361C2×C42—222no—
362C2×C42—222no—
363C2×C42—221no—
364C2×C42C22×D1111yescharacteristic
365#106—114no—
366#106C22×D1118yes—
367C4⋊C8—118no—
368C4⋊C8C22×D1114yes—
369#103—118no—
370#103—114no—
371#103—118no—
372#103—118no—
373#102—114no—
374#102C22×D1118yes—
375#97—118no—
376C4×C8—114no—
377C2×C11—82no—
378C2×C11#336914yescomplemented
379C2×C11C2×#54811yescharacteristic
380C2×C11C22×#13711yescharacteristic
381C2×C11C2×#57711yescharacteristic
382C24—21no—
383C2×Q8—24no—
384C2×Q8—82no—
385C2×Q8—114no—
386C2×Q8—114no—
387C2×Q8—112no—
388C2×Q8—114no—
389C2×Q8—228no—
390C2×Q8—224no—
391C2×Q8—221no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—224no—
395C2×Q8—224no—
396C2×Q8—884no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4C23×D1112yes—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—44no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—221no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413Q16—2216no—
414SD16—228no—
415C2×C8—24no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8C23×D1114yes—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—114no—
425C4⋊C4—118no—
426C4⋊C4—112no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—221no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4C23×D1114yes—
435C4⋊C4C23×D1112yes—
436C22⋊C4—24no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C42—114no—
440C42—114no—
441C42—228no—
442C42—228no—
443C42—224no—
444C42D4×D1112yes—
445C42C23×D1112yes—
446C11C2×#336911yescharacteristic, complemented, Sylow
447C23—22no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23C2×D4×D1111yescharacteristic
452Q8—84no—
453Q8—114no—
454Q8—228no—
455Q8—224no—
456Q8—222no—
457Q8—224no—
458Q8—224no—
459Q8—444no—
460Q8—888no—
461D4—22no—
462D4—22no—
463D4—42no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—44no—
469C2×C4—48no—
470C2×C4—114no—
471C2×C4—114no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—222no—
476C2×C4—224no—
477C2×C4—222no—
478C2×C4—442no—
479C2×C4—444no—
480C2×C4#6696814yes—
481C2×C4C2×D4×D1112yes—
482C2×C4C2×D4×D1112yes—
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4#6704012yes—
485C2×C4#41×D1112yes—
486C2×C4C24×D1111yescharacteristic
487C8—24no—
488C8—222no—
489C8—222no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—84no—
494C22#1062316412yes—
495C22C2×#6696812yes—
496C22#1062330612yes—
497C22C22×D4×D1111yescharacteristic
498C4—22no—
499C4—42no—
500C4—44no—
501C4—224no—
502C4—224no—
503C4—224no—
504C4—444no—
505C4—442no—
506C4#1062316412yes—
507C4C2×#6696814yes—
508C4C2×#6704011yescharacteristic
509C4C2×#41×D1111yescharacteristic
510C2—82no—
511C2#1308135514yesdirect product factor
512C2C2×#1062316411yescharacteristic
513C2C22×#6696811yescharacteristic
514C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#476D11
hypocenterC11C2×#3369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623253C2semidirect
3. #13081355C2direct (N × H)
5. C2×#10622706C2semidirect
6. C2×#10622467C2semidirect
8. C2×#10622462C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622466C2semidirect
22. #10623253C22semidirect
42. #10622706C22semidirect
49. #10622467C22semidirect
50. #10622466C22semidirect
51. #10622462C22semidirect
52. #10622444C22semidirect
378. C2×C11#3369semidirect
446. C11C2×#3369semidirect
511. C2#13081355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232532
C2×#106230732
#130813552
C2×#106223782
C2×#106227062
C2×#106224672
C2×#106223802
C2×#106224622
C2×#106224442
C2×#106224662
C2×C4×#43242
C2×C11×#4762
C2×#336911