Finite Group Databasebeta

← C2×#13081230 #15632510

Subgroups — C2×#13081230 #15632510

Order 2816.

1866 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×#10623263C211yesmaximal, characteristic
2C2×#10623261C211yesmaximal, characteristic
3#13081230C2116yesmaximal, direct product factor
4C2×#10622480C212yesmaximal, complemented
5C2×#10622475C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622707C211yesmaximal, characteristic, complemented
8C2×#10622481C212yesmaximal, complemented
9C2×C4×Dic44C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic
11C2×#10622474C212yesmaximal, complemented
12C2×C11×#498C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000—21no—
16C2×#66999—22no—
17C2×Q8×Dic11—21no—
18C22×Dic44C2211yescharacteristic
19C22×#4313C2212yes—
20#10623263—24no—
21#10623263C2218yes—
22#10623261—24no—
23#10623261C2218yes—
24C2×#66951—22no—
25C2×#66950C2212yes—
26C2×#66950C2212yes—
27C2×#66946—21no—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66943—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#498C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×#106C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C2×(C2×D11)⋊C8C2212yes—
39C2×#66882C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622707C2218yescomplemented
43#10622704C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622481C22116yescomplemented
50#10622480C22116yescomplemented
51#10622475C22116yescomplemented
52#10622474C22116yescomplemented
53C4×Dic44C2218yescomplemented
54#10622301C2218yes—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×D44D411yescharacteristic
58C22×C4×D11—22no—
59C22×C4×D11C2312yes—
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
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⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11C2311yescharacteristic
73#67000—28no—
74#66999—216no—
75Q8×Dic11—28no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4D412yes—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—22no—
91C22×C11⋊C8C2312yes—
92C2×Dic44—24no—
93C2×Dic44C2314yes—
94C2×#4313—28no—
95C2×#4313C2318yes—
96#66951—216no—
97#66950—24no—
98#66950—24no—
99#66950C2318yes—
100#66950C2318yes—
101#66946—28no—
102#66945—24no—
103#66945C2318yes—
104C4⋊C4×D11—24no—
105C4⋊C4×D11C2318yes—
106#66943—28no—
107C4×D44D414yes—
108C4×D44C2314yes—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22C2314yes—
112C4×Dic22C2314yes—
113C11×#106C2318yes—
114C11×#106C2318yes—
115C4×C8×C11C2314yes—
116(C2×D11)⋊C8C2318yes—
117#66882C2314yes—
118#66880C2314yes—
119#66880C2314yes—
120#66874C2318yes—
121#66874C2318yes—
122#66872C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3356—111nomaximal, Sylow
126C23×D11C2×D412yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—24no—
129C2×Q8×C11—44no—
130C2×Q8×C11—82no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D412yes—
141C2×D44—24no—
142C2×D44C2×D414yes—
143C2×C4×D11—28no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—84no—
147C2×C4×D11C2×D414yes—
148C2×C4×D11C2414yes—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22C2412yes—
156C2×Dic22C2412yes—
157C2×C8×C11—22no—
158C2×C8×C11#4114yes—
159C2×C8×C11C2412yes—
160C2×C8×C11C2412yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2414yes—
167C42×C11C2×D412yes—
168C42×C11C2412yes—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4C2×D418yes—
173C4⋊Dic11—28no—
174C4⋊Dic11—28no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×D414yes—
178C4⋊Dic11C2412yes—
179C4⋊Dic11C2412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183C4×Dic11—28no—
184C4×Dic11—24no—
185C4×Dic11—24no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8C2414yes—
188Dic44—28no—
189#4313—216no—
190C2×#556—111no—
191C2×#554—111no—
192#3356—1116no—
193C2×#498D1111yescharacteristic, complemented
194C2×#485—112no—
195C2×#483—112no—
196C2×#477—111no—
197C2×#475—111no—
198C2×#470—112no—
199C2×C4×Q16—111no—
200C2×#436—111no—
201C2×#428—112no—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11C22×D414yes—
207Q8×C11—48no—
208Q8×C11—84no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11#13714yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C2×#4112yes—
219C2×C4×C112−1+412yes—
220C2×C4×C11C2511yescharacteristic
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11C22×D414yes—
231D44—28no—
232C4×D11—28no—
233C4×D11—24no—
234C4×D11—24no—
235C4×D11—88no—
236Dic22—22no—
237Dic22—22no—
238Dic22—22no—
239Dic22—22no—
240Dic22—42no—
241Dic22—42no—
242C8×C11—22no—
243C8×C11C2×#4114yes—
244C11⋊C8—24no—
245C22×Q16—111no—
246C22×M16—112no—
247#556—118no—
248#556—224no—
249#554—118no—
250#554—224no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#126—222no—
254C2×#125—221no—
255C2×#124—221no—
256C2×C22⋊Q8—112no—
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8—222no—
259C2×C4×Q8—111no—
260C2×C4×Q8—111no—
261C2×C4×Q8—221no—
262C2×C4×D4—111no—
263C2×C4×D4—221no—
264C2×#117—112no—
265C22×C4⋊C4—112no—
266#498C2×D1118yescomplemented
267#485—1116no—
268#483—1116no—
269#477—118no—
270#475—118no—
271#470—1116no—
272C4×Q16—118no—
273#436—118no—
274#428—1116no—
275C2×#107—111no—
276C2×#107—112no—
277C2×#106—112no—
278C2×#106C2×D1112yes—
279C2×#106C2×D1112yes—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—112no—
284C2×#103—112no—
285C2×C22⋊C8—112no—
286C2×C4×C8C2×D1111yescharacteristic
287C22×C11#54712yes—
288C22×C11C2×#13712yes—
289C22×C11#57712yes—
290C22×C11C23×D411yescharacteristic
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—48no—
295C4×C11—22no—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11#54712yes—
299C4×C11C2×#13714yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—24no—
303Dic11—42no—
304Dic11—42no—
305Dic11—42no—
306Dic11—42no—
307C22×Q8—21no—
308C22×Q8—21no—
309C22×Q8—111no—
310C22×Q8—111no—
311C22×D4—111no—
312C23×C4—112no—
313C23×C4—222no—
314C2×Q16—114no—
315C2×Q16—224no—
316C2×M16—118no—
317C2×M16—228no—
318C22×C8—112no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8C22×D1114yes—
324C4⋊Q8C22×D1114yes—
325#126—2216no—
326#125—228no—
327#124—228no—
328C22⋊Q8—118no—
329C22⋊Q8—118no—
330C22⋊Q8—2216no—
331C22⋊Q8—224no—
332C22⋊Q8—224no—
333C4×Q8—114no—
334C4×Q8—114no—
335C4×Q8—228no—
336C4×Q8—222no—
337C4×Q8—222no—
338C4×D4—114no—
339C4×D4—114no—
340C4×D4—228no—
341#117—118no—
342#117—224no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1112yes—
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C42—222no—
362C2×C42—221no—
363C2×C42—221no—
364C2×C42C22×D1111yescharacteristic
365#107—114no—
366#107—118no—
367#106—118no—
368#106C22×D1118yes—
369#106C22×D1118yes—
370C4⋊C8—114no—
371#103—114no—
372#103—114no—
373#103—118no—
374#103—118no—
375C22⋊C8—118no—
376C4×C8C22×D1114yes—
377C2×C11#335614yescomplemented
378C2×C11C2×#54711yescharacteristic
379C2×C11C22×#13711yescharacteristic
380C2×C11C2×#57711yescharacteristic
381D11—44no—
382C24—112no—
383C2×Q8—24no—
384C2×Q8—24no—
385C2×Q8—44no—
386C2×Q8—82no—
387C2×Q8—112no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×D4—114no—
396C2×D4—224no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—112no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—228no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—884no—
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413Q16—228no—
414M16—2216no—
415C2×C8—22no—
416C2×C8—114no—
417C2×C8—224no—
418C2×C8#434314yes—
419C2×C8C23×D1112yes—
420C2×C8C23×D1112yes—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—114no—
426C4⋊C4—112no—
427C4⋊C4—112no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—228no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4C23×D1114yes—
436C4⋊C4C23×D1114yes—
437C22⋊C4—118no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C22⋊C4—228no—
441C42—228no—
442C42—224no—
443C42—224no—
444C42D4×D1112yes—
445C42C23×D1112yes—
446C11C2×#335611yescharacteristic, complemented, Sylow
447C23—114no—
448C23—224no—
449C23—224no—
450C23—224no—
451C23C2×D4×D1111yescharacteristic
452Q8—48no—
453Q8—84no—
454Q8—222no—
455Q8—222no—
456Q8—222no—
457Q8—222no—
458Q8—442no—
459Q8—442no—
460D4—228no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—114no—
467C2×C4—224no—
468C2×C4—228no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—888no—
480C2×C4#6696814yes—
481C2×C4C2×D4×D1112yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×D4×D1112yes—
484C2×C4C2×#434312yes—
485C2×C4#6704012yes—
486C2×C4C24×D1111yescharacteristic
487C8—22no—
488C8—224no—
489C8C2×#434314yes—
490C22—224no—
491C22—224no—
492C22—224no—
493C22—448no—
494C22#1062325712yes—
495C22C2×#6696812yes—
496C22#1062329312yes—
497C22C22×D4×D1111yescharacteristic
498C4—22no—
499C4—44no—
500C4—44no—
501C4—224no—
502C4—442no—
503C4—442no—
504C4—442no—
505C4—442no—
506C4#1062325712yes—
507C4C2×#6696814yes—
508C4C22×#434311yescharacteristic
509C4C2×#6704011yescharacteristic
510C2—444no—
511C2#1308123014yesdirect product factor
512C2C2×#1062325711yescharacteristic
513C2C22×#6696811yescharacteristic
514C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#498D11
hypocenterC11C2×#3356
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13081230C2direct (N × H)
4. C2×#10622480C2semidirect
5. C2×#10622475C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622707C2semidirect
8. C2×#10622481C2semidirect
9. C2×C4×Dic44C2semidirect
11. C2×#10622474C2semidirect
12. C2×C11×#498C2semidirect
34. C11×#498C22semidirect
42. #10622707C22semidirect
43. #10622704C22semidirect
49. #10622481C22semidirect
50. #10622480C22semidirect
51. #10622475C22semidirect
52. #10622474C22semidirect
53. C4×Dic44C22semidirect
193. C2×#498D11semidirect
266. #498C2×D11semidirect
377. C2×C11#3356semidirect
446. C11C2×#3356semidirect
511. C2#13081230direct (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×#106232612
#130812302
C2×#106224802
C2×#106224752
C2×#106227042
C2×#106227072
C2×#106224812
C2×C4×Dic442
C2×#106223012
C2×#106224742
C2×C11×#4982
C2×#335611