Finite Group Databasebeta

← C2×#13081332 #15633446

Subgroups — C2×#13081332 #15633446

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081332C2116yesmaximal, direct product factor
4C2×#10622378C212yesmaximal, complemented
5C2×#10622294C211yesmaximal, characteristic, complemented
6C2×#10622488C212yesmaximal, complemented
7C2×#10622620C211yesmaximal, characteristic, complemented
8C2×#10622766C212yesmaximal
9C2×#10622632C211yesmaximal, characteristic, complemented
10C2×#10622292C211yesmaximal, characteristic, complemented
11C2×#10622370C212yesmaximal, complemented
12C2×C4×C11×D8C211yesmaximal, characteristic
13C23×Dic22—21no—
14C22×C11×D8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66989C2212yes—
18C2×D4×Dic11C2212yes—
19C22×#4324C2212yes—
20C2×#66979—21no—
21C2×#66977—21no—
22C2×#66977—21no—
23#10623073—24no—
24#10623073C2218yescomplemented
25D4×Dic22—24no—
26D4×Dic22C2218yescomplemented
27C2×#66941C2212yes—
28C2×#66940C2212yes—
29C2×#66932—22no—
30C2×#66931—22no—
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×D8C2218yes—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40#10622766C22116yes—
41C2×#66880C2212yes—
42C2×#66880C2212yes—
43C2×#66879C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622632C2218yescomplemented
46#10622620C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622488C22116yescomplemented
51#10622378C22116yescomplemented
52#10622370C22116yescomplemented
53#10622294C2218yescomplemented
54#10622292C2218yescomplemented
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×Dic11—22no—
60C22×Dic22—21no—
61C22×Dic22—22no—
62C22×Dic22—28no—
63C22×Dic22—48no—
64C22×Dic22D411yescharacteristic
65C22×Dic22C2312yes—
66C2×C11×D8—24no—
67C2×C11×D8C2314yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C4×D4×C11C2314yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82#66989—24no—
83#66989C2318yes—
84D4×Dic11—24no—
85D4×Dic11C2318yes—
86C2×#4324—28no—
87C2×#4324C2318yes—
88#66979—28no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2312yes—
94#66977—28no—
95#66977—28no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4D412yes—
99C2×C4×Dic11—22no—
100C2×C4×Dic11C2312yes—
101C22×C11⋊C8C2312yes—
102#66941—24no—
103#66941C2318yes—
104#66940—24no—
105#66940C2318yes—
106#66932—216no—
107#66931—216no—
108#66922—22no—
109#66922—22no—
110#66922C2314yes—
111#66922C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#107C2314yes—
115C11×#102C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66896C2318yes—
119#66880C2318yes—
120#66880C2318yes—
121#66879C2318yes—
122Dic11⋊C8C2318yes—
123#66874C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3367—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11#4114yes—
135C2×D4×C11C2412yes—
136C2×D4×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—28no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—48no—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152C2×Dic22—28no—
153C2×Dic22—24no—
154C2×Dic22—22no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22—24no—
158C2×Dic22—432no—
159C2×Dic22—48no—
160C2×Dic22—44no—
161C2×Dic22C2×D414yes—
162C2×Dic22C2414yes—
163C11×D8—28no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11C2412yes—
167C2×C8×C11C2412yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C2412yes—
171C11×C4⋊C4C2412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C42×C11C2×D412yes—
175C42×C11C2412yes—
176C22⋊Dic11—28no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179#4324—216no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—24no—
184C4⋊Dic11C2×D414yes—
185C4⋊Dic11C2414yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4C2×D418yes—
189C4×Dic11—28no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2414yes—
192C2×C11⋊C8—24no—
193C2×C11⋊C8C2414yes—
194C2×#556—111no—
195C2×D4×Q8—111no—
196#3367—1116no—
197C2×#489—112no—
198C2×#487—111no—
199C2×#477—112no—
200C2×#474—111no—
201C2×#463—112no—
202C2×#461—111no—
203C2×#446—111no—
204C2×#440—112no—
205C2×C4×D8D1111yescharacteristic
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11C22×D411yescharacteristic
215D4×C11—24no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—42no—
220D4×C11C2×#4114yes—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11—48no—
228C2×C4×C11AGL(1,ℤ/8)14yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C112−1+412yes—
234C2×C4×C11C2511yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—416no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11C22×D414yes—
243C2×Dic11C22×D414yes—
244Dic22—28no—
245Dic22—24no—
246Dic22—24no—
247Dic22—416no—
248Dic22—44no—
249Dic22—48no—
250C8×C11—22no—
251C8×C11—22no—
252C11⋊C8—24no—
253C23×Q8—221no—
254C22×SD16—112no—
255C22×D8C2×D1111yescharacteristic
256#556—118no—
257#556—224no—
258D4×Q8—118no—
259D4×Q8—224no—
260C2×C4⋊Q8—112no—
261C2×C4⋊Q8—111no—
262C2×C4⋊Q8—111no—
263C2×#126—222no—
264C2×#124—112no—
265C2×C22⋊Q8—222no—
266C2×C22⋊Q8—221no—
267C2×C22⋊Q8—221no—
268C2×C4×Q8—111no—
269C2×C4×Q8—112no—
270C2×C4×D4—112no—
271C2×C4×D4C2×D1111yescharacteristic
272C2×C4×D4C2×D1111yescharacteristic
273C2×#117—221no—
274#489—1116no—
275#487—118no—
276#477—1116no—
277#474—118no—
278#463—1116no—
279#461—118no—
280#446—118no—
281#440—1116no—
282C4×D8C2×D1118yes—
283C2×#107—112no—
284C2×#107C2×D1111yescharacteristic
285C2×C4⋊C8—112no—
286C2×C4⋊C8—111no—
287C2×#103—112no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#102—112no—
291C2×#102C2×D1111yescharacteristic
292C2×#102C2×D1111yescharacteristic
293C2×#97—112no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—24no—
296C22×C11—48no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—84no—
303C22×C11#54812yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11#54812yes—
311C4×C11C2×AGL(1,ℤ/8)14yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×2−1+411yescharacteristic
314Dic11—24no—
315Dic11—24no—
316Dic11—44no—
317Dic11—44no—
318C22×Q8—111no—
319C22×Q8—112no—
320C22×Q8—222no—
321C22×Q8—228no—
322C22×Q8—221no—
323C22×Q8—448no—
324C22×D4C22×D1111yescharacteristic
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—222no—
329C2×SD16—118no—
330C2×SD16—228no—
331C2×D8—24no—
332C2×D8C22×D1114yes—
333C22×C8—112no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—118no—
337C4⋊Q8—114no—
338C4⋊Q8—114no—
339C4⋊Q8—224no—
340C4⋊Q8—222no—
341C4⋊Q8—222no—
342#126—2216no—
343#124—118no—
344#124—224no—
345C22⋊Q8—2216no—
346C22⋊Q8—228no—
347C22⋊Q8—228no—
348C4×Q8—114no—
349C4×Q8—114no—
350C4×Q8—118no—
351C4×Q8—224no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—118no—
355C4×D4—224no—
356C4×D4C22×D1114yes—
357C4×D4C22×D1114yes—
358#117—228no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—112no—
375C2×C42—222no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107C22×D1114yes—
379C4⋊C8—118no—
380C4⋊C8—114no—
381#103—118no—
382#103—118no—
383#103—118no—
384#102—118no—
385#102C22×D1114yes—
386#102C22×D1114yes—
387#97—118no—
388C4×C8C22×D1114yes—
389C2×C11—44no—
390C2×C11—82no—
391C2×C11#336714yescomplemented
392C2×C11C2×#54811yescharacteristic
393C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C11C2×#57811yescharacteristic
395C24—21no—
396C24—21no—
397C2×Q8—114no—
398C2×Q8—114no—
399C2×Q8—228no—
400C2×Q8—224no—
401C2×Q8—222no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—224no—
405C2×Q8—448no—
406C2×Q8—4432no—
407C2×Q8—444no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4#433914yes—
414C2×D4C23×D1112yes—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—228no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—448no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—2216no—
432D8—28no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—114no—
436C2×C8—224no—
437C2×C8C23×D1112yes—
438C2×C8C23×D1112yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—114no—
442C4⋊C4—118no—
443C4⋊C4—114no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C4⋊C4—222no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4C23×D1112yes—
451C4⋊C4C23×D1112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C42—114no—
458C42—114no—
459C42—228no—
460C42D4×D1112yes—
461C42C23×D1112yes—
462C11C2×#336711yescharacteristic, complemented, Sylow
463C23—24no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23C2×D4×D1111yescharacteristic
472Q8—228no—
473Q8—224no—
474Q8—224no—
475Q8—4416no—
476Q8—448no—
477Q8—444no—
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—42no—
483D4C2×#433914yes—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—114no—
492C2×C4—114no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—4416no—
498C2×C4—444no—
499C2×C4—444no—
500C2×C4#6696414yes—
501C2×C4C2×#433912yes—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1112yes—
504C2×C4C2×D4×D1111yescharacteristic
505C2×C4#6704312yes—
506C2×C4C24×D1111yescharacteristic
507C8—22no—
508C8—22no—
509C8—224no—
510C22—24no—
511C22—42no—
512C22—48no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22#1062308312yes—
519C22C2×#6696412yes—
520C22#1062330212yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—224no—
526C4—224no—
527C4—444no—
528C4—444no—
529C4#1062308312yes—
530C4C2×#6696414yes—
531C4C22×#433911yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—44no—
534C2—82no—
535C2#1308133214yesdirect product factor
536C2C2×#1062308311yescharacteristic
537C2C22×#6696411yescharacteristic
538C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11C2×#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081332C2direct (N × H)
4. C2×#10622378C2semidirect
5. C2×#10622294C2semidirect
6. C2×#10622488C2semidirect
7. C2×#10622620C2semidirect
9. C2×#10622632C2semidirect
10. C2×#10622292C2semidirect
11. C2×#10622370C2semidirect
24. #10623073C22semidirect
26. D4×Dic22C22semidirect
45. #10622632C22semidirect
46. #10622620C22semidirect
50. #10622488C22semidirect
51. #10622378C22semidirect
52. #10622370C22semidirect
53. #10622294C22semidirect
54. #10622292C22semidirect
391. C2×C11#3367semidirect
462. C11C2×#3367semidirect
535. C2#13081332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×D4×Dic222
#130813322
C2×#106223782
C2×#106222942
C2×#106224882
C2×#106226202
C2×#106227662
C2×#106226322
C2×#106222922
C2×#106223702
C2×C4×C11×D82
C2×#336711