Finite Group Databasebeta

← C2×#13081322 #15633423

Subgroups — C2×#13081322 #15633423

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081322C2116yesmaximal, direct product factor
4C2×#10622377C212yesmaximal, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622484C212yesmaximal, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622399C212yesmaximal, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622482C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999—22no—
17C2×#66993C2212yes—
18C22×#4323C2211yescharacteristic
19C2×#66983—21no—
20C22×D88C2212yes—
21#10623261—24no—
22#10623261C2218yescomplemented
23#10623084—24no—
24#10623084C2218yescomplemented
25C2×#66950—21no—
26C2×#66946C2212yes—
27C2×#66946C2212yes—
28C2×C4⋊C4×D11—21no—
29C2×#66943C2212yes—
30C2×#66937—22no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#476C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66885C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622701C2218yescomplemented
43C4×#4323C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622484C22116yescomplemented
50#10622482C22116yescomplemented
51#10622456C2218yescomplemented
52#10622444C2218yescomplemented
53#10622399C22116yescomplemented
54#10622377C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×Dic22D411yescharacteristic
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C4×D4×C11—22no—
74C4×D4×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80#66999—216no—
81#66993—24no—
82#66993C2318yes—
83C2×#4323—24no—
84C2×#4323C2314yes—
85#66983—28no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4D412yes—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×D88—28no—
98C2×D88C2318yes—
99#66950—28no—
100#66946—24no—
101#66946—24no—
102#66946C2318yes—
103#66946C2318yes—
104C4⋊C4×D11—28no—
105#66943—24no—
106#66943C2318yes—
107#66937—216no—
108#66927—22no—
109#66927C2314yes—
110C4×D44—22no—
111C4×D44C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#102C2318yes—
117#66896C2314yes—
118#66885C2318yes—
119#66879C2318yes—
120Dic11⋊C8C2318yes—
121#66873C2314yes—
122#66873C2318yes—
123#66873C2318yes—
124#66871C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3366—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C23×D11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—82no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11C2412yes—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—44no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—28no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—84no—
147C22×Dic11—21no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150#4339—432no—
151C2×D44—21no—
152C2×D44—22no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—22no—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44—82no—
160C2×D44#4114yescomplemented
161C2×D44C2414yes—
162C2×D44C2412yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—48no—
167C2×C4×D11—44no—
168C2×C4×D11—84no—
169C2×Dic22—24no—
170C2×Dic22C2×D414yes—
171C2×C8×C11—24no—
172C2×C8×C11C2414yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2414yes—
178C11×C22⋊C4—24no—
179C42×C11C2×D412yes—
180C42×C11C2412yes—
181#4323—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—24no—
185C4⋊Dic11—28no—
186C4⋊Dic11—21no—
187C4⋊Dic11C2×D414yes—
188C4⋊Dic11C2412yes—
189Dic11⋊C4—28no—
190Dic11⋊C4C2×D418yes—
191C4×Dic11C2×D414yes—
192C4×Dic11C2414yes—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2412yes—
197D88—216no—
198C2×#554—111no—
199C2×#550—111no—
200#3366—1116no—
201C2×#490—112no—
202C2×#486—111no—
203C2×#478—112no—
204C2×#476D1111yescharacteristic, complemented
205C2×#459—111no—
206C2×#459—112no—
207C2×#446—111no—
208C2×#442—112no—
209C2×C4×D8—111no—
210C23×C11—22no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223Q8×C11—84no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11—48no—
233C2×C4×C11AGL(1,ℤ/8)14yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C112−1+412yes—
239C2×C4×C11C2511yescharacteristic
240C22⋊D11—416no—
241C22⋊D11—88no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—42no—
246C2×Dic11C22×D414yes—
247C2×Dic11C22×D414yes—
248D44—24no—
249D44—24no—
250D44—22no—
251D44—24no—
252D44—44no—
253D44—48no—
254D44—84no—
255D44C2×#4114yescomplemented
256C4×D11—416no—
257C4×D11—48no—
258C4×D11—88no—
259Dic22—28no—
260C8×C11—24no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C22×#41—221no—
264C22×D8—111no—
265C22×D8—112no—
266#554—118no—
267#554—224no—
268#550—118no—
269#550—224no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×#127—112no—
272C2×#127—111no—
273C2×#125—112no—
274C2×C22⋊Q8—221no—
275C2×C22⋊Q8—222no—
276C2×#121—222no—
277C2×#121—221no—
278C2×C4×Q8—111no—
279C2×C4×D4—112no—
280C2×C4×D4—112no—
281C2×C4×D4—111no—
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4—221no—
284#490—1116no—
285#486—118no—
286#478—1116no—
287#476C2×D1118yescomplemented
288#459—118no—
289#459—1116no—
290#446—118no—
291#442—1116no—
292C4×D8—118no—
293C2×#107—111no—
294C2×#106C2×D1112yes—
295C2×C4⋊C8—112no—
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×#102—111no—
298C2×#102—112no—
299C2×#102—112no—
300C2×#102—112no—
301C2×#102—111no—
302C2×#102C2×D1112yes—
303C2×#97—112no—
304C2×C4×C8—111no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—84no—
309C22×C11#54812yes—
310C22×C11C2×AGL(1,ℤ/8)12yes—
311C22×C11#57612yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—24no—
314C2×D11—48no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—88no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—44no—
324C4×C11#54812yes—
325C4×C11C2×AGL(1,ℤ/8)14yes—
326C4×C11C22×#4111yescharacteristic
327C4×C11C2×2−1+411yescharacteristic
328Dic11—24no—
329Dic11—24no—
330Dic11—42no—
331C2×#41—228no—
332C2×#41—448no—
333C22×Q8—21no—
334C22×Q8—111no—
335C22×D4—111no—
336C22×D4—112no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—222no—
344C23×C4—222no—
345C23×C4—221no—
346C2×D8—114no—
347C2×D8—118no—
348C2×D8—228no—
349C2×D8—224no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1112yes—
353C4⋊Q8—22no—
354C4⋊Q8C22×D1114yes—
355#127—118no—
356#127—114no—
357#127—224no—
358#127—222no—
359#125—118no—
360#125—224no—
361C22⋊Q8—228no—
362C22⋊Q8—2216no—
363#121—2216no—
364#121—228no—
365C4×Q8—114no—
366C4×Q8—114no—
367C4×D4—22no—
368C4×D4—118no—
369C4×D4—118no—
370C4×D4—114no—
371C4×D4—224no—
372C4×D4—224no—
373C4×D4—222no—
374C4×D4C22×D1114yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1112yes—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—221no—
388C2×C42—112no—
389C2×C42C22×D1111yescharacteristic
390#107—114no—
391#106C22×D1118yes—
392C4⋊C8—118no—
393C4⋊C8C22×D1114yes—
394#102—114no—
395#102—118no—
396#102—114no—
397#102—118no—
398#102—118no—
399#102C22×D1118yes—
400#97—118no—
401C4×C8—114no—
402C2×C11—82no—
403C2×C11#336614yescomplemented
404C2×C11C2×#54811yescharacteristic
405C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
406C2×C11C2×#57611yescharacteristic
407D11—44no—
408D11—84no—
409C24—21no—
410C24—221no—
411C24—222no—
412#41—4432no—
413C2×Q8—24no—
414C2×Q8—82no—
415C2×Q8—114no—
416C2×Q8—224no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—114no—
421C2×D4—112no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—221no—
426C2×D4—222no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—222no—
430C2×D4—224no—
431C2×D4—224no—
432C2×D4—448no—
433C2×D4—444no—
434C2×D4—882no—
435C2×D4—884no—
436C2×D4C23×D1112yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—44no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—228no—
444C22×C4—228no—
445C22×C4—221no—
446C22×C4—224no—
447C22×C4—448no—
448C22×C4—444no—
449C22×C4—884no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453D8—2216no—
454D8—228no—
455C2×C8—24no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8C23×D1114yes—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—114no—
465C4⋊C4—118no—
466C4⋊C4—112no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—221no—
470C4⋊C4C23×D1114yes—
471C4⋊C4C23×D1112yes—
472C22⋊C4—24no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C22⋊C4—224no—
476C42—114no—
477C42—114no—
478C42D4×D1112yes—
479C42C23×D1112yes—
480C11C2×#336611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—224no—
486C23—222no—
487C23—224no—
488C23—442no—
489C23—442no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23C2×D4×D1111yescharacteristic
494Q8—84no—
495Q8—228no—
496D4—22no—
497D4—22no—
498D4—42no—
499D4—114no—
500D4—224no—
501D4—222no—
502D4—224no—
503D4—224no—
504D4—4416no—
505D4—448no—
506D4—444no—
507D4—884no—
508D4—888no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—48no—
515C2×C4—114no—
516C2×C4—114no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—4416no—
521C2×C4—442no—
522C2×C4—448no—
523C2×C4—888no—
524C2×C4#6696714yes—
525C2×C4C2×D4×D1112yes—
526C2×C4C2×D4×D1112yes—
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4#6704012yes—
529C2×C4#41×D1112yes—
530C2×C4C24×D1111yescharacteristic
531C8—24no—
532C8—222no—
533C8—222no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—84no—
538C22—224no—
539C22—442no—
540C22—442no—
541C22—448no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—888no—
546C22#1062316412yes—
547C22C2×#6696712yes—
548C22#1062330512yes—
549C22C22×D4×D1111yescharacteristic
550C4—22no—
551C4—42no—
552C4—44no—
553C4—224no—
554C4—224no—
555C4—442no—
556C4#1062316412yes—
557C4C2×#6696714yes—
558C4C2×#6704011yescharacteristic
559C4C2×#41×D1111yescharacteristic
560C2—82no—
561C2—444no—
562C2—884no—
563C2#1308132214yesdirect product factor
564C2C2×#1062316411yescharacteristic
565C2C22×#6696711yescharacteristic
566C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
hypercenterC2×#476D11
hypocenterC11C2×#3366
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×#10623261C2semidirect
2. C2×#10623084C2semidirect
3. #13081322C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622399C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622482C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#476C2semidirect
22. #10623261C22semidirect
24. #10623084C22semidirect
34. C11×#476C22semidirect
42. #10622701C22semidirect
43. C4×#4323C22semidirect
49. #10622484C22semidirect
50. #10622482C22semidirect
51. #10622456C22semidirect
52. #10622444C22semidirect
53. #10622399C22semidirect
54. #10622377C22semidirect
160. C2×D44#41semidirect
204. C2×#476D11semidirect
255. D44C2×#41semidirect
287. #476C2×D11semidirect
403. C2×C11#3366semidirect
480. C11C2×#3366semidirect
563. C2#13081322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106230842
#130813222
C2×#106223772
C2×#106227012
C2×#106224842
C2×#106224562
C2×#106223992
C2×#106224442
C2×#106224822
C2×C4×#43232
C2×C11×#4762
C2×#336611