Finite Group Databasebeta

← C2×#13081665 #15634761

Subgroups — C2×#13081665 #15634761

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2#13081665C2116yesmaximal, direct product factor
3C2×#10622699C212yesmaximal, complemented
4C2×#10622698C211yesmaximal, characteristic
5C2×#10622641C212yesmaximal, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622640C211yesmaximal, characteristic
8C2×#10622696C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×C4×#4326C211yesmaximal, characteristic, complemented
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C11×#557—24no—
14C11×#557C2218yescomplemented
15C2×C11×C4⋊Q8C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×#125—22no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#67000—21no—
24C22×#4326C2211yescharacteristic
25C22×#4326C2212yes—
26C22×#4325C2212yes—
27C22×#4325C2212yes—
28C22×#4325C2212yes—
29#10623116—24no—
30#10623116C2218yes—
31C2×#66947—22no—
32C2×#66946—21no—
33C2×#66928C2212yes—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×C4×Dic22C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2212yes—
39#10622703C2218yescomplemented
40#10622699C22116yescomplemented
41#10622698C2218yes—
42#10622696C22116yescomplemented
43C4×#4326C2218yescomplemented
44#10622641C22116yescomplemented
45#10622640C2218yes—
46#10622639C22116yescomplemented
47#10622637C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66873C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D44—21no—
59C22×D44—21no—
60C22×D44C2312yes—
61C22×C4×D11—22no—
62C22×Dic22C2311yescharacteristic
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8C2318yes—
66C11×C4⋊Q8C2314yes—
67C11×#125—28no—
68C11×#125—216no—
69C4×Q8×C11—28no—
70C4×Q8×C11—22no—
71C4×Q8×C11—24no—
72C4×Q8×C11D414yes—
73C4×Q8×C11C2318yes—
74C4×Q8×C11C2314yes—
75C4×Q8×C11C2314yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89#67000—28no—
90C2×#4326—24no—
91C2×#4326—44no—
92C2×#4326C2314yes—
93C2×#4326C2318yes—
94C2×#4325—28no—
95C2×#4325—44no—
96C2×#4325—44no—
97C2×#4325C2318yes—
98C2×#4325C2318yes—
99C2×#4325C2318yes—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109#66947—216no—
110#66946—28no—
111#66928—24no—
112#66928C2318yes—
113#66927—22no—
114#66927C2314yes—
115C4×D44—24no—
116C4×D44C2318yes—
117C4×Dic22—22no—
118C4×Dic22C2314yes—
119#66899C2318yes—
120#66899C2314yes—
121#66874C2314yes—
122#66873C2318yes—
123#66871C2314yes—
124C4⋊(C11⋊C8)C2314yes—
125C4⋊(C11⋊C8)C2318yes—
126#66867C2318yes—
127C4×C11⋊C8C2314yes—
128C2×#3400—111nomaximal, Sylow
129C23×D11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11—24no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2×D414yes—
138C2×Q8×C11C2414yes—
139C2×Q8×C11C2412yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C2×D44—22no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—44no—
156C2×D44—82no—
157C2×D44C2414yes—
158C2×C4×D11—28no—
159C2×C4×D11—84no—
160C2×Dic22—21no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22C2412yes—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×D414yes—
172C11×C4⋊C4C2×D418yes—
173C11×C4⋊C4C2412yes—
174C42×C11—28no—
175C42×C11—24no—
176C42×C11C2×D412yes—
177C42×C11C2×D414yes—
178C42×C11C2412yes—
179C42×C11C2414yes—
180#4326—28no—
181#4326—48no—
182#4325—216no—
183#4325—48no—
184#4325—48no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2412yes—
190Dic11⋊C4—24no—
191C4×Dic11—24no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8#4114yes—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2414yes—
197C2×C11⋊C8C2412yes—
198C2×#559—111no—
199C2×#557D1111yescharacteristic, complemented
200#3400—1116no—
201C2×#497—112no—
202C2×#492—111no—
203C2×#464—112no—
204C2×#462—111no—
205C2×#460—111no—
206C2×#461—112no—
207C2×#446—111no—
208C2×#440—112no—
209C2×C4×Q16—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—24no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215Q8×C11—28no—
216Q8×C11—24no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—24no—
220Q8×C11—44no—
221Q8×C11—42no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11#13714yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C11H(5,𝔽2)12yes—
239C2×C4×C11C2511yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244D44—24no—
245D44—24no—
246D44—44no—
247D44—48no—
248D44—84no—
249C4×D11—88no—
250Dic22—22no—
251Dic22—22no—
252Dic22—42no—
253C11⋊C8—22no—
254C11⋊C8—24no—
255C11⋊C8C2×#4114yes—
256C22×Q16—111no—
257C22×Q16—112no—
258C22×SD16—112no—
259C22×SD16—112no—
260C22×SD16—112no—
261#559—118no—
262#559—224no—
263#557—24no—
264#557C2×D1118yescomplemented
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×C4⋊Q8C2×D1112yes—
267C2×#127—111no—
268C2×#125—21no—
269C2×#125—22no—
270C2×#124—112no—
271C2×#124—221no—
272C2×#123—222no—
273C2×C4×Q8—21no—
274C2×C4×Q8—111no—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×Q8C2×D1112yes—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—112no—
279C2×C4×D4—221no—
280#497—1116no—
281#492—118no—
282#464—1116no—
283#462—118no—
284#461—1116no—
285#460—118no—
286#446—118no—
287#440—1116no—
288C4×Q16—118no—
289C2×#107—111no—
290C2×C4⋊C8—112no—
291C2×C4⋊C8—111no—
292C2×#103—111no—
293C2×#103—112no—
294C2×#103—111no—
295C2×#102—112no—
296C2×#97—112no—
297C2×C4×C8—111no—
298C22×C11#55012yes—
299C22×C11C2×#13712yes—
300C22×C11#57712yes—
301C22×C11C23×D411yescharacteristic
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—88no—
306C4×C11—24no—
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11#55012yes—
313C4×C11C2×#13714yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×H(5,𝔽2)11yescharacteristic
316Dic11—42no—
317Dic11—42no—
318C22×Q8—111no—
319C22×Q8C22⋊D1111yescharacteristic
320C22×Q8C22×D1112yes—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—112no—
323C22×D4—221no—
324C22×D4—221no—
325C23×C4—222no—
326C2×Q16—114no—
327C2×Q16—118no—
328C2×Q16—224no—
329C2×Q16—444no—
330C2×SD16—118no—
331C2×SD16—118no—
332C2×SD16—118no—
333C2×SD16—228no—
334C2×SD16—444no—
335C2×SD16—444no—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8—112no—
339C4⋊Q8—24no—
340C4⋊Q8—22no—
341C4⋊Q8C22×D1118yes—
342C4⋊Q8C22×D1114yes—
343#127—114no—
344#127—222no—
345#125—28no—
346#125—216no—
347#124—118no—
348#124—228no—
349#124—224no—
350#123—2216no—
351C4×Q8—28no—
352C4×Q8—24no—
353C4×Q8—22no—
354C4×Q8—114no—
355C4×Q8—222no—
356C4×Q8C22⋊D1114yes—
357C4×Q8C22×D1114yes—
358C4×Q8C22×D1118yes—
359C4×Q8C22×D1114yes—
360C4×D4—118no—
361C4×D4—228no—
362C4×D4—224no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1112yes—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42—221no—
380C2×C42C22×D1112yes—
381C2×C42C22×D1111yescharacteristic
382#107—114no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#103—118no—
387#103—114no—
388#102—118no—
389#97—118no—
390C4×C8—114no—
391C2×C11#340014yescomplemented
392C2×C11C2×#55011yescharacteristic
393C2×C11C22×#13711yescharacteristic
394C2×C11C2×#57711yescharacteristic
395D11—84no—
396C24—222no—
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—24no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—24no—
404C2×Q8—112no—
405C2×Q8—221no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8C2×C22⋊D1114yes—
409C2×Q8C23×D1114yes—
410C2×Q8C23×D1112yes—
411C2×D4—114no—
412C2×D4—224no—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4—222no—
416C2×D4—224no—
417C2×D4—444no—
418C2×D4—882no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—228no—
425C22×C4—884no—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1112yes—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431Q16—228no—
432Q16—448no—
433SD16—2216no—
434SD16—448no—
435SD16—448no—
436C2×C8—114no—
437C2×C8—112no—
438C2×C8—112no—
439C2×C8—114no—
440C2×C8—222no—
441C2×C8—224no—
442C4⋊C4—28no—
443C4⋊C4—24no—
444C4⋊C4—28no—
445C4⋊C4—24no—
446C4⋊C4—28no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—112no—
450C4⋊C4—221no—
451C4⋊C4—224no—
452C4⋊C4C2×C22⋊D1114yes—
453C4⋊C4C2×C22⋊D1118yes—
454C4⋊C4C23×D1112yes—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C22⋊C4—228no—
458C42—28no—
459C42—24no—
460C42—224no—
461C42C2×C22⋊D1114yes—
462C42C2×C22⋊D1112yes—
463C42C23×D1112yes—
464C42C23×D1114yes—
465C11C2×#340011yescharacteristic, complemented, Sylow
466C23—224no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23C22×C22⋊D1111yescharacteristic
471Q8—28no—
472Q8—24no—
473Q8—22no—
474Q8—22no—
475Q8—24no—
476Q8—44no—
477Q8—42no—
478Q8—222no—
479Q8—222no—
480Q8—442no—
481D4—224no—
482D4—224no—
483D4—448no—
484D4—444no—
485D4—884no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—888no—
500C2×C4#6699514yes—
501C2×C4#41×D1112yes—
502C2×C4#6704212yes—
503C2×C4C22×C22⋊D1114yes—
504C2×C4C22×C22⋊D1114yes—
505C2×C4C22×C22⋊D1112yes—
506C2×C4C22×C22⋊D1112yes—
507C2×C4C22×C22⋊D1111yescharacteristic
508C2×C4C24×D1111yescharacteristic
509C8—114no—
510C8—222no—
511C8—224no—
512C22—444no—
513C22—444no—
514C22—444no—
515C22—888no—
516C22C2×#6699512yes—
517C22#1062336512yes—
518C22#1062336812yes—
519C22C23×C22⋊D1111yescharacteristic
520C4—24no—
521C4—24no—
522C4—22no—
523C4—42no—
524C4—44no—
525C4—42no—
526C4—442no—
527C4—442no—
528C4C2×#6699514yes—
529C4#1062336512yes—
530C4C2×#41×D1111yescharacteristic
531C4C2×#6704211yescharacteristic
532C2—884no—
533C2#1308166514yesdirect product factor
534C2C2×#1062336511yescharacteristic
535C2C22×#6699511yescharacteristic
536C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#557D11
hypocenterC11C2×#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081665C2direct (N × H)
3. C2×#10622699C2semidirect
5. C2×#10622641C2semidirect
6. C2×#10622703C2semidirect
8. C2×#10622696C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622639C2semidirect
11. C2×C4×#4326C2semidirect
12. C2×C11×#557C2semidirect
14. C11×#557C22semidirect
39. #10622703C22semidirect
40. #10622699C22semidirect
42. #10622696C22semidirect
43. C4×#4326C22semidirect
44. #10622641C22semidirect
46. #10622639C22semidirect
47. #10622637C22semidirect
199. C2×#557D11semidirect
264. #557C2×D11semidirect
391. C2×C11#3400semidirect
465. C11C2×#3400semidirect
533. C2#13081665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130816652
C2×#106226992
C2×#106226982
C2×#106226412
C2×#106227032
C2×#106226402
C2×#106226962
C2×#106226372
C2×#106226392
C2×C4×#43262
C2×C11×#5572
C2×#340011