Finite Group Databasebeta

← C2×#13081669 #15634765

Subgroups — C2×#13081669 #15634765

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×#10623101C211yesmaximal, characteristic, complemented
2#13081669C2116yesmaximal, direct product factor
3C2×#10622673C212yesmaximal, complemented
4C2×#10622689C211yesmaximal, characteristic
5C2×#10622667C212yesmaximal, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622688C211yesmaximal, characteristic
8C2×#10622632C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×C4×#4326C211yesmaximal, characteristic, complemented
12C2×C11×#559C211yesmaximal, characteristic
13C11×#559—24no—
14C11×#559C2218yes—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124—21no—
17C2×C11×#124C2212yes—
18C2×C11×#123—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2212yes—
23C2×Q8×Dic11—21no—
24C22×#4326C2211yescharacteristic
25C22×#4326C2212yes—
26C22×#4324C2212yes—
27C22×#4324C2212yes—
28C22×#4324C2212yes—
29#10623101—24no—
30#10623101C2218yescomplemented
31C2×#66943—21no—
32C2×#66943—22no—
33C2×#66922C2212yes—
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×#66899C2211yescharacteristic
38C2×#66896C2212yes—
39#10622689C2218yes—
40#10622688C2218yes—
41#10622673C22116yescomplemented
42#10622667C22116yescomplemented
43#10622644C2218yescomplemented
44C4×#4326C2218yescomplemented
45#10622637C2218yescomplemented
46#10622632C22116yescomplemented
47#10622631C22116yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66874C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C23×C4×C11—22no—
61C22×Dic22C2312yes—
62C22×Dic22C2311yescharacteristic
63C11×#127—22no—
64C11×#127C2314yes—
65C11×#124—28no—
66C11×#124—24no—
67C11×#124C2318yes—
68C11×#123—216no—
69C4×Q8×C11—22no—
70C4×Q8×C11D414yes—
71C4×Q8×C11C2314yes—
72C4×Q8×C11C2314yes—
73C4×D4×C11—28no—
74C4×D4×C11—24no—
75C4×D4×C11C2318yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2312yes—
86Q8×Dic11—28no—
87C2×#4326—24no—
88C2×#4326—44no—
89C2×#4326C2314yes—
90C2×#4326C2318yes—
91C2×#4324—28no—
92C2×#4324—44no—
93C2×#4324—44no—
94C2×#4324C2318yes—
95C2×#4324C2318yes—
96C2×#4324C2318yes—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109#66943—28no—
110#66943—216no—
111#66922—24no—
112#66922—22no—
113#66922C2318yes—
114#66922C2314yes—
115C4×Dic22—24no—
116C4×Dic22—22no—
117C4×Dic22C2318yes—
118C4×Dic22C2314yes—
119#66899C2314yes—
120#66896C2318yes—
121#66874C2318yes—
122#66874C2314yes—
123#66871C2314yes—
124C4⋊(C11⋊C8)C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126#66867C2318yes—
127C4×C11⋊C8C2314yes—
128C2×#3400—111nomaximal, Sylow
129C24×C11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11C2412yes—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—44no—
142C2×D4×C11—82no—
143C2×D4×C11C2414yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—28no—
147C22×C4×C11—84no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C2×Dic22—22no—
157C2×Dic22—21no—
158C2×Dic22—24no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—24no—
162C2×Dic22C2414yes—
163C2×Dic22C2412yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C2×D414yes—
167C11×C4⋊C4C2×D418yes—
168C11×C4⋊C4C2412yes—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C42×C11—24no—
173C42×C11C2×D414yes—
174C42×C11C2×D412yes—
175C42×C11C2412yes—
176C42×C11C2414yes—
177#4326—28no—
178#4326—48no—
179#4324—216no—
180#4324—48no—
181#4324—48no—
182C4⋊Dic11—21no—
183C4⋊Dic11—28no—
184C4⋊Dic11—24no—
185C4⋊Dic11—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11C2412yes—
188Dic11⋊C4—28no—
189Dic11⋊C4—24no—
190C4×Dic11—28no—
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×#559D1111yescharacteristic
199C2×#557—111no—
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×C11—24no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—28no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—42no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—44no—
222D4×C11—48no—
223D4×C11—84no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—88no—
232C2×C4×C11#13714yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11H(5,𝔽2)12yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247Dic22—24no—
248Dic22—22no—
249Dic22—22no—
250Dic22—24no—
251Dic22—44no—
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—24no—
262#559C2×D1118yes—
263#557—118no—
264#557—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8—112no—
267C2×#127C2×D1111yescharacteristic
268C2×#125—221no—
269C2×#125—222no—
270C2×#124—21no—
271C2×#124C2×D1112yes—
272C2×#123—22no—
273C2×C4×Q8—111no—
274C2×C4×Q8—112no—
275C2×C4×Q8—221no—
276C2×C4×Q8C2×D1111yescharacteristic
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—21no—
279C2×C4×D4C2×D1112yes—
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—111no—
294C2×#103—112no—
295C2×#102—112no—
296C2×#97—112no—
297C2×C4×C8—111no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—88no—
302C22×C11#55012yes—
303C22×C11C2×#13712yes—
304C22×C11#57712yes—
305C22×C11C23×D411yescharacteristic
306C4×C11—24no—
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11#55012yes—
312C4×C11C2×#13714yes—
313C4×C11C22×#4111yescharacteristic
314C4×C11C2×H(5,𝔽2)11yescharacteristic
315Dic11—44no—
316Dic11—42no—
317Dic11—42no—
318C22×Q8—112no—
319C22×Q8—111no—
320C22×Q8C22⋊D1111yescharacteristic
321C22×Q8C22×D1111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C22×D1112yes—
325C23×C4—22no—
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—118no—
340C4⋊Q8—114no—
341C4⋊Q8—224no—
342C4⋊Q8—222no—
343#127—22no—
344#127C22×D1114yes—
345#125—228no—
346#125—2216no—
347#124—28no—
348#124—24no—
349#124C22×D1118yes—
350#123—216no—
351C4×Q8—22no—
352C4×Q8—114no—
353C4×Q8—118no—
354C4×Q8—228no—
355C4×Q8—224no—
356C4×Q8—222no—
357C4×Q8C22⋊D1114yes—
358C4×Q8C22×D1114yes—
359C4×Q8C22×D1114yes—
360C4×D4—28no—
361C4×D4—24no—
362C4×D4C22×D1118yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1112yes—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C42—21no—
378C2×C42—222no—
379C2×C42—221no—
380C2×C42C22×D1112yes—
381C2×C42C22×D1111yescharacteristic
382#107—114no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#103—114no—
387#103—118no—
388#102—118no—
389#97—118no—
390C4×C8—114no—
391C2×C11—84no—
392C2×C11#340014yescomplemented
393C2×C11C2×#55011yescharacteristic
394C2×C11C22×#13711yescharacteristic
395C2×C11C2×#57711yescharacteristic
396C24—22no—
397C2×Q8—24no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—114no—
402C2×Q8—112no—
403C2×Q8—222no—
404C2×Q8—221no—
405C2×Q8—224no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—224no—
409C2×Q8C2×C22⋊D1114yes—
410C2×Q8C23×D1112yes—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—44no—
417C2×D4—82no—
418C2×D4C23×D1114yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—28no—
422C22×C4—84no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—221no—
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—24no—
443C4⋊C4—21no—
444C4⋊C4—112no—
445C4⋊C4—221no—
446C4⋊C4—228no—
447C4⋊C4—224no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4—228no—
451C4⋊C4—224no—
452C4⋊C4C2×C22⋊D1114yes—
453C4⋊C4C2×C22⋊D1118yes—
454C4⋊C4C23×D1112yes—
455C22⋊C4—28no—
456C22⋊C4—28no—
457C22⋊C4—28no—
458C42—24no—
459C42—228no—
460C42—224no—
461C42C2×C22⋊D1114yes—
462C42C2×C22⋊D1112yes—
463C42C23×D1112yes—
464C42C23×D1114yes—
465C11C2×#340011yescharacteristic, complemented, Sylow
466C23—24no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23C22×C22⋊D1111yescharacteristic
471Q8—28no—
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—224no—
476Q8—222no—
477Q8—222no—
478Q8—224no—
479Q8—444no—
480Q8—442no—
481D4—24no—
482D4—24no—
483D4—48no—
484D4—44no—
485D4—84no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—88no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4#6700414yes—
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—44no—
513C22—44no—
514C22—44no—
515C22—88no—
516C22C2×#6700412yes—
517C22#1062336512yes—
518C22#1062336712yes—
519C22C23×C22⋊D1111yescharacteristic
520C4—24no—
521C4—24no—
522C4—22no—
523C4—42no—
524C4—42no—
525C4—444no—
526C4—442no—
527C4—442no—
528C4C2×#6700414yes—
529C4#1062336512yes—
530C4C2×#41×D1111yescharacteristic
531C4C2×#6704211yescharacteristic
532C2—84no—
533C2#1308166914yesdirect product factor
534C2C2×#1062336511yescharacteristic
535C2C22×#6700411yescharacteristic
536C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11C2×#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
2. #13081669C2direct (N × H)
3. C2×#10622673C2semidirect
5. C2×#10622667C2semidirect
6. C2×#10622644C2semidirect
8. C2×#10622632C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622631C2semidirect
11. C2×C4×#4326C2semidirect
30. #10623101C22semidirect
41. #10622673C22semidirect
42. #10622667C22semidirect
43. #10622644C22semidirect
44. C4×#4326C22semidirect
45. #10622637C22semidirect
46. #10622632C22semidirect
47. #10622631C22semidirect
392. C2×C11#3400semidirect
465. C11C2×#3400semidirect
533. C2#13081669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
#130816692
C2×#106226732
C2×#106226892
C2×#106226672
C2×#106226442
C2×#106226882
C2×#106226322
C2×#106226372
C2×#106226312
C2×C4×#43262
C2×C11×#5592
C2×#340011