Finite Group Databasebeta

← C2×#13081426 #15633504

Subgroups — C2×#13081426 #15633504

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic22C211yesmaximal, characteristic, complemented
2#13081426C2116yesmaximal, direct product factor
3C2×#10622668C212yesmaximal, complemented
4C2×#10622683C211yesmaximal, characteristic
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622620C212yesmaximal, complemented
7C2×#10622667C212yesmaximal, complemented
8C2×#10622688C211yesmaximal, characteristic
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×#4324C2212yes—
26Q8×Dic22—24no—
27Q8×Dic22C2218yescomplemented
28C2×#66941—21no—
29C2×#66941—22no—
30C2×#66922C2212yes—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×#66896C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2212yes—
39#10622688C2218yes—
40#10622683C2218yes—
41#10622668C22116yescomplemented
42#10622667C22116yescomplemented
43C4×#4326C2218yescomplemented
44#10622637C2218yescomplemented
45#10622634C2218yescomplemented
46#10622631C22116yescomplemented
47#10622620C22116yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
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×Dic22—22no—
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C11×#127—22no—
65C11×#127C2314yes—
66C11×#124—28no—
67C11×#124—24no—
68C11×#124C2318yes—
69C11×#123—216no—
70C4×Q8×C11—22no—
71C4×Q8×C11D414yes—
72C4×Q8×C11C2314yes—
73C4×Q8×C11C2314yes—
74C4×D4×C11—28no—
75C4×D4×C11—24no—
76C4×D4×C11C2318yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87Q8×Dic11—28no—
88C2×#4326—24no—
89C2×#4326C2314yes—
90C2×#4324—28no—
91C2×#4324C2318yes—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2312yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66941—28no—
104#66941—216no—
105#66922—24no—
106#66922—22no—
107#66922C2318yes—
108#66922C2314yes—
109C4×Dic22—24no—
110C4×Dic22—22no—
111C4×Dic22C2318yes—
112C4×Dic22C2314yes—
113#66899C2318yes—
114#66899C2314yes—
115#66896C2318yes—
116#66896C2318yes—
117#66896C2318yes—
118#66874C2314yes—
119#66871C2314yes—
120#66871C2318yes—
121C4⋊(C11⋊C8)C2318yes—
122C4⋊(C11⋊C8)C2314yes—
123#66867C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3375—111nomaximal, Sylow
126C24×C11—22no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D414yes—
132C2×Q8×C11C2412yes—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—44no—
139C2×D4×C11—82no—
140C2×D4×C11C2414yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—28no—
144C22×C4×C11—84no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C2×Dic22—21no—
154C2×Dic22—28no—
155C2×Dic22—24no—
156C2×Dic22—22no—
157C2×Dic22—84no—
158C2×Dic22—82no—
159C2×Dic22#4114yes—
160C2×Dic22C2412yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D418yes—
165C11×C4⋊C4C2412yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C42×C11—24no—
170C42×C11C2×D414yes—
171C42×C11C2×D412yes—
172C42×C11C2412yes—
173C42×C11C2414yes—
174#4326—28no—
175#4324—216no—
176C4⋊Dic11—22no—
177C4⋊Dic11—21no—
178C4⋊Dic11—28no—
179C4⋊Dic11—24no—
180C4⋊Dic11C2412yes—
181C4⋊Dic11C2414yes—
182Dic11⋊C4—28no—
183Dic11⋊C4—24no—
184C4×Dic11—28no—
185C4×Dic11—24no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2414yes—
192C2×#559D1111yescharacteristic
193C2×Q82—111no—
194#3375—1116no—
195C2×#489—112no—
196C2×#486—111no—
197C2×#477—111no—
198C2×#474—112no—
199C2×#464—112no—
200C2×#460—111no—
201C2×#446—111no—
202C2×#440—112no—
203C2×C4×Q16—111no—
204C23×C11—24no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11C22×D411yescharacteristic
209Q8×C11—28no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213D4×C11—24no—
214D4×C11—24no—
215D4×C11—44no—
216D4×C11—48no—
217D4×C11—84no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—88no—
226C2×C4×C11#13714yes—
227C2×C4×C11C22×D414yes—
228C2×C4×C11C22×D414yes—
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—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—44no—
241Dic22—24no—
242Dic22—22no—
243Dic22—88no—
244Dic22—84no—
245Dic22C2×#4114yes—
246C11⋊C8—24no—
247C11⋊C8—22no—
248C11⋊C8—22no—
249C22×Q16—111no—
250C22×SD16—112no—
251#559—24no—
252#559C2×D1118yes—
253Q82—118no—
254Q82—224no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8—112no—
257C2×C4⋊Q8—221no—
258C2×C4⋊Q8—222no—
259C2×#127C2×D1111yescharacteristic
260C2×#124—21no—
261C2×#124C2×D1112yes—
262C2×#123—22no—
263C2×C4×Q8—111no—
264C2×C4×Q8—112no—
265C2×C4×Q8—221no—
266C2×C4×Q8C2×D1111yescharacteristic
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4C2×D1112yes—
270#489—1116no—
271#486—118no—
272#477—118no—
273#474—1116no—
274#464—1116no—
275#460—118no—
276#446—118no—
277#440—1116no—
278C4×Q16—118no—
279C2×#107—112no—
280C2×#107—111no—
281C2×C4⋊C8—111no—
282C2×C4⋊C8—112no—
283C2×#103—112no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×#97—112no—
290C2×C4×C8—111no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—88no—
295C22×C11#54812yes—
296C22×C11C2×#13712yes—
297C22×C11#57612yes—
298C22×C11C23×D411yescharacteristic
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—22no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11#54812yes—
305C4×C11C2×#13714yes—
306C4×C11C22×#4111yescharacteristic
307C4×C11C2×2−1+411yescharacteristic
308Dic11—24no—
309Dic11—42no—
310Dic11—44no—
311C22×Q8—111no—
312C22×Q8—222no—
313C22×Q8—221no—
314C22×Q8C22⋊D1111yescharacteristic
315C22×Q8C22×D1111yescharacteristic
316C22×D4—21no—
317C22×D4—21no—
318C22×D4C22×D1112yes—
319C23×C4—22no—
320C2×Q16—114no—
321C2×Q16—224no—
322C2×SD16—118no—
323C2×SD16—228no—
324C22×C8—112no—
325C22×C8—111no—
326C22×C8—111no—
327C4⋊Q8—118no—
328C4⋊Q8—114no—
329C4⋊Q8—228no—
330C4⋊Q8—2216no—
331C4⋊Q8—224no—
332C4⋊Q8—222no—
333#127—22no—
334#127C22×D1114yes—
335#124—28no—
336#124—24no—
337#124C22×D1118yes—
338#123—216no—
339C4×Q8—22no—
340C4×Q8—114no—
341C4×Q8—118no—
342C4×Q8—228no—
343C4×Q8—224no—
344C4×Q8—222no—
345C4×Q8C22⋊D1114yes—
346C4×Q8C22×D1114yes—
347C4×Q8C22×D1114yes—
348C4×D4—28no—
349C4×D4—24no—
350C4×D4C22×D1118yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4C22⋊D1111yescharacteristic
359C2×C4⋊C4C22⋊D1112yes—
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C42—21no—
365C2×C42—222no—
366C2×C42—221no—
367C2×C42C22×D1112yes—
368C2×C42C22×D1111yescharacteristic
369#107—114no—
370#107—118no—
371C4⋊C8—114no—
372C4⋊C8—118no—
373#103—114no—
374#103—118no—
375#103—114no—
376#102—118no—
377#102—118no—
378#102—118no—
379#97—118no—
380C4×C8—114no—
381C2×C11—84no—
382C2×C11#337514yescomplemented
383C2×C11C2×#54811yescharacteristic
384C2×C11C22×#13711yescharacteristic
385C2×C11C2×#57611yescharacteristic
386C24—22no—
387C2×Q8—24no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—114no—
392C2×Q8—112no—
393C2×Q8—222no—
394C2×Q8—221no—
395C2×Q8—228no—
396C2×Q8—224no—
397C2×Q8—884no—
398C2×Q8—882no—
399C2×Q8C2×C22⋊D1114yes—
400C2×Q8C23×D1112yes—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—44no—
407C2×D4—82no—
408C2×D4C23×D1114yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—28no—
412C22×C4—84no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—221no—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1112yes—
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421Q16—228no—
422SD16—2216no—
423C2×C8—112no—
424C2×C8—112no—
425C2×C8—114no—
426C2×C8—224no—
427C2×C8—222no—
428C2×C8—222no—
429C4⋊C4—24no—
430C4⋊C4—21no—
431C4⋊C4—114no—
432C4⋊C4—112no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C4⋊C4—228no—
436C4⋊C4—224no—
437C4⋊C4—228no—
438C4⋊C4—224no—
439C4⋊C4C2×C22⋊D1114yes—
440C4⋊C4C2×C22⋊D1118yes—
441C4⋊C4C23×D1112yes—
442C22⋊C4—28no—
443C22⋊C4—28no—
444C22⋊C4—28no—
445C42—24no—
446C42—228no—
447C42—224no—
448C42C2×C22⋊D1114yes—
449C42C2×C22⋊D1112yes—
450C42C23×D1112yes—
451C42C23×D1114yes—
452C11C2×#337511yescharacteristic, complemented, Sylow
453C23—24no—
454C23—44no—
455C23—44no—
456C23—44no—
457C23C22×C22⋊D1111yescharacteristic
458Q8—28no—
459Q8—22no—
460Q8—22no—
461Q8—42no—
462Q8—114no—
463Q8—224no—
464Q8—222no—
465Q8—888no—
466Q8—884no—
467D4—24no—
468D4—24no—
469D4—48no—
470D4—44no—
471D4—84no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—88no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—442no—
485C2×C4—444no—
486C2×C4#6700414yes—
487C2×C4#41×D1112yes—
488C2×C4#6704312yes—
489C2×C4C22×C22⋊D1114yes—
490C2×C4C22×C22⋊D1114yes—
491C2×C4C22×C22⋊D1112yes—
492C2×C4C22×C22⋊D1112yes—
493C2×C4C22×C22⋊D1111yescharacteristic
494C2×C4C24×D1111yescharacteristic
495C8—224no—
496C8—222no—
497C8—222no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—88no—
502C22C2×#6700412yes—
503C22#1062336212yes—
504C22#1062336612yes—
505C22C23×C22⋊D1111yescharacteristic
506C4—24no—
507C4—24no—
508C4—22no—
509C4—42no—
510C4—42no—
511C4—224no—
512C4—442no—
513C4—444no—
514C4C2×#6700414yes—
515C4#1062336212yes—
516C4C2×#41×D1111yescharacteristic
517C4C2×#6704311yescharacteristic
518C2—84no—
519C2#1308142614yesdirect product factor
520C2C2×#1062336211yescharacteristic
521C2C22×#6700411yescharacteristic
522C2C2×#1062336611yescharacteristic
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×#3375
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×Q8×Dic22C2semidirect
2. #13081426C2direct (N × H)
3. C2×#10622668C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622667C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622631C2semidirect
11. C2×C4×#4326C2semidirect
27. Q8×Dic22C22semidirect
41. #10622668C22semidirect
42. #10622667C22semidirect
43. C4×#4326C22semidirect
44. #10622637C22semidirect
45. #10622634C22semidirect
46. #10622631C22semidirect
47. #10622620C22semidirect
382. C2×C11#3375semidirect
452. C11C2×#3375semidirect
519. C2#13081426direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
#130814262
C2×#106226682
C2×#106226832
C2×#106226342
C2×#106226202
C2×#106226672
C2×#106226882
C2×#106226372
C2×#106226312
C2×C4×#43262
C2×C11×#5592
C2×#337511