Finite Group Databasebeta

← C2×#13081341 #15633468

Subgroups — C2×#13081341 #15633468

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2#13081341C2116yesmaximal, direct product factor
3C2×#10622684C212yesmaximal, complemented
4C2×#10622683C211yesmaximal, characteristic, complemented
5C2×#10622622C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622688C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic
13C22×C11×#41—21no—
14C11×#550—24no—
15C11×#550C2218yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#127C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×#66997—21no—
24C22×#4324C2211yescharacteristic
25C22×#4324C2212yes—
26#10623098—24no—
27#10623098C2218yescomplemented
28C2×#66942—22no—
29C2×#66940—21no—
30C2×#66923C2212yes—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×#66896C2212yes—
35C2×#66896C2212yes—
36C2×#66896C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66896C2212yes—
39#10622688C2218yescomplemented
40#10622688C22116yescomplemented
41#10622684C22116yescomplemented
42#10622683C2218yescomplemented
43#10622637C2218yescomplemented
44#10622631C22116yescomplemented
45C4×#4324C2218yescomplemented
46#10622622C22116yescomplemented
47#10622620C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11—21no—
66C22×Dic22—21no—
67C22×Dic22C2311yescharacteristic
68C11×#127—22no—
69C11×#127—24no—
70C11×#127C2314yes—
71C11×#127C2318yes—
72C11×#121—28no—
73C11×#121—216no—
74C4×Q8×C11D414yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11C2314yes—
79C4×D4×C11C2318yes—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87#66997—28no—
88C2×#4324—24no—
89C2×#4324—28no—
90C2×#4324C2314yes—
91C2×#4324C2318yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66942—216no—
105#66940—28no—
106#66923—24no—
107#66923C2318yes—
108#66922—22no—
109#66922C2314yes—
110C4×Dic22—24no—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113C4×Dic22C2318yes—
114#66896C2318yes—
115#66896C2318yes—
116#66896C2318yes—
117#66896C2314yes—
118#66896C2318yes—
119#66874C2314yes—
120#66872C2314yes—
121#66871C2318yes—
122C4⋊(C11⋊C8)C2314yes—
123C4⋊(C11⋊C8)C2318yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3368—111nomaximal, Sylow
127C24×C11—22no—
128C24×C11—21no—
129C11×#41—432no—
130C2×Q8×C11—24no—
131C2×Q8×C11C2×D414yes—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—28no—
135C2×D4×C11—24no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—48no—
143C2×D4×C11—44no—
144C2×D4×C11—84no—
145C2×D4×C11—82no—
146C2×D4×C11C2412yes—
147C2×D4×C11C2414yes—
148C22×C4×C11—21no—
149C22×C4×C11—28no—
150C22×C4×C11—24no—
151C22×C4×C11—48no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C2×Dic22—21no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—44no—
165C2×Dic22#4114yescomplemented
166C2×Dic22C2412yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C2×D414yes—
169C11×C4⋊C4C2×D418yes—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—24no—
173C42×C11C2×D412yes—
174C42×C11C2×D414yes—
175C42×C11C2412yes—
176C42×C11C2414yes—
177#4324—28no—
178#4324—216no—
179C4⋊Dic11—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—24no—
182C4⋊Dic11C2414yes—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—24no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2414yes—
196C2×#557—111no—
197C2×#550D1111yescharacteristic
198#3368—1116no—
199C2×#490—112no—
200C2×#486—111no—
201C2×#478—112no—
202C2×#474—111no—
203C2×#460—111no—
204C2×#460—112no—
205C2×#446—111no—
206C2×#440—112no—
207C2×C4×SD16—111no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—44no—
211C23×C11—42no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—42no—
216C23×C11C22×D411yescharacteristic
217Q8×C11—28no—
218D4×C11—22no—
219D4×C11—24no—
220D4×C11—22no—
221D4×C11—24no—
222D4×C11—416no—
223D4×C11—42no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—88no—
227D4×C11—84no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—416no—
233C2×C4×C11—42no—
234C2×C4×C11—48no—
235C2×C4×C11AGL(1,ℤ/8)14yes—
236C2×C4×C11C22×D414yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C112−1+412yes—
243C2×C4×C11C2511yescharacteristic
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—42no—
250Dic22—24no—
251Dic22—22no—
252Dic22—48no—
253Dic22C2×#4114yescomplemented
254C11⋊C8—22no—
255C11⋊C8—24no—
256C11⋊C8—22no—
257C22×#41—21no—
258C22×SD16—111no—
259C22×SD16—112no—
260#557—118no—
261#557—224no—
262#550—24no—
263#550C2×D1118yes—
264C2×C4⋊Q8—111no—
265C2×C4⋊Q8—221no—
266C2×#127C2×D1111yescharacteristic
267C2×#127C2×D1112yes—
268C2×#125—112no—
269C2×#125—222no—
270C2×#121—21no—
271C2×#121—22no—
272C2×C4×Q8—111no—
273C2×C4×Q8—112no—
274C2×C4×Q8—221no—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4C2×D1112yes—
277C2×C4×D4C2×D1111yescharacteristic
278#490—1116no—
279#486—118no—
280#478—1116no—
281#474—118no—
282#460—1116no—
283#460—118no—
284#446—118no—
285#440—1116no—
286C4×SD16—118no—
287C2×#107—112no—
288C2×#106—111no—
289C2×C4⋊C8—112no—
290C2×C4⋊C8—111no—
291C2×#103—111no—
292C2×#102—112no—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—111no—
296C2×#102—112no—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—88no—
306C22×C11—84no—
307C22×C11#54812yes—
308C22×C11C2×AGL(1,ℤ/8)12yes—
309C22×C11#57712yes—
310C22×C11C23×D411yescharacteristic
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11#54812yes—
316C4×C11C2×AGL(1,ℤ/8)14yes—
317C4×C11C22×#4111yescharacteristic
318C4×C11C2×2−1+411yescharacteristic
319Dic11—24no—
320Dic11—44no—
321Dic11—42no—
322C2×#41—28no—
323C2×#41—48no—
324C22×Q8—111no—
325C22×Q8—221no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—21no—
331C22×D4C22×D1112yes—
332C22×D4C22×D1111yescharacteristic
333C23×C4—22no—
334C23×C4—21no—
335C2×SD16—114no—
336C2×SD16—118no—
337C2×SD16—224no—
338C2×SD16—228no—
339C22×C8—111no—
340C22×C8—112no—
341C22×C8—111no—
342C4⋊Q8—114no—
343C4⋊Q8—228no—
344C4⋊Q8—222no—
345#127—24no—
346#127—22no—
347#127C22×D1114yes—
348#127C22×D1118yes—
349#125—118no—
350#125—2216no—
351#125—224no—
352#121—28no—
353#121—216no—
354C4×Q8—114no—
355C4×Q8—118no—
356C4×Q8—228no—
357C4×Q8—224no—
358C4×Q8—222no—
359C4×Q8C22⋊D1114yes—
360C4×Q8C22×D1114yes—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4C22×D1114yes—
364C4×D4C22×D1118yes—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1112yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C42—222no—
378C2×C42—221no—
379C2×C42C22×D1112yes—
380C2×C42C22×D1111yescharacteristic
381#107—118no—
382#106—114no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#102—114no—
387#102—118no—
388#102—118no—
389#102—118no—
390#102—118no—
391#97—118no—
392C4×C8—114no—
393C2×C11—84no—
394C2×C11—82no—
395C2×C11#336814yescomplemented
396C2×C11C2×#54811yescharacteristic
397C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C11C2×#57711yescharacteristic
399C24—22no—
400C24—21no—
401#41—432no—
402C2×Q8—24no—
403C2×Q8—114no—
404C2×Q8—112no—
405C2×Q8—222no—
406C2×Q8—221no—
407C2×Q8—224no—
408C2×Q8—444no—
409C2×Q8C2×C22⋊D1114yes—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—28no—
417C2×D4—24no—
418C2×D4—28no—
419C2×D4—24no—
420C2×D4—48no—
421C2×D4—44no—
422C2×D4—84no—
423C2×D4—82no—
424C2×D4C23×D1112yes—
425C2×D4C23×D1114yes—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—48no—
430C22×C4—44no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—228no—
440SD16—2216no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—114no—
444C2×C8—222no—
445C2×C8—224no—
446C2×C8—222no—
447C4⋊C4—21no—
448C4⋊C4—112no—
449C4⋊C4—114no—
450C4⋊C4—221no—
451C4⋊C4—222no—
452C4⋊C4—224no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4C2×C22⋊D1114yes—
458C4⋊C4C2×C22⋊D1118yes—
459C4⋊C4C23×D1112yes—
460C22⋊C4—28no—
461C22⋊C4—24no—
462C42—228no—
463C42—224no—
464C42C2×C22⋊D1114yes—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C42C23×D1114yes—
468C11C2×#336811yescharacteristic, complemented, Sylow
469C23—24no—
470C23—22no—
471C23—44no—
472C23—42no—
473C23—44no—
474C23—42no—
475C23—44no—
476C23—42no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—28no—
479Q8—114no—
480Q8—224no—
481Q8—222no—
482Q8—448no—
483D4—22no—
484D4—24no—
485D4—22no—
486D4—24no—
487D4—416no—
488D4—48no—
489D4—42no—
490D4—44no—
491D4—88no—
492D4—84no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—416no—
498C2×C4—42no—
499C2×C4—48no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—444no—
505C2×C4—442no—
506C2×C4#6698514yes—
507C2×C4#41×D1112yes—
508C2×C4#6704312yes—
509C2×C4C22×C22⋊D1114yes—
510C2×C4C22×C22⋊D1112yes—
511C2×C4C22×C22⋊D1114yes—
512C2×C4C22×C22⋊D1112yes—
513C2×C4C22×C22⋊D1111yescharacteristic
514C2×C4C24×D1111yescharacteristic
515C8—222no—
516C8—224no—
517C8—222no—
518C22—44no—
519C22—42no—
520C22—44no—
521C22—42no—
522C22—44no—
523C22—42no—
524C22—88no—
525C22—84no—
526C22C2×#6698512yes—
527C22#1062336212yes—
528C22#1062336712yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—24no—
531C4—24no—
532C4—22no—
533C4—42no—
534C4—224no—
535C4—444no—
536C4—442no—
537C4C2×#6698514yes—
538C4#1062336212yes—
539C4C2×#41×D1111yescharacteristic
540C4C2×#6704311yescharacteristic
541C2—84no—
542C2—82no—
543C2#1308134114yesdirect product factor
544C2C2×#1062336211yescharacteristic
545C2C22×#6698511yescharacteristic
546C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
2. #13081341C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622683C2semidirect
5. C2×#10622622C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622688C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622631C2semidirect
11. C2×C4×#4324C2semidirect
27. #10623098C22semidirect
39. #10622688C22semidirect
40. #10622688C22semidirect
41. #10622684C22semidirect
42. #10622683C22semidirect
43. #10622637C22semidirect
44. #10622631C22semidirect
45. C4×#4324C22semidirect
46. #10622622C22semidirect
47. #10622620C22semidirect
165. C2×Dic22#41semidirect
253. Dic22C2×#41semidirect
395. C2×C11#3368semidirect
468. C11C2×#3368semidirect
543. C2#13081341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
#130813412
C2×#106226842
C2×#106226832
C2×#106226222
C2×#106226202
C2×#106226882
C2×#106226372
C2×#106226312
C2×C4×#43242
C2×C11×#5502
C2×#336811