Finite Group Databasebeta

← C2×#13081673 #15634769

Subgroups — C2×#13081673 #15634769

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
2C2×#10623252C211yesmaximal, characteristic, complemented
3#13081673C2116yesmaximal, direct product factor
4C2×#10622803C212yesmaximal, complemented
5C2×#10622698C211yesmaximal, characteristic
6C2×#10622798C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic
8C2×#10622431C212yesmaximal, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×C4×#4326C211yesmaximal, characteristic, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C2×Q8×Dic11C2212yes—
18C2×#66997C2212yes—
19C22×#4326C2211yescharacteristic
20C22×#4325C2212yes—
21C22×#4325C2212yes—
22C22×#4314C2212yes—
23#10623252—24no—
24#10623252C2218yescomplemented
25#10623116—24no—
26#10623116C2218yes—
27C2×#66947—22no—
28C2×#66946C2212yes—
29C2×#66943—21no—
30C2×#66942—22no—
31C2×#66940—21no—
32C2×#66928—21no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44—21no—
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#462C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66899C2211yescharacteristic
41#10622803C22116yescomplemented
42#10622798C22116yescomplemented
43C2×#66885C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622698C2218yes—
47C4×#4326C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622461C2218yes—
52#10622444C2218yescomplemented
53#10622431C22116yescomplemented
54#10622430C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2311yescharacteristic
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×C4×D11—22no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2311yescharacteristic
63C2×C11×Q16—44no—
64C2×C11×Q16C2318yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#67000—24no—
77#67000C2318yes—
78Q8×Dic11—24no—
79Q8×Dic11C2318yes—
80#66997—24no—
81#66997C2318yes—
82C2×#4326—24no—
83C2×#4326C2314yes—
84C2×#4325—28no—
85C2×#4325—44no—
86C2×#4325C2318yes—
87C2×#4325C2318yes—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D412yes—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11C2312yes—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×#4314—44no—
104C2×#4314C2318yes—
105#66947—216no—
106#66946—24no—
107#66946C2318yes—
108#66943—28no—
109#66942—216no—
110#66940—28no—
111#66928—28no—
112#66927—22no—
113#66927C2314yes—
114C4×D44—28no—
115C4×Dic22—22no—
116C4×Dic22D414yes—
117C4×Dic22C2314yes—
118C4×Dic22C2314yes—
119C11×C4⋊C8C2314yes—
120C11×#103C2318yes—
121#66899C2314yes—
122#66885C2318yes—
123#66879C2318yes—
124Dic11⋊C8C2318yes—
125#66874C2314yes—
126#66871C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3400—111nomaximal, Sylow
129C23×D11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—21no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—22no—
136C2×Q8×C11C2412yes—
137C2×Q8×C11C2414yes—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×D44—24no—
149C2×D44—22no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—44no—
154C2×D44—82no—
155C2×D44C2414yes—
156C2×C4×D11—28no—
157C2×C4×D11—84no—
158C2×Dic22—24no—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22C2×D414yes—
163C2×Dic22C2412yes—
164C11×Q16—48no—
165C2×C8×C11—24no—
166C2×C8×C11C2414yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4C2412yes—
172C42×C11—24no—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175#4326—28no—
176#4325—216no—
177#4325—48no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—28no—
182C4⋊Dic11—21no—
183C4⋊Dic11C2×D414yes—
184C4⋊Dic11C2412yes—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4—24no—
188Dic11⋊C4C2×D418yes—
189C4×Dic11—28no—
190C4×Dic11—24no—
191C4×Dic11C2×D414yes—
192C4×Dic11C2414yes—
193C2×C11⋊C8—22no—
194C2×C11⋊C8#4114yes—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2412yes—
197#4314—48no—
198C2×#559—111no—
199C2×#557—111no—
200#3400—1116no—
201C2×#497—112no—
202C2×#492—111no—
203C2×#464—112no—
204C2×#462D1111yescharacteristic, complemented
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—24no—
216Q8×C11—22no—
217Q8×C11—24no—
218Q8×C11—22no—
219Q8×C11—44no—
220Q8×C11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11#13714yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C11H(5,𝔽2)12yes—
234C2×C4×C11C2511yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11C22×D414yes—
242C2×Dic11C22×D414yes—
243D44—24no—
244D44—24no—
245D44—44no—
246D44—48no—
247D44—84no—
248C4×D11—88no—
249Dic22—28no—
250Dic22—22no—
251Dic22—22no—
252Dic22—42no—
253C8×C11—24no—
254C11⋊C8—22no—
255C11⋊C8C2×#4114yes—
256C22×Q16—111no—
257C22×Q16C2×D1112yes—
258C22×SD16—112no—
259C22×SD16—112no—
260C22×SD16—112no—
261#559—118no—
262#559—224no—
263#557—118no—
264#557—224no—
265C2×C4⋊Q8—112no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#127—111no—
268C2×#125—222no—
269C2×#125—221no—
270C2×#124—112no—
271C2×#124—221no—
272C2×#123—222no—
273C2×C4×Q8—111no—
274C2×C4×Q8—112no—
275C2×C4×Q8—111no—
276C2×C4×Q8—221no—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—112no—
279C2×C4×D4—221no—
280#497—1116no—
281#492—118no—
282#464—1116no—
283#462C2×D1118yescomplemented
284#461—1116no—
285#460—118no—
286#446—118no—
287#440—1116no—
288C4×Q16—118no—
289C2×#107—111no—
290C2×C4⋊C8—112no—
291C2×C4⋊C8C2×D1111yescharacteristic
292C2×#103—111no—
293C2×#103—111no—
294C2×#103C2×D1112yes—
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—22no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11#55012yes—
311C4×C11C2×#13714yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×H(5,𝔽2)11yescharacteristic
314Dic11—24no—
315Dic11—24no—
316Dic11—42no—
317Dic11—42no—
318C22×Q8—111no—
319C22×Q8—111no—
320C22×Q8C22×D1112yes—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—112no—
323C22×D4—221no—
324C22×D4—221no—
325C23×C4—222no—
326C2×Q16—44no—
327C2×Q16—114no—
328C2×Q16—224no—
329C2×Q16C22×D1118yes—
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×C8C22×D1112yes—
339C4⋊Q8—22no—
340C4⋊Q8—118no—
341C4⋊Q8—224no—
342C4⋊Q8C22×D1114yes—
343#127—114no—
344#127—222no—
345#125—2216no—
346#125—228no—
347#124—118no—
348#124—228no—
349#124—224no—
350#123—2216no—
351C4×Q8—22no—
352C4×Q8—114no—
353C4×Q8—114no—
354C4×Q8—118no—
355C4×Q8—114no—
356C4×Q8—224no—
357C4×Q8—228no—
358C4×Q8—222no—
359C4×Q8C22×D1114yes—
360C4×D4—118no—
361C4×D4—228no—
362C4×D4—224no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—21no—
378C2×C42—112no—
379C2×C42—222no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—114no—
383C4⋊C8—118no—
384C4⋊C8C22×D1114yes—
385#103—114no—
386#103—114no—
387#103C22×D1118yes—
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—21no—
398C2×Q8—22no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—24no—
402C2×Q8—22no—
403C2×Q8—114no—
404C2×Q8—112no—
405C2×Q8—224no—
406C2×Q8—221no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8C23×D1112yes—
410C2×Q8C23×D1114yes—
411C2×D4—114no—
412C2×D4—224no—
413C2×D4—222no—
414C2×D4—224no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—444no—
418C2×D4—882no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—228no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—884no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431Q16—48no—
432Q16—228no—
433SD16—2216no—
434SD16—448no—
435SD16—448no—
436C2×C8—24no—
437C2×C8—114no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—222no—
441C2×C8C23×D1114yes—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—114no—
447C4⋊C4—118no—
448C4⋊C4—112no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—221no—
453C4⋊C4—224no—
454C4⋊C4C23×D1112yes—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C22⋊C4—228no—
458C42—24no—
459C42—114no—
460C42—114no—
461C42—228no—
462C42—224no—
463C42D4×D1112yes—
464C42C23×D1112yes—
465C11C2×#340011yescharacteristic, complemented, Sylow
466C23—224no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23C2×D4×D1111yescharacteristic
471Q8—24no—
472Q8—22no—
473Q8—24no—
474Q8—22no—
475Q8—42no—
476Q8—44no—
477Q8—228no—
478Q8—222no—
479Q8—222no—
480Q8—442no—
481D4—224no—
482D4—224no—
483D4—448no—
484D4—444no—
485D4—884no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—114no—
494C2×C4—114no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—888no—
502C2×C4#6697114yes—
503C2×C4C2×D4×D1112yes—
504C2×C4C2×D4×D1112yes—
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4#6703712yes—
507C2×C4#41×D1112yes—
508C2×C4C24×D1111yescharacteristic
509C8—24no—
510C8—114no—
511C8—222no—
512C22—444no—
513C22—444no—
514C22—444no—
515C22—888no—
516C22#1062313012yes—
517C22C2×#6697112yes—
518C22#1062330912yes—
519C22C22×D4×D1111yescharacteristic
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—224no—
525C4—224no—
526C4—442no—
527C4—442no—
528C4#1062313012yes—
529C4C2×#6697114yes—
530C4C2×#6703711yescharacteristic
531C4C2×#41×D1111yescharacteristic
532C2—884no—
533C2#1308167314yesdirect product factor
534C2C2×#1062313011yescharacteristic
535C2C22×#6697111yescharacteristic
536C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#462D11
hypocenterC11C2×#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#10623252C2semidirect
3. #13081673C2direct (N × H)
4. C2×#10622803C2semidirect
6. C2×#10622798C2semidirect
8. C2×#10622431C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622430C2semidirect
11. C2×C4×#4326C2semidirect
12. C2×C11×#462C2semidirect
24. #10623252C22semidirect
37. C11×#462C22semidirect
41. #10622803C22semidirect
42. #10622798C22semidirect
47. C4×#4326C22semidirect
52. #10622444C22semidirect
53. #10622431C22semidirect
54. #10622430C22semidirect
204. C2×#462D11semidirect
283. #462C2×D11semidirect
391. C2×C11#3400semidirect
465. C11C2×#3400semidirect
533. C2#13081673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106232522
#130816732
C2×#106228032
C2×#106226982
C2×#106227982
C2×#106224612
C2×#106224312
C2×#106224442
C2×#106224302
C2×C4×#43262
C2×C11×#4622
C2×#340011