Finite Group Databasebeta

← C2×#13079801 #15625873

Subgroups — C2×#13079801 #15625873

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic, complemented
3#13079801C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622315C211yesmaximal, characteristic, complemented
6C2×#10622684C211yesmaximal, characteristic, complemented
7C2×#10622390C212yesmaximal, complemented
8C2×#10622387C212yesmaximal, complemented
9C2×#10622376C212yesmaximal, complemented
10C2×#10622379C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#490C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×#66991—21no—
17C2×#66991C2212yes—
18C2×#66989—21no—
19C2×D4×Dic11—21no—
20C2×D4×Dic11C2212yes—
21#10623247—24no—
22#10623247C2218yes—
23D11×#125—24no—
24D11×#125C2218yescomplemented
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66943C2211yescharacteristic
30C2×#66943C2211yescharacteristic
31C2×#66942—21no—
32C2×#66942—21no—
33C2×C42×D11C2211yescharacteristic
34C2×#66923C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#490C2218yescomplemented
37C2×C11×#102C2212yes—
38C2×C11×#102C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66881C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622684C2218yescomplemented
47#10622678C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622390C22116yescomplemented
52#10622387C22116yescomplemented
53#10622379C22116yescomplemented
54#10622376C22116yescomplemented
55#10622318C2218yescomplemented
56#10622315C2218yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C22×C22⋊D11—22no—
61C23×Dic11—22no—
62C2×#4341—28no—
63C2×#4341—48no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×Dic22—21no—
70C22×C8×C11C2312yes—
71C11×#127—22no—
72C11×#127C2314yes—
73C11×#125—22no—
74C11×#125C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82#66991—24no—
83#66991—28no—
84#66991C2318yes—
85#66989—28no—
86D4×Dic11—24no—
87D4×Dic11—28no—
88D4×Dic11C2318yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2312yes—
105C4⋊C4×D11—28no—
106C4⋊C4×D11—28no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11C2314yes—
110C4⋊C4×D11C2314yes—
111#66943—22no—
112#66943—22no—
113#66943C2314yes—
114#66943C2314yes—
115#66942—28no—
116#66942—28no—
117C42×D11D414yes—
118C42×D11C2314yes—
119#66923—22no—
120#66923C2314yes—
121#66922—22no—
122#66922C2314yes—
123C11×#102C2318yes—
124C11×#102C2318yes—
125C11×#97C2314yes—
126#66896C2318yes—
127#66896C2318yes—
128(C2×D11)⋊C8C2318yes—
129#66882C2318yes—
130#66881C2318yes—
131Dic11⋊C8C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66867C2314yes—
135C2×#3234—111nomaximal, Sylow
136C24×C11—22no—
137C23×D11C2×D411yescharacteristic
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—28no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11C2414yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—28no—
151C2×C22⋊D11—48no—
152C22×Dic11—28no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—48no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160#4341—432no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11C2×D412yes—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2412yes—
172C2×Dic22—24no—
173C2×Dic22—44no—
174C2×C8×C11—24no—
175C2×C8×C11C2414yes—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2412yes—
181C11×C4⋊C4C2412yes—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—28no—
185C22⋊Dic11—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11—22no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2414yes—
193C4⋊Dic11C2412yes—
194C4⋊Dic11C2412yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201C4×Dic11C2×D412yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2×D414yes—
204C4×Dic11C2412yes—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2414yes—
207C2×#532—111no—
208C22×#125—111no—
209#3234—1116no—
210C2×#501—111no—
211C2×#501—111no—
212C2×#490—111no—
213C2×#490D1111yescharacteristic, complemented
214C2×#481—112no—
215C2×#480—112no—
216C2×#478—112no—
217C2×#478—112no—
218C2×#432—111no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11AGL(1,ℤ/8)14yes—
227C22×D11C22×D412yes—
228D4×C11—28no—
229D4×C11—48no—
230D4×C11—48no—
231D4×C11—44no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C112−1+414yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—416no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—416no—
251C2×Dic11—44no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11C22×D412yes—
255C2×Dic11C22×D412yes—
256C2×Dic11C22×D412yes—
257C4×D11—28no—
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—44no—
261C4×D11—48no—
262C4×D11—48no—
263Dic22—48no—
264C8×C11—24no—
265C11⋊C8—24no—
266C22×#41—221no—
267#532—118no—
268#532—224no—
269C2×C4⋊Q8—111no—
270C2×#127C2×D1111yescharacteristic
271C2×#125—118no—
272C2×#125—111no—
273C2×#125—111no—
274C2×#125—111no—
275C2×#125—221no—
276C2×#125—221no—
277C2×#125—224no—
278C2×#125C2×D1111yescharacteristic
279C2×#124—221no—
280C2×#121—112no—
281C2×#121—221no—
282C2×C4×D4—112no—
283C2×C4×D4—221no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—221no—
287C22×C4⋊C4—221no—
288C22×C42—111no—
289#501—118no—
290#501—118no—
291#490—118no—
292#490C2×D1118yescomplemented
293#481—1116no—
294#480—1116no—
295#478—1116no—
296#478—1116no—
297#432—118no—
298C2×#107—112no—
299C2×#107—112no—
300C2×#106—112no—
301C2×#106—112no—
302C2×C4⋊C8—112no—
303C2×#102—112no—
304C2×#102—112no—
305C2×#102C2×D1112yes—
306C2×#102C2×D1112yes—
307C2×C22⋊C8—112no—
308C2×#97—111no—
309C2×#97C2×D1111yescharacteristic
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—88no—
314C22×C11#53612yes—
315C22×C11C2×AGL(1,ℤ/8)12yes—
316C22×C11#57512yes—
317C22×C11C23×D411yescharacteristic
318C2×D11—22no—
319C2×D11—28no—
320C2×D11—22no—
321C2×D11C2×AGL(1,ℤ/8)14yes—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11#53612yes—
327C4×C11C2×2−1+412yes—
328Dic11—22no—
329Dic11—22no—
330Dic11—22no—
331Dic11—44no—
332Dic11—42no—
333Dic11—42no—
334C2×#41—228no—
335C2×#41—448no—
336C22×Q8—221no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—222no—
340C22×D4C22×D1112yes—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—221no—
345C23×C4—221no—
346C23×C4—222no—
347C22×C8—112no—
348C22×C8C22×D1112yes—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351#127—22no—
352#127C22×D1114yes—
353#125—22no—
354#125—114no—
355#125—114no—
356#125—114no—
357#125—228no—
358#125—228no—
359#125—222no—
360#125—222no—
361#125—222no—
362#125C22×D1114yes—
363#124—228no—
364#121—118no—
365#121—224no—
366#121—228no—
367C4×D4—118no—
368C4×D4—224no—
369C4×D4—228no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—114no—
398C2×C42—114no—
399C2×C42C22×D1111yescharacteristic
400#107—118no—
401#107—118no—
402#106—118no—
403#106—118no—
404C4⋊C8—118no—
405#102—118no—
406#102—118no—
407#102C22×D1118yes—
408#102C22×D1118yes—
409C22⋊C8—118no—
410#97—114no—
411#97C22×D1114yes—
412C2×C11—84no—
413C2×C11#323414yescomplemented
414C2×C11C2×#53611yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C11C2×#57511yescharacteristic
417D11—24no—
418C24—22no—
419C24—111no—
420#41—4432no—
421C2×Q8—224no—
422C2×Q8—444no—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—228no—
430C2×D4—448no—
431C2×D4C23×D1114yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—228no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—442no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4—448no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—24no—
457C2×C8—114no—
458C2×C8—224no—
459C2×C8C23×D1114yes—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—114no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4—224no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—222no—
476C4⋊C4—224no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4C23×D1112yes—
480C4⋊C4C23×D1112yes—
481C22⋊C4—228no—
482C22⋊C4—228no—
483C42—114no—
484C42—112no—
485C42—114no—
486C42—112no—
487C42D4×D1112yes—
488C42C23×D1112yes—
489C11C2×#323411yescharacteristic, complemented, Sylow
490C23—24no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—114no—
495C23—112no—
496C23—222no—
497C23—222no—
498C23C2×D4×D1111yescharacteristic
499Q8—448no—
500D4—28no—
501D4—48no—
502D4—48no—
503D4—44no—
504D4—4416no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—112no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—228no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—444no—
524C2×C4—448no—
525C2×C4—448no—
526C2×C4—4416no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4C2×D4×D1112yes—
531C2×C4C2×D4×D1112yes—
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4#6704314yes—
534C2×C4C24×D1111yescharacteristic
535C8—24no—
536C8—224no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—88no—
541C22—114no—
542C22—222no—
543C22—222no—
544C22—228no—
545C22#1062320612yes—
546C22D11×AGL(1,ℤ/8)12yes—
547C22#1062330412yes—
548C22C22×D4×D1111yescharacteristic
549C4—22no—
550C4—22no—
551C4—42no—
552C4—42no—
553C4—222no—
554C4—222no—
555C4—222no—
556C4—444no—
557C4—442no—
558C4—442no—
559C4#1062320612yes—
560C4C2×#6704312yes—
561C2—84no—
562C2—224no—
563C2#1307980114yesdirect product factor
564C2C2×#1062320611yescharacteristic
565C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
566C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
prime radicalC2×#10623247C2
hypercenterC2×#490D11
hypocenterC11C2×#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. C2×D11×#125C2semidirect
3. #13079801C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622315C2semidirect
6. C2×#10622684C2semidirect
7. C2×#10622390C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622376C2semidirect
10. C2×#10622379C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#490C2semidirect
24. D11×#125C22semidirect
36. C11×#490C22semidirect
46. #10622684C22semidirect
47. #10622678C22semidirect
51. #10622390C22semidirect
52. #10622387C22semidirect
53. #10622379C22semidirect
54. #10622376C22semidirect
55. #10622318C22semidirect
56. #10622315C22semidirect
213. C2×#490D11semidirect
292. #490C2×D11semidirect
413. C2×C11#3234semidirect
489. C11C2×#3234semidirect
563. C2#13079801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×D11×#1252
#130798012
C2×#106226782
C2×#106223152
C2×#106226842
C2×#106223902
C2×#106223872
C2×#106223762
C2×#106223792
C2×#106223182
C2×C11×#4902
C2×#323411