Finite Group Databasebeta

← C2×#13081482 #15634202

Subgroups — C2×#13081482 #15634202

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623074C211yesmaximal, characteristic, complemented
3#13081482C2116yesmaximal, direct product factor
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622471C212yesmaximal, complemented
6C2×#10622376C212yesmaximal, complemented
7C2×#10622484C212yesmaximal, complemented
8C2×#10622455C211yesmaximal, characteristic, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4323C211yesmaximal, characteristic
11C2×#10622369C212yesmaximal
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999—22no—
16C2×D4×Dic11C2212yes—
17C22×#4323C2211yescharacteristic
18C22×C4⋊Dic11—21no—
19C2×#66977—21no—
20#10623261—24no—
21#10623261C2218yescomplemented
22#10623074—24no—
23#10623074C2218yescomplemented
24C2×#66950—21no—
25C2×#66946C2212yes—
26C2×C4⋊C4×D11—21no—
27C2×#66943C2212yes—
28C2×#66943C2212yes—
29C2×#66931—22no—
30C2×C4×D44C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#476C2218yescomplemented
34C2×C11×#106C2212yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66885C2212yes—
39C2×#66881C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622691C2218yescomplemented
43C4×#4323C2218yes—
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2212yes—
47C2×#66871C2212yes—
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622484C22116yescomplemented
50#10622471C22116yescomplemented
51#10622455C2218yescomplemented
52#10622443C2218yescomplemented
53#10622376C22116yescomplemented
54#10622369C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22—21no—
63C22×Dic22D411yescharacteristic
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C4×D4×C11—22no—
68C4×D4×C11C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75#66999—216no—
76D4×Dic11—24no—
77D4×Dic11C2318yes—
78C2×#4323Q818yescomplemented
79C2×#4323C2314yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—28no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—28no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4D412yes—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66950—28no—
97#66946—24no—
98#66946C2318yes—
99C4⋊C4×D11—28no—
100#66943—24no—
101#66943—24no—
102#66943C2318yes—
103#66943C2318yes—
104#66931—216no—
105C4×D44—22no—
106C4×D44C2314yes—
107#66922—22no—
108#66922C2314yes—
109C4×Dic22D414yes—
110C4×Dic22C2314yes—
111C11×#106C2318yes—
112C11×C4⋊C8C2314yes—
113C11×#102C2318yes—
114#66896C2314yes—
115#66885C2318yes—
116#66881C2318yes—
117Dic11⋊C8C2318yes—
118C8×Dic11C2318yes—
119#66873C2314yes—
120#66871C2314yes—
121#66871C2318yes—
122#66871C2318yes—
123C4×C11⋊C8C2314yes—
124C2×#3380—111nomaximal, Sylow
125C24×C11—21no—
126C23×D11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—82no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11C2×Q814yes—
132C2×D4×C11C2412yes—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—44no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—28no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—84no—
144C22×Dic11C2×D412yes—
145C22×Dic11C2×D412yes—
146C2×D44—21no—
147C2×D44—22no—
148C2×D44C2×Q814yes—
149C2×D44C2412yes—
150C2×C4×D11—28no—
151C2×C4×D11—24no—
152C2×C4×D11—44no—
153C2×C4×D11—84no—
154C2×Dic22—24no—
155C2×Dic22—24no—
156C2×Dic22—82no—
157C2×Dic22C2×D414yes—
158C2×C8×C11—24no—
159C2×C8×C11C2414yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4C2414yes—
164C11×C4⋊C4C2412yes—
165C11×C22⋊C4—24no—
166C42×C11C2×D412yes—
167C42×C11C2412yes—
168C22⋊Dic11—28no—
169#4323C2×Q8116yescomplemented
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—24no—
172C4⋊Dic11—28no—
173C4⋊Dic11—28no—
174C4⋊Dic11—22no—
175C4⋊Dic11—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×D414yes—
178C4⋊Dic11C2414yes—
179C4⋊Dic11C2412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4C2×D418yes—
183C4×Dic11C2×D414yes—
184C4×Dic11C2414yes—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2×Q814yes—
187C2×C11⋊C8C2412yes—
188C2×C11⋊C8C2412yes—
189C2×#554—111no—
190C2×#554—111no—
191#3380—1116no—
192C2×#500—111no—
193C2×#499—112no—
194C2×#478—112no—
195C2×#478—112no—
196C2×#476—111no—
197C2×#476D1111yescharacteristic, complemented
198C2×C8×Q8—111no—
199C2×C4×D8—112no—
200C2×C4×D8—111no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206C22×D11—24no—
207C22×D11—22no—
208C22×D11—42no—
209C22×D11—42no—
210Q8×C11—84no—
211D4×C11—24no—
212D4×C11—22no—
213D4×C11C22×Q814yes—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—48no—
220C2×C4×C11#13514yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×Q812yes—
225C2×C4×C112−1+412yes—
226C2×C4×C11C2511yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—42no—
232C2×Dic11—44no—
233C2×Dic11—88no—
234C2×Dic11C22×D414yes—
235C2×Dic11C22×D414yes—
236D44—24no—
237D44—22no—
238D44C22×Q814yes—
239C4×D11—48no—
240C4×D11—88no—
241Dic22—28no—
242Dic22—84no—
243C8×C11—24no—
244C11⋊C8—22no—
245C11⋊C8C22×Q814yes—
246C22×D8—111no—
247#554—118no—
248#554—118no—
249#554—224no—
250#554—224no—
251C2×C4⋊Q8—111no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#125—112no—
254C2×#125—112no—
255C2×C22⋊Q8—222no—
256C2×C22⋊Q8—221no—
257C2×C22⋊Q8—222no—
258C2×C22⋊Q8—221no—
259C2×C4×Q8—111no—
260C2×C4×D4—112no—
261C2×C4×D4—112no—
262C2×C4×D4—111no—
263C2×C4×D4C2×D1111yescharacteristic
264C22×C4⋊C4—221no—
265C22×C4⋊C4—221no—
266#500—118no—
267#499—1116no—
268#478—1116no—
269#478—1116no—
270#476—118no—
271#476C2×D1118yescomplemented
272C8×Q8—118no—
273C4×D8—118no—
274C4×D8—1116no—
275C2×#107—112no—
276C2×#107—111no—
277C2×#107—112no—
278C2×#106—112no—
279C2×#106C2×D1112yes—
280C2×C4⋊C8—112no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—112no—
284C2×#102—111no—
285C2×#102C2×D1112yes—
286C2×C4×C8—112no—
287C2×C4×C8—111no—
288C22×C11—24no—
289C22×C11—48no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11D4×Q812yes—
293C22×C11C2×#13512yes—
294C22×C11#57612yes—
295C22×C11C23×D411yescharacteristic
296C2×D11—24no—
297C2×D11—48no—
298C2×D11—42no—
299C2×D11—42no—
300C4×C11—22no—
301C4×C11—42no—
302C4×C11—44no—
303C4×C11D4×Q812yes—
304C4×C11C2×#13514yes—
305C4×C11C23×Q811yescharacteristic
306C4×C11C2×2−1+411yescharacteristic
307Dic11—24no—
308Dic11—24no—
309Dic11—42no—
310Dic11—44no—
311C22×Q8—21no—
312C22×Q8—111no—
313C22×Q8—221no—
314C22×D4—111no—
315C22×D4C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—222no—
318C23×C4—222no—
319C23×C4—221no—
320C2×D8—118no—
321C2×D8—114no—
322C22×C8—111no—
323C22×C8—111no—
324C22×C8C22×D1112yes—
325C4⋊Q8—22no—
326C4⋊Q8—114no—
327C4⋊Q8—222no—
328C4⋊Q8C22×D1114yes—
329#125—118no—
330#125—118no—
331#125—224no—
332#125—224no—
333C22⋊Q8—2216no—
334C22⋊Q8—228no—
335C22⋊Q8—2216no—
336C22⋊Q8—228no—
337C4×Q8—114no—
338C4×Q8—114no—
339C4×D4—22no—
340C4×D4—118no—
341C4×D4—118no—
342C4×D4—114no—
343C4×D4—224no—
344C4×D4—224no—
345C4×D4—222no—
346C4×D4C22×D1114yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1112yes—
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—221no—
365C2×C42—112no—
366C2×C42C22×D1111yescharacteristic
367#107—114no—
368#107—118no—
369#107—118no—
370#106—118no—
371#106C22×D1118yes—
372C4⋊C8—118no—
373C4⋊C8C22×D1114yes—
374#102—114no—
375#102—118no—
376#102—114no—
377#102C22×D1118yes—
378C4×C8—118no—
379C4×C8—114no—
380C2×C11—44no—
381C2×C11#338014yescomplemented
382C2×C11C2×D4×Q811yescharacteristic
383C2×C11C22×#13511yescharacteristic
384C2×C11C2×#57611yescharacteristic
385D11—44no—
386C24—21no—
387C24—221no—
388C2×Q8—24no—
389C2×Q8—82no—
390C2×Q8—114no—
391C2×Q8—224no—
392C2×Q8—224no—
393C2×Q8—882no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—114no—
397C2×D4—112no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4Q8×D1114yes—
401C2×D4C23×D1112yes—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—44no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—228no—
409C22×C4—228no—
410C22×C4—221no—
411C22×C4—222no—
412C22×C4—224no—
413C22×C4—444no—
414C22×C4—884no—
415C22×C4—884no—
416C22×C4D4×D1111yescharacteristic
417C22×C4D4×D1111yescharacteristic
418C22×C4C23×D1111yescharacteristic
419D8—1116no—
420C2×C8—24no—
421C2×C8—114no—
422C2×C8—112no—
423C2×C8—112no—
424C2×C8—222no—
425C2×C8C23×D1114yes—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—114no—
430C4⋊C4—118no—
431C4⋊C4—112no—
432C4⋊C4—114no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—221no—
438C4⋊C4—222no—
439C4⋊C4—224no—
440C4⋊C4C23×D1112yes—
441C4⋊C4C23×D1114yes—
442C22⋊C4—24no—
443C22⋊C4—228no—
444C22⋊C4—228no—
445C22⋊C4—224no—
446C42—114no—
447C42—114no—
448C42D4×D1112yes—
449C42C23×D1112yes—
450C11C2×#338011yescharacteristic, complemented, Sylow
451C23—24no—
452C23—22no—
453C23—42no—
454C23—42no—
455C23—224no—
456C23—222no—
457C23—442no—
458C23—442no—
459C23C2×D4×D1111yescharacteristic
460Q8—84no—
461Q8—228no—
462Q8—884no—
463D4—24no—
464D4—22no—
465D4—114no—
466D4—224no—
467D4—222no—
468D4C2×Q8×D1114yes—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—48no—
475C2×C4—114no—
476C2×C4—114no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—442no—
482C2×C4—444no—
483C2×C4—448no—
484C2×C4—888no—
485C2×C4—888no—
486C2×C4#6696914yes—
487C2×C4C2×D4×D1112yes—
488C2×C4C2×D4×D1112yes—
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4C2×Q8×D1112yes—
491C2×C4#6704312yes—
492C2×C4C24×D1111yescharacteristic
493C8—24no—
494C8—114no—
495C8—222no—
496C22—24no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—224no—
501C22—448no—
502C22—442no—
503C22—442no—
504C22#1062316312yes—
505C22C2×#6696912yes—
506C22#1062330512yes—
507C22C22×D4×D1111yescharacteristic
508C4—22no—
509C4—42no—
510C4—44no—
511C4—224no—
512C4—224no—
513C4—442no—
514C4—444no—
515C4#1062316312yes—
516C4C2×#6696914yes—
517C4C22×Q8×D1111yescharacteristic
518C4C2×#6704311yescharacteristic
519C2—44no—
520C2—444no—
521C2#1308148214yesdirect product factor
522C2C2×#1062316311yescharacteristic
523C2C22×#6696911yescharacteristic
524C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#476D11
hypocenterC11C2×#3380
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
2. C2×#10623074C2semidirect
3. #13081482C2direct (N × H)
4. C2×#10622691C2semidirect
5. C2×#10622471C2semidirect
6. C2×#10622376C2semidirect
7. C2×#10622484C2semidirect
8. C2×#10622455C2semidirect
9. C2×#10622443C2semidirect
12. C2×C11×#476C2semidirect
21. #10623261C22semidirect
23. #10623074C22semidirect
33. C11×#476C22semidirect
42. #10622691C22semidirect
49. #10622484C22semidirect
50. #10622471C22semidirect
51. #10622455C22semidirect
52. #10622443C22semidirect
53. #10622376C22semidirect
78. C2×#4323Q8semidirect
169. #4323C2×Q8semidirect
197. C2×#476D11semidirect
271. #476C2×D11semidirect
381. C2×C11#3380semidirect
450. C11C2×#3380semidirect
521. C2#13081482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106230742
#130814822
C2×#106226912
C2×#106224712
C2×#106223762
C2×#106224842
C2×#106224552
C2×#106224432
C2×C4×#43232
C2×#106223692
C2×C11×#4762
C2×#338011