Finite Group Databasebeta

← C2×#13067132 #14720889

Subgroups — C2×#13067132 #14720889

Order 2816.

1898 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×#10622820C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13067132C218yesmaximal, direct product factor
4C2×#10622175C214yesmaximal, complemented
5C22×C11×#121C211yesmaximal, characteristic
6C23×D4×C11—21no—
7C23×D4×C11C411yescharacteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#121—22no—
11C2×C11×#121—21no—
12C2×C11×#121—22no—
13C2×C11×#121C412yescomplemented
14C2×C11×#121C414yescomplemented
15C2×C11×#121C2212yes—
16C2×C11×#121C2214yes—
17C22×C11×C4⋊C4C411yescharacteristic, complemented
18C22×C11×C22⋊C4—21no—
19C22×C22⋊Dic11—21no—
20C22×C4×Dic11—21no—
21C22×#4318—21no—
22C4×C22⋊Dic11—22no—
23C4×C22⋊Dic11C2214yescomplemented
24C2×C11⋊#95C2212yescomplemented
25#10622820—22no—
26#10622820C2214yescomplemented
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)C2212yescomplemented
29#10622175C22116yescomplemented
30C25×C11—21no—
31C25×C11D411yescharacteristic
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11—44no—
39C22×D4×C11—48no—
40C22×D4×C11C2×C412yes—
41C22×D4×C11C2×C414yescomplemented
42C23×C4×C11—21no—
43C23×C4×C11—44no—
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2×C412yes—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D412yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D412yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×Dic11—22no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121—24no—
58C11×#121—22no—
59C11×#121—24no—
60C11×#121—22no—
61C11×#121—24no—
62C11×#121C2×C414yes—
63C11×#121C2×C418yescomplemented
64C11×#121C2314yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2×C412yes—
68C2×C11×C4⋊C4C2×C414yescomplemented
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—24no—
73C2×C22⋊Dic11—28no—
74C2×C22⋊Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—44no—
77C2×#4318—24no—
78C2×#4318—44no—
79C22×C11⋊C8—22no—
80C11⋊#95—22no—
81C11⋊#95C2314yescomplemented
82C22⋊(C11⋊C8)—24no—
83C22⋊(C11⋊C8)—22no—
84C22⋊(C11⋊C8)C2314yescomplemented
85C2×#1507—111nomaximal, Sylow
86C24×C11—24no—
87C24×C11—24no—
88C24×C11—22no—
89C24×C11—24no—
90C24×C11—42no—
91C24×C11—44no—
92C24×C11—44no—
93C24×C11—44no—
94C24×C11C22⋊C411yescharacteristic
95C24×C11C22⋊C412yes—
96C24×C11C22⋊C411yescharacteristic
97C24×C11C2×D412yes—
98C24×C11C2×D411yescharacteristic
99C2×D4×C11—24no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—24no—
104C2×D4×C11—48no—
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—416no—
108C2×D4×C11—416no—
109C2×D4×C11—48no—
110C2×D4×C11—48no—
111C2×D4×C11—44no—
112C2×D4×C11C22×C414yes—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—44no—
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C22⋊C412yes—
128C22×C4×C11C22⋊C412yes—
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22⋊C412yes—
131C22×C4×C11C22⋊C412yes—
132C22×C4×C11C22⋊C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—28no—
145C22×Dic11—24no—
146C22×Dic11—44no—
147C22×Dic11—44no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4C22×C414yes—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—24no—
154C22⋊Dic11—216no—
155C4×Dic11—48no—
156#4318—48no—
157C2×C11⋊C8—24no—
158C2×C11⋊C8—44no—
159C22×#121D1111yescharacteristic
160C2×#407—111no—
161C2×C4×C22⋊C4—111no—
162#1507—118no—
163C2×#327—114no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—416no—
179C23×C11—48no—
180C23×C11—48no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—48no—
184C23×C11—44no—
185C23×C11—816no—
186C23×C11#10414yes—
187C23×C11C2×C22⋊C412yes—
188C23×C11C2×C22⋊C411yescharacteristic
189C23×C11C2×C22⋊C412yes—
190C23×C11C2×C22⋊C411yescharacteristic
191C23×C11AGL(1,ℤ/8)14yes—
192C23×C11C22×D411yescharacteristic
193D4×C11—44no—
194D4×C11—44no—
195D4×C11—416no—
196D4×C11—48no—
197D4×C11—48no—
198D4×C11—48no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—48no—
218C2×C4×C11—44no—
219C2×C4×C11#9914yes—
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×Dic11—28no—
227C2×Dic11—44no—
228C2×Dic11—416no—
229C2×Dic11—44no—
230C11⋊C8—44no—
231C23×D4—21no—
232C23×D4Dic1111yescharacteristic, complemented
233C24×C4C2×D1111yescharacteristic
234C22×M16—221no—
235C2×#121—21no—
236C2×#121—22no—
237C2×#121—21no—
238C2×#121—22no—
239C2×#121Dic1112yescomplemented
240C2×#121Dic1114yescomplemented
241C2×#121C2×D1112yes—
242C2×#121C2×D1114yes—
243C22×C4⋊C4Dic1111yescharacteristic, complemented
244C22×C22⋊C4—21no—
245C22×C22⋊C4—221no—
246C22×C42—221no—
247#407—114no—
248#407—222no—
249C2×C22⋊C8—112no—
250C2×C22⋊C8—221no—
251C4×C22⋊C4—114no—
252C4×C22⋊C4—222no—
253C2×#95—112no—
254#327—1116no—
255C22×C11—22no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—22no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—28no—
262C22×C11—28no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—48no—
267C22×C11—48no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—816no—
273C22×C11—88no—
274C22×C11C2×#9912yes—
275C22×C11#41812yes—
276C22×C11#41812yes—
277C22×C11C2×#10414yes—
278C22×C11C2×#10412yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)12yes—
281C4×C11—21no—
282C4×C11—22no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—44no—
287C4×C11C2×#9914yes—
288Dic11—48no—
289C25—21no—
290C25C22⋊D1111yescharacteristic
291C22×D4—24no—
292C22×D4—22no—
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—44no—
298C22×D4—48no—
299C22×D4C2×Dic1112yes—
300C22×D4C2×Dic1114yescomplemented
301C23×C4—21no—
302C23×C4—44no—
303C23×C4—222no—
304C23×C4C2×Dic1111yescharacteristic
305C23×C4C2×Dic1112yes—
306C23×C4C2×Dic1111yescharacteristic
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22⋊D1111yescharacteristic
309C23×C4C22⋊D1112yes—
310C23×C4C22⋊D1111yescharacteristic
311C23×C4C22⋊D1112yes—
312C23×C4C22×D1111yescharacteristic
313C23×C4C22×D1112yes—
314C2×M16—224no—
315C2×M16—444no—
316C22×C8—222no—
317#121—24no—
318#121—24no—
319#121—24no—
320#121—22no—
321#121—24no—
322#121—22no—
323#121—24no—
324#121C2×Dic1114yes—
325#121C2×Dic1118yescomplemented
326#121C22×D1114yes—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4C2×Dic1112yes—
330C2×C4⋊C4C2×Dic1114yescomplemented
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—228no—
336C2×C22⋊C4—224no—
337C2×C42—224no—
338C2×C42—444no—
339C22⋊C8—114no—
340C22⋊C8—222no—
341C22⋊C8—224no—
342#95—114no—
343#95—222no—
344C2×C11—22no—
345C2×C11—24no—
346C2×C11—22no—
347C2×C11—42no—
348C2×C11—84no—
349C2×C11#150714yescomplemented
350C2×C11C22×#9911yescharacteristic
351C2×C11C2×#41811yescharacteristic
352C2×C11C22×#10411yescharacteristic
353C24—24no—
354C24—24no—
355C24—24no—
356C24—22no—
357C24—42no—
358C24—44no—
359C24—44no—
360C24—44no—
361C24C22⋊Dic1111yescharacteristic
362C24C22⋊Dic1112yes—
363C24C22⋊Dic1111yescharacteristic
364C24C2×C22⋊D1112yes—
365C24C2×C22⋊D1111yescharacteristic
366C2×D4—24no—
367C2×D4—28no—
368C2×D4—24no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—44no—
372C2×D4—48no—
373C2×D4—48no—
374C2×D4—416no—
375C2×D4—416no—
376C2×D4—48no—
377C2×D4—48no—
378C2×D4—44no—
379C2×D4C22×Dic1114yes—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—228no—
394C22×C4—224no—
395C22×C4—444no—
396C22×C4—444no—
397C22×C4C22⋊Dic1112yes—
398C22×C4C22⋊Dic1112yes—
399C22×C4C22⋊Dic1112yes—
400C22×C4C22⋊Dic1111yescharacteristic
401C22×C4C22⋊Dic1112yes—
402C22×C4C22⋊Dic1112yes—
403C22×C4C22⋊Dic1111yescharacteristic
404C22×C4C22×Dic1112yes—
405C22×C4C22×Dic1111yescharacteristic
406C22×C4C22×Dic1111yescharacteristic
407C22×C4C22×Dic1112yes—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1112yes—
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C23×D1111yescharacteristic
415M16—448no—
416C2×C8—224no—
417C2×C8—444no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4C22×Dic1114yes—
421C22⋊C4—24no—
422C22⋊C4—28no—
423C22⋊C4—24no—
424C22⋊C4—2216no—
425C42—448no—
426C11C2×#150711yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—24no—
432C23—24no—
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—416no—
442C23—48no—
443C23—48no—
444C23—44no—
445C23—44no—
446C23—48no—
447C23—44no—
448C23—816no—
449C23#6690114yes—
450C23#6698514yes—
451C23C2×C22⋊Dic1112yes—
452C23C2×C22⋊Dic1111yescharacteristic
453C23C2×C22⋊Dic1112yes—
454C23C2×C22⋊Dic1111yescharacteristic
455C23C22×C22⋊D1111yescharacteristic
456D4—44no—
457D4—44no—
458D4—416no—
459D4—48no—
460D4—48no—
461D4—48no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—44no—
482C2×C4—228no—
483C2×C4—444no—
484C2×C4—4416no—
485C2×C4—444no—
486C2×C4#6689814yes—
487C2×C4C2×C22⋊Dic1111yescharacteristic
488C2×C4C2×C22⋊Dic1112yes—
489C2×C4C2×C22⋊Dic1111yescharacteristic
490C2×C4C2×C22⋊Dic1112yes—
491C2×C4C23×Dic1111yescharacteristic
492C2×C4C22×C22⋊D1111yescharacteristic
493C8—444no—
494C22—21no—
495C22—22no—
496C22—21no—
497C22—28no—
498C22—28no—
499C22—22no—
500C22—21no—
501C22—21no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—48no—
506C22—48no—
507C22—44no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—816no—
512C22—88no—
513C22#1062282812yes—
514C22#1062282812yes—
515C22C2×#6689812yes—
516C22C2×#6690114yes—
517C22C2×#6690112yes—
518C22C2×#6698512yes—
519C22C22×C22⋊Dic1111yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—22no—
524C4—21no—
525C4—44no—
526C4—448no—
527C4C2×#6689814yes—
528C2—22no—
529C2—24no—
530C2—22no—
531C2—42no—
532C2—84no—
533C2#1306713214yesdirect product factor
534C2C22×#6689811yescharacteristic
535C2C2×#1062282811yescharacteristic
536C2C22×#6690111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C2×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#1507
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13067132C2direct (N × H)
4. C2×#10622175C2semidirect
7. C23×D4×C11C4semidirect
13. C2×C11×#121C4semidirect
14. C2×C11×#121C4semidirect
17. C22×C11×C4⋊C4C4semidirect
23. C4×C22⋊Dic11C22semidirect
24. C2×C11⋊#95C22semidirect
26. #10622820C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622175C22semidirect
41. C22×D4×C11C2×C4semidirect
63. C11×#121C2×C4semidirect
68. C2×C11×C4⋊C4C2×C4semidirect
81. C11⋊#95C23semidirect
84. C22⋊(C11⋊C8)C23semidirect
232. C23×D4Dic11semidirect
239. C2×#121Dic11semidirect
240. C2×#121Dic11semidirect
243. C22×C4⋊C4Dic11semidirect
300. C22×D4C2×Dic11semidirect
325. #121C2×Dic11semidirect
330. C2×C4⋊C4C2×Dic11semidirect
349. C2×C11#1507semidirect
426. C11C2×#1507semidirect
533. C2#13067132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228202
C2×C4×C22⋊Dic112
#130671322
C2×#106221752
C22×C11×#1212
C2×#150711