Finite Group Databasebeta

← C2×#13070051 #14782600

Subgroups — C2×#13070051 #14782600

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66881C211yesmaximal, characteristic, complemented
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5#13070051C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×C11⋊#95—21no—
19C2×C11⋊#95—21no—
20C2×(C2×D11)⋊C8—24no—
21C2×(C2×D11)⋊C8C2214yes—
22C2×#66881—24no—
23C2×#66881C2214yescomplemented
24#10622600—22no—
25#10622600—22no—
26#10622600C2214yes—
27#10622600C2214yes—
28C11×#340C2214yescomplemented
29#10622167C2214yescomplemented
30#10622167C2214yescomplemented
31C24×D11D411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C23×Dic11—21no—
37C23×Dic11D411yescharacteristic
38C22×C4×D11—22no—
39C22×C4×D11—22no—
40C22×C4×D11—22no—
41C22×C4×D11—22no—
42C22×C4×D11—22no—
43C22×C4×D11—22no—
44C22×C4×D11D412yes—
45C22×C4×D11C2312yes—
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11D414yes—
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—44no—
61C2×(C2×D11)⋊C4—44no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70C22×C11⋊C8—22no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8C2312yes—
74C11⋊#95—24no—
75C11⋊#95—24no—
76(C2×D11)⋊C8—28no—
77#66881—28no—
78C2×#2077—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11—22no—
81C23×D11—22no—
82C23×D11—22no—
83C23×D11—22no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11SD1614yes—
87C23×D11C2×D412yes—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11#4112yes—
99C22×C4×C11#4112yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×C4×C11#4112yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—42no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11—42no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11C2×D412yes—
116C2×C4×D11—24no—
117C2×C4×D11—24no—
118C2×C4×D11—24no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C8×C11—28no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C2×D414yes—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139(C2×D11)⋊C4—48no—
140(C2×D11)⋊C4—48no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—44no—
151C22×#106—111no—
152C22×C22⋊C8—111no—
153C2×#380—111no—
154C2×#380—111no—
155#2077—118no—
156C2×#340—111no—
157C2×#340—111no—
158C2×#340D1111yescharacteristic, complemented
159C23×C11#12112yes—
160C23×C11#12312yes—
161C23×C11#12312yes—
162C23×C11C2×SD1612yes—
163C23×C11#13512yes—
164C23×C11AGL(1,ℤ/8)12yes—
165C23×C11#13712yes—
166C23×C11C22×D411yescharacteristic
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—28no—
174C22×D11—28no—
175C22×D11—28no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—44no—
179C22×D11—44no—
180C22×D11C2×SD1614yes—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—84no—
188C2×C4×C11—84no—
189C2×C4×C11#12112yes—
190C2×C4×C11#12312yes—
191C2×C4×C11#12312yes—
192C2×C4×C11#12314yes—
193C2×C4×C11#12414yes—
194C2×C4×C11#12614yes—
195C2×C4×C11#12614yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—44no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—84no—
213C2×Dic11—84no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—48no—
219C8×C11—24no—
220C11⋊C8—42no—
221C24×C4—111no—
222C23×C8—111no—
223C23×C8C2×D1111yescharacteristic
224C22×C4⋊C4—111no—
225C22×C4⋊C4—111no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C22⋊C4—221no—
229C22×C22⋊C4—221no—
230C2×#106—114no—
231C2×#106—224no—
232C2×C22⋊C8—114no—
233C2×C22⋊C8—224no—
234#380—114no—
235#380—114no—
236#380—222no—
237#380—222no—
238C2×#95—221no—
239C2×#95—221no—
240#340—114no—
241#340—114no—
242#340C2×D1114yescomplemented
243C22×C11#39714yes—
244C22×C11#46514yes—
245C22×C11#46814yes—
246C22×C11#48114yes—
247C22×C11#48214yes—
248C22×C11#48314yes—
249C22×C11#48514yes—
250C22×C11C2×#12111yescharacteristic
251C22×C11C2×#12311yescharacteristic
252C22×C11C2×#12311yescharacteristic
253C22×C11C22×SD1611yescharacteristic
254C22×C11C2×#13511yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C11C2×#13711yescharacteristic
257C2×D11—24no—
258C2×D11—24no—
259C2×D11—24no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—416no—
263C2×D11—42no—
264C2×D11—42no—
265C4×C11—82no—
266C4×C11—82no—
267C4×C11#39714yes—
268C4×C11C2×#12311yescharacteristic
269C4×C11C2×#12411yescharacteristic
270C4×C11C2×#12611yescharacteristic
271C4×C11C2×#12611yescharacteristic
272Dic11—42no—
273Dic11—82no—
274Dic11—82no—
275C25—111no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—111no—
279C23×C4—112no—
280C23×C4—112no—
281C23×C4—222no—
282C23×C4—222no—
283C23×C4—222no—
284C23×C4—222no—
285C23×C4—222no—
286C23×C4—222no—
287C23×C4—221no—
288C23×C4—221no—
289C23×C4C22×D1111yescharacteristic
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—112no—
293C22×C8—222no—
294C22×C8—222no—
295C22×C8—222no—
296C22×C8D4414yes—
297C22×C8C22×D1112yes—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—224no—
315C2×C22⋊C4—224no—
316C2×C22⋊C4—444no—
317C2×C22⋊C4—444no—
318#106—228no—
319C22⋊C8—228no—
320#95—224no—
321#95—224no—
322C2×C11#207718yescomplemented
323C2×C11C2×#39711yescharacteristic
324C2×C11C2×#46511yescharacteristic
325C2×C11C2×#46811yescharacteristic
326C2×C11C2×#48311yescharacteristic
327C2×C11C2×#48211yescharacteristic
328C2×C11C2×#48511yescharacteristic
329C2×C11C2×#48111yescharacteristic
330D11—44no—
331C24—114no—
332C24—112no—
333C24—222no—
334C24—222no—
335C24—222no—
336C24—222no—
337C24—222no—
338C24—222no—
339C24D4×D1111yescharacteristic
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—112no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—224no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—444no—
364C22×C4—444no—
365C22×C4—444no—
366C22×C4—444no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—442no—
373C22×C4C2×D4412yes—
374C22×C4#433912yes—
375C22×C4#433912yes—
376C22×C4D4×D1111yescharacteristic
377C22×C4#434112yes—
378C22×C4#434112yes—
379C22×C4#434312yes—
380C22×C4C23×D1111yescharacteristic
381C2×C8—28no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—444no—
388C2×C8C2×D4414yes—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—442no—
400C4⋊C4—442no—
401C22⋊C4—448no—
402C22⋊C4—448no—
403C11C2×#207711yescharacteristic, complemented, Sylow
404C23—114no—
405C23—228no—
406C23—222no—
407C23—222no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23—222no—
412C23—228no—
413C23—228no—
414C23—444no—
415C23—444no—
416C23—444no—
417C23—444no—
418C23#6693612yes—
419C23#6693612yes—
420C23#6694812yes—
421C23#6696412yes—
422C23SD16×D1112yes—
423C23#6696912yes—
424C23#6697112yes—
425C23C2×D4×D1111yescharacteristic
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—84no—
433C2×C4—84no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—444no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—448no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—884no—
450C2×C4—884no—
451C2×C4#6692814yes—
452C2×C4#6693612yes—
453C2×C4#6693612yes—
454C2×C4#6693914yes—
455C2×C4#6694812yes—
456C2×C4#6695114yes—
457C2×C4#6695114yes—
458C2×C4C22×D4411yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C2×#433911yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C2×#434311yescharacteristic
464C8—24no—
465C8—442no—
466C22—224no—
467C22—224no—
468C22—224no—
469C22—442no—
470C22—442no—
471C22—4416no—
472C22—442no—
473C22—442no—
474C22#1062228714yes—
475C22#1062239014yes—
476C22#1062239214yes—
477C22#1062241814yes—
478C22#1062242814yes—
479C22#1062247714yes—
480C22#1062249914yes—
481C22C2×#6693611yescharacteristic
482C22C2×#6693611yescharacteristic
483C22C2×#6694811yescharacteristic
484C22C2×#6696411yescharacteristic
485C22C2×SD16×D1111yescharacteristic
486C22C2×#6696911yescharacteristic
487C22C2×#6697111yescharacteristic
488C4—82no—
489C4—82no—
490C4—442no—
491C4—882no—
492C4—882no—
493C4#1062228714yes—
494C4C2×#6692811yescharacteristic
495C4C2×#6693911yescharacteristic
496C4C2×#6695111yescharacteristic
497C4C2×#6695111yescharacteristic
498C2—444no—
499C2#1307005118yesdirect product factor
500C2C2×#1062228711yescharacteristic
501C2C2×#1062247711yescharacteristic
502C2C2×#1062249911yescharacteristic
503C2C2×#1062241811yescharacteristic
504C2C2×#1062239211yescharacteristic
505C2C2×#1062242811yescharacteristic
506C2C2×#1062239011yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC24×D11D4
hypercenterC2×#340D11
hypocenterC11C2×#2077
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#66881C2semidirect
5. #13070051C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622167C2semidirect
8. C2×C11×#340C2semidirect
23. C2×#66881C22semidirect
28. C11×#340C22semidirect
29. #10622167C22semidirect
30. #10622167C22semidirect
158. C2×#340D11semidirect
242. #340C2×D11semidirect
322. C2×C11#2077semidirect
403. C11C2×#2077semidirect
499. C2#13070051direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668812
C22×(C2×D11)⋊C82
C2×#106226002
#130700512
C2×#106221672
C2×C11×#3402
C2×#207711