Finite Group Databasebeta

← C4×#10622801 #14760274

Subgroups — C4×#10622801 #14760274

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622801C211yesmaximal, characteristic
2C2×C4×C8×D11C211yesmaximal, characteristic
3C4×#66999C212yesmaximal
4#13069478C211yesmaximal, characteristic, complemented
5#13069347C211yesmaximal, characteristic, complemented
6#13069289C212yesmaximal, complemented
7#13069036C212yesmaximal
8#13068642C211yesmaximal, characteristic
9C4×#66882C211yesmaximal, characteristic, complemented
10C4×#66899C212yesmaximal, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×#66999C2212yes—
15C22×C8×D11C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C4×C11×Q16—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622843C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25#10622801C418yesdirect product factor
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622602—22no—
31#10622600C2212yes—
32#10622591—22no—
33#10622586C2212yes—
34C4×(C2×D11)⋊C4—22no—
35C4×C4⋊Dic11C2212yes—
36C4×Dic11⋊C4—22no—
37C2×C4×C11⋊C8C2211yescharacteristic
38C4×C8×D11—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16C2×C414yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—24no—
52C4×Q8×C11—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—22no—
56C2×C42×C11C2311yescharacteristic
57#66999—24no—
58#66999C2×C418yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×C8×D11—22no—
72C2×C8×D11—22no—
73C2×C8×D11—22no—
74C2×C8×D11—22no—
75C2×C8×D11—22no—
76C2×C8×D11C2×C414yes—
77C42×D11—22no—
78C42×D11—22no—
79C11×#107—22no—
80C11×#103—24no—
81C4×C8×C11D414yes—
82#66899—24no—
83#66899C2×C418yescomplemented
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—22no—
90#66882C2×C414yescomplemented
91C8×Dic11—22no—
92C8×Dic11—22no—
93C4×C11⋊C8—22no—
94C4×#467—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11Q1614yescomplemented
122C2×C4×D11C22×C412yes—
123C2×C4×D11#4112yes—
124C11×Q16—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—44no—
134C42×C11—44no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—28no—
138(C2×D11)⋊C4—44no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11C22×C414yes—
143Dic11⋊C4—28no—
144Dic11⋊C4—44no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—44no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8#4112yes—
156C8×D11—28no—
157C8×D11—28no—
158C2×#467—111no—
159C2×C4×Q16D1111yescharacteristic, complemented
160C22×C4×C8—111no—
161C4×C22⋊Q8—112no—
162#1969—111no—
163#1942—111no—
164#1933—112no—
165#1892—112no—
166#1808—111no—
167C4×#107—111no—
168C4×#103—112no—
169C23×C11C22×D411yescharacteristic
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11C4×D412yes—
175C22×D11C2×Q1612yes—
176C22×D11#13512yes—
177Q8×C11—24no—
178Q8×C11—24no—
179Q8×C11—42no—
180Q8×C11—42no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11C2×Q1612yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—24no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11C4×D412yes—
212C2×Dic11C2×Q1612yes—
213C2×Dic11#13512yes—
214C4×D11—28no—
215C4×D11—22no—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—28no—
220C8×C11—22no—
221C8×C11C4×D414yes—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C22×Q16C2×D1111yescharacteristic
225C23×C8—111no—
226C23×C8—111no—
227C2×C22⋊Q8—112no—
228C2×C4×Q8C2×D1112yes—
229C22×C42—111no—
230#467—118no—
231C4×Q16—24no—
232C2×#107—111no—
233C2×#107—111no—
234C2×#107C2×D1111yescharacteristic
235C2×#103—112no—
236C2×#103—112no—
237C2×#103C2×D1112yes—
238C2×C4×C8—111no—
239C2×C4×C8—111no—
240C2×C4×C8—111no—
241C2×C4×C8—224no—
242C2×C4×C8C2×D1111yescharacteristic
243#391—112no—
244#389—112no—
245#387—222no—
246#385—222no—
247#380—112no—
248C4×C4⋊C4—112no—
249C4×C4⋊C4—222no—
250C4×C22⋊C4—222no—
251#340—112no—
252#340—112no—
253#340—112no—
254C22×C11C2×C4×D411yescharacteristic
255C22×C11C2×#12111yescharacteristic
256C22×C11#53211yescharacteristic
257C22×C11C22×Q1611yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×#13511yescharacteristic
261C2×D11—22no—
262C2×D11—22no—
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11C4×Q1614yescomplemented
268C4×C11—22no—
269C4×C11—44no—
270C4×C11—82no—
271C4×C11#46714yescomplemented
272C4×C11C2×C4×D411yescharacteristic
273C4×C11C4×#4111yescharacteristic
274C4×C11#52511yescharacteristic
275C4×C11#52911yescharacteristic
276Dic11—22no—
277Dic11—22no—
278Dic11—22no—
279Dic11—44no—
280Dic11—82no—
281C22×Q8C22×D1112yes—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—111no—
285C2×Q16—22no—
286C2×Q16—22no—
287C2×Q16C4×D1114yescomplemented
288C22×C8—111no—
289C22×C8—111no—
290C22×C8—114no—
291C22×C8—222no—
292C22×C8—222no—
293C22×C8—222no—
294C22×C8—222no—
295C22×C8—222no—
296C22×C8C22×D1111yescharacteristic
297C22×C8C22×D1111yescharacteristic
298C22⋊Q8—118no—
299C22⋊Q8—224no—
300C4×Q8—24no—
301C4×Q8—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4C22×D1112yes—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—22no—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—222no—
315C2×C42—222no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318#107—22no—
319#107—114no—
320#107—222no—
321#103—24no—
322#103—118no—
323#103—224no—
324C4×C8—222no—
325C4×C8—222no—
326C4×C8—222no—
327C4×C8C22⋊D1114yes—
328#95—222no—
329#95—222no—
330#95—222no—
331#95—222no—
332#95—222no—
333C2×C11C4×#12111yescharacteristic
334C2×C11C2×C4×Q1611yescharacteristic
335C2×C11C4×#13511yescharacteristic
336C2×C11C2×#46711yescharacteristic
337C2×C11#305011yescharacteristic
338C2×C11#316811yescharacteristic
339C2×C11#317011yescharacteristic
340D11—24no—
341C24—111no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8C2×C4×D1114yes—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—114no—
354C22×C4—112no—
355C22×C4—112no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370Q16—28no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—112no—
374C2×C8—112no—
375C2×C8—228no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—228no—
381C2×C8C2×C4×D1112yes—
382C2×C8#433912yes—
383C2×C8C2×C22⋊D1112yes—
384C2×C8C2×C22⋊D1112yes—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—44no—
388C4⋊C4—114no—
389C4⋊C4—228no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—444no—
394C22⋊C4—228no—
395C22⋊C4—444no—
396C42—44no—
397C42—222no—
398C42—222no—
399C42—221no—
400C42—221no—
401C42—444no—
402C42#434112yes—
403C42C2×C22⋊D1112yes—
404C11C4×#46711yescharacteristic, complemented, Sylow
405C23—112no—
406C23—112no—
407C23—112no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23C2×D4×D1111yescharacteristic
413Q8—24no—
414Q8—24no—
415Q8—42no—
416Q8—42no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—228no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—228no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—224no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4Q16×D1112yes—
447C2×C4#6697212yes—
448C2×C4#6699112yes—
449C2×C4#6699112yes—
450C2×C4C22×C4×D1111yescharacteristic
451C2×C4C2×#433911yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#41×D1111yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—22no—
457C8—222no—
458C8—222no—
459C8C4×C22⋊D1114yes—
460C22—114no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22C4×D4×D1111yescharacteristic
468C22#1062307911yescharacteristic
469C22C2×Q16×D1111yescharacteristic
470C22C2×#6697211yescharacteristic
471C22D11×#13511yescharacteristic
472C22D11×#13511yescharacteristic
473C22C2×#6699111yescharacteristic
474C4—22no—
475C4—44no—
476C4—82no—
477C4—222no—
478C4—222no—
479C4—222no—
480C4—444no—
481C4—882no—
482C4#1062280114yesdirect product factor
483C4C4×#434111yescharacteristic
484C4#1062308811yescharacteristic
485C4C2×C4×C22⋊D1111yescharacteristic
486C4#1062335911yescharacteristic
487C2—224no—
488C2C4×#6699111yescharacteristic
489C2C4×Q16×D1111yescharacteristic
490C2C4×#6697211yescharacteristic
491C2C2×#1062280111yescharacteristic
492C2#1307819311yescharacteristic
493C2#1307918911yescharacteristic
494C2#1307919911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11C4×#467
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #13069478C2semidirect
5. #13069347C2semidirect
6. #13069289C2semidirect
9. C4×#66882C2semidirect
10. C4×#66899C2semidirect
11. C2×C4×C11×Q16C2semidirect
25. #10622801C4direct (N × H)
48. C2×C11×Q16C2×C4semidirect
83. #66899C2×C4semidirect
90. #66882C2×C4semidirect
121. C2×C4×D11Q16semidirect
159. C2×C4×Q16D11semidirect
267. C2×D11C4×Q16semidirect
271. C4×C11#467semidirect
287. C2×Q16C4×D11semidirect
404. C11C4×#467semidirect
482. C4#10622801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228012
C2×C4×C8×D112
C4×#669992
#130694782
#130693472
#130692892
#130690362
#130686422
C4×#668822
C4×#668992
C2×C4×C11×Q162
C4×#46711