Finite Group Databasebeta

← D11×C4⋊#95 #14674875

Subgroups — D11×C4⋊#95 #14674875

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C212yesmaximal
2C22×C42×D11C211yesmaximal, characteristic
3C2×D11×#95C214yesmaximal
4#13066846C211yesmaximal, characteristic, complemented
5#13066845C212yesmaximal, complemented
6Dic11⋊#95C214yesmaximal, complemented
7C11×C4⋊#95C211yesmaximal, characteristic, complemented
8C23×C4×D11C2214yes—
9C23×C4×D11C2212yes—
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C22×Dic11⋊C4C2214yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C2×C4⋊C4×D11—28no—
18C2×C4⋊C4×D11—28no—
19C2×C4⋊C4×D11C4116yescomplemented
20C2×C42×D11—28no—
21C2×C42×D11C418yescomplemented
22C2×C11×#95C2214yes—
23C2×C11⋊#95C2218yes—
24C2×C11⋊#95C2214yes—
25D11×#95—216no—
26C24×D11C2311yescharacteristic
27C23×C4×C11C2314yes—
28C23×C4×C11C2312yes—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11C2314yes—
31C23×Dic11C2312yes—
32C23×Dic11C2311yescharacteristic
33C22×C4×D11—28no—
34C22×C4×D11—28no—
35C22×C4×D11—28no—
36C22×C4×D11—28no—
37C22×C4×D11—216no—
38C22×C4×D11—216no—
39C22×C4×D11C2×C4116yes—
40C22×C4×D11C2×C418yes—
41C22×C4×D11C2×C414yes—
42C22×C4×D11C2×C418yes—
43C22×C4×D11D418yes—
44C22×C4×D11D418yes—
45C22×C4×D11D414yes—
46C22×C4×D11Q818yes—
47C22×C4×D11Q814yes—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4C2×C418yescomplemented
51C2×C42×C11—24no—
52C2×C42×C11C2×C414yescomplemented
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—24no—
55C2×C4⋊Dic11C2×C418yescomplemented
56C2×Dic11⋊C4—28no—
57C2×Dic11⋊C4—28no—
58C2×Dic11⋊C4C2×C4116yescomplemented
59C2×C4×Dic11—24no—
60C2×C4×Dic11—28no—
61C2×C4×Dic11C2×C418yescomplemented
62C2×C4×Dic11C2×C414yescomplemented
63C4⋊C4×D11—264no—
64C42×D11—232no—
65C11×#95—28no—
66C11⋊#95—28no—
67C11⋊#95—216no—
68C2×C4⋊#95—111nomaximal, Sylow
69C24×C11C2411yescharacteristic
70C23×D11C22×C412yes—
71C23×D11C22×C414yes—
72C23×D11C2×D414yes—
73C23×D11C2×D412yes—
74C23×D11C2×D414yes—
75C23×D11C2×Q812yes—
76C23×D11C2×Q814yes—
77C23×D11#4118yes—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—28no—
84C22×C4×C11C22×C418yes—
85C22×C4×C11C22×C414yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C414yes—
88C22×C4×C11C2×D414yes—
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11C2×Q812yes—
93C22×Dic11—24no—
94C22×Dic11—28no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—28no—
99C22×Dic11C22×C418yes—
100C22×Dic11C22×C414yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C414yes—
103C22×Dic11C2×D414yes—
104C22×Dic11C2×D414yes—
105C22×Dic11C2×D412yes—
106C22×Dic11C2×Q814yes—
107C22×Dic11C2×Q812yes—
108C2×C4×D11—216no—
109C2×C4×D11—232no—
110C2×C4×D11—216no—
111C2×C4×D11—264no—
112C2×C4×D11—232no—
113C2×C4×D11—232no—
114C2×C4×D11—432no—
115C2×C4×D11—416no—
116C2×C4×D11—416no—
117C2×C4×D11C42116yes—
118C2×C4×D11C22⋊C4116yes—
119C2×C4×D11C22⋊C4132yes—
120C2×C4×D11C4⋊C4116yes—
121C2×C4×D11C4⋊C4132yes—
122C2×C4×D11C4⋊C4132yescomplemented
123C11×C4⋊C4—216no—
124C42×C11—28no—
125C4⋊Dic11—216no—
126Dic11⋊C4—232no—
127C4×Dic11—216no—
128C4×Dic11—28no—
129C23×C4⋊C4—112no—
130C23×C42—111no—
131C22×#95—114no—
132C4⋊#95—111no—
133C4⋊#95—114no—
134C4⋊#95—112no—
135C4⋊#95D1111yescharacteristic, direct product factor
136C23×C11C23×C411yescharacteristic
137C23×C11C23×C412yes—
138C23×C11C22×D412yes—
139C23×C11C22×D411yescharacteristic
140C23×C11C22×D412yes—
141C23×C11C22×Q811yescharacteristic
142C23×C11C22×Q812yes—
143C23×C11C2×#4114yes—
144C22×D11C2×C4214yes—
145C22×D11C2×C22⋊C414yes—
146C22×D11C2×C22⋊C418yes—
147C22×D11C2×C4⋊C414yes—
148C22×D11C2×C4⋊C418yes—
149C22×D11C2×C4⋊C418yes—
150C22×D11#11718yes—
151C22×D11C4×D4116yes—
152C22×D11C4×Q8116yes—
153C22×D11#121116yes—
154C22×D11C22⋊Q8116yes—
155C22×D11#12418yes—
156C22×D11#12518yes—
157C22×D11#12714yes—
158C22×D11C4⋊Q818yes—
159C22×D11C4⋊Q814yes—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—28no—
163C2×C4×C11—28no—
164C2×C4×C11—28no—
165C2×C4×C11—216no—
166C2×C4×C11—48no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11C2×C4214yes—
170C2×C4×C11C2×C22⋊C414yes—
171C2×C4×C11C2×C22⋊C418yes—
172C2×C4×C11C2×C4⋊C414yes—
173C2×C4×C11C2×C4⋊C418yes—
174C2×C4×C11C2×C4⋊C418yescomplemented
175C2×Dic11—24no—
176C2×Dic11—24no—
177C2×Dic11—28no—
178C2×Dic11—28no—
179C2×Dic11—28no—
180C2×Dic11—216no—
181C2×Dic11—48no—
182C2×Dic11—44no—
183C2×Dic11—44no—
184C2×Dic11C2×C4214yes—
185C2×Dic11C2×C22⋊C414yes—
186C2×Dic11C2×C22⋊C418yes—
187C2×Dic11C2×C4⋊C414yes—
188C2×Dic11C2×C4⋊C418yes—
189C2×Dic11C2×C4⋊C418yescomplemented
190C4×D11—264no—
191C4×D11—464no—
192C4×D11#95164yescomplemented
193C24×C4—111no—
194C24×C4—112no—
195C24×C4—114no—
196C22×C4⋊C4—114no—
197C22×C4⋊C4—112no—
198C22×C4⋊C4—1116no—
199C22×C4⋊C4—228no—
200C22×C4⋊C4—228no—
201C22×C4⋊C4C2×D1112yes—
202C22×C42—112no—
203C22×C42—111no—
204C22×C42—118no—
205C22×C42—228no—
206C22×C42C2×D1111yescharacteristic
207C2×#95—118no—
208C2×#95—114no—
209C2×#95—2216no—
210C2×#95C2×D1114yes—
211C22×C11C22×C4211yescharacteristic
212C22×C11C22×C22⋊C411yescharacteristic
213C22×C11C22×C22⋊C412yes—
214C22×C11C22×C4⋊C411yescharacteristic
215C22×C11C22×C4⋊C412yes—
216C22×C11C22×C4⋊C412yes—
217C22×C11C2×#11712yes—
218C22×C11C2×C4×D414yes—
219C22×C11C2×C4×Q814yes—
220C22×C11C2×#12114yes—
221C22×C11C2×C22⋊Q814yes—
222C22×C11C2×#12412yes—
223C22×C11C2×#12512yes—
224C22×C11C2×#12711yescharacteristic
225C22×C11C2×C4⋊Q812yes—
226C22×C11C2×C4⋊Q811yescharacteristic
227C2×D11C2×#9518yes—
228C2×D11C4×C4⋊C4116yes—
229C2×D11#380116yes—
230C2×D11#38218yes—
231C2×D11#38418yes—
232C2×D11#389132yes—
233C2×D11#390116yes—
234C2×D11#391116yes—
235C4×C11—28no—
236C4×C11—48no—
237C4×C11C2×#9518yescomplemented
238Dic11—28no—
239Dic11—48no—
240Dic11C2×#9518yescomplemented
241C25—111no—
242C23×C4—111no—
243C23×C4—118no—
244C23×C4—114no—
245C23×C4—114no—
246C23×C4—118no—
247C23×C4—114no—
248C23×C4—112no—
249C23×C4—118no—
250C23×C4—118no—
251C23×C4—118no—
252C23×C4—114no—
253C23×C4—1116no—
254C23×C4—228no—
255C23×C4—228no—
256C23×C4—228no—
257C23×C4—228no—
258C23×C4—2216no—
259C23×C4—2216no—
260C23×C4C22×D1114yes—
261C23×C4C22×D1112yes—
262C23×C4C22×D1111yescharacteristic
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—1116no—
266C2×C4⋊C4—118no—
267C2×C4⋊C4—2264no—
268C2×C4⋊C4—228no—
269C2×C4⋊C4—228no—
270C2×C4⋊C4—224no—
271C2×C4⋊C4—224no—
272C2×C4⋊C4C4×D1118yescomplemented
273C2×C42—24no—
274C2×C42—118no—
275C2×C42—114no—
276C2×C42—2232no—
277C2×C42—228no—
278C2×C42—224no—
279C2×C42C4×D1114yescomplemented
280#95—28no—
281#95—2216no—
282#95—228no—
283C2×C11C22×#9511yescharacteristic
284C2×C11C2×C4×C4⋊C412yes—
285C2×C11C2×#38012yes—
286C2×C11C2×#38211yescharacteristic
287C2×C11C2×#38411yescharacteristic
288C2×C11C2×#38914yes—
289C2×C11C2×#39012yes—
290C2×C11C2×#39112yes—
291D11C4⋊#95116yesdirect product factor
292C24—112no—
293C24—114no—
294C24—112no—
295C24—114no—
296C24—114no—
297C24—112no—
298C24—114no—
299C24—118no—
300C24C23×D1111yescharacteristic
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—28no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—28no—
307C22×C4—112no—
308C22×C4—114no—
309C22×C4—114no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—1116no—
313C22×C4—1116no—
314C22×C4—1132no—
315C22×C4—1132no—
316C22×C4—1116no—
317C22×C4—114no—
318C22×C4—114no—
319C22×C4—114no—
320C22×C4—1132no—
321C22×C4—118no—
322C22×C4—2216no—
323C22×C4—2216no—
324C22×C4—2232no—
325C22×C4—2232no—
326C22×C4—2232no—
327C22×C4—2264no—
328C22×C4—224no—
329C22×C4—224no—
330C22×C4—228no—
331C22×C4—224no—
332C22×C4—224no—
333C22×C4—228no—
334C22×C4—4416no—
335C22×C4—4432no—
336C22×C4—4416no—
337C22×C4C2×C4×D1118yes—
338C22×C4C2×C4×D1114yes—
339C22×C4C2×C4×D1112yes—
340C22×C4C2×C4×D1114yes—
341C22×C4D4×D1114yes—
342C22×C4D4×D1114yes—
343C22×C4D4×D1112yes—
344C22×C4Q8×D1114yes—
345C22×C4Q8×D1112yes—
346C4⋊C4—216no—
347C4⋊C4—2232no—
348C4⋊C4—2216no—
349C42—28no—
350C42—2216no—
351C42—228no—
352C11C2×C4⋊#9511yescharacteristic, complemented, Sylow
353C23—114no—
354C23—118no—
355C23—114no—
356C23—114no—
357C23—114no—
358C23—118no—
359C23—114no—
360C23—118no—
361C23—118no—
362C23—118no—
363C23—1116no—
364C23—1116no—
365C23—1116no—
366C23—1116no—
367C23—118no—
368C23—118no—
369C23C22×C4×D1111yescharacteristic
370C23C22×C4×D1112yes—
371C23C2×D4×D1111yescharacteristic
372C23C2×D4×D1112yes—
373C23C2×D4×D1112yes—
374C23C2×Q8×D1111yescharacteristic
375C23C2×Q8×D1112yes—
376C23#41×D1114yes—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—28no—
380C2×C4—28no—
381C2×C4—28no—
382C2×C4—216no—
383C2×C4—44no—
384C2×C4—48no—
385C2×C4—44no—
386C2×C4—114no—
387C2×C4—114no—
388C2×C4—118no—
389C2×C4—114no—
390C2×C4—118no—
391C2×C4—1164no—
392C2×C4—118no—
393C2×C4—2264no—
394C2×C4—224no—
395C2×C4—224no—
396C2×C4—228no—
397C2×C4—228no—
398C2×C4—228no—
399C2×C4—2216no—
400C2×C4—4464no—
401C2×C4—444no—
402C2×C4—448no—
403C2×C4—444no—
404C2×C4C42×D1114yes—
405C2×C4C22⋊C4×D1114yes—
406C2×C4C22⋊C4×D1118yes—
407C2×C4C4⋊C4×D1114yes—
408C2×C4C4⋊C4×D1118yes—
409C2×C4C4⋊C4×D1118yescomplemented
410C22—118no—
411C22—1116no—
412C22—1116no—
413C22—118no—
414C22—118no—
415C22—1132no—
416C22—1116no—
417C22—1116no—
418C22C2×C42×D1111yescharacteristic
419C22C2×C22⋊C4×D1111yescharacteristic
420C22C2×C22⋊C4×D1112yes—
421C22C2×C4⋊C4×D1111yescharacteristic
422C22C2×C4⋊C4×D1112yes—
423C22C2×C4⋊C4×D1112yes—
424C22D11×#11712yes—
425C22C4×D4×D1114yes—
426C22C4×Q8×D1114yes—
427C22D11×#12114yes—
428C22D11×C22⋊Q814yes—
429C22D11×#12412yes—
430C22D11×#12512yes—
431C22D11×#12711yescharacteristic
432C22D11×C4⋊Q812yes—
433C22D11×C4⋊Q811yescharacteristic
434C4—28no—
435C4—48no—
436C4—118no—
437C4—228no—
438C4—448no—
439C4D11×#9518yescomplemented
440C2—1116no—
441C2C2×D11×#9511yescharacteristic
442C2C4×C4⋊C4×D1112yes—
443C2D11×#38012yes—
444C2D11×#38211yescharacteristic
445C2D11×#38411yescharacteristic
446C2D11×#38914yes—
447C2D11×#39012yes—
448C2D11×#39112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11C2×C4⋊#95
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066846C2semidirect
5. #13066845C2semidirect
6. Dic11⋊#95C2semidirect
7. C11×C4⋊#95C2semidirect
19. C2×C4⋊C4×D11C4semidirect
21. C2×C42×D11C4semidirect
50. C2×C11×C4⋊C4C2×C4semidirect
52. C2×C42×C11C2×C4semidirect
55. C2×C4⋊Dic11C2×C4semidirect
58. C2×Dic11⋊C4C2×C4semidirect
61. C2×C4×Dic11C2×C4semidirect
62. C2×C4×Dic11C2×C4semidirect
122. C2×C4×D11C4⋊C4semidirect
135. C4⋊#95D11direct (N × H)
174. C2×C4×C11C2×C4⋊C4semidirect
189. C2×Dic11C2×C4⋊C4semidirect
192. C4×D11#95semidirect
237. C4×C11C2×#95semidirect
240. Dic11C2×#95semidirect
272. C2×C4⋊C4C4×D11semidirect
279. C2×C42C4×D11semidirect
291. D11C4⋊#95direct (N × H)
352. C11C2×C4⋊#95semidirect
409. C2×C4C4⋊C4×D11semidirect
439. C4D11×#95semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C22×C42×D112
C2×D11×#952
#130668462
#130668452
Dic11⋊#952
C11×C4⋊#952
C2×C4⋊#9511