Finite Group Databasebeta

← C11×#21402 #14598595

Subgroups — C11×#21402 #14598595

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C22×C4×C8×C11C211yesmaximal, characteristic, complemented
3C11×#2283C211yesmaximal, characteristic, complemented
4C11×#1991C212yesmaximal, complemented
5C11×#1958C212yesmaximal, complemented
6C11×#1893C212yesmaximal
7C11×#1892C212yesmaximal, complemented
8C4×C11×#103C212yesmaximal, complemented
9C4×C11×#102C212yesmaximal, complemented
10C23×C8×C11C2212yes—
11C11×#529—24no—
12C11×#529C418yescomplemented
13C2×C11×#126—21no—
14C2×C11×#125C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C22×C42×C11C2211yescharacteristic
24C2×C11×#103C2214yes—
25C2×C11×#102C2214yes—
26C2×C4×C8×C11—24no—
27C2×C4×C8×C11C2212yes—
28C2×C4×C8×C11C2212yes—
29C11×#383—21no—
30C11×#382C2212yes—
31C11×#381—21no—
32C11×#380C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C22⋊C4—21no—
35C11×#376—21no—
36C11×#340C2214yes—
37C11×#340C2214yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11—24no—
46C22×C8×C11—28no—
47C22×C8×C11C2314yes—
48C11×#126—28no—
49C11×#125—22no—
50C11×#125C2×C414yes—
51C11×#124—22no—
52C11×#124C2×C414yes—
53C11×#123—28no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8C2×C414yes—
56C11×#121—22no—
57C11×#121C2×C414yes—
58C4×Q8×C11—22no—
59C4×Q8×C11C2×C414yes—
60C4×D4×C11—28no—
61C4×D4×C11—22no—
62C4×D4×C11C2×C414yes—
63C11×#117—28no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C42×C11—21no—
78C2×C42×C11—22no—
79C2×C42×C11C2×C414yes—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D414yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×#103—28no—
86C11×#102—28no—
87C4×C8×C11—24no—
88C4×C8×C11—24no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93#21402C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—24no—
98C2×Q8×C11C22×C412yes—
99C2×D4×C11—24no—
100C2×D4×C11—21no—
101C2×D4×C11—24no—
102C2×D4×C11—44no—
103C2×D4×C11C22×C412yes—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—44no—
113C22×C4×C11C22⋊C414yes—
114C22×C4×C11C22⋊C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C8×C11—216no—
124C2×C8×C11—24no—
125C2×C8×C11—24no—
126C2×C8×C11#4118yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C42×C11—24no—
144C42×C11—44no—
145C42×C11C22⋊C414yes—
146C42×C11C22⋊C414yes—
147C42×C11C22×C412yes—
148C42×C11C22×C412yes—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C2×#529C2×C1111yescharacteristic
152C22×C4×C8C2×C1111yescharacteristic, complemented
153#2283C2×C1111yescharacteristic, complemented
154#1991C2×C1112yescomplemented
155#1958C2×C1112yescomplemented
156#1893C2×C1112yes—
157#1892C2×C1112yescomplemented
158C4×#103C2×C1112yescomplemented
159C4×#102C2×C1112yescomplemented
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11C2×C22⋊C412yes—
167C23×C11#13514yes—
168C23×C11C22×D411yescharacteristic
169Q8×C11—24no—
170Q8×C11—42no—
171D4×C11—24no—
172D4×C11—48no—
173D4×C11—42no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—28no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—48no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C2×C22⋊C412yes—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11#13514yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4114yes—
201C8×C11—28no—
202C23×C8C22×C1112yes—
203#529—24no—
204#529C4×C1118yescomplemented
205C2×#126—21no—
206C2×#125C22×C1111yescharacteristic
207C2×#124C22×C1111yescharacteristic
208C2×#123—21no—
209C2×C22⋊Q8C22×C1111yescharacteristic
210C2×#121C22×C1111yescharacteristic
211C2×C4×Q8C22×C1111yescharacteristic
212C2×C4×D4—21no—
213C2×C4×D4C22×C1111yescharacteristic
214C2×#117—21no—
215C22×C42C22×C1111yescharacteristic
216C2×#103C22×C1114yes—
217C2×#102C22×C1114yes—
218C2×C4×C8—24no—
219C2×C4×C8C22×C1112yes—
220C2×C4×C8C22×C1112yes—
221#383—21no—
222#382C22×C1112yes—
223#381—21no—
224#380C22×C1112yes—
225C4×C4⋊C4C22×C1112yes—
226C4×C22⋊C4—21no—
227#376—21no—
228#340C22×C1114yes—
229#340C22×C1114yes—
230C22×C11—22no—
231C22×C11—28no—
232C22×C11—22no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—84no—
237C22×C11#41614yes—
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11#53212yes—
240C22×C11C2×#13512yes—
241C22×C11C2×#13512yes—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—84no—
250C4×C11#41614yes—
251C4×C11C4×#4112yes—
252C4×C11#52512yes—
253C22×Q8C23×C1111yescharacteristic
254C22×D4—21no—
255C22×D4C23×C1111yescharacteristic
256C23×C4—21no—
257C23×C4D4×C1111yescharacteristic
258C23×C4D4×C1111yescharacteristic
259C23×C4C23×C1111yescharacteristic
260C22×C8—24no—
261C22×C8—28no—
262C22×C8C23×C1114yes—
263#126—28no—
264#125—22no—
265#125C2×C4×C1114yes—
266#124—22no—
267#124C2×C4×C1114yes—
268#123—28no—
269C22⋊Q8—22no—
270C22⋊Q8C2×C4×C1114yes—
271#121—22no—
272#121C2×C4×C1114yes—
273C4×Q8—22no—
274C4×Q8C2×C4×C1114yes—
275C4×D4—28no—
276C4×D4—22no—
277C4×D4C2×C4×C1114yes—
278#117—28no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4C23×C1114yes—
284C2×C4⋊C4C23×C1111yescharacteristic
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C42—21no—
293C2×C42—22no—
294C2×C42C2×C4×C1114yes—
295C2×C42D4×C1111yescharacteristic
296C2×C42D4×C1111yescharacteristic
297C2×C42D4×C1114yes—
298C2×C42C23×C1111yescharacteristic
299C2×C42C23×C1111yescharacteristic
300#103—28no—
301#102—28no—
302C4×C8—24no—
303C4×C8—24no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—22no—
308C2×C11—24no—
309C2×C11—82no—
310C2×C11#229711yescharacteristic
311C2×C11C2×#41611yescharacteristic
312C2×C11C2×#41611yescharacteristic
313C2×C11#316814yes—
314C24—21no—
315C24C2×D4×C1111yescharacteristic
316C2×Q8—21no—
317C2×Q8—24no—
318C2×Q8C22×C4×C1112yes—
319C2×D4—24no—
320C2×D4—21no—
321C2×D4—24no—
322C2×D4—44no—
323C2×D4C22×C4×C1112yes—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—44no—
333C22×C4C11×C22⋊C414yes—
334C22×C4C11×C22⋊C414yes—
335C22×C4C22×C4×C1112yes—
336C22×C4C2×D4×C1111yescharacteristic
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C2×D4×C1111yescharacteristic
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1112yes—
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C24×C1111yescharacteristic
343C2×C8—216no—
344C2×C8—24no—
345C2×C8—24no—
346C2×C8C11×#4118yes—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4C22×C4×C1112yes—
356C4⋊C4C22×C4×C1112yes—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—44no—
363C42—24no—
364C42—44no—
365C42C11×C22⋊C414yes—
366C42C11×C22⋊C414yes—
367C42C22×C4×C1112yes—
368C42C22×C4×C1112yes—
369C42C2×D4×C1112yes—
370C42C2×D4×C1112yes—
371C11#2140211yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—22no—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23C2×C11×C22⋊C412yes—
379C23C11×#13514yes—
380C23C22×D4×C1111yescharacteristic
381Q8—24no—
382Q8—42no—
383D4—24no—
384D4—48no—
385D4—42no—
386C2×C4—22no—
387C2×C4—28no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—28no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—48no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4C2×C11×C22⋊C412yes—
405C2×C4C2×C11×C22⋊C412yes—
406C2×C4C2×C11×C22⋊C412yes—
407C2×C4C2×C11×C22⋊C412yes—
408C2×C4C2×C11×C22⋊C412yes—
409C2×C4C11×#13514yes—
410C2×C4C23×C4×C1111yescharacteristic
411C2×C4C22×D4×C1111yescharacteristic
412C2×C4C2×C11×#4114yes—
413C8—28no—
414C22—22no—
415C22—28no—
416C22—22no—
417C22—42no—
418C22—42no—
419C22—42no—
420C22—84no—
421C22C11×#41614yes—
422C22C22×C11×C22⋊C411yescharacteristic
423C22C11×#53212yes—
424C22C2×C11×#13512yes—
425C22C2×C11×#13512yes—
426C4—22no—
427C4—22no—
428C4—22no—
429C4—22no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—84no—
434C4C11×#41614yes—
435C4C4×C11×#4112yes—
436C4C11×#52512yes—
437C2—24no—
438C2—82no—
439C2C11×#229711yescharacteristic
440C2C2×C11×#41611yescharacteristic
441C2C2×C11×#41611yescharacteristic
442C2C11×#316814yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C8×C11C2semidirect
3. C11×#2283C2semidirect
4. C11×#1991C2semidirect
5. C11×#1958C2semidirect
7. C11×#1892C2semidirect
8. C4×C11×#103C2semidirect
9. C4×C11×#102C2semidirect
12. C11×#529C4semidirect
93. #21402C11direct (N × H)
152. C22×C4×C8C2×C11semidirect
153. #2283C2×C11semidirect
154. #1991C2×C11semidirect
155. #1958C2×C11semidirect
157. #1892C2×C11semidirect
158. C4×#103C2×C11semidirect
159. C4×#102C2×C11semidirect
204. #529C4×C11semidirect
371. C11#21402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C22×C4×C8×C112
C11×#22832
C11×#19912
C11×#19582
C11×#18932
C11×#18922
C4×C11×#1032
C4×C11×#1022
#2140211