Finite Group Databasebeta

← C11×#21403 #14598596

Subgroups — C11×#21403 #14598596

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C4×C11×M16C211yesmaximal, characteristic, complemented
3C11×#2285C211yesmaximal, characteristic, complemented
4C11×#1992C212yesmaximal, complemented
5C11×#1959C212yesmaximal, complemented
6C11×#1895C212yesmaximal
7C11×#1894C212yesmaximal, complemented
8C4×C11×#103C212yesmaximal, complemented
9C4×C11×#102C212yesmaximal, complemented
10C22×C11×M16C2212yes—
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—
23C2×C11×#117—21no—
24C22×C42×C11C2211yescharacteristic
25C2×C11×#103C2214yes—
26C2×C11×#102C2214yes—
27C4×C11×M16—24no—
28C2×C11×#97C2212yes—
29C2×C4×C8×C11C2212yes—
30C11×#384C2212yes—
31C11×#382—21no—
32C11×#380—21no—
33C11×#380C2212yes—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
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
45C2×C11×M16—24no—
46C2×C11×M16—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—
64C11×#117—44no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11—22no—
82C2×C42×C11C2×C414yes—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D414yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×#103—28no—
89C11×#102—28no—
90C11×#97—24no—
91C4×C8×C11—24no—
92C11×#95—22no—
93C11×#95—22no—
94#21403C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—21no—
98C2×Q8×C11—24no—
99C2×Q8×C11C22×C412yes—
100C2×D4×C11—24no—
101C2×D4×C11—21no—
102C2×D4×C11—24no—
103C2×D4×C11—44no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C11×M16—216no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11#4118yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4C22×C412yes—
141C11×C4⋊C4C22×C412yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—44no—
148C42×C11—24no—
149C42×C11—44no—
150C42×C11C22⋊C414yes—
151C42×C11C22⋊C414yes—
152C42×C11C22×C412yes—
153C42×C11C22×C412yes—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C2×#529C2×C1111yescharacteristic
157C2×C4×M16C2×C1111yescharacteristic, complemented
158#2285C2×C1111yescharacteristic, complemented
159#1992C2×C1112yescomplemented
160#1959C2×C1112yescomplemented
161#1895C2×C1112yes—
162#1894C2×C1112yescomplemented
163C4×#103C2×C1112yescomplemented
164C4×#102C2×C1112yescomplemented
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—42no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—42no—
174C23×C11C2×C22⋊C412yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—24no—
177Q8×C11—42no—
178D4×C11—24no—
179D4×C11—48no—
180D4×C11—42no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—28no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—48no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11AGL(1,ℤ/8)12yes—
207C2×C4×C11#13712yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4114yes—
211C8×C11—28no—
212C22×M16C22×C1112yes—
213#529—24no—
214#529C4×C1118yescomplemented
215C2×#126—21no—
216C2×#125C22×C1111yescharacteristic
217C2×#124C22×C1111yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8C22×C1111yescharacteristic
220C2×#121C22×C1111yescharacteristic
221C2×C4×Q8C22×C1111yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C22×C1111yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C22×C42C22×C1111yescharacteristic
227C2×#103C22×C1114yes—
228C2×#102C22×C1114yes—
229C4×M16—24no—
230C2×#97C22×C1112yes—
231C2×C4×C8C22×C1112yes—
232#384C22×C1112yes—
233#382—21no—
234#380—21no—
235#380C22×C1112yes—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C22×C1112yes—
238#340C22×C1114yes—
239#340C22×C1114yes—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11C22×C22⋊C411yescharacteristic
251C22×C11#53212yes—
252C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C22×C11#57512yes—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—84no—
263C4×C11#41714yes—
264C4×C11C4×#4112yes—
265C4×C11#52512yes—
266C22×Q8C23×C1111yescharacteristic
267C22×D4—21no—
268C22×D4C23×C1111yescharacteristic
269C23×C4—21no—
270C23×C4D4×C1111yescharacteristic
271C23×C4D4×C1111yescharacteristic
272C23×C4C23×C1111yescharacteristic
273C2×M16—24no—
274C2×M16—28no—
275C22×C8C23×C1114yes—
276#126—28no—
277#125—22no—
278#125C2×C4×C1114yes—
279#124—22no—
280#124C2×C4×C1114yes—
281#123—28no—
282C22⋊Q8—22no—
283C22⋊Q8C2×C4×C1114yes—
284#121—22no—
285#121C2×C4×C1114yes—
286C4×Q8—22no—
287C4×Q8C2×C4×C1114yes—
288C4×D4—28no—
289C4×D4—22no—
290C4×D4C2×C4×C1114yes—
291#117—28no—
292#117—44no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4C23×C1114yes—
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C4⋊C4C23×C1111yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C42—21no—
309C2×C42—22no—
310C2×C42C2×C4×C1114yes—
311C2×C42D4×C1111yescharacteristic
312C2×C42D4×C1111yescharacteristic
313C2×C42D4×C1114yes—
314C2×C42C23×C1111yescharacteristic
315C2×C42C23×C1111yescharacteristic
316#103—28no—
317#102—28no—
318#97—24no—
319C4×C8—24no—
320#95—22no—
321#95—22no—
322C2×C11—42no—
323C2×C11—82no—
324C2×C11#229711yescharacteristic
325C2×C11C2×#41711yescharacteristic
326C2×C11#289611yescharacteristic
327C2×C11#317112yes—
328C2×C11#317212yes—
329C24—21no—
330C24C2×D4×C1111yescharacteristic
331C2×Q8—21no—
332C2×Q8—24no—
333C2×Q8C22×C4×C1112yes—
334C2×D4—24no—
335C2×D4—21no—
336C2×D4—24no—
337C2×D4—44no—
338C2×D4C22×C4×C1112yes—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4C11×C22⋊C414yes—
351C22×C4C11×C22⋊C414yes—
352C22×C4C22×C4×C1112yes—
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C24×C1111yescharacteristic
360M16—216no—
361C2×C8—24no—
362C2×C8—24no—
363C2×C8C11×#4118yes—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—44no—
373C4⋊C4—44no—
374C4⋊C4C22×C4×C1112yes—
375C4⋊C4C22×C4×C1112yes—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—44no—
382C42—24no—
383C42—44no—
384C42C11×C22⋊C414yes—
385C42C11×C22⋊C414yes—
386C42C22×C4×C1112yes—
387C42C22×C4×C1112yes—
388C42C2×D4×C1112yes—
389C42C2×D4×C1112yes—
390C11#2140311yescharacteristic, direct product factor, Sylow
391C23—22no—
392C23—21no—
393C23—21no—
394C23—22no—
395C23—22no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23C2×C11×C22⋊C412yes—
401C23C22×D4×C1111yescharacteristic
402Q8—24no—
403Q8—42no—
404D4—24no—
405D4—48no—
406D4—42no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—28no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—48no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4C2×C11×C22⋊C412yes—
428C2×C4C2×C11×C22⋊C412yes—
429C2×C4C2×C11×C22⋊C412yes—
430C2×C4C2×C11×C22⋊C412yes—
431C2×C4C2×C11×C22⋊C412yes—
432C2×C4C11×AGL(1,ℤ/8)12yes—
433C2×C4C11×#13712yes—
434C2×C4C23×C4×C1111yescharacteristic
435C2×C4C22×D4×C1111yescharacteristic
436C2×C4C2×C11×#4114yes—
437C8—28no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—82no—
448C22C22×C11×C22⋊C411yescharacteristic
449C22C11×#53212yes—
450C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
451C22C2×C11×#13711yescharacteristic
452C22C11×#57512yes—
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—84no—
461C4C11×#41714yes—
462C4C4×C11×#4112yes—
463C4C11×#52512yes—
464C2—42no—
465C2—82no—
466C2C11×#229711yescharacteristic
467C2C2×C11×#41711yescharacteristic
468C2C11×#289611yescharacteristic
469C2C11×#317112yes—
470C2C11×#317212yes—
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. C2×C4×C11×M16C2semidirect
3. C11×#2285C2semidirect
4. C11×#1992C2semidirect
5. C11×#1959C2semidirect
7. C11×#1894C2semidirect
8. C4×C11×#103C2semidirect
9. C4×C11×#102C2semidirect
12. C11×#529C4semidirect
94. #21403C11direct (N × H)
157. C2×C4×M16C2×C11semidirect
158. #2285C2×C11semidirect
159. #1992C2×C11semidirect
160. #1959C2×C11semidirect
162. #1894C2×C11semidirect
163. C4×#103C2×C11semidirect
164. C4×#102C2×C11semidirect
214. #529C4×C11semidirect
390. C11#21403direct (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
C2×C4×C11×M162
C11×#22852
C11×#19922
C11×#19592
C11×#18952
C11×#18942
C4×C11×#1032
C4×C11×#1022
#2140311