Finite Group Databasebeta

← C11×#20954 #14598147

Subgroups — C11×#20954 #14598147

Order 2816.

1694 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×#536C211yesmaximal, characteristic
2C2×C11×#519C211yesmaximal, characteristic, complemented
3C11×#2896C212yesmaximal
4C22×C11×#101C211yesmaximal, characteristic, complemented
5C11×#1888C214yesmaximal, complemented
6C11×#1886C214yesmaximal, complemented
7C11×#1733C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×M16C2212yes—
11C11×#536—24no—
12C11×#536C418yescomplemented
13C2×C11×C4⋊Q8C2212yes—
14C2×C11×#124C2212yes—
15C2×C11×#123—22no—
16C2×C11×C22⋊Q8—22no—
17C11×#519—22no—
18C11×#519—24no—
19C11×#519C2214yes—
20C2×C4×Q8×C11—24no—
21C2×C11×#117—22no—
22C2×C11×#117C2212yes—
23C2×C11×#117C2211yescharacteristic
24C11×#419C2214yes—
25C11×#418C2214yes—
26C11×#417—24no—
27C11×#416—24no—
28C2×C11×#101—24no—
29C2×C11×#101C2214yes—
30C11×#339C2218yes—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C2×C11×#41—24no—
35C2×C11×#41C2×C414yes—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—24no—
39C22×Q8×C11C2×C414yes—
40C22×Q8×C11D414yes—
41C22×Q8×C11D412yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Q8×C11C2312yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—24no—
51C2×C11×M16—24no—
52C2×C11×M16C2314yes—
53C22×C8×C11—22no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8C2×C418yescomplemented
56C11×#124—24no—
57C11×#124C2×C418yescomplemented
58C11×#123—216no—
59C11×C22⋊Q8—216no—
60C4×Q8×C11—216no—
61C4×Q8×C11—216no—
62C11×#117—28no—
63C11×#117—28no—
64C11×#117—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117C2×C414yes—
68C11×#117D414yes—
69C11×#117C2314yes—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4D414yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—24no—
77C2×C42×C11—24no—
78C2×C42×C11—22no—
79C2×C42×C11C2312yes—
80C11×#103—28no—
81C11×#102—28no—
82C11×#101—28no—
83#20954C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C24×C11C2×D411yescharacteristic
86C11×#41—28no—
87C11×#41—28no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—28no—
91C2×Q8×C11—28no—
92C2×Q8×C11—24no—
93C2×Q8×C11—28no—
94C2×Q8×C11—28no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11—21no—
98C2×Q8×C11—24no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22⋊C418yes—
102C2×Q8×C11C22×C412yes—
103C2×Q8×C11C22×C414yes—
104C2×Q8×C11C2×D414yes—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—42no—
112C2×D4×C11C22×C412yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C22⋊C418yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4114yes—
130C22×C4×C11C2411yescharacteristic
131C11×M16—24no—
132C11×M16—24no—
133C11×M16—44no—
134C2×C8×C11—24no—
135C2×C8×C11—44no—
136C11×C4⋊C4—216no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—216no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4C2×D418yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—216no—
145C42×C11—216no—
146C42×C11—24no—
147C42×C11—24no—
148C42×C11—22no—
149C42×C11C22×C414yes—
150C2×#536C2×C1111yescharacteristic
151C2×#519C2×C1111yescharacteristic, complemented
152#2896C2×C1112yes—
153C22×#101C2×C1111yescharacteristic, complemented
154#1888C2×C1114yescomplemented
155#1886C2×C1114yescomplemented
156#1733C2×C1112yescomplemented
157C23×C11—22no—
158C23×C11—42no—
159C23×C11—44no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C2×C22⋊C412yes—
163C23×C11#12011yescharacteristic
164C23×C11#12011yescharacteristic
165C23×C11#12312yes—
166C23×C11C22×D411yescharacteristic
167Q8×C11—28no—
168Q8×C11—28no—
169Q8×C11—216no—
170Q8×C11—24no—
171Q8×C11—42no—
172D4×C11—24no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—42no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—28no—
179C2×C4×C11—28no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—28no—
183C2×C4×C11—44no—
184C2×C4×C11—48no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—48no—
188C2×C4×C11C2×C22⋊C418yes—
189C2×C4×C11C2×C22⋊C412yes—
190C2×C4×C11C4×D414yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11#12012yes—
193C2×C4×C11#12114yes—
194C2×C4×C11#12114yes—
195C2×C4×C11#12312yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D412yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4112yes—
200C8×C11—44no—
201C22×#41C22×C1111yescharacteristic
202C23×Q8C22×C1111yescharacteristic
203C22×M16C22×C1112yes—
204#536—24no—
205#536C4×C1118yescomplemented
206C2×C4⋊Q8C22×C1112yes—
207C2×#124C22×C1112yes—
208C2×#123—22no—
209C2×C22⋊Q8—22no—
210#519—22no—
211#519—24no—
212#519C22×C1114yes—
213C2×C4×Q8—24no—
214C2×#117—22no—
215C2×#117C22×C1112yes—
216C2×#117C22×C1111yescharacteristic
217#419C22×C1114yes—
218#418C22×C1114yes—
219#417—24no—
220#416—24no—
221C2×#101—24no—
222C2×#101C22×C1114yes—
223#339C22×C1118yes—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—44no—
230C22×C11—42no—
231C22×C11—82no—
232C22×C11—82no—
233C22×C11#38612yes—
234C22×C11#38612yes—
235C22×C11C22×C22⋊C411yescharacteristic
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×#12311yescharacteristic
238C4×C11—28no—
239C4×C11—44no—
240C4×C11—48no—
241C4×C11—42no—
242C4×C11#38614yes—
243C4×C11C2×C4×D412yes—
244C4×C11C2×#12112yes—
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—22no—
248C2×#41—24no—
249C2×#41C2×C4×C1114yes—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—24no—
253C22×Q8C2×C4×C1114yes—
254C22×Q8D4×C1114yes—
255C22×Q8D4×C1112yes—
256C22×Q8C23×C1111yescharacteristic
257C22×Q8C23×C1112yes—
258C22×D4—21no—
259C22×D4C23×C1111yescharacteristic
260C23×C4—21no—
261C23×C4D4×C1112yes—
262C23×C4C23×C1111yescharacteristic
263C2×M16—22no—
264C2×M16—24no—
265C2×M16—24no—
266C2×M16C23×C1114yes—
267C22×C8—22no—
268C4⋊Q8—24no—
269C4⋊Q8C2×C4×C1118yescomplemented
270#124—24no—
271#124C2×C4×C1118yescomplemented
272#123—216no—
273C22⋊Q8—216no—
274C4×Q8—216no—
275C4×Q8—216no—
276#117—28no—
277#117—28no—
278#117—22no—
279#117—22no—
280#117—22no—
281#117C2×C4×C1114yes—
282#117D4×C1114yes—
283#117C23×C1114yes—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4D4×C1114yes—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—24no—
291C2×C42—24no—
292C2×C42—22no—
293C2×C42C23×C1112yes—
294#103—28no—
295#102—28no—
296#101—28no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—22no—
300C2×C11—22no—
301C2×C11—82no—
302C2×C11C2×#38611yescharacteristic
303C2×C11#302012yes—
304C24—21no—
305C24C2×D4×C1111yescharacteristic
306#41—28no—
307#41—28no—
308#41—44no—
309#41—44no—
310C2×Q8—28no—
311C2×Q8—28no—
312C2×Q8—24no—
313C2×Q8—28no—
314C2×Q8—28no—
315C2×Q8—24no—
316C2×Q8—24no—
317C2×Q8—21no—
318C2×Q8—24no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8C11×C22⋊C418yes—
322C2×Q8C22×C4×C1112yes—
323C2×Q8C22×C4×C1114yes—
324C2×Q8C2×D4×C1114yes—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—42no—
332C2×D4C22×C4×C1112yes—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4C11×C22⋊C418yes—
343C22×C4C22×C4×C1112yes—
344C22×C4C2×D4×C1114yes—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C11×#4114yes—
350C22×C4C24×C1111yescharacteristic
351M16—24no—
352M16—24no—
353M16—44no—
354C2×C8—24no—
355C2×C8—44no—
356C4⋊C4—216no—
357C4⋊C4—24no—
358C4⋊C4—216no—
359C4⋊C4—24no—
360C4⋊C4C2×D4×C1118yes—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—216no—
365C42—216no—
366C42—24no—
367C42—24no—
368C42—22no—
369C42C22×C4×C1114yes—
370C11#2095411yescharacteristic, direct product factor, Sylow
371C23—22no—
372C23—42no—
373C23—44no—
374C23—41no—
375C23—41no—
376C23C2×C11×C22⋊C412yes—
377C23C11×#12011yescharacteristic
378C23C11×#12011yescharacteristic
379C23C11×#12312yes—
380C23C22×D4×C1111yescharacteristic
381Q8—28no—
382Q8—28no—
383Q8—216no—
384Q8—24no—
385Q8—42no—
386D4—24no—
387D4—44no—
388D4—44no—
389D4—42no—
390C2×C4—24no—
391C2×C4—28no—
392C2×C4—28no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—28no—
397C2×C4—44no—
398C2×C4—48no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—48no—
402C2×C4C2×C11×C22⋊C418yes—
403C2×C4C2×C11×C22⋊C412yes—
404C2×C4C4×D4×C1114yes—
405C2×C4C4×D4×C1114yes—
406C2×C4C11×#12012yes—
407C2×C4C11×#12114yes—
408C2×C4C11×#12114yes—
409C2×C4C11×#12312yes—
410C2×C4C23×C4×C1111yescharacteristic
411C2×C4C22×D4×C1112yes—
412C2×C4C22×D4×C1111yescharacteristic
413C2×C4C2×C11×#4112yes—
414C8—44no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—44no—
421C22—42no—
422C22—82no—
423C22—82no—
424C22C11×#38612yes—
425C22C11×#38612yes—
426C22C22×C11×C22⋊C411yescharacteristic
427C22C2×C11×#12011yescharacteristic
428C22C2×C11×#12311yescharacteristic
429C4—28no—
430C4—44no—
431C4—48no—
432C4—42no—
433C4C11×#38614yes—
434C4C2×C4×D4×C1112yes—
435C4C2×C11×#12112yes—
436C2—21no—
437C2—21no—
438C2—22no—
439C2—22no—
440C2—82no—
441C2C2×C11×#38611yescharacteristic
442C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#519C2semidirect
4. C22×C11×#101C2semidirect
5. C11×#1888C2semidirect
6. C11×#1886C2semidirect
7. C11×#1733C2semidirect
12. C11×#536C4semidirect
55. C11×C4⋊Q8C2×C4semidirect
57. C11×#124C2×C4semidirect
83. #20954C11direct (N × H)
151. C2×#519C2×C11semidirect
153. C22×#101C2×C11semidirect
154. #1888C2×C11semidirect
155. #1886C2×C11semidirect
156. #1733C2×C11semidirect
205. #536C4×C11semidirect
269. C4⋊Q8C2×C4×C11semidirect
271. #124C2×C4×C11semidirect
370. C11#20954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#5192
C11×#28962
C22×C11×#1012
C11×#18882
C11×#18862
C11×#17332
#2095411