Finite Group Databasebeta

← C11×#21285 #14598478

Subgroups — C11×#21285 #14598478

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×SD16C211yesmaximal, characteristic
2C11×#2320C211yesmaximal, characteristic, complemented
3C11×#2319C211yesmaximal, characteristic
4C11×#1973C212yesmaximal
5C11×#1944C212yesmaximal, complemented
6C11×#1934C212yesmaximal
7C11×#1933C212yesmaximal, complemented
8C4×C11×#107C211yesmaximal, characteristic, complemented
9C11×#1763C211yesmaximal, characteristic, complemented
10C11×#1762C211yesmaximal, characteristic
11C11×#1726C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C4×C11×SD16C418yescomplemented
16C2×C11×#107C2212yes—
17C2×C11×#106C2211yescharacteristic
18C2×C11×#103C2212yes—
19C2×C11×#103C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C11×#102C2211yescharacteristic
22C2×C11×#97C2212yes—
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391C2212yes—
27C11×#390C2212yes—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#388—22no—
31C11×#387—22no—
32C11×#383—21no—
33C11×#382—21no—
34C11×#381—21no—
35C11×#380—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×SD16—24no—
46C2×C11×SD16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11C2×C414yes—
52C4×D4×C11—22no—
53C4×D4×C11C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69C11×#107—24no—
70C11×#106C2×C414yes—
71C11×#103—24no—
72C11×#103C2×C414yes—
73C11×#102—24no—
74C11×#102C2×C414yes—
75C11×#97—24no—
76C11×#97—22no—
77C4×C8×C11—24no—
78C4×C8×C11C2×C414yes—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95D411yescharacteristic
86C11×#95D411yescharacteristic
87C11×#95D412yes—
88#21285C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C11×SD16—28no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C22×C412yes—
115C2×C8×C11C22×C412yes—
116C2×C8×C11#4114yes—
117C2×C8×C11#4114yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—82no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4C22×C412yes—
128C11×C4⋊C4C22×C412yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—82no—
131C11×C22⋊C4—82no—
132C42×C11—24no—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11—81no—
136C42×C11—81no—
137C42×C11C22×C412yes—
138C42×C11#4112yes—
139C2×C4×SD16C2×C1111yescharacteristic
140#2320C2×C1111yescharacteristic, complemented
141#2319C2×C1111yescharacteristic
142#1973C2×C1112yes—
143#1944C2×C1112yescomplemented
144#1934C2×C1112yes—
145#1933C2×C1112yescomplemented
146C4×#107C2×C1111yescharacteristic, complemented
147#1763C2×C1111yescharacteristic, complemented
148#1762C2×C1111yescharacteristic
149#1726C2×C1111yescharacteristic, complemented
150C23×C11—22no—
151C23×C11—42no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11C22×D411yescharacteristic
156Q8×C11—22no—
157Q8×C11—22no—
158Q8×C11—42no—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—42no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—84no—
185C2×C4×C11C4×D412yes—
186C2×C4×C11C4×D412yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C2×#4112yes—
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C8×C11—22no—
192C8×C11—24no—
193C8×C11#11714yes—
194C22×SD16C22×C1111yescharacteristic
195C2×C4×Q8C22×C1111yescharacteristic
196C2×C4×D4C22×C1111yescharacteristic
197C4×SD16C4×C1118yescomplemented
198C2×#107C22×C1112yes—
199C2×#106C22×C1111yescharacteristic
200C2×#103C22×C1112yes—
201C2×#103C22×C1111yescharacteristic
202C2×#102C22×C1112yes—
203C2×#102C22×C1111yescharacteristic
204C2×#97C22×C1112yes—
205C2×#97C22×C1111yescharacteristic
206C2×C4×C8C22×C1112yes—
207C2×C4×C8C22×C1111yescharacteristic
208#391C22×C1112yes—
209#390C22×C1112yes—
210#389C22×C1112yes—
211#389C22×C1112yes—
212#388—22no—
213#387—22no—
214#383—21no—
215#382—21no—
216#381—21no—
217#380—21no—
218C4×C4⋊C4C22×C1111yescharacteristic
219C4×C4⋊C4C22×C1111yescharacteristic
220#376C22×C1111yescharacteristic
221#340C22×C1112yes—
222#340C22×C1112yes—
223#340C22×C1112yes—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11C2×C4×D411yescharacteristic
230C22×C11#53212yes—
231C22×C11#57611yescharacteristic
232C22×C11#57712yes—
233C22×C11#57811yescharacteristic
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11—82no—
243C4×C11C2×#11711yescharacteristic
244C4×C11C4×#4111yescharacteristic
245C4×C11#52912yes—
246C22×Q8C23×C1111yescharacteristic
247C22×D4C23×C1111yescharacteristic
248C23×C4—21no—
249C2×SD16—24no—
250C2×SD16C2×C4×C1114yes—
251C22×C8C23×C1111yescharacteristic
252C22×C8C23×C1112yes—
253C22×C8C23×C1111yescharacteristic
254C4×Q8—22no—
255C4×Q8C2×C4×C1114yes—
256C4×D4—22no—
257C4×D4C2×C4×C1114yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4C23×C1112yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1111yescharacteristic
264C2×C4⋊C4C23×C1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42C23×C1112yes—
272C2×C42C23×C1111yescharacteristic
273#107—24no—
274#106C2×C4×C1114yes—
275#103—24no—
276#103C2×C4×C1114yes—
277#102—24no—
278#102C2×C4×C1114yes—
279#97—24no—
280#97—22no—
281C4×C8—24no—
282C4×C8C2×C4×C1114yes—
283#95—21no—
284#95—21no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95D4×C1111yescharacteristic
290#95D4×C1111yescharacteristic
291#95D4×C1112yes—
292C2×C11—82no—
293C2×C11#229311yescharacteristic
294C2×C11#294911yescharacteristic
295C2×C11#295111yescharacteristic
296C2×C11#317812yes—
297C2×C11#317912yes—
298C24—21no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8C22×C4×C1112yes—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4C22×C4×C1112yes—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—82no—
314C22×C4C2×D4×C1112yes—
315C22×C4C2×D4×C1112yes—
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C24×C1111yescharacteristic
319SD16—28no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8C22×C4×C1112yes—
324C2×C8C22×C4×C1112yes—
325C2×C8C11×#4114yes—
326C2×C8C11×#4114yes—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—82no—
335C4⋊C4—82no—
336C4⋊C4C22×C4×C1112yes—
337C4⋊C4C22×C4×C1112yes—
338C22⋊C4—24no—
339C22⋊C4—82no—
340C22⋊C4—82no—
341C42—24no—
342C42—22no—
343C42—22no—
344C42—81no—
345C42—81no—
346C42C22×C4×C1112yes—
347C42C11×#4112yes—
348C11#2128511yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23—42no—
351C23—41no—
352C23—42no—
353C23—41no—
354C23C22×D4×C1111yescharacteristic
355Q8—22no—
356Q8—22no—
357Q8—42no—
358D4—22no—
359D4—22no—
360D4—42no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—84no—
384C2×C4C4×D4×C1112yes—
385C2×C4C4×D4×C1112yes—
386C2×C4C23×C4×C1111yescharacteristic
387C2×C4C2×C11×#4112yes—
388C2×C4C2×C11×#4112yes—
389C2×C4C2×C11×#4111yescharacteristic
390C8—22no—
391C8—24no—
392C8C11×#11714yes—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—82no—
397C22—82no—
398C22C2×C4×D4×C1111yescharacteristic
399C22C11×#53212yes—
400C22C11×#57611yescharacteristic
401C22C11×#57712yes—
402C22C11×#57811yescharacteristic
403C4—22no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—82no—
411C4—82no—
412C4C2×C11×#11711yescharacteristic
413C4C4×C11×#4111yescharacteristic
414C4C11×#52912yes—
415C2—82no—
416C2C11×#229311yescharacteristic
417C2C11×#294911yescharacteristic
418C2C11×#295111yescharacteristic
419C2C11×#317812yes—
420C2C11×#317912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2320C2semidirect
5. C11×#1944C2semidirect
7. C11×#1933C2semidirect
8. C4×C11×#107C2semidirect
9. C11×#1763C2semidirect
11. C11×#1726C2semidirect
15. C4×C11×SD16C4semidirect
88. #21285C11direct (N × H)
140. #2320C2×C11semidirect
143. #1944C2×C11semidirect
145. #1933C2×C11semidirect
146. C4×#107C2×C11semidirect
147. #1763C2×C11semidirect
149. #1726C2×C11semidirect
197. C4×SD16C4×C11semidirect
348. C11#21285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×SD162
C11×#23202
C11×#23192
C11×#19732
C11×#19442
C11×#19342
C11×#19332
C4×C11×#1072
C11×#17632
C11×#17622
C11×#17262
#2128511