Finite Group Databasebeta

← C11×#24581 #14601774

Subgroups — C11×#24581 #14601774

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic, complemented
3C11×#2504C211yesmaximal, characteristic
4C11×#2344C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×C11×#117—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#480—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106—24no—
21C2×C11×#106C2212yes—
22C2×C11×#106C2212yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#397—22no—
29C11×#390C2212yes—
30C11×#389C2212yes—
31C11×#387—22no—
32C11×#386—21no—
33C11×#386—21no—
34C11×#382C2212yes—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C8×C11—22no—
49C22×C8×C11—24no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×#121—22no—
54C11×#121—22no—
55C11×#117—44no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C11×#107—22no—
77C11×#107—22no—
78C11×#106—24no—
79C11×#106—24no—
80C11×C4⋊C8—24no—
81C11×#102—24no—
82C11×#102—22no—
83C11×#102—22no—
84C11×C22⋊C8—22no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24581C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C2×D4×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C2×C8×C11—28no—
120C2×C8×C11—22no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11#4114yes—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C2×D412yes—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—82no—
145C11×C22⋊C4—82no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—44no—
149C2×#480C2×C1111yescharacteristic
150C22×#106C2×C1111yescharacteristic, complemented
151#2504C2×C1111yescharacteristic
152#2344C2×C1111yescharacteristic, complemented
153#2085C2×C1112yescomplemented
154#2065C2×C1112yescomplemented
155#1949C2×C1112yescomplemented
156#1926C2×C1112yescomplemented
157#1893C2×C1111yescharacteristic
158#1850C2×C1111yescharacteristic, complemented
159#1824C2×C1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11#12112yes—
168C23×C11#13512yes—
169C23×C11AGL(1,ℤ/8)12yes—
170C23×C11C22×D411yescharacteristic
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—42no—
174D4×C11—84no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—48no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—84no—
202C2×C4×C11#12112yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C112−1+412yes—
207C8×C11—24no—
208C8×C11—41no—
209C8×C11—41no—
210C23×C8C22×C1111yescharacteristic
211C2×#121C22×C1111yescharacteristic
212C2×#117—21no—
213C22×C4⋊C4C22×C1111yescharacteristic
214C22×C4⋊C4C22×C1111yescharacteristic
215#480—24no—
216C2×#107C22×C1111yescharacteristic
217C2×#107C22×C1111yescharacteristic
218C2×#106—24no—
219C2×#106C22×C1112yes—
220C2×#106C22×C1112yes—
221C2×C4⋊C8C22×C1112yes—
222C2×#102C22×C1111yescharacteristic
223C2×#102C22×C1111yescharacteristic
224C2×#102C22×C1112yes—
225C2×C22⋊C8C22×C1111yescharacteristic
226#397—22no—
227#390C22×C1112yes—
228#389C22×C1112yes—
229#387—22no—
230#386—21no—
231#386—21no—
232#382C22×C1112yes—
233#381—21no—
234#380C22×C1111yescharacteristic
235C4×C4⋊C4C22×C1112yes—
236C4×C22⋊C4C22×C1111yescharacteristic
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#336C22×C1112yes—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11#46314yes—
251C22×C11C2×#12111yescharacteristic
252C22×C11#54712yes—
253C22×C11C2×#13511yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C11#57712yes—
256C4×C11—22no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11—81no—
263C4×C11—82no—
264C4×C11#52511yescharacteristic
265C4×C11#53611yescharacteristic
266C4×C11#55212yes—
267C22×D4—21no—
268C22×D4C23×C1111yescharacteristic
269C23×C4—21no—
270C23×C4—21no—
271C23×C4C23×C1111yescharacteristic
272C22×C8—22no—
273C22×C8—24no—
274C22×C8C23×C1111yescharacteristic
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1112yes—
277#121—22no—
278#121—22no—
279#117—44no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4D4×C1114yes—
287C2×C4⋊C4C23×C1112yes—
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4D4×C1111yescharacteristic
297C2×C22⋊C4D4×C1111yescharacteristic
298C2×C42—22no—
299C2×C42C23×C1112yes—
300#107—22no—
301#107—22no—
302#106—24no—
303#106—24no—
304C4⋊C8—24no—
305#102—24no—
306#102—22no—
307#102—22no—
308C22⋊C8—22no—
309#95—22no—
310#95—21no—
311#95—22no—
312#95—22no—
313#95—22no—
314#95D4×C1112yes—
315C2×C11—24no—
316C2×C11—161no—
317C2×C11#241311yescharacteristic
318C2×C11C2×#46311yescharacteristic
319C2×C11#304311yescharacteristic
320C2×C11#333712yes—
321C2×C11#334512yes—
322C24—21no—
323C24C2×D4×C1111yescharacteristic
324C2×D4—21no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—42no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—82no—
343C22×C4C2×D4×C1112yes—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1112yes—
347C22×C4C11×#4112yes—
348C22×C4C24×C1111yescharacteristic
349C2×C8—28no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8C11×#4114yes—
357C4⋊C4—24no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—44no—
367C4⋊C4—42no—
368C4⋊C4C2×D4×C1112yes—
369C4⋊C4C2×D4×C1112yes—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—82no—
375C22⋊C4—82no—
376C42—22no—
377C42—22no—
378C42—44no—
379C11#2458111yescharacteristic, direct product factor, Sylow
380C23—22no—
381C23—22no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—42no—
387C23C11×#12112yes—
388C23C11×#13512yes—
389C23C11×AGL(1,ℤ/8)12yes—
390C23C22×D4×C1111yescharacteristic
391D4—41no—
392D4—41no—
393D4—42no—
394D4—84no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—48no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—84no—
422C2×C4C11×#12112yes—
423C2×C4C22×D4×C1111yescharacteristic
424C2×C4C2×C11×#4112yes—
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C11×2−1+412yes—
427C8—24no—
428C8—41no—
429C8—41no—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—24no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—82no—
438C22—82no—
439C22C11×#46314yes—
440C22C2×C11×#12111yescharacteristic
441C22C11×#54712yes—
442C22C2×C11×#13511yescharacteristic
443C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
444C22C11×#57712yes—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—81no—
451C4—82no—
452C4—82no—
453C4C11×#52511yescharacteristic
454C4C11×#53611yescharacteristic
455C4C11×#55212yes—
456C2—24no—
457C2—161no—
458C2C11×#241311yescharacteristic
459C2C2×C11×#46311yescharacteristic
460C2C11×#304311yescharacteristic
461C2C11×#333712yes—
462C2C11×#334512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#106C2semidirect
4. C11×#2344C2semidirect
5. C11×#2085C2semidirect
6. C11×#2065C2semidirect
7. C11×#1949C2semidirect
8. C11×#1926C2semidirect
10. C11×#1850C2semidirect
11. C11×#1824C2semidirect
91. #24581C11direct (N × H)
150. C22×#106C2×C11semidirect
152. #2344C2×C11semidirect
153. #2085C2×C11semidirect
154. #2065C2×C11semidirect
155. #1949C2×C11semidirect
156. #1926C2×C11semidirect
158. #1850C2×C11semidirect
159. #1824C2×C11semidirect
379. C11#24581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C22×C11×#1062
C11×#25042
C11×#23442
C11×#20852
C11×#20652
C11×#19492
C11×#19262
C11×#18932
C11×#18502
C11×#18242
#2458111