Finite Group Databasebeta

← C11×#24578 #14601771

Subgroups — C11×#24578 #14601771

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#481C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2084C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1948C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×#123—21no—
14C2×C11×#123—21no—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C11×#481—24no—
19C2×C11×#106—24no—
20C2×C11×#106C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#399—22no—
30C11×#390C2212yes—
31C11×#389C2212yes—
32C11×#387—22no—
33C11×#384C2212yes—
34C11×#380—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4—21no—
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×#123—44no—
54C11×#123—44no—
55C11×#121—22no—
56C11×#121—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D414yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C11×#106—24no—
80C11×#106—24no—
81C11×#106—22no—
82C11×#106—22no—
83C11×C4⋊C8—24no—
84C11×#102—24no—
85C11×#102—22no—
86C11×#102—22no—
87C11×C22⋊C8—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95D412yes—
92#24578C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—22no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C2×C8×C11—28no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11#4114yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—82no—
141C11×C4⋊C4C2×D412yes—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4SD1614yes—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—82no—
152C2×#481C2×C1111yescharacteristic
153C22×#106C2×C1111yescharacteristic, complemented
154#2501C2×C1111yescharacteristic
155#2345C2×C1111yescharacteristic, complemented
156#2084C2×C1112yescomplemented
157#2065C2×C1112yescomplemented
158#1948C2×C1112yescomplemented
159#1926C2×C1112yescomplemented
160#1893C2×C1111yescharacteristic
161#1850C2×C1111yescharacteristic, complemented
162#1823C2×C1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11#12112yes—
171C23×C11C2×SD1612yes—
172C23×C11AGL(1,ℤ/8)12yes—
173C23×C11C22×D411yescharacteristic
174D4×C11—41no—
175D4×C11—41no—
176D4×C11—42no—
177D4×C11—84no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—84no—
201C2×C4×C11—84no—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×SD1614yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4112yes—
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C112−1+412yes—
208C8×C11—24no—
209C8×C11—41no—
210C8×C11—41no—
211C23×C8C22×C1111yescharacteristic
212C2×#123—21no—
213C2×#123—21no—
214C2×#121C22×C1111yescharacteristic
215C22×C4⋊C4C22×C1111yescharacteristic
216C22×C4⋊C4C22×C1111yescharacteristic
217#481—24no—
218C2×#106—24no—
219C2×#106C22×C1112yes—
220C2×#106C22×C1111yescharacteristic
221C2×#106C22×C1111yescharacteristic
222C2×#106C22×C1112yes—
223C2×C4⋊C8C22×C1112yes—
224C2×#102C22×C1111yescharacteristic
225C2×#102C22×C1112yes—
226C2×#102C22×C1111yescharacteristic
227C2×C22⋊C8C22×C1111yescharacteristic
228#399—22no—
229#390C22×C1112yes—
230#389C22×C1112yes—
231#387—22no—
232#384C22×C1112yes—
233#380—21no—
234#380C22×C1111yescharacteristic
235C4×C4⋊C4C22×C1112yes—
236C4×C22⋊C4—21no—
237C4×C22⋊C4C22×C1111yescharacteristic
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1112yes—
242C22×C11—24no—
243C22×C11—24no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11#46014yes—
252C22×C11C2×#12111yescharacteristic
253C22×C11#54712yes—
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C11#57712yes—
257C4×C11—24no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—82no—
263C4×C11—82no—
264C4×C11—81no—
265C4×C11#52511yescharacteristic
266C4×C11#53611yescharacteristic
267C4×C11#55212yes—
268C22×D4—21no—
269C22×D4C23×C1111yescharacteristic
270C23×C4—21no—
271C23×C4—21no—
272C23×C4C23×C1111yescharacteristic
273C22×C8—22no—
274C22×C8—24no—
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1111yescharacteristic
277C22×C8C23×C1112yes—
278#123—44no—
279#123—44no—
280#121—22no—
281#121—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4D4×C1114yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4D4×C1111yescharacteristic
301C2×C22⋊C4D4×C1111yescharacteristic
302C2×C42—22no—
303C2×C42C23×C1112yes—
304#106—24no—
305#106—24no—
306#106—22no—
307#106—22no—
308C4⋊C8—24no—
309#102—24no—
310#102—22no—
311#102—22no—
312C22⋊C8—22no—
313#95—22no—
314#95—22no—
315#95—21no—
316#95D4×C1112yes—
317C2×C11—24no—
318C2×C11—161no—
319C2×C11#241311yescharacteristic
320C2×C11C2×#46011yescharacteristic
321C2×C11#304211yescharacteristic
322C2×C11#333512yes—
323C2×C11#334512yes—
324C24—21no—
325C24C2×D4×C1111yescharacteristic
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—22no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—42no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—82no—
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C22×C4C11×#4112yes—
350C22×C4C24×C1111yescharacteristic
351C2×C8—28no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8C11×#4114yes—
359C4⋊C4—24no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—44no—
369C4⋊C4—42no—
370C4⋊C4—44no—
371C4⋊C4—82no—
372C4⋊C4C2×D4×C1112yes—
373C4⋊C4C2×D4×C1112yes—
374C22⋊C4—22no—
375C22⋊C4—44no—
376C22⋊C4—42no—
377C22⋊C4—42no—
378C22⋊C4—44no—
379C22⋊C4C11×SD1614yes—
380C42—22no—
381C42—22no—
382C42—82no—
383C11#2457811yescharacteristic, direct product factor, Sylow
384C23—22no—
385C23—22no—
386C23—41no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23C11×#12112yes—
392C23C2×C11×SD1612yes—
393C23C11×AGL(1,ℤ/8)12yes—
394C23C22×D4×C1111yescharacteristic
395D4—41no—
396D4—41no—
397D4—42no—
398D4—84no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4C11×#12112yes—
424C2×C4C2×C11×SD1614yes—
425C2×C4C22×D4×C1111yescharacteristic
426C2×C4C2×C11×#4112yes—
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C11×2−1+412yes—
429C8—24no—
430C8—41no—
431C8—41no—
432C22—22no—
433C22—22no—
434C22—24no—
435C22—24no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—82no—
440C22—82no—
441C22C11×#46014yes—
442C22C2×C11×#12111yescharacteristic
443C22C11×#54712yes—
444C22C22×C11×SD1611yescharacteristic
445C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
446C22C11×#57712yes—
447C4—22no—
448C4—24no—
449C4—42no—
450C4—42no—
451C4—42no—
452C4—82no—
453C4—81no—
454C4—82no—
455C4C11×#52511yescharacteristic
456C4C11×#53611yescharacteristic
457C4C11×#55212yes—
458C2—24no—
459C2—161no—
460C2C11×#241311yescharacteristic
461C2C2×C11×#46011yescharacteristic
462C2C11×#304211yescharacteristic
463C2C11×#333512yes—
464C2C11×#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×#2345C2semidirect
5. C11×#2084C2semidirect
6. C11×#2065C2semidirect
7. C11×#1948C2semidirect
8. C11×#1926C2semidirect
10. C11×#1850C2semidirect
11. C11×#1823C2semidirect
92. #24578C11direct (N × H)
153. C22×#106C2×C11semidirect
155. #2345C2×C11semidirect
156. #2084C2×C11semidirect
157. #2065C2×C11semidirect
158. #1948C2×C11semidirect
159. #1926C2×C11semidirect
161. #1850C2×C11semidirect
162. #1823C2×C11semidirect
383. C11#24578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C22×C11×#1062
C11×#25012
C11×#23452
C11×#20842
C11×#20652
C11×#19482
C11×#19262
C11×#18932
C11×#18502
C11×#18232
#2457811