Finite Group Databasebeta

← C11×#24594 #14601787

Subgroups — C11×#24594 #14601787

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic, complemented
5C11×#2084C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1947C212yesmaximal, complemented
8C11×#1925C212yesmaximal, complemented
9C11×#1895C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×C11×#123—22no—
14C2×C11×#121C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#482—24no—
18C11×#428—24no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#399—21no—
29C11×#399—21no—
30C11×#390C2212yes—
31C11×#389C2212yes—
32C11×#388—22no—
33C11×#384C2212yes—
34C11×#382—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#376—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—22no—
48C2×C11×M16—24no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×#123—48no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#117—22no—
56C11×#117D414yes—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
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⋊C4—21no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11—21no—
75C2×C42×C11—22no—
76C2×C42×C11C2312yes—
77C11×#107—24no—
78C11×#107—22no—
79C11×#106—24no—
80C11×#106—22no—
81C11×C4⋊C8—24no—
82C11×#102—24no—
83C11×#102—22no—
84C11×#102—22no—
85C11×C22⋊C8—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24594C1111yesmaximal, 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—44no—
99C2×D4×C11—42no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C11×M16—28no—
116C2×C8×C11—22no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11#4114yes—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—44no—
134C11×C4⋊C4—82no—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—81no—
143C42×C11—24no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—44no—
147C2×#482C2×C1111yescharacteristic
148C2×#428C2×C1111yescharacteristic, complemented
149#2501C2×C1111yescharacteristic
150#2346C2×C1111yescharacteristic, complemented
151#2084C2×C1112yescomplemented
152#2065C2×C1112yescomplemented
153#1947C2×C1112yescomplemented
154#1925C2×C1112yescomplemented
155#1895C2×C1111yescharacteristic
156#1851C2×C1111yescharacteristic, complemented
157#1824C2×C1111yescharacteristic, complemented
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11#12112yes—
168C23×C11C22×D411yescharacteristic
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—42no—
172D4×C11—84no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
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—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—84no—
196C2×C4×C11#12112yes—
197C2×C4×C11AGL(1,ℤ/8)14yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4112yes—
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C112−1+412yes—
202C8×C11—24no—
203C8×C11—41no—
204C8×C11—41no—
205C22×M16C22×C1111yescharacteristic
206C2×#123—22no—
207C2×#121C22×C1111yescharacteristic
208C2×#117C22×C1111yescharacteristic
209C22×C4⋊C4C22×C1111yescharacteristic
210#482—24no—
211#428—24no—
212C2×#107C22×C1111yescharacteristic
213C2×#107C22×C1112yes—
214C2×#106C22×C1111yescharacteristic
215C2×#106C22×C1112yes—
216C2×C4⋊C8C22×C1112yes—
217C2×#102C22×C1111yescharacteristic
218C2×#102C22×C1111yescharacteristic
219C2×#102C22×C1112yes—
220C2×C22⋊C8C22×C1111yescharacteristic
221#399—21no—
222#399—21no—
223#390C22×C1112yes—
224#389C22×C1112yes—
225#388—22no—
226#384C22×C1112yes—
227#382—21no—
228#380C22×C1111yescharacteristic
229C4×C4⋊C4C22×C1112yes—
230C4×C22⋊C4C22×C1111yescharacteristic
231#376—21no—
232#340C22×C1112yes—
233#340C22×C1112yes—
234#340C22×C1112yes—
235#336C22×C1112yes—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11C2×#12111yescharacteristic
247C22×C11#54712yes—
248C22×C11C2×AGL(1,ℤ/8)12yes—
249C22×C11#57711yescharacteristic
250C22×C11#57811yescharacteristic
251C4×C11—24no—
252C4×C11—22no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11—82no—
258C4×C11—81no—
259C4×C11#52511yescharacteristic
260C4×C11#53611yescharacteristic
261C4×C11#55212yes—
262C22×D4—21no—
263C22×D4C23×C1111yescharacteristic
264C23×C4—21no—
265C23×C4C23×C1111yescharacteristic
266C2×M16—22no—
267C2×M16—24no—
268C22×C8C23×C1111yescharacteristic
269C22×C8C23×C1111yescharacteristic
270C22×C8C23×C1112yes—
271#123—48no—
272#121—22no—
273#121—22no—
274#117—22no—
275#117D4×C1114yes—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1111yescharacteristic
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4D4×C1112yes—
293C2×C42—21no—
294C2×C42—22no—
295C2×C42C23×C1112yes—
296#107—24no—
297#107—22no—
298#106—24no—
299#106—22no—
300C4⋊C8—24no—
301#102—24no—
302#102—22no—
303#102—22no—
304C22⋊C8—22no—
305#95—21no—
306#95—22no—
307#95—22no—
308#95D4×C1111yescharacteristic
309#95D4×C1111yescharacteristic
310C2×C11—42no—
311C2×C11—161no—
312C2×C11#241311yescharacteristic
313C2×C11#303811yescharacteristic
314C2×C11#304611yescharacteristic
315C2×C11#334312yes—
316C2×C11#335412yes—
317C24—21no—
318C24C2×D4×C1111yescharacteristic
319C2×D4—21no—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—22no—
323C2×D4—44no—
324C2×D4—42no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—44no—
333C22×C4—42no—
334C22×C4C2×D4×C1112yes—
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1112yes—
337C22×C4C2×D4×C1112yes—
338C22×C4C11×#4112yes—
339C22×C4C24×C1111yescharacteristic
340M16—28no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8C11×#4114yes—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—44no—
357C4⋊C4—42no—
358C4⋊C4—44no—
359C4⋊C4—82no—
360C4⋊C4C2×D4×C1112yes—
361C4⋊C4C2×D4×C1112yes—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—44no—
365C22⋊C4—42no—
366C22⋊C4—44no—
367C22⋊C4—81no—
368C42—24no—
369C42—22no—
370C42—22no—
371C42—44no—
372C11#2459411yescharacteristic, direct product factor, Sylow
373C23—22no—
374C23—22no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—42no—
379C23—42no—
380C23—41no—
381C23—41no—
382C23C11×#12112yes—
383C23C22×D4×C1111yescharacteristic
384D4—41no—
385D4—41no—
386D4—42no—
387D4—84no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4C11×#12112yes—
412C2×C4C11×AGL(1,ℤ/8)14yes—
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C2×C11×#4112yes—
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C11×2−1+412yes—
417C8—24no—
418C8—41no—
419C8—41no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—82no—
429C22—82no—
430C22C2×C11×#12111yescharacteristic
431C22C11×#54712yes—
432C22C2×C11×AGL(1,ℤ/8)12yes—
433C22C11×#57711yescharacteristic
434C22C11×#57811yescharacteristic
435C4—22no—
436C4—24no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—82no—
441C4—81no—
442C4—82no—
443C4C11×#52511yescharacteristic
444C4C11×#53611yescharacteristic
445C4C11×#55212yes—
446C2—42no—
447C2—161no—
448C2C11×#241311yescharacteristic
449C2C11×#303811yescharacteristic
450C2C11×#304611yescharacteristic
451C2C11×#334312yes—
452C2C11×#335412yes—
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. C2×C11×#428C2semidirect
4. C11×#2346C2semidirect
5. C11×#2084C2semidirect
6. C11×#2065C2semidirect
7. C11×#1947C2semidirect
8. C11×#1925C2semidirect
10. C11×#1851C2semidirect
11. C11×#1824C2semidirect
91. #24594C11direct (N × H)
148. C2×#428C2×C11semidirect
150. #2346C2×C11semidirect
151. #2084C2×C11semidirect
152. #2065C2×C11semidirect
153. #1947C2×C11semidirect
154. #1925C2×C11semidirect
156. #1851C2×C11semidirect
157. #1824C2×C11semidirect
372. C11#24594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C2×C11×#4282
C11×#25012
C11×#23462
C11×#20842
C11×#20652
C11×#19472
C11×#19252
C11×#18952
C11×#18512
C11×#18242
#2459411