Finite Group Databasebeta

← C11×#24599 #14601792

Subgroups — C11×#24599 #14601792

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 450 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×#2504C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1895C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#482—24no—
17C11×#428—24no—
18C2×C11×#107C2212yes—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#397—21no—
28C11×#397—21no—
29C11×#390C2212yes—
30C11×#389C2212yes—
31C11×#388—22no—
32C11×#386—22no—
33C11×#382—21no—
34C11×#382C2212yes—
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×#121—22no—
53C11×#121—22no—
54C11×#117—22no—
55C11×#117D414yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4D412yes—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C11×#107—24no—
75C11×#107—22no—
76C11×#106—24no—
77C11×#106—22no—
78C11×C4⋊C8—24no—
79C11×#102—24no—
80C11×#102—22no—
81C11×#102—22no—
82C11×C22⋊C8—22no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95D411yescharacteristic
89C11×#95D411yescharacteristic
90#24599C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—21no—
92C24×C11C2×D411yescharacteristic
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—44no—
98C2×D4×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—81no—
108C22×C4×C11—81no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
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—42no—
132C11×C4⋊C4—82no—
133C11×C4⋊C4C2×D412yes—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—82no—
139C11×C22⋊C4—82no—
140C11×C22⋊C4—81no—
141C42×C11—24no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—44no—
145C2×#482C2×C1111yescharacteristic
146C2×#428C2×C1111yescharacteristic, complemented
147#2504C2×C1111yescharacteristic
148#2346C2×C1111yescharacteristic, complemented
149#2085C2×C1112yescomplemented
150#2067C2×C1112yescomplemented
151#1949C2×C1112yescomplemented
152#1926C2×C1112yescomplemented
153#1895C2×C1111yescharacteristic
154#1851C2×C1111yescharacteristic, complemented
155#1823C2×C1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12112yes—
166C23×C11C22×D411yescharacteristic
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—42no—
170D4×C11—84no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
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—84no—
195C2×C4×C11#12112yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4112yes—
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C112−1+412yes—
200C8×C11—24no—
201C8×C11—41no—
202C8×C11—41no—
203C22×M16C22×C1111yescharacteristic
204C2×#121C22×C1111yescharacteristic
205C2×#117C22×C1111yescharacteristic
206C22×C4⋊C4C22×C1111yescharacteristic
207#482—24no—
208#428—24no—
209C2×#107C22×C1111yescharacteristic
210C2×#107C22×C1112yes—
211C2×#106C22×C1111yescharacteristic
212C2×#106C22×C1112yes—
213C2×C4⋊C8C22×C1112yes—
214C2×#102C22×C1111yescharacteristic
215C2×#102C22×C1111yescharacteristic
216C2×#102C22×C1112yes—
217C2×C22⋊C8C22×C1111yescharacteristic
218#397—21no—
219#397—21no—
220#390C22×C1112yes—
221#389C22×C1112yes—
222#388—22no—
223#386—22no—
224#382—21no—
225#382C22×C1112yes—
226#380C22×C1111yescharacteristic
227C4×C4⋊C4C22×C1112yes—
228C4×C22⋊C4C22×C1111yescharacteristic
229#376—21no—
230#340C22×C1112yes—
231#340C22×C1112yes—
232#340C22×C1112yes—
233#336C22×C1112yes—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11C2×#12111yescharacteristic
245C22×C11#54712yes—
246C22×C11#57512yes—
247C22×C11#57611yescharacteristic
248C22×C11#57711yescharacteristic
249C4×C11—22no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—82no—
257C4×C11#52511yescharacteristic
258C4×C11#53611yescharacteristic
259C4×C11#55212yes—
260C22×D4—21no—
261C22×D4C23×C1111yescharacteristic
262C23×C4—21no—
263C23×C4C23×C1111yescharacteristic
264C2×M16—22no—
265C2×M16—24no—
266C22×C8C23×C1111yescharacteristic
267C22×C8C23×C1111yescharacteristic
268C22×C8C23×C1112yes—
269#121—22no—
270#121—22no—
271#117—22no—
272#117D4×C1114yes—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4C23×C1112yes—
278C2×C4⋊C4C23×C1111yescharacteristic
279C2×C4⋊C4C23×C1112yes—
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C4⋊C4C23×C1111yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4D4×C1112yes—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42C23×C1112yes—
291#107—24no—
292#107—22no—
293#106—24no—
294#106—22no—
295C4⋊C8—24no—
296#102—24no—
297#102—22no—
298#102—22no—
299C22⋊C8—22no—
300#95—21no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—22no—
305#95D4×C1111yescharacteristic
306#95D4×C1111yescharacteristic
307C2×C11—42no—
308C2×C11—161no—
309C2×C11#241311yescharacteristic
310C2×C11#304011yescharacteristic
311C2×C11#304511yescharacteristic
312C2×C11#334712yes—
313C2×C11#335112yes—
314C24—21no—
315C24C2×D4×C1111yescharacteristic
316C2×D4—21no—
317C2×D4—22no—
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—44no—
321C2×D4—42no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—42no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1112yes—
336C22×C4C11×#4112yes—
337C22×C4C24×C1111yescharacteristic
338M16—28no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8C11×#4114yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—82no—
356C4⋊C4C2×D4×C1112yes—
357C4⋊C4C2×D4×C1112yes—
358C22⋊C4—24no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—82no—
362C22⋊C4—82no—
363C22⋊C4—81no—
364C42—24no—
365C42—22no—
366C42—22no—
367C42—44no—
368C11#2459911yescharacteristic, direct product factor, Sylow
369C23—22no—
370C23—22no—
371C23—21no—
372C23—21no—
373C23—41no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23C11×#12112yes—
379C23C22×D4×C1111yescharacteristic
380D4—41no—
381D4—41no—
382D4—42no—
383D4—84no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—84no—
408C2×C4C11×#12112yes—
409C2×C4C22×D4×C1111yescharacteristic
410C2×C4C2×C11×#4112yes—
411C2×C4C2×C11×#4111yescharacteristic
412C2×C4C11×2−1+412yes—
413C8—24no—
414C8—41no—
415C8—41no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—42no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—82no—
425C22—82no—
426C22C2×C11×#12111yescharacteristic
427C22C11×#54712yes—
428C22C11×#57512yes—
429C22C11×#57611yescharacteristic
430C22C11×#57711yescharacteristic
431C4—22no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—81no—
437C4—82no—
438C4—82no—
439C4C11×#52511yescharacteristic
440C4C11×#53611yescharacteristic
441C4C11×#55212yes—
442C2—42no—
443C2—161no—
444C2C11×#241311yescharacteristic
445C2C11×#304011yescharacteristic
446C2C11×#304511yescharacteristic
447C2C11×#334712yes—
448C2C11×#335112yes—
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×#2085C2semidirect
6. C11×#2067C2semidirect
7. C11×#1949C2semidirect
8. C11×#1926C2semidirect
10. C11×#1851C2semidirect
11. C11×#1823C2semidirect
90. #24599C11direct (N × H)
146. C2×#428C2×C11semidirect
148. #2346C2×C11semidirect
149. #2085C2×C11semidirect
150. #2067C2×C11semidirect
151. #1949C2×C11semidirect
152. #1926C2×C11semidirect
154. #1851C2×C11semidirect
155. #1823C2×C11semidirect
368. C11#24599direct (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×#25042
C11×#23462
C11×#20852
C11×#20672
C11×#19492
C11×#19262
C11×#18952
C11×#18512
C11×#18232
#2459911