Finite Group Databasebeta

← C11×#24583 #14601776

Subgroups — C11×#24583 #14601776

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#481C211yesmaximal, characteristic
2C22×C11×#107C211yesmaximal, characteristic, complemented
3C11×#2504C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#1949C212yesmaximal, complemented
8C11×#1925C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#481—24no—
17C2×C11×#107—24no—
18C2×C11×#107C2212yes—
19C2×C11×#107C2212yes—
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#397—22no—
28C11×#390C2212yes—
29C11×#389C2212yes—
30C11×#387—22no—
31C11×#386—21no—
32C11×#386—21no—
33C11×#382C2212yes—
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×#121—22no—
54C11×#121—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C11×#107—24no—
76C11×#107—24no—
77C11×#106—22no—
78C11×#106—22no—
79C11×C4⋊C8—24no—
80C11×#102—24no—
81C11×#102—22no—
82C11×#102—22no—
83C11×C22⋊C8—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D412yes—
90#24583C1111yesmaximal, 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—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—82no—
110C22×C4×C11—82no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C2×C8×C11—28no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11#4114yes—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4C2×D412yes—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—82no—
143C11×C22⋊C4—82no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—82no—
147C2×#481C2×C1111yescharacteristic
148C22×#107C2×C1111yescharacteristic, complemented
149#2504C2×C1111yescharacteristic
150#2345C2×C1111yescharacteristic, complemented
151#2085C2×C1112yescomplemented
152#2067C2×C1112yescomplemented
153#1949C2×C1112yescomplemented
154#1925C2×C1112yescomplemented
155#1893C2×C1111yescharacteristic
156#1850C2×C1111yescharacteristic, complemented
157#1824C2×C1111yescharacteristic, complemented
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—42no—
165C23×C11#12112yes—
166C23×C11#13512yes—
167C23×C11#13712yes—
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—24no—
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—22no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—84no—
197C2×C4×C11—84no—
198C2×C4×C11#12112yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4112yes—
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C112−1+412yes—
203C8×C11—24no—
204C8×C11—41no—
205C8×C11—41no—
206C23×C8C22×C1111yescharacteristic
207C2×#121C22×C1111yescharacteristic
208C22×C4⋊C4C22×C1111yescharacteristic
209C22×C4⋊C4C22×C1111yescharacteristic
210#481—24no—
211C2×#107—24no—
212C2×#107C22×C1112yes—
213C2×#107C22×C1112yes—
214C2×#106C22×C1111yescharacteristic
215C2×#106C22×C1111yescharacteristic
216C2×C4⋊C8C22×C1112yes—
217C2×#102C22×C1111yescharacteristic
218C2×#102C22×C1111yescharacteristic
219C2×#102C22×C1112yes—
220C2×C22⋊C8C22×C1111yescharacteristic
221#397—22no—
222#390C22×C1112yes—
223#389C22×C1112yes—
224#387—22no—
225#386—21no—
226#386—21no—
227#382C22×C1112yes—
228#380—21no—
229#380C22×C1111yescharacteristic
230C4×C4⋊C4C22×C1112yes—
231C4×C22⋊C4—21no—
232C4×C22⋊C4C22×C1111yescharacteristic
233#340C22×C1112yes—
234#340C22×C1112yes—
235#340C22×C1112yes—
236#336C22×C1112yes—
237C22×C11—24no—
238C22×C11—24no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#46414yes—
247C22×C11C2×#12111yescharacteristic
248C22×C11#54712yes—
249C22×C11C2×#13511yescharacteristic
250C22×C11C2×#13711yescharacteristic
251C22×C11#57612yes—
252C4×C11—22no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11—81no—
259C4×C11—82no—
260C4×C11#52511yescharacteristic
261C4×C11#53611yescharacteristic
262C4×C11#55212yes—
263C22×D4—21no—
264C22×D4C23×C1111yescharacteristic
265C23×C4—21no—
266C23×C4—21no—
267C23×C4C23×C1111yescharacteristic
268C22×C8—22no—
269C22×C8—24no—
270C22×C8C23×C1111yescharacteristic
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1112yes—
273#121—22no—
274#121—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4D4×C1114yes—
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⋊C4D4×C1111yescharacteristic
292C2×C22⋊C4D4×C1111yescharacteristic
293C2×C42—22no—
294C2×C42C23×C1112yes—
295#107—24no—
296#107—24no—
297#106—22no—
298#106—22no—
299C4⋊C8—24no—
300#102—24no—
301#102—22no—
302#102—22no—
303C22⋊C8—22no—
304#95—22no—
305#95—22no—
306#95—21no—
307#95—22no—
308#95—22no—
309#95D4×C1112yes—
310C2×C11—24no—
311C2×C11—161no—
312C2×C11#241311yescharacteristic
313C2×C11C2×#46411yescharacteristic
314C2×C11#304111yescharacteristic
315C2×C11#333912yes—
316C2×C11#334612yes—
317C24—21no—
318C24C2×D4×C1111yescharacteristic
319C2×D4—21no—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—22no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—42no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—82no—
336C22×C4—82no—
337C22×C4C2×D4×C1112yes—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1112yes—
341C22×C4C11×#4112yes—
342C22×C4C24×C1111yescharacteristic
343C2×C8—28no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8C11×#4114yes—
351C4⋊C4—24no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—42no—
361C4⋊C4—82no—
362C4⋊C4C2×D4×C1112yes—
363C4⋊C4C2×D4×C1112yes—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—42no—
367C22⋊C4—42no—
368C22⋊C4—82no—
369C22⋊C4—82no—
370C42—22no—
371C42—22no—
372C42—82no—
373C11#2458311yescharacteristic, direct product factor, Sylow
374C23—22no—
375C23—22no—
376C23—41no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23C11×#12112yes—
382C23C11×#13512yes—
383C23C11×#13712yes—
384C23C22×D4×C1111yescharacteristic
385D4—41no—
386D4—41no—
387D4—42no—
388D4—84no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4C11×#12112yes—
415C2×C4C22×D4×C1111yescharacteristic
416C2×C4C2×C11×#4112yes—
417C2×C4C2×C11×#4111yescharacteristic
418C2×C4C11×2−1+412yes—
419C8—24no—
420C8—41no—
421C8—41no—
422C22—22no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—82no—
430C22—82no—
431C22C11×#46414yes—
432C22C2×C11×#12111yescharacteristic
433C22C11×#54712yes—
434C22C2×C11×#13511yescharacteristic
435C22C2×C11×#13711yescharacteristic
436C22C11×#57612yes—
437C4—22no—
438C4—42no—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—82no—
444C4—82no—
445C4C11×#52511yescharacteristic
446C4C11×#53611yescharacteristic
447C4C11×#55212yes—
448C2—24no—
449C2—161no—
450C2C11×#241311yescharacteristic
451C2C2×C11×#46411yescharacteristic
452C2C11×#304111yescharacteristic
453C2C11×#333912yes—
454C2C11×#334612yes—
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×#107C2semidirect
4. C11×#2345C2semidirect
5. C11×#2085C2semidirect
6. C11×#2067C2semidirect
7. C11×#1949C2semidirect
8. C11×#1925C2semidirect
10. C11×#1850C2semidirect
11. C11×#1824C2semidirect
90. #24583C11direct (N × H)
148. C22×#107C2×C11semidirect
150. #2345C2×C11semidirect
151. #2085C2×C11semidirect
152. #2067C2×C11semidirect
153. #1949C2×C11semidirect
154. #1925C2×C11semidirect
156. #1850C2×C11semidirect
157. #1824C2×C11semidirect
373. C11#24583direct (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×#1072
C11×#25042
C11×#23452
C11×#20852
C11×#20672
C11×#19492
C11×#19252
C11×#18932
C11×#18502
C11×#18242
#2458311