Finite Group Databasebeta

← C11×#24580 #14601773

Subgroups — C11×#24580 #14601773

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic
3C11×#2502C211yesmaximal, characteristic
4C11×#2344C211yesmaximal, characteristic
5C11×#2084C212yesmaximal, complemented
6C11×#2066C212yesmaximal, complemented
7C11×#1948C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1892C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic
11C11×#1824C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#117—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#483—24no—
18C2×C11×#106—24no—
19C2×C11×#106C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#398—22no—
29C11×#391C2212yes—
30C11×#389C2212yes—
31C11×#387—22no—
32C11×#385—21no—
33C11×#385—21no—
34C11×#384C2212yes—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C22×C8×C11—22no—
48C22×C8×C11—24no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×#117—44no—
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⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C11×#106—24no—
77C11×#106—24no—
78C11×#106—22no—
79C11×#106—22no—
80C11×C4⋊C8—24no—
81C11×#103—24no—
82C11×#103—22no—
83C11×#103—22no—
84C11×C22⋊C8—22no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24580C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C2×C8×C11—28no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11#4114yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—82no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4C2×D412yes—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4SD1614yes—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—44no—
147C2×#483C2×C1111yescharacteristic
148C22×#106C2×C1111yescharacteristic
149#2502C2×C1111yescharacteristic
150#2344C2×C1111yescharacteristic
151#2084C2×C1112yescomplemented
152#2066C2×C1112yescomplemented
153#1948C2×C1112yescomplemented
154#1927C2×C1112yescomplemented
155#1892C2×C1111yescharacteristic
156#1850C2×C1111yescharacteristic
157#1824C2×C1111yescharacteristic
158C23×C11—22no—
159C23×C11—22no—
160C23×C11#12112yes—
161C23×C11C2×SD1612yes—
162C23×C11#13712yes—
163C23×C11C22×D411yescharacteristic
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—48no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
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—84no—
194C2×C4×C11#12112yes—
195C2×C4×C11C2×SD1614yes—
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—
203C23×C8C22×C1111yescharacteristic
204C2×C22⋊Q8C22×C1111yescharacteristic
205C2×#117—21no—
206C22×C4⋊C4C22×C1111yescharacteristic
207C22×C4⋊C4C22×C1111yescharacteristic
208#483—24no—
209C2×#106—24no—
210C2×#106C22×C1111yescharacteristic
211C2×#106C22×C1111yescharacteristic
212C2×#106C22×C1112yes—
213C2×#106C22×C1112yes—
214C2×C4⋊C8C22×C1112yes—
215C2×#103C22×C1111yescharacteristic
216C2×#103C22×C1111yescharacteristic
217C2×#103C22×C1112yes—
218C2×C22⋊C8C22×C1111yescharacteristic
219#398—22no—
220#391C22×C1112yes—
221#389C22×C1112yes—
222#387—22no—
223#385—21no—
224#385—21no—
225#384C22×C1112yes—
226#381—21no—
227#380C22×C1111yescharacteristic
228C4×C4⋊C4C22×C1112yes—
229C4×C22⋊C4C22×C1111yescharacteristic
230#340C22×C1112yes—
231#340C22×C1112yes—
232#340C22×C1112yes—
233#336C22×C1112yes—
234C22×C11—24no—
235C22×C11—24no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11#46114yes—
239C22×C11C2×#12111yescharacteristic
240C22×C11#54712yes—
241C22×C11C22×SD1611yescharacteristic
242C22×C11C2×#13711yescharacteristic
243C22×C11#57712yes—
244C4×C11—24no—
245C4×C11—22no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—82no—
253C4×C11#52511yescharacteristic
254C4×C11#53611yescharacteristic
255C4×C11#55212yes—
256C22×Q8C23×C1111yescharacteristic
257C23×C4—21no—
258C23×C4—21no—
259C23×C4C23×C1111yescharacteristic
260C22×C8—22no—
261C22×C8—24no—
262C22×C8C23×C1111yescharacteristic
263C22×C8C23×C1111yescharacteristic
264C22×C8C23×C1112yes—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267#117—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4D4×C1114yes—
278C2×C4⋊C4C23×C1112yes—
279C2×C4⋊C4C23×C1111yescharacteristic
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1111yescharacteristic
282C2×C4⋊C4C23×C1111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4D4×C1111yescharacteristic
286C2×C22⋊C4D4×C1111yescharacteristic
287C2×C42—22no—
288C2×C42C23×C1112yes—
289#106—24no—
290#106—24no—
291#106—22no—
292#106—22no—
293C4⋊C8—24no—
294#103—24no—
295#103—22no—
296#103—22no—
297C22⋊C8—22no—
298#95—22no—
299#95—21no—
300#95—22no—
301#95—22no—
302#95—22no—
303#95D4×C1112yes—
304C2×C11—24no—
305C2×C11#241311yescharacteristic
306C2×C11C2×#46111yescharacteristic
307C2×C11#304311yescharacteristic
308C2×C11#333512yes—
309C2×C11#334412yes—
310C24C2×D4×C1111yescharacteristic
311C2×Q8—21no—
312C2×Q8—22no—
313C2×Q8—21no—
314C2×Q8—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—82no—
328C22×C4C2×D4×C1112yes—
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C2×D4×C1112yes—
331C22×C4C2×D4×C1112yes—
332C22×C4C11×#4112yes—
333C22×C4C24×C1111yescharacteristic
334C2×C8—28no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8C11×#4114yes—
342C4⋊C4—24no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—44no—
354C4⋊C4—82no—
355C4⋊C4—82no—
356C4⋊C4C2×D4×C1112yes—
357C4⋊C4C2×D4×C1112yes—
358C22⋊C4—22no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4C11×SD1614yes—
362C42—22no—
363C42—22no—
364C42—44no—
365C11#2458011yescharacteristic, direct product factor, Sylow
366C23—22no—
367C23—22no—
368C23C11×#12112yes—
369C23C2×C11×SD1612yes—
370C23C11×#13712yes—
371C23C22×D4×C1111yescharacteristic
372Q8—41no—
373Q8—41no—
374Q8—42no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—48no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—84no—
402C2×C4C11×#12112yes—
403C2×C4C2×C11×SD1614yes—
404C2×C4C22×D4×C1111yescharacteristic
405C2×C4C2×C11×#4112yes—
406C2×C4C2×C11×#4111yescharacteristic
407C2×C4C11×2−1+412yes—
408C8—24no—
409C8—41no—
410C8—41no—
411C22—22no—
412C22—22no—
413C22—24no—
414C22—24no—
415C22C11×#46114yes—
416C22C2×C11×#12111yescharacteristic
417C22C11×#54712yes—
418C22C22×C11×SD1611yescharacteristic
419C22C2×C11×#13711yescharacteristic
420C22C11×#57712yes—
421C4—22no—
422C4—24no—
423C4—42no—
424C4—42no—
425C4—42no—
426C4—81no—
427C4—82no—
428C4—81no—
429C4—82no—
430C4C11×#52511yescharacteristic
431C4C11×#53611yescharacteristic
432C4C11×#55212yes—
433C2—24no—
434C2C11×#241311yescharacteristic
435C2C2×C11×#46111yescharacteristic
436C2C11×#304311yescharacteristic
437C2C11×#333512yes—
438C2C11×#334412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
5. C11×#2084C2semidirect
6. C11×#2066C2semidirect
7. C11×#1948C2semidirect
8. C11×#1927C2semidirect
91. #24580C11direct (N × H)
151. #2084C2×C11semidirect
152. #2066C2×C11semidirect
153. #1948C2×C11semidirect
154. #1927C2×C11semidirect
365. C11#24580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C22×C11×#1062
C11×#25022
C11×#23442
C11×#20842
C11×#20662
C11×#19482
C11×#19272
C11×#18922
C11×#18502
C11×#18242
#2458011