Finite Group Databasebeta

← C11×#22267 #14599460

Subgroups — C11×#22267 #14599460

Order 2816.

994 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×#435C212yesmaximal, complemented
2C11×#2397C211yesmaximal, characteristic
3C11×#1954C212yesmaximal, complemented
4C11×#1870C212yesmaximal, complemented
5C11×#1870C212yesmaximal, complemented
6C11×#1869C212yesmaximal, complemented
7C11×#1869C212yesmaximal, complemented
8C11×#1832C211yesmaximal, characteristic, complemented
9C11×#1746C211yesmaximal, characteristic, complemented
10C22×C11×M16C2212yes—
11C23×C8×C11C2212yes—
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C11×#435—28no—
17C2×C11×C4⋊C8C2212yes—
18C2×C11×C22⋊C8C2212yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#399C412yes—
27C11×#399C412yes—
28C11×#392C412yes—
29C11×#392C412yes—
30C11×#376C2211yescharacteristic
31C11×#336C2211yescharacteristic
32C11×#336C2212yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C11×#336C2211yescharacteristic
36C22×D4×C11C2×C411yescharacteristic
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C2×C11×M16—24no—
43C2×C11×M16—42no—
44C2×C11×M16—42no—
45C22×C8×C11—24no—
46C22×C8×C11—42no—
47C22×C8×C11—42no—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C4×D4×C11—24no—
53C4×D4×C11—24no—
54C4×D4×C11—42no—
55C4×D4×C11—42no—
56C4×D4×C11—42no—
57C4×D4×C11—42no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C412yes—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C412yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C11×C4⋊C8—24no—
72C11×C22⋊C8—24no—
73C11×C22⋊C8—24no—
74C11×C22⋊C8—42no—
75C11×C22⋊C8—42no—
76C11×C22⋊C8—42no—
77C11×C22⋊C8—42no—
78C11×#97D414yescomplemented
79C4×C8×C11—22no—
80C11×#95C2×C412yes—
81C11×#95C2×C412yes—
82#22267C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11C22×C412yes—
84C24×C11C22×C412yes—
85C2×D4×C11—24no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—24no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2411yescharacteristic
114C11×M16—48no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—48no—
127C2×C8×C11C2×D414yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—42no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142C2×#435C2×C1112yescomplemented
143#2397C2×C1111yescharacteristic
144#1954C2×C1112yescomplemented
145#1870C2×C1112yescomplemented
146#1870C2×C1112yescomplemented
147#1869C2×C1112yescomplemented
148#1869C2×C1112yescomplemented
149#1832C2×C1111yescharacteristic, complemented
150#1746C2×C1111yescharacteristic, complemented
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11#13114yes—
165C23×C11C23×C411yescharacteristic
166D4×C11—48no—
167D4×C11—44no—
168D4×C11—48no—
169D4×C11—44no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
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—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C4×D414yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)12yes—
197C2×C4×C11H(5,𝔽2)12yes—
198C8×C11—24no—
199C8×C11—42no—
200C8×C11—42no—
201C8×C11—42no—
202C22×M16C22×C1112yes—
203C23×C8C22×C1112yes—
204C2×C4×D4C22×C1112yes—
205C2×C4×D4C22×C1111yescharacteristic
206C2×C4×D4C22×C1112yes—
207C2×C4×D4C22×C1111yescharacteristic
208#435—28no—
209C2×C4⋊C8C22×C1112yes—
210C2×C22⋊C8C22×C1112yes—
211C2×C22⋊C8C22×C1112yes—
212C2×C22⋊C8C22×C1112yes—
213C2×C22⋊C8C22×C1112yes—
214C2×C22⋊C8C22×C1112yes—
215C2×C22⋊C8C22×C1112yes—
216C2×#97C22×C1111yescharacteristic
217C2×C4×C8C22×C1111yescharacteristic
218#399C4×C1112yes—
219#399C4×C1112yes—
220#392C4×C1112yes—
221#392C4×C1112yes—
222#376C22×C1111yescharacteristic
223#336C22×C1111yescharacteristic
224#336C22×C1112yes—
225#336C22×C1111yescharacteristic
226#336C22×C1112yes—
227#336C22×C1112yes—
228C22×C11—24no—
229C22×C11—24no—
230C22×C11—24no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11#51811yescharacteristic
244C22×C11#51811yescharacteristic
245C22×C11C2×#13112yes—
246C22×C11#56812yes—
247C4×C11—24no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—41no—
252C4×C11—41no—
253C4×C11#53512yes—
254C4×C11#54012yes—
255C22×D4C2×C4×C1111yescharacteristic
256C22×D4C2×C4×C1112yes—
257C22×D4C2×C4×C1112yes—
258C22×D4C2×C4×C1111yescharacteristic
259C23×C4C23×C1112yes—
260C23×C4C23×C1112yes—
261C2×M16—24no—
262C2×M16—42no—
263C2×M16—42no—
264C22×C8—24no—
265C22×C8—42no—
266C22×C8—42no—
267C22×C8C23×C1112yes—
268C22×C8C23×C1112yes—
269C22×C8C23×C1112yes—
270C22×C8C23×C1112yes—
271C4×D4—24no—
272C4×D4—24no—
273C4×D4—42no—
274C4×D4—42no—
275C4×D4—42no—
276C4×D4—42no—
277C2×C4⋊C4C2×C4×C1112yes—
278C2×C4⋊C4C2×C4×C1111yescharacteristic
279C2×C4⋊C4C2×C4×C1112yes—
280C2×C4⋊C4C2×C4×C1111yescharacteristic
281C2×C22⋊C4C2×C4×C1112yes—
282C2×C22⋊C4C2×C4×C1112yes—
283C2×C22⋊C4C2×C4×C1112yes—
284C2×C22⋊C4C2×C4×C1112yes—
285C2×C22⋊C4C2×C4×C1112yes—
286C2×C22⋊C4C2×C4×C1112yes—
287C2×C42C23×C1111yescharacteristic
288C2×C42C23×C1111yescharacteristic
289C2×C42C23×C1111yescharacteristic
290C4⋊C8—24no—
291C22⋊C8—24no—
292C22⋊C8—24no—
293C22⋊C8—42no—
294C22⋊C8—42no—
295C22⋊C8—42no—
296C22⋊C8—42no—
297#97D4×C1114yescomplemented
298C4×C8—22no—
299#95C2×C4×C1112yes—
300#95C2×C4×C1112yes—
301C2×C11—44no—
302C2×C11—82no—
303C2×C11#232811yescharacteristic
304C2×C11#293312yes—
305C2×C11#297612yes—
306C2×C11#297711yescharacteristic
307C2×C11#297811yescharacteristic
308C24C22×C4×C1112yes—
309C24C22×C4×C1112yes—
310C2×D4—24no—
311C2×D4—24no—
312C2×D4—24no—
313C2×D4—24no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—42no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4C22×C4×C1111yescharacteristic
333C22×C4C22×C4×C1112yes—
334C22×C4C22×C4×C1111yescharacteristic
335C22×C4C22×C4×C1112yes—
336C22×C4C22×C4×C1112yes—
337C22×C4C22×C4×C1112yes—
338C22×C4C24×C1111yescharacteristic
339M16—48no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—48no—
352C2×C8C2×D4×C1114yes—
353C4⋊C4—24no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—22no—
364C42—22no—
365C42C2×D4×C1112yes—
366C42C11×#4112yes—
367C11#2226711yescharacteristic, direct product factor, Sylow
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23C11×#13114yes—
382C23C23×C4×C1111yescharacteristic
383D4—48no—
384D4—44no—
385D4—48no—
386D4—44no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4C4×D4×C1114yes—
411C2×C4C22×D4×C1111yescharacteristic
412C2×C4C2×C11×#4111yescharacteristic
413C2×C4C11×H(5,𝔽2)12yes—
414C2×C4C11×H(5,𝔽2)12yes—
415C8—24no—
416C8—42no—
417C8—42no—
418C8—42no—
419C22—24no—
420C22—24no—
421C22—24no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22C2×C4×D4×C1111yescharacteristic
434C22C11×#51811yescharacteristic
435C22C11×#51811yescharacteristic
436C22C2×C11×#13112yes—
437C22C11×#56812yes—
438C4—24no—
439C4—42no—
440C4—41no—
441C4—41no—
442C4—42no—
443C4—42no—
444C4C11×#53512yes—
445C4C11×#54012yes—
446C2—44no—
447C2—82no—
448C2C11×#232811yescharacteristic
449C2C11×#293312yes—
450C2C11×#297612yes—
451C2C11×#297711yescharacteristic
452C2C11×#297811yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#2397C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
3. C11×#1954C2semidirect
4. C11×#1870C2semidirect
5. C11×#1870C2semidirect
6. C11×#1869C2semidirect
7. C11×#1869C2semidirect
8. C11×#1832C2semidirect
9. C11×#1746C2semidirect
78. C11×#97D4semidirect
82. #22267C11direct (N × H)
142. C2×#435C2×C11semidirect
144. #1954C2×C11semidirect
145. #1870C2×C11semidirect
146. #1870C2×C11semidirect
147. #1869C2×C11semidirect
148. #1869C2×C11semidirect
149. #1832C2×C11semidirect
150. #1746C2×C11semidirect
297. #97D4×C11semidirect
367. C11#22267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C11×#23972
C11×#19542
C11×#18702
C11×#18692
C11×#18322
C11×#17462
#2226711