Finite Group Databasebeta

← C11×#22567 #14599760

Subgroups — C11×#22567 #14599760

Order 2816.

962 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#103C211yesmaximal, characteristic
2C11×#2345C211yesmaximal, characteristic
3Q8×C11×C22⋊C4C211yesmaximal, characteristic
4C11×#1935C212yesmaximal, complemented
5C11×#1927C212yesmaximal, complemented
6C11×#1865C212yesmaximal, complemented
7C11×#1824C211yesmaximal, characteristic
8C11×#1807C211yesmaximal, characteristic
9C11×#1787C211yesmaximal, characteristic
10C11×#1763C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×C11×#106C2212yes—
17C2×C11×#103C418yescomplemented
18C2×C11×#103C2212yes—
19C2×C11×#103C2212yes—
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2212yes—
26C11×#391—22no—
27C11×#391C2212yes—
28C11×#389C2212yes—
29C11×#387—22no—
30C11×#380—21no—
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C11×#380C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C22⋊C4—21no—
36C4×C11×C22⋊C4—21no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11—42no—
53C22×C8×C11C2×C414yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C4×Q8×C11—24no—
58C4×Q8×C11—42no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C11×#106—42no—
76C11×#103—24no—
77C11×#103—42no—
78C11×#103C2×C414yes—
79C11×#103C2×C414yes—
80C11×#103C2×C414yes—
81C11×#103C2×C414yes—
82C11×C22⋊C8—22no—
83C11×#97—42no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—21no—
90C11×#95D412yes—
91#22567C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—28no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—44no—
101C2×Q8×C11—44no—
102C2×Q8×C11—48no—
103C2×Q8×C11C22×C412yes—
104C2×Q8×C11C22×C412yes—
105C2×Q8×C11#4114yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—44no—
117C22×C4×C11—82no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—44no—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—82no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C22×C412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—42no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—44no—
150C42×C11—82no—
151C22×#103C2×C1111yescharacteristic
152#2345C2×C1111yescharacteristic
153Q8×C22⋊C4C2×C1111yescharacteristic
154#1935C2×C1112yescomplemented
155#1927C2×C1112yescomplemented
156#1865C2×C1112yescomplemented
157#1824C2×C1111yescharacteristic
158#1807C2×C1111yescharacteristic
159#1787C2×C1111yescharacteristic
160#1763C2×C1112yescomplemented
161#1752C2×C1111yescharacteristic
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C4×D412yes—
165C23×C11#13712yes—
166C23×C11#13712yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—24no—
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—48no—
173Q8×C11—42no—
174Q8×C11#11714yes—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—48no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—84no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C2×#4112yes—
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)12yes—
206C8×C11—22no—
207C8×C11—22no—
208C8×C11—42no—
209C23×Q8C22×C1111yescharacteristic
210C23×C8C22×C1111yescharacteristic
211C2×C4×Q8C22×C1112yes—
212C22×C4⋊C4C22×C1111yescharacteristic
213C2×#106C22×C1112yes—
214C2×#103C4×C1118yescomplemented
215C2×#103C22×C1112yes—
216C2×#103C22×C1112yes—
217C2×#103C22×C1111yescharacteristic
218C2×#103C22×C1111yescharacteristic
219C2×#103C22×C1111yescharacteristic
220C2×#103C22×C1111yescharacteristic
221C2×C22⋊C8C22×C1111yescharacteristic
222C2×#97C22×C1112yes—
223#391—22no—
224#391C22×C1112yes—
225#389C22×C1112yes—
226#387—22no—
227#380—21no—
228#380—21no—
229#380C22×C1111yescharacteristic
230#380C22×C1111yescharacteristic
231C4×C4⋊C4C22×C1112yes—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—21no—
234C4×C22⋊C4C22×C1111yescharacteristic
235#340C22×C1112yes—
236#340C22×C1112yes—
237#340C22×C1112yes—
238#336C22×C1112yes—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11#44114yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54612yes—
246C22×C11C2×#13711yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—24no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11—82no—
258C4×C11C2×#11711yescharacteristic
259C4×C11#51811yescharacteristic
260C4×C11#55112yes—
261C22×Q8—21no—
262C22×Q8—22no—
263C22×Q8—24no—
264C22×Q8—42no—
265C22×Q8C2×C4×C1114yes—
266C22×Q8C23×C1111yescharacteristic
267C22×Q8C23×C1111yescharacteristic
268C23×C4—21no—
269C23×C4—21no—
270C23×C4C23×C1111yescharacteristic
271C22×C8—42no—
272C22×C8C2×C4×C1114yes—
273C22×C8C23×C1112yes—
274C22×C8C23×C1111yescharacteristic
275C22×C8C23×C1111yescharacteristic
276C4×Q8—24no—
277C4×Q8—42no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4C2×C4×C1114yes—
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1111yescharacteristic
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4D4×C1111yescharacteristic
290C2×C22⋊C4D4×C1111yescharacteristic
291C2×C42—22no—
292C2×C42—22no—
293C2×C42C23×C1112yes—
294#106—42no—
295#103—24no—
296#103—42no—
297#103C2×C4×C1114yes—
298#103C2×C4×C1114yes—
299#103C2×C4×C1114yes—
300#103C2×C4×C1114yes—
301C22⋊C8—22no—
302#97—42no—
303#95—22no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—21no—
308#95—21no—
309#95D4×C1112yes—
310C2×C11—24no—
311C2×C11#234211yescharacteristic
312C2×C11C2×#44111yescharacteristic
313C2×C11#294911yescharacteristic
314C2×C11#331612yes—
315C2×C11#332012yes—
316C24C2×D4×C1111yescharacteristic
317C2×Q8—24no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—28no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8—48no—
327C2×Q8C22×C4×C1112yes—
328C2×Q8C22×C4×C1112yes—
329C2×Q8C11×#4114yes—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—44no—
341C22×C4—82no—
342C22×C4C22×C4×C1112yes—
343C22×C4C2×D4×C1112yes—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C11×#4112yes—
347C22×C4C24×C1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—44no—
354C2×C8C22×C4×C1112yes—
355C2×C8C22×C4×C1112yes—
356C4⋊C4—24no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—44no—
364C4⋊C4—82no—
365C4⋊C4C22×C4×C1112yes—
366C4⋊C4C22×C4×C1112yes—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C42—22no—
372C42—22no—
373C42—44no—
374C42—82no—
375C11#2256711yescharacteristic, direct product factor, Sylow
376C23—22no—
377C23—22no—
378C23C4×D4×C1112yes—
379C23C11×#13712yes—
380C23C11×#13712yes—
381C23C22×D4×C1111yescharacteristic
382Q8—22no—
383Q8—24no—
384Q8—22no—
385Q8—22no—
386Q8—48no—
387Q8—42no—
388Q8C11×#11714yes—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—84no—
415C2×C4C4×D4×C1112yes—
416C2×C4C23×C4×C1111yescharacteristic
417C2×C4C2×C11×#4112yes—
418C2×C4C2×C11×#4111yescharacteristic
419C2×C4C11×H(5,𝔽2)12yes—
420C8—22no—
421C8—22no—
422C8—42no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22C11×#44114yes—
428C22C2×C4×D4×C1111yescharacteristic
429C22C11×#54612yes—
430C22C2×C11×#13711yescharacteristic
431C22C2×C11×#13711yescharacteristic
432C22C11×#57712yes—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—82no—
441C4—82no—
442C4C2×C11×#11711yescharacteristic
443C4C11×#51811yescharacteristic
444C4C11×#55112yes—
445C2—24no—
446C2C11×#234211yescharacteristic
447C2C2×C11×#44111yescharacteristic
448C2C11×#294911yescharacteristic
449C2C11×#331612yes—
450C2C11×#332012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×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
4. C11×#1935C2semidirect
5. C11×#1927C2semidirect
6. C11×#1865C2semidirect
10. C11×#1763C2semidirect
17. C2×C11×#103C4semidirect
91. #22567C11direct (N × H)
154. #1935C2×C11semidirect
155. #1927C2×C11semidirect
156. #1865C2×C11semidirect
160. #1763C2×C11semidirect
214. C2×#103C4×C11semidirect
375. C11#22567direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1032
C11×#23452
Q8×C11×C22⋊C42
C11×#19352
C11×#19272
C11×#18652
C11×#18242
C11×#18072
C11×#17872
C11×#17632
C11×#17522
#2256711