Finite Group Databasebeta

← C11×#24992 #14602185

Subgroups — C11×#24992 #14602185

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2538C211yesmaximal, characteristic
2Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C11×#2100C212yesmaximal, complemented
4C11×#2071C212yesmaximal
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal
8C11×#1919C212yesmaximal, complemented
9C11×#1834C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic
11C4×C11×#102C211yesmaximal, characteristic
12C2×C11×C22⋊Q8—21no—
13C2×C4×Q8×C11—21no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#106C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#396—22no—
23C11×#390C2212yes—
24C11×#389—21no—
25C11×#389—22no—
26C11×#389C2212yes—
27C11×#384C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C11×#384C2212yes—
30C11×#380—21no—
31C4×C11×C4⋊C4C2212yes—
32C4×C11×C4⋊C4C2211yescharacteristic
33C11×#340C2211yescharacteristic
34C11×#340C2212yes—
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2211yescharacteristic
39C11×#336C2212yes—
40C11×#336C2212yes—
41C22×Q8×C11D411yescharacteristic
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C11×C22⋊Q8—44no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—44no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#106—24no—
75C11×C4⋊C8—22no—
76C11×#102—24no—
77C11×#102—22no—
78C11×#102—22no—
79C4×C8×C11—22no—
80C11×#95—22no—
81C11×#95—21no—
82C11×#95—22no—
83#24992C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11SD1614yes—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11#4112yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—81no—
132C11×C4⋊C4—81no—
133C11×C4⋊C4—82no—
134C11×C4⋊C4#4112yes—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—82no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—44no—
141C42×C11—42no—
142C42×C11#4112yes—
143C42×C11#4112yes—
144#2538C2×C1111yescharacteristic
145Q8×C4⋊C4C2×C1111yescharacteristic, complemented
146#2100C2×C1112yescomplemented
147#2071C2×C1112yes—
148#1984C2×C1111yescharacteristic, complemented
149#1948C2×C1111yescharacteristic, complemented
150#1926C2×C1112yes—
151#1919C2×C1112yescomplemented
152#1834C2×C1111yescharacteristic, complemented
153#1802C2×C1111yescharacteristic
154C4×#102C2×C1111yescharacteristic
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C22×D411yescharacteristic
163Q8×C11—28no—
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—41no—
167D4×C11—41no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—84no—
191C2×C4×C11#12312yes—
192C2×C4×C11#12312yes—
193C2×C4×C11C2×SD1614yes—
194C2×C4×C11C2×SD1612yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C8×C11—42no—
203C8×C11—41no—
204C8×C11—41no—
205C2×C22⋊Q8—21no—
206C2×C4×Q8—21no—
207C2×C4×Q8C22×C1111yescharacteristic
208C2×C4×D4C22×C1111yescharacteristic
209C2×#106C22×C1112yes—
210C2×C4⋊C8C22×C1111yescharacteristic
211C2×#102C22×C1112yes—
212C2×#102C22×C1111yescharacteristic
213C2×#102C22×C1111yescharacteristic
214C2×C4×C8C22×C1111yescharacteristic
215#396—22no—
216#390C22×C1112yes—
217#389—21no—
218#389—22no—
219#389C22×C1112yes—
220#384C22×C1111yescharacteristic
221#384C22×C1112yes—
222#384C22×C1111yescharacteristic
223#380—21no—
224C4×C4⋊C4C22×C1112yes—
225C4×C4⋊C4C22×C1111yescharacteristic
226#340C22×C1112yes—
227#340C22×C1112yes—
228#340C22×C1112yes—
229#340C22×C1112yes—
230#340C22×C1111yescharacteristic
231#340C22×C1111yescharacteristic
232#336C22×C1112yes—
233#336C22×C1112yes—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11C2×#12311yescharacteristic
242C22×C11#54811yescharacteristic
243C22×C11#54811yescharacteristic
244C22×C11C22×SD1611yescharacteristic
245C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C11#57611yescharacteristic
247C22×C11#57811yescharacteristic
248C4×C11—24no—
249C4×C11—22no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—81no—
253C4×C11—82no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11#48114yes—
257C4×C11#52911yescharacteristic
258C4×C11#54111yescharacteristic
259C4×C11#55211yescharacteristic
260C4×C11#55611yescharacteristic
261C22×Q8D4×C1111yescharacteristic
262C22×D4C23×C1111yescharacteristic
263C23×C4—21no—
264C22×C8C23×C1111yescharacteristic
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1112yes—
267C22⋊Q8—44no—
268C4×Q8—22no—
269C4×Q8—22no—
270C4×Q8—44no—
271C4×D4—22no—
272C4×D4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4D4×C1111yescharacteristic
281C2×C4⋊C4D4×C1112yes—
282C2×C4⋊C4C23×C1111yescharacteristic
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1111yescharacteristic
285C2×C4⋊C4C23×C1112yes—
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C42—22no—
291C2×C42—21no—
292C2×C42C23×C1112yes—
293C2×C42C23×C1111yescharacteristic
294#106—24no—
295C4⋊C8—22no—
296#102—24no—
297#102—22no—
298#102—22no—
299C4×C8—22no—
300#95—22no—
301#95—21no—
302#95—22no—
303C2×C11—82no—
304C2×C11#242111yescharacteristic
305C2×C11C2×#48111yescharacteristic
306C2×C11#309811yescharacteristic
307C2×C11#335911yescharacteristic
308C2×C11#336211yescharacteristic
309C2×C11#336611yescharacteristic
310C2×C11#336711yescharacteristic
311C24—21no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8C11×SD1614yes—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4C11×#4112yes—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4C2×D4×C1112yes—
330C22×C4C2×D4×C1111yescharacteristic
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C24×C1111yescharacteristic
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—44no—
355C4⋊C4—42no—
356C4⋊C4—44no—
357C4⋊C4—42no—
358C4⋊C4—81no—
359C4⋊C4—81no—
360C4⋊C4—82no—
361C4⋊C4C11×#4112yes—
362C22⋊C4—42no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C42—22no—
366C42—22no—
367C42—44no—
368C42—42no—
369C42C11×#4112yes—
370C42C11×#4112yes—
371C11#2499211yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C22×D4×C1111yescharacteristic
380Q8—28no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—84no—
408C2×C4C11×#12312yes—
409C2×C4C11×#12312yes—
410C2×C4C2×C11×SD1614yes—
411C2×C4C2×C11×SD1612yes—
412C2×C4C11×AGL(1,ℤ/8)12yes—
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C2×C4C11×2−1+411yescharacteristic
419C8—42no—
420C8—41no—
421C8—41no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×C11×#12311yescharacteristic
430C22C11×#54811yescharacteristic
431C22C11×#54811yescharacteristic
432C22C22×C11×SD1611yescharacteristic
433C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
434C22C11×#57611yescharacteristic
435C22C11×#57811yescharacteristic
436C4—24no—
437C4—22no—
438C4—42no—
439C4—42no—
440C4—81no—
441C4—82no—
442C4—82no—
443C4—81no—
444C4C11×#48114yes—
445C4C11×#52911yescharacteristic
446C4C11×#54111yescharacteristic
447C4C11×#55211yescharacteristic
448C4C11×#55611yescharacteristic
449C2—82no—
450C2C11×#242111yescharacteristic
451C2C2×C11×#48111yescharacteristic
452C2C11×#309811yescharacteristic
453C2C11×#335911yescharacteristic
454C2C11×#336211yescharacteristic
455C2C11×#336611yescharacteristic
456C2C11×#336711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C11×C4⋊C4C2semidirect
3. C11×#2100C2semidirect
5. C11×#1984C2semidirect
6. C11×#1948C2semidirect
8. C11×#1919C2semidirect
9. C11×#1834C2semidirect
83. #24992C11direct (N × H)
145. Q8×C4⋊C4C2×C11semidirect
146. #2100C2×C11semidirect
148. #1984C2×C11semidirect
149. #1948C2×C11semidirect
151. #1919C2×C11semidirect
152. #1834C2×C11semidirect
371. C11#24992direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25382
Q8×C11×C4⋊C42
C11×#21002
C11×#20712
C11×#19842
C11×#19482
C11×#19262
C11×#19192
C11×#18342
C11×#18022
C4×C11×#1022
#2499211