Finite Group Databasebeta

← C11×#24991 #14602184

Subgroups — C11×#24991 #14602184

Order 2816.

706 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
1C11×#2538C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic, complemented
3C11×#2101C212yesmaximal, complemented
4C11×#2073C212yesmaximal
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1926C212yesmaximal
8C11×#1920C212yesmaximal, complemented
9C11×#1834C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic
11C4×C11×#102C211yesmaximal, characteristic
12C2×C11×C22⋊Q8—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#106C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102C2211yescharacteristic
18C2×C11×#102C2212yes—
19C2×C11×#102C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#396—22no—
22C11×#391—21no—
23C11×#390C2212yes—
24C11×#389C2212yes—
25C11×#387—22no—
26C11×#384C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C11×#382C2212yes—
29C11×#380—21no—
30C4×C11×C4⋊C4—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×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—21no—
68C2×C42×C11—22no—
69C2×C42×C11C2312yes—
70C2×C42×C11C2311yescharacteristic
71C11×#106—24no—
72C11×C4⋊C8—22no—
73C11×#102—24no—
74C11×#102—22no—
75C11×#102—22no—
76C4×C8×C11—22no—
77C11×#95—22no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#24991C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11#4112yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—22no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—81no—
130C11×C4⋊C4—81no—
131C11×C4⋊C4#4112yes—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—82no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—42no—
138C42×C11—82no—
139C42×C11#4112yes—
140C42×C11#4112yes—
141#2538C2×C1111yescharacteristic
142#2355C2×C1111yescharacteristic, complemented
143#2101C2×C1112yescomplemented
144#2073C2×C1112yes—
145#1984C2×C1111yescharacteristic, complemented
146#1948C2×C1111yescharacteristic, complemented
147#1926C2×C1112yes—
148#1920C2×C1112yescomplemented
149#1834C2×C1111yescharacteristic, complemented
150#1802C2×C1111yescharacteristic
151C4×#102C2×C1111yescharacteristic
152C23×C11—22no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11C22×D411yescharacteristic
160Q8×C11—44no—
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—41no—
164D4×C11—41no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—84no—
189C2×C4×C11#12312yes—
190C2×C4×C11#12312yes—
191C2×C4×C11#13512yes—
192C2×C4×C11AGL(1,ℤ/8)12yes—
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C8×C11—42no—
200C8×C11—41no—
201C8×C11—41no—
202C2×C22⋊Q8—21no—
203C2×C4×Q8C22×C1111yescharacteristic
204C2×C4×D4C22×C1111yescharacteristic
205C2×#106C22×C1112yes—
206C2×C4⋊C8C22×C1111yescharacteristic
207C2×#102C22×C1112yes—
208C2×#102C22×C1111yescharacteristic
209C2×#102C22×C1111yescharacteristic
210C2×C4×C8C22×C1111yescharacteristic
211#396—22no—
212#391—21no—
213#390C22×C1112yes—
214#389C22×C1112yes—
215#387—22no—
216#384C22×C1111yescharacteristic
217#384C22×C1111yescharacteristic
218#382C22×C1112yes—
219#380—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4C22×C1112yes—
222C4×C4⋊C4C22×C1111yescharacteristic
223#340C22×C1112yes—
224#340C22×C1112yes—
225#340C22×C1112yes—
226#340C22×C1112yes—
227#340C22×C1111yescharacteristic
228#340C22×C1111yescharacteristic
229#336C22×C1112yes—
230#336C22×C1112yes—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C2×#12311yescharacteristic
239C22×C11#54811yescharacteristic
240C22×C11#54811yescharacteristic
241C22×C11C2×#13511yescharacteristic
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C11#57711yescharacteristic
244C22×C11#57711yescharacteristic
245C4×C11—22no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—82no—
252C4×C11—82no—
253C4×C11#48214yes—
254C4×C11#52911yescharacteristic
255C4×C11#54111yescharacteristic
256C4×C11#55211yescharacteristic
257C4×C11#55611yescharacteristic
258C22×Q8D4×C1111yescharacteristic
259C22×D4C23×C1111yescharacteristic
260C23×C4—21no—
261C22×C8C23×C1111yescharacteristic
262C22×C8C23×C1111yescharacteristic
263C22×C8C23×C1112yes—
264C22⋊Q8—44no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×D4—22no—
268C4×D4—22no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1111yescharacteristic
275C2×C4⋊C4D4×C1112yes—
276C2×C4⋊C4C23×C1111yescharacteristic
277C2×C4⋊C4C23×C1111yescharacteristic
278C2×C4⋊C4C23×C1112yes—
279C2×C4⋊C4C23×C1112yes—
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C42—21no—
285C2×C42—22no—
286C2×C42C23×C1112yes—
287C2×C42C23×C1111yescharacteristic
288#106—24no—
289C4⋊C8—22no—
290#102—24no—
291#102—22no—
292#102—22no—
293C4×C8—22no—
294#95—22no—
295#95—21no—
296#95—22no—
297#95—22no—
298#95—22no—
299C2×C11—82no—
300C2×C11#242111yescharacteristic
301C2×C11C2×#48211yescharacteristic
302C2×C11#309911yescharacteristic
303C2×C11#336011yescharacteristic
304C2×C11#336011yescharacteristic
305C2×C11#336811yescharacteristic
306C2×C11#337311yescharacteristic
307C24—21no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4C11×#4112yes—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4C2×D4×C1112yes—
326C22×C4C2×D4×C1112yes—
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C24×C1111yescharacteristic
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—44no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—81no—
354C4⋊C4—81no—
355C4⋊C4C11×#4112yes—
356C22⋊C4—44no—
357C22⋊C4—42no—
358C22⋊C4—82no—
359C42—22no—
360C42—22no—
361C42—42no—
362C42—82no—
363C42C11×#4112yes—
364C42C11×#4112yes—
365C11#2499111yescharacteristic, direct product factor, Sylow
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23C22×D4×C1111yescharacteristic
374Q8—44no—
375D4—22no—
376D4—22no—
377D4—41no—
378D4—41no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—84no—
403C2×C4C11×#12312yes—
404C2×C4C11×#12312yes—
405C2×C4C11×#13512yes—
406C2×C4C11×AGL(1,ℤ/8)12yes—
407C2×C4C2×C11×#4111yescharacteristic
408C2×C4C2×C11×#4111yescharacteristic
409C2×C4C2×C11×#4111yescharacteristic
410C2×C4C2×C11×#4111yescharacteristic
411C2×C4C11×2−1+411yescharacteristic
412C2×C4C11×2−1+411yescharacteristic
413C8—42no—
414C8—41no—
415C8—41no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C2×C11×#12311yescharacteristic
424C22C11×#54811yescharacteristic
425C22C11×#54811yescharacteristic
426C22C2×C11×#13511yescharacteristic
427C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
428C22C11×#57711yescharacteristic
429C22C11×#57711yescharacteristic
430C4—22no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—82no—
437C4—82no—
438C4C11×#48214yes—
439C4C11×#52911yescharacteristic
440C4C11×#54111yescharacteristic
441C4C11×#55211yescharacteristic
442C4C11×#55611yescharacteristic
443C2—82no—
444C2C11×#242111yescharacteristic
445C2C2×C11×#48211yescharacteristic
446C2C11×#309911yescharacteristic
447C2C11×#336011yescharacteristic
448C2C11×#336011yescharacteristic
449C2C11×#336811yescharacteristic
450C2C11×#337311yescharacteristic
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. C11×#2355C2semidirect
3. C11×#2101C2semidirect
5. C11×#1984C2semidirect
6. C11×#1948C2semidirect
8. C11×#1920C2semidirect
9. C11×#1834C2semidirect
82. #24991C11direct (N × H)
142. #2355C2×C11semidirect
143. #2101C2×C11semidirect
145. #1984C2×C11semidirect
146. #1948C2×C11semidirect
148. #1920C2×C11semidirect
149. #1834C2×C11semidirect
365. C11#24991direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25382
C11×#23552
C11×#21012
C11×#20732
C11×#19842
C11×#19482
C11×#19262
C11×#19202
C11×#18342
C11×#18022
C4×C11×#1022
#2499111