Finite Group Databasebeta

← C11×#24997 #14602190

Subgroups — C11×#24997 #14602190

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2582C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic
3C11×#2101C212yesmaximal
4C11×#2074C212yesmaximal
5C11×#1984C211yesmaximal, characteristic
6C11×#1948C211yesmaximal, characteristic
7C11×#1927C212yesmaximal
8C11×#1919C212yesmaximal
9C11×#1834C211yesmaximal, characteristic
10C11×#1803C211yesmaximal, characteristic
11C4×C11×#103C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C11×#106C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103C2211yescharacteristic
17C2×C11×#103C2212yes—
18C2×C11×#103C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C11×#398—22no—
21C11×#391—21no—
22C11×#391—21no—
23C11×#391C2212yes—
24C11×#389—21no—
25C11×#389C2212yes—
26C11×#387—22no—
27C11×#384C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C11×#382C2212yes—
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×Q8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C4×Q8×C11—22no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—22no—
66C2×C42×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68C11×#106—24no—
69C11×C4⋊C8—22no—
70C11×#103—24no—
71C11×#103—22no—
72C11×#103—22no—
73C4×C8×C11—22no—
74C11×#95—22no—
75C11×#95—21no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#24997C1111yesmaximal, characteristic, direct product factor, Sylow
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11#4112yes—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11—22no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4—81no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4#4112yes—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—42no—
132C42×C11—42no—
133C42×C11—82no—
134C42×C11#4112yes—
135C42×C11#4112yes—
136#2582C2×C1111yescharacteristic
137#2355C2×C1111yescharacteristic
138#2101C2×C1112yes—
139#2074C2×C1112yes—
140#1984C2×C1111yescharacteristic
141#1948C2×C1111yescharacteristic
142#1927C2×C1112yes—
143#1919C2×C1112yes—
144#1834C2×C1111yescharacteristic
145#1803C2×C1111yescharacteristic
146C4×#103C2×C1111yescharacteristic
147C23×C11C22×D411yescharacteristic
148Q8×C11—22no—
149Q8×C11—22no—
150Q8×C11—41no—
151Q8×C11—41no—
152Q8×C11—44no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11#12312yes—
180C2×C4×C11#12312yes—
181C2×C4×C11#13512yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C112−1+411yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C8×C11—42no—
190C8×C11—41no—
191C8×C11—41no—
192C2×C4×Q8C22×C1111yescharacteristic
193C2×C4×Q8C22×C1111yescharacteristic
194C2×#106C22×C1112yes—
195C2×C4⋊C8C22×C1111yescharacteristic
196C2×#103C22×C1112yes—
197C2×#103C22×C1111yescharacteristic
198C2×#103C22×C1111yescharacteristic
199C2×C4×C8C22×C1111yescharacteristic
200#398—22no—
201#391—21no—
202#391—21no—
203#391C22×C1112yes—
204#389—21no—
205#389C22×C1112yes—
206#387—22no—
207#384C22×C1111yescharacteristic
208#384C22×C1111yescharacteristic
209#382C22×C1112yes—
210C4×C4⋊C4—21no—
211C4×C4⋊C4C22×C1112yes—
212C4×C4⋊C4C22×C1111yescharacteristic
213#340C22×C1112yes—
214#340C22×C1112yes—
215#340C22×C1112yes—
216#340C22×C1112yes—
217#340C22×C1111yescharacteristic
218#340C22×C1111yescharacteristic
219#336C22×C1112yes—
220#336C22×C1112yes—
221C22×C11C2×#12311yescharacteristic
222C22×C11#54811yescharacteristic
223C22×C11#54811yescharacteristic
224C22×C11C2×#13511yescharacteristic
225C22×C11C2×#13711yescharacteristic
226C22×C11#57711yescharacteristic
227C22×C11#57711yescharacteristic
228C4×C11—22no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11—82no—
235C4×C11—82no—
236C4×C11—81no—
237C4×C11#48514yes—
238C4×C11#52911yescharacteristic
239C4×C11#54111yescharacteristic
240C4×C11#55211yescharacteristic
241C4×C11#55611yescharacteristic
242C22×Q8D4×C1111yescharacteristic
243C22×Q8C23×C1111yescharacteristic
244C22×C8C23×C1111yescharacteristic
245C22×C8C23×C1111yescharacteristic
246C22×C8C23×C1112yes—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4D4×C1111yescharacteristic
258C2×C4⋊C4D4×C1112yes—
259C2×C4⋊C4C23×C1111yescharacteristic
260C2×C4⋊C4C23×C1111yescharacteristic
261C2×C4⋊C4C23×C1112yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1111yescharacteristic
264C2×C42—21no—
265C2×C42—21no—
266C2×C42—22no—
267C2×C42C23×C1112yes—
268C2×C42C23×C1111yescharacteristic
269#106—24no—
270C4⋊C8—22no—
271#103—24no—
272#103—22no—
273#103—22no—
274C4×C8—22no—
275#95—22no—
276#95—21no—
277#95—22no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282C2×C11#242111yescharacteristic
283C2×C11C2×#48511yescharacteristic
284C2×C11#309911yescharacteristic
285C2×C11#336511yescharacteristic
286C2×C11#336511yescharacteristic
287C2×C11#336911yescharacteristic
288C2×C11#337211yescharacteristic
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8C11×#4112yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4C2×D4×C1112yes—
305C22×C4C2×D4×C1112yes—
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C2×D4×C1111yescharacteristic
308C22×C4C24×C1111yescharacteristic
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C4⋊C4—22no—
319C4⋊C4—24no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—82no—
335C4⋊C4C11×#4112yes—
336C42—22no—
337C42—22no—
338C42—42no—
339C42—42no—
340C42—82no—
341C42C11×#4112yes—
342C42C11×#4112yes—
343C11#2499711yescharacteristic, direct product factor, Sylow
344C23C22×D4×C1111yescharacteristic
345Q8—22no—
346Q8—22no—
347Q8—41no—
348Q8—41no—
349Q8—44no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4C11×#12312yes—
377C2×C4C11×#12312yes—
378C2×C4C11×#13512yes—
379C2×C4C11×#13712yes—
380C2×C4C2×C11×#4111yescharacteristic
381C2×C4C2×C11×#4111yescharacteristic
382C2×C4C2×C11×#4111yescharacteristic
383C2×C4C2×C11×#4111yescharacteristic
384C2×C4C11×2−1+411yescharacteristic
385C2×C4C11×2−1+411yescharacteristic
386C8—42no—
387C8—41no—
388C8—41no—
389C22C2×C11×#12311yescharacteristic
390C22C11×#54811yescharacteristic
391C22C11×#54811yescharacteristic
392C22C2×C11×#13511yescharacteristic
393C22C2×C11×#13711yescharacteristic
394C22C11×#57711yescharacteristic
395C22C11×#57711yescharacteristic
396C4—22no—
397C4—42no—
398C4—42no—
399C4—42no—
400C4—42no—
401C4—81no—
402C4—82no—
403C4—82no—
404C4—81no—
405C4C11×#48514yes—
406C4C11×#52911yescharacteristic
407C4C11×#54111yescharacteristic
408C4C11×#55211yescharacteristic
409C4C11×#55611yescharacteristic
410C2C11×#242111yescharacteristic
411C2C2×C11×#48511yescharacteristic
412C2C11×#309911yescharacteristic
413C2C11×#336511yescharacteristic
414C2C11×#336511yescharacteristic
415C2C11×#336911yescharacteristic
416C2C11×#337211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
81. #24997C11direct (N × H)
343. C11#24997direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25822
C11×#23552
C11×#21012
C11×#20742
C11×#19842
C11×#19482
C11×#19272
C11×#19192
C11×#18342
C11×#18032
C4×C11×#1032
#2499711