Finite Group Databasebeta

← C11×#24994 #14602187

Subgroups — C11×#24994 #14602187

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2582C211yesmaximal, characteristic
2Q8×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2099C212yesmaximal
4C11×#2072C212yesmaximal
5C11×#1984C211yesmaximal, characteristic
6C11×#1948C211yesmaximal, characteristic
7C11×#1927C212yesmaximal
8C11×#1920C212yesmaximal
9C11×#1834C211yesmaximal, characteristic
10C11×#1803C211yesmaximal, characteristic
11C4×C11×#103C211yesmaximal, characteristic
12C2×C4×Q8×C11—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C11×#106C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103C2211yescharacteristic
18C2×C11×#103C2212yes—
19C2×C11×#103C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#398—22no—
22C11×#391—21no—
23C11×#391C2212yes—
24C11×#389—21no—
25C11×#389—21no—
26C11×#389—22no—
27C11×#389C2212yes—
28C11×#384C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C11×#384C2212yes—
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—
50C4×Q8×C11—44no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—22no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11C2312yes—
70C2×C42×C11C2311yescharacteristic
71C11×#106—24no—
72C11×C4⋊C8—22no—
73C11×#103—24no—
74C11×#103—22no—
75C11×#103—22no—
76C4×C8×C11—22no—
77C11×#95—22no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#24994C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11SD1614yes—
91C2×Q8×C11#4112yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—22no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—81no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4—82no—
130C11×C4⋊C4—82no—
131C11×C4⋊C4#4112yes—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—42no—
135C42×C11—44no—
136C42×C11—42no—
137C42×C11#4112yes—
138C42×C11#4112yes—
139#2582C2×C1111yescharacteristic
140Q8×C4⋊C4C2×C1111yescharacteristic
141#2099C2×C1112yes—
142#2072C2×C1112yes—
143#1984C2×C1111yescharacteristic
144#1948C2×C1111yescharacteristic
145#1927C2×C1112yes—
146#1920C2×C1112yes—
147#1834C2×C1111yescharacteristic
148#1803C2×C1111yescharacteristic
149C4×#103C2×C1111yescharacteristic
150C23×C11C22×D411yescharacteristic
151Q8×C11—28no—
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—41no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11#12312yes—
182C2×C4×C11#12312yes—
183C2×C4×C11C2×SD1614yes—
184C2×C4×C11C2×SD1612yes—
185C2×C4×C11#13712yes—
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C8×C11—42no—
193C8×C11—41no—
194C8×C11—41no—
195C2×C4×Q8—21no—
196C2×C4×Q8C22×C1111yescharacteristic
197C2×C4×Q8C22×C1111yescharacteristic
198C2×#106C22×C1112yes—
199C2×C4⋊C8C22×C1111yescharacteristic
200C2×#103C22×C1112yes—
201C2×#103C22×C1111yescharacteristic
202C2×#103C22×C1111yescharacteristic
203C2×C4×C8C22×C1111yescharacteristic
204#398—22no—
205#391—21no—
206#391C22×C1112yes—
207#389—21no—
208#389—21no—
209#389—22no—
210#389C22×C1112yes—
211#384C22×C1111yescharacteristic
212#384C22×C1111yescharacteristic
213#384C22×C1112yes—
214C4×C4⋊C4C22×C1112yes—
215C4×C4⋊C4C22×C1111yescharacteristic
216#340C22×C1112yes—
217#340C22×C1112yes—
218#340C22×C1112yes—
219#340C22×C1112yes—
220#340C22×C1111yescharacteristic
221#340C22×C1111yescharacteristic
222#336C22×C1112yes—
223#336C22×C1112yes—
224C22×C11C2×#12311yescharacteristic
225C22×C11#54811yescharacteristic
226C22×C11#54811yescharacteristic
227C22×C11C22×SD1611yescharacteristic
228C22×C11C2×#13711yescharacteristic
229C22×C11#57611yescharacteristic
230C22×C11#57811yescharacteristic
231C4×C11—24no—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—81no—
237C4×C11—82no—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11#48314yes—
241C4×C11#52911yescharacteristic
242C4×C11#54111yescharacteristic
243C4×C11#55211yescharacteristic
244C4×C11#55611yescharacteristic
245C22×Q8D4×C1111yescharacteristic
246C22×Q8C23×C1111yescharacteristic
247C22×C8C23×C1111yescharacteristic
248C22×C8C23×C1111yescharacteristic
249C22×C8C23×C1112yes—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×Q8—22no—
253C4×Q8—22no—
254C4×Q8—44no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4D4×C1111yescharacteristic
264C2×C4⋊C4D4×C1112yes—
265C2×C4⋊C4C23×C1111yescharacteristic
266C2×C4⋊C4C23×C1112yes—
267C2×C4⋊C4C23×C1111yescharacteristic
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1111yescharacteristic
270C2×C42—22no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C23×C1112yes—
274C2×C42C23×C1111yescharacteristic
275#106—24no—
276C4⋊C8—22no—
277#103—24no—
278#103—22no—
279#103—22no—
280C4×C8—22no—
281#95—22no—
282#95—21no—
283#95—22no—
284#95—22no—
285#95—22no—
286C2×C11#242111yescharacteristic
287C2×C11C2×#48311yescharacteristic
288C2×C11#309811yescharacteristic
289C2×C11#335911yescharacteristic
290C2×C11#336211yescharacteristic
291C2×C11#337411yescharacteristic
292C2×C11#337511yescharacteristic
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8C11×SD1614yes—
301C2×Q8C11×#4112yes—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4C2×D4×C1112yes—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C24×C1111yescharacteristic
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—21no—
321C2×C8—21no—
322C4⋊C4—24no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—42no—
334C4⋊C4—44no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—81no—
338C4⋊C4—81no—
339C4⋊C4—82no—
340C4⋊C4—82no—
341C4⋊C4C11×#4112yes—
342C42—22no—
343C42—22no—
344C42—42no—
345C42—44no—
346C42—42no—
347C42C11×#4112yes—
348C42C11×#4112yes—
349C11#2499411yescharacteristic, direct product factor, Sylow
350C23C22×D4×C1111yescharacteristic
351Q8—28no—
352Q8—22no—
353Q8—22no—
354Q8—41no—
355Q8—41no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4C11×#12312yes—
382C2×C4C11×#12312yes—
383C2×C4C2×C11×SD1614yes—
384C2×C4C2×C11×SD1612yes—
385C2×C4C11×#13712yes—
386C2×C4C2×C11×#4111yescharacteristic
387C2×C4C2×C11×#4111yescharacteristic
388C2×C4C2×C11×#4111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C2×C4C11×2−1+411yescharacteristic
391C2×C4C11×2−1+411yescharacteristic
392C8—42no—
393C8—41no—
394C8—41no—
395C22C2×C11×#12311yescharacteristic
396C22C11×#54811yescharacteristic
397C22C11×#54811yescharacteristic
398C22C22×C11×SD1611yescharacteristic
399C22C2×C11×#13711yescharacteristic
400C22C11×#57611yescharacteristic
401C22C11×#57811yescharacteristic
402C4—24no—
403C4—22no—
404C4—42no—
405C4—42no—
406C4—42no—
407C4—81no—
408C4—82no—
409C4—81no—
410C4—82no—
411C4C11×#48314yes—
412C4C11×#52911yescharacteristic
413C4C11×#54111yescharacteristic
414C4C11×#55211yescharacteristic
415C4C11×#55611yescharacteristic
416C2C11×#242111yescharacteristic
417C2C2×C11×#48311yescharacteristic
418C2C11×#309811yescharacteristic
419C2C11×#335911yescharacteristic
420C2C11×#336211yescharacteristic
421C2C11×#337411yescharacteristic
422C2C11×#337511yescharacteristic
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
82. #24994C11direct (N × H)
349. C11#24994direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25822
Q8×C11×C4⋊C42
C11×#20992
C11×#20722
C11×#19842
C11×#19482
C11×#19272
C11×#19202
C11×#18342
C11×#18032
C4×C11×#1032
#2499411