Finite Group Databasebeta

← C11×#22831 #14600024

Subgroups — C11×#22831 #14600024

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2295C211yesmaximal, characteristic
2C11×#1985C212yesmaximal
3C11×#1917C212yesmaximal
4C11×#1916C212yesmaximal
5C11×#1840C212yesmaximal
6C11×#1831C211yesmaximal, characteristic
7C11×#1771C212yesmaximal
8C11×#1767C211yesmaximal, characteristic
9C11×#1746C212yesmaximal
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×#97C2212yes—
14C2×C11×#97C2212yes—
15C2×C4×C8×C11C2212yes—
16C11×#391C411yescharacteristic
17C11×#391C411yescharacteristic
18C11×#389C411yescharacteristic
19C11×#389C411yescharacteristic
20C11×#387C412yes—
21C11×#387C412yes—
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C11×#376C2212yes—
25C43×C11C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C11×#336C2212yes—
28C11×#336C2212yes—
29C11×#336C2212yes—
30C11×#336C2211yescharacteristic
31C11×#336C2212yes—
32C11×#336C2212yes—
33C11×#336C2212yes—
34C11×#336C2211yescharacteristic
35C11×#336C2212yes—
36C11×#336C2211yescharacteristic
37C22×Q8×C11C2×C411yescharacteristic
38C22×C8×C11C2312yes—
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C11×C4⋊C8—24no—
60C11×C4⋊C8—24no—
61C11×#97—24no—
62C11×#97—24no—
63C4×C8×C11—24no—
64C11×#95C2×C412yes—
65C11×#95C2×C412yes—
66C11×#95C2×C412yes—
67C11×#95C2×C412yes—
68C11×#95C2×C412yes—
69C11×#95C2×C412yes—
70C11×#95C2×C412yes—
71#22831C1111yesmaximal, characteristic, direct product factor, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C412yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11#4114yes—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11#4112yes—
115C42×C11#4112yes—
116#2295C2×C1111yescharacteristic
117#1985C2×C1112yes—
118#1917C2×C1112yes—
119#1916C2×C1112yes—
120#1840C2×C1112yes—
121#1831C2×C1111yescharacteristic
122#1771C2×C1112yes—
123#1767C2×C1111yescharacteristic
124#1746C2×C1112yes—
125C23×C11C23×C411yescharacteristic
126Q8×C11—44no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11#11712yes—
155C2×C4×C11#11712yes—
156C2×C4×C11#13112yes—
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4112yes—
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C112−1+412yes—
161C8×C11—24no—
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—42no—
165C2×C4×Q8C22×C1111yescharacteristic
166C2×C4⋊C8C22×C1112yes—
167C2×C4⋊C8C22×C1112yes—
168C2×#97C22×C1112yes—
169C2×#97C22×C1112yes—
170C2×C4×C8C22×C1112yes—
171#391C4×C1111yescharacteristic
172#391C4×C1111yescharacteristic
173#389C4×C1111yescharacteristic
174#389C4×C1111yescharacteristic
175#387C4×C1112yes—
176#387C4×C1112yes—
177C4×C4⋊C4C22×C1112yes—
178C4×C4⋊C4C22×C1111yescharacteristic
179#376C22×C1112yes—
180C43C22×C1111yescharacteristic
181#336C22×C1112yes—
182#336C22×C1111yescharacteristic
183#336C22×C1111yescharacteristic
184#336C22×C1111yescharacteristic
185#336C22×C1112yes—
186#336C22×C1112yes—
187#336C22×C1112yes—
188#336C22×C1112yes—
189#336C22×C1112yes—
190#336C22×C1112yes—
191#336C22×C1111yescharacteristic
192C22×C11C2×#11711yescharacteristic
193C22×C11C4×#4111yescharacteristic
194C22×C11#51911yescharacteristic
195C22×C11C2×#13111yescharacteristic
196C22×C11#56811yescharacteristic
197C22×C11#56811yescharacteristic
198C22×C11#56811yescharacteristic
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11—42no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11#55212yes—
210C4×C11#55612yes—
211C22×Q8C2×C4×C1111yescharacteristic
212C22×C8C23×C1112yes—
213C22×C8C23×C1112yes—
214C22×C8C23×C1112yes—
215C22×C8C23×C1112yes—
216C4×Q8—22no—
217C4×Q8—22no—
218C2×C4⋊C4C2×C4×C1112yes—
219C2×C4⋊C4C2×C4×C1111yescharacteristic
220C2×C4⋊C4C2×C4×C1112yes—
221C2×C4⋊C4C2×C4×C1112yes—
222C2×C4⋊C4C2×C4×C1111yescharacteristic
223C2×C4⋊C4C2×C4×C1111yescharacteristic
224C2×C42C2×C4×C1111yescharacteristic
225C2×C42C2×C4×C1111yescharacteristic
226C2×C42C2×C4×C1111yescharacteristic
227C2×C42C2×C4×C1111yescharacteristic
228C2×C42C23×C1112yes—
229C2×C42C23×C1111yescharacteristic
230C2×C42C23×C1111yescharacteristic
231C2×C42C23×C1112yes—
232C2×C42C23×C1111yescharacteristic
233C4⋊C8—24no—
234C4⋊C8—24no—
235#97—24no—
236#97—24no—
237C4×C8—24no—
238#95C2×C4×C1112yes—
239#95C2×C4×C1112yes—
240#95C2×C4×C1112yes—
241#95C2×C4×C1112yes—
242#95C2×C4×C1112yes—
243#95C2×C4×C1112yes—
244#95C2×C4×C1112yes—
245C2×C11#235611yescharacteristic
246C2×C11#292111yescharacteristic
247C2×C11#292511yescharacteristic
248C2×C11#296711yescharacteristic
249C2×C11#296811yescharacteristic
250C2×C11#298511yescharacteristic
251C2×C11#298711yescharacteristic
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C22×C4C22×C4×C1111yescharacteristic
256C22×C4C22×C4×C1111yescharacteristic
257C22×C4C22×C4×C1112yes—
258C22×C4C22×C4×C1112yes—
259C22×C4C22×C4×C1112yes—
260C22×C4C22×C4×C1111yescharacteristic
261C22×C4C22×C4×C1112yes—
262C22×C4C22×C4×C1111yescharacteristic
263C22×C4C22×C4×C1111yescharacteristic
264C22×C4C22×C4×C1111yescharacteristic
265C22×C4C24×C1111yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8C11×#4114yes—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C42—41no—
294C42C11×#4112yes—
295C42C11×#4112yes—
296C11#2283111yescharacteristic, direct product factor, Sylow
297C23C23×C4×C1111yescharacteristic
298Q8—44no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4C11×#11712yes—
327C2×C4C11×#11712yes—
328C2×C4C11×#13112yes—
329C2×C4C2×C11×#4111yescharacteristic
330C2×C4C2×C11×#4112yes—
331C2×C4C2×C11×#4111yescharacteristic
332C2×C4C11×2−1+412yes—
333C8—24no—
334C8—42no—
335C8—42no—
336C8—42no—
337C22C2×C11×#11711yescharacteristic
338C22C4×C11×#4111yescharacteristic
339C22C11×#51911yescharacteristic
340C22C2×C11×#13111yescharacteristic
341C22C11×#56811yescharacteristic
342C22C11×#56811yescharacteristic
343C22C11×#56811yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—42no—
348C4—42no—
349C4—41no—
350C4—42no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4C11×#55212yes—
355C4C11×#55612yes—
356C2C11×#235611yescharacteristic
357C2C11×#292111yescharacteristic
358C2C11×#292511yescharacteristic
359C2C11×#296711yescharacteristic
360C2C11×#296811yescharacteristic
361C2C11×#298511yescharacteristic
362C2C11×#298711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socle, prime radicalC23×C11C23×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
71. #22831C11direct (N × H)
296. C11#22831direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22952
C11×#19852
C11×#19172
C11×#19162
C11×#18402
C11×#18312
C11×#17712
C11×#17672
C11×#17462
#2283111