Finite Group Databasebeta

← C11×#23367 #14600560

Subgroups — C11×#23367 #14600560

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2399C211yesmaximal, characteristic
2C11×#1985C211yesmaximal, characteristic
3C11×#1984C212yesmaximal
4C11×#1984C211yesmaximal, characteristic
5C11×#1917C212yesmaximal
6C11×#1916C212yesmaximal
7C11×#1916C212yesmaximal
8C11×#1916C212yesmaximal
9C11×#1840C212yesmaximal
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2212yes—
15C2×C11×#97C2211yescharacteristic
16C2×C4×C8×C11C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#398C412yes—
19C11×#398C411yescharacteristic
20C11×#398C411yescharacteristic
21C11×#395C411yescharacteristic
22C11×#395C411yescharacteristic
23C11×#395C412yes—
24C4×C11×C4⋊C4C2212yes—
25C4×C11×C4⋊C4C2212yes—
26C11×#376C2211yescharacteristic
27C11×#336C2212yes—
28C11×#336C2212yes—
29C11×#336C2212yes—
30C11×#336C2212yes—
31C11×#336C2212yes—
32C11×#336C2212yes—
33C11×#336C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C11×#336C2212yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Q8×C11C2×C411yescharacteristic
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C4×Q8×C11—41no—
44C4×Q8×C11—41no—
45C4×Q8×C11—41no—
46C4×Q8×C11—41no—
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4C2×C412yes—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C11×C4⋊C4C2×C412yes—
53C2×C11×C4⋊C4C2×C411yescharacteristic
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C4⋊C4C2×C411yescharacteristic
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2312yes—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C11×C4⋊C8—41no—
62C11×C4⋊C8—41no—
63C11×C4⋊C8—42no—
64C11×#97—41no—
65C4×C8×C11—41no—
66C4×C8×C11—42no—
67C11×#95C2×C411yescharacteristic
68C11×#95C2×C412yes—
69C11×#95C2×C411yescharacteristic
70C11×#95C2×C412yes—
71C11×#95C2×C412yes—
72C11×#95C2×C412yes—
73C11×#95C2×C412yes—
74#23367C1111yesmaximal, characteristic, direct product factor, Sylow
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—24no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—24no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—21no—
111C42×C11—22no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11—22no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—22no—
119C42×C11—22no—
120#2399C2×C1111yescharacteristic
121#1985C2×C1111yescharacteristic
122#1984C2×C1112yes—
123#1984C2×C1111yescharacteristic
124#1917C2×C1112yes—
125#1916C2×C1112yes—
126#1916C2×C1112yes—
127#1916C2×C1112yes—
128#1840C2×C1112yes—
129C23×C11C23×C411yescharacteristic
130Q8×C11—44no—
131Q8×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11#13112yes—
158C2×C4×C11#13114yes—
159C2×C4×C11H(5,𝔽2)11yescharacteristic
160C2×C4×C11H(5,𝔽2)11yescharacteristic
161C2×C4×C112−1+412yes—
162C2×C4×C112−1+412yes—
163C8×C11—42no—
164C8×C11—42no—
165C8×C11—42no—
166C8×C11—42no—
167C2×C4×Q8C22×C1111yescharacteristic
168C2×C4×Q8C22×C1111yescharacteristic
169C2×C4⋊C8C22×C1111yescharacteristic
170C2×C4⋊C8C22×C1111yescharacteristic
171C2×C4⋊C8C22×C1112yes—
172C2×#97C22×C1111yescharacteristic
173C2×C4×C8C22×C1112yes—
174C2×C4×C8C22×C1111yescharacteristic
175#398C4×C1112yes—
176#398C4×C1111yescharacteristic
177#398C4×C1111yescharacteristic
178#395C4×C1111yescharacteristic
179#395C4×C1111yescharacteristic
180#395C4×C1112yes—
181C4×C4⋊C4C22×C1112yes—
182C4×C4⋊C4C22×C1112yes—
183#376C22×C1111yescharacteristic
184#336C22×C1112yes—
185#336C22×C1112yes—
186#336C22×C1112yes—
187#336C22×C1112yes—
188#336C22×C1112yes—
189#336C22×C1112yes—
190#336C22×C1112yes—
191#336C22×C1112yes—
192#336C22×C1112yes—
193#336C22×C1112yes—
194C22×C11#51811yescharacteristic
195C22×C11#51912yes—
196C22×C11C2×#13111yescharacteristic
197C22×C11C2×#13112yes—
198C22×C11#56811yescharacteristic
199C4×C11—22no—
200C4×C11—24no—
201C4×C11—42no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—42no—
208C4×C11—42no—
209C4×C11#56311yescharacteristic
210C4×C11#56311yescharacteristic
211C4×C11#56312yes—
212C22×Q8C2×C4×C1111yescharacteristic
213C22×Q8C2×C4×C1111yescharacteristic
214C22×C8C23×C1112yes—
215C22×C8C23×C1112yes—
216C22×C8C23×C1112yes—
217C22×C8C23×C1112yes—
218C4×Q8—41no—
219C4×Q8—41no—
220C4×Q8—41no—
221C4×Q8—41no—
222C2×C4⋊C4C2×C4×C1112yes—
223C2×C4⋊C4C2×C4×C1112yes—
224C2×C4⋊C4C2×C4×C1112yes—
225C2×C4⋊C4C2×C4×C1111yescharacteristic
226C2×C4⋊C4C2×C4×C1112yes—
227C2×C4⋊C4C2×C4×C1111yescharacteristic
228C2×C4⋊C4C2×C4×C1111yescharacteristic
229C2×C4⋊C4C2×C4×C1111yescharacteristic
230C2×C4⋊C4C2×C4×C1112yes—
231C2×C42C23×C1111yescharacteristic
232C2×C42C23×C1112yes—
233C2×C42C23×C1111yescharacteristic
234C2×C42C23×C1111yescharacteristic
235C2×C42C23×C1112yes—
236C4⋊C8—41no—
237C4⋊C8—41no—
238C4⋊C8—42no—
239#97—41no—
240C4×C8—41no—
241C4×C8—42no—
242#95C2×C4×C1111yescharacteristic
243#95C2×C4×C1112yes—
244#95C2×C4×C1111yescharacteristic
245#95C2×C4×C1112yes—
246#95C2×C4×C1112yes—
247#95C2×C4×C1112yes—
248#95C2×C4×C1112yes—
249C2×C11#238111yescharacteristic
250C2×C11#297611yescharacteristic
251C2×C11#297711yescharacteristic
252C2×C11#298512yes—
253C2×C11#298612yes—
254C2×Q8—24no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C22×C4C22×C4×C1112yes—
260C22×C4C22×C4×C1112yes—
261C22×C4C22×C4×C1111yescharacteristic
262C22×C4C22×C4×C1111yescharacteristic
263C22×C4C22×C4×C1112yes—
264C22×C4C22×C4×C1111yescharacteristic
265C22×C4C22×C4×C1111yescharacteristic
266C22×C4C22×C4×C1111yescharacteristic
267C22×C4C22×C4×C1112yes—
268C22×C4C22×C4×C1111yescharacteristic
269C22×C4C24×C1111yescharacteristic
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—24no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—24no—
278C2×C8—22no—
279C2×C8—22no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C42—21no—
290C42—22no—
291C42—21no—
292C42—21no—
293C42—22no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—22no—
298C42—22no—
299C11#2336711yescharacteristic, direct product factor, Sylow
300C23C23×C4×C1111yescharacteristic
301Q8—44no—
302Q8—44no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4C11×#13112yes—
329C2×C4C11×#13114yes—
330C2×C4C11×H(5,𝔽2)11yescharacteristic
331C2×C4C11×H(5,𝔽2)11yescharacteristic
332C2×C4C11×2−1+412yes—
333C2×C4C11×2−1+412yes—
334C8—42no—
335C8—42no—
336C8—42no—
337C8—42no—
338C22C11×#51811yescharacteristic
339C22C11×#51912yes—
340C22C2×C11×#13111yescharacteristic
341C22C2×C11×#13112yes—
342C22C11×#56811yescharacteristic
343C4—22no—
344C4—24no—
345C4—41no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—42no—
353C4C11×#56311yescharacteristic
354C4C11×#56311yescharacteristic
355C4C11×#56312yes—
356C2C11×#238111yescharacteristic
357C2C11×#297611yescharacteristic
358C2C11×#297711yescharacteristic
359C2C11×#298512yes—
360C2C11×#298612yes—
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
74. #23367C11direct (N × H)
299. C11#23367direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23992
C11×#19852
C11×#19842
C11×#19172
C11×#19162
C11×#18402
#2336711