Finite Group Databasebeta

← C11×#2493 #13065331

Subgroups — C11×#2493 #13065331

Order 1408.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#401C211yesmaximal, characteristic, complemented
2C11×#400C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#400C211yesmaximal, characteristic, complemented
5C11×#387C211yesmaximal, characteristic, complemented
6C11×#387C211yesmaximal, characteristic, complemented
7C11×#387C211yesmaximal, characteristic, complemented
8C11×#385C211yesmaximal, characteristic
9C11×#385C211yesmaximal, characteristic
10C11×#383C211yesmaximal, characteristic, complemented
11C11×#381C211yesmaximal, characteristic
12C11×#381C211yesmaximal, characteristic
13C11×#380C211yesmaximal, characteristic
14C4×C11×C22⋊C4C211yesmaximal, characteristic
15C2×C11×#95C211yesmaximal, characteristic
16C23×C4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C42×C11C2211yescharacteristic
30C2×C42×C11C2211yescharacteristic
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C42×C11—22no—
86C42×C11—41no—
87#2493C1111yesmaximal, characteristic, direct product factor, Sylow
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11#4112yes—
93C23×C11#4112yes—
94C23×C11#4112yes—
95C23×C11C2411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
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—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11#4112yes—
140C2×C4×C11#4112yes—
141#401C2×C1111yescharacteristic, complemented
142#400C2×C1111yescharacteristic, complemented
143#400C2×C1111yescharacteristic, complemented
144#400C2×C1111yescharacteristic, complemented
145#387C2×C1111yescharacteristic, complemented
146#387C2×C1111yescharacteristic, complemented
147#387C2×C1111yescharacteristic, complemented
148#385C2×C1111yescharacteristic
149#385C2×C1111yescharacteristic
150#383C2×C1111yescharacteristic, complemented
151#381C2×C1111yescharacteristic
152#381C2×C1111yescharacteristic
153#380C2×C1111yescharacteristic
154C4×C22⋊C4C2×C1111yescharacteristic
155C2×#95C2×C1111yescharacteristic
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11#12614yes—
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11C2×#4111yescharacteristic
166C22×C11C2×#4111yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11H(5,𝔽2)11yescharacteristic
169C22×C112−1+411yescharacteristic
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C23×C4C22×C1111yescharacteristic
185C23×C4C22×C1111yescharacteristic
186C23×C4C22×C1111yescharacteristic
187C2×C4⋊C4C22×C1111yescharacteristic
188C2×C4⋊C4C22×C1111yescharacteristic
189C2×C4⋊C4C22×C1111yescharacteristic
190C2×C4⋊C4C22×C1111yescharacteristic
191C2×C4⋊C4C22×C1111yescharacteristic
192C2×C4⋊C4C22×C1111yescharacteristic
193C2×C22⋊C4C22×C1111yescharacteristic
194C2×C22⋊C4C22×C1111yescharacteristic
195C2×C22⋊C4C22×C1111yescharacteristic
196C2×C22⋊C4C22×C1111yescharacteristic
197C2×C42C22×C1111yescharacteristic
198C2×C42C22×C1111yescharacteristic
199#95C22×C1111yescharacteristic
200#95C22×C1111yescharacteristic
201#95C22×C1111yescharacteristic
202#95C22×C1111yescharacteristic
203#95C22×C1111yescharacteristic
204#95C22×C1111yescharacteristic
205#95C22×C1111yescharacteristic
206#95C22×C1111yescharacteristic
207#95C22×C1111yescharacteristic
208#95C22×C1111yescharacteristic
209#95C22×C1111yescharacteristic
210#95C22×C1111yescharacteristic
211#95C22×C1111yescharacteristic
212#95C22×C1111yescharacteristic
213#95C22×C1111yescharacteristic
214#95C22×C1111yescharacteristic
215#95C22×C1111yescharacteristic
216#95C22×C1111yescharacteristic
217#95C22×C1111yescharacteristic
218#95C22×C1111yescharacteristic
219C2×C11—24no—
220C2×C11C2×#12611yescharacteristic
221C2×C11#52911yescharacteristic
222C2×C11#53911yescharacteristic
223C2×C11#55111yescharacteristic
224C2×C11#55111yescharacteristic
225C2×C11#55211yescharacteristic
226C2×C11#55211yescharacteristic
227C24C23×C1111yescharacteristic
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C23×C1111yescharacteristic
238C22×C4C23×C1111yescharacteristic
239C22×C4C23×C1111yescharacteristic
240C22×C4C23×C1111yescharacteristic
241C22×C4C23×C1111yescharacteristic
242C22×C4C23×C1111yescharacteristic
243C22×C4C23×C1111yescharacteristic
244C22×C4C23×C1111yescharacteristic
245C22×C4C23×C1111yescharacteristic
246C22×C4C23×C1111yescharacteristic
247C22×C4C23×C1111yescharacteristic
248C22×C4C23×C1111yescharacteristic
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C42—22no—
262C42—41no—
263C11#249311yescharacteristic, direct product factor, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C11×#4112yes—
269C23C11×#4112yes—
270C23C11×#4112yes—
271C23C24×C1111yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4C11×#4112yes—
316C2×C4C11×#4112yes—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22C11×#12614yes—
324C22C2×C11×#4111yescharacteristic
325C22C2×C11×#4111yescharacteristic
326C22C2×C11×#4111yescharacteristic
327C22C2×C11×#4111yescharacteristic
328C22C2×C11×#4111yescharacteristic
329C22C11×H(5,𝔽2)11yescharacteristic
330C22C11×2−1+411yescharacteristic
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C2—24no—
346C2C2×C11×#12611yescharacteristic
347C2C11×#52911yescharacteristic
348C2C11×#53911yescharacteristic
349C2C11×#55111yescharacteristic
350C2C11×#55111yescharacteristic
351C2C11×#55211yescharacteristic
352C2C11×#55211yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC24×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#401C2semidirect
2. C11×#400C2semidirect
3. C11×#400C2semidirect
4. C11×#400C2semidirect
5. C11×#387C2semidirect
6. C11×#387C2semidirect
7. C11×#387C2semidirect
10. C11×#383C2semidirect
87. #2493C11direct (N × H)
141. #401C2×C11semidirect
142. #400C2×C11semidirect
143. #400C2×C11semidirect
144. #400C2×C11semidirect
145. #387C2×C11semidirect
146. #387C2×C11semidirect
147. #387C2×C11semidirect
150. #383C2×C11semidirect
263. C11#2493direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#4012
C11×#4002
C11×#3872
C11×#3852
C11×#3832
C11×#3812
C11×#3802
C4×C11×C22⋊C42
C2×C11×#952
#249311