Finite Group Databasebeta

← C11×#18189 #14595382

Subgroups — C11×#18189 #14595382

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3113C212yesmaximal
3C11×#2399C211yesmaximal, characteristic
4C11×#1611C214yesmaximal
5C11×#1605C214yesmaximal
6C11×#1506C212yesmaximal
7C11×#1467C211yesmaximal, characteristic
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#483C2214yes—
19C11×#475—22no—
20C11×#462—22no—
21C11×#451C2214yes—
22C11×#441—24no—
23C11×#432C2212yes—
24C11×#398—21no—
25C11×#398C2212yes—
26C11×#395—21no—
27C11×#395C2212yes—
28C4×C11×C4⋊C4—22no—
29C11×#376C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C2×C11×Q16—24no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8D412yes—
40C11×C4⋊Q8D412yes—
41C11×#125—24no—
42C11×#125—24no—
43C11×#125—28no—
44C11×#125—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C11×#117—24no—
59C11×#117—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11D412yes—
69C2×C42×C11C2311yescharacteristic
70C11×#106—24no—
71C11×C4⋊C8—22no—
72C11×#103—24no—
73C11×#103—24no—
74C11×C22⋊C8C2314yes—
75C11×#97—22no—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18189C1111yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C2×Q8×C11C2×D414yes—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C11×Q16—48no—
97C2×C8×C11—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—28no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—44no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—44no—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—24no—
115C42×C11—24no—
116C42×C11—28no—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11—24no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#3502C2×C1111yescharacteristic
125#3113C2×C1112yes—
126#2399C2×C1111yescharacteristic
127#1611C2×C1114yes—
128#1605C2×C1114yes—
129#1506C2×C1112yes—
130#1467C2×C1111yescharacteristic
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—24no—
134Q8×C11—44no—
135Q8×C11—42no—
136Q8×C11—44no—
137Q8×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12012yes—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#13714yes—
159C2×C4×C11C22×D412yes—
160C8×C11—44no—
161Q82—22no—
162#557—22no—
163#557—24no—
164#544—21no—
165#544C22×C1114yes—
166#533—22no—
167#533C22×C1112yes—
168#519—21no—
169C2×C4×Q8C22×C1111yescharacteristic
170C2×C4×Q8C22×C1111yescharacteristic
171#483C22×C1114yes—
172#475—22no—
173#462—22no—
174#451C22×C1114yes—
175#441—24no—
176#432C22×C1112yes—
177#398—21no—
178#398C22×C1112yes—
179#395—21no—
180#395C22×C1112yes—
181C4×C4⋊C4—22no—
182#376C22×C1111yescharacteristic
183#328C22×C1118yes—
184#324C22×C1114yes—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11C2×#12011yescharacteristic
188C22×C11C2×#13712yes—
189C4×C11—22no—
190C4×C11—24no—
191C4×C11—21no—
192C4×C11—22no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11—42no—
196C4×C11—42no—
197C4×C11—44no—
198C4×C11—81no—
199C4×C11#45612yes—
200C22×Q8D4×C1111yescharacteristic
201C22×Q8C23×C1111yescharacteristic
202C2×Q16—24no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—24no—
206C4⋊Q8—28no—
207C4⋊Q8D4×C1112yes—
208C4⋊Q8D4×C1112yes—
209#125—24no—
210#125—24no—
211#125—28no—
212#125—22no—
213C22⋊Q8—22no—
214C22⋊Q8—24no—
215C22⋊Q8C23×C1114yes—
216C4×Q8—24no—
217C4×Q8—24no—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8D4×C1114yes—
226#117—24no—
227#117—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4D4×C1111yescharacteristic
232C2×C4⋊C4C23×C1111yescharacteristic
233C2×C4⋊C4C23×C1112yes—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42D4×C1112yes—
237C2×C42C23×C1111yescharacteristic
238#106—24no—
239C4⋊C8—22no—
240#103—24no—
241#103—24no—
242C22⋊C8C23×C1114yes—
243#97—22no—
244#95—21no—
245#95—22no—
246#95—22no—
247#95C23×C1112yes—
248C2×C11—22no—
249C2×C11#300411yescharacteristic
250C2×C11C2×#45611yescharacteristic
251C2×C11#302511yescharacteristic
252C2×Q8—24no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—24no—
256C2×Q8—22no—
257C2×Q8—42no—
258C2×Q8C2×D4×C1114yes—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1112yes—
265C22×C4C2×D4×C1112yes—
266C22×C4C24×C1111yescharacteristic
267Q16—48no—
268C2×C8—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—28no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—44no—
282C4⋊C4—42no—
283C4⋊C4—44no—
284C4⋊C4C2×D4×C1114yes—
285C22⋊C4—24no—
286C42—24no—
287C42—28no—
288C42—22no—
289C42—22no—
290C42—24no—
291C42—41no—
292C42—41no—
293C42C2×D4×C1112yes—
294C42C2×D4×C1112yes—
295C11#1818911yescharacteristic, direct product factor, Sylow
296C23C22×D4×C1111yescharacteristic
297Q8—28no—
298Q8—24no—
299Q8—44no—
300Q8—42no—
301Q8—44no—
302Q8—84no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4C11×#12011yescharacteristic
321C2×C4C11×#12012yes—
322C2×C4C11×#12011yescharacteristic
323C2×C4C11×#13714yes—
324C2×C4C22×D4×C1112yes—
325C8—44no—
326C22—21no—
327C22—21no—
328C22C2×C11×#12011yescharacteristic
329C22C2×C11×#13712yes—
330C4—22no—
331C4—24no—
332C4—21no—
333C4—22no—
334C4—44no—
335C4—44no—
336C4—42no—
337C4—42no—
338C4—44no—
339C4—81no—
340C4C11×#45612yes—
341C2—22no—
342C2C11×#300411yescharacteristic
343C2C2×C11×#45611yescharacteristic
344C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
80. #18189C11direct (N × H)
295. C11#18189direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#31132
C11×#23992
C11×#16112
C11×#16052
C11×#15062
C11×#14672
#1818911