Finite Group Databasebeta

← C11×#18221 #14595414

Subgroups — C11×#18221 #14595414

Order 2816.

890 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3104C212yesmaximal
3C11×#2581C211yesmaximal, characteristic
4C11×#1617C214yesmaximal
5C11×#1605C214yesmaximal
6C11×#1518C212yesmaximal
7C11×#1461C211yesmaximal, 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×#484C2214yes—
19C11×#477—22no—
20C11×#462—22no—
21C11×#451C2214yes—
22C4×C11×Q16—24no—
23C11×#431C2212yes—
24C11×#400C2212yes—
25C11×#395C2212yes—
26C11×#391—21no—
27C11×#389—21no—
28C11×#387—22no—
29C11×#382C2211yescharacteristic
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—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11—21no—
67C2×C42×C11D412yes—
68C2×C42×C11C2311yescharacteristic
69C11×#107—24no—
70C11×C4⋊C8—22no—
71C11×#103—24no—
72C11×#103—24no—
73C11×C22⋊C8C2314yes—
74C4×C8×C11—22no—
75C11×#95—21no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18221C1111yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C2×Q8×C11Q1614yescomplemented
88C2×Q8×C11C2×D414yes—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C11×Q16—48no—
98C2×C8×C11—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—44no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—24no—
117C42×C11—28no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—24no—
121C42×C11—42no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#3502C2×C1111yescharacteristic
125#3104C2×C1112yes—
126#2581C2×C1111yescharacteristic
127#1617C2×C1114yes—
128#1605C2×C1114yes—
129#1518C2×C1112yes—
130#1461C2×C1111yescharacteristic
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—24no—
134Q8×C11—44no—
135Q8×C11—44no—
136Q8×C11—42no—
137Q8×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12012yes—
157C2×C4×C11C2×Q1614yes—
158C2×C4×C11C2×Q1612yes—
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D412yes—
161C8×C11—44no—
162Q82—22no—
163#557—22no—
164#557—24no—
165#544—21no—
166#544C22×C1114yes—
167#533—22no—
168#533C22×C1112yes—
169#519—21no—
170C2×C4×Q8C22×C1111yescharacteristic
171C2×C4×Q8C22×C1111yescharacteristic
172#484C22×C1114yes—
173#477—22no—
174#462—22no—
175#451C22×C1114yes—
176C4×Q16—24no—
177#431C22×C1112yes—
178#400C22×C1112yes—
179#395C22×C1112yes—
180#391—21no—
181#389—21no—
182#387—22no—
183#382C22×C1111yescharacteristic
184#328C22×C1118yes—
185#324C22×C1114yes—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11C2×#12011yescharacteristic
189C22×C11C22×Q1611yescharacteristic
190C22×C11C2×#13711yescharacteristic
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—22no—
195C4×C11—44no—
196C4×C11—42no—
197C4×C11—42no—
198C4×C11—44no—
199C4×C11—82no—
200C4×C11—81no—
201C4×C11#45114yes—
202C22×Q8D4×C1111yescharacteristic
203C22×Q8C23×C1111yescharacteristic
204C2×Q16—24no—
205C4⋊Q8—22no—
206C4⋊Q8—22no—
207C4⋊Q8—24no—
208C4⋊Q8—28no—
209C4⋊Q8D4×C1112yes—
210C4⋊Q8D4×C1112yes—
211#125—24no—
212#125—24no—
213#125—28no—
214#125—22no—
215C22⋊Q8—22no—
216C22⋊Q8—24no—
217C22⋊Q8C23×C1114yes—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×Q8—24no—
221C4×Q8—24no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8D4×C1114yes—
228#117—24no—
229#117—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4D4×C1111yescharacteristic
234C2×C4⋊C4C23×C1111yescharacteristic
235C2×C4⋊C4C23×C1112yes—
236C2×C42—21no—
237C2×C42D4×C1112yes—
238C2×C42C23×C1111yescharacteristic
239#107—24no—
240C4⋊C8—22no—
241#103—24no—
242#103—24no—
243C22⋊C8C23×C1114yes—
244C4×C8—22no—
245#95—21no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95C23×C1112yes—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11C2×#45111yescharacteristic
253C2×C11#302011yescharacteristic
254C2×C11#302511yescharacteristic
255C2×Q8—24no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×Q8C11×Q1614yescomplemented
262C2×Q8C2×D4×C1114yes—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4C2×D4×C1112yes—
267C22×C4C2×D4×C1112yes—
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C24×C1111yescharacteristic
271Q16—48no—
272C2×C8—24no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—28no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4—44no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4C2×D4×C1114yes—
290C22⋊C4—24no—
291C42—28no—
292C42—22no—
293C42—22no—
294C42—24no—
295C42—42no—
296C42C2×D4×C1112yes—
297C42C2×D4×C1112yes—
298C11#1822111yescharacteristic, direct product factor, Sylow
299C23C22×D4×C1111yescharacteristic
300Q8—28no—
301Q8—24no—
302Q8—44no—
303Q8—44no—
304Q8—42no—
305Q8—84no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4C11×#12011yescharacteristic
323C2×C4C11×#12011yescharacteristic
324C2×C4C11×#12012yes—
325C2×C4C2×C11×Q1614yes—
326C2×C4C2×C11×Q1612yes—
327C2×C4C11×#13712yes—
328C2×C4C22×D4×C1112yes—
329C8—44no—
330C22—21no—
331C22—21no—
332C22C2×C11×#12011yescharacteristic
333C22C22×C11×Q1611yescharacteristic
334C22C2×C11×#13711yescharacteristic
335C4—24no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—44no—
340C4—42no—
341C4—42no—
342C4—44no—
343C4—82no—
344C4—81no—
345C4C11×#45114yes—
346C2—21no—
347C2—21no—
348C2C2×C11×#45111yescharacteristic
349C2C11×#302011yescharacteristic
350C2C11×#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. #18221C11direct (N × H)
87. C2×Q8×C11Q16semidirect
261. C2×Q8C11×Q16semidirect
298. C11#18221direct (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×#31042
C11×#25812
C11×#16172
C11×#16052
C11×#15182
C11×#14612
#1822111