Finite Group Databasebeta

← C11×#9122 #14586315

Subgroups — C11×#9122 #14586315

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×M16C211yesmaximal, characteristic
2C11×#2851C211yesmaximal, characteristic
3C11×#1749C211yesmaximal, characteristic
4C2×C11×#330C212yesmaximal, complemented
5C11×#1295C212yesmaximal, complemented
6C22×C11×M16—21no—
7C2×C11×#125C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C2×C11×C22⋊C8—21no—
10C4×C11×M16—24no—
11C2×C11×#97C2212yes—
12C2×C11×#97C2212yes—
13C2×C4×C8×C11—21no—
14C11×#389C411yescharacteristic
15C11×#389C411yescharacteristic
16C11×#387—21no—
17C11×#387—21no—
18C11×#385—21no—
19C11×#385—21no—
20C11×#382C2211yescharacteristic
21C11×#380C411yescharacteristic
22C11×#380C411yescharacteristic
23C11×#336—21no—
24C11×#330—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C2×C11×M16—24no—
29C2×C11×M16—24no—
30C2×C11×M16—24no—
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C11×#125—22no—
34C11×#125—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11—22no—
46C2×C42×C11—22no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C11×C22⋊C8—24no—
52C11×#97—22no—
53C11×#97—22no—
54C11×#97—22no—
55C11×#97D414yes—
56C4×C8×C11—24no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63#9122C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C22⋊C411yescharacteristic
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×M16—216no—
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C42×C11—22no—
104C42×C11—21no—
105C42×C11—22no—
106C42×C11—21no—
107C42×C11C2×D412yes—
108C42×C11#4112yes—
109C2×C4×M16C2×C1111yescharacteristic
110#2851C2×C1111yescharacteristic
111#1749C2×C1111yescharacteristic
112C2×#330C2×C1112yescomplemented
113#1295C2×C1112yescomplemented
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11#10412yes—
121C23×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11—24no—
123C2×C4×C11—24no—
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—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11#10112yes—
151C2×C4×C11#10412yes—
152C2×C4×C11#10412yes—
153C2×C4×C11C4×D412yes—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12112yes—
156C2×C4×C11#12311yescharacteristic
157C8×C11—28no—
158C8×C11—44no—
159C22×M16—21no—
160C2×#125C22×C1111yescharacteristic
161C22×C42C22×C1111yescharacteristic
162C2×C22⋊C8—21no—
163C4×M16—24no—
164C2×#97C22×C1112yes—
165C2×#97C22×C1112yes—
166C2×C4×C8—21no—
167#389C4×C1111yescharacteristic
168#389C4×C1111yescharacteristic
169#387—21no—
170#387—21no—
171#385—21no—
172#385—21no—
173#382C22×C1111yescharacteristic
174#380C4×C1111yescharacteristic
175#380C4×C1111yescharacteristic
176#336—21no—
177#330—24no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11#38611yescharacteristic
186C22×C11C2×#10111yescharacteristic
187C22×C11#41311yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C22×C11C2×#10411yescharacteristic
191C22×C11#42111yescharacteristic
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C23×C4C2×C4×C1111yescharacteristic
204C23×C4D4×C1111yescharacteristic
205C23×C4D4×C1111yescharacteristic
206C2×M16—24no—
207C2×M16—24no—
208C2×M16—24no—
209C22×C8—22no—
210C22×C8—22no—
211#125—22no—
212#125—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×C4×C1111yescharacteristic
218C2×C4⋊C4C2×C4×C1111yescharacteristic
219C2×C4⋊C4C2×C4×C1111yescharacteristic
220C2×C4⋊C4C2×C4×C1111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C2×C4×C1111yescharacteristic
226C2×C42D4×C1111yescharacteristic
227C2×C42D4×C1111yescharacteristic
228C2×C42C23×C1111yescharacteristic
229C22⋊C8—24no—
230#97—22no—
231#97—22no—
232#97—22no—
233#97D4×C1114yes—
234C4×C8—24no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×C11—42no—
242C2×C11#152411yescharacteristic
243C2×C11#152611yescharacteristic
244C2×C11#152811yescharacteristic
245C2×C11#152911yescharacteristic
246C2×C11#187111yescharacteristic
247C2×C11#189611yescharacteristic
248C2×C11#190111yescharacteristic
249C24C11×C22⋊C411yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C11×C22⋊C411yescharacteristic
265C22×C4C11×C22⋊C411yescharacteristic
266C22×C4C11×C22⋊C411yescharacteristic
267C22×C4C22×C4×C1111yescharacteristic
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270M16—216no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—22no—
289C42—21no—
290C42—22no—
291C42—21no—
292C42C2×D4×C1112yes—
293C42C11×#4112yes—
294C11#912211yescharacteristic, direct product factor, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23C11×#10412yes—
302C23C2×C11×C22⋊C411yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4C11×#10112yes—
332C2×C4C11×#10412yes—
333C2×C4C11×#10412yes—
334C2×C4C4×D4×C1112yes—
335C2×C4C11×#12011yescharacteristic
336C2×C4C11×#12112yes—
337C2×C4C11×#12311yescharacteristic
338C8—28no—
339C8—44no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C11×#38611yescharacteristic
348C22C2×C11×#10111yescharacteristic
349C22C11×#41311yescharacteristic
350C22C2×C11×#10411yescharacteristic
351C22C2×C11×#10411yescharacteristic
352C22C2×C11×#10411yescharacteristic
353C22C11×#42111yescharacteristic
354C4—22no—
355C4—22no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—22no—
360C4—22no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C2—42no—
366C2C11×#152411yescharacteristic
367C2C11×#152611yescharacteristic
368C2C11×#152811yescharacteristic
369C2C11×#152911yescharacteristic
370C2C11×#187111yescharacteristic
371C2C11×#189611yescharacteristic
372C2C11×#190111yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#330C2semidirect
5. C11×#1295C2semidirect
63. #9122C11direct (N × H)
112. C2×#330C2×C11semidirect
113. #1295C2×C11semidirect
294. C11#9122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×M162
C11×#28512
C11×#17492
C2×C11×#3302
C11×#12952
#912211