Finite Group Databasebeta

← C11×#9183 #14586376

Subgroups — C11×#9183 #14586376

Order 2816.

532 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2973C211yesmaximal, characteristic
2C11×#2638C211yesmaximal, characteristic
3C4×C11×#99C211yesmaximal, characteristic
4C11×#1508C212yesmaximal, complemented
5C11×#1284C212yesmaximal, complemented
6C2×C11×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#435—24no—
9C11×#432—21no—
10C2×C11×#99—21no—
11C11×#407C2212yes—
12C2×C11×C22⋊C8—21no—
13C11×#398C411yescharacteristic, complemented
14C11×#397—21no—
15C11×#397C411yescharacteristic, complemented
16C11×#395C411yescharacteristic, complemented
17C11×#394—21no—
18C11×#393C411yescharacteristic, complemented
19C11×#387—21no—
20C11×#385—21no—
21C11×#381C2211yescharacteristic
22C4×C11×C22⋊C4C2212yes—
23C11×#342—21no—
24C11×#328—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C2×C11×M16—22no—
30C22×C8×C11—22no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—22no—
33C4×D4×C11—22no—
34C4×D4×C11—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C42×C11—22no—
48C2×C42×C11D411yescharacteristic
49C11×C4⋊C8—22no—
50C11×#99—24no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8D414yes—
54C11×#97—22no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—22no—
61C11×#95C2×C411yescharacteristic
62C11×#95C2×C411yescharacteristic
63#9183C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C22⋊C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—81no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—42no—
78C22×C4×C11—81no—
79C22×C4×C11—81no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4112yes—
87C11×M16—82no—
88C2×C8×C11—24no—
89C2×C8×C11—82no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—24no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—82no—
107#2973C2×C1111yescharacteristic
108#2638C2×C1111yescharacteristic
109C4×#99C2×C1111yescharacteristic
110#1508C2×C1112yescomplemented
111#1284C2×C1112yescomplemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#10412yes—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11#12112yes—
123Q8×C11—82no—
124D4×C11—44no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
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—81no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11C4×D412yes—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C8×C11—44no—
157C2×C22⋊Q8C22×C1111yescharacteristic
158C2×C4×D4C22×C1111yescharacteristic
159#435—24no—
160#432—21no—
161C2×#99—21no—
162#407C22×C1112yes—
163C2×C22⋊C8—21no—
164#398C4×C1111yescharacteristic, complemented
165#397—21no—
166#397C4×C1111yescharacteristic, complemented
167#395C4×C1111yescharacteristic, complemented
168#394—21no—
169#393C4×C1111yescharacteristic, complemented
170#387—21no—
171#385—21no—
172#381C22×C1111yescharacteristic
173C4×C22⋊C4C22×C1112yes—
174#342—21no—
175#328—24no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—42no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11#38611yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C22×C11#42111yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—84no—
200C4×C11—81no—
201C4×C11—81no—
202C22×Q8C2×C4×C1111yescharacteristic
203C22×D4D4×C1111yescharacteristic
204C23×C4D4×C1111yescharacteristic
205C23×C4C23×C1111yescharacteristic
206C2×M16—22no—
207C22×C8—22no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C1111yescharacteristic
216C2×C4⋊C4C2×C4×C1111yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4C2×C4×C1111yescharacteristic
223C2×C22⋊C4D4×C1111yescharacteristic
224C2×C42—22no—
225C2×C42D4×C1111yescharacteristic
226C4⋊C8—22no—
227#99—24no—
228C22⋊C8—22no—
229C22⋊C8—22no—
230C22⋊C8D4×C1114yes—
231#97—22no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—22no—
238#95C2×C4×C1111yescharacteristic
239#95C2×C4×C1111yescharacteristic
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—42no—
243C2×C11—42no—
244C2×C11#187111yescharacteristic
245C2×C11#190911yescharacteristic
246C2×C11#191311yescharacteristic
247C24C11×C22⋊C411yescharacteristic
248C24C2×D4×C1111yescharacteristic
249C2×Q8—22no—
250C2×Q8—81no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C11×C22⋊C411yescharacteristic
264C22×C4C11×C22⋊C411yescharacteristic
265C22×C4C11×C22⋊C411yescharacteristic
266C22×C4C22×C4×C1111yescharacteristic
267C22×C4C2×D4×C1112yes—
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C11×#4112yes—
270M16—82no—
271C2×C8—24no—
272C2×C8—82no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—81no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—24no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—81no—
286C22⋊C4—81no—
287C42—21no—
288C42—21no—
289C42—82no—
290C11#918311yescharacteristic, direct product factor, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C11×#10412yes—
300C23C2×C11×C22⋊C411yescharacteristic
301C23C11×#12112yes—
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
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—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4C4×D4×C1112yes—
333C2×C4C11×#12011yescharacteristic
334C2×C4C11×#12311yescharacteristic
335C8—44no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C11×#38611yescharacteristic
349C22C2×C11×#10411yescharacteristic
350C22C11×#42111yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—84no—
360C4—81no—
361C4—81no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—42no—
366C2C11×#187111yescharacteristic
367C2C11×#190911yescharacteristic
368C2C11×#191311yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1508C2semidirect
5. C11×#1284C2semidirect
13. C11×#398C4semidirect
15. C11×#397C4semidirect
16. C11×#395C4semidirect
18. C11×#393C4semidirect
63. #9183C11direct (N × H)
110. #1508C2×C11semidirect
111. #1284C2×C11semidirect
164. #398C4×C11semidirect
166. #397C4×C11semidirect
167. #395C4×C11semidirect
169. #393C4×C11semidirect
290. C11#9183direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29732
C11×#26382
C4×C11×#992
C11×#15082
C11×#12842
#918311