Finite Group Databasebeta

← C11×#9409 #14586602

Subgroups — C11×#9409 #14586602

Order 2816.

840 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2539C211yesmaximal, characteristic
2C11×#2273C211yesmaximal, characteristic, complemented
3C11×#1507C212yesmaximal, complemented
4C11×#1462C211yesmaximal, characteristic, complemented
5C11×#1297C212yesmaximal, complemented
6C2×C11×#123—21no—
7C2×C11×#121C2211yescharacteristic
8C2×C11×#120—21no—
9C22×C11×C22⋊C4—21no—
10C22×C11×C22⋊C4C2211yescharacteristic
11C11×#407C2212yes—
12C11×#399C412yescomplemented
13C11×#392C412yescomplemented
14C11×#390—22no—
15C4×C11×C22⋊C4—21no—
16C4×C11×C22⋊C4—24no—
17C4×C11×C22⋊C4C2211yescharacteristic
18C4×C11×C22⋊C4C2212yes—
19C11×#327—24no—
20C11×#323—22no—
21C25×C11D411yescharacteristic
22C22×D4×C11—21no—
23C22×D4×C11—22no—
24C22×D4×C11C2×C411yescharacteristic, complemented
25C23×C4×C11—22no—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C2×C11×M16—22no—
29C11×#123—44no—
30C11×#121—22no—
31C11×#121—22no—
32C11×#120—44no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
35C2×C11×C22⋊C4—28no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4C2×C412yes—
45C2×C11×C22⋊C4D412yes—
46C2×C42×C11—22no—
47C2×C42×C11—22no—
48C2×C42×C11—21no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C11×#95—22no—
52C11×#95C2×C412yescomplemented
53C11×#95D414yescomplemented
54#9409C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11—21no—
56C24×C11—24no—
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—42no—
60C24×C11—81no—
61C24×C11C22⋊C412yes—
62C24×C11C2×D411yescharacteristic
63C2×D4×C11—22no—
64C2×D4×C11—44no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C2×D4×C11—44no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—82no—
71C2×D4×C11—81no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—24no—
75C22×C4×C11—28no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—81no—
80C22×C4×C11—82no—
81C22×C4×C11—82no—
82C22×C4×C11C22⋊C412yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4112yes—
87C11×M16—82no—
88C2×C8×C11—42no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—44no—
91C11×C22⋊C4—28no—
92C11×C22⋊C4—28no—
93C11×C22⋊C4—24no—
94C11×C22⋊C4—24no—
95C11×C22⋊C4—24no—
96C11×C22⋊C4—44no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—42no—
99C42×C11—82no—
100C42×C11—81no—
101C42×C11—82no—
102#2539C2×C1111yescharacteristic
103#2273C2×C1111yescharacteristic, complemented
104#1507C2×C1112yescomplemented
105#1462C2×C1111yescharacteristic, complemented
106#1297C2×C1112yescomplemented
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—24no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—41no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—41no—
123C23×C11—42no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11—88no—
127C23×C11#10414yes—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12311yescharacteristic
131D4×C11—82no—
132D4×C11—88no—
133D4×C11—82no—
134D4×C11—82no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—44no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—88no—
153C2×C4×C11C4×D412yes—
154C2×C4×C11#12112yes—
155C8×C11—82no—
156C2×#123—21no—
157C2×#121C22×C1111yescharacteristic
158C2×#120—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4C22×C1111yescharacteristic
161#407C22×C1112yes—
162#399C4×C1112yescomplemented
163#392C4×C1112yescomplemented
164#390—22no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—24no—
167C4×C22⋊C4C22×C1111yescharacteristic
168C4×C22⋊C4C22×C1112yes—
169#327—24no—
170#323—22no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—24no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—44no—
180C22×C11—44no—
181C22×C11—44no—
182C22×C11—44no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—84no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#38611yescharacteristic
193C22×C11C2×#10412yes—
194C22×C11#45312yes—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—48no—
198C4×C11—44no—
199C4×C11—42no—
200C4×C11—81no—
201C25D4×C1111yescharacteristic
202C22×D4—21no—
203C22×D4—22no—
204C22×D4C2×C4×C1111yescharacteristic, complemented
205C23×C4—22no—
206C23×C4D4×C1111yescharacteristic
207C23×C4C23×C1111yescharacteristic
208C2×M16—22no—
209#123—44no—
210#121—22no—
211#121—22no—
212#120—44no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
215C2×C22⋊C4—22no—
216C2×C22⋊C4—28no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4C2×C4×C1112yes—
225C2×C22⋊C4D4×C1112yes—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—21no—
229C22⋊C8—22no—
230C22⋊C8—22no—
231#95—22no—
232#95C2×C4×C1112yescomplemented
233#95D4×C1114yescomplemented
234C2×C11—22no—
235C2×C11—22no—
236C2×C11—41no—
237C2×C11—44no—
238C2×C11—161no—
239C2×C11#188711yescharacteristic
240C2×C11#189611yescharacteristic
241C2×C11#191311yescharacteristic
242C24—21no—
243C24—24no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—81no—
248C24C11×C22⋊C412yes—
249C24C2×D4×C1111yescharacteristic
250C2×D4—22no—
251C2×D4—44no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—82no—
258C2×D4—81no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—81no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4C11×C22⋊C412yes—
270C22×C4C22×C4×C1111yescharacteristic
271C22×C4C2×D4×C1112yes—
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C11×#4112yes—
274M16—82no—
275C2×C8—42no—
276C4⋊C4—22no—
277C4⋊C4—44no—
278C22⋊C4—28no—
279C22⋊C4—28no—
280C22⋊C4—24no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—44no—
284C22⋊C4—44no—
285C22⋊C4—42no—
286C42—82no—
287C42—81no—
288C42—82no—
289C11#940911yescharacteristic, direct product factor, Sylow
290C23—22no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—41no—
302C23—41no—
303C23—42no—
304C23—42no—
305C23—41no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—88no—
310C23C11×#10414yes—
311C23C2×C11×C22⋊C411yescharacteristic
312C23C11×#12011yescharacteristic
313C23C11×#12311yescharacteristic
314D4—82no—
315D4—88no—
316D4—82no—
317D4—82no—
318C2×C4—28no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—88no—
336C2×C4C4×D4×C1112yes—
337C2×C4C11×#12112yes—
338C8—82no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—24no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—84no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C11×#38611yescharacteristic
361C22C2×C11×#10412yes—
362C22C11×#45312yes—
363C4—22no—
364C4—22no—
365C4—48no—
366C4—44no—
367C4—42no—
368C4—81no—
369C2—22no—
370C2—22no—
371C2—41no—
372C2—44no—
373C2—161no—
374C2C11×#188711yescharacteristic
375C2C11×#189611yescharacteristic
376C2C11×#191311yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC11×#2539C2
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
2. C11×#2273C2semidirect
3. C11×#1507C2semidirect
4. C11×#1462C2semidirect
5. C11×#1297C2semidirect
12. C11×#399C4semidirect
13. C11×#392C4semidirect
24. C22×D4×C11C2×C4semidirect
34. C2×C11×C4⋊C4C2×C4semidirect
52. C11×#95C2×C4semidirect
53. C11×#95D4semidirect
54. #9409C11direct (N × H)
103. #2273C2×C11semidirect
104. #1507C2×C11semidirect
105. #1462C2×C11semidirect
106. #1297C2×C11semidirect
162. #399C4×C11semidirect
163. #392C4×C11semidirect
204. C22×D4C2×C4×C11semidirect
214. C2×C4⋊C4C2×C4×C11semidirect
232. #95C2×C4×C11semidirect
233. #95D4×C11semidirect
289. C11#9409direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25392
C11×#22732
C11×#15072
C11×#14622
C11×#12972
#940911