Finite Group Databasebeta

← C11×#19077 #14596270

Subgroups — C11×#19077 #14596270

Order 2816.

996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3550C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic
3C11×#3138C212yesmaximal, complemented
4C11×#1657C218yesmaximal, complemented
5C11×#1526C212yesmaximal, complemented
6C11×#1525C211yesmaximal, characteristic, complemented
7C2×C11×AGL(1,ℤ/8)—22no—
8C11×#563C2214yescomplemented
9C11×#559—21no—
10Q82×C11—21no—
11C11×#556—22no—
12D4×Q8×C11—22no—
13C11×#542—24no—
14C11×#536—22no—
15C11×#533C2212yes—
16C11×#532C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C11×#496C2214yes—
19C11×#493—21no—
20C11×#492—21no—
21C11×#490C2218yes—
22C11×#486—22no—
23C11×#486—22no—
24C11×#418—24no—
25C4×C11×M16C2211yescharacteristic
26C4×C11×M16C2212yes—
27C11×#330C2218yescomplemented
28C11×#329C2214yescomplemented
29C2×C11×#41D412yes—
30C22×Q8×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—21no—
33C11×AGL(1,ℤ/8)—48no—
34C2×C11×SD16—24no—
35C2×C11×D8—24no—
36C2×C11×M16—21no—
37C2×C11×M16—22no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D412yes—
43C11×#127—21no—
44C11×#127—22no—
45C11×#127D411yescharacteristic
46C11×#127C2312yes—
47C11×#126—28no—
48C11×#125C2314yes—
49C11×#124—24no—
50C11×#124—24no—
51C11×#124C2312yes—
52C11×#123—24no—
53C11×#123—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—28no—
58C11×#121—22no—
59C4×Q8×C11—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—22no—
64C11×#117—22no—
65C11×#117D414yes—
66C2×C42×C11C2311yescharacteristic
67C11×#102—28no—
68C11×#102—28no—
69C11×#97C2314yes—
70C11×#97C2312yes—
71C4×C8×C11—21no—
72C4×C8×C11—22no—
73#19077C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—41no—
75C11×#41—44no—
76C2×Q8×C11—24no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—84no—
80C2×Q8×C11C2×D412yes—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—48no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C11×SD16—48no—
95C11×D8—48no—
96C11×M16—24no—
97C11×M16—44no—
98C2×C8×C11—22no—
99C2×C8×C11—24no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4C2×D414yes—
107C11×C4⋊C4C2×D414yes—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—24no—
112C42×C11—24no—
113C42×C11—24no—
114C42×C11C2×D412yes—
115C42×C11C2×D411yescharacteristic
116C42×C11C2411yescharacteristic
117#3550C2×C1111yescharacteristic, complemented
118#3151C2×C1111yescharacteristic
119#3138C2×C1112yescomplemented
120#1657C2×C1118yescomplemented
121#1526C2×C1112yescomplemented
122#1525C2×C1111yescharacteristic, complemented
123C23×C11—22no—
124C23×C11—42no—
125C23×C11—82no—
126C23×C11—84no—
127C23×C11#12011yescharacteristic
128Q8×C11—42no—
129Q8×C11—44no—
130Q8×C11—44no—
131Q8×C11—84no—
132D4×C11—42no—
133D4×C11—44no—
134D4×C11—48no—
135D4×C11—44no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—84no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—44no—
145C2×C4×C11—84no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12012yes—
148C2×C4×C11C22×D412yes—
149C2×C4×C11C22×D411yescharacteristic
150C8×C11—24no—
151C8×C11—44no—
152C2×AGL(1,ℤ/8)—22no—
153#563C22×C1114yescomplemented
154#559—21no—
155Q82—21no—
156#556—22no—
157D4×Q8—22no—
158#542—24no—
159#536—22no—
160#533C22×C1112yes—
161#532C22×C1111yescharacteristic
162C2×#127C22×C1111yescharacteristic
163#496C22×C1114yes—
164#493—21no—
165#492—21no—
166#490C22×C1118yes—
167#486—22no—
168#486—22no—
169#418—24no—
170C4×M16C22×C1112yes—
171C4×M16C22×C1111yescharacteristic
172#330C22×C1118yescomplemented
173#329C22×C1114yescomplemented
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—44no—
178C22×C11—82no—
179C22×C11—84no—
180C22×C11—164no—
181C22×C11C2×#12011yescharacteristic
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—42no—
185C4×C11—44no—
186C4×C11—44no—
187C4×C11#45312yes—
188C4×C11#45414yes—
189C2×#41D4×C1112yes—
190C22×Q8—22no—
191C22×D4—21no—
192C22×D4—22no—
193AGL(1,ℤ/8)—48no—
194C2×SD16—24no—
195C2×D8—24no—
196C2×M16—21no—
197C2×M16—22no—
198C4⋊Q8—24no—
199C4⋊Q8—24no—
200C4⋊Q8D4×C1111yescharacteristic
201C4⋊Q8D4×C1112yes—
202C4⋊Q8D4×C1112yes—
203#127—22no—
204#127—21no—
205#127D4×C1111yescharacteristic
206#127C23×C1112yes—
207#126—28no—
208#125C23×C1114yes—
209#124—24no—
210#124—24no—
211#124C23×C1112yes—
212#123—24no—
213#123—24no—
214C22⋊Q8—24no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—28no—
218#121—22no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×D4—24no—
223C4×D4—22no—
224#117—22no—
225#117D4×C1114yes—
226C2×C42C23×C1111yescharacteristic
227#102—28no—
228#102—28no—
229#97C23×C1114yes—
230#97C23×C1112yes—
231C4×C8—22no—
232C4×C8—21no—
233C2×C11—41no—
234C2×C11—82no—
235C2×C11—162no—
236C2×C11C2×#45311yescharacteristic
237C2×C11C2×#45412yes—
238C24—41no—
239#41—44no—
240C2×Q8—24no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—84no—
244C2×Q8C2×D4×C1112yes—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—24no—
248C2×D4—22no—
249C2×D4—44no—
250C2×D4—48no—
251C2×D4—41no—
252C2×D4—42no—
253C2×D4C2×D4×C1112yes—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4C2×D4×C1112yes—
257C22×C4C2×D4×C1111yescharacteristic
258SD16—48no—
259D8—48no—
260M16—24no—
261M16—44no—
262C2×C8—22no—
263C2×C8—24no—
264C4⋊C4—28no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4C2×D4×C1114yes—
271C4⋊C4C2×D4×C1114yes—
272C22⋊C4—24no—
273C22⋊C4—28no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C42—24no—
277C42—24no—
278C42C2×D4×C1112yes—
279C42C2×D4×C1111yescharacteristic
280C42C24×C1111yescharacteristic
281C11#1907711yescharacteristic, direct product factor, Sylow
282C23—22no—
283C23—42no—
284C23—82no—
285C23—84no—
286C23C11×#12011yescharacteristic
287Q8—42no—
288Q8—44no—
289Q8—44no—
290Q8—84no—
291D4—42no—
292D4—44no—
293D4—48no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—84no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—44no—
304C2×C4—84no—
305C2×C4C11×#12011yescharacteristic
306C2×C4C11×#12012yes—
307C2×C4C22×D4×C1112yes—
308C2×C4C22×D4×C1111yescharacteristic
309C8—24no—
310C8—44no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—44no—
315C22—82no—
316C22—84no—
317C22—164no—
318C22C2×C11×#12011yescharacteristic
319C4—21no—
320C4—22no—
321C4—42no—
322C4—44no—
323C4—44no—
324C4C11×#45312yes—
325C4C11×#45414yes—
326C2—41no—
327C2—82no—
328C2—162no—
329C2C2×C11×#45311yescharacteristic
330C2C2×C11×#45412yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3550C2semidirect
3. C11×#3138C2semidirect
4. C11×#1657C2semidirect
5. C11×#1526C2semidirect
6. C11×#1525C2semidirect
8. C11×#563C22semidirect
27. C11×#330C22semidirect
28. C11×#329C22semidirect
73. #19077C11direct (N × H)
117. #3550C2×C11semidirect
119. #3138C2×C11semidirect
120. #1657C2×C11semidirect
121. #1526C2×C11semidirect
122. #1525C2×C11semidirect
153. #563C22×C11semidirect
172. #330C22×C11semidirect
173. #329C22×C11semidirect
281. C11#19077direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#31512
C11×#31382
C11×#16572
C11×#15262
C11×#15252
#1907711