Finite Group Databasebeta

← C11×#19065 #14596258

Subgroups — C11×#19065 #14596258

Order 2816.

920 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 222 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×#3548C211yesmaximal, characteristic
2C11×#3216C212yesmaximal, complemented
3C11×#3162C211yesmaximal, characteristic, complemented
4C11×#1661C218yesmaximal, complemented
5C11×#1537C211yesmaximal, characteristic, complemented
6C11×#1530C212yesmaximal, complemented
7C11×#562C2214yes—
8C11×#554—22no—
9C11×#550—22no—
10C11×#547—22no—
11C11×#540—22no—
12C11×#537—24no—
13C11×#533C2211yescharacteristic
14C11×#533C2211yescharacteristic
15C11×#532C2212yes—
16C11×#501—22no—
17C11×#501C2214yes—
18C11×#497C2214yes—
19C11×#489C2214yes—
20C11×#462—22no—
21C11×#460—22no—
22C11×#452—24no—
23C11×#432C2212yes—
24C11×#427—22no—
25C2×C11×#97C2211yescharacteristic
26C11×#330C2214yes—
27C11×#329C2218yes—
28C2×C11×#41—24no—
29C2×C11×#41D414yes—
30C2×C11×Q16—24no—
31C2×C11×SD16—24no—
32C22×C8×C11—21no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8C2312yes—
36C11×#127—22no—
37C11×#127D412yes—
38C11×#125—22no—
39C11×#125—21no—
40C11×#125C2312yes—
41C11×#124C2314yes—
42C11×#123—28no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C11×#121—28no—
48C11×#121—24no—
49C11×#121—28no—
50C11×#121—22no—
51C11×#121—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—24no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C11×#117—21no—
58C11×#117D412yes—
59C2×C11×C4⋊C4—24no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—24no—
62C11×#106—24no—
63C11×C4⋊C8—22no—
64C11×#103—24no—
65C11×#102—24no—
66C11×C22⋊C8—22no—
67C11×#97—21no—
68C11×#97C2314yes—
69C11×#97C2312yes—
70#19065C1111yesmaximal, characteristic, direct product factor, Sylow
71C11×#41—84no—
72C11×#41—88no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11C2×D414yes—
76C2×D4×C11—28no—
77C2×D4×C11—24no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11C2×D414yes—
81C22×C4×C11—28no—
82C22×C4×C11—24no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C11×Q16—84no—
86C11×SD16—84no—
87C2×C8×C11—24no—
88C2×C8×C11—22no—
89C2×C8×C11—24no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4C2×D414yes—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—41no—
104C42×C11—22no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D412yes—
108C42×C11C2411yescharacteristic
109#3548C2×C1111yescharacteristic
110#3216C2×C1112yescomplemented
111#3162C2×C1111yescharacteristic, complemented
112#1661C2×C1118yescomplemented
113#1537C2×C1111yescharacteristic, complemented
114#1530C2×C1112yescomplemented
115C23×C11—24no—
116C23×C11#12011yescharacteristic
117Q8×C11—44no—
118Q8×C11—44no—
119Q8×C11—42no—
120Q8×C11—42no—
121D4×C11—44no—
122D4×C11—44no—
123D4×C11—44no—
124D4×C11—84no—
125D4×C11—88no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—42no—
130C2×C4×C11—48no—
131C2×C4×C11—42no—
132C2×C4×C11—88no—
133C2×C4×C11#12012yes—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C22×D412yes—
137C8×C11—24no—
138C8×C11—44no—
139#562C22×C1114yes—
140#554—22no—
141#550—22no—
142#547—22no—
143#540—22no—
144#537—24no—
145#533C22×C1111yescharacteristic
146#533C22×C1111yescharacteristic
147#532C22×C1112yes—
148#501—22no—
149#501C22×C1114yes—
150#497C22×C1114yes—
151#489C22×C1114yes—
152#462—22no—
153#460—22no—
154#452—24no—
155#432C22×C1112yes—
156#427—22no—
157C2×#97C22×C1111yescharacteristic
158#330C22×C1114yes—
159#329C22×C1118yes—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—44no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11C2×#12011yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—44no—
170C4×C11—44no—
171C4×C11—82no—
172C4×C11#45612yes—
173C2×#41—24no—
174C2×#41D4×C1114yes—
175C2×Q16—24no—
176C2×SD16—24no—
177C22×C8—21no—
178C4⋊Q8D4×C1112yes—
179C4⋊Q8D4×C1112yes—
180C4⋊Q8C23×C1112yes—
181#127—22no—
182#127D4×C1112yes—
183#125—22no—
184#125—21no—
185#125C23×C1112yes—
186#124C23×C1114yes—
187#123—28no—
188C22⋊Q8—24no—
189C22⋊Q8—28no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192#121—28no—
193#121—24no—
194#121—28no—
195#121—22no—
196#121—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—24no—
200C4×D4—22no—
201C4×D4—22no—
202#117—21no—
203#117D4×C1112yes—
204C2×C4⋊C4—24no—
205C2×C42C23×C1111yescharacteristic
206#107—24no—
207#106—24no—
208C4⋊C8—22no—
209#103—24no—
210#102—24no—
211C22⋊C8—22no—
212#97—21no—
213#97C23×C1112yes—
214#97C23×C1114yes—
215C2×C11—41no—
216C2×C11—84no—
217C2×C11C2×#45611yescharacteristic
218C2×C11#301912yes—
219#41—84no—
220#41—88no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8C2×D4×C1114yes—
224C2×D4—28no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4C2×D4×C1114yes—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4C2×D4×C1111yescharacteristic
232C22×C4C2×D4×C1112yes—
233Q16—84no—
234SD16—84no—
235C2×C8—24no—
236C2×C8—22no—
237C2×C8—24no—
238C4⋊C4—28no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C4⋊C4C2×D4×C1114yes—
247C22⋊C4—28no—
248C22⋊C4—22no—
249C22⋊C4—24no—
250C22⋊C4—24no—
251C22⋊C4—41no—
252C42—22no—
253C42—41no—
254C42C2×D4×C1111yescharacteristic
255C42C2×D4×C1112yes—
256C42C24×C1111yescharacteristic
257C11#1906511yescharacteristic, direct product factor, Sylow
258C23—24no—
259C23C11×#12011yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—42no—
263Q8—42no—
264D4—44no—
265D4—44no—
266D4—44no—
267D4—84no—
268D4—88no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—48no—
274C2×C4—42no—
275C2×C4—88no—
276C2×C4C11×#12012yes—
277C2×C4C11×#12011yescharacteristic
278C2×C4C22×D4×C1111yescharacteristic
279C2×C4C22×D4×C1112yes—
280C8—24no—
281C8—44no—
282C22—21no—
283C22—22no—
284C22—44no—
285C22—44no—
286C22—44no—
287C22C2×C11×#12011yescharacteristic
288C4—21no—
289C4—22no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—82no—
294C4C11×#45612yes—
295C2—41no—
296C2—84no—
297C2C2×C11×#45611yescharacteristic
298C2C11×#301912yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3548C2
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
2. C11×#3216C2semidirect
3. C11×#3162C2semidirect
4. C11×#1661C2semidirect
5. C11×#1537C2semidirect
6. C11×#1530C2semidirect
70. #19065C11direct (N × H)
110. #3216C2×C11semidirect
111. #3162C2×C11semidirect
112. #1661C2×C11semidirect
113. #1537C2×C11semidirect
114. #1530C2×C11semidirect
257. C11#19065direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#32162
C11×#31622
C11×#16612
C11×#15372
C11×#15302
#1906511