Finite Group Databasebeta

← C11×#19084 #14596277

Subgroups — C11×#19084 #14596277

Order 2816.

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

normal subgroups only

This group has 824 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×#3556C211yesmaximal, characteristic
2C11×#3165C212yesmaximal
3C11×#3139C211yesmaximal, characteristic
4C11×#1663C218yesmaximal, complemented
5C11×#1526C212yesmaximal
6C11×#1526C211yesmaximal, characteristic
7C11×#564C2214yes—
8C11×#557—22no—
9C11×#557—22no—
10C11×#557—22no—
11C11×#541—22no—
12C11×#541—24no—
13C11×#533C2212yes—
14C11×#533C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C11×#501C2218yes—
17C11×#500—22no—
18C11×#498—22no—
19C11×#491C2214yes—
20C11×#487—22no—
21C11×#428—24no—
22C11×#419—22no—
23C4×C11×M16C2212yes—
24C4×C11×M16C2211yescharacteristic
25C11×#330C2218yes—
26C11×#330C2214yes—
27C22×Q8×C11—21no—
28C2×C11×M16—22no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—22no—
31C11×C4⋊Q8—24no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8D412yes—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8C2312yes—
38C11×#126—28no—
39C11×#125—22no—
40C11×#125—24no—
41C11×#125—28no—
42C11×#125—28no—
43C11×#125—28no—
44C11×#125C2312yes—
45C11×#125C2314yes—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C11×#117D412yes—
56C11×#117D414yes—
57C2×C11×C4⋊C4—22no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—28no—
60C11×#106—28no—
61C11×#103—28no—
62C11×#97C2312yes—
63C11×#97C2314yes—
64C4×C8×C11—22no—
65C4×C8×C11—21no—
66#19084C1111yesmaximal, characteristic, direct product factor, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—44no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D411yescharacteristic
76C11×M16—28no—
77C11×M16—42no—
78C2×C8×C11—24no—
79C2×C8×C11—22no—
80C11×C4⋊C4—28no—
81C11×C4⋊C4—28no—
82C11×C4⋊C4—28no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4C2×D414yes—
92C11×C4⋊C4C2×D414yes—
93C11×C4⋊C4C2×D414yes—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—24no—
96C42×C11—28no—
97C42×C11—22no—
98C42×C11—24no—
99C42×C11C2×D412yes—
100C42×C11C2×D411yescharacteristic
101C42×C11C2411yescharacteristic
102#3556C2×C1111yescharacteristic
103#3165C2×C1112yes—
104#3139C2×C1111yescharacteristic
105#1663C2×C1118yescomplemented
106#1526C2×C1111yescharacteristic
107#1526C2×C1112yes—
108C23×C11#12011yescharacteristic
109Q8×C11—44no—
110Q8×C11—44no—
111Q8×C11—44no—
112Q8×C11—44no—
113Q8×C11—82no—
114C2×C4×C11—22no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12012yes—
123C2×C4×C11C22×D412yes—
124C2×C4×C11C22×D411yescharacteristic
125C8×C11—28no—
126C8×C11—42no—
127#564C22×C1114yes—
128#557—22no—
129#557—22no—
130#557—22no—
131#541—22no—
132#541—24no—
133#533C22×C1111yescharacteristic
134#533C22×C1112yes—
135C2×C4⋊Q8C22×C1111yescharacteristic
136#501C22×C1118yes—
137#500—22no—
138#498—22no—
139#491C22×C1114yes—
140#487—22no—
141#428—24no—
142#419—22no—
143C4×M16C22×C1111yescharacteristic
144C4×M16C22×C1112yes—
145#330C22×C1118yes—
146#330C22×C1114yes—
147C22×C11—21no—
148C22×C11—22no—
149C22×C11C2×#12011yescharacteristic
150C4×C11—21no—
151C4×C11—22no—
152C4×C11—44no—
153C4×C11—44no—
154C4×C11—44no—
155C4×C11—82no—
156C4×C11#45412yes—
157C4×C11#45614yes—
158C22×Q8—21no—
159C2×M16—22no—
160C2×M16—21no—
161C4⋊Q8—22no—
162C4⋊Q8—24no—
163C4⋊Q8—22no—
164C4⋊Q8—21no—
165C4⋊Q8D4×C1112yes—
166C4⋊Q8D4×C1112yes—
167C4⋊Q8D4×C1112yes—
168C4⋊Q8C23×C1112yes—
169#126—28no—
170#125—22no—
171#125—24no—
172#125—28no—
173#125—28no—
174#125—28no—
175#125C23×C1112yes—
176#125C23×C1114yes—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C4×Q8—24no—
181C4×Q8—24no—
182C4×Q8—24no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186#117D4×C1112yes—
187#117D4×C1114yes—
188C2×C4⋊C4—22no—
189C2×C42C23×C1111yescharacteristic
190#107—28no—
191#106—28no—
192#103—28no—
193#97C23×C1112yes—
194#97C23×C1114yes—
195C4×C8—21no—
196C4×C8—22no—
197C2×C11—41no—
198C2×C11C2×#45411yescharacteristic
199C2×C11C2×#45612yes—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C2×Q8—41no—
206C22×C4—41no—
207C22×C4C2×D4×C1112yes—
208C22×C4C2×D4×C1111yescharacteristic
209M16—28no—
210M16—42no—
211C2×C8—24no—
212C2×C8—22no—
213C4⋊C4—28no—
214C4⋊C4—28no—
215C4⋊C4—28no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—24no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—42no—
224C4⋊C4C2×D4×C1114yes—
225C4⋊C4C2×D4×C1114yes—
226C4⋊C4C2×D4×C1114yes—
227C22⋊C4—22no—
228C22⋊C4—24no—
229C42—28no—
230C42—22no—
231C42—24no—
232C42C2×D4×C1112yes—
233C42C2×D4×C1111yescharacteristic
234C42C24×C1111yescharacteristic
235C11#1908411yescharacteristic, direct product factor, Sylow
236C23C11×#12011yescharacteristic
237Q8—44no—
238Q8—44no—
239Q8—44no—
240Q8—44no—
241Q8—82no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—42no—
248C2×C4—82no—
249C2×C4C11×#12011yescharacteristic
250C2×C4C11×#12012yes—
251C2×C4C22×D4×C1112yes—
252C2×C4C22×D4×C1111yescharacteristic
253C8—28no—
254C8—42no—
255C22—21no—
256C22—22no—
257C22C2×C11×#12011yescharacteristic
258C4—21no—
259C4—22no—
260C4—44no—
261C4—44no—
262C4—44no—
263C4—82no—
264C4C11×#45412yes—
265C4C11×#45614yes—
266C2—41no—
267C2C2×C11×#45411yescharacteristic
268C2C2×C11×#45612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#120
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
4. C11×#1663C2semidirect
66. #19084C11direct (N × H)
105. #1663C2×C11semidirect
235. C11#19084direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35562
C11×#31652
C11×#31392
C11×#16632
C11×#15262
#1908411