Finite Group Databasebeta

← C11×#9983 #14587176

Subgroups — C11×#9983 #14587176

Order 2816.

602 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3094C212yesmaximal, complemented
2C11×#2815C211yesmaximal, characteristic
3C11×#1820C211yesmaximal, characteristic, complemented
4C11×#1510C212yesmaximal, complemented
5C11×#1306C211yesmaximal, characteristic, complemented
6C2×C11×#121C2212yes—
7C2×C11×#117C2211yescharacteristic
8C11×#482—24no—
9C11×#481—22no—
10C11×#480—22no—
11C11×#428—22no—
12C11×#418—22no—
13C11×#407C2212yes—
14C11×#397—22no—
15C11×#392—22no—
16C11×#392—22no—
17C11×#381C2211yescharacteristic
18C11×#381C2211yescharacteristic
19C11×#342—22no—
20C11×#327—24no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11D412yes—
24C23×C4×C11C2311yescharacteristic
25C2×C11×M16—22no—
26C11×#121—22no—
27C11×#121—22no—
28C11×#121—22no—
29C11×#121—22no—
30C11×#117—22no—
31C11×#117—22no—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C4⋊C4D412yescomplemented
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4D412yes—
39C2×C42×C11—21no—
40C11×#107—24no—
41C11×#106—24no—
42C11×#102—24no—
43C11×#102—24no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8D414yescomplemented
46C11×#95—22no—
47C11×#95—22no—
48C11×#95—22no—
49#9983C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—22no—
51C24×C11C2×D411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—44no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—84no—
58C2×D4×C11—84no—
59C2×D4×C11—82no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—42no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D412yes—
68C22×C4×C11#4111yescharacteristic
69C11×M16—44no—
70C2×C8×C11—24no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—84no—
82C42×C11—42no—
83#3094C2×C1112yescomplemented
84#2815C2×C1111yescharacteristic
85#1820C2×C1111yescharacteristic, complemented
86#1510C2×C1112yescomplemented
87#1306C2×C1111yescharacteristic, complemented
88C23×C11—22no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—44no—
93C23×C11—42no—
94C23×C11—44no—
95C23×C11#12011yescharacteristic
96C23×C11#12111yescharacteristic
97C23×C11#12711yescharacteristic
98D4×C11—44no—
99D4×C11—82no—
100D4×C11—84no—
101D4×C11—84no—
102D4×C11—88no—
103C2×C4×C11—24no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—44no—
108C2×C4×C11—44no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—82no—
113C2×C4×C11—81no—
114C2×C4×C11—82no—
115C2×C4×C11#12012yes—
116C2×C4×C11#12112yes—
117C8×C11—44no—
118C2×#121C22×C1112yes—
119C2×#117C22×C1111yescharacteristic
120#482—24no—
121#481—22no—
122#480—22no—
123#428—22no—
124#418—22no—
125#407C22×C1112yes—
126#397—22no—
127#392—22no—
128#392—22no—
129#381C22×C1111yescharacteristic
130#381C22×C1111yescharacteristic
131#342—22no—
132#327—24no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—82no—
139C22×C11—84no—
140C22×C11—84no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11—82no—
144C22×C11#39211yescharacteristic
145C22×C11#45812yes—
146C4×C11—22no—
147C4×C11—22no—
148C4×C11—82no—
149C4×C11—82no—
150C4×C11—82no—
151C4×C11—161no—
152C22×D4—22no—
153C22×D4—22no—
154C22×D4D4×C1112yes—
155C23×C4C23×C1111yescharacteristic
156C2×M16—22no—
157#121—22no—
158#121—22no—
159#121—22no—
160#121—22no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4D4×C1112yes—
164C2×C4⋊C4D4×C1112yescomplemented
165C2×C22⋊C4—21no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—24no—
169C2×C22⋊C4D4×C1112yes—
170C2×C42—21no—
171#107—24no—
172#106—24no—
173#102—24no—
174#102—24no—
175C22⋊C8—22no—
176C22⋊C8D4×C1114yescomplemented
177#95—22no—
178#95—22no—
179#95—22no—
180C2×C11—22no—
181C2×C11—41no—
182C2×C11—41no—
183C2×C11—162no—
184C2×C11#200812yes—
185C2×C11#202211yescharacteristic
186C24—22no—
187C24C2×D4×C1111yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—44no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—84no—
194C2×D4—84no—
195C2×D4—82no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4C2×D4×C1112yes—
202C22×C4C2×D4×C1111yescharacteristic
203C22×C4C2×D4×C1112yes—
204C22×C4C11×#4111yescharacteristic
205M16—44no—
206C2×C8—24no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—84no—
218C42—42no—
219C11#998311yescharacteristic, direct product factor, Sylow
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—44no—
225C23—42no—
226C23—44no—
227C23C11×#12011yescharacteristic
228C23C11×#12111yescharacteristic
229C23C11×#12711yescharacteristic
230D4—44no—
231D4—82no—
232D4—84no—
233D4—84no—
234D4—88no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4C11×#12012yes—
248C2×C4C11×#12112yes—
249C8—44no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—84no—
257C22—84no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22C11×#39211yescharacteristic
262C22C11×#45812yes—
263C4—22no—
264C4—22no—
265C4—82no—
266C4—82no—
267C4—82no—
268C4—161no—
269C2—22no—
270C2—41no—
271C2—41no—
272C2—162no—
273C2C11×#200812yes—
274C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC11×#2815C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3094C2semidirect
3. C11×#1820C2semidirect
4. C11×#1510C2semidirect
5. C11×#1306C2semidirect
33. C2×C11×C4⋊C4D4semidirect
45. C11×C22⋊C8D4semidirect
49. #9983C11direct (N × H)
83. #3094C2×C11semidirect
85. #1820C2×C11semidirect
86. #1510C2×C11semidirect
87. #1306C2×C11semidirect
164. C2×C4⋊C4D4×C11semidirect
176. C22⋊C8D4×C11semidirect
219. C11#9983direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C11×#28152
C11×#18202
C11×#15102
C11×#13062
#998311