Finite Group Databasebeta

← C11×#1913 #13064751

Subgroups — C11×#1913 #13064751

Order 1408.

380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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×#534C211yesmaximal, characteristic
2C11×#518C211yesmaximal, characteristic, complemented
3C2×C11×#99C211yesmaximal, characteristic, complemented
4C2×C11×#99C212yesmaximal, complemented
5C11×#342C212yesmaximal, complemented
6C22×D4×C11C2211yescharacteristic
7C22×D4×C11C2211yescharacteristic
8C11×#123—21no—
9C11×#123C412yescomplemented
10C11×#121—22no—
11C11×#120—21no—
12C11×#120C412yescomplemented
13C4×D4×C11—24no—
14C11×#117—21no—
15C2×C11×C22⋊C4—21no—
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C11×#99—22no—
20C11×#99—24no—
21C24×C11C2×C411yescharacteristic, complemented
22C24×C11D411yescharacteristic
23C24×C11C2311yescharacteristic
24C2×D4×C11—22no—
25C2×D4×C11—22no—
26C2×D4×C11—22no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—22no—
30C2×D4×C11—22no—
31C2×D4×C11C2×C412yes—
32C2×D4×C11D412yes—
33C22×C4×C11—22no—
34C22×C4×C11—22no—
35C22×C4×C11—21no—
36C22×C4×C11—22no—
37C22×C4×C11C2×C411yescharacteristic, complemented
38C22×C4×C11D411yescharacteristic
39C11×C4⋊C4—22no—
40C11×C4⋊C4—22no—
41C11×C22⋊C4—22no—
42C11×C22⋊C4—22no—
43C11×C22⋊C4—22no—
44C11×C22⋊C4—21no—
45C11×C22⋊C4—22no—
46C11×C22⋊C4—22no—
47C11×C22⋊C4—22no—
48C11×C22⋊C4C2×C412yescomplemented
49C11×C22⋊C4D414yescomplemented
50C42×C11—22no—
51#1913C1111yesmaximal, characteristic, direct product factor, Sylow
52C23×C11—21no—
53C23×C11—21no—
54C23×C11—21no—
55C23×C11—22no—
56C23×C11—81no—
57C23×C11—81no—
58C23×C11—81no—
59C23×C11C22⋊C412yes—
60C23×C11C22×C411yescharacteristic
61C23×C11C2×D411yescharacteristic
62C23×C11C2×D411yescharacteristic
63C23×C11C2×D412yes—
64C23×C11#4112yes—
65D4×C11—24no—
66D4×C11—24no—
67D4×C11—41no—
68D4×C11—42no—
69D4×C11—41no—
70D4×C11—82no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—42no—
78C2×C4×C11—82no—
79C2×C4×C11—82no—
80C2×C4×C11—81no—
81C2×C4×C11—82no—
82C2×C4×C11C22⋊C412yes—
83#534C2×C1111yescharacteristic
84#518C2×C1111yescharacteristic, complemented
85C2×#99C2×C1111yescharacteristic, complemented
86C2×#99C2×C1112yescomplemented
87#342C2×C1112yescomplemented
88C22×C11—22no—
89C22×C11—42no—
90C22×C11—41no—
91C22×C11—42no—
92C22×C11—41no—
93C22×C11—41no—
94C22×C11—42no—
95C22×C11—42no—
96C22×C11—42no—
97C22×C11—41no—
98C22×C11—81no—
99C22×C11—82no—
100C22×C11C2×C22⋊C411yescharacteristic
101C22×C11C4×D412yes—
102C22×C11#12011yescharacteristic
103C22×C11#12112yes—
104C22×C11#12311yescharacteristic
105C4×C11—22no—
106C4×C11—44no—
107C4×C11—42no—
108C4×C11—41no—
109C4×C11—82no—
110C22×D4C22×C1111yescharacteristic
111C22×D4C22×C1111yescharacteristic
112#123—21no—
113#123C4×C1112yescomplemented
114#121—22no—
115#120—21no—
116#120C4×C1112yescomplemented
117C4×D4—24no—
118#117—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4C22×C1112yes—
121C2×C22⋊C4C22×C1111yescharacteristic
122C2×C22⋊C4C22×C1112yes—
123#99—22no—
124#99—24no—
125C2×C11—21no—
126C2×C11—21no—
127C2×C11—22no—
128C2×C11—22no—
129C2×C11—21no—
130C2×C11—42no—
131C2×C11—81no—
132C2×C11#38611yescharacteristic
133C24C2×C4×C1111yescharacteristic, complemented
134C24D4×C1111yescharacteristic
135C24C23×C1111yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4C2×C4×C1112yes—
144C2×D4D4×C1112yes—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—22no—
149C22×C4C2×C4×C1111yescharacteristic, complemented
150C22×C4D4×C1111yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—22no—
153C22⋊C4—22no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—21no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4C2×C4×C1112yescomplemented
161C22⋊C4D4×C1114yescomplemented
162C42—22no—
163C11#191311yescharacteristic, direct product factor, Sylow
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C11×C22⋊C412yes—
172C23C22×C4×C1111yescharacteristic
173C23C2×D4×C1111yescharacteristic
174C23C2×D4×C1111yescharacteristic
175C23C2×D4×C1112yes—
176C23C11×#4112yes—
177D4—24no—
178D4—24no—
179D4—41no—
180D4—42no—
181D4—41no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4—81no—
193C2×C4—82no—
194C2×C4C11×C22⋊C412yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22C2×C11×C22⋊C411yescharacteristic
208C22C4×D4×C1112yes—
209C22C11×#12011yescharacteristic
210C22C11×#12112yes—
211C22C11×#12311yescharacteristic
212C4—22no—
213C4—44no—
214C4—42no—
215C4—41no—
216C4—82no—
217C2—21no—
218C2—21no—
219C2—22no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2C11×#38611yescharacteristic
subgroupG/H
center, socleC2×C11#386
commutatorC23C22×C4×C11
Frattini, cosocleC24C23×C11
prime radicalC11×#534C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#518C2semidirect
3. C2×C11×#99C2semidirect
4. C2×C11×#99C2semidirect
5. C11×#342C2semidirect
9. C11×#123C4semidirect
12. C11×#120C4semidirect
21. C24×C11C2×C4semidirect
37. C22×C4×C11C2×C4semidirect
48. C11×C22⋊C4C2×C4semidirect
49. C11×C22⋊C4D4semidirect
51. #1913C11direct (N × H)
84. #518C2×C11semidirect
85. C2×#99C2×C11semidirect
86. C2×#99C2×C11semidirect
87. #342C2×C11semidirect
113. #123C4×C11semidirect
116. #120C4×C11semidirect
133. C24C2×C4×C11semidirect
149. C22×C4C2×C4×C11semidirect
160. C22⋊C4C2×C4×C11semidirect
161. C22⋊C4D4×C11semidirect
163. C11#1913direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5342
C11×#5182
C2×C11×#992
C11×#3422
#191311