Finite Group Databasebeta

← C11×#11518 #14588711

Subgroups — C11×#11518 #14588711

Order 2816.

446 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2296C211yesmaximal, characteristic
2C11×#1464C212yesmaximal
3C11×#1326C214yesmaximal
4C2×C11×#117C411yescharacteristic
5C2×C11×#117C2211yescharacteristic
6C22×C42×C11C411yescharacteristic
7C11×#432—22no—
8C11×#389—22no—
9C11×#385C412yes—
10C11×#385C2212yes—
11C4×C11×C4⋊C4—22no—
12C11×#324—22no—
13C11×#323C2214yes—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11C2×C412yes—
16C11×#117—24no—
17C11×#117—42no—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C11×C22⋊C4C2×C412yes—
23C2×C11×C22⋊C4C2×C411yescharacteristic
24C2×C11×C22⋊C4C2311yescharacteristic
25C2×C42×C11—21no—
26C2×C42×C11—21no—
27C2×C42×C11—21no—
28C2×C42×C11—42no—
29C2×C42×C11D412yes—
30C11×C4⋊C8—42no—
31C11×C22⋊C8—24no—
32C11×#97—42no—
33C11×#95—22no—
34C11×#95—22no—
35#11518C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11C22×C411yescharacteristic
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—44no—
43C22×C4×C11—42no—
44C22×C4×C11C22⋊C411yescharacteristic
45C22×C4×C11C22⋊C412yes—
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C2×D412yes—
48C2×C8×C11—44no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—44no—
52C11×C4⋊C4—44no—
53C11×C22⋊C4—22no—
54C11×C22⋊C4—41no—
55C11×C22⋊C4—41no—
56C11×C22⋊C4M1614yes—
57C42×C11—24no—
58C42×C11—22no—
59C42×C11—22no—
60C42×C11—42no—
61C42×C11—42no—
62#2296C2×C1111yescharacteristic
63#1464C2×C1112yes—
64#1326C2×C1114yes—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—42no—
68C23×C11C2×C22⋊C411yescharacteristic
69C23×C11C2×M1612yes—
70C2×C4×C11—28no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—24no—
76C2×C4×C11—24no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11—44no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—44no—
87C2×C4×C11#9912yes—
88C2×C4×C11#10112yes—
89C8×C11—84no—
90C2×#117C4×C1111yescharacteristic
91C2×#117C22×C1111yescharacteristic
92C22×C42C4×C1111yescharacteristic
93#432—22no—
94#389—22no—
95#385C4×C1112yes—
96#385C22×C1112yes—
97C4×C4⋊C4—22no—
98#324—22no—
99#323C22×C1114yes—
100C22×C11—22no—
101C22×C11—22no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11#40711yescharacteristic
106C22×C11C2×#9911yescharacteristic
107C22×C11C2×#10111yescharacteristic
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—44no—
111C4×C11—42no—
112C4×C11—44no—
113C4×C11—42no—
114C23×C4C2×C4×C1111yescharacteristic
115C23×C4C2×C4×C1112yes—
116#117—24no—
117#117—42no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4D4×C1112yes—
122C2×C22⋊C4C2×C4×C1112yes—
123C2×C22⋊C4C2×C4×C1111yescharacteristic
124C2×C22⋊C4C23×C1111yescharacteristic
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—42no—
129C2×C42D4×C1112yes—
130C4⋊C8—42no—
131C22⋊C8—24no—
132#97—42no—
133#95—22no—
134#95—22no—
135C2×C11—21no—
136C2×C11—21no—
137C2×C11—42no—
138C2×C11#146311yescharacteristic
139C2×C11#212012yes—
140C24C22×C4×C1111yescharacteristic
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—44no—
147C22×C4—42no—
148C22×C4C11×C22⋊C411yescharacteristic
149C22×C4C11×C22⋊C411yescharacteristic
150C22×C4C11×C22⋊C412yes—
151C22×C4C2×D4×C1112yes—
152C2×C8—44no—
153C4⋊C4—24no—
154C4⋊C4—42no—
155C4⋊C4—44no—
156C4⋊C4—44no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—41no—
160C22⋊C4C11×M1614yes—
161C42—24no—
162C42—22no—
163C42—22no—
164C42—42no—
165C42—42no—
166C11#1151811yescharacteristic, direct product factor, Sylow
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×C11×C22⋊C411yescharacteristic
171C23C2×C11×M1612yes—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4C11×#9912yes—
190C2×C4C11×#10112yes—
191C8—84no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C11×#40711yescharacteristic
198C22C2×C11×#9911yescharacteristic
199C22C2×C11×#10111yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—42no—
204C4—44no—
205C4—42no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2C11×#146311yescharacteristic
210C2C11×#212012yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
35. #11518C11direct (N × H)
166. C11#11518direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22962
C11×#14642
C11×#13262
#1151811