Finite Group Databasebeta

← C11×#11382 #14588575

Subgroups — C11×#11382 #14588575

Order 2816.

1142 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 1142 conjugacy classes of subgroups — too many to draw. Only its 286 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
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×C11×#343C214yesmaximal
3C11×#1728C212yesmaximal
4C23×Q8×C11C412yes—
5C22×C11×M16C2214yes—
6C2×C11×C4⋊Q8—28no—
7C2×C11×C4⋊Q8—24no—
8C22×C11×C4⋊C4C412yes—
9C22×C11×C4⋊C4C2212yes—
10C22×C42×C11C2211yescharacteristic
11C11×#343—28no—
12C11×#336—24no—
13C22×Q8×C11—28no—
14C22×Q8×C11—24no—
15C22×Q8×C11—48no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11C2×C411yescharacteristic
18C23×C4×C11C2×C414yes—
19C23×C4×C11C2311yescharacteristic
20C2×C11×M16—24no—
21C2×C11×M16—28no—
22C2×C11×M16—28no—
23C2×C11×M16Q818yescomplemented
24C22×C8×C11—24no—
25C11×C4⋊Q8—232no—
26C2×C11×C4⋊C4—28no—
27C2×C11×C4⋊C4—24no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4D418yes—
31C2×C42×C11—24no—
32C2×C42×C11D414yes—
33#11382C1111yesmaximal, characteristic, direct product factor, Sylow
34C24×C11C22×C411yescharacteristic
35C2×Q8×C11—216no—
36C2×Q8×C11—432no—
37C2×Q8×C11—48no—
38C2×Q8×C11—48no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—24no—
42C22×C4×C11—24no—
43C22×C4×C11—24no—
44C22×C4×C11—24no—
45C22×C4×C11—48no—
46C22×C4×C11C22⋊C412yes—
47C22×C4×C11C22⋊C412yes—
48C22×C4×C11C22⋊C418yes—
49C22×C4×C11C2×D414yes—
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×Q814yes—
52C22×C4×C11#4114yes—
53C11×M16—216no—
54C11×M16—48no—
55C2×C8×C11—28no—
56C2×C8×C11—44no—
57C2×C8×C11—44no—
58C11×C4⋊C4—216no—
59C11×C4⋊C4—216no—
60C42×C11—28no—
61C22×C4⋊Q8C2×C1111yescharacteristic
62C2×#343C2×C1114yes—
63#1728C2×C1112yes—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11C2×C22⋊C412yes—
67C23×C11C2×C22⋊C411yescharacteristic
68C23×C11C4×Q814yes—
69Q8×C11—432no—
70C2×C4×C11—28no—
71C2×C4×C11—28no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—28no—
77C2×C4×C11—48no—
78C2×C4×C11—48no—
79C2×C4×C11—48no—
80C2×C4×C11#10014yes—
81C2×C4×C11#10114yes—
82C2×C4×C11#12014yes—
83C2×C4×C11C22⋊Q814yes—
84C2×C4×C11C22⋊Q818yes—
85C2×C4×C11#12412yes—
86C2×C4×C11#12414yes—
87C2×C4×C11C4⋊Q814yes—
88C2×C4×C11C4⋊Q812yes—
89C8×C11—48no—
90C23×Q8C4×C1112yes—
91C22×M16C22×C1114yes—
92C2×C4⋊Q8—28no—
93C2×C4⋊Q8—24no—
94C22×C4⋊C4C4×C1112yes—
95C22×C4⋊C4C22×C1112yes—
96C22×C42C22×C1111yescharacteristic
97#343—28no—
98#336—24no—
99C22×C11—28no—
100C22×C11—22no—
101C22×C11—22no—
102C22×C11#37911yescharacteristic
103C22×C11#39114yes—
104C22×C11#39112yes—
105C22×C11C2×#10012yes—
106C22×C11C2×#10112yes—
107C4×C11—24no—
108C4×C11—24no—
109C4×C11—48no—
110C4×C11#39314yes—
111C4×C11#39514yes—
112C22×Q8—28no—
113C22×Q8—24no—
114C22×Q8—48no—
115C23×C4C2×C4×C1111yescharacteristic
116C23×C4C2×C4×C1111yescharacteristic
117C23×C4C2×C4×C1114yes—
118C23×C4C23×C1111yescharacteristic
119C2×M16—24no—
120C2×M16—28no—
121C2×M16—28no—
122C2×M16Q8×C1118yescomplemented
123C22×C8—24no—
124C4⋊Q8—232no—
125C2×C4⋊C4—28no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—24no—
128C2×C4⋊C4—24no—
129C2×C4⋊C4D4×C1118yes—
130C2×C42—24no—
131C2×C42D4×C1114yes—
132C2×C11—24no—
133C2×C11#144611yescharacteristic
134C2×C11#178311yescharacteristic
135C2×C11#178411yescharacteristic
136C2×C11#199714yes—
137C24C22×C4×C1111yescharacteristic
138C2×Q8—216no—
139C2×Q8—432no—
140C2×Q8—48no—
141C2×Q8—48no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—24no—
146C22×C4—24no—
147C22×C4—24no—
148C22×C4—48no—
149C22×C4C11×C22⋊C412yes—
150C22×C4C11×C22⋊C412yes—
151C22×C4C11×C22⋊C418yes—
152C22×C4C2×D4×C1114yes—
153C22×C4C2×D4×C1112yes—
154C22×C4C2×Q8×C1114yes—
155C22×C4C11×#4114yes—
156M16—216no—
157M16—48no—
158C2×C8—28no—
159C2×C8—44no—
160C2×C8—44no—
161C4⋊C4—216no—
162C4⋊C4—216no—
163C42—28no—
164C11#1138211yescharacteristic, direct product factor, Sylow
165C23—22no—
166C23—22no—
167C23C2×C11×C22⋊C412yes—
168C23C2×C11×C22⋊C411yescharacteristic
169C23C4×Q8×C1114yes—
170Q8—432no—
171C2×C4—28no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—28no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—48no—
181C2×C4C11×#10014yes—
182C2×C4C11×#10114yes—
183C2×C4C11×#12014yes—
184C2×C4C11×C22⋊Q814yes—
185C2×C4C11×C22⋊Q818yes—
186C2×C4C11×#12412yes—
187C2×C4C11×#12414yes—
188C2×C4C11×C4⋊Q814yes—
189C2×C4C11×C4⋊Q812yes—
190C8—48no—
191C22—28no—
192C22—22no—
193C22—22no—
194C22C11×#37911yescharacteristic
195C22C11×#39114yes—
196C22C11×#39112yes—
197C22C2×C11×#10012yes—
198C22C2×C11×#10112yes—
199C4—24no—
200C4—24no—
201C4—48no—
202C4C11×#39314yes—
203C4C11×#39514yes—
204C2—24no—
205C2C11×#144611yescharacteristic
206C2C11×#178311yescharacteristic
207C2C11×#178411yescharacteristic
208C2C11×#199714yes—
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
23. C2×C11×M16Q8semidirect
33. #11382C11direct (N × H)
122. C2×M16Q8×C11semidirect
164. C11#11382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#3432
C11×#17282
#1138211