Finite Group Databasebeta

← C11×#10299 #14587492

Subgroups — C11×#10299 #14587492

Order 2816.

576 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3229C212yesmaximal
2C11×#2868C211yesmaximal, characteristic
3C11×#1994C211yesmaximal, characteristic
4C11×#1546C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×C11×C4⋊Q8—22no—
8C2×C11×C4⋊Q8C2212yes—
9C11×#498—22no—
10C11×#487—22no—
11C11×#483—24no—
12C11×#475—24no—
13C11×#431C2212yes—
14C11×#423C2211yescharacteristic
15C11×#384—24no—
16C43×C11C2211yescharacteristic
17C11×#339—22no—
18C11×#332—24no—
19C22×Q8×C11—22no—
20C2×C11×M16—21no—
21C11×C4⋊Q8—22no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—44no—
26C11×C4⋊Q8—44no—
27C11×C4⋊Q8D412yes—
28C11×#125—21no—
29C11×C22⋊Q8—22no—
30C4×Q8×C11—22no—
31C11×#117—21no—
32C2×C11×C4⋊C4—28no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4D414yes—
35C2×C42×C11—22no—
36C2×C42×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38C11×#106—28no—
39C11×C4⋊C8—22no—
40C11×C4⋊C8D414yes—
41C11×#103—28no—
42C11×C22⋊C8—22no—
43C4×C8×C11—22no—
44#10299C1111yesmaximal, characteristic, direct product factor, Sylow
45C2×Q8×C11—22no—
46C2×Q8×C11—42no—
47C2×Q8×C11—42no—
48C2×Q8×C11—44no—
49C2×Q8×C11—44no—
50C22×C4×C11—22no—
51C22×C4×C11—24no—
52C22×C4×C11C2×D412yes—
53C22×C4×C11C2×D411yescharacteristic
54C11×M16—42no—
55C2×C8×C11—24no—
56C2×C8×C11—41no—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—24no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—416no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—41no—
66C42×C11—28no—
67C42×C11—22no—
68C42×C11—41no—
69C42×C11SD1614yes—
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D412yes—
72C42×C11#4111yescharacteristic
73#3229C2×C1112yes—
74#2868C2×C1111yescharacteristic
75#1994C2×C1111yescharacteristic
76#1546C2×C1112yes—
77#1276C2×C1111yescharacteristic
78C23×C11#12011yescharacteristic
79Q8×C11—44no—
80Q8×C11—84no—
81Q8×C11—82no—
82Q8×C11—82no—
83C2×C4×C11—28no—
84C2×C4×C11—24no—
85C2×C4×C11—24no—
86C2×C4×C11—42no—
87C2×C4×C11—44no—
88C2×C4×C11—48no—
89C2×C4×C11#12012yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11#12711yescharacteristic
93C2×C4×C11C2×SD1612yes—
94C2×C4×C11AGL(1,ℤ/8)12yes—
95C8×C11—44no—
96C8×C11—81no—
97#533C22×C1111yescharacteristic
98C2×C4⋊Q8—22no—
99C2×C4⋊Q8C22×C1112yes—
100#498—22no—
101#487—22no—
102#483—24no—
103#475—24no—
104#431C22×C1112yes—
105#423C22×C1111yescharacteristic
106#384—24no—
107C43C22×C1111yescharacteristic
108#339—22no—
109#332—24no—
110C22×C11—22no—
111C22×C11#39211yescharacteristic
112C22×C11#45012yes—
113C4×C11—28no—
114C4×C11—22no—
115C4×C11—82no—
116C4×C11—84no—
117C4×C11#45614yes—
118C4×C11#46012yes—
119C4×C11#49211yescharacteristic
120C4×C11#49611yescharacteristic
121C22×Q8—22no—
122C2×M16—21no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—44no—
128C4⋊Q8—44no—
129C4⋊Q8D4×C1112yes—
130#125—21no—
131C22⋊Q8—22no—
132C4×Q8—22no—
133#117—21no—
134C2×C4⋊C4—28no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C1114yes—
137C2×C42—22no—
138C2×C42D4×C1112yes—
139C2×C42C23×C1111yescharacteristic
140#106—28no—
141C4⋊C8—22no—
142C4⋊C8D4×C1114yes—
143#103—28no—
144C22⋊C8—22no—
145C4×C8—22no—
146C2×C11—22no—
147C2×C11#200512yes—
148C2×C11#201411yescharacteristic
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—44no—
153C2×Q8—44no—
154C22×C4—22no—
155C22×C4—24no—
156C22×C4C2×D4×C1112yes—
157C22×C4C2×D4×C1111yescharacteristic
158M16—42no—
159C2×C8—24no—
160C2×C8—41no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—416no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C22⋊C4—41no—
170C42—28no—
171C42—22no—
172C42—41no—
173C42C11×SD1614yes—
174C42C2×D4×C1111yescharacteristic
175C42C2×D4×C1112yes—
176C42C11×#4111yescharacteristic
177C11#1029911yescharacteristic, direct product factor, Sylow
178C23C11×#12011yescharacteristic
179Q8—44no—
180Q8—82no—
181Q8—82no—
182Q8—84no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—48no—
189C2×C4C11×#12012yes—
190C2×C4C11×#12112yes—
191C2×C4C11×#12111yescharacteristic
192C2×C4C11×#12711yescharacteristic
193C2×C4C2×C11×SD1612yes—
194C2×C4C11×AGL(1,ℤ/8)12yes—
195C8—44no—
196C8—81no—
197C22—22no—
198C22C11×#39211yescharacteristic
199C22C11×#45012yes—
200C4—28no—
201C4—22no—
202C4—82no—
203C4—84no—
204C4C11×#45614yes—
205C4C11×#46012yes—
206C4C11×#49211yescharacteristic
207C4C11×#49611yescharacteristic
208C2—22no—
209C2C11×#200512yes—
210C2C11×#201411yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
44. #10299C11direct (N × H)
177. C11#10299direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#28682
C11×#19942
C11×#15462
C11×#12762
#1029911