Finite Group Databasebeta

← C11×#11992 #14589185

Subgroups — C11×#11992 #14589185

Order 2816.

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

normal subgroups only

This group has 412 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×#3151C211yesmaximal, characteristic
2C11×#2165C212yesmaximal, complemented
3C11×#1359C212yesmaximal, complemented
4C11×#1357C212yesmaximal, complemented
5C2×C11×AGL(1,ℤ/8)—22no—
6C11×#532C411yescharacteristic
7C2×C11×#127C411yescharacteristic
8C11×#496—22no—
9C11×#493C411yescharacteristic
10C11×#493C2211yescharacteristic
11C11×#492C411yescharacteristic
12C11×#492C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14C11×#364C2214yescomplemented
15C11×#349—22no—
16C11×#347—22no—
17C2×C11×#41—21no—
18C22×D4×C11—21no—
19C22×D4×C11—41no—
20C11×AGL(1,ℤ/8)—48no—
21C2×C11×SD16—22no—
22C2×C11×SD16—22no—
23C2×C11×D8—22no—
24C2×C11×D8—22no—
25C2×C11×M16D412yes—
26C11×C4⋊Q8C2×C411yescharacteristic
27C11×#127—21no—
28C11×#127—41no—
29C11×#127C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#127C2×C411yescharacteristic
32C11×#124—21no—
33C11×#121—41no—
34C4×D4×C11—41no—
35C2×C42×C11C2×C411yescharacteristic
36C11×M32—24no—
37C11×#97D412yes—
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11C2311yescharacteristic
40#11992C1111yesmaximal, characteristic, direct product factor, Sylow
41C24×C11—41no—
42C11×#41—44no—
43C2×Q8×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11—44no—
48C2×D4×C11—42no—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—84no—
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11C22⋊C411yescharacteristic
58C11×SD16—44no—
59C11×SD16—44no—
60C11×D8—44no—
61C11×D8—44no—
62C11×M16—24no—
63C2×C8×C11C22⋊C412yes—
64C2×C8×C11C2×D412yes—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—42no—
67C42×C11—21no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11C22×C411yescharacteristic
70C11×C16—44no—
71#3151C2×C1111yescharacteristic
72#2165C2×C1112yescomplemented
73#1359C2×C1112yescomplemented
74#1357C2×C1112yescomplemented
75C23×C11—41no—
76C23×C11—41no—
77C23×C11—41no—
78C23×C11—82no—
79C23×C11—84no—
80C23×C11#10011yescharacteristic
81Q8×C11—42no—
82D4×C11—42no—
83D4×C11—42no—
84D4×C11—42no—
85D4×C11—82no—
86D4×C11—82no—
87D4×C11—82no—
88D4×C11—82no—
89D4×C11—84no—
90D4×C11—82no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—82no—
97C2×C4×C11#10011yescharacteristic
98C2×C4×C11C2×C22⋊C411yescharacteristic
99C8×C11—22no—
100C8×C11AGL(1,ℤ/8)14yes—
101C2×AGL(1,ℤ/8)—22no—
102#532C4×C1111yescharacteristic
103C2×#127C4×C1111yescharacteristic
104#496—22no—
105#493C4×C1111yescharacteristic
106#493C22×C1111yescharacteristic
107#492C4×C1111yescharacteristic
108#492C22×C1111yescharacteristic
109C4×M16C22×C1111yescharacteristic
110#364C22×C1114yescomplemented
111#349—22no—
112#347—22no—
113C22×C11—21no—
114C22×C11—41no—
115C22×C11—82no—
116C22×C11—82no—
117C22×C11—82no—
118C22×C11—81no—
119C22×C11—81no—
120C22×C11—81no—
121C22×C11—164no—
122C22×C11C2×#10011yescharacteristic
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—81no—
127C4×C11#41812yes—
128C2×#41—21no—
129C22×D4—21no—
130C22×D4—41no—
131AGL(1,ℤ/8)—48no—
132C2×SD16—22no—
133C2×SD16—22no—
134C2×D8—22no—
135C2×D8—22no—
136C2×M16D4×C1112yes—
137C4⋊Q8C2×C4×C1111yescharacteristic
138#127—21no—
139#127—41no—
140#127C2×C4×C1111yescharacteristic
141#127C2×C4×C1111yescharacteristic
142#127C2×C4×C1111yescharacteristic
143#124—21no—
144#121—41no—
145C4×D4—41no—
146C2×C42C2×C4×C1111yescharacteristic
147M32—24no—
148#97D4×C1112yes—
149C4×C8C2×C4×C1111yescharacteristic
150C4×C8C23×C1111yescharacteristic
151C2×C11—21no—
152C2×C11—41no—
153C2×C11—161no—
154C2×C11—161no—
155C2×C11—161no—
156C2×C11#155511yescharacteristic
157C24—41no—
158#41—44no—
159C2×Q8—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—44no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—42no—
168C2×D4—41no—
169C2×D4—41no—
170C2×D4—84no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4C11×C22⋊C411yescharacteristic
174SD16—44no—
175SD16—44no—
176D8—44no—
177D8—44no—
178M16—24no—
179C2×C8C11×C22⋊C412yes—
180C2×C8C2×D4×C1112yes—
181C4⋊C4—41no—
182C22⋊C4—42no—
183C42—21no—
184C42C11×C22⋊C411yescharacteristic
185C42C22×C4×C1111yescharacteristic
186C16—44no—
187C11#1199211yescharacteristic, direct product factor, Sylow
188C23—41no—
189C23—41no—
190C23—41no—
191C23—82no—
192C23—84no—
193C23C11×#10011yescharacteristic
194Q8—42no—
195D4—42no—
196D4—42no—
197D4—42no—
198D4—82no—
199D4—82no—
200D4—82no—
201D4—82no—
202D4—84no—
203D4—82no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—82no—
210C2×C4C11×#10011yescharacteristic
211C2×C4C2×C11×C22⋊C411yescharacteristic
212C8—22no—
213C8C11×AGL(1,ℤ/8)14yes—
214C22—21no—
215C22—41no—
216C22—82no—
217C22—82no—
218C22—82no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22—164no—
223C22C2×C11×#10011yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—81no—
228C4C11×#41812yes—
229C2—21no—
230C2—41no—
231C2—161no—
232C2—161no—
233C2—161no—
234C2C11×#155511yescharacteristic
subgroupG/H
center, socleC2×C11#1555
commutatorC42C22×C4×C11
Frattini, cosocleC4×C8C23×C11
prime radicalC11×#3151C2
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2165C2semidirect
3. C11×#1359C2semidirect
4. C11×#1357C2semidirect
14. C11×#364C22semidirect
40. #11992C11direct (N × H)
72. #2165C2×C11semidirect
73. #1359C2×C11semidirect
74. #1357C2×C11semidirect
110. #364C22×C11semidirect
187. C11#11992direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31512
C11×#21652
C11×#13592
C11×#13572
#1199211