Finite Group Databasebeta

← C11×#11450 #14588643

Subgroups — C11×#11450 #14588643

Order 2816.

434 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2317C211yesmaximal, characteristic
2C11×#1458C212yesmaximal
3C11×#1325C214yesmaximal, complemented
4C2×C11×#117C411yescharacteristic
5C2×C11×#117C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C11×#431—22no—
8C11×#389—22no—
9C11×#385—22no—
10C11×#384C2212yes—
11C11×#382C412yes—
12C11×#324C2214yes—
13C11×#323—22no—
14C23×C4×C11—21no—
15C23×C4×C11C2×C411yescharacteristic
16C11×#117—22no—
17C11×#117—42no—
18C11×#117C814yescomplemented
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—21no—
21C2×C11×C4⋊C4—24no—
22C2×C11×C4⋊C4—42no—
23C2×C11×C4⋊C4C2×C412yes—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4D412yes—
28C2×C42×C11C2×C412yes—
29C2×C42×C11D412yes—
30C11×C4⋊C8—42no—
31C11×C22⋊C8—24no—
32C4×C8×C11—42no—
33C11×#95—24no—
34#11450C1111yesmaximal, characteristic, direct product factor, Sylow
35C24×C11C22⋊C411yescharacteristic
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—42no—
41C22×C4×C11—82no—
42C22×C4×C11C22⋊C412yes—
43C22×C4×C11C22⋊C411yescharacteristic
44C22×C4×C11C2×C812yes—
45C22×C4×C11M1612yes—
46C22×C4×C11C22×C411yescharacteristic
47C22×C4×C11C2×D412yes—
48C2×C8×C11—44no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—41no—
51C11×C4⋊C4—41no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—84no—
55C11×C22⋊C4—24no—
56C11×C22⋊C4—42no—
57C42×C11—22no—
58C42×C11—22no—
59C42×C11—22no—
60C42×C11C2×C814yes—
61#2317C2×C1111yescharacteristic
62#1458C2×C1112yes—
63#1325C2×C1114yescomplemented
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11C22⋊C812yes—
69C23×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—24no—
73C2×C4×C11—24no—
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—42no—
81C2×C4×C11—44no—
82C2×C4×C11—42no—
83C2×C4×C11—84no—
84C2×C4×C11C22⋊C812yes—
85C2×C4×C11#9912yes—
86C2×C4×C11#10112yes—
87C2×C4×C11C22×C811yescharacteristic
88C2×C4×C11C2×M1611yescharacteristic
89C8×C11—84no—
90C2×#117C4×C1111yescharacteristic
91C2×#117C22×C1111yescharacteristic
92C22×C4⋊C4C4×C1111yescharacteristic
93#431—22no—
94#389—22no—
95#385—22no—
96#384C22×C1112yes—
97#382C4×C1112yes—
98#324C22×C1114yes—
99#323—22no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—22no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11C2×C22⋊C811yescharacteristic
108C22×C11C2×#9911yescharacteristic
109C22×C11C2×#10111yescharacteristic
110C4×C11—21no—
111C4×C11—21no—
112C4×C11—44no—
113C4×C11—42no—
114C4×C11—42no—
115C4×C11—82no—
116C4×C11#32414yes—
117C23×C4—21no—
118C23×C4C2×C4×C1111yescharacteristic
119#117—22no—
120#117—42no—
121#117C8×C1114yescomplemented
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4C2×C4×C1112yes—
127C2×C4⋊C4C2×C4×C1111yescharacteristic
128C2×C4⋊C4C23×C1111yescharacteristic
129C2×C22⋊C4—21no—
130C2×C22⋊C4D4×C1112yes—
131C2×C42C2×C4×C1112yes—
132C2×C42D4×C1112yes—
133C4⋊C8—42no—
134C22⋊C8—24no—
135C4×C8—42no—
136#95—24no—
137C2×C11—21no—
138C2×C11—21no—
139C2×C11—42no—
140C2×C11C2×#32411yescharacteristic
141C2×C11#212811yescharacteristic
142C2×C11#213511yescharacteristic
143C24C11×C22⋊C411yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—82no—
150C22×C4C11×C22⋊C412yes—
151C22×C4C11×C22⋊C411yescharacteristic
152C22×C4C2×C8×C1112yes—
153C22×C4C11×M1612yes—
154C22×C4C22×C4×C1111yescharacteristic
155C22×C4C2×D4×C1112yes—
156C2×C8—44no—
157C4⋊C4—24no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—84no—
163C22⋊C4—24no—
164C22⋊C4—42no—
165C42—22no—
166C42—22no—
167C42—22no—
168C42C2×C8×C1114yes—
169C11#1145011yescharacteristic, direct product factor, Sylow
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23C11×C22⋊C812yes—
175C23C2×C11×C22⋊C411yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4C11×C22⋊C812yes—
191C2×C4C11×#9912yes—
192C2×C4C11×#10112yes—
193C2×C4C22×C8×C1111yescharacteristic
194C2×C4C2×C11×M1611yescharacteristic
195C8—84no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×C11×C22⋊C811yescharacteristic
204C22C2×C11×#9911yescharacteristic
205C22C2×C11×#10111yescharacteristic
206C4—21no—
207C4—21no—
208C4—44no—
209C4—42no—
210C4—42no—
211C4—82no—
212C4C11×#32414yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×C11×#32411yescharacteristic
217C2C11×#212811yescharacteristic
218C2C11×#213511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C2×C4 ▷ 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
3. C11×#1325C2semidirect
18. C11×#117C8semidirect
34. #11450C11direct (N × H)
63. #1325C2×C11semidirect
121. #117C8×C11semidirect
169. C11#11450direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23172
C11×#14582
C11×#13252
#1145011