Finite Group Databasebeta

← #14647172

Subgroups — #14647172

Order 2816.

554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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
1#13068378C212yesmaximal
2#13066497C214yesmaximal, complemented
3C2×C11×#382C211yesmaximal, characteristic
4C22×C11×C4⋊C4C411yescharacteristic
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C42×C11C2211yescharacteristic
7C11×#382—22no—
8C11×#382C412yes—
9C11×#382C2212yes—
10C2×C11×#95—22no—
11C2×C22⋊(C11⋊C8)—22no—
12C2×#66867C2214yes—
13#10622162—22no—
14C23×C4×C11—21no—
15C23×C4×C11—21no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D412yes—
18C2×C11×C4⋊C4—21no—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4—42no—
21C2×C11×C4⋊C4—42no—
22C2×C11×C4⋊C4C2×C412yes—
23C2×C11×C4⋊C4C2×C412yes—
24C2×C42×C11—24no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C22×C11⋊C8—24no—
29C11×#95—24no—
30C11×#95—24no—
31C22⋊(C11⋊C8)—28no—
32#66867—28no—
33#8718—111nomaximal, Sylow
34C24×C11C22⋊C411yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11—24no—
39C22×C4×C11—24no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—42no—
43C22×C4×C11—44no—
44C22×C4×C11—42no—
45C22×C4×C11—42no—
46C22×C4×C11—44no—
47C22×C4×C11C22⋊C412yes—
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C22×C411yescharacteristic
50C22×C4×C11C2×D412yes—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C42×C11—22no—
56C42×C11—24no—
57C42×C11#4114yes—
58C2×C11⋊C8—28no—
59C2×C11⋊C8—44no—
60C2×C11⋊C8—44no—
61C2×#382D1111yescharacteristic
62#1749—112no—
63#1295—114no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—22no—
67C23×C11#10012yes—
68C23×C11#10414yes—
69C23×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11—28no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—48no—
81C2×C4×C11—42no—
82C2×C4×C11—42no—
83C2×C4×C11—44no—
84C2×C4×C11—44no—
85C2×C4×C11—84no—
86C2×C4×C11—84no—
87C2×C4×C11#10112yes—
88C2×C4×C11#11712yes—
89C2×C4×C11#12314yes—
90C11⋊C8—48no—
91C22×C4⋊C4Dic1111yescharacteristic
92C22×C4⋊C4Dic1111yescharacteristic
93C22×C42C2×D1111yescharacteristic
94C2×C22⋊C8—222no—
95C2×#97—114no—
96#382—22no—
97#382Dic1112yes—
98#382C2×D1112yes—
99C2×#95—22no—
100#336—222no—
101C22×C11—22no—
102C22×C11—24no—
103C22×C11—24no—
104C22×C11—22no—
105C22×C11#32914yes—
106C22×C11#38111yescharacteristic
107C22×C11C2×#10011yescharacteristic
108C22×C11C2×#10111yescharacteristic
109C22×C11C2×#10412yes—
110C22×C11#42112yes—
111C4×C11—22no—
112C4×C11—22no—
113C4×C11—24no—
114C4×C11—42no—
115C4×C11—82no—
116C4×C11—82no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4C2×Dic1111yescharacteristic
120C23×C4C22⋊D1112yes—
121C22×C8—224no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4C2×Dic1112yes—
127C2×C4⋊C4C2×Dic1112yes—
128C2×C42—24no—
129C2×C42C2×Dic1111yescharacteristic
130C2×C42C22⋊D1112yes—
131C2×C42C22×D1111yescharacteristic
132C22⋊C8—228no—
133#97—228no—
134#95—24no—
135#95—24no—
136C2×C11—24no—
137C2×C11C2×#32911yescharacteristic
138C2×C11#152812yes—
139C2×C11#153311yescharacteristic
140C2×C11#182111yescharacteristic
141C2×C11#182612yes—
142C24C22⋊Dic1111yescharacteristic
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4—24no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—42no—
151C22×C4—44no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—44no—
155C22×C4C22⋊Dic1112yes—
156C22×C4C22⋊Dic1111yescharacteristic
157C22×C4C22×Dic1111yescharacteristic
158C22×C4C2×C22⋊D1112yes—
159C2×C8—228no—
160C2×C8—444no—
161C2×C8—444no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C42—22no—
167C42—24no—
168C42#433914yes—
169C11#871811yescharacteristic, complemented, Sylow
170C23—21no—
171C23—21no—
172C23—22no—
173C23#6689712yes—
174C23#6690114yes—
175C23C2×C22⋊Dic1111yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—84no—
192C2×C4—84no—
193C2×C4#6690012yes—
194C2×C4#6697912yes—
195C2×C4#6698214yes—
196C8—448no—
197C22—22no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22#1062217814yes—
202C22#1062282411yescharacteristic
203C22C2×#6689711yescharacteristic
204C22C2×#6690011yescharacteristic
205C22C2×#6690112yes—
206C22#1062284912yes—
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—24no—
214C2C2×#1062217811yescharacteristic
215C2#1306721812yes—
216C2#1306724011yescharacteristic
217C2#1306869611yescharacteristic
218C2#1306871512yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#382C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#382D11
hypocenterC11#8718
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #13066497C2semidirect
169. C11#8718semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130664972
C2×C11×#3822
#871811