Finite Group Databasebeta

← #14645281

Subgroups — #14645281

Order 2816.

802 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 187 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#13068596C212yesmaximal
2C2×#10622185C214yesmaximal, complemented
3C2×C11×#533C211yesmaximal, characteristic
4C11×#533—28no—
5C2×C11×C4⋊Q8C2212yes—
6C2×C11×#125C412yes—
7C2×C11×C22⋊Q8—22no—
8C2×C4×Q8×C11—22no—
9C2×C11×#117C412yes—
10C22×C42×C11C2211yescharacteristic
11C2×C22⋊(C11⋊C8)—22no—
12C2×C4⋊(C11⋊C8)C2214yes—
13#10622185—28no—
14#10622162—22no—
15C22×Q8×C11—22no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D412yes—
18C11×C4⋊Q8—24no—
19C11×C4⋊Q8D418yes—
20C11×#125—28no—
21C11×C22⋊Q8—216no—
22C4×Q8×C11—216no—
23C11×#117—28no—
24C2×C11×C4⋊C4—24no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4C2×C414yes—
27C2×C11×C22⋊C4—22no—
28C2×C42×C11—22no—
29C2×C42×C11—24no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D412yes—
32C2×C42×C11C2311yescharacteristic
33C22×C11⋊C8—24no—
34C22⋊(C11⋊C8)—44no—
35C4⋊(C11⋊C8)—28no—
36#8345—111nomaximal, Sylow
37C24×C11C22⋊C411yescharacteristic
38C2×Q8×C11—28no—
39C2×Q8×C11—44no—
40C2×Q8×C11—42no—
41C2×Q8×C11—42no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—24no—
46C22×C4×C11—24no—
47C22×C4×C11—24no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11C22⋊C412yes—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C2×D412yes—
54C11×C4⋊C4—216no—
55C11×C4⋊C4—24no—
56C11×C4⋊C4—28no—
57C11×C4⋊C4C22⋊C418yes—
58C11×C22⋊C4—28no—
59C42×C11—28no—
60C42×C11—22no—
61C42×C11—24no—
62C42×C11C2×D414yes—
63C2×C11⋊C8—44no—
64C2×C11⋊C8—44no—
65C2×C11⋊C8—44no—
66C2×#533D1111yescharacteristic
67#1797—112no—
68C2×#332—114no—
69C23×C11—21no—
70C23×C11—21no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11#10112yes—
74C23×C11C2×C22⋊C411yescharacteristic
75Q8×C11—48no—
76Q8×C11—48no—
77C2×C4×C11—28no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—28no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—44no—
87C2×C4×C11—44no—
88C2×C4×C11—44no—
89C2×C4×C11—44no—
90C2×C4×C11#10112yes—
91C2×C4×C11C2×C22⋊C412yes—
92C2×C4×C11#12014yes—
93C2×C4×C11#13514yes—
94C2×C4×C11AGL(1,ℤ/8)12yes—
95C2×C4×C11#13712yes—
96C11⋊C8—84no—
97#533—28no—
98C2×C4⋊Q8C2×D1112yes—
99C2×#125Dic1112yes—
100C2×C22⋊Q8—22no—
101C2×C4×Q8—22no—
102C2×#117Dic1112yes—
103C22×C42C2×D1111yescharacteristic
104C2×C4⋊C8—114no—
105C2×C22⋊C8—222no—
106#336—222no—
107#332—228no—
108C22×C11—24no—
109C22×C11—22no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—42no—
113C22×C11#37911yescharacteristic
114C22×C11C2×#10111yescharacteristic
115C22×C11C2×#10111yescharacteristic
116C22×C11#41612yes—
117C22×C11#41712yes—
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—42no—
121C4×C11—48no—
122C4×C11#44914yes—
123C4×C11#45214yes—
124C22×Q8—22no—
125C23×C4C2×Dic1111yescharacteristic
126C23×C4C22⋊D1112yes—
127C22×C8—224no—
128C4⋊Q8—24no—
129C4⋊Q8C22⋊D1118yes—
130#125—28no—
131C22⋊Q8—216no—
132C4×Q8—216no—
133#117—28no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C2×Dic1114yes—
137C2×C22⋊C4—22no—
138C2×C42—22no—
139C2×C42—24no—
140C2×C42C2×Dic1111yescharacteristic
141C2×C42C22⋊D1112yes—
142C2×C42C22×D1111yescharacteristic
143C4⋊C8—228no—
144C22⋊C8—444no—
145C2×C11—42no—
146C2×C11#154411yescharacteristic
147C2×C11#155212yes—
148C2×C11#156111yescharacteristic
149C2×C11#178411yescharacteristic
150C2×C11#178812yes—
151C24C22⋊Dic1111yescharacteristic
152C2×Q8—28no—
153C2×Q8—42no—
154C2×Q8—44no—
155C2×Q8—42no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4C22⋊Dic1112yes—
165C22×C4C22⋊Dic1111yescharacteristic
166C22×C4C22×Dic1111yescharacteristic
167C22×C4C2×C22⋊D1112yes—
168C2×C8—444no—
169C2×C8—444no—
170C2×C8—444no—
171C4⋊C4—216no—
172C4⋊C4—24no—
173C4⋊C4—28no—
174C4⋊C4C22⋊Dic1118yes—
175C22⋊C4—28no—
176C42—28no—
177C42—22no—
178C42—24no—
179C42C2×C22⋊D1114yes—
180C11#834511yescharacteristic, complemented, Sylow
181C23—21no—
182C23—22no—
183C23—22no—
184C23—21no—
185C23#6690012yes—
186C23C2×C22⋊Dic1111yescharacteristic
187Q8—48no—
188Q8—48no—
189C2×C4—28no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—28no—
198C2×C4—44no—
199C2×C4—44no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4#6690012yes—
203C2×C4#6700212yes—
204C2×C4#6700314yes—
205C2×C4#6700412yes—
206C2×C4C2×C22⋊Dic1112yes—
207C2×C4#6700614yes—
208C8—884no—
209C22—24no—
210C22—22no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22C2×#6690011yescharacteristic
215C22C2×#6690011yescharacteristic
216C22#1062284512yes—
217C22#1062284612yes—
218C22#1062286011yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—48no—
223C4#1062285114yes—
224C4#1062285214yes—
225C2—42no—
226C2#1306728111yescharacteristic
227C2#1306731612yes—
228C2#1306735411yescharacteristic
229C2#1306854011yescharacteristic
230C2#1306855612yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#533C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#533D11
hypocenterC11#8345
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. C2×#10622185C2semidirect
180. C11#8345semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221852
C2×C11×#5332
#834511