Finite Group Databasebeta

← #14646407

Subgroups — #14646407

Order 2816.

1026 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 163 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#13068540C212yesmaximal
2#13066946C214yesmaximal
3C22×C11×C4⋊Q8C211yesmaximal, characteristic
4C23×Q8×C11C411yescharacteristic
5C23×Q8×C11C2211yescharacteristic
6C2×C11×C4⋊Q8—24no—
7C2×C11×C4⋊Q8—28no—
8C22×C11×C4⋊C4C412yes—
9C22×C11×C4⋊C4C2212yes—
10C22×C42×C11C411yescharacteristic
11C2×#66900—24no—
12#10622820C2214yes—
13#10622166—28no—
14C22×Q8×C11—24no—
15C22×Q8×C11—22no—
16C22×Q8×C11—24no—
17C22×Q8×C11—44no—
18C22×Q8×C11—44no—
19C22×Q8×C11D414yes—
20C23×C4×C11C2×C412yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11C2×C412yes—
24C23×C4×C11C2311yescharacteristic
25C11×C4⋊Q8—232no—
26C2×C11×C4⋊C4—24no—
27C2×C11×C4⋊C4—24no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—24no—
31C2×C11×C4⋊C4D418yes—
32C2×C42×C11—22no—
33C2×C42×C11—24no—
34C2×#4318—24no—
35#66900—48no—
36C22⋊(C11⋊C8)—28no—
37#8551—111nomaximal, Sylow
38C24×C11C22×C411yescharacteristic
39C2×Q8×C11—28no—
40C2×Q8×C11—28no—
41C2×Q8×C11—28no—
42C2×Q8×C11—44no—
43C2×Q8×C11—416no—
44C2×Q8×C11—416no—
45C2×Q8×C11—44no—
46C2×Q8×C11—44no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—24no—
51C22×C4×C11—28no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11—44no—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22⋊C414yes—
61C22×C4×C11C22⋊C414yes—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D414yes—
64C11×C4⋊C4—216no—
65C11×C4⋊C4—216no—
66C42×C11—28no—
67#4318—48no—
68C2×C11⋊C8—44no—
69C22×C4⋊Q8D1111yescharacteristic
70#1784—112no—
71#1463—114no—
72C23×C11—22no—
73C23×C11—24no—
74C23×C11C2×C22⋊C411yescharacteristic
75C23×C11C2×C22⋊C412yes—
76Q8×C11—416no—
77Q8×C11—416no—
78C2×C4×C11—28no—
79C2×C4×C11—28no—
80C2×C4×C11—28no—
81C2×C4×C11—24no—
82C2×C4×C11—22no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11—24no—
86C2×C4×C11—22no—
87C2×C4×C11—24no—
88C2×C4×C11—24no—
89C2×C4×C11—44no—
90C2×C4×C11—44no—
91C2×C4×C11—44no—
92C2×C4×C11—44no—
93C2×C4×C11—44no—
94C2×C4×C11#9914yes—
95C2×C4×C11#10118yescomplemented
96C2×C4×C11#12014yes—
97C11⋊C8—84no—
98C23×Q8Dic1111yescharacteristic
99C23×Q8C2×D1111yescharacteristic
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—28no—
102C22×C4⋊C4Dic1112yes—
103C22×C4⋊C4C2×D1112yes—
104C22×C42Dic1111yescharacteristic
105C2×#101—224no—
106#407—114no—
107#324—228no—
108C22×C11—28no—
109C22×C11—22no—
110C22×C11—22no—
111C22×C11—22no—
112C22×C11#37911yescharacteristic
113C22×C11C2×#9912yes—
114C22×C11C2×#10114yes—
115C4×C11—24no—
116C4×C11—24no—
117C4×C11—28no—
118C4×C11—42no—
119C4×C11—44no—
120C22×Q8—24no—
121C22×Q8—22no—
122C22×Q8—24no—
123C22×Q8—44no—
124C22×Q8—44no—
125C22×Q8C22⋊D1114yes—
126C23×C4C2×Dic1112yes—
127C23×C4C2×Dic1111yescharacteristic
128C23×C4C2×Dic1111yescharacteristic
129C23×C4C2×Dic1112yes—
130C23×C4C22×D1111yescharacteristic
131C2×M16—224no—
132C4⋊Q8—232no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4C22⋊D1118yes—
139C2×C42—22no—
140C2×C42—24no—
141#101—448no—
142C22⋊C8—228no—
143C2×C11—22no—
144C2×C11—24no—
145C2×C11#178111yescharacteristic
146C2×C11#178412yes—
147C24C22×Dic1111yescharacteristic
148C2×Q8—28no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—44no—
152C2×Q8—416no—
153C2×Q8—416no—
154C2×Q8—44no—
155C2×Q8—44no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—28no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—44no—
167C22×C4C22⋊Dic1112yes—
168C22×C4C22⋊Dic1112yes—
169C22×C4C22⋊Dic1114yes—
170C22×C4C22⋊Dic1114yes—
171C22×C4C2×C22⋊D1112yes—
172C22×C4C2×C22⋊D1114yes—
173M16—448no—
174C2×C8—444no—
175C4⋊C4—216no—
176C4⋊C4—216no—
177C42—28no—
178C11#855111yescharacteristic, complemented, Sylow
179C23—22no—
180C23—24no—
181C23C2×C22⋊Dic1111yescharacteristic
182C23C2×C22⋊Dic1112yes—
183Q8—416no—
184Q8—416no—
185C2×C4—28no—
186C2×C4—28no—
187C2×C4—28no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—44no—
197C2×C4—44no—
198C2×C4—44no—
199C2×C4—44no—
200C2×C4—44no—
201C2×C4#6689814yes—
202C2×C4#6690018yescomplemented
203C2×C4#6700614yes—
204C8—884no—
205C22—28no—
206C22—22no—
207C22—22no—
208C22—22no—
209C22C2×#6689812yes—
210C22C2×#6690014yes—
211C22#1062286011yescharacteristic
212C4—24no—
213C4—24no—
214C4—28no—
215C4—42no—
216C4—44no—
217C2—22no—
218C2—24no—
219C2#1306853111yescharacteristic
220C2#1306854012yes—
subgroupG/H
centerC22#10622860
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×C4⋊Q8C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC22×C4⋊Q8D11
hypocenterC11#8551
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
95. C2×C4×C11#101semidirect
178. C11#8551semidirect
202. C2×C4#66900semidirect

Maximal subgroups

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

subgroupindex
#130685402
#130669462
C22×C11×C4⋊Q82
#855111