Finite Group Databasebeta

← #14645269

Subgroups — #14645269

Order 2816.

1030 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 227 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×#10622184C214yesmaximal, complemented
3C22×C11×C4⋊Q8C211yesmaximal, characteristic
4C23×Q8×C11C412yes—
5C2×C11×C4⋊Q8—28no—
6C2×C11×C4⋊Q8—22no—
7C2×C11×C4⋊Q8C412yes—
8C2×C11×C4⋊Q8C2212yes—
9C22×C11×C4⋊C4—22no—
10C22×C42×C11C2211yescharacteristic
11C2×C22⋊(C11⋊C8)—22no—
12C2×C4⋊(C11⋊C8)C2214yes—
13#10622184—28no—
14#10622162—22no—
15C22×Q8×C11—28no—
16C22×Q8×C11—22no—
17C22×Q8×C11—44no—
18C22×Q8×C11—44no—
19C22×Q8×C11C2×C414yes—
20C23×C4×C11—22no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D412yes—
23C11×C4⋊Q8—216no—
24C11×C4⋊Q8—28no—
25C11×C4⋊Q8—24no—
26C11×C4⋊Q8D418yes—
27C2×C11×C4⋊C4—216no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4—24no—
30C2×C42×C11—24no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D412yes—
33C2×C42×C11C2311yescharacteristic
34C22×C11⋊C8—24no—
35C22⋊(C11⋊C8)—44no—
36C4⋊(C11⋊C8)—28no—
37#8342—111nomaximal, Sylow
38C24×C11C22⋊C411yescharacteristic
39C2×Q8×C11—28no—
40C2×Q8×C11—24no—
41C2×Q8×C11—432no—
42C2×Q8×C11—44no—
43C2×Q8×C11—44no—
44C2×Q8×C11—44no—
45C2×Q8×C11—44no—
46C2×Q8×C11C22⋊C418yes—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—24no—
51C22×C4×C11—24no—
52C22×C4×C11—28no—
53C22×C4×C11—24no—
54C22×C4×C11—44no—
55C22×C4×C11—44no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11SD1614yes—
59C22×C4×C11Q1614yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D412yes—
62C11×C4⋊C4—216no—
63C11×C4⋊C4—216no—
64C42×C11—22no—
65C42×C11—24no—
66C42×C11C2×D414yes—
67C2×C11⋊C8—44no—
68C2×C11⋊C8—44no—
69C2×C11⋊C8—44no—
70C22×C4⋊Q8D1111yescharacteristic
71#1797—112no—
72C2×#333—114no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11#10012yes—
77C23×C11#10314yes—
78C23×C11C2×C22⋊C411yescharacteristic
79Q8×C11—48no—
80Q8×C11—416no—
81Q8×C11—48no—
82C2×C4×C11—28no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—28no—
90C2×C4×C11—28no—
91C2×C4×C11—28no—
92C2×C4×C11—416no—
93C2×C4×C11—44no—
94C2×C4×C11—44no—
95C2×C4×C11#10012yes—
96C2×C4×C11#10314yes—
97C2×C4×C11C2×C22⋊C412yes—
98C2×C4×C11#12014yes—
99C2×C4×C11C2×SD1612yes—
100C2×C4×C11C2×Q1612yes—
101C2×C4×C11#13714yes—
102C11⋊C8—84no—
103C23×Q8Dic1112yes—
104C2×C4⋊Q8—28no—
105C2×C4⋊Q8—22no—
106C2×C4⋊Q8Dic1112yes—
107C2×C4⋊Q8C2×D1112yes—
108C22×C4⋊C4—22no—
109C22×C42C2×D1111yescharacteristic
110C2×C4⋊C8—114no—
111C2×C22⋊C8—222no—
112#336—222no—
113#333—228no—
114C22×C11—24no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—24no—
118C22×C11#33314yescomplemented
119C22×C11#37911yescharacteristic
120C22×C11C2×#10011yescharacteristic
121C22×C11C2×#10011yescharacteristic
122C22×C11C2×#10312yes—
123C22×C11#41912yes—
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—24no—
127C4×C11—48no—
128C4×C11#44814yes—
129C4×C11#45114yes—
130C22×Q8—28no—
131C22×Q8—22no—
132C22×Q8—44no—
133C22×Q8—44no—
134C22×Q8C2×Dic1114yes—
135C23×C4—22no—
136C23×C4C2×Dic1111yescharacteristic
137C23×C4C22⋊D1112yes—
138C22×C8—224no—
139C4⋊Q8—216no—
140C4⋊Q8—28no—
141C4⋊Q8—24no—
142C4⋊Q8C22⋊D1118yes—
143C2×C4⋊C4—216no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—24no—
146C2×C42—24no—
147C2×C42C2×Dic1111yescharacteristic
148C2×C42C22⋊D1112yes—
149C2×C42C22×D1111yescharacteristic
150C4⋊C8—228no—
151C22⋊C8—444no—
152C2×C11—24no—
153C2×C11C2×#33311yescharacteristic
154C2×C11#154812yes—
155C2×C11#155811yescharacteristic
156C2×C11#178311yescharacteristic
157C2×C11#178712yes—
158C24C22⋊Dic1111yescharacteristic
159C2×Q8—28no—
160C2×Q8—24no—
161C2×Q8—432no—
162C2×Q8—44no—
163C2×Q8—44no—
164C2×Q8—44no—
165C2×Q8—44no—
166C2×Q8C22⋊Dic1118yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—24no—
172C22×C4—28no—
173C22×C4—24no—
174C22×C4—44no—
175C22×C4—44no—
176C22×C4#432514yes—
177C22×C4#432614yes—
178C22×C4C22⋊Dic1111yescharacteristic
179C22×C4C22⋊Dic1112yes—
180C22×C4C22×Dic1111yescharacteristic
181C22×C4C2×C22⋊D1112yes—
182C2×C8—444no—
183C2×C8—444no—
184C2×C8—444no—
185C4⋊C4—216no—
186C4⋊C4—216no—
187C42—22no—
188C42—24no—
189C42C2×C22⋊D1114yes—
190C11#834211yescharacteristic, complemented, Sylow
191C23—21no—
192C23—22no—
193C23—21no—
194C23#6689712yes—
195C23#6689914yes—
196C23C2×C22⋊Dic1111yescharacteristic
197Q8—48no—
198Q8—416no—
199Q8—48no—
200C2×C4—28no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—28no—
208C2×C4—28no—
209C2×C4—28no—
210C2×C4—416no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4#6689712yes—
214C2×C4#6689914yes—
215C2×C4C2×#432512yes—
216C2×C4#6699514yes—
217C2×C4C2×#432612yes—
218C2×C4C2×C22⋊Dic1112yes—
219C2×C4#6700614yes—
220C8—884no—
221C22—24no—
222C22—24no—
223C22—22no—
224C22—22no—
225C22#1062218414yescomplemented
226C22C2×#6689711yescharacteristic
227C22C2×#6689711yescharacteristic
228C22C2×#6689912yes—
229C22#1062283812yes—
230C22#1062286011yescharacteristic
231C4—24no—
232C4—22no—
233C4—22no—
234C4—48no—
235C4#1062284014yes—
236C4#1062284114yes—
237C2—24no—
238C2C2×#1062218411yescharacteristic
239C2#1306729712yes—
240C2#1306734211yescharacteristic
241C2#1306853711yescharacteristic
242C2#1306855112yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC22×C4⋊Q8D11
hypocenterC11#8342
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622184C2semidirect
118. C22×C11#333semidirect
190. C11#8342semidirect
225. C22#10622184semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221842
C22×C11×C4⋊Q82
#834211