Finite Group Databasebeta

← #14652887

Subgroups — #14652887

Order 2816.

466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 151 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#13068733C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal
4C2×#10622185C212yesmaximal
5C11×#2862C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C4⋊Q8C2211yescharacteristic
8C11×#391—21no—
9C11×#391—21no—
10C11×#391C414yes—
11C11×#382—22no—
12C43×C11C2211yescharacteristic
13C2×C4⋊(C11⋊C8)C2212yes—
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×#66867—21no—
16#10622185—24no—
17#10622184—24no—
18#10622162—21no—
19#10622162—22no—
20C22×Q8×C11—21no—
21C22×Q8×C11C2×C412yes—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C42×C11C2×C412yes—
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D412yes—
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C22×C11⋊C8—22no—
36C22×C11⋊C8—22no—
37C11×#95—24no—
38C11×#95—24no—
39C4⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)D414yes—
43#66867—42no—
44#9709—111nomaximal, Sylow
45C2×Q8×C11—24no—
46C2×Q8×C11—44no—
47C2×Q8×C11—42no—
48C2×Q8×C11—42no—
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C11×C4⋊C4—24no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C42×C11—22no—
65C42×C11—21no—
66C42×C11—21no—
67C42×C11—24no—
68C42×C11—42no—
69C42×C11C2×D412yes—
70C42×C11#4112yes—
71C2×C11⋊C8—24no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—44no—
76#2862D1111yescharacteristic
77#1831—111no—
78#1767—111no—
79C2×#333—112no—
80C2×#332—112no—
81C23×C11C2×C22⋊C411yescharacteristic
82Q8×C11—84no—
83Q8×C11—82no—
84Q8×C11—82no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—44no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11C4×D412yes—
98C2×C4×C11#12112yes—
99C2×C4×C11#12411yescharacteristic
100C2×C4×C11#12711yescharacteristic
101C2×C4×C11#13512yes—
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C11#13714yes—
104C2×C4×C11#13711yescharacteristic
105C11⋊C8—44no—
106C11⋊C8—82no—
107C2×C4⋊Q8C2×D1111yescharacteristic
108C2×C4⋊Q8C2×D1111yescharacteristic
109C2×C4⋊C8—112no—
110C2×C4⋊C8—112no—
111C2×#97—221no—
112#391—21no—
113#391—21no—
114#391Dic1114yes—
115#382—22no—
116C43C2×D1111yescharacteristic
117#336—222no—
118#336—221no—
119#333—224no—
120#332—224no—
121C22×C11#39011yescharacteristic
122C22×C11#41312yes—
123C22×C11#41611yescharacteristic
124C22×C11#41711yescharacteristic
125C22×C11#41912yes—
126C4×C11—22no—
127C4×C11—42no—
128C4×C11—42no—
129C4×C11—82no—
130C4×C11—82no—
131C4×C11#46312yes—
132C4×C11#46412yes—
133C4×C11#49112yes—
134C4×C11#49712yes—
135C22×Q8—21no—
136C22×Q8C2×Dic1112yes—
137C22×C8—222no—
138C22×C8—222no—
139C4⋊Q8—22no—
140C4⋊Q8—22no—
141C4⋊Q8—22no—
142C4⋊Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4C2×Dic1112yes—
147C2×C42C2×Dic1112yes—
148C2×C42C22⋊D1112yes—
149C2×C42C22⋊D1111yescharacteristic
150C2×C42C22⋊D1111yescharacteristic
151C2×C42C22×D1111yescharacteristic
152C4⋊C8—114no—
153C4⋊C8—222no—
154C4⋊C8—222no—
155C4⋊C8—222no—
156#97—442no—
157#95—24no—
158#95—24no—
159C2×C11#155412yes—
160C2×C11#155912yes—
161C2×C11#196011yescharacteristic
162C2×C11#196711yescharacteristic
163C2×C11#198311yescharacteristic
164C2×Q8—24no—
165C2×Q8—44no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—42no—
169C2×Q8—41no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4C22⋊Dic1112yes—
173C22×C4C22⋊Dic1112yes—
174C22×C4C22×Dic1111yescharacteristic
175C22×C4C2×C22⋊D1111yescharacteristic
176C22×C4C2×C22⋊D1111yescharacteristic
177C2×C8—224no—
178C2×C8—442no—
179C2×C8—442no—
180C2×C8—442no—
181C2×C8—444no—
182C4⋊C4—24no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C42—24no—
189C42—21no—
190C42—22no—
191C42—21no—
192C42—42no—
193C42D4×D1112yes—
194C42#434112yes—
195C11#970911yescharacteristic, complemented, Sylow
196C23C2×C22⋊Dic1111yescharacteristic
197Q8—84no—
198Q8—82no—
199Q8—82no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4D4×Dic1112yes—
213C2×C4#6698911yescharacteristic
214C2×C4#6699112yes—
215C2×C4#6699311yescharacteristic
216C2×C4#6699514yes—
217C2×C4#6700211yescharacteristic
218C2×C4#6700312yes—
219C2×C4#6700411yescharacteristic
220C8—444no—
221C8—882no—
222C22#1062283411yescharacteristic
223C22#1062283812yes—
224C22#1062284511yescharacteristic
225C22#1062284611yescharacteristic
226C22#1062285012yes—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—82no—
231C4—82no—
232C4#1062266712yes—
233C4#1062267012yes—
234C4#1062269512yes—
235C4#1062269912yes—
236C2#1306732612yes—
237C2#1306734612yes—
238C2#1306943711yescharacteristic
239C2#1306946611yescharacteristic
240C2#1306954911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2862C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2862D11
hypocenterC11#9709
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2862

Complements

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

NH ≅ G/Ntype
195. C11#9709semidirect

Maximal subgroups

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

subgroupindex
#130687332
#130684692
C2×#106221842
C2×#106221852
C11×#28622
#970911