Finite Group Databasebeta

← #14652884

Subgroups — #14652884

Order 2816.

466 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 143 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#13076994C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic
3C2×#10622119C212yesmaximal
4C2×#10622124C212yesmaximal
5C11×#1831C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C43×C11C2211yescharacteristic
10#10622549—22no—
11#10622542—21no—
12#10622542—21no—
13#10622542C414yes—
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×#66867—21no—
16C11×#336—22no—
17#10622162—21no—
18#10622124—24no—
19#10622119—24no—
20C22×Dic22—21no—
21C22×Dic22C2×C412yes—
22C22×C8×C11—22no—
23C2×C42×C11C2×C412yes—
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11C2×C412yes—
32C22×C11⋊C8—22no—
33#66922—22no—
34#66922—22no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11⋊#95—24no—
40C11⋊#95—24no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)D414yes—
43#66867—42no—
44#9709—111nomaximal, Sylow
45C22×C4×C11C22⋊C412yes—
46C22×C4×C11C22⋊C412yes—
47C22×C4×C11C22×C411yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C22×Dic11—22no—
51C22×Dic11—22no—
52C2×Dic22—24no—
53C2×Dic22—44no—
54C2×Dic22—42no—
55C2×Dic22—42no—
56C2×Dic22—41no—
57C2×Dic22—41no—
58C2×C8×C11—42no—
59C2×C8×C11—44no—
60C42×C11—22no—
61C42×C11—21no—
62C42×C11—21no—
63C42×C11—24no—
64C42×C11—42no—
65C42×C11C2×D412yes—
66C42×C11#4112yes—
67C4⋊Dic11—24no—
68C4⋊Dic11—42no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76#2862—111no—
77#1831D1111yescharacteristic
78#1767—111no—
79C2×#333—112no—
80C2×#332—112no—
81C23×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11C4×D412yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12411yescharacteristic
92C2×C4×C11#12711yescharacteristic
93C2×C4×C11#13512yes—
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C11#13711yescharacteristic
96C2×C4×C11#13714yes—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—44no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102Dic22—82no—
103Dic22—82no—
104Dic22—84no—
105C8×C11—82no—
106C11⋊C8—44no—
107C2×C4⋊Q8—111no—
108C2×C4⋊Q8—111no—
109C2×C4⋊C8—112no—
110C2×C4⋊C8C2×D1112yes—
111C2×#97—221no—
112#391—114no—
113#391—221no—
114#391—221no—
115#382—222no—
116C43C2×D1111yescharacteristic
117#336—22no—
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#46312yes—
130C4×C11#46412yes—
131C4×C11#49112yes—
132C4×C11#49712yes—
133Dic11—82no—
134Dic11—82no—
135C22×Q8—112no—
136C22×Q8—221no—
137C22×C8—22no—
138C22×C8—222no—
139C4⋊Q8—222no—
140C4⋊Q8—222no—
141C4⋊Q8—222no—
142C4⋊Q8—222no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—221no—
147C2×C42C4×D1112yes—
148C2×C42D4411yescharacteristic
149C2×C42D4411yescharacteristic
150C2×C42C22⋊D1112yes—
151C2×C42C22×D1111yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—114no—
155C4⋊C8—222no—
156#97—442no—
157#95—224no—
158#95—224no—
159C2×C11#155412yes—
160C2×C11#155912yes—
161C2×C11#196011yescharacteristic
162C2×C11#196711yescharacteristic
163C2×C11#198311yescharacteristic
164C2×Q8—224no—
165C2×Q8—444no—
166C2×Q8—442no—
167C2×Q8—442no—
168C2×Q8—441no—
169C2×Q8—441no—
170C22×C4—222no—
171C22×C4—222no—
172C22×C4(C2×D11)⋊C412yes—
173C22×C4(C2×D11)⋊C412yes—
174C22×C4C2×C4×D1111yescharacteristic
175C22×C4C2×D4411yescharacteristic
176C22×C4C2×C22⋊D1111yescharacteristic
177C2×C8—42no—
178C2×C8—44no—
179C2×C8—224no—
180C2×C8—442no—
181C2×C8—442no—
182C4⋊C4—224no—
183C4⋊C4—442no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C4⋊C4—441no—
187C4⋊C4—441no—
188C42—22no—
189C42—21no—
190C42—21no—
191C42—24no—
192C42—42no—
193C42D4×D1112yes—
194C42#434312yes—
195C11#970911yescharacteristic, complemented, Sylow
196C23C2×(C2×D11)⋊C411yescharacteristic
197Q8—884no—
198Q8—882no—
199Q8—882no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—442no—
208C2×C4—444no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4#6694612yes—
213C2×C4#6694812yes—
214C2×C4#6695712yes—
215C2×C4#6696111yescharacteristic
216C2×C4#6696211yescharacteristic
217C2×C4#6699311yescharacteristic
218C2×C4#6700011yescharacteristic
219C2×C4#6700414yes—
220C8—82no—
221C8—444no—
222C22#1062260111yescharacteristic
223C22#1062261712yes—
224C22#1062272611yescharacteristic
225C22#1062274512yes—
226C22#1062274611yescharacteristic
227C4—22no—
228C4—42no—
229C4—42no—
230C4—882no—
231C4—882no—
232C4#1062245712yes—
233C4#1062245812yes—
234C4#1062267312yes—
235C4#1062268212yes—
236C2#1306732412yes—
237C2#1306734712yes—
238C2#1306943511yescharacteristic
239C2#1306946311yescharacteristic
240C2#1306954611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1831C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1831D11
hypocenterC11#9709
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1831

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
#130769942
#130684692
C2×#106221192
C2×#106221242
C11×#18312
#970911