Finite Group Databasebeta

← #14651183

Subgroups — #14651183

Order 2816.

486 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 119 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#13073601C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067287C212yesmaximal
4#13066518C212yesmaximal
5C11×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66997—21no—
8C2×#66922C2211yescharacteristic
9C11×#446—24no—
10C11×#432—22no—
11C11×#431C2212yes—
12C2×#66900—21no—
13#10622596C414yes—
14#10622587—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622541—22no—
17#10622537C2212yes—
18#10622168—21no—
19#10622124—24no—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22—21no—
22C4×Q8×C11—22no—
23C4×Q8×C11—22no—
24C2×C11×C4⋊C4C2×C412yes—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28#66997—44no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11C2×C412yes—
32C2×Dic11⋊C4—24no—
33C2×C4×Dic11—21no—
34C2×#4318—22no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8—24no—
38C11×C4⋊C8D414yes—
39C11×C22⋊C8—22no—
40C11×#97—24no—
41C4×C8×C11—22no—
42#66900—42no—
43C11⋊#95—24no—
44C11⋊#95C2×C412yes—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47#9402—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—21no—
50C2×Q8×C11—22no—
51C2×Q8×C11—21no—
52C22×C4×C11C22⋊C412yes—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22×C411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—22no—
58C22×Dic11—22no—
59C2×Dic22—42no—
60C2×Dic22—42no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×C8×C11—24no—
64C11×C4⋊C4—24no—
65C11×C4⋊C4—22no—
66C42×C11—22no—
67C42×C11—22no—
68C42×C11C2×D412yes—
69C42×C11#4112yes—
70C4⋊Dic11—24no—
71C4⋊Dic11—24no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74Dic11⋊C4—48no—
75C4×Dic11—42no—
76#4318—42no—
77#4318—42no—
78C2×C11⋊C8—42no—
79#2983D1111yescharacteristic
80#2546—111no—
81#1801—111no—
82#1546—112no—
83#1303—112no—
84C23×C11C2×C22⋊C411yescharacteristic
85Q8×C11—42no—
86Q8×C11—42no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11C4×D412yes—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11#12112yes—
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)12yes—
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C11#13711yescharacteristic
101C2×Dic11—24no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107Dic22—82no—
108Dic22—82no—
109C8×C11—44no—
110C11⋊C8—82no—
111C2×C4⋊Q8—111no—
112C2×C4⋊Q8—221no—
113C2×C4×Q8C2×D1111yescharacteristic
114#446—24no—
115#432—22no—
116#431C2×D1112yes—
117#423—112no—
118C2×#101—221no—
119#398—114no—
120#391—221no—
121#389—222no—
122C4×C4⋊C4—111no—
123#343—221no—
124#332—224no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11#38611yescharacteristic
128C22×C11#41711yescharacteristic
129C22×C11#41811yescharacteristic
130C4×C11—21no—
131C4×C11—22no—
132C4×C11—42no—
133C4×C11—42no—
134C4×C11#45612yes—
135C4×C11#46812yes—
136C4×C11#46912yes—
137Dic11—44no—
138Dic11—82no—
139C22×Q8—221no—
140C22×Q8D4411yescharacteristic
141C2×M16—222no—
142C4⋊Q8—222no—
143C4⋊Q8—222no—
144C4⋊Q8—444no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—224no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4C4×D1112yes—
152C2×C4⋊C4D4411yescharacteristic
153C2×C42—221no—
154C2×C42C22⋊D1112yes—
155C2×C42C22×D1111yescharacteristic
156C4⋊C8—24no—
157C4⋊C8—222no—
158C4⋊C8—222no—
159C4⋊C8C22⋊D1114yes—
160#101—442no—
161C22⋊C8—22no—
162#97—24no—
163C4×C8—22no—
164#95—112no—
165#95—224no—
166C2×C11—21no—
167C2×C11—21no—
168C2×C11#188611yescharacteristic
169C2×C11#189511yescharacteristic
170C2×C11#191511yescharacteristic
171C2×Q8—21no—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—442no—
176C2×Q8—441no—
177C2×Q8—441no—
178C2×Q8—442no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4(C2×D11)⋊C412yes—
182C22×C4(C2×D11)⋊C412yes—
183C22×C4C2×C4×D1111yescharacteristic
184C22×C4C2×D4411yescharacteristic
185C22×C4C2×C22⋊D1111yescharacteristic
186M16—442no—
187M16—442no—
188C2×C8—24no—
189C2×C8—442no—
190C4⋊C4—24no—
191C4⋊C4—22no—
192C4⋊C4—224no—
193C4⋊C4—224no—
194C4⋊C4—448no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C42—22no—
198C42—22no—
199C42—442no—
200C42#433912yes—
201C42C2×C22⋊D1112yes—
202C11#940211yescharacteristic, complemented, Sylow
203C23C2×(C2×D11)⋊C411yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—882no—
207Q8—882no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—224no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4#6696112yes—
222C2×C4#6696111yescharacteristic
223C2×C4#6696211yescharacteristic
224C2×C4C4×C22⋊D1112yes—
225C2×C4#6698211yescharacteristic
226C2×C4#6698312yes—
227C2×C4#6700611yescharacteristic
228C8—44no—
229C8—882no—
230C22—21no—
231C22—21no—
232C22#1062274411yescharacteristic
233C22#1062274611yescharacteristic
234C22#1062282611yescharacteristic
235C4—22no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—444no—
240C4—882no—
241C4#1062274712yes—
242C4#1062274812yes—
243C4#1062285912yes—
244C2—21no—
245C2—21no—
246C2#1306900911yescharacteristic
247C2#1306905411yescharacteristic
248C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#9402
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
202. C11#9402semidirect

Maximal subgroups

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

subgroupindex
#130736012
#130686122
#130672872
#130665182
C11×#29832
#940211