Finite Group Databasebeta

← #14651143

Subgroups — #14651143

Order 2816.

506 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 135 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×#2982C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66997—21no—
8C2×#66922C2211yescharacteristic
9C8×Q8×C11—24no—
10C11×#431—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—42no—
29#66997—42no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33C2×Dic11⋊C4—24no—
34C2×C4×Dic11—21no—
35C2×#4318—22no—
36#66922—22no—
37#66922—22no—
38C11×C4⋊C8—24no—
39C11×C4⋊C8D414yes—
40C11×C22⋊C8—22no—
41C4×C8×C11—24no—
42C4×C8×C11—22no—
43#66900—42no—
44C11⋊#95—24no—
45C11⋊#95C2×C412yes—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48#9394—111nomaximal, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11D812yes—
52C2×Q8×C11SD1612yes—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C22×Dic11—22no—
60C2×Dic22—42no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×Dic22—42no—
64C2×C8×C11—24no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C42×C11—22no—
68C42×C11—22no—
69C42×C11C2×D412yes—
70C42×C11#4112yes—
71C4⋊Dic11—24no—
72C4⋊Dic11—24no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75Dic11⋊C4—48no—
76C4×Dic11—41no—
77C4×Dic11—41no—
78#4318—42no—
79#4318—42no—
80C2×C11⋊C8—42no—
81#2982D1111yescharacteristic
82#2546—111no—
83#1801—111no—
84#1546—112no—
85#1303—112no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—24no—
88Q8×C11—24no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11#10214yes—
96C2×C4×C11C4×D412yes—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11#12112yes—
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11C2×D811yescharacteristic
101C2×C4×C11C2×SD1611yescharacteristic
102C2×C4×C11#13512yes—
103C2×Dic11—24no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109Dic22—82no—
110Dic22—82no—
111C8×C11—44no—
112C11⋊C8—82no—
113C2×C4⋊Q8—111no—
114C2×C4⋊Q8—221no—
115C2×C4×Q8C2×D1111yescharacteristic
116C8×Q8—24no—
117#431—22no—
118#431C2×D1112yes—
119#423—112no—
120C2×#101—221no—
121#398—114no—
122#391—221no—
123#389—222no—
124C4×C4⋊C4—111no—
125#343—221no—
126#332—224no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11#38611yescharacteristic
130C22×C11C2×#10211yescharacteristic
131C22×C11#41611yescharacteristic
132C4×C11—21no—
133C4×C11—24no—
134C4×C11—22no—
135C4×C11—42no—
136C4×C11#45612yes—
137C4×C11#46512yes—
138C4×C11#46612yes—
139Dic11—44no—
140Dic11—82no—
141C22×Q8—221no—
142C22×Q8D4411yescharacteristic
143C2×M16—222no—
144C4⋊Q8—222no—
145C4⋊Q8—222no—
146C4⋊Q8—442no—
147C4⋊Q8—442no—
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—224no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4C4×D1112yes—
155C2×C4⋊C4D4411yescharacteristic
156C2×C42—221no—
157C2×C42C22⋊D1112yes—
158C2×C42C22×D1111yescharacteristic
159C4⋊C8—24no—
160C4⋊C8—222no—
161C4⋊C8—222no—
162C4⋊C8C22⋊D1114yes—
163#101—442no—
164C22⋊C8—22no—
165C4×C8—24no—
166C4×C8—22no—
167#95—112no—
168#95—224no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#188611yescharacteristic
172C2×C11#189311yescharacteristic
173C2×C11#191511yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—441no—
177C2×Q8—441no—
178C2×Q8—442no—
179C2×Q8—442no—
180C2×Q8#431412yes—
181C2×Q8D8812yes—
182C22×C4—222no—
183C22×C4—222no—
184C22×C4(C2×D11)⋊C412yes—
185C22×C4(C2×D11)⋊C412yes—
186C22×C4C2×C4×D1111yescharacteristic
187C22×C4C2×D4411yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189M16—442no—
190M16—442no—
191C2×C8—24no—
192C2×C8—442no—
193C4⋊C4—24no—
194C4⋊C4—22no—
195C4⋊C4—224no—
196C4⋊C4—224no—
197C4⋊C4—448no—
198C4⋊C4—441no—
199C4⋊C4—441no—
200C42—22no—
201C42—22no—
202C42—441no—
203C42—441no—
204C42#433912yes—
205C42C2×C22⋊D1112yes—
206C11#939411yescharacteristic, complemented, Sylow
207C23C2×(C2×D11)⋊C411yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—882no—
211Q8—882no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—224no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4#6688514yes—
225C2×C4C2×#431411yescharacteristic
226C2×C4C2×D8811yescharacteristic
227C2×C4#6695712yes—
228C2×C4C4×C22⋊D1112yes—
229C2×C4#6698211yescharacteristic
230C2×C4#6698312yes—
231C2×C4#6700611yescharacteristic
232C8—44no—
233C8—882no—
234C22—21no—
235C22—21no—
236C22C2×#6688511yescharacteristic
237C22#1062272611yescharacteristic
238C22#1062282611yescharacteristic
239C4—22no—
240C4—21no—
241C4—24no—
242C4—42no—
243C4—444no—
244C4—882no—
245C4#1062272712yes—
246C4#1062272812yes—
247C4#1062285912yes—
248C2—21no—
249C2—21no—
250C2#1306900911yescharacteristic
251C2#1306904411yescharacteristic
252C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9394
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
206. C11#9394semidirect

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×#29822
#939411