Finite Group Databasebeta

← #14651189

Subgroups — #14651189

Order 2816.

570 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 123 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#13077657C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067301C212yesmaximal, complemented
4#13066519C212yesmaximal, complemented
5C11×#2542C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C22⋊Q8—22no—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#399C414yes—
10C11×#390—21no—
11C11×#384—21no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66897—21no—
14#10622820—22no—
15#10622625—24no—
16#10622538C2212yes—
17#10622537C2212yes—
18#10622185—24no—
19#10622168—21no—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C22⋊Q8—48no—
26C4×D4×C11—22no—
27C4×D4×C11—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—24no—
34C2×C11×C22⋊C4C2×C412yes—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4318—24no—
38C2×#4318—22no—
39C11×#95C2×C412yes—
40#66897—42no—
41C22⋊(C11⋊C8)—24no—
42C22⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46C4×C11⋊C8—22no—
47#9403—111nomaximal, Sylow
48C24×C11C22⋊C412yes—
49C2×Q8×C11—44no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×D4×C11—22no—
53C2×D4×C11—21no—
54C2×D4×C11—22no—
55C2×D4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—44no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—48no—
69C11×C4⋊C4—42no—
70C11×C22⋊C4—24no—
71C11×C22⋊C4—48no—
72C42×C11—41no—
73C42×C11—41no—
74C42×C11C2×D412yes—
75C42×C11#4112yes—
76#4318—42no—
77#4318—42no—
78#4318—84no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—42no—
81#2975—111no—
82#2542D1111yescharacteristic
83#1800—111no—
84#1549—112no—
85#1303—112no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11C2×C22⋊C411yescharacteristic
92Q8×C11—82no—
93Q8×C11—82no—
94D4×C11—42no—
95D4×C11—42no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—44no—
103C2×C4×C11—42no—
104C2×C4×C11—44no—
105C2×C4×C11—42no—
106C2×C4×C11—82no—
107C2×C4×C11C4×D412yes—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12311yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C11#13712yes—
113C2×C4×C11#13711yescharacteristic
114C11⋊C8—44no—
115C11⋊C8—82no—
116C2×C4⋊Q8C2×D1111yescharacteristic
117C2×C22⋊Q8—22no—
118C2×C4×D4C2×D1111yescharacteristic
119#436—224no—
120#431—112no—
121#423—112no—
122C2×#100—221no—
123#407—222no—
124#399Dic1114yes—
125#390—21no—
126#384—21no—
127C4×C4⋊C4C2×D1111yescharacteristic
128#343—221no—
129#332—224no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11—44no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—82no—
137C22×C11#38611yescharacteristic
138C22×C11#41711yescharacteristic
139C22×C11#41911yescharacteristic
140C4×C11—21no—
141C4×C11—22no—
142C4×C11—44no—
143C4×C11—42no—
144C4×C11—82no—
145C4×C11#45312yes—
146C4×C11#46812yes—
147C4×C11#47012yes—
148C22×Q8—21no—
149C22×D4C22⋊D1111yescharacteristic
150C23×C4C22⋊D1112yes—
151C2×M16—224no—
152C2×M16—222no—
153C4⋊Q8—22no—
154C4⋊Q8—22no—
155C22⋊Q8—48no—
156C4×D4—22no—
157C4×D4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×Dic1112yes—
162C2×C4⋊C4C22⋊D1111yescharacteristic
163C2×C22⋊C4—24no—
164C2×C22⋊C4C2×Dic1112yes—
165C2×C42—21no—
166C2×C42C22×D1111yescharacteristic
167C4⋊C8—114no—
168C4⋊C8—222no—
169C4⋊C8—222no—
170#100—442no—
171C22⋊C8—224no—
172C22⋊C8—222no—
173C4×C8—222no—
174#95C2×Dic1112yes—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11—82no—
178C2×C11#188711yescharacteristic
179C2×C11#189411yescharacteristic
180C2×C11#191511yescharacteristic
181C24C22⋊Dic1112yes—
182C2×Q8—44no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—44no—
194C22×C4C22⋊Dic1112yes—
195C22×C4C22×Dic1111yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198M16—442no—
199M16—442no—
200M16—884no—
201C2×C8—224no—
202C2×C8—442no—
203C4⋊C4—24no—
204C4⋊C4—22no—
205C4⋊C4—24no—
206C4⋊C4—48no—
207C4⋊C4—42no—
208C22⋊C4—24no—
209C22⋊C4—48no—
210C42—41no—
211C42—41no—
212C42D4×D1112yes—
213C42#434112yes—
214C11#940311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊Dic1111yescharacteristic
221Q8—82no—
222Q8—82no—
223D4—42no—
224D4—42no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4D4×Dic1112yes—
237C2×C4#6698811yescharacteristic
238C2×C4#6699011yescharacteristic
239C2×C4#6699212yes—
240C2×C4#6699512yes—
241C2×C4#6700211yescharacteristic
242C2×C4#6700411yescharacteristic
243C8—444no—
244C8—882no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22#1062283311yescharacteristic
253C22#1062283811yescharacteristic
254C22#1062284511yescharacteristic
255C4—22no—
256C4—21no—
257C4—44no—
258C4—42no—
259C4—82no—
260C4#1062266212yes—
261C4#1062266512yes—
262C4#1062269012yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2#1306901511yescharacteristic
267C2#1306905011yescharacteristic
268C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2542C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2542D11
hypocenterC11#9403
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
4. #13066519C2semidirect
214. C11#9403semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130686082
#130673012
#130665192
C11×#25422
#940311