Finite Group Databasebeta

← #14651149

Subgroups — #14651149

Order 2816.

594 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 139 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#13077640C211yesmaximal, 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—
14C2×C22⋊(C11⋊C8)—22no—
15D4×C11⋊C8—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—22no—
38C22×C11⋊C8—24no—
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#9395—111nomaximal, Sylow
48C24×C11C22⋊C412yes—
49C2×Q8×C11—44no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11SD1612yes—
55C2×D4×C11Q1612yes—
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—42no—
73C42×C11C2×D412yes—
74C42×C11#4112yes—
75#4318—42no—
76#4318—42no—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—84no—
80#2972—111no—
81#2542D1111yescharacteristic
82#1800—111no—
83#1549—112no—
84#1303—112no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11#10314yes—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—82no—
92Q8×C11—82no—
93D4×C11—24no—
94D4×C11—24no—
95C2×C4×C11—22no—
96C2×C4×C11—24no—
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—44no—
102C2×C4×C11—42no—
103C2×C4×C11—44no—
104C2×C4×C11—42no—
105C2×C4×C11—82no—
106C2×C4×C11C4×D412yes—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12112yes—
109C2×C4×C11#12311yescharacteristic
110C2×C4×C11C2×SD1611yescharacteristic
111C2×C4×C11C2×Q1611yescharacteristic
112C2×C4×C11#13512yes—
113C11⋊C8—44no—
114C11⋊C8—82no—
115C2×C4⋊Q8C2×D1111yescharacteristic
116C2×C22⋊Q8—22no—
117C2×C4×D4C2×D1111yescharacteristic
118C8×D4—224no—
119#431—112no—
120#423—112no—
121C2×#100—221no—
122C2×C22⋊C8—222no—
123#399Dic1114yes—
124#390—21no—
125#384—21no—
126C4×C4⋊C4C2×D1111yescharacteristic
127#343—221no—
128#332—224no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11—24no—
132C22×C11—44no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—82no—
136C22×C11#38611yescharacteristic
137C22×C11C2×#10311yescharacteristic
138C22×C11#41611yescharacteristic
139C4×C11—21no—
140C4×C11—22no—
141C4×C11—44no—
142C4×C11—42no—
143C4×C11—82no—
144C4×C11#45312yes—
145C4×C11#46512yes—
146C4×C11#46712yes—
147C22×Q8—21no—
148C22×D4C22⋊D1111yescharacteristic
149C23×C4C22⋊D1112yes—
150C2×M16—222no—
151C22×C8—224no—
152C4⋊Q8—22no—
153C4⋊Q8—22no—
154C22⋊Q8—48no—
155C4×D4—22no—
156C4×D4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4C2×Dic1112yes—
161C2×C4⋊C4C22⋊D1111yescharacteristic
162C2×C22⋊C4—24no—
163C2×C22⋊C4C2×Dic1112yes—
164C2×C42—21no—
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—114no—
167C4⋊C8—222no—
168C4⋊C8—222no—
169#100—442no—
170C22⋊C8—224no—
171C22⋊C8—222no—
172C4×C8—222no—
173#95C2×Dic1112yes—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11—44no—
177C2×C11#188711yescharacteristic
178C2×C11#189211yescharacteristic
179C2×C11#191511yescharacteristic
180C24C22⋊Dic1112yes—
181C2×Q8—44no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4#432512yes—
187C2×D4#432612yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—44no—
193C22×C4C22⋊Dic1112yes—
194C22×C4C22×Dic1111yescharacteristic
195C22×C4C2×C22⋊D1111yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197M16—442no—
198M16—442no—
199C2×C8—224no—
200C2×C8—442no—
201C2×C8—884no—
202C4⋊C4—24no—
203C4⋊C4—22no—
204C4⋊C4—24no—
205C4⋊C4—48no—
206C4⋊C4—42no—
207C22⋊C4—24no—
208C22⋊C4—48no—
209C42—42no—
210C42D4×D1112yes—
211C42#434112yes—
212C11#939511yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—42no—
216C23—42no—
217C23#6689914yes—
218C23C2×C22⋊Dic1111yescharacteristic
219Q8—82no—
220Q8—82no—
221D4—24no—
222D4—24no—
223C2×C4—22no—
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—82no—
234C2×C4D4×Dic1112yes—
235C2×C4#6698811yescharacteristic
236C2×C4#6699011yescharacteristic
237C2×C4#6699212yes—
238C2×C4C2×#432511yescharacteristic
239C2×C4C2×#432611yescharacteristic
240C2×C4#6700312yes—
241C8—444no—
242C8—882no—
243C22—21no—
244C22—21no—
245C22—24no—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—82no—
250C22#1062283311yescharacteristic
251C22C2×#6689911yescharacteristic
252C22#1062284611yescharacteristic
253C4—22no—
254C4—21no—
255C4—44no—
256C4—42no—
257C4—82no—
258C4#1062266112yes—
259C4#1062266412yes—
260C4#1062269012yes—
261C2—21no—
262C2—21no—
263C2—44no—
264C2#1306901511yescharacteristic
265C2#1306904011yescharacteristic
266C2#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#9395
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
212. C11#9395semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130686082
#130673012
#130665192
C11×#25422
#939511