Finite Group Databasebeta

← #14663442

Subgroups — #14663442

Order 2816.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#13066960C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066562C214yesmaximal
4C11×#2567C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#395—21no—
8C11×#395—21no—
9C11×#391C412yes—
10C11×#389—21no—
11C11×#389—21no—
12C11×#384C2212yes—
13C4×C11×C4⋊C4C411yescharacteristic
14#10622539—21no—
15#10622538—21no—
16#10622166—21no—
17#10622166—21no—
18#10622166C2212yes—
19#10622166C2212yes—
20C22×Q8×C11—21no—
21C22×Q8×C11C2×C411yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C42×C11C2×C412yes—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—22no—
41C22⋊(C11⋊C8)—22no—
42C22⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—41no—
44C4⋊(C11⋊C8)—41no—
45#66867—41no—
46C4×C11⋊C8—41no—
47#11574—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—41no—
51C2×Q8×C11—42no—
52C2×Q8×C11—82no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C11×C4⋊C4—24no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—82no—
70C11×C4⋊C4—82no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—24no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2567D1111yescharacteristic
81#1467—111no—
82#1461—111no—
83#1325—114no—
84C23×C11C2×C22⋊C411yescharacteristic
85Q8×C11—44no—
86Q8×C11—84no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—24no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11#9911yescharacteristic
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11#10112yes—
110C2×C4×C11#13112yes—
111C11⋊C8—82no—
112C11⋊C8—82no—
113C2×C4⋊Q8Dic1111yescharacteristic
114C2×C4×Q8C2×D1111yescharacteristic
115#432—221no—
116#431—221no—
117#395—21no—
118#395—21no—
119#391Dic1112yes—
120#389—21no—
121#389—21no—
122#384C2×D1112yes—
123C4×C4⋊C4Dic1111yescharacteristic
124#324—112no—
125#324—112no—
126#324—221no—
127#324—221no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#40811yescharacteristic
131C22×C11C2×#9911yescharacteristic
132C22×C11C2×#10111yescharacteristic
133C4×C11—21no—
134C4×C11—22no—
135C4×C11—22no—
136C4×C11—44no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—82no—
142C4×C11#35612yes—
143C22×Q8—21no—
144C22×Q8C2×Dic1111yescharacteristic
145C4⋊Q8—41no—
146C4⋊Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4C2×Dic1112yes—
154C2×C4⋊C4C22⋊D1111yescharacteristic
155C2×C4⋊C4C22⋊D1111yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C42C2×Dic1112yes—
158C2×C42C2×Dic1111yescharacteristic
159C2×C42C22⋊D1111yescharacteristic
160C2×C42C22⋊D1111yescharacteristic
161C4⋊C8—441no—
162C4⋊C8—441no—
163C22⋊C8—222no—
164C22⋊C8—222no—
165#97—441no—
166C4×C8—441no—
167#95—21no—
168#95—22no—
169#95—22no—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11#147211yescharacteristic
173C2×C11#212811yescharacteristic
174C2×C11C2×#35611yescharacteristic
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—82no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C22⋊Dic1111yescharacteristic
183C22×C4C22⋊Dic1111yescharacteristic
184C22×C4C22⋊Dic1111yescharacteristic
185C22×C4C22⋊Dic1111yescharacteristic
186C22×C4C22×Dic1111yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189C2×C8—442no—
190C2×C8—442no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—24no—
207C11#1157411yescharacteristic, complemented, Sylow
208C23C2×C22⋊Dic1111yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#6689811yescharacteristic
232C2×C4#6689811yescharacteristic
233C2×C4#6690012yes—
234C2×C4#6700112yes—
235C8—882no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22C2×#6689811yescharacteristic
240C22C2×#6690011yescharacteristic
241C22#1062284711yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#1062218612yes—
252C2—21no—
253C2—21no—
254C2#1306698011yescharacteristic
255C2#1307028811yescharacteristic
256C2C2×#1062218611yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2567C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2567D11
hypocenterC11#11574
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
207. C11#11574semidirect

Maximal subgroups

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

subgroupindex
#130669602
#130669402
#130665622
C11×#25672
#1157411