Finite Group Databasebeta

← #14663438

Subgroups — #14663438

Order 2816.

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

normal subgroups only

This group has 358 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#13066560C214yesmaximal
4C11×#2568C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#400—21no—
8C11×#400—21no—
9C11×#391—21no—
10C11×#391—21no—
11C11×#391C412yes—
12C11×#382C2212yes—
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⋊C4C2×C412yes—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C412yes—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C11×#95—21no—
37C11×#95—22no—
38C11×#95—22no—
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#11573—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—41no—
51C2×Q8×C11—44no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78#2568D1111yescharacteristic
79#1467—111no—
80#1461—111no—
81#1324—114no—
82C23×C11C2×C22⋊C411yescharacteristic
83Q8×C11—44no—
84Q8×C11—82no—
85Q8×C11—82no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—44no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11#9911yescharacteristic
106C2×C4×C11#9911yescharacteristic
107C2×C4×C11#10112yes—
108C2×C4×C11#13112yes—
109C11⋊C8—82no—
110C11⋊C8—82no—
111C2×C4⋊Q8Dic1111yescharacteristic
112C2×C4×Q8C2×D1111yescharacteristic
113#432—221no—
114#431—221no—
115#400—21no—
116#400—21no—
117#391—21no—
118#391—21no—
119#391Dic1112yes—
120#382C2×D1112yes—
121C4×C4⋊C4Dic1111yescharacteristic
122#324—112no—
123#324—112no—
124#324—221no—
125#324—221no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11#40811yescharacteristic
129C22×C11C2×#9911yescharacteristic
130C22×C11C2×#10111yescharacteristic
131C4×C11—21no—
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—41no—
135C4×C11—41no—
136C4×C11—41no—
137C4×C11—41no—
138C4×C11—82no—
139C4×C11—82no—
140C4×C11#35512yes—
141C22×Q8—21no—
142C22×Q8C2×Dic1111yescharacteristic
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4C2×Dic1112yes—
150C2×C4⋊C4C22⋊D1111yescharacteristic
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22×D1111yescharacteristic
153C2×C42C2×Dic1112yes—
154C2×C42C2×Dic1111yescharacteristic
155C2×C42C22⋊D1111yescharacteristic
156C2×C42C22⋊D1111yescharacteristic
157C4⋊C8—441no—
158C4⋊C8—441no—
159C22⋊C8—222no—
160C22⋊C8—222no—
161#97—441no—
162C4×C8—441no—
163#95—21no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×C11—21no—
169C2×C11—21no—
170C2×C11#147211yescharacteristic
171C2×C11#212911yescharacteristic
172C2×C11C2×#35511yescharacteristic
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—44no—
177C2×Q8—41no—
178C2×Q8—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic1111yescharacteristic
182C22×C4C22⋊Dic1111yescharacteristic
183C22×C4C22⋊Dic1111yescharacteristic
184C22×C4C22⋊Dic1111yescharacteristic
185C22×C4C22×Dic1111yescharacteristic
186C22×C4C2×C22⋊D1111yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C2×C8—442no—
189C2×C8—442no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—24no—
203C11#1157311yescharacteristic, complemented, Sylow
204C23C2×C22⋊Dic1111yescharacteristic
205Q8—44no—
206Q8—82no—
207Q8—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—44no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4#6689811yescharacteristic
228C2×C4#6689811yescharacteristic
229C2×C4#6690012yes—
230C2×C4#6700112yes—
231C8—882no—
232C8—882no—
233C22—21no—
234C22—21no—
235C22C2×#6689811yescharacteristic
236C22C2×#6690011yescharacteristic
237C22#1062284711yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—82no—
246C4—82no—
247C4#1062218012yes—
248C2—21no—
249C2—21no—
250C2#1306698011yescharacteristic
251C2#1307029111yescharacteristic
252C2C2×#1062218011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2568C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2568D11
hypocenterC11#11573
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
203. C11#11573semidirect

Maximal subgroups

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

subgroupindex
#130669602
#130669402
#130665602
C11×#25682
#1157311