Finite Group Databasebeta

← #14663439

Subgroups — #14663439

Order 2816.

358 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 87 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#13073828C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066559C214yesmaximal
4C11×#1467C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C11×#432—21no—
8#10622843C412yes—
9#10622599—21no—
10#10622599—21no—
11#10622590C2212yes—
12C4×C4⋊Dic11C411yescharacteristic
13#10622542—21no—
14#10622542—21no—
15#10622538—21no—
16C11×#324—21no—
17C11×#324C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11C2×C411yescharacteristic
21C22×Dic22—21no—
22C4×Q8×C11—41no—
23C4×Q8×C11—41no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33C2×C4×Dic11C2×C412yes—
34#66922—41no—
35#66922—41no—
36C11×C4⋊C8—41no—
37C11×C22⋊C8—22no—
38C11×#97—41no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95—21no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—41no—
46C4×C11⋊C8—41no—
47#11573—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—41no—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C22×Dic11—22no—
60C2×Dic22—44no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×C8×C11—42no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C42×C11—21no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—42no—
76C4×Dic11—24no—
77C2×C11⋊C8—42no—
78#2568—111no—
79#1467D1111yescharacteristic
80#1461—111no—
81#1324—114no—
82C23×C11C2×C22⋊C411yescharacteristic
83Q8×C11—44no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11#9911yescharacteristic
99C2×C4×C11#9911yescharacteristic
100C2×C4×C11#10112yes—
101C2×C4×C11#13112yes—
102C2×Dic11—42no—
103C2×Dic11—44no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107Dic22—82no—
108Dic22—82no—
109C8×C11—82no—
110C11⋊C8—82no—
111C2×C4⋊Q8—111no—
112C2×C4×Q8C2×D1111yescharacteristic
113#432—21no—
114#431—221no—
115#400—221no—
116#400—221no—
117#391—112no—
118#391—221no—
119#391—221no—
120#382—112no—
121C4×C4⋊C4—111no—
122#324—21no—
123#324—112no—
124#324—221no—
125#324C2×D1112yes—
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#35512yes—
139Dic11—82no—
140Dic11—82no—
141C22×Q8—221no—
142C22×Q8C4×D1111yescharacteristic
143C4⋊Q8—441no—
144C4⋊Q8—441no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4D4411yescharacteristic
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22×D1111yescharacteristic
153C2×C42—112no—
154C2×C42C4×D1111yescharacteristic
155C2×C42D4411yescharacteristic
156C2×C42C22⋊D1111yescharacteristic
157C4⋊C8—41no—
158C4⋊C8—441no—
159C22⋊C8—22no—
160C22⋊C8—222no—
161#97—41no—
162C4×C8—441no—
163#95—221no—
164#95—222no—
165#95—222no—
166#95—222no—
167#95—222no—
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—444no—
177C2×Q8—441no—
178C2×Q8—441no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4(C2×D11)⋊C411yescharacteristic
182C22×C4(C2×D11)⋊C411yescharacteristic
183C22×C4(C2×D11)⋊C411yescharacteristic
184C22×C4(C2×D11)⋊C411yescharacteristic
185C22×C4C2×C4×D1111yescharacteristic
186C22×C4C2×D4411yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C2×C8—42no—
189C2×C8—442no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—224no—
203C11#1157311yescharacteristic, complemented, Sylow
204C23C2×(C2×D11)⋊C411yescharacteristic
205Q8—44no—
206Q8—882no—
207Q8—882no—
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—442no—
223C2×C4—444no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4#6687011yescharacteristic
228C2×C4#6687011yescharacteristic
229C2×C4#6688812yes—
230C2×C4#6696012yes—
231C8—82no—
232C8—882no—
233C22—21no—
234C22—21no—
235C22C2×#6687011yescharacteristic
236C22#1062274211yescharacteristic
237C22C2×#6688811yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—882no—
246C4—882no—
247C4#1062211512yes—
248C2—21no—
249C2—21no—
250C2#1306698111yescharacteristic
251C2#1307029011yescharacteristic
252C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11573
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

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
#130738282
#130669402
#130665592
C11×#14672
#1157311