Finite Group Databasebeta

← #14664424

Subgroups — #14664424

Order 2816.

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

normal subgroups only

This group has 394 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#13073821C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic
3#13066645C214yesmaximal
4C4×C11×#101C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C2×C11×#101—21no—
8C4×C11×M16—21no—
9#10622843—21no—
10#10622592C412yes—
11#10622592C2212yes—
12#10622589—21no—
13C4×C4⋊Dic11C411yescharacteristic
14#10622541—21no—
15#10622541—21no—
16#10622539—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22C2×C412yes—
22C2×C11×M16—22no—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—22no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37#66922—41no—
38#66922—41no—
39C11×#101—24no—
40C11×#97—41no—
41C4×C8×C11—41no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11795—111nomaximal, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—41no—
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—42no—
62C2×Dic22—82no—
63C11×M16—24no—
64C11×M16—42no—
65C2×C8×C11—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—82no—
80Dic11⋊C4—82no—
81C4×Dic11—42no—
82C2×C11⋊C8—42no—
83#2567—111no—
84C4×#101D1111yescharacteristic
85#1467—111no—
86#1354—114no—
87C23×C11C2×C22⋊C411yescharacteristic
88Q8×C11—44no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11#9911yescharacteristic
104C2×C4×C11#9911yescharacteristic
105C2×C4×C11#10412yes—
106C2×C4×C11#13712yes—
107C2×Dic11—24no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113Dic22—84no—
114C8×C11—44no—
115C11⋊C8—82no—
116C2×C4⋊Q8—111no—
117C2×C4×Q8C2×D1111yescharacteristic
118#432—221no—
119C2×#101—21no—
120C4×M16—21no—
121#395—112no—
122#395—112no—
123#391—221no—
124#389—221no—
125#389—221no—
126#384—221no—
127C4×C4⋊C4—111no—
128#343C2×D1112yes—
129#324—112no—
130#324—221no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11C2×#9911yescharacteristic
134C22×C11#41911yescharacteristic
135C22×C11C2×#10411yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11#35612yes—
144Dic11—44no—
145Dic11—82no—
146C22×Q8—112no—
147C22×Q8C22⋊D1111yescharacteristic
148C2×M16—22no—
149C4⋊Q8—441no—
150C4⋊Q8—441no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4C4×D1111yescharacteristic
159C2×C4⋊C4D4411yescharacteristic
160C2×C4⋊C4C22×D1111yescharacteristic
161C2×C42—221no—
162C2×C42C4×D1111yescharacteristic
163C2×C42D4411yescharacteristic
164C2×C42C22⋊D1111yescharacteristic
165C4⋊C8—441no—
166#101—24no—
167C22⋊C8—222no—
168#97—41no—
169#97—441no—
170C4×C8—41no—
171#95—112no—
172#95—222no—
173#95—222no—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11#150811yescharacteristic
177C2×C11#212211yescharacteristic
178C2×C11C2×#35611yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—442no—
183C2×Q8—882no—
184C22×C4—222no—
185C22×C4—222no—
186C22×C4(C2×D11)⋊C411yescharacteristic
187C22×C4(C2×D11)⋊C411yescharacteristic
188C22×C4(C2×D11)⋊C411yescharacteristic
189C22×C4(C2×D11)⋊C411yescharacteristic
190C22×C4C2×C4×D1111yescharacteristic
191C22×C4C2×D4411yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193M16—24no—
194M16—42no—
195C2×C8—42no—
196C2×C8—442no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—224no—
201C4⋊C4—442no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4—882no—
205C4⋊C4—882no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—442no—
213C11#1179511yescharacteristic, complemented, Sylow
214C23C2×(C2×D11)⋊C411yescharacteristic
215Q8—44no—
216Q8—884no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—224no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4—442no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4#6686912yes—
238C2×C4#6687011yescharacteristic
239C2×C4#6687011yescharacteristic
240C2×C4#6700412yes—
241C8—44no—
242C8—882no—
243C22—21no—
244C22—21no—
245C22C2×#6686911yescharacteristic
246C22C2×#6687011yescharacteristic
247C22#1062261711yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—444no—
256C4—882no—
257C4#1062211612yes—
258C2—21no—
259C2—21no—
260C2#1306713511yescharacteristic
261C2#1307026711yescharacteristic
262C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#101D11
hypocenterC11#11795
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
213. C11#11795semidirect

Maximal subgroups

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

subgroupindex
#130738212
#130669602
#130666452
C4×C11×#1012
#1179511