Finite Group Databasebeta

← #14672457

Subgroups — #14672457

Order 2816.

404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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#13068612C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic
3#13066743C214yesmaximal
4C11×#2568C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#400—21no—
8C11×#400—21no—
9C11×#391—21no—
10C11×#391—21no—
11C11×#391C2212yes—
12C11×#382C412yes—
13C4×C11×C4⋊C4C411yescharacteristic
14C2×#66900C2212yes—
15C2×#66900C2212yes—
16#10622537—21no—
17C4×#4318—21no—
18#10622168—21no—
19#10622168—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11C2311yescharacteristic
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⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C412yes—
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×#4318—22no—
37C2×#4318—22no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43#66900—22no—
44#66900—24no—
45#66900Q814yescomplemented
46C4⋊(C11⋊C8)—41no—
47C4⋊(C11⋊C8)—41no—
48#66867—41no—
49C4×C11⋊C8—41no—
50#13301—111nomaximal, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11—44no—
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Q8×C11C2×Q812yes—
57C2×Q8×C11#4112yes—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—42no—
80#4318—24no—
81#4318—42no—
82#4318—42no—
83#4318—42no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86#2568D1111yescharacteristic
87#1801—111no—
88C4×#101—111no—
89#1394—114no—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—42no—
92Q8×C11—42no—
93Q8×C11—82no—
94Q8×C11—82no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—44no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11C4×Q812yes—
116C2×C4×C11C22⋊Q812yes—
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11C4⋊Q811yescharacteristic
119C11⋊C8—44no—
120C11⋊C8—82no—
121C2×C4⋊Q8Dic1111yescharacteristic
122C2×C4×Q8C2×D1111yescharacteristic
123#423—221no—
124C2×#101—112no—
125C2×#101—112no—
126C4×M16—221no—
127#400—21no—
128#400—21no—
129#391—21no—
130#391—21no—
131#391C2×D1112yes—
132#382Dic1112yes—
133C4×C4⋊C4Dic1111yescharacteristic
134#343—221no—
135#343—221no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#39111yescharacteristic
139C22×C11C2×#9911yescharacteristic
140C22×C11#41011yescharacteristic
141C4×C11—21no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—82no—
150C4×C11—82no—
151C4×C11#35512yes—
152C22×Q8—21no—
153C22×Q8C22×D1111yescharacteristic
154C2×M16—222no—
155C2×M16—222no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×Dic1112yes—
163C2×C4⋊C4C2×Dic1111yescharacteristic
164C2×C4⋊C4C22⋊D1111yescharacteristic
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C42C2×Dic1111yescharacteristic
167C2×C42C2×Dic1112yes—
168C2×C42C22⋊D1111yescharacteristic
169C2×C42C22⋊D1111yescharacteristic
170C4⋊C8—441no—
171C4⋊C8—441no—
172#101—114no—
173#101—222no—
174#101—224no—
175#97—441no—
176C4×C8—441no—
177#95—21no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11#199611yescharacteristic
185C2×C11C2×#35511yescharacteristic
186C2×C11#213511yescharacteristic
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—44no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8Q8×D1112yes—
193C2×Q8#434312yes—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4C22⋊Dic1111yescharacteristic
197C22×C4C22⋊Dic1111yescharacteristic
198C22×C4C22⋊Dic1111yescharacteristic
199C22×C4C22⋊Dic1111yescharacteristic
200C22×C4C22×Dic1111yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203M16—224no—
204M16—442no—
205M16—442no—
206M16—442no—
207C2×C8—442no—
208C2×C8—442no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—42no—
222C11#1330111yescharacteristic, complemented, Sylow
223C23C2×C22⋊Dic1111yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—82no—
227Q8—82no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4#6689811yescharacteristic
247C2×C4#6689811yescharacteristic
248C2×C4#6699711yescharacteristic
249C2×C4Q8×Dic1112yes—
250C2×C4#6699912yes—
251C2×C4#6700011yescharacteristic
252C8—444no—
253C8—882no—
254C22—21no—
255C22—21no—
256C22C2×#6689811yescharacteristic
257C22#1062284311yescharacteristic
258C22#1062285311yescharacteristic
259C4—22no—
260C4—21no—
261C4—21no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C4#1062218012yes—
270C2—21no—
271C2—21no—
272C2#1306960211yescharacteristic
273C2C2×#1062218011yescharacteristic
274C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#2568C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#2568D11
hypocenterC11#13301
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
45. #66900Q8semidirect
222. C11#13301semidirect

Maximal subgroups

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

subgroupindex
#130686122
C4×#669002
#130667432
C11×#25682
#1330111