Finite Group Databasebeta

← #14672456

Subgroups — #14672456

Order 2816.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068612C211yesmaximal, characteristic
3#13066742C214yesmaximal
4C4×C11×#101C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C2×C11×#101C2212yes—
8C4×C11×M16—21no—
9#10622843C2212yes—
10C2×#66900C2212yes—
11#10622599—21no—
12#10622599—21no—
13#10622590C412yes—
14C4×C4⋊Dic11C411yescharacteristic
15#10622542—21no—
16#10622542—21no—
17#10622537—21no—
18C11×#343—21no—
19#10622168—21no—
20C22×Q8×C11C2311yescharacteristic
21C22×Dic22—21no—
22C2×C11×M16—22no—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×C4×Dic11C2×C412yes—
35C2×#4318—22no—
36#66922—41no—
37#66922—41no—
38C11×#101—22no—
39C11×#101Q814yescomplemented
40C11×#97—41no—
41C4×C8×C11—41no—
42#66900—24no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—21no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C4⋊(C11⋊C8)—41no—
49C4⋊(C11⋊C8)—41no—
50#13301—111nomaximal, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11C2×Q812yes—
54C2×Q8×C11#4112yes—
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
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—44no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C11×M16—24no—
68C11×M16—42no—
69C2×C8×C11—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4×Dic11—42no—
83#4318—42no—
84#4318—42no—
85C2×C11⋊C8—42no—
86#2568—111no—
87#1801—111no—
88C4×#101D1111yescharacteristic
89#1394—114no—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—42no—
92Q8×C11—42no—
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—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11#9911yescharacteristic
107C2×C4×C11#9911yescharacteristic
108C2×C4×C11C4×Q812yes—
109C2×C4×C11C22⋊Q812yes—
110C2×C4×C11#12411yescharacteristic
111C2×C4×C11C4⋊Q811yescharacteristic
112C2×Dic11—42no—
113C2×Dic11—44no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117Dic22—82no—
118Dic22—82no—
119C8×C11—44no—
120C11⋊C8—82no—
121C2×C4⋊Q8—111no—
122C2×C4×Q8C2×D1111yescharacteristic
123#423—221no—
124C2×#101—112no—
125C2×#101C2×D1112yes—
126C4×M16—21no—
127#400—221no—
128#400—221no—
129#391—112no—
130#391—221no—
131#391—221no—
132#382—112no—
133C4×C4⋊C4—111no—
134#343—21no—
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#35512yes—
150Dic11—82no—
151Dic11—82no—
152C22×Q8—221no—
153C22×Q8C22×D1111yescharacteristic
154C2×M16—22no—
155C2×M16—222no—
156C4⋊Q8—441no—
157C4⋊Q8—441no—
158C4×Q8—41no—
159C4×Q8—41no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4C4×D1111yescharacteristic
164C2×C4⋊C4D4411yescharacteristic
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C42—112no—
167C2×C42C4×D1111yescharacteristic
168C2×C42D4411yescharacteristic
169C2×C42C22⋊D1111yescharacteristic
170C4⋊C8—441no—
171C4⋊C8—441no—
172#101—22no—
173#101—224no—
174#101Dic2214yescomplemented
175#97—41no—
176C4×C8—41no—
177#95—221no—
178#95—222no—
179#95—222no—
180#95—222no—
181#95—222no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11#199611yescharacteristic
185C2×C11C2×#35511yescharacteristic
186C2×C11#213511yescharacteristic
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—444no—
190C2×Q8—441no—
191C2×Q8—441no—
192C2×Q8C2×Dic2212yes—
193C2×Q8#433912yes—
194C22×C4—222no—
195C22×C4—222no—
196C22×C4(C2×D11)⋊C411yescharacteristic
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4(C2×D11)⋊C411yescharacteristic
200C22×C4C2×C4×D1111yescharacteristic
201C22×C4C2×D4411yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203M16—24no—
204M16—42no—
205M16—442no—
206M16—442no—
207C2×C8—42no—
208C2×C8—442no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—442no—
213C4⋊C4—442no—
214C4⋊C4—442no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—442no—
222C11#1330111yescharacteristic, complemented, Sylow
223C23C2×(C2×D11)⋊C411yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—882no—
227Q8—882no—
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—442no—
242C2×C4—444no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4#6687011yescharacteristic
247C2×C4#6687011yescharacteristic
248C2×C4C4×Dic2212yes—
249C2×C4#6692211yescharacteristic
250C2×C4#6692811yescharacteristic
251C2×C4#6697712yes—
252C8—44no—
253C8—882no—
254C22—21no—
255C22—21no—
256C22#1062254211yescharacteristic
257C22C2×#6687011yescharacteristic
258C22#1062261911yescharacteristic
259C4—22no—
260C4—21no—
261C4—22no—
262C4—21no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—882no—
268C4—882no—
269C4#1062211512yes—
270C2—21no—
271C2—21no—
272C2#1306960111yescharacteristic
273C2C2×#1062211511yescharacteristic
274C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenterC4×#101D11
hypocenterC11#13301
LCSG ▷ C22×C4×C11 ▷ C22×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
39. C11×#101Q8semidirect
174. #101Dic22semidirect
222. C11#13301semidirect

Maximal subgroups

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

subgroupindex
#130738282
#130686122
#130667422
C4×C11×#1012
#1330111