Finite Group Databasebeta

← #14671983

Subgroups — #14671983

Order 2816.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#13077321C211yesmaximal, characteristic
2#13070382C211yesmaximal, characteristic, complemented
3#13070245C212yesmaximal, complemented
4C2×#10622152C212yesmaximal, complemented
5C11×#2110C211yesmaximal, characteristic, complemented
6C2×#66954C2211yescharacteristic
7C22×#4313C2211yescharacteristic
8#10623055C411yescharacteristic
9C2×C11×M32C2212yes—
10C11×#405C2211yescharacteristic
11#10622742C411yescharacteristic
12#10622739C411yescharacteristic
13C2×#66876C2212yes—
14#10622612C411yescharacteristic
15#10622319—22no—
16#10622301—22no—
17C11×#347—22no—
18#10622153—24no—
19#10622152—24no—
20#10622101—22no—
21C2×#4339C2×C411yescharacteristic
22C22×C4×D11C2×C411yescharacteristic
23C2×C11×M16C2×C411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C11×#117C2×C411yescharacteristic
26C2×#4318C2×C411yescharacteristic
27C22×C11⋊C8C2×C411yescharacteristic
28#66954—22no—
29#66954—22no—
30C2×#4313—21no—
31C2×#4313—21no—
32C2×#4313—22no—
33C2×#4313—21no—
34C2×#4313—22no—
35C2×C8×D11—21no—
36#66950—21no—
37#66948—21no—
38#66939—21no—
39#66935—21no—
40C4×D44—22no—
41C11×M32—22no—
42C11×M32D414yescomplemented
43C2×C11×C16—22no—
44C11×#97D412yes—
45C4×C8×C11D412yes—
46(C2×D11)⋊C8—22no—
47(C2×D11)⋊C8—22no—
48#66876—22no—
49#66876—22no—
50C2×C11⋊C16—22no—
51C4⋊(C11⋊C8)—22no—
52#13201—111nomaximal, Sylow
53C23×D11M1611yescharacteristic
54C22×C4×C11C22×C411yescharacteristic
55C2×C22⋊D11—21no—
56C22×Dic11M1611yescharacteristic
57#4339—22no—
58#4339—22no—
59C2×D44—22no—
60C2×D44M1611yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—22no—
64C2×C4×D11—21no—
65C2×C4×D11—22no—
66C2×Dic22M1611yescharacteristic
67C11×M16—22no—
68C2×C8×C11C22⋊C412yes—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×D412yes—
72C2×C8×C11#4112yes—
73C11×C4⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11C22⋊C412yes—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—22no—
78C4⋊Dic11—22no—
79#4318—22no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—22no—
83#4313—42no—
84#4313—41no—
85#4313—41no—
86#4313—41no—
87#4313—41no—
88C8×D11—42no—
89C11×C16—24no—
90C11⋊C16—42no—
91#2930—111no—
92#2153—111no—
93#2117—112no—
94C2×#349—112no—
95#2110D1111yescharacteristic, complemented
96C23×C11C2×M1611yescharacteristic
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—22no—
100C22×D11—81no—
101C2×C4×C11—22no—
102C2×C4×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11C4×D412yes—
104C2×C4×C11C2×M1611yescharacteristic
105C2×C4×C11#13112yes—
106C22⋊D11—42no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110D44—22no—
111D44—82no—
112C4×D11—41no—
113C4×D11—41no—
114C4×D11—41no—
115C4×D11—41no—
116C4×D11—42no—
117Dic22—22no—
118C8×C11—22no—
119C8×C11#12112yes—
120C8×C11#12411yescharacteristic
121C8×C11#12711yescharacteristic
122C11⋊C8—41no—
123C11⋊C8—41no—
124C2×#131—111no—
125C22×M16—111no—
126#525—111no—
127C2×M32—112no—
128C2×M32C2×D1112yes—
129#436—222no—
130#435—222no—
131#424—111no—
132#408—111no—
133#407—111no—
134#405C2×D1111yescharacteristic
135#364—222no—
136#350—224no—
137#349—224no—
138#347—22no—
139C22×C11—41no—
140C22×C11#40711yescharacteristic
141C22×C11#43512yes—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—42no—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—82no—
148C4×C11—42no—
149C4×C11#39011yescharacteristic
150C4×C11#40811yescharacteristic
151C4×C11#43512yes—
152Dic11—41no—
153Dic11—41no—
154C2×#41—111no—
155C23×C4—111no—
156#131—222no—
157#131—222no—
158C2×M16—111no—
159C2×M16—222no—
160C2×M16—221no—
161C2×M16—221no—
162C2×M16—222no—
163C2×M16—221no—
164C2×M16C4×D1111yescharacteristic
165C22×C8—111no—
166C22×C8—221no—
167C22×C8C22×D1111yescharacteristic
168#123—221no—
169C22⋊Q8—221no—
170#121—221no—
171#120—221no—
172C4×D4—222no—
173#117C4×D1111yescharacteristic
174M32—22no—
175M32—222no—
176M32—222no—
177M32D4414yescomplemented
178C2×C16—22no—
179C2×C16—222no—
180C4⋊C8—222no—
181C22⋊C8—222no—
182C22⋊C8—222no—
183#97C22⋊D1112yes—
184C4×C8D4412yes—
185C2×C11—21no—
186C2×C11—22no—
187C2×C11#195511yescharacteristic
188D11—81no—
189D11—81no—
190C24—111no—
191#41—222no—
192#41—222no—
193C2×Q8—111no—
194C2×D4—111no—
195C2×D4—222no—
196C2×D4—221no—
197C22×C4—111no—
198C22×C4—222no—
199C22×C4—221no—
200C22×C4—222no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4C2×C4×D1111yescharacteristic
204M16—22no—
205M16—222no—
206M16—441no—
207M16—441no—
208M16—441no—
209M16—441no—
210M16—442no—
211C2×C8—222no—
212C2×C8—221no—
213C2×C8—221no—
214C2×C8—442no—
215C2×C8(C2×D11)⋊C412yes—
216C2×C8C2×D4411yescharacteristic
217C2×C8C2×D4412yes—
218C2×C8#433912yes—
219C2×C8C2×C22⋊D1111yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—222no—
222C22⋊C4—21no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C42(C2×D11)⋊C412yes—
226C16—24no—
227C16—442no—
228C11#1320111yescharacteristic, complemented, Sylow
229C23—221no—
230C23—221no—
231C23—222no—
232C23—881no—
233C23M16×D1111yescharacteristic
234Q8—222no—
235D4—222no—
236D4—442no—
237D4—882no—
238C2×C4—22no—
239C2×C4—221no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—441no—
245C2×C4—441no—
246C2×C4—442no—
247C2×C4C4×D4412yes—
248C2×C4M16×D1111yescharacteristic
249C2×C4#6696012yes—
250C2×C4C2×(C2×D11)⋊C411yescharacteristic
251C8—22no—
252C8—441no—
253C8—441no—
254C8#6692711yescharacteristic
255C8#6692811yescharacteristic
256C8#6698312yes—
257C22—41no—
258C22—441no—
259C22—442no—
260C22—441no—
261C22—441no—
262C22—441no—
263C22—882no—
264C22#1062231912yes—
265C22#1062273911yescharacteristic
266C4—42no—
267C4—441no—
268C4—441no—
269C4#1062231912yes—
270C4#1062255211yescharacteristic
271C4#1062274211yescharacteristic
272C2—21no—
273C2—22no—
274C2—881no—
275C2—881no—
276C2#1306941411yescharacteristic
subgroupG/H
centerC4#10622552
commutatorC22×C4×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2110C2
socleC2×C11#1955
prime radical#10623055C4
cosocleC22×C8×C11C23
hypercenter#2110D11
hypocenterC11#13201
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
2. #13070382C2semidirect
3. #13070245C2semidirect
4. C2×#10622152C2semidirect
5. C11×#2110C2semidirect
42. C11×M32D4semidirect
95. #2110D11semidirect
177. M32D44semidirect
228. C11#13201semidirect

Maximal subgroups

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

subgroupindex
#130773212
#130703822
#130702452
C2×#106221522
C11×#21102
#1320111