Finite Group Databasebeta

← #14657249

Subgroups — #14657249

Order 2816.

518 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076662C211yesmaximal, characteristic
2#13069432C212yesmaximal, complemented
3#13068749C211yesmaximal, characteristic, complemented
4C2×#10622102C212yesmaximal, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66928C2212yes—
7C2×C11×#97C2212yes—
8C11×#382C2211yescharacteristic
9C2×#66885—22no—
10C2×#66880—22no—
11#10622604—22no—
12#10622548C2211yescharacteristic
13C2×#66867C2211yescharacteristic
14#10622286—22no—
15#10622284—22no—
16#10622167—22no—
17#10622102—24no—
18C22×D44—22no—
19C22×D44D412yes—
20C22×Dic22D412yes—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×(C2×D11)⋊C4—22no—
25C2×(C2×D11)⋊C4—22no—
26C2×(C2×D11)⋊C4—22no—
27C2×(C2×D11)⋊C4—22no—
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—21no—
30C22×C11⋊C8—21no—
31#66928—22no—
32#66928—22no—
33#66928—22no—
34#66928—22no—
35C11×#97—22no—
36C11×#97—22no—
37C11×#95—22no—
38C11⋊#95—22no—
39#66885—44no—
40#66880—44no—
41#66867—21no—
42#66867D412yescomplemented
43#10425—111nomaximal, Sylow
44C23×D11—22no—
45C22×C4×C11—22no—
46C22×C4×C11C2×D412yes—
47C22×C4×C11C2×D411yescharacteristic
48C22×Dic11—22no—
49C22×Dic11—41no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—82no—
55C2×D44—82no—
56C2×D44—82no—
57C2×Dic22—22no—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C2×Dic22—42no—
61C2×C8×C11—24no—
62C2×C8×C11—42no—
63C2×C8×C11—42no—
64C11×C4⋊C4—42no—
65C42×C11C2×D411yescharacteristic
66C42×C11#4111yescharacteristic
67C42×C11#4112yes—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—82no—
73(C2×D11)⋊C4—82no—
74C4⋊Dic11—42no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80#2819—111no—
81#1959—112no—
82#1836—111no—
83C2×#329—112no—
84#1295D1111yescharacteristic, complemented
85C23×C11#12011yescharacteristic
86C22×D11—42no—
87C22×D11—42no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11#12112yes—
101C2×C4×C11#12111yescharacteristic
102C2×C4×C11#12312yes—
103C2×C4×C11#12411yescharacteristic
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—82no—
108C2×Dic11—81no—
109D44—44no—
110D44—82no—
111D44—88no—
112Dic22—44no—
113Dic22—82no—
114C8×C11—44no—
115C11⋊C8—42no—
116C2×#124—112no—
117C2×#103—222no—
118C2×#102—222no—
119C2×#97—111no—
120C2×#97C2×D1112yes—
121#394—222no—
122#393—222no—
123#392—222no—
124#384—111no—
125#382C2×D1111yescharacteristic
126#340—222no—
127#329—224no—
128C22×C11#39411yescharacteristic
129C22×C11#45312yes—
130C22×C11#45411yescharacteristic
131C22×C11#45511yescharacteristic
132C22×C11#45512yes—
133C2×D11—82no—
134C2×D11—82no—
135C2×D11—82no—
136C2×D11—82no—
137C2×D11—82no—
138C2×D11—82no—
139C2×D11—82no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—82no—
145Dic11—82no—
146Dic11—161no—
147C22×Q8—112no—
148C22×D4—112no—
149C22×D4—222no—
150C22×C8—22no—
151C22×C8—221no—
152#124—222no—
153#124—222no—
154#124—222no—
155#124—222no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4D4412yes—
159C2×C22⋊C4—222no—
160C2×C22⋊C4—222no—
161C2×C22⋊C4—222no—
162C2×C22⋊C4—222no—
163C2×C42C22×D1111yescharacteristic
164#103—444no—
165#102—444no—
166#97—22no—
167#97—22no—
168#97—112no—
169#97—221no—
170#95—22no—
171#95—222no—
172C2×C11#165611yescharacteristic
173C2×C11#165912yes—
174C2×C11#166211yescharacteristic
175C2×C11#203712yes—
176C2×C11#204011yescharacteristic
177D11—162no—
178C24—222no—
179C2×Q8—222no—
180C2×Q8—222no—
181C2×Q8—442no—
182C2×Q8—442no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—442no—
186C2×D4—442no—
187C2×D4—882no—
188C2×D4—882no—
189C2×D4—882no—
190C22×C4—22no—
191C22×C4—222no—
192C22×C4—441no—
193C22×C4C2×D4411yescharacteristic
194C22×C4D4×D1112yes—
195C2×C8—24no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—222no—
199C2×C8—441no—
200C2×C8—441no—
201C4⋊C4—42no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C22⋊C4—442no—
208C22⋊C4—442no—
209C22⋊C4—882no—
210C22⋊C4—882no—
211C42#433912yes—
212C42D4×D1111yescharacteristic
213C42#434311yescharacteristic
214C11#1042511yescharacteristic, complemented, Sylow
215C23—442no—
216C23—442no—
217C23—442no—
218C23—442no—
219C23—442no—
220C23—442no—
221C23—442no—
222C23#6693511yescharacteristic
223Q8—444no—
224Q8—882no—
225D4—444no—
226D4—882no—
227D4—888no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—881no—
239C2×C4—882no—
240C2×C4#6692811yescharacteristic
241C2×C4#6693712yes—
242C2×C4#6694712yes—
243C2×C4#6694811yescharacteristic
244C8—44no—
245C8—442no—
246C22—882no—
247C22—882no—
248C22—882no—
249C22—882no—
250C22—882no—
251C22—882no—
252C22—882no—
253C22#1062228511yescharacteristic
254C22#1062235911yescharacteristic
255C22#1062236611yescharacteristic
256C22#1062243512yes—
257C22#1062243812yes—
258C4—22no—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—82no—
263C4—882no—
264C4—1761no—
265C2—1762no—
266C2#1306791111yescharacteristic
267C2#1306792412yes—
268C2#1306794011yescharacteristic
269C2#1306982912yes—
270C2#1306984611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11#120
prime radical#13076662C2
hypercenter#1295D11
hypocenterC11#10425
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #13069432C2semidirect
3. #13068749C2semidirect
4. C2×#10622102C2semidirect
5. C11×#1295C2semidirect
42. #66867D4semidirect
84. #1295D11semidirect
214. C11#10425semidirect

Maximal subgroups

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

subgroupindex
#130766622
#130694322
#130687492
C2×#106221022
C11×#12952
#1042511