Finite Group Databasebeta

← #14671237

Subgroups — #14671237

Order 2816.

470 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 127 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#13078278C211yesmaximal, characteristic
2#13070353C212yesmaximal, complemented
3#13068662C211yesmaximal, characteristic, complemented
4#13066722C212yesmaximal, complemented
5C11×#3407C211yesmaximal, characteristic, complemented
6C2×C11×#131C2211yescharacteristic
7#10623364—21no—
8C2×#66957C2211yescharacteristic
9C11×#504—24no—
10C2×C11×M32—22no—
11C2×C11×M32C2212yes—
12#10622853—21no—
13#10622750C412yescomplemented
14#10622748C412yescomplemented
15#10622746—21no—
16#10622727—22no—
17#10622719C2212yes—
18C2×#66881C2211yescharacteristic
19#10622195—21no—
20#10622156—24no—
21C2×C11×#41D411yescharacteristic
22C2×#4339—21no—
23C11×#131—22no—
24C11×#131—22no—
25C2×C11×M16C2×C412yes—
26C2×C11×M16D411yescharacteristic
27C22×C8×C11D412yes—
28C22×C8×C11C2311yescharacteristic
29#66999—41no—
30#66992—42no—
31#66991—41no—
32#66983—22no—
33#66979—22no—
34C2×C4⋊Dic11—21no—
35#66977—22no—
36C2×Dic44C2×C411yescharacteristic
37#66957—22no—
38#66957—22no—
39C2×D88C2×C411yescharacteristic
40C2×#4314—21no—
41C11×M32—24no—
42C11×M32—22no—
43C11×M32D414yescomplemented
44C2×C11×C16—24no—
45C2×C11×C16—22no—
46#66898—42no—
47#66885—22no—
48#66882—22no—
49#66881—21no—
50#66881—22no—
51#66881C2×C412yes—
52#66880—22no—
53#13077—111nomaximal, Sylow
54C11×#41—22no—
55C11×#41—22no—
56C2×Q8×C11SD1611yescharacteristic
57C2×D4×C11D812yes—
58C2×D4×C11SD1611yescharacteristic
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—42no—
62C2×C22⋊D11—41no—
63C22×Dic11—41no—
64#4339—42no—
65#4339—42no—
66C2×D44—21no—
67C2×C4×D11—41no—
68C2×Dic22—21no—
69C11×M16—24no—
70C11×M16—22no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11C22⋊C412yes—
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11C2×D412yes—
77C2×C8×C11#4112yes—
78C22⋊Dic11—42no—
79C22⋊Dic11—42no—
80(C2×D11)⋊C4—42no—
81C4⋊Dic11—22no—
82C4⋊Dic11—42no—
83C4⋊Dic11—41no—
84Dic11⋊C4—42no—
85C4×Dic11—42no—
86Dic44—22no—
87D88—22no—
88#4314—41no—
89#4314—41no—
90C11×C16—24no—
91#3407D1111yescharacteristic, complemented
92#3060—111no—
93#2145—112no—
94#1812—111no—
95#1386—112no—
96C23×C11#10212yes—
97C23×C11C2×D811yescharacteristic
98C22×D11—41no—
99Q8×C11—22no—
100D4×C11—24no—
101D4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11#10212yes—
105C2×C4×C11C2×C22⋊C411yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11C2×SD1611yescharacteristic
108C2×C4×C11#13512yes—
109C22⋊D11—82no—
110C22⋊D11—162no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113C2×Dic11—82no—
114C2×Dic11—161no—
115D44—41no—
116D44—41no—
117C4×D11—82no—
118Dic22—41no—
119Dic22—41no—
120C8×C11—22no—
121C8×C11C4×D412yes—
122C8×C11#12011yescharacteristic
123C8×C11#12311yescharacteristic
124C2×#135—111no—
125C2×#131C2×D1111yescharacteristic
126#537—221no—
127#504—24no—
128C2×M32—22no—
129C2×M32C2×D1112yes—
130#470—112no—
131#469—112no—
132#465—222no—
133#427—112no—
134C2×#106—111no—
135#417—221no—
136#410—221no—
137#360—224no—
138H(3,ℤ/4)—221no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11C2×#10211yescharacteristic
143C22×C11#46612yes—
144C2×D11—81no—
145C2×D11—81no—
146C2×D11—81no—
147C4×C11—22no—
148C4×C11#38611yescharacteristic
149C4×C11#41611yescharacteristic
150C4×C11#46512yes—
151Dic11—82no—
152Dic11—81no—
153Dic11—162no—
154C2×#41—221no—
155C2×#41D4411yescharacteristic
156#135—222no—
157#135—222no—
158C2×Q16—111no—
159C2×SD16—221no—
160C2×D8—111no—
161#131—22no—
162#131—22no—
163C2×M16C4×D1112yes—
164C2×M16D4411yescharacteristic
165C22×C8C22⋊D1112yes—
166C22×C8C22×D1111yescharacteristic
167C22⋊Q8—222no—
168C22⋊Q8—441no—
169#121—222no—
170#121—441no—
171#121—442no—
172#117—222no—
173C2×C4⋊C4—221no—
174M32—24no—
175M32—22no—
176M32C22⋊D1114yescomplemented
177C2×C16—24no—
178C2×C16—22no—
179#107—222no—
180#106—112no—
181#106—221no—
182#106—222no—
183#103—222no—
184#102—222no—
185#99—442no—
186C2×C11—21no—
187C2×C11—22no—
188C2×C11—42no—
189C2×C11#189311yescharacteristic
190D11—161no—
191#41—22no—
192#41—22no—
193#41—442no—
194#41—442no—
195C2×Q8—221no—
196C2×Q8#431411yescharacteristic
197C2×D4—221no—
198C2×D4—441no—
199C2×D4—442no—
200C2×D4#431411yescharacteristic
201C2×D4D8812yes—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4(C2×D11)⋊C412yes—
205C22×C4C2×D4411yescharacteristic
206Q16—222no—
207SD16—441no—
208SD16—441no—
209D8—222no—
210M16—22no—
211M16—24no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8(C2×D11)⋊C412yes—
215C2×C8C2×C4×D1111yescharacteristic
216C2×C8#433912yes—
217C2×C8C2×C22⋊D1112yes—
218C2×C8C2×C22⋊D1111yescharacteristic
219C4⋊C4—222no—
220C4⋊C4—442no—
221C4⋊C4—441no—
222C4⋊C4—442no—
223C22⋊C4—442no—
224C22⋊C4—442no—
225C22⋊C4—442no—
226C42—442no—
227C16—24no—
228C11#1307711yescharacteristic, complemented, Sylow
229C23—441no—
230C23#6688512yes—
231C23C2×D8811yescharacteristic
232Q8—22no—
233Q8—441no—
234Q8—441no—
235D4—24no—
236D4—22no—
237D4—441no—
238D4—441no—
239D4—882no—
240D4—1762no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—442no—
244C2×C4—441no—
245C2×C4—882no—
246C2×C4—882no—
247C2×C4—1761no—
248C2×C4#6688512yes—
249C2×C4C2×#431411yescharacteristic
250C2×C4#6695712yes—
251C2×C4C2×(C2×D11)⋊C411yescharacteristic
252C2×C4#6698312yes—
253C8—22no—
254C8C4×C22⋊D1112yes—
255C8#6698211yescharacteristic
256C8#6700611yescharacteristic
257C22—22no—
258C22—41no—
259C22—42no—
260C22—881no—
261C22—881no—
262C22—881no—
263C22C2×#6688511yescharacteristic
264C22#1062272812yes—
265C4—22no—
266C4—882no—
267C4—881no—
268C4—1762no—
269C4#1062272611yescharacteristic
270C4#1062272712yes—
271C4#1062282611yescharacteristic
272C2—21no—
273C2—22no—
274C2—42no—
275C2—1761no—
276C2#1306904411yescharacteristic
subgroupG/H
centerC2#13069044
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#3407C2
socleC2×C11#1893
prime radical#13078278C2
cosocleC22×C8×C11C23
hypercenter#3407D11
hypocenterC11#13077
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #13070353C2semidirect
3. #13068662C2semidirect
4. #13066722C2semidirect
5. C11×#3407C2semidirect
13. #10622750C4semidirect
14. #10622748C4semidirect
43. C11×M32D4semidirect
91. #3407D11semidirect
176. M32C22⋊D11semidirect
228. C11#13077semidirect

Maximal subgroups

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

subgroupindex
#130782782
#130703532
#130686622
#130667222
C11×#34072
#1307711