Finite Group Databasebeta

← #14670813

Subgroups — #14670813

Order 2816.

496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#10622750C211yesmaximal, characteristic
2C2×#10622134C212yesmaximal, complemented
3C2×#10622191C211yesmaximal, characteristic
4#13066716C212yesmaximal, complemented
5C2×C11×#430C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C22×C11×M16C2211yescharacteristic
8C2×#66977—21no—
9C22×Dic44C2211yescharacteristic
10C11×#430—24no—
11C2×C11×#108—21no—
12C2×C11×#108C2212yes—
13#10622750—22no—
14#10622750C414yes—
15C2×#66881C2211yescharacteristic
16C2×#66880—21no—
17C2×#66876C2212yes—
18#10622191—22no—
19#10622134—24no—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C2×C11×M16—22no—
23C2×C11×M16—22no—
24C2×C11×M16—24no—
25C2×C11×M16—22no—
26C2×C11×M16—41no—
27C2×C11×M16—42no—
28C2×C11×M16C2×C412yes—
29C2×C11×M16D412yes—
30C22×C8×C11—41no—
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C2×C22⋊Dic11—41no—
34C2×C4⋊Dic11—21no—
35#66977—24no—
36#66977—42no—
37C2×Dic11⋊C4—41no—
38C2×Dic44—22no—
39C2×Dic44—22no—
40C2×Dic44—21no—
41C2×Dic44C2×C412yes—
42C11×#108—24no—
43C11×#108—22no—
44C11×#108D414yes—
45#66881—21no—
46#66881C2×C412yes—
47#66880—24no—
48#66876—22no—
49#66876—22no—
50C2×C11⋊C16—22no—
51#13009—111nomaximal, Sylow
52C24×C11SD1611yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11D812yes—
59C22×C4×C11SD1611yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—41no—
62C22×Dic11—41no—
63C2×Dic22—22no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C11×M16—24no—
70C11×M16—24no—
71C11×M16—24no—
72C11×M16—44no—
73C11×M16—42no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—44no—
77C2×C8×C11—42no—
78C2×C8×C11C22⋊C412yes—
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D412yes—
82C2×C8×C11#4112yes—
83C22⋊Dic11—44no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86Dic11⋊C4—44no—
87Dic44—24no—
88Dic44—42no—
89C11⋊C16—42no—
90C2×#470—111no—
91C2×#430D1111yescharacteristic
92C2×#362—112no—
93C2×#349—111no—
94#1383—112no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—42no—
98C23×C11#10212yes—
99C23×C11C2×SD1611yescharacteristic
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11#10212yes—
107C2×C4×C11C2×C22⋊C411yescharacteristic
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12311yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C11#13711yescharacteristic
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—82no—
116C2×Dic11—81no—
117C2×Dic11—81no—
118Dic22—42no—
119Dic22—42no—
120Dic22—81no—
121Dic22—81no—
122C8×C11—22no—
123C8×C11—44no—
124C8×C11C4×D412yes—
125C8×C11#12112yes—
126C22×Q16—111no—
127C22×M16—21no—
128C22×M16C2×D1111yescharacteristic
129C2×C22⋊Q8—221no—
130C2×M32—112no—
131#470—114no—
132#470—222no—
133#430—24no—
134C2×#108—21no—
135C2×#108C2×D1112yes—
136C2×#106—111no—
137C2×#103—221no—
138#362—224no—
139#349—222no—
140C22×C11—22no—
141C22×C11—22no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—81no—
145C22×C11C2×#10211yescharacteristic
146C22×C11#44811yescharacteristic
147C22×C11#48111yescharacteristic
148C4×C11—22no—
149C4×C11#38611yescharacteristic
150C4×C11#41711yescharacteristic
151C4×C11#44711yescharacteristic
152C4×C11#48011yescharacteristic
153Dic11—82no—
154Dic11—82no—
155C22×Q8—221no—
156C23×C4C22⋊D1111yescharacteristic
157C2×Q16—112no—
158C2×Q16—221no—
159C2×Q16—222no—
160C2×Q16—222no—
161C2×M16—22no—
162C2×M16—22no—
163C2×M16—24no—
164C2×M16—22no—
165C2×M16—41no—
166C2×M16—42no—
167C2×M16C4×D1112yes—
168C2×M16D4412yes—
169C22×C8—41no—
170C22×C8C22⋊D1111yescharacteristic
171C22×C8C22×D1111yescharacteristic
172C22⋊Q8—224no—
173C22⋊Q8—442no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—441no—
176C2×C22⋊C4—441no—
177M32—222no—
178M32—222no—
179C2×C16—222no—
180#108—24no—
181#108—22no—
182#108C22⋊D1114yes—
183#106—112no—
184#106—221no—
185#103—224no—
186C2×C11—21no—
187C2×C11—21no—
188C2×C11—42no—
189C2×C11#187411yescharacteristic
190C2×C11#223912yes—
191C24#432511yescharacteristic
192C2×Q8—222no—
193C2×Q8—441no—
194C2×Q8—441no—
195C2×Q8—441no—
196C2×Q8—441no—
197C2×Q8—441no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4(C2×D11)⋊C412yes—
205C22×C4#432312yes—
206C22×C4#432511yescharacteristic
207C22×C4C2×C22⋊D1111yescharacteristic
208Q16—224no—
209Q16—442no—
210M16—24no—
211M16—24no—
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—44no—
218C2×C8—42no—
219C2×C8(C2×D11)⋊C412yes—
220C2×C8C2×C4×D1111yescharacteristic
221C2×C8C2×D4411yescharacteristic
222C2×C8#433912yes—
223C2×C8C2×C22⋊D1112yes—
224C4⋊C4—222no—
225C4⋊C4—444no—
226C4⋊C4—441no—
227C22⋊C4—444no—
228C16—442no—
229C11#1300911yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—42no—
233C23#6687312yes—
234C23C2×#432511yescharacteristic
235Q8—442no—
236Q8—442no—
237Q8—881no—
238Q8—881no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—882no—
248C2×C4—881no—
249C2×C4—881no—
250C2×C4#6687312yes—
251C2×C4C2×(C2×D11)⋊C411yescharacteristic
252C2×C4#6698211yescharacteristic
253C2×C4C2×#432311yescharacteristic
254C2×C4#6698511yescharacteristic
255C2×C4#6699511yescharacteristic
256C2×C4#6700611yescharacteristic
257C8—22no—
258C8—44no—
259C8C4×C22⋊D1112yes—
260C8#6698312yes—
261C22—22no—
262C22—22no—
263C22—42no—
264C22—42no—
265C22—81no—
266C22C2×#6687311yescharacteristic
267C22#1062258111yescharacteristic
268C22#1062284011yescharacteristic
269C4—22no—
270C4—882no—
271C4—882no—
272C4#1062257911yescharacteristic
273C4#1062258011yescharacteristic
274C4#1062282611yescharacteristic
275C4#1062283011yescharacteristic
276C2—21no—
277C2—21no—
278C2—42no—
279C2#1306893311yescharacteristic
280C2#1307083512yes—
subgroupG/H
centerC22#10622581
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#430C2
socleC22×C11#481
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#430D11
hypocenterC11#13009
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
2. C2×#10622134C2semidirect
4. #13066716C2semidirect
229. C11#13009semidirect

Maximal subgroups

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

subgroupindex
C2×#106227502
C2×#106221342
C2×#106221912
#130667162
C2×C11×#4302
#1300911