Finite Group Databasebeta

← #14674440

Subgroups — #14674440

Order 2816.

288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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×#10622160C211yesmaximal, characteristic, complemented
2C2×#10622158C211yesmaximal, characteristic, complemented
3#13070707C211yesmaximal, characteristic, complemented
4#13066797C211yesmaximal, characteristic, complemented
5#13066794C211yesmaximal, characteristic, complemented
6C22⋊(C11⋊C32)C211yesmaximal, characteristic, complemented
7C2×C11×#508C211yesmaximal, characteristic
8C2×C11×#135—21no—
9C11×#508—22no—
10C11×#508—22no—
11C2×C11×Q32C2211yescharacteristic
12C2×C11×SD32—21no—
13C2×C11×D16C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15#10622729—21no—
16C2×Dic88C2211yescharacteristic
17#10622160—22no—
18#10622158—22no—
19#10622142C2211yescharacteristic
20#10622141—21no—
21C2×C11⋊C32C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×C11×#41—41no—
24C11×#135—24no—
25C11×#135—42no—
26C2×C11×Q16—21no—
27C2×C11×SD16—41no—
28C2×C11×D8—21no—
29C22×C8×C11D411yescharacteristic
30#66977—41no—
31C2×Dic44—21no—
32C11×Q32—21no—
33C11×Q32D412yes—
34C11×SD32—24no—
35C11×D16—21no—
36C11×D16D412yes—
37C2×C11×C16—21no—
38C2×C11×C16—21no—
39C2×C11×C16D411yescharacteristic
40C2×C11×C16C2311yescharacteristic
41#66882—21no—
42#66880—41no—
43Dic88—21no—
44Dic88—21no—
45C11⋊C32—21no—
46C11⋊C32—21no—
47#13666—111nomaximal, Sylow
48C11×#41—44no—
49C11×#41—82no—
50C2×Q8×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11—81no—
53C22×C4×C11—81no—
54C22×C4×C11D811yescharacteristic
55C2×Dic22—41no—
56C11×Q16—22no—
57C11×Q16—41no—
58C11×SD16—44no—
59C11×D8—22no—
60C11×D8—41no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C2×C8×C11D811yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C22⋊Dic11—81no—
66C4⋊Dic11—41no—
67Dic11⋊C4—81no—
68Dic44—41no—
69Dic44—41no—
70C11×C16—21no—
71C11×C16C2×D411yescharacteristic
72C11×C16C2×D411yescharacteristic
73C2×#508D1111yescharacteristic
74C2×Q64—111no—
75C2×SD64—111no—
76#2216—111no—
77#1416—111no—
78#1415—111no—
79C22⋊C32—111no—
80C23×C11—81no—
81C23×C11D1611yescharacteristic
82Q8×C11—42no—
83Q8×C11—81no—
84D4×C11—42no—
85D4×C11—84no—
86D4×C11—81no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—84no—
90C2×C4×C11—81no—
91C2×C4×C11D1611yescharacteristic
92C2×C4×C11C2×D811yescharacteristic
93C2×Dic11—81no—
94C2×Dic11—81no—
95Dic22—81no—
96Dic22—81no—
97C8×C11—21no—
98C8×C11#12011yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C2×#135—21no—
101#508—22no—
102#508—22no—
103C2×Q32—111no—
104C2×Q32C2×D1111yescharacteristic
105C2×SD32—21no—
106C2×D16C2×D1111yescharacteristic
107C22×C16C2×D1111yescharacteristic
108#467—221no—
109Q64—222no—
110SD64—222no—
111C2×C32—111no—
112C2×C32—111no—
113#366—111no—
114#358—221no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—82no—
119C22×C11—161no—
120C22×C11—161no—
121C22×C11C2×D1611yescharacteristic
122C4×C11—21no—
123C4×C11—82no—
124C4×C11#44711yescharacteristic
125C4×C11#50911yescharacteristic
126Dic11—161no—
127Dic11—161no—
128C2×#41—41no—
129#135—24no—
130#135—42no—
131C2×Q16—21no—
132C2×Q16—221no—
133C2×SD16—41no—
134C2×D8—21no—
135C22×C8C22⋊D1111yescharacteristic
136C22⋊Q8—441no—
137Q32—21no—
138Q32—221no—
139Q32—221no—
140Q32C22⋊D1112yes—
141SD32—24no—
142D16—21no—
143D16C22⋊D1112yes—
144C2×C16—21no—
145C2×C16—21no—
146C2×C16C22⋊D1111yescharacteristic
147C2×C16C22×D1111yescharacteristic
148#107—221no—
149#103—441no—
150C32—221no—
151C32—221no—
152C2×C11—41no—
153C2×C11—162no—
154C2×C11#218411yescharacteristic
155C2×C11#226211yescharacteristic
156C2×C11#226411yescharacteristic
157#41—44no—
158#41—82no—
159C2×Q8—41no—
160C2×Q8—441no—
161C2×D4—41no—
162C2×D4—81no—
163C22×C4—81no—
164C22×C4#432311yescharacteristic
165Q16—22no—
166Q16—41no—
167Q16—441no—
168Q16—441no—
169SD16—44no—
170D8—22no—
171D8—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8#432311yescharacteristic
175C2×C8C2×C22⋊D1111yescharacteristic
176C4⋊C4—441no—
177C4⋊C4—881no—
178C22⋊C4—881no—
179C16—21no—
180C16C2×C22⋊D1111yescharacteristic
181C16C2×C22⋊D1111yescharacteristic
182C11#1366611yescharacteristic, complemented, Sylow
183C23—81no—
184C23#6689011yescharacteristic
185Q8—42no—
186Q8—81no—
187Q8—881no—
188Q8—881no—
189D4—42no—
190D4—84no—
191D4—81no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—84no—
195C2×C4—81no—
196C2×C4—881no—
197C2×C4—881no—
198C2×C4#6689011yescharacteristic
199C2×C4C2×#432311yescharacteristic
200C8—21no—
201C8#6698511yescharacteristic
202C8#6700611yescharacteristic
203C22—21no—
204C22—21no—
205C22—21no—
206C22—82no—
207C22—161no—
208C22—161no—
209C22C2×#6689011yescharacteristic
210C4—21no—
211C4—82no—
212C4—1761no—
213C4—1761no—
214C4#1062276011yescharacteristic
215C4#1062283011yescharacteristic
216C2—41no—
217C2—162no—
218C2#1307052811yescharacteristic
219C2#1307092311yescharacteristic
220C2#1307093311yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
Fitting, prime radicalC2×C11×#508C2
socleC22×C11C2×D16
hypercenterC2×#508D11
hypocenterC11#13666
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622160C2semidirect
2. C2×#10622158C2semidirect
3. #13070707C2semidirect
4. #13066797C2semidirect
5. #13066794C2semidirect
6. C22⋊(C11⋊C32)C2semidirect
182. C11#13666semidirect

Maximal subgroups

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

subgroupindex
C2×#106221602
C2×#106221582
#130707072
#130667972
#130667942
C22⋊(C11⋊C32)2
C2×C11×#5082
#1366611