Finite Group Databasebeta

← #14674439

Subgroups — #14674439

Order 2816.

288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 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×#10622532C211yesmaximal, characteristic
2C2×#10622159C211yesmaximal, characteristic, complemented
3#13070704C211yesmaximal, characteristic, complemented
4#13066797C211yesmaximal, characteristic, complemented
5#13066795C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic, complemented
7C2×C11×Q64C211yesmaximal, characteristic, complemented
8C2×#66972—21no—
9C2×C11×Q32C2211yescharacteristic
10C2×C11×Q32C2211yescharacteristic
11#10622801—21no—
12C2×#66892—21no—
13#10622532—22no—
14#10622532—22no—
15C2×D176C2211yescharacteristic
16C2×C16×D11C2211yescharacteristic
17C11×Q64—22no—
18C2×C11×C32C2211yescharacteristic
19#10622202—21no—
20#10622159—22no—
21#10622142C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×#4343—41no—
24C2×C11×Q16—21no—
25C2×C11×Q16—21no—
26#66999—41no—
27C2×#4325—41no—
28#66972—24no—
29#66972—42no—
30C2×D88—21no—
31C2×C8×D11D411yescharacteristic
32C11×Q32—21no—
33C11×Q32—21no—
34C11×Q32—21no—
35C11×Q32D412yes—
36C2×C11×C16C2311yescharacteristic
37#66899—41no—
38#66892—24no—
39#66882—21no—
40C2×C11⋊C16D411yescharacteristic
41D176—21no—
42D176D412yes—
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13666—111nomaximal, Sylow
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50#4343—44no—
51#4343—82no—
52C2×D44—41no—
53C2×D44—81no—
54C2×C4×D11—81no—
55C2×C4×D11D811yescharacteristic
56C11×Q16—22no—
57C11×Q16—41no—
58C11×Q16—41no—
59C11×Q16—41no—
60C2×C8×C11C2×D411yescharacteristic
61#4325—44no—
62(C2×D11)⋊C4—81no—
63C4⋊Dic11—41no—
64Dic11⋊C4—81no—
65C2×C11⋊C8D811yescharacteristic
66D88—22no—
67D88—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C2×#508—111no—
74C2×Q64D1111yescharacteristic, complemented
75C2×SD64—111no—
76#2216—111no—
77#1416—111no—
78#1415—111no—
79C22⋊C32—111no—
80C22×D11—81no—
81C22×D11D1611yescharacteristic
82Q8×C11—42no—
83Q8×C11—81no—
84Q8×C11—81no—
85Q8×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11—81no—
88C2×C4×C11C2×D811yescharacteristic
89C2×Dic11—81no—
90C2×Dic11D1611yescharacteristic
91D44—42no—
92D44—84no—
93D44—81no—
94C4×D11—21no—
95C4×D11—21no—
96C4×D11—84no—
97C8×C11#12011yescharacteristic
98C8×C11AGL(1,ℤ/8)11yescharacteristic
99C11⋊C8—21no—
100C2×#135—221no—
101#508—222no—
102#508—222no—
103C2×Q32C2×D1111yescharacteristic
104C2×Q32C2×D1111yescharacteristic
105C2×SD32—221no—
106C2×D16—111no—
107C22×C16—111no—
108#467—221no—
109Q64—22no—
110SD64—222no—
111C2×C32—111no—
112C2×C32C2×D1111yescharacteristic
113#366—111no—
114#358—221no—
115C22×C11C2×D1611yescharacteristic
116C2×D11—21no—
117C2×D11—21no—
118C2×D11—21no—
119C2×D11—82no—
120C2×D11—161no—
121C2×D11—161no—
122C4×C11—82no—
123C4×C11—161no—
124C4×C11#44711yescharacteristic
125C4×C11#50911yescharacteristic
126Dic11—21no—
127Dic11—161no—
128C2×#41—441no—
129#135—224no—
130#135—442no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×SD16—441no—
134C2×D8—221no—
135C22×C8—111no—
136C22⋊Q8—441no—
137Q32—21no—
138Q32—21no—
139Q32—21no—
140Q32C22⋊D1112yes—
141SD32—224no—
142D16—112no—
143D16—221no—
144C2×C16—111no—
145C2×C16—221no—
146C2×C16—221no—
147C2×C16C22×D1111yescharacteristic
148#107—221no—
149#103—441no—
150C32—21no—
151C32—221no—
152C2×C11#218411yescharacteristic
153C2×C11#226211yescharacteristic
154C2×C11#226411yescharacteristic
155D11—41no—
156D11—162no—
157#41—444no—
158#41—882no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×D4—441no—
162C2×D4—881no—
163C22×C4—111no—
164C22×C4—881no—
165Q16—22no—
166Q16—41no—
167Q16—41no—
168Q16—41no—
169SD16—444no—
170D8—222no—
171D8—441no—
172C2×C8—111no—
173C2×C8—221no—
174C2×C8—221no—
175C2×C8D4×D1111yescharacteristic
176C4⋊C4—441no—
177C4⋊C4—881no—
178C22⋊C4—881no—
179C16—221no—
180C16D4×D1111yescharacteristic
181C16C2×C22⋊D1111yescharacteristic
182C11#1366611yescharacteristic, complemented, Sylow
183C23—111no—
184C23—881no—
185Q8—42no—
186Q8—81no—
187Q8—81no—
188Q8—81no—
189D4—442no—
190D4—884no—
191D4—881no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—111no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—884no—
198C2×C4—881no—
199C2×C4D8×D1111yescharacteristic
200C8—221no—
201C8#6696411yescharacteristic
202C8#6699011yescharacteristic
203C22—221no—
204C22—221no—
205C22—221no—
206C22—882no—
207C22—1761no—
208C22—1761no—
209C22D11×D1611yescharacteristic
210C4—82no—
211C4—161no—
212C4—221no—
213C4—1761no—
214C4#1062252411yescharacteristic
215C4#1062276911yescharacteristic
216C2—441no—
217C2—1762no—
218C2#1307052611yescharacteristic
219C2#1307092611yescharacteristic
220C2#1307093511yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×Q64C2
socleC22×C11C2×D16
prime radicalC2×#10622532C2
hypercenterC2×Q64D11
hypocenterC11#13666
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q64

Complements

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

NH ≅ G/Ntype
2. C2×#10622159C2semidirect
3. #13070704C2semidirect
4. #13066797C2semidirect
5. #13066795C2semidirect
6. (C2×D11)⋊C32C2semidirect
7. C2×C11×Q64C2semidirect
74. C2×Q64D11semidirect
182. C11#13666semidirect

Maximal subgroups

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

subgroupindex
C2×#106225322
C2×#106221592
#130707042
#130667972
#130667952
(C2×D11)⋊C322
C2×C11×Q642
#1366611