Finite Group Databasebeta

← #14664754

Subgroups — #14664754

Order 2816.

300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079202C211yesmaximal, characteristic
2#13068754C211yesmaximal, characteristic
3#13066635C214yesmaximal
4C11×#2163C211yesmaximal, characteristic
5#10623001—21no—
6C2×C4×C8×C11C2211yescharacteristic
7#10622729—21no—
8#10622729C2212yes—
9#10622537—21no—
10#10622312C411yescharacteristic
11C4×Dic44—21no—
12C4×Dic44C412yes—
13#10622295C411yescharacteristic
14#10622294—21no—
15C11×C4⋊C16—21no—
16C11×C22⋊C16C2212yes—
17C11×#346—21no—
18#10622190—21no—
19#10622190C2212yes—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66979—41no—
24#66977—22no—
25#66977—41no—
26C2×#4318—22no—
27C2×Dic44—21no—
28C2×Dic44C2×C412yes—
29#66923—41no—
30#66922—21no—
31#66922—21no—
32C4×Dic22—22no—
33C4×Dic22—41no—
34C2×C11×C16—22no—
35C4×C8×C11C2×C411yescharacteristic
36C4×C8×C11C2×C411yescharacteristic
37C4×C8×C11D411yescharacteristic
38C4×C8×C11D411yescharacteristic
39#66882—21no—
40#66882C2×C412yes—
41#66880—22no—
42#66880—22no—
43C4⋊(C11⋊C8)—41no—
44C4⋊(C11⋊C8)—41no—
45#11865—111nomaximal, Sylow
46C22×C4×C11SD1611yescharacteristic
47C22×C4×C11SD1611yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C2×Dic22—22no—
50C2×Dic22—41no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11C22⋊C411yescharacteristic
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22×C411yescharacteristic
56C2×C8×C11C2×D411yescharacteristic
57C42×C11C22⋊C411yescharacteristic
58C42×C11C22⋊C411yescharacteristic
59C42×C11D811yescharacteristic
60C42×C11D811yescharacteristic
61C22⋊Dic11—42no—
62C4⋊Dic11—22no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68C4×Dic11—42no—
69#4318—42no—
70#4318—42no—
71C2×C11⋊C8—42no—
72Dic44—42no—
73Dic44—42no—
74C11×C16—42no—
75#3170—111no—
76#2163D1111yescharacteristic
77#1837—111no—
78#1350—114no—
79C23×C11C2×SD1611yescharacteristic
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11#10211yescharacteristic
85C2×C4×C11#10211yescharacteristic
86C2×C4×C11#10211yescharacteristic
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11C2×D811yescharacteristic
90C2×Dic11—42no—
91C2×Dic11—42no—
92Dic22—42no—
93Dic22—42no—
94Dic22—82no—
95C8×C11—21no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C11⋊C8—82no—
100#533—221no—
101#500—111no—
102#494—111no—
103#487—221no—
104#467—112no—
105#467—221no—
106C4×Q16—112no—
107C4×Q16—221no—
108#423—221no—
109C2×C4×C8C2×D1111yescharacteristic
110C4⋊C16—21no—
111C22⋊C16C2×D1112yes—
112#346—21no—
113#341—112no—
114#341—221no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11C2×#10211yescharacteristic
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11#36212yes—
124C4×C11#41011yescharacteristic
125C4×C11#42111yescharacteristic
126Dic11—82no—
127Dic11—82no—
128C2×Q16—112no—
129C2×Q16—221no—
130C2×M16—222no—
131C22×C8D4411yescharacteristic
132C22×C8C22×D1111yescharacteristic
133C4⋊Q8—221no—
134C4⋊Q8—221no—
135#125—441no—
136C22⋊Q8—222no—
137C22⋊Q8—441no—
138C4×Q8—222no—
139C4×Q8—441no—
140#117—441no—
141C2×C42D4411yescharacteristic
142C2×C16—22no—
143#107—112no—
144#107—221no—
145C4⋊C8—441no—
146C4⋊C8—441no—
147#103—222no—
148#103—222no—
149C4×C8C4×D1111yescharacteristic
150C4×C8C4×D1111yescharacteristic
151C4×C8C22⋊D1111yescharacteristic
152C4×C8C22⋊D1111yescharacteristic
153C2×C11—41no—
154C2×C11#151711yescharacteristic
155C2×C11#214311yescharacteristic
156C2×C11C2×#36211yescharacteristic
157C2×Q8—222no—
158C2×Q8—441no—
159C22×C4#431411yescharacteristic
160C22×C4#431411yescharacteristic
161C22×C4C2×D4411yescharacteristic
162Q16—442no—
163Q16—442no—
164M16—442no—
165M16—442no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—442no—
169C2×C8(C2×D11)⋊C411yescharacteristic
170C2×C8(C2×D11)⋊C411yescharacteristic
171C2×C8C2×C4×D1111yescharacteristic
172C2×C8C2×C22⋊D1111yescharacteristic
173C4⋊C4—222no—
174C4⋊C4—441no—
175C4⋊C4—441no—
176C4⋊C4—442no—
177C4⋊C4—441no—
178C4⋊C4—442no—
179C22⋊C4—442no—
180C42—442no—
181C42D8811yescharacteristic
182C42D8811yescharacteristic
183C42(C2×D11)⋊C411yescharacteristic
184C42(C2×D11)⋊C411yescharacteristic
185C16—42no—
186C11#1186511yescharacteristic, complemented, Sylow
187C23C2×#431411yescharacteristic
188Q8—442no—
189Q8—442no—
190Q8—882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4#6688511yescharacteristic
198C2×C4#6688511yescharacteristic
199C2×C4#6688511yescharacteristic
200C2×C4#6688511yescharacteristic
201C2×C4C2×D8811yescharacteristic
202C2×C4C2×(C2×D11)⋊C411yescharacteristic
203C8—21no—
204C8—21no—
205C8—21no—
206C8—21no—
207C8—882no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22C2×#6688511yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—882no—
217C4—882no—
218C4#1062215512yes—
219C4#1062261911yescharacteristic
220C4#1062275211yescharacteristic
221C2—41no—
222C2#1306717711yescharacteristic
223C2#1307034511yescharacteristic
224C2C2×#1062215511yescharacteristic
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2163C2
socleC22×C11C2×#102
prime radicalC23×C11C2×SD16
cosocleC22×C8×C11C23
hypercenter#2163D11
hypocenterC11#11865
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
186. C11#11865semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130687542
#130666352
C11×#21632
#1186511