Finite Group Databasebeta

← #14664969

Subgroups — #14664969

Order 2816.

274 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 71 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#13078997C211yesmaximal, characteristic
2#13070428C211yesmaximal, characteristic
3#13066650C214yesmaximal, complemented
4C11×#2165C211yesmaximal, characteristic
5#10623001C411yescharacteristic
6C2×#66922C411yescharacteristic
7C4×C11×M16C2211yescharacteristic
8#10622733—21no—
9#10622733—21no—
10#10622316C412yes—
11#10622316C2212yes—
12#10622294—21no—
13#10622294—21no—
14C11×#364—21no—
15C11×#349—21no—
16C11×#347C2212yes—
17#10622191—21no—
18#10622104C2212yes—
19#10622101—21no—
20C22×Dic22—21no—
21C2×C11×M16D411yescharacteristic
22C2×C11×M16D411yescharacteristic
23C2×C42×C11C2×C411yescharacteristic
24#66979—21no—
25C2×C4⋊Dic11—41no—
26#66977—41no—
27#66923C2×C412yes—
28#66922—21no—
29#66922—21no—
30#66922—41no—
31#66922C2×C412yes—
32C4×Dic22—41no—
33C11×M32—22no—
34C11×#97C2×C411yescharacteristic
35C11×#97C2311yescharacteristic
36C4×C8×C11D411yescharacteristic
37C4×C8×C11D411yescharacteristic
38#66880—22no—
39#66880—22no—
40#66880—22no—
41#66880—22no—
42#66876—22no—
43#11916—111nomaximal, Sylow
44C22×C4×C11—21no—
45C22×C4×C11C22⋊C411yescharacteristic
46C22×Dic11—41no—
47C2×Dic22—22no—
48C2×Dic22—42no—
49C2×Dic22—42no—
50C2×Dic22—41no—
51C2×Dic22—41no—
52C11×M16—41no—
53C11×M16—41no—
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C42×C11—21no—
59C42×C11C22⋊C411yescharacteristic
60C42×C11C22×C411yescharacteristic
61C22⋊Dic11—41no—
62C4⋊Dic11—22no—
63C4⋊Dic11—42no—
64C4⋊Dic11—41no—
65C4⋊Dic11—42no—
66Dic11⋊C4—42no—
67C4×Dic11—41no—
68C11×C16—42no—
69C11⋊C16—42no—
70#3139—111no—
71#2165—111no—
72#2165D1111yescharacteristic
73#1356—114no—
74C23×C11#10011yescharacteristic
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—42no—
80C2×C4×C11#10011yescharacteristic
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—82no—
85Dic22—42no—
86Dic22—42no—
87Dic22—82no—
88Dic22—82no—
89C8×C11—21no—
90C8×C11—21no—
91C8×C11—21no—
92C8×C11—21no—
93#533—111no—
94C2×C4⋊Q8—111no—
95#491—112no—
96#491—112no—
97#487—221no—
98#487—221no—
99#419—221no—
100#419—221no—
101C4×M16C2×D1111yescharacteristic
102#364—21no—
103#364—221no—
104#349—21no—
105#349—221no—
106#347—112no—
107#347C2×D1112yes—
108C22×C11—21no—
109C22×C11—41no—
110C22×C11C2×#10011yescharacteristic
111C4×C11—22no—
112C4×C11—21no—
113C4×C11—41no—
114C4×C11#42111yescharacteristic
115C4×C11#42111yescharacteristic
116Dic11—82no—
117Dic11—82no—
118C22×Q8—221no—
119C2×M16D4411yescharacteristic
120C2×M16C22⋊D1111yescharacteristic
121C4⋊Q8—112no—
122C4⋊Q8—221no—
123C4⋊Q8—221no—
124C4⋊Q8—441no—
125#125—112no—
126C22⋊Q8—441no—
127C4×Q8—441no—
128#117—221no—
129C2×C4⋊C4—441no—
130C2×C42C4×D1111yescharacteristic
131M32—22no—
132M32—222no—
133#103—222no—
134#103—222no—
135#103—222no—
136#103—222no—
137#97C4×D1111yescharacteristic
138#97C22×D1111yescharacteristic
139C4×C8D4411yescharacteristic
140C4×C8C22⋊D1111yescharacteristic
141C2×C11—21no—
142C2×C11—41no—
143C2×C11#153311yescharacteristic
144C2×Q8—222no—
145C2×Q8—441no—
146C2×Q8—442no—
147C2×Q8—442no—
148C2×Q8—441no—
149C22×C4—21no—
150C22×C4—441no—
151C22×C4(C2×D11)⋊C411yescharacteristic
152M16—41no—
153M16—41no—
154C2×C8(C2×D11)⋊C411yescharacteristic
155C2×C8(C2×D11)⋊C411yescharacteristic
156C2×C8C2×D4411yescharacteristic
157C2×C8C2×C22⋊D1111yescharacteristic
158C4⋊C4—222no—
159C4⋊C4—442no—
160C4⋊C4—442no—
161C4⋊C4—442no—
162C4⋊C4—441no—
163C22⋊C4—441no—
164C42—21no—
165C42—441no—
166C42(C2×D11)⋊C411yescharacteristic
167C42C2×C4×D1111yescharacteristic
168C16—42no—
169C16—442no—
170C11#1191611yescharacteristic, complemented, Sylow
171C23#6688711yescharacteristic
172Q8—442no—
173Q8—442no—
174Q8—882no—
175Q8—882no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—442no—
182C2×C4—442no—
183C2×C4—882no—
184C2×C4#6688711yescharacteristic
185C2×C4C2×(C2×D11)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8—21no—
190C22—21no—
191C22—41no—
192C22C2×#6688711yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—882no—
197C4—882no—
198C4#1062261811yescharacteristic
199C4#1062275211yescharacteristic
200C2—21no—
201C2—41no—
202C2#1306723911yescharacteristic
subgroupG/H
centerC2#13067239
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#2165C2
socleC2×C11#1533
prime radicalC23×C11#100
cosocleC11×#97C23
hypercenter#2165D11
hypocenterC11#11916
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
3. #13066650C2semidirect
170. C11#11916semidirect

Maximal subgroups

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

subgroupindex
#130789972
#130704282
#130666502
C11×#21652
#1191611