Finite Group Databasebeta

← #14641272

Subgroups — #14641272

Order 2816.

238 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 37 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#13069737C211yesmaximal, characteristic
2#13066737C211yesmaximal, characteristic
3C11×#1321C211yesmaximal, characteristic
4C2×#67004—21no—
5C22×Dic44C411yescharacteristic, complemented
6C11×#408C2211yescharacteristic
7#10622853—21no—
8C2×#66888—21no—
9C11×#349—21no—
10#10622190C411yescharacteristic, complemented
11C2×C11×#41D411yescharacteristic
12C22×Dic22—21no—
13C2×C11×M16D411yescharacteristic
14C22×C8×C11C2×C411yescharacteristic
15#67004—42no—
16#67004—42no—
17C2×#4326—41no—
18C2×#4324—41no—
19#66979—41no—
20C2×#4318—21no—
21C2×Dic44—41no—
22C2×Dic44—42no—
23C11×M32—41no—
24C11×C22⋊C8—41no—
25#66898—22no—
26#66898—41no—
27#66888—42no—
28#7399—111nomaximal, Sylow
29C11×#41—41no—
30C11×#41—41no—
31C2×Q8×C11SD1611yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11D811yescharacteristic
34C22×C4×C11—21no—
35C22×C4×C11C22⋊C411yescharacteristic
36C22×Dic11—41no—
37C2×Dic22—22no—
38C2×Dic22—41no—
39C2×Dic22—41no—
40C2×Dic22—41no—
41C2×Dic22—41no—
42C2×Dic22—41no—
43C11×M16—41no—
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11—41no—
47C22⋊Dic11—42no—
48#4326—44no—
49#4324—44no—
50C4⋊Dic11—81no—
51C4×Dic11—81no—
52#4318—22no—
53#4318—41no—
54C2×C11⋊C8—41no—
55Dic44—42no—
56Dic44—42no—
57C11×C16—81no—
58#2020—111no—
59#1391—111no—
60#1321D1111yescharacteristic
61C23×C11—21no—
62C23×C11#10411yescharacteristic
63Q8×C11—41no—
64D4×C11—41no—
65D4×C11—81no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11#9911yescharacteristic
72C2×C4×C11#10211yescharacteristic
73C2×Dic11—42no—
74C2×Dic11—81no—
75C2×Dic11—81no—
76C2×Dic11—82no—
77Dic22—42no—
78Dic22—42no—
79Dic22—81no—
80Dic22—81no—
81C8×C11—41no—
82C8×C11—41no—
83C11⋊C8—42no—
84C2×#137—221no—
85C22×Q16—111no—
86C2×#101—221no—
87#410—221no—
88#408C2×D1111yescharacteristic
89#349—21no—
90#341—111no—
91C22×C11—21no—
92C22×C11—41no—
93C22×C11—41no—
94C22×C11—81no—
95C22×C11#32711yescharacteristic
96C4×C11—21no—
97C4×C11—41no—
98C4×C11AΣL(1,𝔽16)11yescharacteristic
99C4×C11#35311yescharacteristic
100Dic11—82no—
101Dic11—162no—
102C2×#41D4411yescharacteristic
103C22×Q8—221no—
104#137—442no—
105#137—442no—
106C2×Q16—441no—
107C2×Q16—442no—
108C2×Q16—441no—
109C2×SD16—441no—
110C2×M16—221no—
111C2×M16C22⋊D1111yescharacteristic
112C22×C8C4×D1111yescharacteristic
113#117—441no—
114M32—41no—
115#101—442no—
116#99—222no—
117#99—441no—
118C22⋊C8—41no—
119C2×C11—21no—
120C2×C11—41no—
121C2×C11—81no—
122C2×C11#134311yescharacteristic
123#41—41no—
124#41—41no—
125C2×Q8—222no—
126C2×Q8—441no—
127C2×Q8—441no—
128C2×Q8—441no—
129C2×Q8—441no—
130C2×Q8—441no—
131C2×Q8#431411yescharacteristic
132C2×D4—21no—
133C2×D4D8811yescharacteristic
134C22×C4—21no—
135C22×C4—441no—
136C22×C4(C2×D11)⋊C411yescharacteristic
137Q16—442no—
138Q16—442no—
139Q16—444no—
140SD16—444no—
141M16—41no—
142M16—222no—
143M16—441no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—441no—
148C4⋊C4—881no—
149C22⋊C4—442no—
150C42—881no—
151C16—81no—
152C11#739911yescharacteristic, complemented, Sylow
153C23—21no—
154C23#6688911yescharacteristic
155Q8—41no—
156Q8—442no—
157Q8—442no—
158Q8—881no—
159Q8—881no—
160D4—41no—
161D4—81no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—442no—
168C2×C4—881no—
169C2×C4—881no—
170C2×C4—882no—
171C2×C4#6687011yescharacteristic
172C2×C4#6688511yescharacteristic
173C8—41no—
174C8—41no—
175C8—442no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—81no—
180C22#1062210811yescharacteristic
181C4—21no—
182C4—41no—
183C4—882no—
184C4—1762no—
185C4#1062211211yescharacteristic
186C4#1062211311yescharacteristic
187C2—21no—
188C2—41no—
189C2—81no—
190C2#1306661411yescharacteristic
subgroupG/H
centerC2#13066614
commutatorC22×C8×C11C2×C4
Frattini#408C2×D11
FittingC11×#1321C2
socleC2×C11#1343
prime radicalC2×C11×#41D4
cosocleC11×#408C22
hypercenter#1321D11
hypocenterC11#7399
LCSG ▷ C22×C8×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1321

Complements

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

NH ≅ G/Ntype
5. C22×Dic44C4semidirect
10. #10622190C4semidirect
152. C11#7399semidirect

Maximal subgroups

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

subgroupindex
#130697372
#130667372
C11×#13212
#739911