Finite Group Databasebeta

← #14641357

Subgroups — #14641357

Order 2816.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#13069762C211yesmaximal, characteristic
2#13066548C211yesmaximal, characteristic
3C11×#1393C211yesmaximal, characteristic
4C2×#66923C411yescharacteristic, complemented
5C2×C11×#99—21no—
6C11×#390C2211yescharacteristic
7C2×#66896—21no—
8#10622167—21no—
9#10622166—21no—
10#10622162C411yescharacteristic, complemented
11C22×D4×C11D411yescharacteristic
12C2×C11×C4⋊C4D411yescharacteristic
13C2×C11×C22⋊C4—41no—
14C2×C11×C22⋊C4—41no—
15C2×C42×C11C2×C411yescharacteristic
16C2×C4⋊Dic11—21no—
17C2×Dic11⋊C4—41no—
18C22×C11⋊C8—21no—
19#66923—42no—
20C11×#99—22no—
21C11×#99—41no—
22#66896—42no—
23C22⋊(C11⋊C8)—41no—
24#7428—111nomaximal, Sylow
25C24×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—41no—
28C2×D4×C11—41no—
29C2×D4×C11SD1611yescharacteristic
30C2×D4×C11Q1611yescharacteristic
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11—81no—
34C22×C4×C11C22⋊C411yescharacteristic
35C22×Dic11—41no—
36C11×C4⋊C4—41no—
37C11×C22⋊C4—42no—
38C11×C22⋊C4—82no—
39C11×C22⋊C4—81no—
40C42×C11—41no—
41C4⋊Dic11—22no—
42C4⋊Dic11—41no—
43Dic11⋊C4—42no—
44Dic11⋊C4—42no—
45C2×C11⋊C8—41no—
46C2×C11⋊C8—41no—
47C2×C11⋊C8—41no—
48C2×C11⋊C8—81no—
49#2025—111no—
50#1393D1111yescharacteristic
51#1318—111no—
52C23×C11—21no—
53C23×C11—21no—
54C23×C11—41no—
55C23×C11—41no—
56C23×C11—81no—
57C23×C11—81no—
58C23×C11#9911yescharacteristic
59D4×C11—41no—
60D4×C11—41no—
61D4×C11—81no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—81no—
69C2×C4×C11—82no—
70C2×C4×C11—161no—
71C2×C4×C11—161no—
72C2×C4×C11#10311yescharacteristic
73C2×C4×C11#10411yescharacteristic
74C2×Dic11—42no—
75C2×Dic11—81no—
76C2×Dic11—81no—
77C11⋊C8—81no—
78C11⋊C8—161no—
79C2×#125—111no—
80C2×#102—221no—
81C2×#99—21no—
82#390C2×D1111yescharacteristic
83#340—221no—
84#336—111no—
85#324—221no—
86C22×C11—21no—
87C22×C11—21no—
88C22×C11—41no—
89C22×C11—41no—
90C22×C11—81no—
91C22×C11—81no—
92C22×C11—81no—
93C22×C11—81no—
94C22×C11—161no—
95C22×C11#32811yescharacteristic
96C22×C11AΣL(1,𝔽16)11yescharacteristic
97C22×C11#35411yescharacteristic
98C4×C11—21no—
99C4×C11—21no—
100C4×C11—81no—
101C4×C11—81no—
102C4×C11—162no—
103Dic11—82no—
104C22×D4C22⋊D1111yescharacteristic
105C22×C8—221no—
106#125—442no—
107C2×C4⋊C4—221no—
108C2×C4⋊C4—441no—
109C2×C4⋊C4D4411yescharacteristic
110C2×C22⋊C4—41no—
111C2×C22⋊C4—41no—
112C2×C42C4×D1111yescharacteristic
113#102—442no—
114#99—22no—
115#99—41no—
116C22⋊C8—441no—
117C2×C11—21no—
118C2×C11—21no—
119C2×C11—81no—
120C2×C11—81no—
121C2×C11#135111yescharacteristic
122C2×C11#141211yescharacteristic
123C2×C11#141411yescharacteristic
124C24—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4#432411yescharacteristic
129C2×D4#432611yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—81no—
133C22×C4—441no—
134C22×C4(C2×D11)⋊C411yescharacteristic
135C2×C8—441no—
136C2×C8—441no—
137C2×C8—441no—
138C2×C8—881no—
139C4⋊C4—41no—
140C4⋊C4—222no—
141C4⋊C4—441no—
142C4⋊C4—442no—
143C4⋊C4—442no—
144C22⋊C4—42no—
145C22⋊C4—82no—
146C22⋊C4—81no—
147C42—41no—
148C11#742811yescharacteristic, complemented, Sylow
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23#6687011yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—161no—
168C2×C4—161no—
169C2×C4—442no—
170C2×C4—881no—
171C2×C4—881no—
172C2×C4#6686911yescharacteristic
173C2×C4#6687411yescharacteristic
174C8—881no—
175C8—1761no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#1062209011yescharacteristic
186C22#1062210911yescharacteristic
187C22#1062211111yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—162no—
193C4—882no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1306663611yescharacteristic
199C2#1306678611yescharacteristic
200C2#1306679011yescharacteristic
subgroupG/H
centerC22#10622111
commutatorC2×C42×C11C2×C4
Frattini#390C2×D11
FittingC11×#1393C2
socleC22×C11#354
prime radicalC22×D4×C11D4
cosocleC11×#390C22
hypercenter#1393D11
hypocenterC11#7428
LCSG ▷ C2×C42×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
4. C2×#66923C4semidirect
10. #10622162C4semidirect
148. C11#7428semidirect

Maximal subgroups

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

subgroupindex
#130697622
#130665482
C11×#13932
#742811