Finite Group Databasebeta

← #14641380

Subgroups — #14641380

Order 2816.

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

normal subgroups only

This group has 224 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#13070149C211yesmaximal, characteristic
2#13066741C211yesmaximal, characteristic
3C11×#1318C211yesmaximal, characteristic
4C11×#390C2211yescharacteristic
5C2×#66898—21no—
6C2×#66896—21no—
7C2×#66872—21no—
8#10622548C411yescharacteristic, complemented
9C11×#324—21no—
10#10622162C411yescharacteristic, complemented
11C22×D4×C11D411yescharacteristic
12C2×C11×C4⋊C4D411yescharacteristic
13C2×C11×C22⋊C4—41no—
14C2×C42×C11C2×C411yescharacteristic
15C2×C22⋊Dic11—41no—
16C2×C4⋊Dic11—21no—
17C2×C4⋊Dic11—41no—
18C22×C11⋊C8—21no—
19C11×C22⋊C8—41no—
20#66898—22no—
21#66898—41no—
22#66896—42no—
23#66872—42no—
24#7435—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×C11C22⋊C411yescharacteristic
34C22×Dic11—41no—
35C22×Dic11—81no—
36C2×C8×C11—81no—
37C11×C4⋊C4—41no—
38C11×C22⋊C4—82no—
39C42×C11—41no—
40C22⋊Dic11—42no—
41C22⋊Dic11—81no—
42C4⋊Dic11—41no—
43C4⋊Dic11—41no—
44C4⋊Dic11—82no—
45C2×C11⋊C8—22no—
46C2×C11⋊C8—41no—
47C2×C11⋊C8—41no—
48#2094—111no—
49#1393—111no—
50#1318D1111yescharacteristic
51C23×C11—21no—
52C23×C11—21no—
53C23×C11—41no—
54C23×C11—41no—
55C23×C11—81no—
56C23×C11—81no—
57C23×C11#9911yescharacteristic
58D4×C11—41no—
59D4×C11—41no—
60D4×C11—81no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—81no—
68C2×C4×C11#10311yescharacteristic
69C2×C4×C11#10411yescharacteristic
70C2×Dic11—82no—
71C2×Dic11—82no—
72C2×Dic11—81no—
73C2×Dic11—161no—
74C2×Dic11—161no—
75C8×C11—161no—
76C11⋊C8—42no—
77C2×#106—221no—
78C2×#102—221no—
79C2×#99—221no—
80#390C2×D1111yescharacteristic
81#384—111no—
82#336—111no—
83#324—21no—
84C22×C11—21no—
85C22×C11—21no—
86C22×C11—41no—
87C22×C11—41no—
88C22×C11—81no—
89C22×C11—81no—
90C22×C11—81no—
91C22×C11—81no—
92C22×C11—161no—
93C22×C11#32811yescharacteristic
94C22×C11#35211yescharacteristic
95C22×C11#35311yescharacteristic
96C4×C11—21no—
97C4×C11—21no—
98C4×C11—42no—
99C4×C11—81no—
100Dic11—162no—
101Dic11—161no—
102C22×D4D4411yescharacteristic
103C22×C8—221no—
104C2×C4⋊C4—221no—
105C2×C4⋊C4—441no—
106C2×C4⋊C4C22⋊D1111yescharacteristic
107C2×C22⋊C4—41no—
108C2×C22⋊C4—441no—
109C2×C42C4×D1111yescharacteristic
110#106—442no—
111#102—442no—
112#99—222no—
113#99—441no—
114C22⋊C8—41no—
115C2×C11—21no—
116C2×C11—21no—
117C2×C11—81no—
118C2×C11—81no—
119C2×C11#135211yescharacteristic
120C2×C11#140611yescharacteristic
121C2×C11#140911yescharacteristic
122C24—21no—
123C2×D4—21no—
124C2×D4—41no—
125C2×D4—41no—
126C2×D4#431411yescharacteristic
127C2×D4Dic4411yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—441no—
131C22×C4—881no—
132C22×C4(C2×D11)⋊C411yescharacteristic
133C2×C8—81no—
134C2×C8—222no—
135C2×C8—441no—
136C2×C8—441no—
137C4⋊C4—41no—
138C4⋊C4—441no—
139C4⋊C4—441no—
140C4⋊C4—882no—
141C22⋊C4—82no—
142C22⋊C4—442no—
143C22⋊C4—881no—
144C42—41no—
145C11#743511yescharacteristic, complemented, Sylow
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#6687011yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—882no—
164C2×C4—882no—
165C2×C4—881no—
166C2×C4—1761no—
167C2×C4—1761no—
168C2×C4#6688011yescharacteristic
169C2×C4#6688911yescharacteristic
170C8—161no—
171C8—442no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1062210511yescharacteristic
182C22#1062211211yescharacteristic
183C22#1062211411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—1762no—
189C4—1761no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1306664111yescharacteristic
195C2#1306677411yescharacteristic
196C2#1306678011yescharacteristic
subgroupG/H
centerC22#10622112
commutatorC2×C42×C11C2×C4
Frattini#390C2×D11
FittingC11×#1318C2
socleC22×C11#353
prime radicalC22×D4×C11D4
cosocleC11×#390C22
hypercenter#1318D11
hypocenterC11#7435
LCSG ▷ C2×C42×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
8. #10622548C4semidirect
10. #10622162C4semidirect
145. C11#7435semidirect

Maximal subgroups

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

subgroupindex
#130701492
#130667412
C11×#13182
#743511