Finite Group Databasebeta

← #14641384

Subgroups — #14641384

Order 2816.

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

normal subgroups only

This group has 194 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#13070159C211yesmaximal, characteristic
2#13066550C211yesmaximal, characteristic
3C11×#1394C211yesmaximal, characteristic
4C2×C11×#101—21no—
5C11×#391C2211yescharacteristic
6C2×#66899—21no—
7C2×#66872—21no—
8#10622548C411yescharacteristic
9#10622166—21no—
10#10622162C411yescharacteristic
11C22×Q8×C11D411yescharacteristic
12C2×C11×M16—41no—
13C2×C11×C4⋊C4D411yescharacteristic
14C2×C42×C11C2×C411yescharacteristic
15C2×C4⋊Dic11—21no—
16C2×C4⋊Dic11—41no—
17C22×C11⋊C8—21no—
18C11×#101—22no—
19C11×#101—41no—
20C11×#95—41no—
21#66899—42no—
22C22⋊(C11⋊C8)—41no—
23#66872—42no—
24#7437—111nomaximal, Sylow
25C2×Q8×C11—21no—
26C2×Q8×C11—41no—
27C2×Q8×C11—41no—
28C2×Q8×C11SD1611yescharacteristic
29C2×Q8×C11Q1611yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11C22⋊C411yescharacteristic
34C22×Dic11—41no—
35C11×M16—42no—
36C11×M16—81no—
37C2×C8×C11—81no—
38C11×C4⋊C4—41no—
39C42×C11—41no—
40C4⋊Dic11—41no—
41C4⋊Dic11—41no—
42C4⋊Dic11—82no—
43C2×C11⋊C8—22no—
44C2×C11⋊C8—41no—
45C2×C11⋊C8—41no—
46C2×C11⋊C8—81no—
47#2096—111no—
48#1394D1111yescharacteristic
49#1319—111no—
50C23×C11#9911yescharacteristic
51Q8×C11—41no—
52Q8×C11—41no—
53Q8×C11—81no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—22no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—81no—
65C2×C4×C11#10311yescharacteristic
66C2×C4×C11#10411yescharacteristic
67C2×Dic11—82no—
68C2×Dic11—81no—
69C8×C11—82no—
70C11⋊C8—42no—
71C11⋊C8—161no—
72C2×#106—221no—
73C2×#103—221no—
74C2×#101—21no—
75#391C2×D1111yescharacteristic
76#384—111no—
77#336—111no—
78#324—221no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11#32811yescharacteristic
82C22×C11#35211yescharacteristic
83C22×C11#35311yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—42no—
87C4×C11—41no—
88C4×C11—41no—
89C4×C11—81no—
90Dic11—161no—
91C22×Q8C22⋊D1111yescharacteristic
92C2×M16—41no—
93C22×C8—221no—
94C2×C4⋊C4—221no—
95C2×C4⋊C4—441no—
96C2×C4⋊C4D4411yescharacteristic
97C2×C42C4×D1111yescharacteristic
98#106—442no—
99#103—442no—
100#101—22no—
101#101—41no—
102C22⋊C8—441no—
103#95—41no—
104C2×C11—21no—
105C2×C11—21no—
106C2×C11#135211yescharacteristic
107C2×C11#140711yescharacteristic
108C2×C11#141011yescharacteristic
109C2×Q8—21no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8#432411yescharacteristic
113C2×Q8#432611yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—441no—
118C22×C4(C2×D11)⋊C411yescharacteristic
119M16—42no—
120M16—81no—
121C2×C8—81no—
122C2×C8—222no—
123C2×C8—441no—
124C2×C8—441no—
125C2×C8—881no—
126C4⋊C4—41no—
127C4⋊C4—441no—
128C4⋊C4—441no—
129C4⋊C4—882no—
130C42—41no—
131C11#743711yescharacteristic, complemented, Sylow
132C23#6687011yescharacteristic
133Q8—41no—
134Q8—41no—
135Q8—81no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—882no—
148C2×C4—881no—
149C2×C4#6686911yescharacteristic
150C2×C4#6687411yescharacteristic
151C8—82no—
152C8—442no—
153C8—1761no—
154C22—21no—
155C22—21no—
156C22#1062209011yescharacteristic
157C22#1062211011yescharacteristic
158C22#1062211211yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—1761no—
166C2—21no—
167C2—21no—
168C2#1306663911yescharacteristic
169C2#1306677711yescharacteristic
170C2#1306678211yescharacteristic
subgroupG/H
centerC22#10622112
commutatorC2×C42×C11C2×C4
Frattini#391C2×D11
FittingC11×#1394C2
socleC22×C11#353
prime radicalC23×C11#99
cosocleC11×#391C22
hypercenter#1394D11
hypocenterC11#7437
LCSG ▷ C2×C42×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1394

Complements

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

NH ≅ G/Ntype
131. C11#7437semidirect

Maximal subgroups

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

subgroupindex
#130701592
#130665502
C11×#13942
#743711