Finite Group Databasebeta

← #14641571

Subgroups — #14641571

Order 2816.

266 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070301C212yesmaximal
2C11×#1963C211yesmaximal, characteristic
3C11×#532C2211yescharacteristic
4C11×#423C411yescharacteristic
5C2×C11×#104—22no—
6C11×#376C411yescharacteristic
7#10622850—22no—
8#10622186—22no—
9#10622180C414yescomplemented
10C2×C11×#41D412yes—
11C2×C11×M16—21no—
12C11×C4⋊Q8D411yescharacteristic
13C11×#127Q811yescharacteristic
14C11×#124C2×C412yes—
15C11×#121—41no—
16C4×D4×C11—41no—
17C2×C42×C11—21no—
18C2×C42×C11C2×C411yescharacteristic
19C2×#4318—42no—
20C11×C4⋊C8—41no—
21C11×#104—44no—
22C11×#95—41no—
23#66900—24no—
24#66897—42no—
25#7507—111nomaximal, Sylow
26C11×#41—42no—
27C11×#41—42no—
28C2×Q8×C11C22⋊C412yes—
29C2×D4×C11—22no—
30C2×D4×C11—41no—
31C2×D4×C11C4⋊C412yes—
32C22×C4×C11—21no—
33C22×C4×C11—22no—
34C22×C4×C11—41no—
35C22×C4×C11C22⋊C411yescharacteristic
36C11×M16—42no—
37C2×C8×C11—41no—
38C11×C4⋊C4—41no—
39C11×C22⋊C4—42no—
40C42×C11—21no—
41C42×C11—22no—
42C42×C11—41no—
43C42×C11C4211yescharacteristic
44C42×C11C4⋊C411yescharacteristic
45#4318—44no—
46#4318—82no—
47C2×C11⋊C8—82no—
48#2132—112no—
49#1963D1111yescharacteristic
50C23×C11—22no—
51C23×C11#9911yescharacteristic
52Q8×C11—42no—
53D4×C11—42no—
54D4×C11—82no—
55D4×C11—82no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—42no—
62C2×C4×C11—42no—
63C2×C4×C11—42no—
64C2×C4×C11—81no—
65C2×C4×C11—82no—
66C2×C4×C11#9511yescharacteristic
67C2×C4×C11#9911yescharacteristic
68C8×C11—81no—
69C11⋊C8—84no—
70#532C2×D1111yescharacteristic
71#423Dic1111yescharacteristic
72C2×#104—22no—
73#413—222no—
74#376Dic1111yescharacteristic
75#356—222no—
76#355—114no—
77C22×C11—21no—
78C22×C11—41no—
79C22×C11—42no—
80C22×C11—82no—
81C22×C11#34211yescharacteristic
82C4×C11—21no—
83C4×C11—41no—
84C4×C11—41no—
85C4×C11—42no—
86C4×C11—82no—
87C4×C11#35311yescharacteristic
88C4×C11#35411yescharacteristic
89C2×#41C22⋊D1112yes—
90C2×M16—21no—
91C2×M16—442no—
92C4⋊Q8D4411yescharacteristic
93#127Dic2211yescharacteristic
94#124C4×D1112yes—
95#121—41no—
96C4×D4—41no—
97C2×C42—21no—
98C2×C42C2×Dic1111yescharacteristic
99C4⋊C8—41no—
100#104—44no—
101#101—224no—
102#100—442no—
103#95—41no—
104C2×C11—21no—
105C2×C11—41no—
106C2×C11—82no—
107C2×C11#139311yescharacteristic
108#41—42no—
109#41—42no—
110C2×Q8(C2×D11)⋊C412yes—
111C2×D4—22no—
112C2×D4—41no—
113C2×D4Dic11⋊C412yes—
114C22×C4—21no—
115C22×C4—22no—
116C22×C4—41no—
117C22×C4C22⋊Dic1111yescharacteristic
118M16—42no—
119M16—444no—
120M16—882no—
121C2×C8—41no—
122C2×C8—882no—
123C4⋊C4—41no—
124C22⋊C4—42no—
125C42—21no—
126C42—22no—
127C42—41no—
128C42C4×Dic1111yescharacteristic
129C42C4⋊Dic1111yescharacteristic
130C11#750711yescharacteristic, complemented, Sylow
131C23—22no—
132C23#6689811yescharacteristic
133Q8—42no—
134D4—42no—
135D4—82no—
136D4—82no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—81no—
146C2×C4—82no—
147C2×C4C11⋊#9511yescharacteristic
148C2×C4#6689811yescharacteristic
149C8—81no—
150C8—884no—
151C22—21no—
152C22—41no—
153C22—42no—
154C22—82no—
155C22#1062216411yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—42no—
160C4—82no—
161C4#1062217911yescharacteristic
162C4#1062218311yescharacteristic
163C2—21no—
164C2—41no—
165C2—82no—
166C2#1306674111yescharacteristic
subgroupG/H
centerC4#10622183
commutatorC42×C11C42
Frattini#532C2×D11
FittingC11×#1963C2
socleC2×C11#1393
prime radical, cosocleC11×#532C22
hypercenter#1963D11
hypocenterC11#7507
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1963

Complements

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

NH ≅ G/Ntype
9. #10622180C4semidirect
130. C11#7507semidirect

Maximal subgroups

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

subgroupindex
#130703012
C11×#19632
#750711