Finite Group Databasebeta

← #14656886

Subgroups — #14656886

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077003C211yesmaximal, characteristic
2#13067180C212yesmaximal
3#13066476C212yesmaximal
4#13066449C211yesmaximal, characteristic
5C11×#1994C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C43×C11C2211yescharacteristic
9#10622549C2212yes—
10#10622546—24no—
11#10622541—22no—
12#10622538C2212yes—
13C11×#339—22no—
14#10622176—24no—
15C2×C11×M16—21no—
16C11×C4⋊Q8Q812yes—
17C11×#125—21no—
18C11×C22⋊Q8—22no—
19C4×Q8×C11—22no—
20C11×#117—21no—
21C2×C42×C11—22no—
22C2×C42×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×Dic11⋊C4—24no—
26C11×C4⋊C8—22no—
27C11⋊#95—24no—
28C11⋊#95—22no—
29C11⋊#95D414yes—
30C22⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4×C11⋊C8—22no—
33#10367—111nomaximal, Sylow
34C2×Q8×C11—22no—
35C22×C4×C11—22no—
36C22×C4×C11C2×D412yes—
37C22×C4×C11C2×D411yescharacteristic
38C22×Dic11—24no—
39C11×M16—42no—
40C2×C8×C11—41no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—22no—
43C11×C4⋊C4—42no—
44C11×C22⋊C4—41no—
45C42×C11—22no—
46C42×C11—22no—
47C42×C11—44no—
48C42×C11—41no—
49C42×C11C2×Q811yescharacteristic
50C42×C11#4111yescharacteristic
51C42×C11#4112yes—
52C4⋊Dic11—42no—
53C4⋊Dic11—42no—
54Dic11⋊C4—48no—
55C2×C11⋊C8—42no—
56#2864—111no—
57#1994D1111yescharacteristic
58#1518—112no—
59#1286—112no—
60#1276—111no—
61C23×C11#12011yescharacteristic
62Q8×C11—82no—
63C2×C4×C11—24no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—42no—
68C2×C4×C11C22⋊Q812yes—
69C2×C4×C11C22⋊Q811yescharacteristic
70C2×C4×C11#12412yes—
71C2×C4×C11#12411yescharacteristic
72C2×C4×C11#13512yes—
73C2×C4×C11#13712yes—
74C2×Dic11—48no—
75C2×Dic11—44no—
76C8×C11—81no—
77C11⋊C8—82no—
78#533C2×D1111yescharacteristic
79#431—112no—
80#423C2×D1111yescharacteristic
81#389—222no—
82#387—224no—
83#382—112no—
84C43C2×D1111yescharacteristic
85#339—22no—
86#328—224no—
87C22×C11—22no—
88C22×C11#39311yescharacteristic
89C22×C11#45212yes—
90C4×C11—22no—
91C4×C11—22no—
92C4×C11—44no—
93C4×C11—82no—
94C4×C11#47912yes—
95C4×C11#48811yescharacteristic
96C4×C11#49111yescharacteristic
97Dic11—84no—
98C2×M16—21no—
99C4⋊Q8Dic2212yes—
100#125—21no—
101C22⋊Q8—22no—
102C4×Q8—22no—
103#117—21no—
104C2×C4⋊C4—224no—
105C2×C4⋊C4—222no—
106C2×C42—22no—
107C2×C42C22⋊D1112yes—
108C2×C42C22×D1111yescharacteristic
109C4⋊C8—22no—
110C4⋊C8—222no—
111C22⋊C8—222no—
112C4×C8—222no—
113#95—114no—
114#95—224no—
115#95—222no—
116C2×C11—22no—
117C2×C11#202611yescharacteristic
118C2×C11#203112yes—
119C2×Q8—22no—
120C22×C4—22no—
121C22×C4—224no—
122C22×C4D4×D1112yes—
123C22×C4C2×C22⋊D1111yescharacteristic
124M16—42no—
125C2×C8—41no—
126C2×C8—442no—
127C4⋊C4—22no—
128C4⋊C4—22no—
129C4⋊C4—42no—
130C4⋊C4—448no—
131C4⋊C4—442no—
132C4⋊C4—442no—
133C22⋊C4—41no—
134C42—22no—
135C42—22no—
136C42—44no—
137C42—41no—
138C42C2×Dic2211yescharacteristic
139C42#433911yescharacteristic
140C42#434112yes—
141C11#1036711yescharacteristic, complemented, Sylow
142C23#6699011yescharacteristic
143Q8—82no—
144C2×C4—24no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—448no—
150C2×C4—444no—
151C2×C4#6693112yes—
152C2×C4#6693812yes—
153C2×C4#6697711yescharacteristic
154C2×C4#6698911yescharacteristic
155C2×C4#6699512yes—
156C2×C4#6700312yes—
157C8—81no—
158C8—882no—
159C22—22no—
160C22#1062256011yescharacteristic
161C22#1062266012yes—
162C4—22no—
163C4—22no—
164C4—44no—
165C4—82no—
166C4—884no—
167C4#1062263512yes—
168C4#1062266911yescharacteristic
169C4#1062269511yescharacteristic
170C2—22no—
171C2#1306976711yescharacteristic
172C2#1306978812yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1994D11
hypocenterC11#10367
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
141. C11#10367semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130671802
#130664762
#130664492
C11×#19942
#1036711