Finite Group Databasebeta

← #14641193

Subgroups — #14641193

Order 2816.

178 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 43 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#13068785C211yesmaximal, characteristic
2#13066560C211yesmaximal, characteristic
3C11×#1324C211yesmaximal, characteristic
4C11×#382C2211yescharacteristic
5C2×#66872—21no—
6C2×#66871—21no—
7#10622548C411yescharacteristic
8C2×#66867C411yescharacteristic
9C11×#324—21no—
10#10622166—21no—
11C2×C11×C4⋊C4D411yescharacteristic
12C2×C11×C4⋊C4D411yescharacteristic
13C2×C42×C11C2×C411yescharacteristic
14C2×C4⋊Dic11—21no—
15C2×C4⋊Dic11—41no—
16C22×C11⋊C8—21no—
17C11×C22⋊C8—41no—
18C11×#95—41no—
19C22⋊(C11⋊C8)—41no—
20#66872—42no—
21#66871—42no—
22#66867—21no—
23#66867C812yescomplemented
24#7372—111nomaximal, Sylow
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11C22⋊C411yescharacteristic
29C22×Dic11—41no—
30C2×C8×C11—81no—
31C11×C4⋊C4—41no—
32C11×C4⋊C4—41no—
33C42×C11—21no—
34C42×C11C2×C811yescharacteristic
35C42×C11M1611yescharacteristic
36C4⋊Dic11—41no—
37C4⋊Dic11—41no—
38C4⋊Dic11—82no—
39C2×C11⋊C8—22no—
40C2×C11⋊C8—22no—
41C2×C11⋊C8—22no—
42C2×C11⋊C8—81no—
43#1847—111no—
44#1324—111no—
45#1324D1111yescharacteristic
46C23×C11#9911yescharacteristic
47C2×C4×C11—21no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—41no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11—41no—
55C2×C4×C11—81no—
56C2×C4×C11—81no—
57C2×C4×C11C22⋊C811yescharacteristic
58C2×C4×C11#10111yescharacteristic
59C2×Dic11—82no—
60C2×Dic11—81no—
61C8×C11—161no—
62C11⋊C8—24no—
63C11⋊C8—161no—
64C2×#107—221no—
65C2×#106—221no—
66C2×#97—111no—
67#384—111no—
68#382C2×D1111yescharacteristic
69#324—21no—
70#324—221no—
71C22×C11—21no—
72C22×C11—21no—
73C22×C11#32411yescharacteristic
74C22×C11#35311yescharacteristic
75C22×C11#35611yescharacteristic
76C4×C11—21no—
77C4×C11—21no—
78C4×C11—41no—
79C4×C11—41no—
80C4×C11—81no—
81C4×C11—81no—
82Dic11—161no—
83C22×C8—221no—
84C2×C4⋊C4—221no—
85C2×C4⋊C4—441no—
86C2×C4⋊C4D4411yescharacteristic
87C2×C4⋊C4C22⋊D1111yescharacteristic
88C2×C42C4×D1111yescharacteristic
89#107—442no—
90#106—442no—
91C22⋊C8—41no—
92C22⋊C8—441no—
93#97—112no—
94#97—221no—
95#95—41no—
96C2×C11—21no—
97C2×C11—21no—
98C2×C11#132511yescharacteristic
99C2×C11#140611yescharacteristic
100C2×C11#140711yescharacteristic
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—441no—
105C22×C4(C2×D11)⋊C411yescharacteristic
106C2×C8—81no—
107C2×C8—222no—
108C2×C8—222no—
109C2×C8—222no—
110C2×C8—881no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—441no—
114C4⋊C4—441no—
115C4⋊C4—882no—
116C42—21no—
117C42C8×D1111yescharacteristic
118C42#431311yescharacteristic
119C11#737211yescharacteristic, complemented, Sylow
120C23#6687011yescharacteristic
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—81no—
130C2×C4—81no—
131C2×C4—882no—
132C2×C4—881no—
133C2×C4(C2×D11)⋊C811yescharacteristic
134C2×C4#6688811yescharacteristic
135C8—161no—
136C8—224no—
137C8—1761no—
138C22—21no—
139C22—21no—
140C22#1062210711yescharacteristic
141C22#1062211211yescharacteristic
142C22#1062211611yescharacteristic
143C4—21no—
144C4—21no—
145C4—41no—
146C4—41no—
147C4—81no—
148C4—81no—
149C4—1761no—
150C2—21no—
151C2—21no—
152C2#1306656111yescharacteristic
153C2#1306677211yescharacteristic
154C2#1306677711yescharacteristic
subgroupG/H
centerC22#10622112
commutatorC42×C11C2×C8
Frattini#382C2×D11
FittingC11×#1324C2
socleC22×C11#353
prime radicalC23×C11#99
cosocleC11×#382C22
hypercenter#1324D11
hypocenterC11#7372
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
23. #66867C8semidirect
119. C11#7372semidirect

Maximal subgroups

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

subgroupindex
#130687852
#130665602
C11×#13242
#737211