Finite Group Databasebeta

← #14640413

Subgroups — #14640413

Order 2816.

224 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 53 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#13068793C211yesmaximal, characteristic
2#13066540C211yesmaximal, characteristic
3C11×#1314C211yesmaximal, characteristic
4C23×C11⋊C8C411yescharacteristic
5C2×C11×C22⋊C8C2211yescharacteristic
6C4×C22⋊Dic11C411yescharacteristic
7C2×Dic11⋊C8—21no—
8C11×C22⋊C16—21no—
9#10622188—21no—
10C22⋊(C11⋊C16)—21no—
11C23×C4×C11C2×C411yescharacteristic
12C22×C8×C11D411yescharacteristic
13C22×C8×C11D411yescharacteristic
14C2×C22⋊Dic11C811yescharacteristic
15C2×C22⋊Dic11C811yescharacteristic
16C2×C4×Dic11—21no—
17C22×C11⋊C8—21no—
18C22×C11⋊C8—42no—
19C22×C11⋊C8—41no—
20C2×C11×C16—41no—
21C11×C22⋊C8—41no—
22C11⋊#95—21no—
23Dic11⋊C8—42no—
24C2×C11⋊C16—41no—
25#7064—111nomaximal, Sylow
26C24×C11C2×C811yescharacteristic
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—41no—
30C22×C4×C11—41no—
31C22×C4×C11C22⋊C411yescharacteristic
32C22×C4×C11M1611yescharacteristic
33C22×Dic11—21no—
34C22×Dic11—21no—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C2×C8×C11—41no—
38C2×C8×C11—41no—
39C22⋊Dic11—21no—
40C22⋊Dic11—41no—
41C22⋊Dic11C1612yescomplemented
42C4×Dic11—41no—
43C4×Dic11—41no—
44C2×C11⋊C8—22no—
45C2×C11⋊C8—41no—
46C2×C11⋊C8—42no—
47C2×C11⋊C8—42no—
48C2×C11⋊C8—41no—
49C11×C16—81no—
50C11⋊C16—81no—
51#1850—111no—
52#1314—111no—
53#1314D1111yescharacteristic
54C23×C11—21no—
55C23×C11—21no—
56C23×C11—41no—
57C23×C11—41no—
58C23×C11C22⋊C811yescharacteristic
59C23×C11C2×C1611yescharacteristic
60C23×C11M3211yescharacteristic
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—42no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11#9911yescharacteristic
69C2×C4×C11#10111yescharacteristic
70C2×Dic11—22no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73C2×Dic11—41no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C8×C11—41no—
77C8×C11—41no—
78C11⋊C8—42no—
79C23×C8—111no—
80C2×C4⋊C8—221no—
81C2×C22⋊C8C2×D1111yescharacteristic
82C4×C22⋊C4—111no—
83C22⋊C16—21no—
84C22⋊C16—221no—
85#336—221no—
86C22×C11—21no—
87C22×C11—21no—
88C22×C11—21no—
89C22×C11—21no—
90C22×C11—41no—
91C22×C11—41no—
92C22×C11—42no—
93C22×C11—41no—
94C22×C11—41no—
95C22×C11#32411yescharacteristic
96C22×C11C22⋊C1611yescharacteristic
97C22×C11#34911yescharacteristic
98C4×C11—21no—
99C4×C11—41no—
100C4×C11AΣL(1,𝔽16)11yescharacteristic
101C4×C11#35211yescharacteristic
102Dic11—42no—
103Dic11—81no—
104C23×C4C4×D1111yescharacteristic
105C22×C8—221no—
106C22×C8—442no—
107C22×C8—441no—
108C22×C8D4411yescharacteristic
109C22×C8C22⋊D1111yescharacteristic
110C2×C22⋊C4—111no—
111C2×C22⋊C4—111no—
112C2×C42—221no—
113C2×C16—41no—
114C2×C16—441no—
115C4⋊C8—442no—
116C22⋊C8—41no—
117#95—221no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11—41no—
121C2×C11—41no—
122C2×C11#132211yescharacteristic
123C2×C11#132611yescharacteristic
124C2×C11#132811yescharacteristic
125C24C8×D1111yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—41no—
129C22×C4—41no—
130C22×C4—221no—
131C22×C4—221no—
132C22×C4#431311yescharacteristic
133C22×C4(C2×D11)⋊C411yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—222no—
139C2×C8—441no—
140C2×C8—442no—
141C2×C8—441no—
142C2×C8—442no—
143C22⋊C4—112no—
144C22⋊C4—221no—
145C22⋊C4—441no—
146C42—441no—
147C42—441no—
148C16—81no—
149C16—881no—
150C11#706411yescharacteristic, complemented, Sylow
151C23—21no—
152C23—21no—
153C23—41no—
154C23—41no—
155C23C16×D1111yescharacteristic
156C23#6686211yescharacteristic
157C23(C2×D11)⋊C811yescharacteristic
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—222no—
166C2×C4—441no—
167C2×C4—441no—
168C2×C4—441no—
169C2×C4—441no—
170C2×C4—441no—
171C2×C4#6687011yescharacteristic
172C2×C4#6688811yescharacteristic
173C8—41no—
174C8—41no—
175C8—442no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—41no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22#1062210711yescharacteristic
186C22(C2×D11)⋊C1611yescharacteristic
187C22#1062215211yescharacteristic
188C4—21no—
189C4—41no—
190C4—442no—
191C4—881no—
192C4#1062211011yescharacteristic
193C4#1062211311yescharacteristic
194C2—21no—
195C2—21no—
196C2—41no—
197C2—41no—
198C2#1306655511yescharacteristic
199C2#1306656511yescharacteristic
200C2#1306656811yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC23×C11C2×C16
FrattiniC2×C22⋊C8C2×D11
FittingC11×#1314C2
socleC22×C11#324
prime radicalC24×C11C2×C8
cosocleC2×C11×C22⋊C8C22
hypercenter#1314D11
hypocenterC11#7064
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
41. C22⋊Dic11C16semidirect
150. C11#7064semidirect

Maximal subgroups

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

subgroupindex
#130687932
#130665402
C11×#13142
#706411