Finite Group Databasebeta

← #14640488

Subgroups — #14640488

Order 2816.

212 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 51 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#13066556C211yesmaximal, characteristic
2#13066491C211yesmaximal, characteristic
3C11×#2056C211yesmaximal, characteristic
4C22×C11×Q16C411yescharacteristic
5C2×C11×C4⋊C8C2211yescharacteristic
6C2×C11×#103—21no—
7C11×#391—21no—
8#10622537—21no—
9C11×#340C411yescharacteristic
10C22⋊(C11⋊C16)—21no—
11C22×Q8×C11—21no—
12C2×C11×Q16—41no—
13C2×C11×Q16—42no—
14C22×C8×C11C2×C411yescharacteristic
15C22×C8×C11D411yescharacteristic
16C2×C11×C4⋊C4—21no—
17C2×C42×C11D411yescharacteristic
18C2×#4318—41no—
19C11×C4⋊C8—41no—
20C11×#103—42no—
21C11×#95—41no—
22C11×#95—41no—
23C2×C11⋊C16—41no—
24C4⋊(C11⋊C8)—22no—
25C4⋊(C11⋊C8)—41no—
26#7090—111nomaximal, Sylow
27C2×Q8×C11—22no—
28C2×Q8×C11—41no—
29C2×Q8×C11—41no—
30C2×Q8×C11—41no—
31C2×Q8×C11—41no—
32C2×Q8×C11—41no—
33C22×C4×C11—41no—
34C22×C4×C11—41no—
35C22×C4×C11C22⋊C411yescharacteristic
36C22×C4×C11D811yescharacteristic
37C22×C4×C11SD1611yescharacteristic
38C11×Q16—42no—
39C11×Q16—42no—
40C2×C8×C11—21no—
41C2×C8×C11—21no—
42C2×C8×C11—41no—
43C2×C8×C11—41no—
44C11×C4⋊C4—41no—
45C11×C4⋊C4—41no—
46C42×C11—21no—
47C42×C11—21no—
48#4318—81no—
49#4318—81no—
50C2×C11⋊C8—42no—
51C11⋊C16—81no—
52#2056D1111yescharacteristic
53#1322—111no—
54#1292—111no—
55C23×C11#10211yescharacteristic
56Q8×C11—42no—
57Q8×C11—42no—
58Q8×C11—81no—
59Q8×C11—81no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—41no—
66C2×C4×C11—42no—
67C2×C4×C11—81no—
68C2×C4×C11—81no—
69C2×C4×C11—81no—
70C2×C4×C11—81no—
71C2×C4×C11—81no—
72C2×C4×C11#9911yescharacteristic
73C2×C4×C11#10411yescharacteristic
74C2×C4×C11SD3211yescharacteristic
75C2×C4×C11Q3211yescharacteristic
76C8×C11—41no—
77C8×C11—41no—
78C11⋊C8—82no—
79C22×Q16Dic1111yescharacteristic
80#423—221no—
81C2×C4⋊C8C2×D1111yescharacteristic
82C2×#103—21no—
83#391—21no—
84C22⋊C16—221no—
85#340Dic1111yescharacteristic
86C22×C11—21no—
87C22×C11—21no—
88C22×C11#32711yescharacteristic
89C22×C11#35811yescharacteristic
90C22×C11#36011yescharacteristic
91C4×C11—21no—
92C4×C11—21no—
93C4×C11—21no—
94C4×C11—41no—
95C4×C11—82no—
96C4×C11—161no—
97C4×C11AΣL(1,𝔽16)11yescharacteristic
98C4×C11#35511yescharacteristic
99C22×Q8—21no—
100C2×Q16—41no—
101C2×Q16—42no—
102C2×M16—441no—
103C22×C8C2×Dic1111yescharacteristic
104C22×C8C22⋊D1111yescharacteristic
105C2×C4⋊C4—21no—
106C2×C42C22⋊D1111yescharacteristic
107C2×C16—441no—
108C4⋊C8—41no—
109C4⋊C8—222no—
110C4⋊C8—441no—
111#103—42no—
112#95—41no—
113#95—41no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11#134211yescharacteristic
117C2×C11#134511yescharacteristic
118C2×C11#134811yescharacteristic
119C2×Q8—22no—
120C2×Q8—41no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8—41no—
124C2×Q8—41no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4#432311yescharacteristic
128C22×C4#432411yescharacteristic
129C22×C4C22⋊Dic1111yescharacteristic
130Q16—42no—
131Q16—42no—
132M16—881no—
133M16—881no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—442no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C42—21no—
142C42—21no—
143C16—881no—
144C11#709011yescharacteristic, complemented, Sylow
145C23#6689611yescharacteristic
146Q8—42no—
147Q8—42no—
148Q8—81no—
149Q8—81no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4#6689211yescharacteristic
163C2×C4#6689311yescharacteristic
164C2×C4#6689811yescharacteristic
165C2×C4#6690111yescharacteristic
166C8—41no—
167C8—41no—
168C8—882no—
169C22—21no—
170C22—21no—
171C22#1062217511yescharacteristic
172C22#1062220211yescharacteristic
173C22#1062220411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—82no—
179C4—161no—
180C4#1062217411yescharacteristic
181C4#1062218011yescharacteristic
182C2—21no—
183C2—21no—
184C2#1306661011yescharacteristic
185C2#1306661911yescharacteristic
186C2#1306662811yescharacteristic
subgroupG/H
centerC22#10622175
commutatorC22×C8×C11C2×C4
FrattiniC2×C4⋊C8C2×D11
FittingC11×#2056C2
socleC22×C11#327
prime radicalC23×C11#102
cosocleC2×C11×C4⋊C8C22
hypercenter#2056D11
hypocenterC11#7090
LCSG ▷ C22×C8×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2056

Complements

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

NH ≅ G/Ntype
144. C11#7090semidirect

Maximal subgroups

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

subgroupindex
#130665562
#130664912
C11×#20562
#709011