Finite Group Databasebeta

← #14644783

Subgroups — #14644783

Order 2816.

384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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#13077551C211yesmaximal, characteristic
2#13067281C211yesmaximal, characteristic
3M16×C11⋊C8C212yesmaximal
4#13066506C212yesmaximal
5C11×#1526C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C4×C11×M16C2212yes—
8#10622637—22no—
9Q8×C11⋊C8—22no—
10#10622612C412yes—
11#10622610C412yes—
12#10622538C2212yes—
13#10622537C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#330C414yes—
16#10622185C414yes—
17#10622093—22no—
18C8×C11⋊C8—22no—
19C2×C11×M16—22no—
20C11×C4⋊Q8C2×C412yes—
21C11×#125C2×C412yes—
22C11×C22⋊Q8—22no—
23C4×Q8×C11—22no—
24C11×#117C2×C412yes—
25C2×C42×C11C2311yescharacteristic
26C2×#4318C2×C412yes—
27C22×C11⋊C8C2×C411yescharacteristic
28C22×C11⋊C8C2×C411yescharacteristic
29C11×#97C2×C414yes—
30C4×C8×C11—22no—
31C22⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—24no—
34C4⋊(C11⋊C8)C2×C414yes—
35#66867—22no—
36C4×C11⋊C8—22no—
37C4×C11⋊C8—22no—
38C4×C11⋊C8D412yes—
39C4×C11⋊C8D412yes—
40#8242—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C22×C4×C11C22×C411yescharacteristic
43C22×C4×C11#4112yes—
44C11×M16—28no—
45C2×C8×C11—24no—
46C11×C4⋊C4—24no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4C4214yes—
49C11×C22⋊C4—22no—
50C42×C11—22no—
51C42×C11C22×C411yescharacteristic
52C42×C11C22×C411yescharacteristic
53C42×C11C2×D412yes—
54#4318—42no—
55C2×C11⋊C8—22no—
56C2×C11⋊C8—22no—
57C2×C11⋊C8—24no—
58C2×C11⋊C8—41no—
59C2×C11⋊C8C22⋊C411yescharacteristic
60C2×C11⋊C8C22⋊C412yes—
61C2×C11⋊C8C22⋊C411yescharacteristic
62#2960—111no—
63#1544—111no—
64#1526D1111yescharacteristic
65C8×M16—112no—
66#1299—112no—
67C23×C11#11711yescharacteristic
68Q8×C11—44no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—24no—
72C2×C4×C11—24no—
73C2×C4×C11C2×C4211yescharacteristic
74C2×C4×C11C2×C22⋊C411yescharacteristic
75C2×C4×C11C4×D412yes—
76C2×C4×C11C4×D412yes—
77C8×C11—28no—
78C11⋊C8—21no—
79C11⋊C8—22no—
80C11⋊C8—42no—
81C11⋊C8—44no—
82C11⋊C8#10112yes—
83#533C2×D1111yescharacteristic
84#446—222no—
85C8×Q8—222no—
86#431—112no—
87#424—112no—
88#423—111no—
89#405—112no—
90C4×M16C2×D1112yes—
91C2×C4×C8—111no—
92#332—114no—
93#330Dic1114yes—
94#322—222no—
95C82—222no—
96C22×C11—21no—
97C22×C11—22no—
98C22×C11C4×C22⋊C411yescharacteristic
99C4×C11—21no—
100C4×C11—22no—
101C4×C11—44no—
102C4×C11C2×#10111yescharacteristic
103C4×C11#41311yescharacteristic
104C4×C11#44314yes—
105C2×M16—22no—
106C2×M16—112no—
107C22×C8—111no—
108C22×C8—111no—
109C4⋊Q8C4×D1112yes—
110#125C2×Dic1112yes—
111C22⋊Q8—22no—
112C4×Q8—22no—
113#117C4×D1112yes—
114C2×C42C22×D1111yescharacteristic
115C4⋊C8—114no—
116C4⋊C8—224no—
117C4⋊C8—222no—
118C22⋊C8—222no—
119#97—222no—
120#97C2×Dic1114yes—
121C4×C8—22no—
122C4×C8—112no—
123C4×C8—112no—
124C4×C8—222no—
125C4×C8—222no—
126C2×C11—41no—
127C2×C11C4×#10111yescharacteristic
128C2×C11#176412yes—
129C2×Q8—22no—
130C22×C4C2×C4×D1111yescharacteristic
131C22×C4#434112yes—
132M16—28no—
133M16—442no—
134C2×C8—24no—
135C2×C8—111no—
136C2×C8—111no—
137C2×C8—112no—
138C2×C8—222no—
139C2×C8—222no—
140C2×C8—224no—
141C2×C8—441no—
142C4⋊C4—22no—
143C4⋊C4—24no—
144C4⋊C4C4×Dic1114yes—
145C22⋊C4—22no—
146C42—22no—
147C42C2×C4×D1111yescharacteristic
148C42D4×D1112yes—
149C42C22×Dic1111yescharacteristic
150C11#824211yescharacteristic, complemented, Sylow
151C23#6693011yescharacteristic
152Q8—44no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—24no—
156C2×C4—24no—
157C2×C4C22⋊C4×D1111yescharacteristic
158C2×C4(C22⋊D11)⋊C412yes—
159C2×C4C2×C4×Dic1111yescharacteristic
160C2×C4D4×Dic1112yes—
161C8—28no—
162C8—112no—
163C8—221no—
164C8—222no—
165C8—442no—
166C8—444no—
167C22—21no—
168C22—22no—
169C22C22⋊C4×Dic1111yescharacteristic
170C4—21no—
171C4—22no—
172C4—44no—
173C4D11×#10111yescharacteristic
174C4#1062236411yescharacteristic
175C4#1062243714yes—
176C2—41no—
177C2#101×Dic1111yescharacteristic
178C2#1306845412yes—
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1526C2
socleC22×C11C4×C22⋊C4
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1526D11
hypocenterC11#8242
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
150. C11#8242semidirect

Maximal subgroups

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

subgroupindex
#130775512
#130672812
M16×C11⋊C82
#130665062
C11×#15262
#824211