Finite Group Databasebeta

← #14640407

Subgroups — #14640407

Order 2816.

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

normal subgroups only

This group has 180 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#13068732C211yesmaximal, characteristic
2#13066556C211yesmaximal, characteristic
3C11×#1322C211yesmaximal, characteristic
4C2×C11×C4⋊C8C2211yescharacteristic
5C42×Dic11C411yescharacteristic
6C2×C4⋊(C11⋊C8)C411yescharacteristic
7C11×C22⋊C16—21no—
8#10622188—21no—
9#10622188—21no—
10C22⋊(C11⋊C16)—21no—
11C22×C8×C11D411yescharacteristic
12C22×C8×C11D411yescharacteristic
13C2×C42×C11C2×C411yescharacteristic
14C2×C4×Dic11—21no—
15C2×C4×Dic11—21no—
16C2×C4×Dic11C811yescharacteristic
17C2×C4×Dic11C811yescharacteristic
18C22×C11⋊C8—21no—
19C2×C11×C16—41no—
20C11×C4⋊C8—41no—
21C2×C11⋊C16—41no—
22C4⋊(C11⋊C8)—41no—
23#7062—111nomaximal, Sylow
24C22×C4×C11C22⋊C411yescharacteristic
25C22×C4×C11C2×C811yescharacteristic
26C22×C4×C11M1611yescharacteristic
27C22×Dic11—21no—
28C22×Dic11—21no—
29C2×C8×C11—21no—
30C2×C8×C11—21no—
31C2×C8×C11—41no—
32C2×C8×C11—41no—
33C42×C11—21no—
34C42×C11—21no—
35C4×Dic11—21no—
36C4×Dic11—41no—
37C4×Dic11—41no—
38C4×Dic11—41no—
39C4×Dic11—42no—
40C4×Dic11C1612yescomplemented
41C2×C11⋊C8—42no—
42C2×C11⋊C8—41no—
43C11×C16—81no—
44C11⋊C16—81no—
45#1831—111no—
46#1322—111no—
47#1322D1111yescharacteristic
48C23×C11C22⋊C811yescharacteristic
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—41no—
55C2×C4×C11#9911yescharacteristic
56C2×C4×C11#10111yescharacteristic
57C2×C4×C11C2×C1611yescharacteristic
58C2×C4×C11M3211yescharacteristic
59C2×Dic11—22no—
60C2×Dic11—22no—
61C2×Dic11—41no—
62C2×Dic11—41no—
63C2×Dic11—41no—
64C2×Dic11—41no—
65C8×C11—41no—
66C8×C11—41no—
67C11⋊C8—81no—
68C2×C4⋊C8—111no—
69C2×C4⋊C8C2×D1111yescharacteristic
70C43—111no—
71C22⋊C16—21no—
72C22⋊C16—221no—
73#336—221no—
74#336—221no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11#32411yescharacteristic
78C22×C11C22⋊C1611yescharacteristic
79C22×C11#34911yescharacteristic
80C4×C11—21no—
81C4×C11—21no—
82C4×C11—21no—
83C4×C11—41no—
84C4×C11#35411yescharacteristic
85C4×C11#35511yescharacteristic
86Dic11—42no—
87Dic11—42no—
88C22×C8—221no—
89C22×C8D4411yescharacteristic
90C22×C8C22⋊D1111yescharacteristic
91C2×C42—111no—
92C2×C42—111no—
93C2×C42—221no—
94C2×C42—221no—
95C2×C42C4×D1111yescharacteristic
96C2×C16—41no—
97C2×C16—441no—
98C4⋊C8—41no—
99C4⋊C8—441no—
100C2×C11—21no—
101C2×C11—21no—
102C2×C11#132211yescharacteristic
103C2×C11#132411yescharacteristic
104C2×C11#132711yescharacteristic
105C22×C4—221no—
106C22×C4—221no—
107C22×C4C8×D1111yescharacteristic
108C22×C4#431311yescharacteristic
109C22×C4(C2×D11)⋊C411yescharacteristic
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—442no—
115C2×C8—441no—
116C42—21no—
117C42—21no—
118C42—112no—
119C42—221no—
120C42—441no—
121C42—441no—
122C42—441no—
123C42—442no—
124C16—81no—
125C16—881no—
126C11#706211yescharacteristic, complemented, Sylow
127C23(C2×D11)⋊C811yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—222no—
135C2×C4—222no—
136C2×C4—441no—
137C2×C4—441no—
138C2×C4—441no—
139C2×C4—441no—
140C2×C4C16×D1111yescharacteristic
141C2×C4#6686211yescharacteristic
142C2×C4#6687011yescharacteristic
143C2×C4#6688811yescharacteristic
144C8—41no—
145C8—41no—
146C8—881no—
147C22—21no—
148C22—21no—
149C22#1062210711yescharacteristic
150C22(C2×D11)⋊C1611yescharacteristic
151C22#1062215211yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—442no—
157C4—442no—
158C4#1062211111yescharacteristic
159C4#1062211511yescharacteristic
160C2—21no—
161C2—21no—
162C2#1306655511yescharacteristic
163C2#1306655911yescharacteristic
164C2#1306656611yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC2×C4×C11C2×C16
FrattiniC2×C4⋊C8C2×D11
FittingC11×#1322C2
socleC22×C11#324
prime radicalC23×C11C22⋊C8
cosocleC2×C11×C4⋊C8C22
hypercenter#1322D11
hypocenterC11#7062
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
40. C4×Dic11C16semidirect
126. C11#7062semidirect

Maximal subgroups

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

subgroupindex
#130687322
#130665562
C11×#13222
#706211