Finite Group Databasebeta

← #14641314

Subgroups — #14641314

Order 2816.

178 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 41 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#13070034C211yesmaximal, characteristic
2#13066743C211yesmaximal, characteristic
3C11×#1319C211yesmaximal, characteristic
4C11×#391C2211yescharacteristic
5C2×#66900—21no—
6C2×#66899—21no—
7#10622549C411yescharacteristic
8C11×#324—21no—
9#10622167—21no—
10#10622162C411yescharacteristic
11C22×Q8×C11D411yescharacteristic
12C2×C11×C4⋊C4D411yescharacteristic
13C2×C42×C11C2×C411yescharacteristic
14C2×C4⋊Dic11—21no—
15C2×#4318—41no—
16C22×C11⋊C8—21no—
17C11×C22⋊C8—41no—
18C11×#95—41no—
19#66900—22no—
20#66900—41no—
21#66899—41no—
22#66899—41no—
23C11⋊#95—41no—
24#7413—111nomaximal, Sylow
25C2×Q8×C11—21no—
26C2×Q8×C11—41no—
27C2×Q8×C11—41no—
28C2×Q8×C11D811yescharacteristic
29C2×Q8×C11SD1611yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11C22⋊C411yescharacteristic
34C22×Dic11—41no—
35C2×C8×C11—81no—
36C11×C4⋊C4—41no—
37C42×C11—41no—
38C4⋊Dic11—41no—
39C4⋊Dic11—41no—
40#4318—42no—
41#4318—81no—
42C2×C11⋊C8—41no—
43C2×C11⋊C8—41no—
44C2×C11⋊C8—41no—
45C2×C11⋊C8—81no—
46#2074—111no—
47#1394—111no—
48#1319D1111yescharacteristic
49C23×C11#9911yescharacteristic
50Q8×C11—41no—
51Q8×C11—41no—
52Q8×C11—81no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—81no—
64C2×C4×C11#10211yescharacteristic
65C2×C4×C11#10411yescharacteristic
66C2×Dic11—81no—
67C2×Dic11—81no—
68C2×Dic11—81no—
69C8×C11—161no—
70C11⋊C8—81no—
71C11⋊C8—82no—
72C2×#103—221no—
73C2×#101—221no—
74#391C2×D1111yescharacteristic
75#382—111no—
76#340—221no—
77#336—111no—
78#324—21no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11#32711yescharacteristic
82C22×C11#35211yescharacteristic
83C22×C11#35411yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—41no—
87C4×C11—41no—
88C4×C11—81no—
89C4×C11—81no—
90Dic11—161no—
91C22×Q8D4411yescharacteristic
92C2×M16—441no—
93C22×C8—221no—
94C2×C4⋊C4—221no—
95C2×C4⋊C4C22⋊D1111yescharacteristic
96C2×C42C4×D1111yescharacteristic
97#103—441no—
98#103—441no—
99#101—222no—
100#101—441no—
101C22⋊C8—41no—
102#95—41no—
103#95—441no—
104C2×C11—21no—
105C2×C11—21no—
106C2×C11#134411yescharacteristic
107C2×C11#141311yescharacteristic
108C2×C11#141411yescharacteristic
109C2×Q8—21no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8#431411yescharacteristic
113C2×Q8D8811yescharacteristic
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—441no—
118C22×C4(C2×D11)⋊C411yescharacteristic
119M16—442no—
120M16—881no—
121C2×C8—81no—
122C2×C8—441no—
123C2×C8—441no—
124C2×C8—441no—
125C2×C8—881no—
126C4⋊C4—41no—
127C4⋊C4—441no—
128C4⋊C4—441no—
129C42—41no—
130C11#741311yescharacteristic, complemented, Sylow
131C23#6687011yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—81no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—81no—
146C2×C4—881no—
147C2×C4—881no—
148C2×C4—881no—
149C2×C4#6688511yescharacteristic
150C2×C4#6688911yescharacteristic
151C8—161no—
152C8—881no—
153C8—882no—
154C22—21no—
155C22—21no—
156C22#1062210811yescharacteristic
157C22#1062211111yescharacteristic
158C22#1062211411yescharacteristic
159C4—21no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—81no—
164C4—81no—
165C4—1761no—
166C2—21no—
167C2—21no—
168C2#1306661711yescharacteristic
169C2#1306678811yescharacteristic
170C2#1306679011yescharacteristic
subgroupG/H
centerC22#10622111
commutatorC2×C42×C11C2×C4
Frattini#391C2×D11
FittingC11×#1319C2
socleC22×C11#354
prime radicalC23×C11#99
cosocleC11×#391C22
hypercenter#1319D11
hypocenterC11#7413
LCSG ▷ C2×C42×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1319

Complements

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

NH ≅ G/Ntype
130. C11#7413semidirect

Maximal subgroups

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

subgroupindex
#130700342
#130667432
C11×#13192
#741311