Finite Group Databasebeta

← #14640596

Subgroups — #14640596

Order 2816.

230 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069593C211yesmaximal, characteristic
2#13066449C211yesmaximal, characteristic
3C11×#1276C211yesmaximal, characteristic
4#10623001C411yescharacteristic
5C11×#431—21no—
6C43×C11C2211yescharacteristic
7#10622538—21no—
8#10622537C411yescharacteristic
9#10622161—21no—
10#10622161—21no—
11C2×C42×C11—41no—
12C2×C42×C11C2×C411yescharacteristic
13C2×C42×C11D411yescharacteristic
14C2×C42×C11D411yescharacteristic
15#66979—21no—
16#66977—41no—
17C2×#4318—21no—
18#66923C812yescomplemented
19#66922—21no—
20C4×Dic22—41no—
21C11×C4⋊C8—22no—
22C11×C22⋊C8—41no—
23C4×C8×C11—41no—
24C22⋊(C11⋊C8)—41no—
25C4⋊(C11⋊C8)—22no—
26C4⋊(C11⋊C8)—41no—
27C4×C11⋊C8—41no—
28#7134—111nomaximal, Sylow
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11C22⋊C411yescharacteristic
33C2×Dic22—41no—
34C2×C8×C11—42no—
35C42×C11—21no—
36C42×C11—21no—
37C42×C11—21no—
38C42×C11—44no—
39C42×C11C2×C811yescharacteristic
40C42×C11M1611yescharacteristic
41C42×C11SD1611yescharacteristic
42C42×C11SD1611yescharacteristic
43C42×C11Q1611yescharacteristic
44C42×C11Q1611yescharacteristic
45C22⋊Dic11—41no—
46C4⋊Dic11—22no—
47C4⋊Dic11—41no—
48Dic11⋊C4—42no—
49C4×Dic11—41no—
50#4318—41no—
51#4318—41no—
52C2×C11⋊C8—42no—
53C2×C11⋊C8—41no—
54#1994—111no—
55#1276—111no—
56#1276D1111yescharacteristic
57C23×C11#9911yescharacteristic
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11C22⋊C811yescharacteristic
68C2×C4×C11#10011yescharacteristic
69C2×C4×C11#10311yescharacteristic
70C2×C4×C11#10311yescharacteristic
71C2×C4×C11#10411yescharacteristic
72C2×C4×C11#10411yescharacteristic
73C2×Dic11—42no—
74Dic22—82no—
75C8×C11—82no—
76C11⋊C8—82no—
77C11⋊C8—81no—
78#533—111no—
79#431—21no—
80#431—221no—
81#423—111no—
82C43C2×D1111yescharacteristic
83#339—221no—
84#339—221no—
85C22×C11—41no—
86C22×C11#32311yescharacteristic
87C22×C11#32811yescharacteristic
88C22×C11#32811yescharacteristic
89C4×C11—22no—
90C4×C11—22no—
91C4×C11—22no—
92C4×C11—41no—
93C4×C11—41no—
94C4×C11—41no—
95C4×C11Q8⋊C811yescharacteristic
96C4×C11Q8⋊C811yescharacteristic
97C4×C11#32911yescharacteristic
98C4×C11#33311yescharacteristic
99Dic11—82no—
100C2×M16—221no—
101C4⋊Q8—221no—
102#125—112no—
103C22⋊Q8—441no—
104C4×Q8—441no—
105#117—221no—
106C2×C42—41no—
107C2×C42C4×D1111yescharacteristic
108C2×C42D4411yescharacteristic
109C2×C42C22⋊D1111yescharacteristic
110C4⋊C8—22no—
111C4⋊C8—222no—
112C4⋊C8—441no—
113C22⋊C8—41no—
114C22⋊C8—441no—
115C4×C8—41no—
116C4×C8—441no—
117C2×C11—21no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11#127211yescharacteristic
121C2×Q8—441no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4(C2×D11)⋊C411yescharacteristic
126M16—441no—
127M16—441no—
128C2×C8—42no—
129C2×C8—442no—
130C2×C8—441no—
131C4⋊C4—222no—
132C4⋊C4—442no—
133C4⋊C4—441no—
134C22⋊C4—441no—
135C42—21no—
136C42—21no—
137C42—21no—
138C42—44no—
139C42—441no—
140C42C8×D1111yescharacteristic
141C42#431311yescharacteristic
142C42#431411yescharacteristic
143C42Dic4411yescharacteristic
144C42#432411yescharacteristic
145C42#432611yescharacteristic
146C11#713411yescharacteristic, complemented, Sylow
147C23#6687011yescharacteristic
148Q8—882no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—442no—
159C2×C4#6686911yescharacteristic
160C2×C4#6687411yescharacteristic
161C2×C4#6688011yescharacteristic
162C2×C4(C2×D11)⋊C811yescharacteristic
163C2×C4#6688711yescharacteristic
164C2×C4#6688911yescharacteristic
165C8—82no—
166C8—882no—
167C8—881no—
168C22—41no—
169C22#1062209011yescharacteristic
170C22#1062210511yescharacteristic
171C22#1062210611yescharacteristic
172C4—22no—
173C4—22no—
174C4—22no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—882no—
179C4#1062209411yescharacteristic
180C4#1062210211yescharacteristic
181C4#1062211911yescharacteristic
182C4#1062212211yescharacteristic
183C2—21no—
184C2—21no—
185C2—21no—
186C2#1306644111yescharacteristic
subgroupG/H
centerC4#10622119
commutatorC42×C11C2×C8
FrattiniC43C2×D11
FittingC11×#1276C2
socleC2×C11#1272
prime radicalC23×C11#99
cosocleC43×C11C22
hypercenter#1276D11
hypocenterC11#7134
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C43 ◁ #1276

Complements

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

NH ≅ G/Ntype
18. #66923C8semidirect
146. C11#7134semidirect

Maximal subgroups

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

subgroupindex
#130695932
#130664492
C11×#12762
#713411