Finite Group Databasebeta

← #14641365

Subgroups — #14641365

Order 2816.

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

normal subgroups only

This group has 236 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#13069772C211yesmaximal, characteristic
2#13066741C211yesmaximal, characteristic
3C11×#1270C211yesmaximal, characteristic
4#10623031C411yescharacteristic, complemented
5C11×#390C2211yescharacteristic
6C2×#66898—21no—
7#10622828—21no—
8C11×#336—21no—
9#10622168C411yescharacteristic, complemented
10#10622161—21no—
11C22×D4×C11D411yescharacteristic
12C22×C8×C11—41no—
13C2×C11×C4⋊C4C2×C411yescharacteristic
14C2×C11×C22⋊C4—41no—
15C2×C42×C11D411yescharacteristic
16C2×C22⋊Dic11—41no—
17#66979—21no—
18#66977—41no—
19C2×#4318—21no—
20#66943—41no—
21#66941—41no—
22#66898—22no—
23#66898—41no—
24#66896—41no—
25#66896—41no—
26#7430—111nomaximal, Sylow
27C24×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—41no—
30C2×D4×C11—41no—
31C2×D4×C11SD1611yescharacteristic
32C2×D4×C11Q1611yescharacteristic
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11C22⋊C411yescharacteristic
36C22×Dic11—81no—
37C2×Dic22—41no—
38C2×C8×C11—42no—
39C2×C8×C11—81no—
40C2×C8×C11—81no—
41C11×C4⋊C4—41no—
42C11×C22⋊C4—81no—
43C11×C22⋊C4—81no—
44C42×C11—41no—
45C22⋊Dic11—42no—
46C22⋊Dic11—41no—
47C22⋊Dic11—81no—
48C4⋊Dic11—21no—
49C4⋊Dic11—21no—
50C4⋊Dic11—41no—
51Dic11⋊C4—42no—
52C4×Dic11—41no—
53#4318—41no—
54#4318—41no—
55C2×C11⋊C8—41no—
56#2027—111no—
57#1393—111no—
58#1270D1111yescharacteristic
59C23×C11—21no—
60C23×C11—21no—
61C23×C11—41no—
62C23×C11—41no—
63C23×C11—81no—
64C23×C11—81no—
65C23×C11#9911yescharacteristic
66D4×C11—41no—
67D4×C11—41no—
68D4×C11—81no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—81no—
77C2×C4×C11#10311yescharacteristic
78C2×C4×C11#10411yescharacteristic
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—82no—
82C2×Dic11—161no—
83C2×Dic11—161no—
84Dic22—161no—
85C8×C11—82no—
86C11⋊C8—81no—
87#544—111no—
88#418—221no—
89C2×#99—221no—
90#390C2×D1111yescharacteristic
91#343—111no—
92#339—221no—
93#336—21no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11—41no—
97C22×C11—41no—
98C22×C11—81no—
99C22×C11—81no—
100C22×C11—81no—
101C22×C11—81no—
102C22×C11—161no—
103C22×C11#32811yescharacteristic
104C22×C11AΣL(1,𝔽16)11yescharacteristic
105C22×C11#35411yescharacteristic
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—41no—
109C4×C11—41no—
110C4×C11—81no—
111Dic11—81no—
112Dic11—81no—
113Dic11—162no—
114C22×D4D4411yescharacteristic
115C2×M16—221no—
116C22×C8—41no—
117C4⋊Q8—441no—
118#125—441no—
119C22⋊Q8—441no—
120#117—221no—
121C2×C4⋊C4C4×D1111yescharacteristic
122C2×C22⋊C4—41no—
123C2×C22⋊C4—441no—
124C2×C42C22⋊D1111yescharacteristic
125#102—441no—
126#102—441no—
127#99—222no—
128#99—441no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—81no—
132C2×C11—81no—
133C2×C11#135111yescharacteristic
134C2×C11#140211yescharacteristic
135C2×C11#140411yescharacteristic
136C24—21no—
137C2×Q8—441no—
138C2×D4—21no—
139C2×D4—41no—
140C2×D4—41no—
141C2×D4#431411yescharacteristic
142C2×D4Dic4411yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—881no—
146C22×C4(C2×D11)⋊C411yescharacteristic
147M16—441no—
148M16—441no—
149C2×C8—42no—
150C2×C8—81no—
151C2×C8—81no—
152C2×C8—441no—
153C4⋊C4—41no—
154C4⋊C4—221no—
155C4⋊C4—221no—
156C4⋊C4—441no—
157C4⋊C4—442no—
158C22⋊C4—81no—
159C22⋊C4—81no—
160C22⋊C4—441no—
161C22⋊C4—442no—
162C22⋊C4—881no—
163C42—41no—
164C42—441no—
165C11#743011yescharacteristic, complemented, Sylow
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23#6687011yescharacteristic
173Q8—1761no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—441no—
186C2×C4—441no—
187C2×C4—882no—
188C2×C4—1761no—
189C2×C4—1761no—
190C2×C4#6688011yescharacteristic
191C2×C4#6688911yescharacteristic
192C8—82no—
193C8—881no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22#1062210511yescharacteristic
204C22#1062211111yescharacteristic
205C22#1062211311yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—881no—
212C4—881no—
213C4—1762no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2#1306663811yescharacteristic
219C2#1306676211yescharacteristic
220C2#1306676811yescharacteristic
subgroupG/H
centerC22#10622113
commutatorC2×C11×C4⋊C4C2×C4
Frattini#390C2×D11
FittingC11×#1270C2
socleC22×C11AΣL(1,𝔽16)
prime radicalC22×D4×C11D4
cosocleC11×#390C22
hypercenter#1270D11
hypocenterC11#7430
LCSG ▷ C2×C11×C4⋊C4 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1270

Complements

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

NH ≅ G/Ntype
4. #10623031C4semidirect
9. #10622168C4semidirect
165. C11#7430semidirect

Maximal subgroups

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

subgroupindex
#130697722
#130667412
C11×#12702
#743011