Finite Group Databasebeta

← #14641545

Subgroups — #14641545

Order 2816.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070301C211yesmaximal, characteristic
2#13067351C211yesmaximal, characteristic
3C11×#1884C211yesmaximal, characteristic
4C11×#568C411yescharacteristic
5C11×#532C2211yescharacteristic
6C11×#421—21no—
7C11×#410C411yescharacteristic
8#10622850—21no—
9#10622537—21no—
10C11×#339—21no—
11#10622186—21no—
12#10622184—21no—
13#10622182C412yescomplemented
14#10622180C412yescomplemented
15C2×C11×#41C2×C411yescharacteristic
16C2×C11×#41D411yescharacteristic
17C11×#131—42no—
18C2×C11×M16—21no—
19C2×C11×M16—41no—
20C11×C4⋊Q8D411yescharacteristic
21C11×#127C2×C411yescharacteristic
22C11×#124C2×C411yescharacteristic
23C11×#124Q811yescharacteristic
24C11×#121—41no—
25C4×D4×C11—41no—
26C11×#117—21no—
27C2×C42×C11D411yescharacteristic
28C2×#4318—41no—
29C2×#4318—41no—
30C11×#104—42no—
31C11×#99—41no—
32#66900—22no—
33#66897—41no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)—41no—
36#7496—111nomaximal, Sylow
37C11×#41—41no—
38C11×#41—41no—
39C11×#41—41no—
40C11×#41—41no—
41C2×Q8×C11C22⋊C411yescharacteristic
42C2×Q8×C11C4⋊C411yescharacteristic
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—41no—
46C2×D4×C11C4211yescharacteristic
47C2×D4×C11C4⋊C411yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C22⋊C411yescharacteristic
52C11×M16—22no—
53C11×M16—42no—
54C11×M16—41no—
55C2×C8×C11—41no—
56C2×C8×C11—42no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C11×C22⋊C4—41no—
60C11×C22⋊C4—41no—
61C11×C22⋊C4—41no—
62C42×C11—21no—
63C42×C11—41no—
64C42×C11C22⋊C411yescharacteristic
65C42×C11C4⋊C411yescharacteristic
66#4318—42no—
67#4318—82no—
68#4318—81no—
69C2×C11⋊C8—42no—
70C2×C11⋊C8—81no—
71#2132—111no—
72#1884D1111yescharacteristic
73#1560—111no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11#9911yescharacteristic
77Q8×C11—41no—
78Q8×C11—41no—
79D4×C11—41no—
80D4×C11—41no—
81D4×C11—42no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—81no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—81no—
98C2×C4×C11#9511yescharacteristic
99C2×C4×C11#9911yescharacteristic
100C8×C11—42no—
101C11⋊C8—82no—
102C11⋊C8—82no—
103#568Dic1111yescharacteristic
104#532C2×D1111yescharacteristic
105#423—221no—
106#421—21no—
107#413—221no—
108#410Dic1111yescharacteristic
109#356—221no—
110#355—112no—
111#339—21no—
112#333—221no—
113#331—112no—
114C22×C11—21no—
115C22×C11—41no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—81no—
119C22×C11—81no—
120C22×C11#34211yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—41no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11—161no—
128C4×C11AΣL(1,𝔽16)11yescharacteristic
129C4×C11#35211yescharacteristic
130C2×#41C2×Dic1111yescharacteristic
131C2×#41C22⋊D1111yescharacteristic
132#131—42no—
133C2×M16—21no—
134C2×M16—41no—
135C2×M16—441no—
136C2×M16—441no—
137C4⋊Q8D4411yescharacteristic
138#127C4×D1111yescharacteristic
139#124Dic2211yescharacteristic
140#124C4×D1111yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—21no—
144C2×C42C22⋊D1111yescharacteristic
145C4⋊C8—222no—
146C4⋊C8—441no—
147#104—42no—
148#101—222no—
149#100—441no—
150#99—41no—
151C2×C11—21no—
152C2×C11—41no—
153C2×C11—81no—
154C2×C11—81no—
155C2×C11#139011yescharacteristic
156#41—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160C2×Q8C4⋊Dic1111yescharacteristic
161C2×Q8(C2×D11)⋊C411yescharacteristic
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4C4×Dic1111yescharacteristic
166C2×D4Dic11⋊C411yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4C22⋊Dic1111yescharacteristic
171M16—22no—
172M16—41no—
173M16—42no—
174M16—442no—
175M16—882no—
176M16—881no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—442no—
180C2×C8—881no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C42—21no—
187C42—41no—
188C42Dic11⋊C411yescharacteristic
189C42(C2×D11)⋊C411yescharacteristic
190C11#749611yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23#6689811yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4C11⋊#9511yescharacteristic
216C2×C4#6689811yescharacteristic
217C8—42no—
218C8—882no—
219C8—882no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#1062216411yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4#1062217411yescharacteristic
235C4#1062217711yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1306673411yescharacteristic
subgroupG/H
centerC2#13066734
commutatorC2×D4×C11C42
Frattini#532C2×D11
FittingC11×#1884C2
socleC2×C11#1390
prime radical, cosocleC11×#532C22
hypercenter#1884D11
hypocenterC11#7496
LCSG ▷ C2×D4×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1884

Complements

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

NH ≅ G/Ntype
13. #10622182C4semidirect
14. #10622180C4semidirect
190. C11#7496semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130673512
C11×#18842
#749611