Finite Group Databasebeta

← #14654645

Subgroups — #14654645

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13078656C212yesmaximal
2#13071909C211yesmaximal, characteristic
3#13069597C211yesmaximal, characteristic
4#13067046C212yesmaximal
5C11×#1274C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C2×C4×Dic22C2212yes—
8C11×#431C2212yes—
9C11×#376C2211yescharacteristic
10C4×C4⋊Dic11—22no—
11#10622537C2211yescharacteristic
12#10622463—22no—
13#10622462—22no—
14#10622352—22no—
15#10622335—22no—
16C4×Dic44—24no—
17#10622274—22no—
18#10622269—22no—
19#10622161—22no—
20#10622094—24no—
21C22×Dic22D412yes—
22C2×C42×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24#66979—21no—
25C2×C4⋊Dic11—24no—
26C2×C4⋊Dic11D412yes—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×C4×Dic11—22no—
30C2×#4318—21no—
31C2×Dic44—24no—
32#66923—21no—
33#66922D412yes—
34C4×Dic22—22no—
35C4×Dic22—22no—
36C4×Dic22—22no—
37C4×Dic22—22no—
38C4×Dic22—22no—
39C11×C4⋊C8—22no—
40C11×C22⋊C8—22no—
41C4×C8×C11D414yes—
42C11×#95—22no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45#66882—24no—
46#66880—24no—
47#66880—24no—
48C4⋊(C11⋊C8)—22no—
49#10017—111nomaximal, Sylow
50C22×C4×C11—22no—
51C22×C4×C11C2×D412yes—
52C22×C4×C11C2×D411yescharacteristic
53C22×Dic11—22no—
54C22×Dic11—22no—
55C2×Dic22—22no—
56C2×Dic22—22no—
57C2×Dic22—22no—
58C2×Dic22—44no—
59C2×C8×C11—24no—
60C42×C11—22no—
61C42×C11Q1614yescomplemented
62C42×C11C2×D411yescharacteristic
63C42×C11C2×D412yes—
64C42×C11#4111yescharacteristic
65C22⋊Dic11—41no—
66C4⋊Dic11—22no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—48no—
71Dic11⋊C4—42no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74C4×Dic11—42no—
75C4×Dic11—42no—
76C4×Dic11—41no—
77#4318—42no—
78C2×C11⋊C8—41no—
79Dic44—48no—
80#3104—112no—
81#2399—111no—
82#1995—111no—
83#1487—112no—
84#1274D1111yescharacteristic
85C23×C11#12011yescharacteristic
86C2×C4×C11—24no—
87C2×C4×C11—42no—
88C2×C4×C11—44no—
89C2×C4×C11#12012yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11#12711yescharacteristic
93C2×C4×C11C2×Q1612yes—
94C2×C4×C11#13712yes—
95C2×Dic11—24no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—44no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101Dic22—24no—
102Dic22—24no—
103Dic22—42no—
104Dic22—42no—
105Dic22—44no—
106C8×C11—44no—
107C11⋊C8—81no—
108#533—111no—
109C2×C4×Q8—112no—
110#484—222no—
111#477—222no—
112#462—222no—
113#451—222no—
114C4×Q16—224no—
115#431C2×D1112yes—
116#423—111no—
117#398—222no—
118#395—222no—
119C4×C4⋊C4—222no—
120#376C2×D1111yescharacteristic
121#339—222no—
122Q8⋊C8—224no—
123C22×C11—22no—
124C22×C11#39211yescharacteristic
125C22×C11#45112yes—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—44no—
129C4×C11#46212yes—
130C4×C11#49411yescharacteristic
131C4×C11#49711yescharacteristic
132Dic11—44no—
133Dic11—82no—
134Dic11—82no—
135C22×Q8—112no—
136C2×Q16—224no—
137C2×M16—221no—
138C4⋊Q8—112no—
139#125—221no—
140C22⋊Q8—222no—
141C4×Q8—222no—
142C4×Q8—222no—
143C4×Q8—222no—
144C4×Q8—222no—
145C4×Q8—222no—
146#117—221no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—224no—
149C2×C4⋊C4—222no—
150C2×C42—222no—
151C2×C42D4412yes—
152C2×C42C22×D1111yescharacteristic
153#107—224no—
154C4⋊C8—22no—
155C4⋊C8—222no—
156#103—224no—
157#103—224no—
158C22⋊C8—22no—
159C4×C8D4414yes—
160#95—22no—
161#95—222no—
162#95—222no—
163C2×C11—22no—
164C2×C11#201012yes—
165C2×C11#201611yescharacteristic
166C2×Q8—222no—
167C2×Q8—222no—
168C2×Q8—222no—
169C2×Q8—444no—
170C22×C4—22no—
171C22×C4—222no—
172C22×C4—222no—
173C22×C4C2×D4411yescharacteristic
174C22×C4D4×D1112yes—
175Q16—448no—
176M16—442no—
177C2×C8—24no—
178C2×C8—441no—
179C4⋊C4—222no—
180C4⋊C4—222no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C4⋊C4—448no—
184C4⋊C4—442no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C22⋊C4—441no—
188C42—22no—
189C42—442no—
190C42—441no—
191C42—442no—
192C42Dic4414yescomplemented
193C42C2×D4412yes—
194C42D4×D1111yescharacteristic
195C42#434311yescharacteristic
196C11#1001711yescharacteristic, complemented, Sylow
197C23#6693511yescharacteristic
198Q8—224no—
199Q8—224no—
200Q8—442no—
201Q8—442no—
202Q8—444no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—224no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—444no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4#6692711yescharacteristic
213C2×C4#6693512yes—
214C2×C4#6694812yes—
215C2×C4#6694811yescharacteristic
216C2×C4C2×Dic4412yes—
217C2×C4#6696212yes—
218C8—44no—
219C8—881no—
220C22—22no—
221C22#1062228411yescharacteristic
222C22#1062235212yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—444no—
227C4—882no—
228C4—882no—
229C4#1062231211yescharacteristic
230C4#1062232811yescharacteristic
231C4#1062246212yes—
232C2—22no—
233C2#1306968412yes—
234C2#1306971811yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#1274D11
hypocenterC11#10017
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
61. C42×C11Q16semidirect
192. C42Dic44semidirect
196. C11#10017semidirect

Maximal subgroups

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

subgroupindex
#130786562
#130719092
#130695972
#130670462
C11×#12742
#1001711