Finite Group Databasebeta

← #14654729

Subgroups — #14654729

Order 2816.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079961C211yesmaximal, characteristic, complemented
2#13078715C212yesmaximal
3#13067230C212yesmaximal, complemented
4#13066486C211yesmaximal, characteristic, complemented
5C11×#1955C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7#10623001C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C11×C22⋊C8—22no—
10C2×C11×#97C2211yescharacteristic
11#10622831—22no—
12#10622729—22no—
13#10622632—22no—
14#10622631—24no—
15#10622620—22no—
16#10622583—22no—
17#10622539C2212yes—
18#10622463—22no—
19#10622462—22no—
20#10622103—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C22×C8×C11—21no—
24C22×C8×C11D412yes—
25C4×D4×C11—22no—
26C4×D4×C11—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4—21no—
29C2×C42×C11C2311yescharacteristic
30C2×#4324—24no—
31#66979—22no—
32#66977—22no—
33#66977—22no—
34C2×Dic44—22no—
35#66923—22no—
36#66922D412yes—
37#66922D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×C22⋊C8—44no—
42C11×#97—22no—
43#66896—24no—
44C22⋊(C11⋊C8)—22no—
45#66882—22no—
46#66880—24no—
47#66874—24no—
48#66871—24no—
49C4⋊(C11⋊C8)—22no—
50#66867D414yes—
51#10030—111nomaximal, Sylow
52C24×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—42no—
55C22×C4×C11—21no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C2×Dic22—22no—
64C2×Dic22—22no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—42no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—22no—
71C11×C22⋊C4—42no—
72C42×C11C2×D412yes—
73C42×C11C2×D412yes—
74C22⋊Dic11—42no—
75#4324—48no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80Dic11⋊C4—42no—
81Dic11⋊C4—42no—
82C4×Dic11—42no—
83C2×C11⋊C8—24no—
84Dic44—82no—
85#3249—111no—
86#3110—112no—
87#1955D1111yescharacteristic
88#1531—112no—
89#1290—111no—
90C23×C11—22no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—42no—
95C23×C11#12111yescharacteristic
96D4×C11—24no—
97D4×C11—42no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—82no—
105C2×C4×C11—81no—
106C2×C4×C11—81no—
107C2×C4×C11#12012yes—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12711yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—42no—
113Dic22—44no—
114Dic22—42no—
115Dic22—42no—
116C8×C11—42no—
117C8×C11—42no—
118C11⋊C8—44no—
119#533—112no—
120C2×C4×D4C2×D1111yescharacteristic
121#484—222no—
122#477—222no—
123#474—222no—
124#467—222no—
125#462—222no—
126#461—222no—
127#450—222no—
128#440—224no—
129#432—112no—
130C2×C4⋊C8C2×D1111yescharacteristic
131C2×C22⋊C8—22no—
132C2×#97C2×D1111yescharacteristic
133#330—224no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—44no—
137C22×C11—42no—
138C22×C11—82no—
139C22×C11—81no—
140C22×C11—81no—
141C22×C11#39211yescharacteristic
142C22×C11#47312yes—
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—22no—
146C4×C11—81no—
147C4×C11#45311yescharacteristic
148C4×C11#45411yescharacteristic
149Dic11—82no—
150Dic11—82no—
151C22×D4D4411yescharacteristic
152C23×C4—21no—
153C2×Q16—222no—
154C2×SD16—224no—
155C22×C8—21no—
156C22×C8C22⋊D1112yes—
157C4⋊Q8—112no—
158C4⋊Q8—112no—
159#125—222no—
160C22⋊Q8—222no—
161C22⋊Q8—222no—
162C4×Q8—222no—
163C4×Q8—222no—
164C4×D4—22no—
165C4×D4—22no—
166#117—222no—
167C2×C4⋊C4D4411yescharacteristic
168C2×C22⋊C4—21no—
169C2×C42C22×D1111yescharacteristic
170#107—224no—
171#107—222no—
172C4⋊C8—22no—
173C4⋊C8—222no—
174#103—224no—
175#103—224no—
176#102—224no—
177C22⋊C8—44no—
178C22⋊C8—222no—
179#97—22no—
180#97—114no—
181C2×C11—22no—
182C2×C11—82no—
183C2×C11#200611yescharacteristic
184C2×C11#201011yescharacteristic
185C2×C11#202011yescharacteristic
186C24—21no—
187C2×Q8—222no—
188C2×Q8—222no—
189C2×D4—22no—
190C2×D4—42no—
191C22×C4—21no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4C2×D4411yescharacteristic
197C22×C4#433911yescharacteristic
198C22×C4C2×C22⋊D1111yescharacteristic
199Q16—882no—
200SD16—448no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—224no—
207C4⋊C4—22no—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—442no—
213C4⋊C4—442no—
214C22⋊C4—42no—
215C22⋊C4—442no—
216C42—442no—
217C42D4×D1112yes—
218C42D4×D1112yes—
219C11#1003011yescharacteristic, complemented, Sylow
220C23—22no—
221C23—42no—
222C23—41no—
223C23—42no—
224C23—41no—
225C23#6698311yescharacteristic
226Q8—444no—
227Q8—442no—
228Q8—442no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4#6693512yes—
243C2×C4#6693712yes—
244C2×C4#6699011yescharacteristic
245C2×C4#6699311yescharacteristic
246C8—42no—
247C8—42no—
248C8—444no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1062257311yescharacteristic
257C22#1062275612yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—882no—
263C4—882no—
264C4#1062267511yescharacteristic
265C4#1062269011yescharacteristic
266C2—22no—
267C2—82no—
268C2#1306965711yescharacteristic
269C2#1306968311yescharacteristic
270C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1955C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1955D11
hypocenterC11#10030
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #13079961C2semidirect
3. #13067230C2semidirect
4. #13066486C2semidirect
219. C11#10030semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130787152
#130672302
#130664862
C11×#19552
#1003011