Finite Group Databasebeta

← #14651587

Subgroups — #14651587

Order 2816.

610 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 111 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#13072903C211yesmaximal, characteristic
2#13068716C212yesmaximal
3#13066946C211yesmaximal, characteristic
4#13066469C212yesmaximal
5C11×#2274C211yesmaximal, characteristic
6C2×C11×#117—21no—
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66979C2211yescharacteristic
9C4×C11×C4⋊C4—24no—
10C4×C11×C22⋊C4—21no—
11C4×C11×C22⋊C4C2212yes—
12#10622824—21no—
13#10622824C2211yescharacteristic
14#10622823—21no—
15#10622820C2212yes—
16#10622599C412yescomplemented
17#10622596C412yescomplemented
18#10622591—22no—
19#10622166—22no—
20#10622161—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C11×#117—28no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11D414yes—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36#66979—22no—
37#66979—22no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11—21no—
42C2×#4318—22no—
43C11×#95—22no—
44C11×#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95C2×C412yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52#9478—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4112yes—
68C22×Dic11—22no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C11×C4⋊C4—28no—
72C11×C4⋊C4—24no—
73C11×C4⋊C4—24no—
74C11×C22⋊C4—28no—
75C42×C11—28no—
76C42×C11—44no—
77C42×C11—82no—
78C22⋊Dic11—42no—
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83Dic11⋊C4—44no—
84C4×Dic11—42no—
85#4318—44no—
86C2×C11⋊C8—42no—
87#2484—111no—
88#2274D1111yescharacteristic
89#1826—112no—
90#1463—111no—
91#1284—112no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12011yescharacteristic
97C23×C11#12311yescharacteristic
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—24no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—24no—
104C2×C4×C11—28no—
105C2×C4×C11—22no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—44no—
110C2×C4×C11—44no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—81no—
114C2×C4×C11#10414yes—
115C2×C4×C11C4×D412yes—
116C2×C4×C11#12112yes—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C11⋊C8—82no—
125C2×#117—21no—
126C2×#117—111no—
127C22×C4⋊C4C2×D1111yescharacteristic
128#407—112no—
129#400—112no—
130#398—112no—
131#387—222no—
132#385—221no—
133#381—111no—
134#381—221no—
135C4×C4⋊C4—24no—
136C4×C22⋊C4—21no—
137C4×C22⋊C4C2×D1112yes—
138#339—224no—
139#324—222no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—44no—
148C22×C11#38611yescharacteristic
149C22×C11C2×#10412yes—
150C22×C11#45812yes—
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—24no—
154C4×C11—48no—
155C4×C11—42no—
156Dic11—82no—
157Dic11—81no—
158Dic11—81no—
159C23×C4C22⋊D1111yescharacteristic
160C23×C4C22⋊D1111yescharacteristic
161C23×C4C22×D1111yescharacteristic
162C2×M16—222no—
163#117—28no—
164#117—222no—
165#117—222no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4C4×D1112yes—
173C2×C4⋊C4D4412yes—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—221no—
176C2×C22⋊C4—221no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—221no—
180C2×C42C22⋊D1114yes—
181C22⋊C8—222no—
182C22⋊C8—222no—
183#95—22no—
184#95—22no—
185#95—112no—
186#95—222no—
187#95—222no—
188#95—222no—
189#95—221no—
190C2×C11—22no—
191C2×C11—22no—
192C2×C11—41no—
193C2×C11#189011yescharacteristic
194C2×C11#189611yescharacteristic
195C2×C11#191211yescharacteristic
196C24C2×C22⋊D1111yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—222no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4(C2×D11)⋊C412yes—
209C22×C4(C2×D11)⋊C412yes—
210C22×C4C2×C4×D1111yescharacteristic
211C22×C4C2×D4411yescharacteristic
212C22×C4#433912yes—
213C22×C4C2×C22⋊D1112yes—
214M16—444no—
215C2×C8—442no—
216C4⋊C4—28no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—444no—
222C22⋊C4—28no—
223C22⋊C4—442no—
224C22⋊C4—441no—
225C22⋊C4—441no—
226C42—28no—
227C42—44no—
228C42—82no—
229C42—442no—
230C11#947811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×(C2×D11)⋊C411yescharacteristic
235C23#6698211yescharacteristic
236C23#6700611yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—28no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—81no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4#6686914yes—
261C2×C4C4×C22⋊D1112yes—
262C2×C4#6698312yes—
263C8—882no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22C2×#6686912yes—
273C22#1062282611yescharacteristic
274C22#1062285612yes—
275C4—24no—
276C4—22no—
277C4—22no—
278C4—48no—
279C4—42no—
280C4—882no—
281C4—881no—
282C4—881no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#1306902911yescharacteristic
287C2#1306905911yescharacteristic
288C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2274C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2274D11
hypocenterC11#9478
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
16. #10622599C4semidirect
17. #10622596C4semidirect
230. C11#9478semidirect

Maximal subgroups

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

subgroupindex
#130729032
#130687162
#130669462
#130664692
C11×#22742
#947811