Finite Group Databasebeta

← #14642957

Subgroups — #14642957

Order 2816.

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

normal subgroups only

This group has 478 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#13075642C211yesmaximal, characteristic
2#13070020C212yesmaximal, complemented
3#13066442C211yesmaximal, characteristic, complemented
4#13066436C212yesmaximal, complemented
5C11×#2096C211yesmaximal, characteristic, complemented
6C2×#67000—21no—
7C2×C11×#106—21no—
8C2×C11×#103—21no—
9C11×#391C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622604—21no—
12C2×#66873—22no—
13#10622552C2212yes—
14#10622284—22no—
15#10622283—22no—
16C11×#336C2211yescharacteristic
17#10622167—22no—
18#10622162C2212yes—
19C22×Q8×C11D411yescharacteristic
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×C8×C11—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28#67000—42no—
29#67000—42no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—22no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×C4⋊Dic11D412yes—
35C2×C4×Dic11—21no—
36C22×C11⋊C8—22no—
37C11×#106—42no—
38C11×#103—42no—
39C11×#95—22no—
40C11⋊#95—21no—
41#66873—44no—
42#7810—111nomaximal, Sylow
43C23×D11—22no—
44C2×Q8×C11—21no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11SD1612yes—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—41no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C2×D44—22no—
55C2×D44—22no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—81no—
60C2×D44—81no—
61C2×D44—81no—
62C2×D44—82no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C42×C11—41no—
72(C2×D11)⋊C4—44no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—42no—
77(C2×D11)⋊C4—82no—
78C4⋊Dic11—42no—
79C4×Dic11—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83#2733—111no—
84#2096D1111yescharacteristic, complemented
85#2071—112no—
86#1272—111no—
87#1270—112no—
88C23×C11#12011yescharacteristic
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96Q8×C11—42no—
97Q8×C11—81no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—82no—
108C2×C4×C11—81no—
109C2×C4×C11C2×SD1611yescharacteristic
110C2×C4×C11#13512yes—
111C2×C4×C11AGL(1,ℤ/8)12yes—
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116D44—44no—
117D44—82no—
118D44—84no—
119D44—84no—
120C8×C11—42no—
121C11⋊C8—82no—
122C2×#124—221no—
123C2×#106—21no—
124C2×#103—21no—
125C2×#102—222no—
126#394—221no—
127#392—222no—
128#391C2×D1111yescharacteristic
129#390—112no—
130#388—222no—
131#384C2×D1111yescharacteristic
132#340—222no—
133#336—112no—
134#336C2×D1111yescharacteristic
135C22×C11#44912yes—
136C22×C11#45011yescharacteristic
137C22×C11#45311yescharacteristic
138C22×C11#45512yes—
139C22×C11#45811yescharacteristic
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C2×D11—82no—
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C4×C11—22no—
148C4×C11—22no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—81no—
153C4×C11—161no—
154Dic11—82no—
155C22×Q8C22⋊D1111yescharacteristic
156C22×D4—112no—
157C22×D4—221no—
158C22×D4—221no—
159C22×C8—21no—
160C22×C8—222no—
161#124—442no—
162#124—442no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4C22⋊D1111yescharacteristic
167C2×C22⋊C4—222no—
168C2×C22⋊C4—222no—
169C2×C22⋊C4—222no—
170C2×C22⋊C4—222no—
171C2×C42—221no—
172C2×C42C22×D1111yescharacteristic
173#106—42no—
174#103—42no—
175#102—444no—
176#95—22no—
177#95—221no—
178C2×C11#161212yes—
179C2×C11#161311yescharacteristic
180C2×C11#162411yescharacteristic
181C2×C11#164212yes—
182C2×C11#165911yescharacteristic
183D11—162no—
184C24—222no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#432512yes—
189C2×D4—222no—
190C2×D4—222no—
191C2×D4—442no—
192C2×D4—442no—
193C2×D4—442no—
194C2×D4—881no—
195C2×D4—881no—
196C2×D4—882no—
197C2×D4—881no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—222no—
202C22×C4D4×D1112yes—
203C22×C4C2×C22⋊D1111yescharacteristic
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—442no—
208C2×C8—442no—
209C2×C8—442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—442no—
216C22⋊C4—444no—
217C22⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—442no—
221C22⋊C4—882no—
222C42—41no—
223C42—442no—
224C11#781011yescharacteristic, complemented, Sylow
225C23—442no—
226C23—442no—
227C23—442no—
228C23—442no—
229C23—442no—
230C23—442no—
231C23—442no—
232C23#6699011yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—444no—
236D4—882no—
237D4—884no—
238D4—884no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—82no—
249C2×C4—81no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4#6696712yes—
254C2×C4#6696912yes—
255C2×C4C2×#432511yescharacteristic
256C2×C4#6700211yescharacteristic
257C8—42no—
258C8—882no—
259C22—882no—
260C22—882no—
261C22—882no—
262C22—882no—
263C22—882no—
264C22—882no—
265C22—882no—
266C22#1062265911yescharacteristic
267C22#1062266611yescharacteristic
268C22#1062269011yescharacteristic
269C22#1062278512yes—
270C22#1062281512yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—161no—
278C4—882no—
279C2—1762no—
280C2#1306762912yes—
281C2#1306763511yescharacteristic
282C2#1306769711yescharacteristic
283C2#1306781512yes—
284C2#1306792011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2096C2
socleC23×C11#120
prime radical#13075642C2
hypercenter#2096D11
hypocenterC11#7810
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
2. #13070020C2semidirect
3. #13066442C2semidirect
4. #13066436C2semidirect
5. C11×#2096C2semidirect
84. #2096D11semidirect
224. C11#7810semidirect

Maximal subgroups

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

subgroupindex
#130756422
#130700202
#130664422
#130664362
C11×#20962
#781011