Finite Group Databasebeta

← #14653189

Subgroups — #14653189

Order 2816.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079195C211yesmaximal, characteristic
2#13068367C211yesmaximal, characteristic, complemented
3#13067228C212yesmaximal, complemented
4#13067125C212yesmaximal, complemented
5C11×#1568C211yesmaximal, characteristic, complemented
6#10623008C2212yes—
7C11×#432C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622728—21no—
10#10622728—21no—
11#10622545C2211yescharacteristic
12C2×#66867C2211yescharacteristic
13#10622308C411yescharacteristic, complemented
14#10622307C412yescomplemented
15C4×D88—21no—
16C4×D88—21no—
17#10622295C411yescharacteristic, complemented
18C11×#335—21no—
19C11×#334—21no—
20#10622188—21no—
21#10622188—21no—
22#10622108—24no—
23#10622102—24no—
24C2×#4339—22no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28#66983—22no—
29#66983—22no—
30C2×C4×Dic11—21no—
31C22×C11⋊C8—21no—
32C2×D88—21no—
33C2×D88—21no—
34#66928—22no—
35#66927C2×C412yes—
36C4×D44—22no—
37C4×D44—22no—
38#66922C2×C412yes—
39C11×C4⋊C8—22no—
40C11×C22⋊C8—22no—
41C11×#97—22no—
42C4×C8×C11C2×C411yescharacteristic
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11D411yescharacteristic
45C4×C8×C11D411yescharacteristic
46C11⋊#95—21no—
47C11⋊#95D412yes—
48#66885—22no—
49#66885—22no—
50#66882—21no—
51#66882—21no—
52#66867—21no—
53#66867D412yes—
54#9764—111nomaximal, Sylow
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C2×C22⋊D11—42no—
59C22×Dic11—22no—
60#4339—84no—
61C2×D44—22no—
62C2×D44—22no—
63C2×D44—22no—
64C2×C4×D11—42no—
65C2×Dic22—22no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C2×C8×C11—42no—
69C2×C8×C11C22⋊C411yescharacteristic
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22⋊C411yescharacteristic
73C42×C11C22×C411yescharacteristic
74C42×C11C2×D411yescharacteristic
75C42×C11C2×D411yescharacteristic
76C42×C11#4111yescharacteristic
77(C2×D11)⋊C4—42no—
78(C2×D11)⋊C4—42no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81C4×Dic11—41no—
82C4×Dic11—41no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86D88—42no—
87D88—42no—
88#3169—111no—
89#1746—111no—
90#1568D1111yescharacteristic, complemented
91#1530—112no—
92#1505—112no—
93C23×C11#12111yescharacteristic
94C22×D11—42no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—41no—
99C2×C4×C11C2×C22⋊C411yescharacteristic
100C2×C4×C11C4×D411yescharacteristic
101C2×C4×C11C4×D411yescharacteristic
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12411yescharacteristic
104C2×C4×C11#12711yescharacteristic
105C22⋊D11—84no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110D44—42no—
111D44—42no—
112D44—82no—
113D44—82no—
114C4×D11—84no—
115Dic22—82no—
116C8×C11—21no—
117C8×C11—21no—
118C8×C11—21no—
119C8×C11—21no—
120C8×C11—82no—
121C11⋊C8—42no—
122#532—112no—
123#500—111no—
124#493—111no—
125#486—112no—
126#466—221no—
127#466—221no—
128C4×D8—221no—
129C4×D8—221no—
130#432C2×D1112yes—
131C2×#97—111no—
132C2×C4×C8C2×D1111yescharacteristic
133#376—111no—
134#336—221no—
135#336—221no—
136#335—21no—
137#334—21no—
138#329—224no—
139#327—224no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11#39011yescharacteristic
143C22×C11#47212yes—
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11#42111yescharacteristic
153C4×C11#42111yescharacteristic
154Dic11—82no—
155Dic11—82no—
156C2×#41—222no—
157C2×D8—221no—
158C2×D8—221no—
159C22×C8—221no—
160C22×C8D4411yescharacteristic
161C22×C8D4411yescharacteristic
162C4⋊Q8—112no—
163#127—112no—
164#124—222no—
165#121—222no—
166#121—222no—
167C4×D4—222no—
168C4×D4—222no—
169C2×C42—221no—
170C2×C42C22×D1111yescharacteristic
171#107—221no—
172#107—221no—
173C4⋊C8—22no—
174#102—222no—
175#102—222no—
176C22⋊C8—22no—
177#97—22no—
178#97—112no—
179#97—221no—
180C4×C8C4×D1111yescharacteristic
181C4×C8C4×D1111yescharacteristic
182C4×C8C22⋊D1111yescharacteristic
183C4×C8C22⋊D1111yescharacteristic
184#95—112no—
185#95—221no—
186C2×C11—22no—
187C2×C11#196311yescharacteristic
188C2×C11#197611yescharacteristic
189C2×C11#197811yescharacteristic
190D11—162no—
191#41—884no—
192C2×Q8—222no—
193C2×D4—222no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4—442no—
197C22×C4—222no—
198C22×C4—442no—
199C22×C4C2×D4411yescharacteristic
200C22×C4D4×D1111yescharacteristic
201C22×C4#434311yescharacteristic
202D8—442no—
203D8—442no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—222no—
208C2×C8—441no—
209C2×C8—441no—
210C2×C8(C2×D11)⋊C411yescharacteristic
211C2×C8(C2×D11)⋊C411yescharacteristic
212C2×C8(C2×D11)⋊C411yescharacteristic
213C2×C8(C2×D11)⋊C411yescharacteristic
214C4⋊C4—222no—
215C4⋊C4—222no—
216C22⋊C4—442no—
217C22⋊C4—442no—
218C42—441no—
219C42—441no—
220C42C2×C4×D1111yescharacteristic
221C42D4×D1111yescharacteristic
222C42#434311yescharacteristic
223C42C2×C22⋊D1111yescharacteristic
224C11#976411yescharacteristic, complemented, Sylow
225C23—442no—
226C23#6694811yescharacteristic
227Q8—882no—
228D4—442no—
229D4—442no—
230D4—882no—
231D4—882no—
232D4—884no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—884no—
242C2×C4#6694611yescharacteristic
243C2×C4#6694611yescharacteristic
244C2×C4#6694811yescharacteristic
245C2×C4C2×(C2×D11)⋊C411yescharacteristic
246C2×C4#6699311yescharacteristic
247C2×C4#6700011yescharacteristic
248C8—21no—
249C8—21no—
250C8—21no—
251C8—21no—
252C8—82no—
253C8—442no—
254C22—21no—
255C22—21no—
256C22—882no—
257C22—882no—
258C22—882no—
259C22#1062251012yes—
260C22#1062260111yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—882no—
267C4—882no—
268C4#1062275211yescharacteristic
269C4#1062275211yescharacteristic
270C2—22no—
271C2—1762no—
272C2#1306944711yescharacteristic
273C2#1306951211yescharacteristic
274C2#1306952411yescharacteristic
subgroupG/H
centerC22#10622601
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1568C2
socleC22×C11#390
prime radical#13079195C2
cosocleC2×C42×C11C23
hypercenter#1568D11
hypocenterC11#9764
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. #13068367C2semidirect
3. #13067228C2semidirect
4. #13067125C2semidirect
5. C11×#1568C2semidirect
13. #10622308C4semidirect
14. #10622307C4semidirect
17. #10622295C4semidirect
90. #1568D11semidirect
224. C11#9764semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130683672
#130672282
#130671252
C11×#15682
#976411