Finite Group Databasebeta

← #14647207

Subgroups — #14647207

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3#13066500C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66979C412yes—
8C2×C11×C4⋊C8C2212yes—
9C2×C11×C22⋊C8—21no—
10#10622825—21no—
11#10622825—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622549C412yes—
14#10622548C2211yescharacteristic
15#10622548C2211yescharacteristic
16C4×C4⋊Dic11—21no—
17C4×C4⋊Dic11—21no—
18C2×C4⋊(C11⋊C8)C2212yes—
19C11×#336—21no—
20#10622162—21no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C8×C11—22no—
25C2×C42×C11—24no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×C22⋊Dic11—22no—
31#66979—44no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C412yes—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4×Dic11—22no—
39C22×C11⋊C8—22no—
40C11×C4⋊C8—24no—
41C11×C22⋊C8—42no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—42no—
45C4⋊(C11⋊C8)—24no—
46#8728—111nomaximal, Sylow
47C24×C11C22⋊C411yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11#4114yes—
74C22⋊Dic11—44no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4×Dic11—44no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87#2285—111no—
88#1797—111no—
89#1797D1111yescharacteristic
90#1296—112no—
91#1296—112no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11#10112yes—
99C23×C11C2×C22⋊C411yescharacteristic
100C2×C4×C11—28no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11#10012yes—
116C2×C4×C11#11712yes—
117C2×C4×C11#12312yes—
118C2×C4×C11#12312yes—
119C2×C4×C11#13512yes—
120C2×C4×C11#13512yes—
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C8×C11—82no—
132C11⋊C8—82no—
133C2×#117—112no—
134C22×C42C2×D1111yescharacteristic
135C2×C4⋊C8—112no—
136C2×C4⋊C8C2×D1112yes—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—221no—
139#384—111no—
140#384—111no—
141#382—112no—
142#380—221no—
143#380—221no—
144C4×C4⋊C4—221no—
145C4×C4⋊C4—221no—
146#336—21no—
147#336—221no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11#38111yescharacteristic
156C22×C11C2×#10011yescharacteristic
157C22×C11C2×#10111yescharacteristic
158C22×C11#41611yescharacteristic
159C22×C11#41611yescharacteristic
160C22×C11#41711yescharacteristic
161C22×C11#41711yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11#48212yes—
167C4×C11#48212yes—
168C4×C11#48512yes—
169C4×C11#48512yes—
170Dic11—82no—
171Dic11—82no—
172C23×C4C4×D1111yescharacteristic
173C23×C4D4411yescharacteristic
174C23×C4C22⋊D1111yescharacteristic
175C22×C8—22no—
176C22×C8—222no—
177#117—444no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—112no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C22⋊C4—222no—
185C2×C42—24no—
186C2×C42—222no—
187C2×C42C4×D1111yescharacteristic
188C2×C42D4411yescharacteristic
189C2×C42C22⋊D1111yescharacteristic
190C2×C42C22×D1111yescharacteristic
191C4⋊C8—24no—
192C4⋊C8—224no—
193C22⋊C8—42no—
194C22⋊C8—442no—
195#95—222no—
196#95—222no—
197C2×C11—42no—
198C2×C11#154311yescharacteristic
199C2×C11#155211yescharacteristic
200C2×C11#155211yescharacteristic
201C2×C11#156011yescharacteristic
202C2×C11#182111yescharacteristic
203C2×C11#182511yescharacteristic
204C2×C11#182511yescharacteristic
205C24(C2×D11)⋊C411yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—222no—
218C22×C4—222no—
219C22×C4(C2×D11)⋊C411yescharacteristic
220C22×C4(C2×D11)⋊C411yescharacteristic
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4C2×C4×D1111yescharacteristic
223C22×C4C2×D4411yescharacteristic
224C22×C4C2×C22⋊D1111yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—442no—
229C2×C8—442no—
230C2×C8—442no—
231C4⋊C4—442no—
232C4⋊C4—442no—
233C4⋊C4—442no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—442no—
239C22⋊C4—444no—
240C42—22no—
241C42—22no—
242C42—22no—
243C42—444no—
244C42#434114yes—
245C11#872811yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23#6688812yes—
253C23C2×(C2×D11)⋊C411yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4#6688712yes—
276C2×C4#6693012yes—
277C2×C4#6693912yes—
278C2×C4#6695712yes—
279C2×C4#6696111yescharacteristic
280C2×C4#6696211yescharacteristic
281C2×C4#6698511yescharacteristic
282C2×C4#6698812yes—
283C2×C4#6699511yescharacteristic
284C2×C4#6700312yes—
285C8—82no—
286C8—882no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22#1062255611yescharacteristic
295C22#1062257911yescharacteristic
296C22#1062261511yescharacteristic
297C22#1062272611yescharacteristic
298C22C2×#6688711yescharacteristic
299C22#1062274611yescharacteristic
300C22C2×#6688811yescharacteristic
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—882no—
306C4—882no—
307C4#1062233612yes—
308C4#1062235012yes—
309C4#1062264812yes—
310C4#1062265812yes—
311C2—42no—
312C2#1306727611yescharacteristic
313C2#1306731411yescharacteristic
314C2#1306731711yescharacteristic
315C2#1306734911yescharacteristic
316C2#1306869411yescharacteristic
317C2#1306870811yescharacteristic
318C2#1306871211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8728
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13066500C2semidirect
4. #13066500C2semidirect
245. C11#8728semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130685962
#130665002
C11×#17972
#872811