Finite Group Databasebeta

← #14647197

Subgroups — #14647197

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 324 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×#66979—21no—
8C2×C11×C4⋊C8C2212yes—
9C2×C11×C22⋊C8—21no—
10#10622825—21no—
11#10622825C412yes—
12C2×C22⋊(C11⋊C8)—21no—
13#10622549—21no—
14#10622548C2211yescharacteristic
15#10622548C2211yescharacteristic
16C4×C4⋊Dic11—21no—
17C4×C4⋊Dic11C412yes—
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—42no—
32#66979—42no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11C2×C412yes—
39C2×C4×Dic11—22no—
40C22×C11⋊C8—22no—
41C11×C4⋊C8—24no—
42C11×C22⋊C8—42no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—42no—
46C4⋊(C11⋊C8)—24no—
47#8726—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D812yes—
62C22×C4×C11SD1612yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C2×C8×C11—42no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11#4114yes—
75C22⋊Dic11—44no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11—42no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4×Dic11—44no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89#2285—111no—
90#1797—111no—
91#1797D1111yescharacteristic
92#1296—112no—
93#1296—112no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11#10212yes—
101C23×C11C2×C22⋊C411yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—44no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11#10212yes—
118C2×C4×C11#11712yes—
119C2×C4×C11#12312yes—
120C2×C4×C11#12312yes—
121C2×C4×C11C2×D811yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11#13512yes—
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13712yes—
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C8×C11—82no—
134C11⋊C8—82no—
135C2×#117—221no—
136C22×C42C2×D1111yescharacteristic
137C2×C4⋊C8—112no—
138C2×C4⋊C8C2×D1112yes—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—221no—
141#384—111no—
142#384—111no—
143#382—221no—
144#380—112no—
145#380—221no—
146C4×C4⋊C4—112no—
147C4×C4⋊C4—221no—
148#336—21no—
149#336—221no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11#38111yescharacteristic
158C22×C11#41311yescharacteristic
159C22×C11#41311yescharacteristic
160C22×C11C2×#10211yescharacteristic
161C22×C11#41611yescharacteristic
162C22×C11#41711yescharacteristic
163C22×C11#41911yescharacteristic
164C4×C11—22no—
165C4×C11—22no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11#48012yes—
169C4×C11#48212yes—
170C4×C11#48312yes—
171C4×C11#48512yes—
172Dic11—82no—
173Dic11—82no—
174C23×C4C4×D1111yescharacteristic
175C23×C4D4411yescharacteristic
176C23×C4C22⋊D1111yescharacteristic
177C22×C8—22no—
178C22×C8—222no—
179#117—442no—
180#117—442no—
181C2×C4⋊C4—112no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C22⋊C4—222no—
188C2×C42—24no—
189C2×C42—222no—
190C2×C42C4×D1111yescharacteristic
191C2×C42D4411yescharacteristic
192C2×C42C22⋊D1111yescharacteristic
193C2×C42C22×D1111yescharacteristic
194C4⋊C8—24no—
195C4⋊C8—224no—
196C22⋊C8—42no—
197C22⋊C8—442no—
198#95—222no—
199#95—222no—
200C2×C11—42no—
201C2×C11#154011yescharacteristic
202C2×C11#154711yescharacteristic
203C2×C11#155411yescharacteristic
204C2×C11#155911yescharacteristic
205C2×C11#182211yescharacteristic
206C2×C11#182311yescharacteristic
207C2×C11#182511yescharacteristic
208C24(C2×D11)⋊C411yescharacteristic
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4#431412yes—
221C22×C4D8812yes—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—442no—
232C2×C8—442no—
233C2×C8—442no—
234C4⋊C4—442no—
235C4⋊C4—442no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—442no—
243C22⋊C4—444no—
244C42—22no—
245C42—22no—
246C42—22no—
247C42—444no—
248C42#434114yes—
249C11#872611yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#6688512yes—
257C23C2×(C2×D11)⋊C411yescharacteristic
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4#6688512yes—
280C2×C4#6693012yes—
281C2×C4#6693912yes—
282C2×C4C2×#431411yescharacteristic
283C2×C4C2×D8811yescharacteristic
284C2×C4#6696212yes—
285C2×C4#6698511yescharacteristic
286C2×C4#6698812yes—
287C2×C4#6699511yescharacteristic
288C2×C4#6700312yes—
289C8—82no—
290C8—882no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22#1062255611yescharacteristic
299C22#1062257911yescharacteristic
300C22#1062261511yescharacteristic
301C22C2×#6688511yescharacteristic
302C22#1062273311yescharacteristic
303C22#1062274511yescharacteristic
304C22#1062274511yescharacteristic
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—882no—
310C4—882no—
311C4#1062233412yes—
312C4#1062234912yes—
313C4#1062264812yes—
314C4#1062265812yes—
315C2—42no—
316C2#1306726311yescharacteristic
317C2#1306729111yescharacteristic
318C2#1306732711yescharacteristic
319C2#1306734411yescharacteristic
320C2#1306869711yescharacteristic
321C2#1306870311yescharacteristic
322C2#1306870811yescharacteristic
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#8726
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
249. C11#8726semidirect

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
#872611