Finite Group Databasebeta

← #14649491

Subgroups — #14649491

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076955C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3C2×#10622105C212yesmaximal
4#13066496C212yesmaximal
5C11×#1817C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C22×C4⋊Dic11—21no—
8C2×#66977C2211yescharacteristic
9C22×C4×Dic11—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622825C2211yescharacteristic
12#10622824—21no—
13#10622823—21no—
14C2×C11⋊#95C2212yes—
15C4×C4⋊Dic11—24no—
16#10622546—22no—
17#10622542C412yescomplemented
18#10622541C412yescomplemented
19C11×#336—22no—
20#10622105—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C22×Dic22C2×C411yescharacteristic
26C22×C8×C11—22no—
27C2×C42×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11C2×C412yes—
30C2×C42×C11D412yes—
31C2×C22⋊Dic11—21no—
32C2×C22⋊Dic11—21no—
33C2×C4⋊Dic11—24no—
34C2×C4⋊Dic11—28no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C412yes—
37#66977—22no—
38#66977—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—24no—
42C2×C4×Dic11—42no—
43C2×C4×Dic11—42no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C11⋊#95—22no—
51C11⋊#95D414yes—
52#9144—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11SD1612yes—
65C22×C4×C11Q1612yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11#4112yes—
70C22×Dic11—28no—
71C22×Dic11—22no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—24no—
75C22×Dic11—44no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C2×Dic22—22no—
79C2×Dic22—42no—
80C2×C8×C11—44no—
81C2×C8×C11—42no—
82C42×C11—24no—
83C42×C11—24no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88C4⋊Dic11—216no—
89C4⋊Dic11—22no—
90C4⋊Dic11—42no—
91Dic11⋊C4—44no—
92Dic11⋊C4—42no—
93C4×Dic11—48no—
94#2855—111no—
95C2×C4×C4⋊C4—111no—
96#1817D1111yescharacteristic
97C2×#328—112no—
98#1294—112no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11#12011yescharacteristic
103C23×C11#12311yescharacteristic
104C23×C11C2×SD1611yescharacteristic
105C23×C11C2×Q1611yescharacteristic
106C23×C11AGL(1,ℤ/8)11yescharacteristic
107C23×C11#13711yescharacteristic
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11#10314yes—
123C2×C4×C11#10414yes—
124C2×C4×C11C4×D412yes—
125C2×C4×C11#12112yes—
126C2×Dic11—28no—
127C2×Dic11—44no—
128C2×Dic11—48no—
129C2×Dic11—48no—
130C2×Dic11—44no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138Dic22—82no—
139C8×C11—82no—
140C2×C22⋊Q8—111no—
141C22×C4⋊C4—221no—
142C22×C42—221no—
143C22×C42C2×D1111yescharacteristic
144C2×C22⋊C8C2×D1112yes—
145#391—112no—
146#389—112no—
147#387—222no—
148#385—221no—
149#381—221no—
150#380—111no—
151C4×C4⋊C4—224no—
152C2×#95—112no—
153#336—22no—
154#328—224no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11#38611yescharacteristic
164C22×C11#41012yes—
165C22×C11C2×#10311yescharacteristic
166C22×C11#41711yescharacteristic
167C22×C11C2×#10412yes—
168C22×C11#45011yescharacteristic
169C22×C11#45111yescharacteristic
170C22×C11#48311yescharacteristic
171C22×C11#48411yescharacteristic
172C4×C11—24no—
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—22no—
176Dic11—48no—
177Dic11—81no—
178Dic11—81no—
179Dic11—82no—
180C22×Q8—111no—
181C23×C4—222no—
182C23×C4D4411yescharacteristic
183C23×C4D4411yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—22no—
186C22⋊Q8—222no—
187C22⋊Q8—222no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—112no—
190C2×C4⋊C4—224no—
191C2×C4⋊C4—228no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—224no—
199C2×C42—442no—
200C2×C42—442no—
201C2×C42C4×D1112yes—
202C2×C42C22⋊D1112yes—
203C22⋊C8—22no—
204C22⋊C8—22no—
205#95—114no—
206#95—222no—
207#95—222no—
208#95—222no—
209#95—222no—
210#95—221no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#150312yes—
216C2×C11#150912yes—
217C2×C11#187211yescharacteristic
218C2×C11#189611yescharacteristic
219C2×C11#189911yescharacteristic
220C24C2×D4411yescharacteristic
221C2×Q8—222no—
222C2×Q8—442no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—42no—
231C22×C4—228no—
232C22×C4—224no—
233C22×C4—222no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—444no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4#431412yes—
240C22×C4Dic4412yes—
241C22×C4(C2×D11)⋊C412yes—
242C22×C4(C2×D11)⋊C412yes—
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4D4×D1112yes—
245C22×C4#434112yes—
246C22×C4C2×C22⋊D1111yescharacteristic
247C2×C8—44no—
248C2×C8—42no—
249C4⋊C4—2216no—
250C4⋊C4—222no—
251C4⋊C4—442no—
252C4⋊C4—444no—
253C4⋊C4—442no—
254C22⋊C4—441no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C22⋊C4—441no—
258C42—24no—
259C42—24no—
260C42—448no—
261C11#914411yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23#6693511yescharacteristic
265C23#6693911yescharacteristic
266C23C2×#431411yescharacteristic
267C23C2×Dic4411yescharacteristic
268C23#6696111yescharacteristic
269C23#6696211yescharacteristic
270C23C2×(C2×D11)⋊C411yescharacteristic
271Q8—882no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—228no—
287C2×C4—444no—
288C2×C4—448no—
289C2×C4—448no—
290C2×C4—444no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4#6688014yes—
299C2×C4#6688914yes—
300C2×C4(C22⋊D11)⋊C412yes—
301C2×C4#6699212yes—
302C8—82no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22#1062233411yescharacteristic
312C22#1062233511yescharacteristic
313C22#1062234411yescharacteristic
314C22#1062235211yescharacteristic
315C22#1062257111yescharacteristic
316C22#1062261912yes—
317C22C2×#6688011yescharacteristic
318C22#1062274611yescharacteristic
319C22C2×#6688912yes—
320C4—24no—
321C4—22no—
322C4—22no—
323C4—24no—
324C4—448no—
325C4—881no—
326C4—881no—
327C4—882no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1306711612yes—
333C2#1306714212yes—
334C2#1306892111yescharacteristic
335C2#1306905711yescharacteristic
336C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#9144
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #10622542C4semidirect
18. #10622541C4semidirect
261. C11#9144semidirect

Maximal subgroups

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

subgroupindex
#130769552
C2×C4×C4⋊Dic112
C2×#106221052
#130664962
C11×#18172
#914411