Finite Group Databasebeta

← #14758303

Subgroups — #14758303

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622537C211yesmaximal, characteristic
2C4×#66979C211yesmaximal, characteristic
3#13069569C214yesmaximal, complemented
4#13069565C214yesmaximal, complemented
5#13068335C214yesmaximal
6C22×C11×C4⋊Q8C211yesmaximal, characteristic
7C23×Q8×C11—21no—
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8—24no—
11C2×C11×C4⋊Q8C418yescomplemented
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊Q8C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2212yes—
18C22×#4318C2212yes—
19C4×C22⋊Dic11—21no—
20C4×C22⋊Dic11—21no—
21C4×C4⋊Dic11C2212yes—
22C4×C4⋊Dic11C2212yes—
23#10622545—21no—
24C42×Dic11—21no—
25#10622537—24no—
26C2×C4⋊(C11⋊C8)C2212yes—
27C2×C4⋊(C11⋊C8)C2212yes—
28#10622167C22116yes—
29C22×Q8×C11—28no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—48no—
33C23×C4×C11—22no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8—24no—
41C11×C4⋊Q8C2×C418yes—
42C11×C4⋊Q8C2×C418yes—
43C2×C11×C4⋊C4—28no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4C2×C418yes—
49C2×C11×C4⋊C4C2314yes—
50C2×C42×C11C2×C414yes—
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D414yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57#66979—24no—
58#66979Q818yescomplemented
59C2×C4⋊Dic11C2314yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×#4318—24no—
64C2×#4318—28no—
65C22×C11⋊C8C2314yes—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C4⋊(C11⋊C8)—24no—
69C4⋊(C11⋊C8)—24no—
70#21313—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—28no—
73C2×Q8×C11—28no—
74C2×Q8×C11—48no—
75C2×Q8×C11—432no—
76C2×Q8×C11—48no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—28no—
80C22×C4×C11—24no—
81C22×C4×C11—48no—
82C22×C4×C11C22⋊C414yes—
83C22×C4×C11C22⋊C414yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11#4114yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—24no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—28no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4C22×C418yes—
100C42×C11C22⋊C414yes—
101C42×C11C22⋊C414yes—
102C42×C11C22×C412yes—
103C42×C11C22×C412yes—
104C42×C11C2×D412yes—
105C42×C11C2×D412yes—
106C22⋊Dic11—28no—
107C4⋊Dic11—24no—
108C4⋊Dic11C2×Q818yescomplemented
109C4×Dic11—28no—
110C4×Dic11—44no—
111C4×Dic11—44no—
112#4318—48no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—28no—
115C22×C4⋊Q8D1111yescharacteristic
116C2×#423—111no—
117C4×#117—111no—
118#1988—114no—
119#1987—114no—
120#1736—114no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11C2×C22⋊C412yes—
124C23×C11C22⋊Q814yes—
125C23×C11C22×D411yescharacteristic
126Q8×C11—416no—
127Q8×C11—416no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—416no—
134C2×C4×C11—48no—
135C2×C4×C11C2×C22⋊C412yes—
136C2×C4×C11C2×C22⋊C412yes—
137C2×C4×C11C2×C22⋊C412yes—
138C2×C4×C11C2×C22⋊C412yes—
139C2×C4×C11C2×C22⋊C412yes—
140C2×C4×C11C4×Q818yes—
141C2×C4×C11C22⋊Q814yes—
142C2×C4×C11#12414yes—
143C2×C4×C11C4⋊Q814yes—
144C2×C4×C11AGL(1,ℤ/8)14yes—
145C2×C4×C11#13714yes—
146C2×C4×C11C23×C411yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×Q812yes—
149C2×C4×C11C2×#4112yes—
150C2×Dic11—28no—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C11⋊C8—44no—
154C23×Q8—21no—
155C22×M16—112no—
156C2×C4⋊Q8—21no—
157C2×C4⋊Q8—21no—
158C2×C4⋊Q8—24no—
159C2×C4⋊Q8Dic1118yescomplemented
160C2×C4⋊Q8C2×D1112yes—
161C2×C4⋊Q8C2×D1112yes—
162C2×#117—112no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2×D1112yes—
165C22×C42C2×D1111yescharacteristic
166#423—224no—
167C2×C4⋊C8—112no—
168C2×C4⋊C8—112no—
169C4×C4⋊C4—112no—
170C4×C4⋊C4—112no—
171C4×C22⋊C4—221no—
172C4×C22⋊C4—221no—
173#376—221no—
174C43—221no—
175#340—1116no—
176C22×C11—28no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#39114yes—
180C22×C11C22×C22⋊C411yescharacteristic
181C22×C11C2×C22⋊Q812yes—
182C22×C11C2×AGL(1,ℤ/8)12yes—
183C22×C11C2×#13712yes—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—48no—
187C4×C11#39114yes—
188C4×C11#41814yes—
189C4×C11#41914yes—
190C4×C11C2×C4×Q812yes—
191C4×C11C2×#12411yescharacteristic
192C4×C11C2×C4⋊Q811yescharacteristic
193Dic11—48no—
194C22×Q8—28no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—48no—
198C23×C4—22no—
199C23×C4C22⋊D1111yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C2×M16—228no—
203C2×M16—224no—
204C22×C8—114no—
205C4⋊Q8—28no—
206C4⋊Q8—28no—
207C4⋊Q8—24no—
208C4⋊Q8—24no—
209C4⋊Q8C2×Dic1118yes—
210C4⋊Q8C2×Dic1118yes—
211#117—118no—
212#117—224no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—114no—
219C2×C4⋊C4C2×Dic1118yes—
220C2×C4⋊C4C22×D1114yes—
221C2×C22⋊C4—222no—
222C2×C42—222no—
223C2×C42—222no—
224C2×C42—222no—
225C2×C42C2×Dic1114yes—
226C2×C42C22⋊D1111yescharacteristic
227C2×C42C22⋊D1111yescharacteristic
228C2×C42C22⋊D1114yes—
229C2×C42C22×D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—224no—
232C4⋊C8—224no—
233#95—222no—
234#95—222no—
235C2×C11—24no—
236C2×C11C2×#39111yescharacteristic
237C2×C11C2×#41811yescharacteristic
238C2×C11C2×#41911yescharacteristic
239C2×C11#307914yes—
240C24C2×C22⋊D1111yescharacteristic
241C2×Q8—28no—
242C2×Q8—28no—
243C2×Q8—48no—
244C2×Q8—432no—
245C2×Q8—48no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—28no—
249C22×C4—24no—
250C22×C4—48no—
251C22×C4—224no—
252C22×C4C22⋊Dic1114yes—
253C22×C4C22⋊Dic1114yes—
254C22×C4Q8×D1114yes—
255C22×C4#434314yes—
256C22×C4C22×Dic1112yes—
257C22×C4C2×C22⋊D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1112yes—
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C23×D1111yescharacteristic
264M16—448no—
265C2×C8—228no—
266C2×C8—224no—
267C4⋊C4—28no—
268C4⋊C4—28no—
269C4⋊C4—28no—
270C4⋊C4—24no—
271C4⋊C4—118no—
272C4⋊C4—224no—
273C4⋊C4C22×Dic1118yes—
274C22⋊C4—228no—
275C42—228no—
276C42—444no—
277C42—444no—
278C42C22⋊Dic1114yes—
279C42C22⋊Dic1114yes—
280C42C22×Dic1112yes—
281C42C22×Dic1112yes—
282C42C2×C22⋊D1112yes—
283C42C2×C22⋊D1112yes—
284C11#2131311yescharacteristic, complemented, Sylow
285C23—22no—
286C23—22no—
287C23#6699914yes—
288C23C2×C22⋊Dic1112yes—
289C23C22×C22⋊D1111yescharacteristic
290Q8—416no—
291Q8—416no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—28no—
297C2×C4—416no—
298C2×C4—48no—
299C2×C4—228no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4#6698514yes—
303C2×C4#6699514yes—
304C2×C4#6699714yes—
305C2×C4Q8×Dic1118yes—
306C2×C4#6699914yes—
307C2×C4#6700014yes—
308C2×C4C2×C22⋊Dic1112yes—
309C2×C4C2×C22⋊Dic1112yes—
310C2×C4C2×C22⋊Dic1112yes—
311C2×C4C2×C22⋊Dic1112yes—
312C2×C4C2×C22⋊Dic1112yes—
313C2×C4C2×Q8×D1112yes—
314C2×C4C2×#434312yes—
315C2×C4C23×Dic1111yescharacteristic
316C2×C4C22×C22⋊D1111yescharacteristic
317C8—444no—
318C22—22no—
319C22—22no—
320C22—28no—
321C22#1062284314yes—
322C22C2×#6698512yes—
323C22C2×#6699512yes—
324C22C2×#6699912yes—
325C22C22×C22⋊Dic1111yescharacteristic
326C4—22no—
327C4—22no—
328C4—48no—
329C4—448no—
330C4#1062282814yes—
331C4#1062283814yes—
332C4#1062284314yes—
333C4C2×#6699711yescharacteristic
334C4C2×Q8×Dic1112yes—
335C4C2×#6700011yescharacteristic
336C2—24no—
337C2C2×#1062284311yescharacteristic
338C2C2×#1062282811yescharacteristic
339C2C2×#1062283811yescharacteristic
340C2#1307842514yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#21313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069569C2semidirect
4. #13069565C2semidirect
11. C2×C11×C4⋊Q8C4semidirect
58. #66979Q8semidirect
108. C4⋊Dic11C2×Q8semidirect
159. C2×C4⋊Q8Dic11semidirect
284. C11#21313semidirect

Maximal subgroups

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

subgroupindex
C2×#106225372
C4×#669792
#130695692
#130695652
#130683352
C22×C11×C4⋊Q82
#2131311