Finite Group Databasebeta

← #14758301

Subgroups — #14758301

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
1C22×#66922C211yesmaximal, characteristic
2C4×#66979C211yesmaximal, characteristic
3#13069567C214yesmaximal, complemented
4#13069563C214yesmaximal, complemented
5#13068336C214yesmaximal
6C2×C11×#423C211yesmaximal, characteristic
7C23×Dic22—21no—
8C22×C11×M16C2212yes—
9C22×C42×C11C2211yescharacteristic
10C2×#66979C2212yes—
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2212yes—
13C2×#66922—21no—
14C2×#66922—21no—
15C2×#66922—24no—
16C2×#66922C418yescomplemented
17C2×#66922C2212yes—
18C2×#66922C2212yes—
19C11×#423—24no—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C4×C22⋊Dic11—21no—
23C4×C22⋊Dic11—21no—
24C4×C4⋊Dic11C2212yes—
25C4×C4⋊Dic11C2212yes—
26#10622545—21no—
27C42×Dic11—21no—
28#10622189C22116yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—22no—
33C22×Dic22—28no—
34C22×Dic22—22no—
35C22×Dic22—22no—
36C22×Dic22—48no—
37C2×C11×M16—24no—
38C2×C11×M16—28no—
39C22×C8×C11C2314yes—
40C2×C42×C11C2×C414yes—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D414yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47#66979—24no—
48#66979Q818yescomplemented
49C2×C4⋊Dic11—28no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2×C418yes—
55C2×C4⋊Dic11C2314yes—
56C2×C4⋊Dic11C2314yes—
57C2×C4×Dic11—22no—
58C2×C4×Dic11—22no—
59C2×C4×Dic11—22no—
60#66922—28no—
61#66922—28no—
62#66922—24no—
63#66922—24no—
64#66922C2×C418yes—
65#66922C2×C418yes—
66C11×C4⋊C8—24no—
67C11×C4⋊C8—24no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#21313—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11C22⋊C414yes—
75C22×C4×C11C22⋊C414yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×Q814yes—
84C22×C4×C11#4114yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—28no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—48no—
90C2×Dic22—28no—
91C2×Dic22—28no—
92C2×Dic22—48no—
93C2×Dic22—432no—
94C2×Dic22—48no—
95C11×M16—48no—
96C2×C8×C11—24no—
97C2×C8×C11—28no—
98C42×C11C22⋊C414yes—
99C42×C11C22⋊C414yes—
100C42×C11C22×C412yes—
101C42×C11C22×C412yes—
102C42×C11C2×D412yes—
103C42×C11C2×D412yes—
104C22⋊Dic11—28no—
105C4⋊Dic11—28no—
106C4⋊Dic11—28no—
107C4⋊Dic11—28no—
108C4⋊Dic11—24no—
109C4⋊Dic11—24no—
110C4⋊Dic11C22×C418yes—
111C4⋊Dic11C2×Q818yescomplemented
112C4×Dic11—28no—
113C4×Dic11—44no—
114C4×Dic11—44no—
115C22×C4⋊Q8—111no—
116C2×#423D1111yescharacteristic
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
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—28no—
129C2×C4×C11—28no—
130C2×C4×C11C2×C22⋊C412yes—
131C2×C4×C11C2×C22⋊C412yes—
132C2×C4×C11C2×C22⋊C412yes—
133C2×C4×C11C2×C22⋊C412yes—
134C2×C4×C11C2×C22⋊C412yes—
135C2×C4×C11C4×Q818yes—
136C2×C4×C11C22⋊Q814yes—
137C2×C4×C11#12414yes—
138C2×C4×C11C4⋊Q814yes—
139C2×C4×C11AGL(1,ℤ/8)14yes—
140C2×C4×C11#13714yes—
141C2×C4×C11C23×C411yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×Q812yes—
144C2×C4×C11C2×#4112yes—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—416no—
148C2×Dic11—44no—
149C2×Dic11—48no—
150C2×Dic11—44no—
151Dic22—416no—
152Dic22—416no—
153C8×C11—44no—
154C23×Q8—221no—
155C22×M16C2×D1112yes—
156C2×C4⋊Q8—112no—
157C2×C4⋊Q8—112no—
158C2×C4⋊Q8—118no—
159C2×C4⋊Q8—221no—
160C2×C4⋊Q8—221no—
161C2×C4⋊Q8—224no—
162C2×#117—112no—
163C22×C4⋊C4—112no—
164C22×C4⋊C4—221no—
165C22×C42C2×D1111yescharacteristic
166#423—24no—
167C2×C4⋊C8C2×D1112yes—
168C2×C4⋊C8C2×D1112yes—
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#39114yes—
187C4×C11#41814yes—
188C4×C11#41914yes—
189C4×C11C2×C4×Q812yes—
190C4×C11C2×#12411yescharacteristic
191C4×C11C2×C4⋊Q811yescharacteristic
192Dic11—48no—
193Dic11—48no—
194C22×Q8—228no—
195C22×Q8—222no—
196C22×Q8—222no—
197C22×Q8—448no—
198C23×C4—222no—
199C23×C4D4411yescharacteristic
200C23×C4D4411yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C2×M16—28no—
203C2×M16—24no—
204C22×C8C22×D1114yes—
205C4⋊Q8—118no—
206C4⋊Q8—118no—
207C4⋊Q8—228no—
208C4⋊Q8—228no—
209C4⋊Q8—224no—
210C4⋊Q8—224no—
211#117—118no—
212#117—224no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—114no—
215C2×C4⋊C4—114no—
216C2×C4⋊C4—228no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—224no—
221C2×C22⋊C4—222no—
222C2×C42—222no—
223C2×C42—222no—
224C2×C42—222no—
225C2×C42C4×D1114yes—
226C2×C42D4411yescharacteristic
227C2×C42D4411yescharacteristic
228C2×C42C22⋊D1114yes—
229C2×C42C22×D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—24no—
232C4⋊C8—24no—
233#95—222no—
234#95—222no—
235C2×C11—24no—
236C2×C11C2×#39111yescharacteristic
237C2×C11C2×#41811yescharacteristic
238C2×C11C2×#41911yescharacteristic
239C2×C11#307914yes—
240C24C2×D4411yescharacteristic
241C2×Q8—228no—
242C2×Q8—228no—
243C2×Q8—448no—
244C2×Q8—4432no—
245C2×Q8—448no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—228no—
249C22×C4—224no—
250C22×C4—224no—
251C22×C4—448no—
252C22×C4(C2×D11)⋊C414yes—
253C22×C4(C2×D11)⋊C414yes—
254C22×C4C2×C4×D1112yes—
255C22×C4C2×D4411yescharacteristic
256C22×C4C2×D4411yescharacteristic
257C22×C4C2×D4411yescharacteristic
258C22×C4C2×D4411yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4#434114yes—
261C22×C4Q8×D1114yes—
262C22×C4C2×C22⋊D1112yes—
263C22×C4C23×D1111yescharacteristic
264M16—48no—
265C2×C8—28no—
266C2×C8—24no—
267C4⋊C4—118no—
268C4⋊C4—118no—
269C4⋊C4—228no—
270C4⋊C4—228no—
271C4⋊C4—228no—
272C4⋊C4—224no—
273C4⋊C4—224no—
274C22⋊C4—228no—
275C42—228no—
276C42—444no—
277C42—444no—
278C42(C2×D11)⋊C414yes—
279C42(C2×D11)⋊C414yes—
280C42C2×C4×D1112yes—
281C42C2×C4×D1112yes—
282C42C2×C22⋊D1112yes—
283C42C2×C22⋊D1112yes—
284C11#2131311yescharacteristic, complemented, Sylow
285C23—22no—
286C23—22no—
287C23#6695014yes—
288C23C2×(C2×D11)⋊C412yes—
289C23C22×D4411yescharacteristic
290Q8—4416no—
291Q8—4416no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—228no—
297C2×C4—228no—
298C2×C4—4416no—
299C2×C4—444no—
300C2×C4—448no—
301C2×C4—444no—
302C2×C4#6694018yes—
303C2×C4#6695014yes—
304C2×C4#6696114yes—
305C2×C4#6696214yes—
306C2×C4C2×(C2×D11)⋊C412yes—
307C2×C4C2×(C2×D11)⋊C412yes—
308C2×C4C2×(C2×D11)⋊C412yes—
309C2×C4C2×(C2×D11)⋊C412yes—
310C2×C4C2×(C2×D11)⋊C412yes—
311C2×C4#6698914yes—
312C2×C4#6699714yes—
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4C2×#434112yes—
315C2×C4C2×Q8×D1112yes—
316C2×C4C22×C22⋊D1111yescharacteristic
317C8—44no—
318C22—22no—
319C22—22no—
320C22—28no—
321C22#1062258714yes—
322C22C2×#6695012yes—
323C22C2×#6696112yes—
324C22C2×#6696212yes—
325C22C22×(C2×D11)⋊C411yescharacteristic
326C4—22no—
327C4—22no—
328C4—448no—
329C4—448no—
330C4#1062258714yes—
331C4#1062273314yes—
332C4#1062274414yes—
333C4C2×#6694012yes—
334C4C2×#6698911yescharacteristic
335C4C2×#6699711yescharacteristic
336C2—24no—
337C2C2×#1062258711yescharacteristic
338C2C2×#1062274411yescharacteristic
339C2C2×#1062273311yescharacteristic
340C2#1307843214yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#423C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#423D11
hypocenterC11#21313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. #13069567C2semidirect
4. #13069563C2semidirect
16. C2×#66922C4semidirect
48. #66979Q8semidirect
111. C4⋊Dic11C2×Q8semidirect
284. C11#21313semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
C4×#669792
#130695672
#130695632
#130683362
C2×C11×#4232
#2131311