Finite Group Databasebeta

← #14719933

Subgroups — #14719933

Order 2816.

948 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623113C211yesmaximal, characteristic
2#13077644C212yesmaximal, complemented
3#13066978C214yesmaximal, complemented
4#13066963C214yesmaximal, complemented
5#13066960C211yesmaximal, characteristic, complemented
6#13066948C212yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×#66999C411yescharacteristic
11#10623113—24no—
12#10623113—24no—
13C2×#66949C2212yes—
14C2×#66948C411yescharacteristic
15C2×#66947C2212yes—
16C2×#66941C411yescharacteristic
17C2×#66929C412yes—
18C2×#66928C412yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622449—24no—
24#10622339C2214yes—
25D11×C22⋊C8C2214yes—
26#10622319—24no—
27C11×#324C2214yes—
28#10622166C2214yes—
29#10622107C2214yes—
30#10622106C2214yes—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D44C2×C412yes—
33C22×D44C2×C411yescharacteristic
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11C2312yes—
36C22×Dic22C2×C412yes—
37C4×Q8×C11—22no—
38C4×Q8×C11—22no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2312yes—
41C2×C42×C11C2×C412yes—
42C2×C42×C11C2311yescharacteristic
43#67000—24no—
44#66999—24no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×(C2×D11)⋊C4C2×C412yes—
47C2×(C2×D11)⋊C4C2×C412yes—
48C2×(C2×D11)⋊C4C2×C412yes—
49C2×(C2×D11)⋊C4C2×C412yes—
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2311yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4C2×C411yescharacteristic
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2311yescharacteristic
57C2×C4×Dic11C2×C411yescharacteristic
58C2×#4313—24no—
59C2×C8×D11—24no—
60#66949—24no—
61#66949—24no—
62#66948—24no—
63#66947—24no—
64#66947—24no—
65#66941—24no—
66#66929—24no—
67#66929—24no—
68#66928—24no—
69#66928—24no—
70C4×D44D414yes—
71C4×D44D414yes—
72#66925—22no—
73#66925—22no—
74C11×C4⋊C8—22no—
75C11×C22⋊C8C2314yes—
76C11×#97—22no—
77C22⋊(C11⋊C8)C2314yes—
78(C2×D11)⋊C8—24no—
79(C2×D11)⋊C8—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#17407—111nomaximal, Sylow
83C23×D11C22×C411yescharacteristic
84C23×D11C22×C412yes—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11C22×C411yescharacteristic
93C22×Dic11C22×C411yescharacteristic
94C22×Dic11C22×C411yescharacteristic
95C22×Dic11C22×C412yes—
96C2×D44—24no—
97C2×D44—42no—
98C2×D44—82no—
99C2×D44C22⋊C414yes—
100C2×C4×D11—22no—
101C2×C4×D11—42no—
102C2×C4×D11—82no—
103C2×C4×D11C2×D414yes—
104C2×C4×D11C2×D414yes—
105C2×Dic22—24no—
106C2×Dic22—82no—
107C2×C8×C11—24no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115(C2×D11)⋊C4—24no—
116(C2×D11)⋊C4—24no—
117(C2×D11)⋊C4—24no—
118(C2×D11)⋊C4—24no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4C22⋊C414yes—
123(C2×D11)⋊C4C22⋊C414yes—
124C4⋊Dic11C22⋊C414yes—
125Dic11⋊C4—24no—
126Dic11⋊C4—24no—
127Dic11⋊C4—21no—
128Dic11⋊C4—21no—
129Dic11⋊C4—22no—
130C4×Dic11—22no—
131C2×C11⋊C8—24no—
132#4313—84no—
133C8×D11—84no—
134C2×#542—111no—
135#2973—112no—
136#1472—114no—
137#1468—114no—
138#1467—111no—
139#1467D1111yescharacteristic, complemented
140#1464—112no—
141C23×C11C23×C411yescharacteristic
142C22×D11—24no—
143C22×D11—21no—
144C22×D11—22no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11C2×C22⋊C414yes—
150Q8×C11—44no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×C22⋊C411yescharacteristic
160C2×C4×C11C2×C22⋊C411yescharacteristic
161C2×C4×C11C22×D412yes—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11C2×C22⋊C414yes—
170D44—44no—
171D44—84no—
172C4×D11—44no—
173C4×D11—44no—
174C4×D11—44no—
175Dic22—84no—
176C8×C11—44no—
177C11⋊C8—44no—
178#542—224no—
179#542—224no—
180C2×C4⋊Q8—111no—
181C2×#126—112no—
182C2×#124—111no—
183C2×#124—112no—
184C2×#123—112no—
185C2×C22⋊Q8—111no—
186C2×C22⋊Q8—112no—
187C2×#121—111no—
188C2×C4×Q8C2×D1111yescharacteristic
189C2×C4×D4—111no—
190C2×#117—111no—
191#435—224no—
192#435—224no—
193#432—112no—
194#432C2×D1112yes—
195#407—114no—
196C2×C22⋊C8—114no—
197#324—114no—
198#324—114no—
199#324C2×D1114yes—
200#323—114no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11C22×C22⋊C411yescharacteristic
204C22×C11#56812yes—
205C2×D11—24no—
206C2×D11—24no—
207C2×D11—24no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—84no—
212C2×D11—82no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—42no—
219Dic11—24no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223C22×Q8—112no—
224C22×Q8C4×D1111yescharacteristic
225C22×D4—111no—
226C22×D4—112no—
227C23×C4—112no—
228C23×C4—111no—
229C2×M16—224no—
230C22×C8—224no—
231C4⋊Q8—224no—
232#126—224no—
233#126—224no—
234#124—224no—
235#124—224no—
236#124—224no—
237#123—224no—
238#123—224no—
239C22⋊Q8—224no—
240C22⋊Q8—224no—
241C22⋊Q8—224no—
242#121—224no—
243C4×Q8—22no—
244C4×Q8—22no—
245C4×D4—114no—
246C4×D4—114no—
247#117—222no—
248#117—222no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—112no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4C4×D1111yescharacteristic
255C2×C4⋊C4C22×D1112yes—
256C2×C22⋊C4—112no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—112no—
259C2×C22⋊C4—112no—
260C2×C22⋊C4—112no—
261C2×C22⋊C4—112no—
262C2×C22⋊C4—111no—
263C2×C42—111no—
264C2×C42C4×D1112yes—
265C2×C42C22×D1111yescharacteristic
266C4⋊C8—22no—
267C4⋊C8—222no—
268C22⋊C8—114no—
269C22⋊C8—224no—
270C22⋊C8—224no—
271C22⋊C8C22×D1114yes—
272#97—22no—
273#97—222no—
274C2×C11—22no—
275C2×C11#287911yescharacteristic
276C2×C11#288311yescharacteristic
277C2×C11#288911yescharacteristic
278D11—44no—
279D11—81no—
280C24—112no—
281C24—111no—
282C2×Q8—22no—
283C2×Q8—42no—
284C2×Q8—224no—
285C2×Q8—882no—
286C2×D4—114no—
287C2×D4—224no—
288C2×D4—442no—
289C2×D4—882no—
290C22×C4—112no—
291C22×C4—114no—
292C22×C4—114no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—222no—
297C22×C4—442no—
298C22×C4—882no—
299C22×C4C2×C4×D1112yes—
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×C4×D1112yes—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C23×D1111yescharacteristic
304M16—884no—
305C2×C8—24no—
306C2×C8—224no—
307C2×C8—884no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—114no—
312C4⋊C4—224no—
313C4⋊C4—224no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—222no—
317C22⋊C4—114no—
318C22⋊C4—114no—
319C22⋊C4—224no—
320C22⋊C4—224no—
321C22⋊C4—224no—
322C22⋊C4—224no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—222no—
326C42—22no—
327C42—22no—
328C42—222no—
329C42D4×D1112yes—
330C42D4×D1112yes—
331C11#1740711yescharacteristic, complemented, Sylow
332C23—114no—
333C23—224no—
334C23—221no—
335C23—222no—
336C23—442no—
337C23—442no—
338C23—441no—
339C23—441no—
340C23C22×C4×D1111yescharacteristic
341Q8—44no—
342Q8—884no—
343D4—444no—
344D4—884no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—114no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—222no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4C22⋊C4×D1111yescharacteristic
364C2×C4C22⋊C4×D1111yescharacteristic
365C2×C4C22⋊C4×D1112yes—
366C2×C4C2×D4×D1112yes—
367C8—44no—
368C8—444no—
369C22—21no—
370C22—21no—
371C22—224no—
372C22—224no—
373C22—224no—
374C22—441no—
375C22—441no—
376C22—441no—
377C22—884no—
378C22—882no—
379C22C2×C22⋊C4×D1111yescharacteristic
380C22#1062327612yes—
381C4—22no—
382C4—22no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—42no—
387C4—224no—
388C4—441no—
389C4—441no—
390C4—441no—
391C2—22no—
392C2—444no—
393C2—881no—
394C2#1307705911yescharacteristic
395C2#1307707511yescharacteristic
396C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17407
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13066978C2semidirect
4. #13066963C2semidirect
5. #13066960C2semidirect
6. #13066948C2semidirect
7. C11×#1467C2semidirect
139. #1467D11semidirect
331. C11#17407semidirect

Maximal subgroups

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

subgroupindex
C2×#106231132
#130776442
#130669782
#130669632
#130669602
#130669482
C11×#14672
#1740711