Finite Group Databasebeta

← #14719699

Subgroups — #14719699

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623105C211yesmaximal, characteristic
2#13077656C212yesmaximal, complemented
3#13066953C214yesmaximal, complemented
4#13066944C214yesmaximal, complemented
5#13066940C211yesmaximal, characteristic, complemented
6#13066928C212yesmaximal, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11#10623105—24no—
12#10623105—24no—
13C2×#66946C411yescharacteristic
14C2×#66946C2212yes—
15C2×C4⋊C4×D11C411yescharacteristic
16C2×C4⋊C4×D11C2212yes—
17C2×C4×D44C412yes—
18C2×C4×D44C2211yescharacteristic
19C2×#66925C412yes—
20C2×#66925C2211yescharacteristic
21C11×#431C2212yes—
22#10622538C2212yes—
23#10622451—24no—
24#10622339C2218yes—
25#10622301—24no—
26C11×#324C2214yes—
27#10622166C2214yes—
28#10622107C2214yes—
29#10622106C2214yes—
30C22×Q8×C11C2×C411yescharacteristic
31C2×#4343—24no—
32C2×#4343—24no—
33C2×#4343—24no—
34C22×D44C2×C412yes—
35C22×D44C2×C411yescharacteristic
36C22×C4×D11C2×C412yes—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11C2×C412yes—
39C22×C4×D11C2×C412yes—
40C22×C4×D11C2312yes—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2312yes—
45C2×C42×C11C2×C412yes—
46C2×C42×C11C2311yescharacteristic
47Q8×Dic11—24no—
48C2×(C2×D11)⋊C4C2×C412yes—
49C2×(C2×D11)⋊C4C2×C411yescharacteristic
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2311yescharacteristic
52C2×C4⋊Dic11C2×C412yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×Dic11⋊C4C2×C411yescharacteristic
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2311yescharacteristic
57C2×C4×Dic11C2×C412yes—
58C2×C4×Dic11C2×C411yescharacteristic
59C2×#4313—28no—
60#66946—24no—
61#66946—28no—
62C4⋊C4×D11—28no—
63C4⋊C4×D11—24no—
64C4×D44—24no—
65C4×D44—24no—
66C4×D44D414yes—
67C4×D44D414yes—
68#66925—22no—
69#66925—22no—
70#66925—24no—
71#66925—24no—
72C11×C4⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C4×C8×C11—22no—
75C22⋊(C11⋊C8)C2314yes—
76(C2×D11)⋊C8—28no—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79#17370—111nomaximal, Sylow
80C23×D11C22×C412yes—
81C23×D11C22×C411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11M1614yescomplemented
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C22×Dic11C22×C411yescharacteristic
91C22×Dic11C22×C411yescharacteristic
92C22×Dic11C22×C411yescharacteristic
93C22×Dic11C22×C412yes—
94#4343—232no—
95C2×D44—24no—
96C2×D44—24no—
97C2×D44—24no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44C22⋊C414yes—
101C2×C4×D11—24no—
102C2×C4×D11—24no—
103C2×C4×D11—24no—
104C2×C4×D11—24no—
105C2×C4×D11—22no—
106C2×C4×D11—24no—
107C2×C4×D11—22no—
108C2×C4×D11—82no—
109C2×C4×D11—82no—
110C2×C4×D11—82no—
111C2×C4×D11M1614yescomplemented
112C2×C4×D11C2×D418yes—
113C2×C8×C11—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—21no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4C22⋊C414yes—
125(C2×D11)⋊C4C22⋊C414yes—
126C4⋊Dic11—24no—
127C4⋊Dic11C22⋊C414yes—
128Dic11⋊C4—24no—
129Dic11⋊C4—21no—
130Dic11⋊C4—21no—
131Dic11⋊C4—22no—
132C4×Dic11—24no—
133C4×Dic11—22no—
134C2×C11⋊C8—24no—
135#4313—88no—
136C2×#520—111no—
137#2975—112no—
138#1465—114no—
139#1463—114no—
140#1461—111no—
141#1461D1111yescharacteristic, complemented
142#1458—112no—
143C23×C11C23×C411yescharacteristic
144C22×D11—21no—
145C22×D11—22no—
146C22×D11—21no—
147C22×D11—22no—
148C22×D11—42no—
149C22×D11—42no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11C2×C22⋊C414yes—
153C22×D11C2×M1612yes—
154Q8×C11—28no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11C2×M1614yes—
165C2×C4×C11C2×M1612yes—
166C2×C4×C11C2×M1612yes—
167C2×C4×C11C22×D412yes—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11C2×C22⋊C414yes—
176C2×Dic11C2×M1612yes—
177D44—216no—
178D44—28no—
179C4×D11—216no—
180C4×D11—28no—
181C4×D11—48no—
182C4×D11—84no—
183C4×D11—84no—
184C8×C11—44no—
185C11⋊C8—44no—
186C22×#41—111no—
187#520—224no—
188#520—224no—
189C2×C4×Q8—111no—
190C2×C4×Q8C2×D1111yescharacteristic
191C2×C4×D4—112no—
192C2×C4×D4—111no—
193C2×C4×D4—111no—
194C2×C4×D4—112no—
195C2×#117—111no—
196C2×#117—112no—
197C22×C4⋊C4—112no—
198C22×C4⋊C4—111no—
199#436—224no—
200#436—224no—
201#431—112no—
202#431C2×D1112yes—
203#407—118no—
204#324—114no—
205#324—114no—
206#324C2×D1114yes—
207#323—114no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11C22×C22⋊C411yescharacteristic
211C22×C11C22×M1611yescharacteristic
212C22×C11C22×M1611yescharacteristic
213C2×D11—24no—
214C2×D11—22no—
215C2×D11—24no—
216C2×D11—24no—
217C2×D11—44no—
218C2×D11—44no—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—42no—
223C4×C11—24no—
224C4×C11—22no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11#40714yes—
229Dic11—22no—
230Dic11—24no—
231Dic11—41no—
232Dic11—41no—
233C2×#41—224no—
234C2×#41—224no—
235C2×#41—224no—
236C22×Q8C4×D1111yescharacteristic
237C22×D4—111no—
238C22×D4—112no—
239C23×C4—111no—
240C23×C4—112no—
241C23×C4—112no—
242C23×C4—112no—
243C23×C4—112no—
244C2×M16—228no—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×Q8—224no—
248C4×D4—114no—
249C4×D4—114no—
250C4×D4—224no—
251C4×D4—224no—
252C4×D4—228no—
253C4×D4—224no—
254#117—224no—
255#117—224no—
256#117—222no—
257#117—222no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—224no—
264C2×C4⋊C4—228no—
265C2×C4⋊C4C4×D1111yescharacteristic
266C2×C4⋊C4C22×D1112yes—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—112no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C42—112no—
272C2×C42—111no—
273C2×C42C4×D1112yes—
274C2×C42C22×D1111yescharacteristic
275C4⋊C8—22no—
276C4⋊C8—222no—
277C22⋊C8—114no—
278C22⋊C8—228no—
279C22⋊C8C22×D1114yes—
280C4×C8—22no—
281C4×C8—222no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11C2×#40711yescharacteristic
285C2×C11#288311yescharacteristic
286C2×C11#288911yescharacteristic
287D11—44no—
288D11—42no—
289C24—112no—
290C24—111no—
291#41—2232no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8#431314yescomplemented
295C2×D4—114no—
296C2×D4—224no—
297C2×D4—224no—
298C2×D4—224no—
299C2×D4—222no—
300C2×D4—222no—
301C22×C4—111no—
302C22×C4—112no—
303C22×C4—114no—
304C22×C4—118no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—224no—
308C22×C4—224no—
309C22×C4—224no—
310C22×C4—224no—
311C22×C4—222no—
312C22×C4—224no—
313C22×C4—222no—
314C22×C4—882no—
315C22×C4—882no—
316C22×C4—882no—
317C22×C4C2×C4×D1112yes—
318C22×C4C2×C4×D1112yes—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4C23×D1111yescharacteristic
322M16—888no—
323C2×C8—24no—
324C2×C8—224no—
325C4⋊C4—22no—
326C4⋊C4—24no—
327C4⋊C4—114no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C22⋊C4—114no—
334C22⋊C4—114no—
335C22⋊C4—224no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—222no—
339C42—22no—
340C42—22no—
341C42—224no—
342C42—222no—
343C42D4×D1112yes—
344C42D4×D1112yes—
345C11#1737011yescharacteristic, complemented, Sylow
346C23—114no—
347C23—112no—
348C23—222no—
349C23—221no—
350C23—221no—
351C23—222no—
352C23—442no—
353C23—442no—
354C23—441no—
355C23—441no—
356C23C22×C4×D1111yescharacteristic
357Q8—28no—
358D4—2216no—
359D4—228no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—114no—
367C2×C4—112no—
368C2×C4—2216no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—228no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—448no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—884no—
379C2×C4—884no—
380C2×C4C22⋊C4×D1111yescharacteristic
381C2×C4C22⋊C4×D1111yescharacteristic
382C2×C4C22⋊C4×D1112yes—
383C2×C4C2×#431314yes—
384C2×C4C2×#431312yes—
385C2×C4M16×D1112yes—
386C2×C4C2×D4×D1112yes—
387C8—44no—
388C8—444no—
389C22—21no—
390C22—21no—
391C22—224no—
392C22—222no—
393C22—224no—
394C22—224no—
395C22—442no—
396C22—444no—
397C22—442no—
398C22—444no—
399C22—441no—
400C22—441no—
401C22C2×C22⋊C4×D1111yescharacteristic
402C22C22×#431311yescharacteristic
403C22C2×M16×D1111yescharacteristic
404C4—24no—
405C4—22no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—222no—
410C4—224no—
411C4—441no—
412C4—441no—
413C4#1062233914yes—
414C2—21no—
415C2—21no—
416C2—444no—
417C2—442no—
418C2C2×#1062233911yescharacteristic
419C2#1307707511yescharacteristic
420C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17370
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13066953C2semidirect
4. #13066944C2semidirect
5. #13066940C2semidirect
6. #13066928C2semidirect
7. C11×#1461C2semidirect
84. C2×Q8×C11M16semidirect
111. C2×C4×D11M16semidirect
141. #1461D11semidirect
294. C2×Q8#4313semidirect
345. C11#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#106231052
#130776562
#130669532
#130669442
#130669402
#130669282
C11×#14612
#1737011