Finite Group Databasebeta

← #14723695

Subgroups — #14723695

Order 2816.

698 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078620C211yesmaximal, characteristic
2#13077551C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic
4#13067476C214yesmaximal, complemented
5#13067431C214yesmaximal, complemented
6#13067390C211yesmaximal, characteristic, complemented
7#13067042C211yesmaximal, characteristic
8#13066909C211yesmaximal, characteristic, complemented
9C11×#1481C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C22×C8×D11—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16#10622697C412yes—
17#10622696C412yes—
18#10622659C412yes—
19#10622656C412yes—
20C4×#4325C2214yes—
21#10622637—21no—
22#10622637C2212yescomplemented
23Q8×C11⋊C8—21no—
24Q8×C11⋊C8C2212yescomplemented
25#10622612—21no—
26#10622610—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622447—21no—
31#10622447—21no—
32#10622447C2212yes—
33#10622447C2212yes—
34C11×Q8⋊C8C2214yescomplemented
35#10622117C2214yescomplemented
36#10622097C2214yes—
37#10622093C2212yescomplemented
38#10622092C2212yescomplemented
39C22×D44C2×C411yescharacteristic
40C22×C4×D11—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8C2×C411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8C2×C412yes—
47C4×Q8×C11—21no—
48C4×Q8×C11C2312yes—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4325C2×C414yes—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×#4318—21no—
55C22×C11⋊C8D411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57C2×C8×D11—22no—
58C2×C8×D11—22no—
59C2×C8×D11—44no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44C2×C412yes—
63C4×D44C2312yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C4×C8×C11C2312yes—
69#66899C2×C414yes—
70C22⋊(C11⋊C8)C2×C412yes—
71(C2×D11)⋊C8—22no—
72(C2×D11)⋊C8—22no—
73#66873C2×C414yes—
74#66872C2×C414yes—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2×C412yes—
79C4⋊(C11⋊C8)C2312yes—
80#66867—22no—
81C4×C11⋊C8—22no—
82C4×C11⋊C8D411yescharacteristic
83C4×C11⋊C8D411yescharacteristic
84C4×C11⋊C8C2312yes—
85C4×C11⋊C8C2311yescharacteristic
86C4×C11⋊C8C2311yescharacteristic
87#17905—111nomaximal, Sylow
88C23×D11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11C22×C412yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C2×D44—24no—
96C2×D44—21no—
97C2×D44C22×C412yes—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22×C412yes—
111C11×C22⋊C4—22no—
112C42×C11—22no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117#4325—28no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11C22×C412yes—
122#4318—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8C22×C414yes—
127C2×C11⋊C8C2×D411yescharacteristic
128C2×C11⋊C8C2×D411yescharacteristic
129C2×C11⋊C8C2×D411yescharacteristic
130C2×C11⋊C8C2×D411yescharacteristic
131C8×D11—44no—
132C8×D11—44no—
133#3101—111no—
134#2960—111no—
135C2×C8×D4—111no—
136#1585—114no—
137SD16⋊C8—114no—
138#1571—111no—
139#1486—111no—
140#1481D1111yescharacteristic, complemented
141#1452—111no—
142C23×C11C4×D411yescharacteristic
143C22×D11—24no—
144C22×D11—22no—
145C22×D11—42no—
146C22×D11—42no—
147Q8×C11—24no—
148Q8×C11—42no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C2×C4×C11#13712yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—42no—
163D44—24no—
164D44—22no—
165D44#13114yes—
166C4×D11—42no—
167C4×D11—42no—
168C4×D11—44no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—21no—
173C11⋊C8—21no—
174C11⋊C8—21no—
175C11⋊C8—21no—
176C11⋊C8—42no—
177C23×C8—221no—
178#533C2×D1111yescharacteristic
179C2×C4×D4—111no—
180#483—112no—
181#476—112no—
182#461—112no—
183#450—112no—
184#446—112no—
185#446—221no—
186C8×Q8—112no—
187C8×Q8—221no—
188C4×SD16—114no—
189C8×D4—112no—
190C8×D4—112no—
191C8×D4—221no—
192C8×D4—221no—
193#431—111no—
194#431C2×D1111yescharacteristic
195#424—221no—
196#423—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198C2×C22⋊C8—221no—
199#405—221no—
200C2×C4×C8—111no—
201#335—114no—
202Q8⋊C8C2×D1114yescomplemented
203D4⋊C8—114no—
204#322—112no—
205#322—112no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#44012yes—
209C22×C11C2×C4×D411yescharacteristic
210C2×D11—24no—
211C2×D11—48no—
212C2×D11—42no—
213C2×D11—42no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—42no—
219C4×C11#44012yes—
220C4×C11C2×#13112yes—
221C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C11C2×#13711yescharacteristic
223Dic11—42no—
224C22×D4—111no—
225C23×C4—221no—
226C2×SD16—114no—
227C2×M16—221no—
228C22×C8—21no—
229C22×C8—111no—
230C22×C8—111no—
231C22×C8—222no—
232C22×C8—222no—
233C22×C8—444no—
234C4⋊Q8C4×D1111yescharacteristic
235C4⋊Q8C4×D1111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8C4×D1112yes—
239C4×Q8—21no—
240C4×Q8C22×D1112yes—
241C4×D4—112no—
242C4×D4—112no—
243C4×D4—221no—
244C4×D4—221no—
245#117—21no—
246C2×C4⋊C4—111no—
247C2×C22⋊C4—221no—
248C2×C42C22×D1111yescharacteristic
249#106—114no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—112no—
254C4⋊C8—222no—
255C4⋊C8—222no—
256C4⋊C8—221no—
257C4⋊C8C22×D1112yes—
258#103—114no—
259#102—114no—
260C22⋊C8—21no—
261C22⋊C8—112no—
262C22⋊C8—222no—
263C22⋊C8—222no—
264#97—222no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8—112no—
268C4×C8—111no—
269C4×C8—111no—
270C4×C8—222no—
271C4×C8C22×D1112yes—
272C2×C11—22no—
273C2×C11#292911yescharacteristic
274C2×C11C2×#44011yescharacteristic
275C2×C11#295511yescharacteristic
276D11—44no—
277C24—221no—
278C2×Q8—21no—
279C2×Q8C2×C4×D1112yes—
280C2×D4—112no—
281C2×D4—224no—
282C2×D4—221no—
283C22×C4—221no—
284C22×C4—222no—
285C22×C4—222no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4C2×C4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4#434111yescharacteristic
291SD16—228no—
292M16—442no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8—114no—
297C2×C8—111no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—111no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—444no—
305C2×C8—444no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—112no—
312C4⋊C4—221no—
313C4⋊C4C2×C4×D1112yes—
314C22⋊C4—22no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C42—22no—
318C42C2×C4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C42C23×D1111yescharacteristic
322C11#1790511yescharacteristic, complemented, Sylow
323C23—224no—
324C23—222no—
325C23—442no—
326C23—442no—
327C23(C22⋊D11)⋊C411yescharacteristic
328Q8—24no—
329Q8—42no—
330D4—114no—
331D4—224no—
332D4—222no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—222no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—444no—
342C2×C4(C22⋊D11)⋊C411yescharacteristic
343C2×C4(C22⋊D11)⋊C411yescharacteristic
344C2×C4(C22⋊D11)⋊C411yescharacteristic
345C2×C4#6696712yes—
346C2×C4#6697112yes—
347C2×C4C22×C4×D1111yescharacteristic
348C2×C4C2×D4×D1111yescharacteristic
349C2×C4C2×#434111yescharacteristic
350C8—42no—
351C8—42no—
352C8—224no—
353C8—221no—
354C8—221no—
355C8—221no—
356C8—221no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—224no—
361C22—448no—
362C22—442no—
363C22—442no—
364C22#1062243012yes—
365C22C2×(C22⋊D11)⋊C411yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—42no—
371C4—442no—
372C4#1062243012yes—
373C4D11×#13112yes—
374C4C2×#6696711yescharacteristic
375C4C2×#6697111yescharacteristic
376C2—22no—
377C2—444no—
378C2#1307731311yescharacteristic
379C2C2×#1062243011yescharacteristic
380C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#17905
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #13077551C2semidirect
4. #13067476C2semidirect
5. #13067431C2semidirect
6. #13067390C2semidirect
8. #13066909C2semidirect
9. C11×#1481C2semidirect
22. #10622637C22semidirect
24. Q8×C11⋊C8C22semidirect
34. C11×Q8⋊C8C22semidirect
35. #10622117C22semidirect
37. #10622093C22semidirect
38. #10622092C22semidirect
140. #1481D11semidirect
202. Q8⋊C8C2×D11semidirect
322. C11#17905semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130775512
C2×#106224472
#130674762
#130674312
#130673902
#130670422
#130669092
C11×#14812
#1790511