Finite Group Databasebeta

← #14723979

Subgroups — #14723979

Order 2816.

666 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#13078624C211yesmaximal, characteristic
2#13077546C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic
4#13067509C214yesmaximal, complemented
5#13067462C214yesmaximal, complemented
6#13067388C211yesmaximal, characteristic, complemented
7#13067020C211yesmaximal, characteristic, complemented
8#13066900C211yesmaximal, characteristic, complemented
9C11×#1486C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4318—21no—
12#10623001C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622831C412yes—
16C2×C22⋊(C11⋊C8)—21no—
17#10622735—21no—
18#10622732—21no—
19#10622632C412yes—
20C4×#4324C2214yes—
21#10622625—21no—
22#10622625—21no—
23#10622625C2212yes—
24#10622625C2212yes—
25#10622621C412yes—
26#10622584C412yes—
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622444—21no—
31#10622444C2212yescomplemented
32#10622443—21no—
33#10622443C2212yescomplemented
34C11×D4⋊C8C2214yes—
35#10622118C2214yescomplemented
36#10622094C2214yescomplemented
37#10622092C2212yescomplemented
38C8×C11⋊C8C2212yescomplemented
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11—21no—
41C2×C11×M16—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11C2×C412yes—
45C4×D4×C11C2312yes—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4324C2×C414yes—
50#66979—21no—
51#66977—21no—
52#66977C2×C412yes—
53C2×#4318—22no—
54C2×#4318—22no—
55C2×#4318—44no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66923—21no—
60#66922C2×C411yescharacteristic
61#66922C2×C411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22C2312yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C4×C8×C11C2312yes—
69#66896C2×C414yes—
70C22⋊(C11⋊C8)—22no—
71C22⋊(C11⋊C8)—22no—
72C22⋊(C11⋊C8)C2×C412yes—
73#66879—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77#66874C2×C414yes—
78#66872C2×C414yes—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2×C412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8D411yescharacteristic
83C4×C11⋊C8D411yescharacteristic
84C4×C11⋊C8C2312yes—
85C4×C11⋊C8C2311yescharacteristic
86C4×C11⋊C8C2311yescharacteristic
87#17930—111nomaximal, Sylow
88C24×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C2×D4×C11C22×C412yes—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×Dic22—21no—
101C2×Dic22C22×C412yes—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4C22×C412yes—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11C2411yescharacteristic
113C22⋊Dic11—22no—
114#4324—44no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11C22×C412yes—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121C4×Dic11—22no—
122#4318—44no—
123#4318—44no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8SD1614yescomplemented
128C2×C11⋊C8C22×C414yes—
129C2×C11⋊C8C2×D411yescharacteristic
130C2×C11⋊C8C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133#3101—111no—
134#2960—111no—
135C2×#436—111no—
136#1590—114no—
137#1583—114no—
138#1570—111no—
139#1486D1111yescharacteristic
140#1481—111no—
141#1450—111no—
142C23×C11—22no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11C4×D411yescharacteristic
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—44no—
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13512yes—
162C2×C4×C11C23×C411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×Dic11—22no—
166C2×Dic11—22no—
167Dic22—24no—
168Dic22—42no—
169C8×C11—42no—
170C8×C11—42no—
171C11⋊C8—24no—
172C11⋊C8—21no—
173C11⋊C8—21no—
174C11⋊C8—42no—
175C11⋊C8C2×SD1612yes—
176C11⋊C8C2×SD1612yes—
177C22×M16—221no—
178#533—111no—
179C2×C4×D4C2×D1111yescharacteristic
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—
189#436—112no—
190#436—112no—
191#436—221no—
192#436—221no—
193#431—111no—
194#431C2×D1111yescharacteristic
195#424—221no—
196#423C2×D1111yescharacteristic
197C2×C4⋊C8—111no—
198C2×C22⋊C8—221no—
199#405—221no—
200C2×C4×C8—111no—
201#334—114no—
202Q8⋊C8—114no—
203D4⋊C8C2×D1114yes—
204#322—112no—
205C82—112no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—42no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—84no—
212C22×C11C4×SD1612yes—
213C22×C11C2×C4×D411yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11C4×SD1612yes—
219C4×C11#56812yes—
220C4×C11C22×SD1611yescharacteristic
221C4×C11C2×#13511yescharacteristic
222Dic11—42no—
223Dic11—42no—
224C22×D4C4×D1111yescharacteristic
225C23×C4—21no—
226C2×SD16—114no—
227C2×M16—21no—
228C2×M16—222no—
229C2×M16—222no—
230C2×M16—444no—
231C22×C8—111no—
232C22×C8—111no—
233C22×C8—221no—
234C4⋊Q8—111no—
235C4⋊Q8—111no—
236#125—221no—
237C22⋊Q8—112no—
238C22⋊Q8—221no—
239C4×Q8—112no—
240C4×Q8—221no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4C4×D1112yes—
244C4×D4C22×D1112yes—
245#117—221no—
246C2×C4⋊C4C4×D1111yescharacteristic
247C2×C22⋊C4—21no—
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—111no—
268C4×C8—112no—
269C4×C8—111no—
270C4×C8—222no—
271C4×C8C22×D1112yes—
272C2×C11—22no—
273C2×C11—82no—
274C2×C11#293011yescharacteristic
275C2×C11C2×C4×SD1611yescharacteristic
276C2×C11#295511yescharacteristic
277C24—21no—
278C2×Q8—112no—
279C2×Q8—221no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4C2×C4×D1112yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C2×C4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4#434111yescharacteristic
291SD16—444no—
292M16—42no—
293M16—444no—
294M16—444no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—114no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—114no—
301C2×C8—111no—
302C2×C8—111no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—442no—
306C4⋊C4—21no—
307C4⋊C4—112no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—222no—
313C4⋊C4C2×C4×D1112yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—222no—
317C42—222no—
318C42C2×C4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C42C23×D1111yescharacteristic
322C11#1793011yescharacteristic, complemented, Sylow
323C23—22no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23(C22⋊D11)⋊C411yescharacteristic
328Q8—224no—
329Q8—442no—
330D4—22no—
331D4—22no—
332D4—42no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4(C22⋊D11)⋊C411yescharacteristic
343C2×C4(C22⋊D11)⋊C411yescharacteristic
344C2×C4(C22⋊D11)⋊C411yescharacteristic
345C2×C4#6696512yes—
346C2×C4SD16×D1112yes—
347C2×C4C22×C4×D1111yescharacteristic
348C2×C4C2×D4×D1111yescharacteristic
349C2×C4C2×#434111yescharacteristic
350C8—42no—
351C8—42no—
352C8—112no—
353C8—112no—
354C8—224no—
355C8—221no—
356C8—221no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—84no—
364C22#1062237112yes—
365C22C2×(C22⋊D11)⋊C411yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—442no—
371C4—442no—
372C4#1062237112yes—
373C4#1062327612yes—
374C4C2×#6696511yescharacteristic
375C4C2×SD16×D1111yescharacteristic
376C2—22no—
377C2—82no—
378C2#1307731511yescharacteristic
379C2C2×#1062237111yescharacteristic
380C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#17930
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077546C2semidirect
4. #13067509C2semidirect
5. #13067462C2semidirect
6. #13067388C2semidirect
7. #13067020C2semidirect
8. #13066900C2semidirect
31. #10622444C22semidirect
33. #10622443C22semidirect
35. #10622118C22semidirect
36. #10622094C22semidirect
37. #10622092C22semidirect
38. C8×C11⋊C8C22semidirect
127. C2×C11⋊C8SD16semidirect
322. C11#17930semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130775462
C2×#106226252
#130675092
#130674622
#130673882
#130670202
#130669002
C11×#14862
#1793011