Finite Group Databasebeta

← #14723637

Subgroups — #14723637

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078616C211yesmaximal, characteristic
2#13077327C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067442C214yesmaximal, complemented
5#13067408C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic, complemented
7#13067016C211yesmaximal, characteristic, complemented
8#13066900C211yesmaximal, characteristic, complemented
9C11×#1486C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C23×C11⋊C8—21no—
12C2×#66960—21no—
13#10623008C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622830C412yes—
17C2×C22⋊(C11⋊C8)—21no—
18#10622742—21no—
19#10622628C412yes—
20C4×#4323C2214yes—
21D4×C11⋊C8—21no—
22D4×C11⋊C8—21no—
23D4×C11⋊C8C2212yes—
24D4×C11⋊C8C2212yes—
25#10622620C412yes—
26#10622580C412yes—
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622451—21no—
31#10622451C2212yescomplemented
32#10622447—21no—
33#10622447C2212yescomplemented
34C11×D4⋊C8C2214yes—
35#10622117C2214yescomplemented
36#10622097C2214yescomplemented
37#10622092C2212yescomplemented
38C8×C11⋊C8C2212yescomplemented
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11—21no—
41C2×#4339—21no—
42C2×C11×M16—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11C2×C412yes—
46C4×D4×C11C2312yes—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4323C2×C414yes—
51#66983—21no—
52#66983C2×C412yes—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—22no—
55C22×C11⋊C8—22no—
56C22×C11⋊C8—44no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66960—44no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927C2×C411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922C2×C411yescharacteristic
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C4×C8×C11C2312yes—
72#66896C2×C414yes—
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75C22⋊(C11⋊C8)C2×C412yes—
76(C2×D11)⋊C8—22no—
77(C2×D11)⋊C8—22no—
78#66873C2×C414yes—
79#66871C2×C414yes—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)C2×C412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8D411yescharacteristic
84C4×C11⋊C8D411yescharacteristic
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2311yescharacteristic
87C4×C11⋊C8C2311yescharacteristic
88#17900—111nomaximal, Sylow
89C24×C11—21no—
90C2×D4×C11—24no—
91C2×D4×C11—21no—
92C2×D4×C11C22×C412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—22no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C22×C412yes—
107C2×C4×D11—22no—
108C2×Dic22—21no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C22×C412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4323—28no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123C4⋊Dic11—21no—
124C4⋊Dic11C22×C412yes—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—44no—
128C2×C11⋊C8—44no—
129C2×C11⋊C8—42no—
130C2×C11⋊C8D814yescomplemented
131C2×C11⋊C8C22×C414yes—
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136#4313—44no—
137C8×D11—44no—
138#3100—111no—
139#2931—111no—
140C2×C8×D4—111no—
141#1581—114no—
142C8×D8—114no—
143#1571—111no—
144#1486D1111yescharacteristic, complemented
145#1480—111no—
146#1450—111no—
147C23×C11—24no—
148C23×C11—22no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11C4×D411yescharacteristic
152C22×D11—22no—
153D4×C11—24no—
154D4×C11—22no—
155D4×C11#13114yescomplemented
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C2×D812yes—
167C2×C4×C11#13512yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C22⋊D11—44no—
172C2×Dic11—22no—
173D44—24no—
174D44—42no—
175D44—42no—
176C4×D11—42no—
177C4×D11—42no—
178Dic22—42no—
179C8×C11—42no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—21no—
183C11⋊C8—21no—
184C11⋊C8—42no—
185C11⋊C8C2×D812yes—
186C11⋊C8C2×D812yes—
187C2×#131—221no—
188C23×C8—221no—
189#532—111no—
190C2×C4×D4C2×D1111yescharacteristic
191#480—112no—
192#474—112no—
193#459—112no—
194#447—112no—
195C4×D8—114no—
196#436—112no—
197#436—221no—
198C8×D4—112no—
199C8×D4—112no—
200C8×D4—112no—
201C8×D4—221no—
202C8×D4—221no—
203C8×D4—221no—
204#431—111no—
205#431C2×D1111yescharacteristic
206#423C2×D1111yescharacteristic
207C2×C4⋊C8—111no—
208#408—221no—
209C2×C22⋊C8—221no—
210C2×C4×C8—111no—
211#335—114no—
212D4⋊C8—114no—
213D4⋊C8C2×D1114yes—
214#322—112no—
215C82—112no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—24no—
219C22×C11—48no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11C4×D812yes—
223C22×C11C2×C4×D411yescharacteristic
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11C4×D812yes—
232C4×C11C2×#13112yes—
233C4×C11C22×D811yescharacteristic
234C4×C11C2×#13511yescharacteristic
235Dic11—42no—
236C2×#41—221no—
237C22×D4C4×D1111yescharacteristic
238C23×C4—21no—
239C2×D8—114no—
240#131—444no—
241C2×M16—21no—
242C2×M16—222no—
243C22×C8—111no—
244C22×C8—111no—
245C22×C8—222no—
246C22×C8—222no—
247C22×C8—222no—
248C22×C8—221no—
249C22×C8—444no—
250C4⋊Q8—111no—
251#127—111no—
252#124—221no—
253#121—112no—
254#121—221no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—112no—
258C4×D4—221no—
259C4×D4C4×D1112yes—
260C4×D4C22×D1112yes—
261C2×C4⋊C4C4×D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#107—114no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8C22×D1112yes—
271#102—114no—
272#102—114no—
273C22⋊C8—21no—
274C22⋊C8—112no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—112no—
283C4×C8—111no—
284C4×C8C22×D1112yes—
285C2×C11—22no—
286C2×C11—44no—
287C2×C11#292911yescharacteristic
288C2×C11C2×C4×D811yescharacteristic
289C2×C11#295511yescharacteristic
290D11—82no—
291C24—21no—
292#41—442no—
293#41—442no—
294C2×Q8—221no—
295C2×D4—24no—
296C2×D4—21no—
297C2×D4—112no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4C2×C4×D1112yes—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—222no—
308C22×C4C2×C4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311D8—228no—
312M16—42no—
313M16—444no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—114no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—114no—
320C2×C8—111no—
321C2×C8—111no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—444no—
325C2×C8—444no—
326C2×C8—444no—
327C2×C8—442no—
328C4⋊C4—21no—
329C4⋊C4—112no—
330C4⋊C4—221no—
331C4⋊C4C2×C4×D1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C42C2×C4×D1111yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1790011yescharacteristic, complemented, Sylow
341C23—24no—
342C23—22no—
343C23—42no—
344C23—42no—
345C23—222no—
346C23(C22⋊D11)⋊C411yescharacteristic
347Q8—442no—
348D4—24no—
349D4—22no—
350D4—224no—
351D4—442no—
352D4—444no—
353D4—442no—
354D4#6696014yescomplemented
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—222no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4(C22⋊D11)⋊C411yescharacteristic
366C2×C4(C22⋊D11)⋊C411yescharacteristic
367C2×C4(C22⋊D11)⋊C411yescharacteristic
368C2×C4D8×D1112yes—
369C2×C4#6696912yes—
370C2×C4C22×C4×D1111yescharacteristic
371C2×C4C2×D4×D1111yescharacteristic
372C2×C4C2×#434111yescharacteristic
373C8—42no—
374C8—42no—
375C8—112no—
376C8—112no—
377C8—224no—
378C8—221no—
379C8—221no—
380C8—442no—
381C22—21no—
382C22—21no—
383C22—24no—
384C22—48no—
385C22—42no—
386C22—42no—
387C22—442no—
388C22—442no—
389C22—442no—
390C22#1062236912yes—
391C22C2×(C22⋊D11)⋊C411yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—42no—
396C4—442no—
397C4#1062236912yes—
398C4C2×#6696012yes—
399C4C2×D8×D1111yescharacteristic
400C4C2×#6696911yescharacteristic
401C2—22no—
402C2—44no—
403C2—882no—
404C2#1307730611yescharacteristic
405C2C2×#1062236911yescharacteristic
406C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C2×C4×D4
prime radical#13078616C2
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#17900
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. #13077327C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. #13067442C2semidirect
5. #13067408C2semidirect
6. #13067392C2semidirect
7. #13067016C2semidirect
8. #13066900C2semidirect
9. C11×#1486C2semidirect
31. #10622451C22semidirect
33. #10622447C22semidirect
35. #10622117C22semidirect
36. #10622097C22semidirect
37. #10622092C22semidirect
38. C8×C11⋊C8C22semidirect
130. C2×C11⋊C8D8semidirect
144. #1486D11semidirect
155. D4×C11#131semidirect
340. C11#17900semidirect
354. D4#66960semidirect

Maximal subgroups

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

subgroupindex
#130786162
#130773272
C2×D4×C11⋊C82
#130674422
#130674082
#130673922
#130670162
#130669002
C11×#14862
#1790011