Finite Group Databasebeta

← #14756704

Subgroups — #14756704

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2#13071081C211yesmaximal, characteristic, complemented
3C4×#66946C211yesmaximal, characteristic, complemented
4#13069239C212yesmaximal, complemented
5#13069190C212yesmaximal, complemented
6#13068961C212yesmaximal
7#13068864C212yesmaximal, complemented
8C4×#66871C211yesmaximal, characteristic, complemented
9C4×#66885C211yesmaximal, characteristic, complemented
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2211yescharacteristic
14C2×#66979—21no—
15C2×#66946C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C42×D11—21no—
18C2×C11×#102C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21#10622834C2212yes—
22C2×#66896C2211yescharacteristic
23C4×C22⋊Dic11—21no—
24C2×#66885C2212yes—
25C4×#4323C418yescomplemented
26#10622598C2212yes—
27C4⋊C4×Dic11C2212yes—
28C2×#66873C2211yescharacteristic
29C2×#66871C2212yes—
30C2×#66871C2211yescharacteristic
31#10622564—22no—
32C4×(C2×D11)⋊C4—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34C42×Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622279—22no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C22×C8×C11C2312yes—
48C4×D4×C11—22no—
49C4×D4×C11C2×C414yescomplemented
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×#4323—24no—
58C2×#4323C2×C414yes—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61#66979—44no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D412yes—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73#66946—24no—
74#66946—24no—
75C4×D44—22no—
76C4×D44C2×C414yes—
77C42×D11—44no—
78C11×#102—24no—
79C4×C8×C11—22no—
80C11×#95—21no—
81#66896C2×C414yescomplemented
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66885—24no—
86#66873C2×C414yes—
87#66871—24no—
88#66871C2×C414yescomplemented
89C4×C11⋊C8C2×C414yescomplemented
90#21113—111nomaximal, Sylow
91C24×C11—21no—
92C23×D11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—22no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—22no—
111C2×D44C22×C412yes—
112C2×D44#4114yes—
113C2×C4×D11—28no—
114C2×C4×D11—24no—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4C22×C412yes—
125C11×C4⋊C4#4114yes—
126C11×C22⋊C4—24no—
127C42×C11—42no—
128C42×C11C22×C412yes—
129C42×C11#4112yes—
130C22⋊Dic11—44no—
131C22⋊Dic11—44no—
132#4323—28no—
133(C2×D11)⋊C4—28no—
134(C2×D11)⋊C4—24no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—44no—
139C4⋊Dic11C22×C412yes—
140C4×Dic11—22no—
141C4×Dic11—22no—
142C4×Dic11—22no—
143C4×Dic11—42no—
144C4×Dic11—44no—
145C4×Dic11—42no—
146C4×Dic11D814yescomplemented
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C2×C4×D8—111no—
152#2293—111no—
153C42×D4—111no—
154#1925—112no—
155#1918—112no—
156#1879—112no—
157#1862—112no—
158C4×#107—111no—
159C4×#102—111no—
160C4×#102D1111yescharacteristic, complemented
161#1744—111no—
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—24no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—42no—
173D4×C11—22no—
174D4×C11—22no—
175D4×C11—42no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—48no—
184C2×C4×C11C4×D412yes—
185C2×C4×C11C4×D412yes—
186C2×C4×C11C2×D812yes—
187C2×C4×C11#13512yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4112yes—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11C2×D814yes—
204D44—22no—
205D44—24no—
206D44#11714yescomplemented
207C4×D11—416no—
208C4×D11—48no—
209C8×C11—42no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C22×D8—111no—
213C2×C4×D4—112no—
214C2×C4×D4—111no—
215C2×C4×D4C2×D1111yescharacteristic
216C2×#117—221no—
217C22×C42—221no—
218C4×D8—118no—
219C2×#107—111no—
220C2×#107—112no—
221C2×#102—111no—
222C2×#102—111no—
223C2×#102—112no—
224C2×#102C2×D1112yes—
225C2×C4×C8—111no—
226C2×C4×C8C2×D1111yescharacteristic
227#390—112no—
228#389—112no—
229#388—222no—
230C4×C4⋊C4—112no—
231C4×C4⋊C4—111no—
232C4×C4⋊C4C2×D1111yescharacteristic
233C4×C22⋊C4—222no—
234C4×C22⋊C4—221no—
235C4×C22⋊C4—221no—
236C43—111no—
237#340—112no—
238#340—112no—
239#340C2×D1112yes—
240#336—112no—
241#336—112no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#52512yes—
249C22×C11C22×D811yescharacteristic
250C22×C11C2×#13511yescharacteristic
251C22×C11#57512yes—
252C2×D11—24no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—42no—
256C2×D11—42no—
257C4×C11—22no—
258C4×C11—44no—
259C4×C11—42no—
260C4×C11C4×D814yes—
261C4×C11C2×#11711yescharacteristic
262C4×C11C4×#4111yescharacteristic
263C4×C11#52912yes—
264Dic11—24no—
265Dic11—42no—
266Dic11—42no—
267Dic11—82no—
268C22×D4—111no—
269C22×D4C22×D1111yescharacteristic
270C23×C4—21no—
271C23×C4—222no—
272C23×C4—221no—
273C2×D8—114no—
274C2×D8—224no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8C22×D1112yes—
278C4×D4—22no—
279C4×D4—114no—
280C4×D4—224no—
281C4×D4—224no—
282C4×D4—222no—
283C4×D4C4×D1114yescomplemented
284#117—444no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C4⋊C4C22×D1112yes—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—21no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—112no—
299C2×C42—112no—
300C2×C42—222no—
301C2×C42—221no—
302C2×C42—444no—
303C2×C42C22×D1111yescharacteristic
304#107—114no—
305#107—224no—
306#102—24no—
307#102—114no—
308#102—114no—
309#102—224no—
310C4×C8—22no—
311C4×C8—114no—
312#95—21no—
313#95—222no—
314#95—222no—
315#95—221no—
316C2×C11—82no—
317C2×C11#229011yescharacteristic
318C2×C11C2×C4×D811yescharacteristic
319C2×C11#294311yescharacteristic
320C2×C11#310012yes—
321C2×C11#310212yes—
322D11—44no—
323C24—21no—
324C24—221no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—112no—
329C2×D4—114no—
330C2×D4—222no—
331C2×D4—221no—
332C2×D4C2×C4×D1112yes—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—112no—
339C22×C4—112no—
340C22×C4—228no—
341C22×C4—221no—
342C22×C4—224no—
343C22×C4—222no—
344C22×C4—444no—
345C22×C4—444no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351D8—228no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—112no—
356C2×C8—112no—
357C2×C8—222no—
358C2×C8—222no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—112no—
362C4⋊C4—221no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—444no—
366C4⋊C4C2×C4×D1112yes—
367C4⋊C4#433914yes—
368C22⋊C4—24no—
369C22⋊C4—228no—
370C22⋊C4—224no—
371C22⋊C4—444no—
372C22⋊C4—444no—
373C42—42no—
374C42—114no—
375C42—222no—
376C42—222no—
377C42—222no—
378C42—442no—
379C42—444no—
380C42—442no—
381C42C2×C4×D1112yes—
382C42#434112yes—
383C11#2111311yescharacteristic, complemented, Sylow
384C23—22no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—222no—
390C23—224no—
391C23—441no—
392C23—441no—
393C23—442no—
394C23C2×D4×D1111yescharacteristic
395D4—22no—
396D4—22no—
397D4—42no—
398D4—114no—
399D4—222no—
400D4—224no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—48no—
409C2×C4—114no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—4416no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—448no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4(C22⋊D11)⋊C412yes—
424C2×C4(C22⋊D11)⋊C412yes—
425C2×C4D8×D1112yes—
426C2×C4#6696912yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×#433912yes—
429C2×C4C2×#434111yescharacteristic
430C2×C4#41×D1112yes—
431C8—42no—
432C8—222no—
433C8—222no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—82no—
438C22—82no—
439C22—224no—
440C22—444no—
441C22—444no—
442C22—442no—
443C22—442no—
444C22C2×(C22⋊D11)⋊C411yescharacteristic
445C22#1062307812yes—
446C22C2×D8×D1111yescharacteristic
447C22C2×#6696911yescharacteristic
448C22#1062329912yes—
449C4—22no—
450C4—44no—
451C4—42no—
452C4—224no—
453C4—442no—
454C4—442no—
455C4—882no—
456C4#1062236914yes—
457C4C4×#433911yescharacteristic
458C4D11×#11711yescharacteristic
459C4#1062308812yes—
460C2—82no—
461C2—444no—
462C2#1307106211yescharacteristic
463C2C2×#1062236911yescharacteristic
464C2#1307741211yescharacteristic
465C2#1307861412yes—
466C2#1307863212yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#21113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #13071081C2semidirect
3. C4×#66946C2semidirect
4. #13069239C2semidirect
5. #13069190C2semidirect
7. #13068864C2semidirect
8. C4×#66871C2semidirect
9. C4×#66885C2semidirect
10. #13068361C2semidirect
11. C4×C11×#102C2semidirect
25. C4×#4323C4semidirect
49. C4×D4×C11C2×C4semidirect
81. #66896C2×C4semidirect
88. #66871C2×C4semidirect
89. C4×C11⋊C8C2×C4semidirect
146. C4×Dic11D8semidirect
160. C4×#102D11semidirect
206. D44#117semidirect
283. C4×D4C4×D11semidirect
383. C11#21113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
#130710812
C4×#669462
#130692392
#130691902
#130689612
#130688642
C4×#668712
C4×#668852
#130683612
C4×C11×#1022
#2111311