Finite Group Databasebeta

← #14756912

Subgroups — #14756912

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2#13071259C211yesmaximal, characteristic, complemented
3#13070976C211yesmaximal, characteristic, complemented
4#13069239C212yesmaximal, complemented
5#13069211C212yesmaximal, complemented
6#13068961C212yesmaximal
7#13068864C212yesmaximal, complemented
8C4×#66871C211yesmaximal, characteristic, complemented
9#13068442C211yesmaximal, characteristic, complemented
10#13068369C211yesmaximal, characteristic, complemented
11C11×#1762C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2211yescharacteristic
14C2×#66946C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C11×#102C2212yes—
17C2×C11×#97C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19#10622834C2212yes—
20C2×#66896C2211yescharacteristic
21#10622825—21no—
22#10622824—21no—
23C2×#66885C2212yes—
24C4×#4323C418yescomplemented
25#10622598C2212yes—
26C4⋊C4×Dic11C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66871C2212yes—
29C2×#66871C2211yescharacteristic
30#10622564—22no—
31C4×(C2×D11)⋊C4—22no—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622545C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622279—21no—
36D11×#95—21no—
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—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69#66946—24no—
70#66946—24no—
71C4×D44—22no—
72C4×D44C2×C414yes—
73C11×#102—24no—
74C11×#97—22no—
75C11×#95—21no—
76#66896C2×C414yescomplemented
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82C11⋊#95D412yes—
83#66885—24no—
84#66873C2×C414yes—
85#66871—24no—
86#66871C2×C414yescomplemented
87C4×C11⋊C8C2×C414yescomplemented
88#21129—111nomaximal, Sylow
89C24×C11—21no—
90C23×D11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11C22×C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D412yes—
105C22×Dic11C2×D412yes—
106C2×D44—21no—
107C2×D44—22no—
108C2×D44C22×C412yes—
109C2×D44#4114yes—
110C2×C4×D11—28no—
111C2×C4×D11—24no—
112C2×C4×D11—82no—
113C2×C4×D11—82no—
114C2×C4×D11—82no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4C22×C412yes—
121C11×C4⋊C4#4114yes—
122C11×C22⋊C4—24no—
123C42×C11—81no—
124C42×C11C22×C412yes—
125C42×C11#4112yes—
126C22⋊Dic11—82no—
127C22⋊Dic11—82no—
128#4323—28no—
129(C2×D11)⋊C4—28no—
130(C2×D11)⋊C4—24no—
131C4⋊Dic11—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—82no—
135C4⋊Dic11C22×C412yes—
136C4×Dic11—22no—
137C4×Dic11—22no—
138C4×Dic11—81no—
139C4×Dic11—82no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8C22×C412yes—
143C2×C11⋊C8C22×C412yes—
144C2×C4×D8—111no—
145#2319—111no—
146#2275—111no—
147#1925—112no—
148#1921—112no—
149#1879—112no—
150#1862—112no—
151C4×#107—111no—
152#1762—111no—
153#1762D1111yescharacteristic, complemented
154#1746—111no—
155C23×C11—22no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—41no—
160C23×C11C22×D411yescharacteristic
161C22×D11—22no—
162C22×D11—24no—
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—41no—
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11C4×D412yes—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195D44—22no—
196D44—24no—
197D44#11714yes—
198C4×D11—84no—
199C4×D11—88no—
200C8×C11—42no—
201C11⋊C8—22no—
202C11⋊C8—22no—
203C22×D8—111no—
204C2×C4×D4—112no—
205C2×C4×D4—111no—
206C2×C4×D4C2×D1111yescharacteristic
207C4×D8—118no—
208C2×#107—111no—
209C2×#107—112no—
210C2×#102—111no—
211C2×#102—111no—
212C2×#102—112no—
213C2×#102C2×D1112yes—
214C2×#97C2×D1111yescharacteristic
215C2×C4×C8—111no—
216#390—112no—
217#389—112no—
218#388—222no—
219#381—221no—
220#380—221no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—111no—
223C4×C4⋊C4C2×D1111yescharacteristic
224C4×C22⋊C4—221no—
225C4×C22⋊C4—222no—
226#376—111no—
227C2×#95—221no—
228#340—112no—
229#340—112no—
230#340C2×D1112yes—
231#336—112no—
232#336—112no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11C2×C4×D411yescharacteristic
239C22×C11#52512yes—
240C22×C11#57611yescharacteristic
241C22×C11#57612yes—
242C22×C11#57811yescharacteristic
243C2×D11—24no—
244C2×D11—44no—
245C2×D11—44no—
246C2×D11—42no—
247C2×D11—42no—
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—44no—
251C4×C11—42no—
252C4×C11C2×#11711yescharacteristic
253C4×C11C4×#4111yescharacteristic
254C4×C11#52912yes—
255Dic11—42no—
256Dic11—42no—
257Dic11—42no—
258Dic11—82no—
259C22×D4—111no—
260C22×D4C22×D1111yescharacteristic
261C23×C4—21no—
262C23×C4—222no—
263C23×C4—221no—
264C2×D8—114no—
265C2×D8—224no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8C22×D1112yes—
269C4×D4—22no—
270C4×D4—114no—
271C4×D4—224no—
272C4×D4—224no—
273C4×D4—222no—
274C4×D4C4×D1114yescomplemented
275C2×C4⋊C4—111no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C4⋊C4C22×D1112yes—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—222no—
285C2×C42—21no—
286C2×C42—112no—
287C2×C42—222no—
288C2×C42—221no—
289C2×C42C22×D1111yescharacteristic
290#107—114no—
291#107—224no—
292#102—24no—
293#102—114no—
294#102—114no—
295#102—224no—
296#97—22no—
297C4×C8—114no—
298#95—21no—
299#95—111no—
300#95—111no—
301#95—112no—
302#95—222no—
303#95—222no—
304#95—221no—
305C2×C11—82no—
306C2×C11#229011yescharacteristic
307C2×C11#294811yescharacteristic
308C2×C11#295111yescharacteristic
309C2×C11#312212yes—
310C2×C11#312412yes—
311D11—44no—
312C24—21no—
313C24—221no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—22no—
317C2×D4—112no—
318C2×D4—114no—
319C2×D4—222no—
320C2×D4—221no—
321C2×D4C2×C4×D1112yes—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—24no—
325C22×C4—82no—
326C22×C4—112no—
327C22×C4—112no—
328C22×C4—228no—
329C22×C4—221no—
330C22×C4—224no—
331C22×C4—222no—
332C22×C4—882no—
333C22×C4—882no—
334C22×C4—882no—
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338D8—228no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—112no—
343C2×C8—112no—
344C2×C8—222no—
345C2×C8—222no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—112no—
349C4⋊C4—221no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—882no—
353C4⋊C4C2×C4×D1112yes—
354C4⋊C4#433914yes—
355C22⋊C4—24no—
356C22⋊C4—228no—
357C22⋊C4—224no—
358C22⋊C4—882no—
359C22⋊C4—882no—
360C42—81no—
361C42—222no—
362C42—222no—
363C42—881no—
364C42—882no—
365C42C2×C4×D1112yes—
366C42#434112yes—
367C11#2112911yescharacteristic, complemented, Sylow
368C23—22no—
369C23—41no—
370C23—42no—
371C23—41no—
372C23—42no—
373C23—222no—
374C23—224no—
375C23—441no—
376C23—442no—
377C23—441no—
378C23C2×D4×D1111yescharacteristic
379D4—22no—
380D4—22no—
381D4—42no—
382D4—114no—
383D4—222no—
384D4—224no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—84no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—884no—
406C2×C4—888no—
407C2×C4(C22⋊D11)⋊C412yes—
408C2×C4(C22⋊D11)⋊C412yes—
409C2×C4C22×C4×D1111yescharacteristic
410C2×C4C2×#433912yes—
411C2×C4C2×#434111yescharacteristic
412C2×C4#41×D1112yes—
413C8—42no—
414C8—222no—
415C8—222no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—82no—
420C22—82no—
421C22—224no—
422C22—444no—
423C22—444no—
424C22—442no—
425C22—442no—
426C22C2×(C22⋊D11)⋊C411yescharacteristic
427C22#1062307812yes—
428C22#1062330511yescharacteristic
429C22#1062330512yes—
430C22#1062331011yescharacteristic
431C4—22no—
432C4—22no—
433C4—44no—
434C4—42no—
435C4—442no—
436C4—442no—
437C4—442no—
438C4—882no—
439C4C4×#433911yescharacteristic
440C4D11×#11711yescharacteristic
441C4#1062308812yes—
442C2—82no—
443C2—444no—
444C2#1307106211yescharacteristic
445C2#1307746411yescharacteristic
446C2#1307748711yescharacteristic
447C2#1307885812yes—
448C2#1307887612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#21129
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #13071259C2semidirect
3. #13070976C2semidirect
4. #13069239C2semidirect
5. #13069211C2semidirect
7. #13068864C2semidirect
8. C4×#66871C2semidirect
9. #13068442C2semidirect
10. #13068369C2semidirect
11. C11×#1762C2semidirect
24. C4×#4323C4semidirect
49. C4×D4×C11C2×C4semidirect
76. #66896C2×C4semidirect
86. #66871C2×C4semidirect
87. C4×C11⋊C8C2×C4semidirect
153. #1762D11semidirect
274. C4×D4C4×D11semidirect
367. C11#21129semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
#130712592
#130709762
#130692392
#130692112
#130689612
#130688642
C4×#668712
#130684422
#130683692
C11×#17622
#2112911