Finite Group Databasebeta

← #14756192

Subgroups — #14756192

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic
3C2×#10622834C211yesmaximal, characteristic
4#117×Dic11C211yesmaximal, characteristic, complemented
5#13069245C214yesmaximal, complemented
6#13069238C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C2×C11×#418C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C22⋊Dic11—22no—
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C11×#418C418yescomplemented
19C2×C11×#102C2214yes—
20#10622834—21no—
21#10622834—21no—
22#10622834C2214yes—
23#10622828—24no—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622734—24no—
27C2×#66882C2212yescomplemented
28C2×#66881C2212yescomplemented
29C4⋊C4×Dic11C2212yescomplemented
30C4⋊C4×Dic11C2212yescomplemented
31C22⋊C4×Dic11—22no—
32#10622545—21no—
33C42×Dic11—21no—
34#10622188C2214yescomplemented
35#10622167C2214yescomplemented
36C25×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11C2×C414yes—
44C22×D4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D412yes—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16C2×C414yes—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117C2×C414yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—48no—
61#66979—22no—
62#66979D414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2312yes—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C22×C11⋊C8C2312yes—
81C11×#102C2×C4116yescomplemented
82#66896—24no—
83#66896—24no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66882—24no—
87#66881—24no—
88#21060—111nomaximal, Sylow
89C24×C11—24no—
90C24×C11—22no—
91C24×C11—44no—
92C24×C11—44no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11C2×D411yescharacteristic
96C2×D4×C11—28no—
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11C22×C414yes—
109C22×C4×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—24no—
119C22×Dic11—24no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124C22×Dic11—44no—
125C22×Dic11—42no—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D412yes—
128C11×M16—28no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11C22×C414yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C414yes—
134C11×C22⋊C4—24no—
135C42×C11—24no—
136C22⋊Dic11—24no—
137C22⋊Dic11—48no—
138C22⋊Dic11—48no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11C2×D412yes—
145C4⋊Dic11C2×D412yes—
146C4×Dic11—24no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—44no—
152C4×Dic11—44no—
153#4318—44no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×#428—111no—
158C2×#418—111no—
159C2×#418D1111yescharacteristic
160C2×#390—111no—
161C4×#117—111no—
162#1926—114no—
163#1925—114no—
164#1736—111no—
165#1728—111no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—416no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—44no—
173C23×C11—44no—
174C23×C11—48no—
175C23×C11—88no—
176C23×C11—84no—
177C23×C11—84no—
178C23×C11C4×D412yes—
179C23×C11#12112yes—
180C23×C11#12312yes—
181C23×C11C22×D411yescharacteristic
182D4×C11—24no—
183D4×C11—24no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—48no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11#11714yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12312yes—
195C2×C4×C11#12414yes—
196C2×C4×C11#12614yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—48no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—44no—
215C2×Dic11—84no—
216C2×Dic11AGL(1,ℤ/8)14yes—
217C8×C11—24no—
218C11⋊C8—42no—
219C23×D4C2×D1111yescharacteristic
220C22×M16—111no—
221C22×M16C2×D1111yescharacteristic
222C2×#117—111no—
223C2×#117C2×D1111yescharacteristic
224C22×C4⋊C4—111no—
225C22×C22⋊C4—222no—
226C22×C42—111no—
227#428—224no—
228C2×#107—112no—
229C2×#106—112no—
230#418—224no—
231#418Dic1118yescomplemented
232C2×#102—112no—
233C2×#102—112no—
234C2×#102C2×D1114yes—
235#390—114no—
236#390—221no—
237#390—221no—
238C4×C4⋊C4—112no—
239C4×C4⋊C4—112no—
240C4×C22⋊C4—222no—
241#376—221no—
242C43—221no—
243#340—114no—
244#336—114no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—48no—
250C22×C11—44no—
251C22×C11—816no—
252C22×C11—84no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11#38814yes—
256C22×C11C2×C4×D411yescharacteristic
257C22×C11C2×#12111yescharacteristic
258C22×C11C2×#12311yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)12yes—
260C22×C11#57512yes—
261C4×C11—44no—
262C4×C11#38814yes—
263C4×C11C2×#11711yescharacteristic
264C4×C11C2×C4×D411yescharacteristic
265C4×C11C2×#12411yescharacteristic
266C4×C11C2×#12611yescharacteristic
267Dic11—24no—
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—82no—
272C25—21no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4C2×Dic1114yes—
280C22×D4C22×D1112yes—
281C23×C4—112no—
282C23×C4—221no—
283C23×C4C22×D1111yescharacteristic
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—222no—
289C2×M16C2×Dic1114yes—
290C22×C8—112no—
291C22×C8C22×D1112yes—
292#117—22no—
293#117—114no—
294#117—222no—
295#117C2×Dic1114yes—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22×D1112yes—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—221no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—224no—
307C2×C22⋊C4—448no—
308C2×C42—21no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—112no—
312C2×C42—222no—
313C2×C42—221no—
314C2×C42—222no—
315C2×C42—222no—
316C2×C42—222no—
317#107—224no—
318#106—224no—
319#102—224no—
320#102—224no—
321#102C2×Dic11116yescomplemented
322#95—222no—
323#95—222no—
324C2×C11—24no—
325C2×C11—84no—
326C2×C11C2×#38811yescharacteristic
327C2×C11C4×AGL(1,ℤ/8)12yes—
328C2×C11#303811yescharacteristic
329C2×C11#304011yescharacteristic
330C2×C11#309412yes—
331C24—24no—
332C24—22no—
333C24—44no—
334C24—44no—
335C24—42no—
336C24—42no—
337C24D4×D1111yescharacteristic
338C2×D4—28no—
339C2×D4—28no—
340C2×D4—24no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—44no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4—44no—
350C2×D4C22×Dic1114yes—
351C22×C4—22no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—224no—
355C22×C4—224no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—442no—
360C22×C4—444no—
361C22×C4—442no—
362C22×C4#433912yes—
363C22×C4#433912yes—
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1112yes—
366C22×C4#434112yes—
367C22×C4#434112yes—
368C22×C4C22×Dic1112yes—
369C22×C4C23×D1111yescharacteristic
370M16—28no—
371M16—444no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8C22×Dic1114yes—
378C4⋊C4—22no—
379C4⋊C4—112no—
380C4⋊C4—112no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—442no—
386C4⋊C4C22×Dic1114yes—
387C22⋊C4—24no—
388C22⋊C4—224no—
389C22⋊C4—448no—
390C22⋊C4—448no—
391C42—24no—
392C42—222no—
393C42—222no—
394C42—224no—
395C42—222no—
396C42—222no—
397C42—444no—
398C42—444no—
399C11#2106011yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—24no—
403C23—416no—
404C23—42no—
405C23—42no—
406C23—44no—
407C23—44no—
408C23—48no—
409C23—88no—
410C23—84no—
411C23—84no—
412C23#6693612yes—
413C23#6693712yes—
414C23D4×Dic1112yes—
415C23C2×D4×D1111yescharacteristic
416D4—24no—
417D4—24no—
418D4—42no—
419D4—42no—
420D4—48no—
421C2×C4—24no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—114no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—448no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—444no—
437C2×C4—884no—
438C2×C4#6693214yes—
439C2×C4#6693612yes—
440C2×C4#6693712yes—
441C2×C4#6693814yes—
442C2×C4#6697914yes—
443C2×C4D4×Dic1114yes—
444C2×C4D4×Dic1112yes—
445C2×C4C2×#433911yescharacteristic
446C2×C4C2×#433911yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C2×C4C2×#434111yescharacteristic
449C2×C4C2×#434111yescharacteristic
450C2×C4C23×Dic1111yescharacteristic
451C8—24no—
452C8—442no—
453C22—24no—
454C22—22no—
455C22—22no—
456C22—24no—
457C22—48no—
458C22—44no—
459C22—816no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22#1062256414yes—
464C22C2×#6693611yescharacteristic
465C22C2×#6693711yescharacteristic
466C22D11×AGL(1,ℤ/8)12yes—
467C22#1062330412yes—
468C22C2×D4×Dic1111yescharacteristic
469C4—44no—
470C4—224no—
471C4—442no—
472C4—442no—
473C4—442no—
474C4—882no—
475C4#1062256414yes—
476C4C2×#6693211yescharacteristic
477C4C2×#6693811yescharacteristic
478C4C2×#6697911yescharacteristic
479C4C2×D4×Dic1111yescharacteristic
480C2—24no—
481C2—84no—
482C2C2×#1062256411yescharacteristic
483C2AGL(1,ℤ/8)×Dic1112yes—
484C2#1307809511yescharacteristic
485C2#1307810911yescharacteristic
486C2#1307855412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#21060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#10622734C2semidirect
4. #117×Dic11C2semidirect
5. #13069245C2semidirect
6. #13069238C2semidirect
7. #13068337C2semidirect
8. #13068309C2semidirect
18. C11×#418C4semidirect
27. C2×#66882C22semidirect
28. C2×#66881C22semidirect
29. C4⋊C4×Dic11C22semidirect
30. C4⋊C4×Dic11C22semidirect
34. #10622188C22semidirect
35. #10622167C22semidirect
81. C11×#102C2×C4semidirect
231. #418Dic11semidirect
321. #102C2×Dic11semidirect
399. C11#21060semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C2×#106228282
C2×#106228342
#117×Dic112
#130692452
#130692382
#130683372
#130683092
C2×C11×#4182
#2106011