Finite Group Databasebeta

← #14756499

Subgroups — #14756499

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622744C211yesmaximal, characteristic
2C2×#10622744C211yesmaximal, characteristic
3#13071099C211yesmaximal, characteristic, complemented
4C2×#10622552C211yesmaximal, characteristic
5#13069313C214yesmaximal, complemented
6#13069299C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C2×C4×C11×M16C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4—22no—
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C4×C11×M16—24no—
19C2×C11×#97C2212yescomplemented
20C2×C4×C8×C11C2212yescomplemented
21#10622823—22no—
22#10622744—24no—
23#10622744C418yescomplemented
24C2×#66885C2214yes—
25C2×#66885C2214yes—
26#10622552—22no—
27#10622552C2212yes—
28#10622552C2212yes—
29C4×Dic11⋊C4—22no—
30#10622541C2212yescomplemented
31#10622541C2212yescomplemented
32#10622189C2214yescomplemented
33#10622189C2214yescomplemented
34C24×D11—21no—
35C23×C4×C11D412yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C22×D44—22no—
39C22×D44—22no—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—21no—
43C22×D44—22no—
44C22×D44C2×C414yes—
45C22×D44C2312yes—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16C2×C414yes—
51C2×C11×M16D414yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—48no—
64#66979—22no—
65#66979—22no—
66#66979—22no—
67#66979C2×C414yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C11×#97—24no—
79C4×C8×C11—24no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66885—28no—
83#66885C2×C4116yescomplemented
84#21095—111nomaximal, Sylow
85C24×C11C2×D411yescharacteristic
86C23×D11—24no—
87C23×D11—22no—
88C23×D11—44no—
89C23×D11—44no—
90C23×D11—42no—
91C23×D11—42no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—42no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—44no—
109C22×Dic11—42no—
110C2×D44—28no—
111C2×D44—24no—
112C2×D44—28no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—42no—
119C2×D44—44no—
120C2×D44—42no—
121C2×D44—44no—
122C2×D44C22×C414yes—
123C11×M16—28no—
124C11×M16—28no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C22×C414yes—
130C2×C8×C11C2×D414yes—
131C42×C11—24no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C22⋊Dic11—24no—
137C22⋊Dic11—42no—
138(C2×D11)⋊C4—48no—
139(C2×D11)⋊C4—48no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—42no—
146C4⋊Dic11C22×C414yes—
147Dic11⋊C4—44no—
148Dic11⋊C4—44no—
149C4×Dic11—24no—
150C4×Dic11—42no—
151C2×#418—111no—
152C2×#418—111no—
153C2×C4×M16D1111yescharacteristic, complemented
154#2296—111no—
155C2×#390—111no—
156#1936—114no—
157#1934—114no—
158#1736—111no—
159#1736—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11C4×D412yes—
163C23×C11#12112yes—
164C23×C11#12412yes—
165C23×C11C22×D411yescharacteristic
166C22×D11—24no—
167C22×D11—416no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—44no—
171C22×D11—44no—
172C22×D11—48no—
173C22×D11—84no—
174C22×D11—84no—
175C22×D11—88no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—48no—
182C2×C4×C11#11714yes—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C4×D414yes—
185C2×C4×C11#12112yes—
186C2×C4×C11#12314yes—
187C2×C4×C11#12412yes—
188C2×C4×C11#12614yes—
189C2×C4×C11AGL(1,ℤ/8)14yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×Dic11—24no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—44no—
203C2×Dic11—42no—
204C2×Dic11—84no—
205D44—24no—
206D44—24no—
207D44—42no—
208D44—42no—
209D44—48no—
210C8×C11—24no—
211C8×C11—24no—
212C23×D4—111no—
213C22×M16C2×D1111yescharacteristic
214C22×M16C2×D1111yescharacteristic
215C2×#117—111no—
216C2×#117—111no—
217C22×C4⋊C4—111no—
218C22×C22⋊C4—222no—
219C22×C42C2×D1111yescharacteristic
220#418—118no—
221#418—224no—
222C2×#102—114no—
223C2×#102—114no—
224C4×M16—24no—
225C2×#97C2×D1112yescomplemented
226C2×C4×C8C2×D1112yescomplemented
227#390—112no—
228#390—112no—
229#390—222no—
230#389—112no—
231#389—112no—
232#385—222no—
233C4×C4⋊C4—222no—
234#340—114no—
235#340—114no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11#38814yes—
241C22×C11C2×C4×D411yescharacteristic
242C22×C11C2×#12111yescharacteristic
243C22×C11C2×#12411yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)12yes—
245C22×C11#57512yes—
246C2×D11—48no—
247C2×D11—44no—
248C2×D11—816no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—84no—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11#38814yes—
255C4×C11C2×#11711yescharacteristic
256C4×C11C2×C4×D411yescharacteristic
257C4×C11C2×#12311yescharacteristic
258C4×C11C2×#12611yescharacteristic
259Dic11—44no—
260Dic11—82no—
261Dic11—82no—
262C25—221no—
263C22×D4—114no—
264C22×D4—112no—
265C22×D4—221no—
266C22×D4—222no—
267C22×D4—222no—
268C22×D4—222no—
269C22×D4—222no—
270C22×D4—222no—
271C23×C4—221no—
272C23×C4D4412yes—
273C23×C4C22×D1111yescharacteristic
274C2×M16—22no—
275C2×M16—22no—
276C2×M16—22no—
277C2×M16—22no—
278C2×M16C4×D1114yes—
279C2×M16C22⋊D1114yes—
280C22×C8C22×D1112yes—
281C22×C8C22×D1112yes—
282#117—114no—
283#117—222no—
284#117—222no—
285#117—222no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—224no—
297C2×C22⋊C4—224no—
298C2×C22⋊C4—448no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—221no—
302C2×C42—221no—
303C2×C42D4412yes—
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306#102—1116no—
307#102—228no—
308#97—24no—
309C4×C8—24no—
310#95—222no—
311#95—222no—
312C2×C11—24no—
313C2×C11C2×#38811yescharacteristic
314C2×C11C4×AGL(1,ℤ/8)12yes—
315C2×C11#305512yes—
316C2×C11#313811yescharacteristic
317C2×C11#314011yescharacteristic
318D11—84no—
319C24—224no—
320C24—222no—
321C24—444no—
322C24—444no—
323C24—442no—
324C24—442no—
325C24C2×D4411yescharacteristic
326C2×D4—114no—
327C2×D4—228no—
328C2×D4—224no—
329C2×D4—228no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—442no—
336C2×D4—444no—
337C2×D4—444no—
338C2×D4—442no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—42no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—444no—
346C22×C4—442no—
347C22×C4C2×C4×D1112yes—
348C22×C4C2×D4412yes—
349C22×C4C2×D4412yes—
350C22×C4C2×D4411yescharacteristic
351C22×C4#433912yes—
352C22×C4#433912yes—
353C22×C4#433912yes—
354C22×C4#433912yes—
355C22×C4C2×C22⋊D1112yes—
356C22×C4C23×D1111yescharacteristic
357M16—28no—
358M16—28no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8C2×C4×D1114yes—
364C2×C8C2×C22⋊D1114yes—
365C4⋊C4—114no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C4⋊C4—442no—
373C4⋊C4—444no—
374C22⋊C4—224no—
375C22⋊C4—448no—
376C22⋊C4—442no—
377C22⋊C4—448no—
378C42—24no—
379C42—21no—
380C42—21no—
381C42—21no—
382C42—21no—
383C42—224no—
384C42—442no—
385C11#2109511yescharacteristic, complemented, Sylow
386C23—22no—
387C23—22no—
388C23—224no—
389C23—4416no—
390C23—442no—
391C23—444no—
392C23—444no—
393C23—448no—
394C23—442no—
395C23—884no—
396C23—888no—
397C23—884no—
398C23C4×D4412yes—
399C23#6692812yes—
400C23#6698312yes—
401C23C22×D4411yescharacteristic
402D4—224no—
403D4—224no—
404D4—442no—
405D4—442no—
406D4—448no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—48no—
413C2×C4—224no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—444no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—884no—
422C2×C4#6692514yes—
423C2×C4C4×D4412yes—
424C2×C4#6692812yes—
425C2×C4#6692914yes—
426C2×C4#6696114yes—
427C2×C4C4×C22⋊D1114yes—
428C2×C4#6698214yes—
429C2×C4#6698312yes—
430C2×C4C22×C4×D1111yescharacteristic
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×#433911yescharacteristic
433C2×C4C2×#433911yescharacteristic
434C2×C4C2×#433911yescharacteristic
435C2×C4C22×C22⋊D1111yescharacteristic
436C8—24no—
437C8—24no—
438C22—24no—
439C22—22no—
440C22—24no—
441C22—22no—
442C22—448no—
443C22—444no—
444C22—8816no—
445C22—882no—
446C22—884no—
447C22—882no—
448C22#1062255314yes—
449C22C2×C4×D4411yescharacteristic
450C22C2×#6692811yescharacteristic
451C22C2×#6696112yes—
452C22#1062327912yes—
453C22C2×#6698311yescharacteristic
454C4—24no—
455C4—42no—
456C4—444no—
457C4—882no—
458C4—882no—
459C4#1062255314yes—
460C4C2×#6692511yescharacteristic
461C4C2×#6692911yescharacteristic
462C4C2×C4×C22⋊D1111yescharacteristic
463C4C2×#6698211yescharacteristic
464C2—24no—
465C2—884no—
466C2C2×#1062255311yescharacteristic
467C2C4×#6696112yes—
468C2#1307823512yes—
469C2#1307899111yescharacteristic
470C2#1307900311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×M16C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×C4×M16D11
hypocenterC11#21095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
3. #13071099C2semidirect
5. #13069313C2semidirect
6. #13069299C2semidirect
7. #13068336C2semidirect
8. #13068336C2semidirect
9. C2×C4×C11×M16C2semidirect
19. C2×C11×#97C22semidirect
20. C2×C4×C8×C11C22semidirect
23. #10622744C4semidirect
30. #10622541C22semidirect
31. #10622541C22semidirect
32. #10622189C22semidirect
33. #10622189C22semidirect
83. #66885C2×C4semidirect
153. C2×C4×M16D11semidirect
225. C2×#97C2×D11semidirect
226. C2×C4×C8C2×D11semidirect
385. C11#21095semidirect

Maximal subgroups

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

subgroupindex
C2×#106227442
#130710992
C2×#106225522
#130693132
#130692992
#130683362
C2×C4×C11×M162
#2109511