Finite Group Databasebeta

← #14758665

Subgroups — #14758665

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3C4×C4⋊C4×D11C211yesmaximal, characteristic
4#13069377C211yesmaximal, characteristic, complemented
5#13069375C211yesmaximal, characteristic, complemented
6#13069374C211yesmaximal, characteristic, complemented
7#13068807C212yesmaximal
8#13068805C212yesmaximal
9#13068516C212yesmaximal, complemented
10#13068512C212yesmaximal, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×C4⋊C4×D11C2211yescharacteristic
14C2×C4⋊C4×D11C2211yescharacteristic
15C2×C42×D11—21no—
16C2×C42×D11C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66882C2212yes—
23C2×#66879C2212yes—
24#10622600—21no—
25#10622600C2212yes—
26#10622590—21no—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11C2211yescharacteristic
29C4⋊C4×Dic11C2211yescharacteristic
30C4⋊C4×Dic11C2212yes—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622448C418yescomplemented
38D11×#95—21no—
39#10622262—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×C4×D11—21no—
45C22×C4×D11—21no—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66945—44no—
74C4⋊C4×D11—22no—
75C4⋊C4×D11—22no—
76C4⋊C4×D11—22no—
77C4⋊C4×D11—22no—
78C42×D11—44no—
79C42×D11C2×C414yes—
80C42×D11Q814yes—
81C11×#106—24no—
82C11×C4⋊C8C2×C414yescomplemented
83C11×#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89(C2×D11)⋊C8C2×C418yes—
90#66882—24no—
91#66879C2×C418yescomplemented
92#66872—24no—
93#66871—24no—
94C4⋊(C11⋊C8)C2×C414yescomplemented
95#21365—111nomaximal, Sylow
96C23×D11C2×D411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C2×C4×D11—24no—
110C2×C4×D11—24no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11C4⋊C414yes—
124C2×C4×D11C4⋊C414yes—
125C2×C4×D11C22×C412yes—
126C2×C4×D11C2×Q812yes—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C22×C414yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4#4112yes—
137C11×C4⋊C4#4112yes—
138C42×C11—42no—
139C42×C11C22×C412yes—
140C42×C11C2×Q812yes—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—42no—
147C4⋊Dic11—42no—
148C4⋊Dic11#4112yes—
149C4⋊Dic11#4112yes—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152C4×Dic11—42no—
153C4×Dic11—42no—
154C4×Dic11—44no—
155C4×Dic11—42no—
156C4×Dic11C4⋊C414yes—
157C4×Dic11C4⋊C414yes—
158C4×Dic11C22×C412yes—
159C4×Dic11C2×Q812yes—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C22×C414yes—
163C2×#432—111no—
164#2285—111no—
165C2×C4×C4⋊C4—111no—
166#1948—111no—
167#1948D1111yescharacteristic, complemented
168#1947—111no—
169#1947—111no—
170#1853—112no—
171#1852—112no—
172#1776—112no—
173#1776—112no—
174C23×C11C22×D411yescharacteristic
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11C2×C4⋊C412yes—
180C22×D11AGL(1,ℤ/8)12yes—
181C22×D11#13712yes—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C2×C4⋊C412yes—
194C2×C4×C11C2×C4⋊C412yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×Q811yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11C2×C4⋊C412yes—
219C2×Dic11C2×C4⋊C412yes—
220C2×Dic11C2×C4⋊C412yes—
221C4×D11—28no—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—28no—
227C4×D11—48no—
228C4×D11—48no—
229C8×C11—24no—
230C11⋊C8—24no—
231C2×#117—221no—
232C22×C4⋊C4—111no—
233C22×C4⋊C4—111no—
234C22×C42—111no—
235C22×C42—221no—
236#432—118no—
237C2×#107—112no—
238C2×#107—112no—
239C2×#106—112no—
240C2×#106C2×D1112yes—
241C2×C4⋊C8—111no—
242C2×C4⋊C8C2×D1111yescharacteristic
243C2×C22⋊C8—112no—
244C2×#97—112no—
245#384—111no—
246#384C2×D1111yescharacteristic
247#382—221no—
248#380—112no—
249#380—221no—
250C4×C4⋊C4—111no—
251C4×C4⋊C4—111no—
252C4×C4⋊C4—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4—221no—
255C4×C4⋊C4—221no—
256C4×C4⋊C4—221no—
257C4×C4⋊C4C2×D1111yescharacteristic
258C2×#95—221no—
259#340—112no—
260#340—112no—
261#340—112no—
262#340C2×D1112yes—
263C22×C11C22×C4⋊C411yescharacteristic
264C22×C11#52511yescharacteristic
265C22×C11#52511yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—22no—
275C2×D11—22no—
276C2×D11#42814yes—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—82no—
281C4×C11#42814yes—
282C4×C11C4×#4111yescharacteristic
283C4×C11C4×#4111yescharacteristic
284C4×C11#53311yescharacteristic
285C4×C11#53311yescharacteristic
286Dic11—22no—
287Dic11—22no—
288Dic11—22no—
289Dic11—42no—
290Dic11—42no—
291Dic11—82no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—221no—
296C23×C4—221no—
297C22×C8—112no—
298C22×C8C22×D1112yes—
299#117—444no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4C22×D1112yes—
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C22⋊C4—222no—
317C2×C42—21no—
318C2×C42—111no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—114no—
322C2×C42—114no—
323C2×C42—222no—
324C2×C42—221no—
325C2×C42—221no—
326C2×C42—221no—
327C2×C42—444no—
328C2×C42C22×D1111yescharacteristic
329#107—224no—
330#107—224no—
331#106—24no—
332#106—224no—
333C4⋊C8—114no—
334C4⋊C8C4×D1114yescomplemented
335C22⋊C8—118no—
336#97—118no—
337#95—21no—
338#95—221no—
339#95—221no—
340#95—222no—
341#95—222no—
342#95—221no—
343C2×C11#229611yescharacteristic
344C2×C11C2×#42811yescharacteristic
345C2×C11C2×#42811yescharacteristic
346C2×C11#310911yescharacteristic
347C2×C11#311011yescharacteristic
348C2×C11#311211yescharacteristic
349C2×C11#311311yescharacteristic
350D11—24no—
351C24—111no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—224no—
365C22×C4—224no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—222no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4D4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4C23×D1111yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—114no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8C2×C4×D1114yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—112no—
395C4⋊C4—112no—
396C4⋊C4—224no—
397C4⋊C4—224no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—442no—
403C4⋊C4—442no—
404C4⋊C4#434112yes—
405C4⋊C4#434312yes—
406C22⋊C4—444no—
407C42—42no—
408C42—114no—
409C42—114no—
410C42—112no—
411C42—112no—
412C42—442no—
413C42—442no—
414C42—444no—
415C42—442no—
416C42C2×C4×D1112yes—
417C42Q8×D1112yes—
418C11#2136511yescharacteristic, complemented, Sylow
419C23—112no—
420C23—112no—
421C23—112no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23C2×D4×D1111yescharacteristic
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—112no—
441C2×C4—228no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—228no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—448no—
456C2×C4—448no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4C4⋊C4×D1112yes—
465C2×C4C4⋊C4×D1112yes—
466C2×C4#6696712yes—
467C2×C4#6696812yes—
468C2×C4C22×C4×D1111yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C2×C4C2×Q8×D1111yescharacteristic
471C2×C4C2×#434311yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C8—24no—
475C8—224no—
476C22—114no—
477C22—222no—
478C22—222no—
479C22—222no—
480C22—222no—
481C22—222no—
482C22—222no—
483C22C2×C4⋊C4×D1111yescharacteristic
484C22#1062313711yescharacteristic
485C22#1062315811yescharacteristic
486C22C2×#6696711yescharacteristic
487C22C2×#6696811yescharacteristic
488C22D11×AGL(1,ℤ/8)11yescharacteristic
489C22D11×#13711yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—222no—
495C4—222no—
496C4—222no—
497C4—442no—
498C4—442no—
499C4—882no—
500C4#1062247414yes—
501C4C4×#434111yescharacteristic
502C4C4×#434311yescharacteristic
503C4#1062321911yescharacteristic
504C4#1062325911yescharacteristic
505C2—224no—
506C2#1307109711yescharacteristic
507C2D11×#42811yescharacteristic
508C2C2×#1062247411yescharacteristic
509C2#1307870911yescharacteristic
510C2#1307871411yescharacteristic
511C2#1307873711yescharacteristic
512C2#1307874811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1948D11
hypocenterC11#21365
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. #13069377C2semidirect
5. #13069375C2semidirect
6. #13069374C2semidirect
9. #13068516C2semidirect
10. #13068512C2semidirect
11. C11×#1948C2semidirect
37. #10622448C4semidirect
82. C11×C4⋊C8C2×C4semidirect
91. #66879C2×C4semidirect
94. C4⋊(C11⋊C8)C2×C4semidirect
167. #1948D11semidirect
334. C4⋊C8C4×D11semidirect
418. C11#21365semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
#130710212
C4×C4⋊C4×D112
#130693772
#130693752
#130693742
#130688072
#130688052
#130685162
#130685122
C11×#19482
#2136511