Finite Group Databasebeta

← #14765445

Subgroups — #14765445

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic11C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic, complemented
3#13069360C212yesmaximal, complemented
4#13069315C212yesmaximal, complemented
5#13069196C212yesmaximal, complemented
6#13068934C211yesmaximal, characteristic
7#13068865C212yesmaximal, complemented
8#13068806C211yesmaximal, characteristic, complemented
9#13068706C211yesmaximal, characteristic, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C2×C11×#481C211yesmaximal, characteristic
12C2×C11×#121C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×D4×Dic11—21no—
15C2×D4×Dic11C2211yescharacteristic
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C11×#481C418yescomplemented
20C2×C11×#106C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×C22⋊C8C2211yescharacteristic
23#10622834C2211yescharacteristic
24#10622833—21no—
25C2×#66896C2212yes—
26#10622825C2211yescharacteristic
27C2×C11⋊#95—21no—
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66882C2212yes—
30C2×#66879C2212yes—
31#10622598—21no—
32#10622598—21no—
33#10622598C2212yes—
34#10622598C2211yescharacteristic
35#10622598C2212yes—
36C4⋊C4×Dic11C2211yescharacteristic
37#10622564—21no—
38C22⋊C4×Dic11—21no—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×C8×C11C2312yes—
53C11×#121—22no—
54C11×#121C2×C414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yescomplemented
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65D4×Dic11—42no—
66D4×Dic11—44no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—42no—
72C2×C4⋊Dic11—44no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4×Dic11—21no—
77C2×C4×Dic11—42no—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83C11×#106C2×C418yescomplemented
84C11×#102C2×C418yescomplemented
85C11×C22⋊C8C2×C414yescomplemented
86#66896—42no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C22⋊(C11⋊C8)—22no—
93#66882—42no—
94#66879—42no—
95#22082—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11C2×D411yescharacteristic
98C2×D4×C11—24no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C22×C414yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C414yes—
142C11×C4⋊C4C22×C412yes—
143C11×C22⋊C4—24no—
144C22⋊Dic11—42no—
145C22⋊Dic11—42no—
146C22⋊Dic11—42no—
147C22⋊Dic11—42no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—42no—
153C4⋊Dic11—44no—
154C4⋊Dic11—42no—
155C4⋊Dic11—44no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—42no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×#481D1111yescharacteristic
165C4×#121—111no—
166C2×#389—111no—
167#1944—112no—
168#1936—112no—
169#1919—112no—
170#1874—111no—
171#1862—112no—
172#1852—111no—
173#1824—111no—
174#1749—111no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C4×D412yes—
187C23×C11AGL(1,ℤ/8)12yes—
188C23×C11#13712yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—24no—
191D4×C11—48no—
192D4×C11—42no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—48no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)12yes—
208C2×C4×C112−1+412yes—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—44no—
221C2×Dic11—44no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—84no—
232C2×Dic11—84no—
233C2×Dic11AGL(1,ℤ/8)12yes—
234C8×C11—24no—
235C11⋊C8—42no—
236C2×#121C2×D1111yescharacteristic
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C22×C4⋊C4—111no—
240C22×C4⋊C4—221no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C42—111no—
243#481Dic1118yescomplemented
244C2×#107—112no—
245C2×#106C2×D1112yes—
246C2×#102—112no—
247C2×#102C2×D1112yes—
248C2×C22⋊C8—111no—
249C2×C22⋊C8C2×D1111yescharacteristic
250C2×#97—112no—
251#390—111no—
252#389—112no—
253#389—112no—
254#389—111no—
255#389—221no—
256#389—221no—
257#388—221no—
258#386—221no—
259#380—111no—
260C4×C4⋊C4—111no—
261C4×C22⋊C4—221no—
262C2×#95—221no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11#44014yes—
282C22×C11C2×C4×D411yescharacteristic
283C22×C11#53411yescharacteristic
284C22×C11#53611yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57511yescharacteristic
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—44no—
292C4×C11#52012yes—
293C4×C11#53912yes—
294Dic11—22no—
295Dic11—41no—
296Dic11—41no—
297Dic11—41no—
298Dic11—82no—
299Dic11—81no—
300Dic11—81no—
301C22×D4—21no—
302C22×D4C22×D1111yescharacteristic
303C23×C4—21no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—221no—
307C23×C4—221no—
308C23×C4C22×D1111yescharacteristic
309C22×C8—112no—
310C22×C8C22×D1112yes—
311#121—22no—
312#121C2×Dic1114yes—
313C4×D4—442no—
314C4×D4—444no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—442no—
325C2×C4⋊C4—444no—
326C2×C4⋊C4C2×Dic1114yescomplemented
327C2×C4⋊C4C22×D1112yes—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—221no—
339C2×C42—442no—
340#107—442no—
341#106C2×Dic1118yescomplemented
342#102—442no—
343#102C2×Dic1118yescomplemented
344C22⋊C8—222no—
345C22⋊C8C2×Dic1114yescomplemented
346#97—442no—
347#95—222no—
348#95—222no—
349#95—221no—
350#95—221no—
351#95—221no—
352C2×C11—24no—
353C2×C11—82no—
354C2×C11#232211yescharacteristic
355C2×C11C2×#44011yescharacteristic
356C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
357C2×C11#319211yescharacteristic
358C2×C11#319611yescharacteristic
359C2×C11#323411yescharacteristic
360C2×C11#323911yescharacteristic
361C24—21no—
362C24D4×D1111yescharacteristic
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4C22×Dic1112yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—442no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4D4×D1111yescharacteristic
397C22×C4#434112yes—
398C22×C4C22×Dic1112yes—
399C22×C4C23×D1111yescharacteristic
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8C22×Dic1114yes—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—442no—
414C4⋊C4—444no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C4⋊C4C22×Dic1114yes—
418C4⋊C4C22×Dic1112yes—
419C22⋊C4—24no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C22⋊C4—442no—
423C22⋊C4—442no—
424C42—222no—
425C42—222no—
426C42—441no—
427C42—441no—
428C42—442no—
429C11#2208211yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23#6696712yes—
442C23#6696812yes—
443C23D4×Dic1112yes—
444C23C2×D4×D1111yescharacteristic
445D4—24no—
446D4—48no—
447D4—42no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—48no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—112no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—444no—
472C2×C4—444no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—442no—
482C2×C4—884no—
483C2×C4—884no—
484C2×C4D4×Dic1112yes—
485C2×C4C2×#434111yescharacteristic
486C2×C4#6704212yes—
487C2×C4#6704312yes—
488C2×C4C23×Dic1111yescharacteristic
489C8—24no—
490C8—442no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22#1062277714yes—
505C22#1062317911yescharacteristic
506C22#1062318411yescharacteristic
507C22C2×#6696711yescharacteristic
508C22C2×#6696811yescharacteristic
509C22D11×AGL(1,ℤ/8)11yescharacteristic
510C22#1062330411yescharacteristic
511C22C2×D4×Dic1111yescharacteristic
512C4—22no—
513C4—42no—
514C4—44no—
515C4—222no—
516C4—441no—
517C4—441no—
518C4—441no—
519C4—881no—
520C4—882no—
521C4—881no—
522C4#1062319612yes—
523C4#1062335812yes—
524C2—24no—
525C2—82no—
526C2#1307128811yescharacteristic
527C2C2×#1062277711yescharacteristic
528C2AGL(1,ℤ/8)×Dic1111yescharacteristic
529C2#1307941511yescharacteristic
530C2#1307944511yescharacteristic
531C2#1307980511yescharacteristic
532C2#1307984411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#481D11
hypocenterC11#22082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#10622598C2semidirect
3. #13069360C2semidirect
4. #13069315C2semidirect
5. #13069196C2semidirect
7. #13068865C2semidirect
8. #13068806C2semidirect
9. #13068706C2semidirect
10. #13068380C2semidirect
19. C11×#481C4semidirect
57. C2×C11×C4⋊C4C2×C4semidirect
83. C11×#106C2×C4semidirect
84. C11×#102C2×C4semidirect
85. C11×C22⋊C8C2×C4semidirect
243. #481Dic11semidirect
326. C2×C4⋊C4C2×Dic11semidirect
341. #106C2×Dic11semidirect
343. #102C2×Dic11semidirect
345. C22⋊C8C2×Dic11semidirect
429. C11#22082semidirect

Maximal subgroups

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

subgroupindex
#121×Dic112
C2×#106225982
#130693602
#130693152
#130691962
#130689342
#130688652
#130688062
#130687062
#130683802
C2×C11×#4812
#2208211