Finite Group Databasebeta

← #14796419

Subgroups — #14796419

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3#13073569C211yesmaximal, characteristic
4#13071528C211yesmaximal, characteristic, complemented
5#13070096C212yesmaximal, complemented
6#13069988C212yesmaximal
7#13069576C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068968C212yesmaximal
10#13068620C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324C2211yescharacteristic
14C2×#66977—21no—
15C2×#66977—21no—
16C2×#66940C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21C11×#384C2211yescharacteristic
22#10622834C2212yes—
23C2×#66896C2211yescharacteristic
24C2×#66881C2212yes—
25C2×#66880C2212yes—
26C2×Dic11⋊C8C2212yes—
27C4×#4324—24no—
28#10622589—21no—
29#10622589C2212yes—
30C4⋊C4×Dic11—21no—
31#10622586C2212yes—
32#10622585—22no—
33C2×#66874C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35#10622562—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622464—24no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×Dic22—21no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×#4324—22no—
59C2×#4324—22no—
60C2×#4324Q814yescomplemented
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66#66977—44no—
67#66977—44no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78#66940—24no—
79#66940—42no—
80#66922—22no—
81#66922—22no—
82C4×Dic22—22no—
83C4×Dic22D414yes—
84C11×C4⋊C8—22no—
85C11×#102—42no—
86#66896—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89#66881—24no—
90#66880—24no—
91Dic11⋊C8—42no—
92#66874—22no—
93#66872—22no—
94C4×C11⋊C8—22no—
95#24813—111nomaximal, Sylow
96C24×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C2×Q812yes—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—42no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22C2×D412yes—
123C2×Dic22C2×Q812yes—
124C2×Dic22#4112yes—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—81no—
134C11×C22⋊C4—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137C22⋊Dic11—44no—
138C22⋊Dic11—44no—
139#4324—28no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11SD1614yescomplemented
146C4⋊Dic11C2×D412yes—
147Dic11⋊C4—24no—
148Dic11⋊C4—44no—
149Dic11⋊C4—44no—
150Dic11⋊C4—44no—
151Dic11⋊C4—82no—
152C4×Dic11—24no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—44no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8C2×Q812yes—
162C2×#475—111no—
163C2×C4×SD16—111no—
164#2542—111no—
165Q8×C4⋊C4—111no—
166#2084—112no—
167#2065—112no—
168#1990—111no—
169#1939—111no—
170#1880—112no—
171#1803—112no—
172#1802D1111yescharacteristic
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—84no—
194C2×C4×C11#12112yes—
195C2×C4×C11#12112yes—
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×Q811yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11C2×SD1614yes—
219Dic22—22no—
220Dic22—22no—
221Dic22—22no—
222Dic22—84no—
223Dic22C22⋊Q814yescomplemented
224C8×C11—42no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227C22×SD16—111no—
228C2×C4⋊Q8—111no—
229C2×C22⋊Q8—221no—
230C2×C22⋊Q8—221no—
231C2×C4×Q8—112no—
232C2×C4×Q8—111no—
233C2×C4×D4C2×D1111yescharacteristic
234#475—224no—
235C4×SD16—224no—
236C2×#106—112no—
237C2×#106—111no—
238C2×C4⋊C8—112no—
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×#103—112no—
241C2×#103—111no—
242C2×#102—111no—
243C2×#102C2×D1112yes—
244C2×C4×C8—111no—
245#399—222no—
246#390—112no—
247#389—112no—
248#389—222no—
249#384—112no—
250#384—221no—
251#384C2×D1111yescharacteristic
252C4×C4⋊C4—111no—
253C4×C4⋊C4—221no—
254#340—112no—
255#340—112no—
256#340C2×D1112yes—
257#336—112no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11#57711yescharacteristic
271C22×C11#57811yescharacteristic
272C4×C11—22no—
273C4×C11—82no—
274C4×C11—81no—
275C4×C11#46014yes—
276C4×C11C2×C22⋊Q811yescharacteristic
277C4×C11#53711yescharacteristic
278C4×C11#55211yescharacteristic
279C4×C11#55411yescharacteristic
280Dic11—24no—
281Dic11—24no—
282Dic11—42no—
283Dic11—42no—
284Dic11—82no—
285C22×Q8—111no—
286C22×Q8—221no—
287C22×D4C22×D1111yescharacteristic
288C23×C4—21no—
289C2×SD16—114no—
290C2×SD16—222no—
291C2×SD16—222no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8C22×D1112yes—
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297C22⋊Q8—444no—
298C22⋊Q8—444no—
299C4×Q8—114no—
300C4×Q8—222no—
301C4×Q8—224no—
302C4×Q8—442no—
303C4×D4—22no—
304C4×D4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C4⋊C4C22×D1112yes—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C42—112no—
323C2×C42—221no—
324C2×C42—222no—
325C2×C42C22×D1111yescharacteristic
326#106—222no—
327#106—224no—
328C4⋊C8—22no—
329C4⋊C8—442no—
330#103—222no—
331#103—224no—
332#102—42no—
333#102—222no—
334C4×C8—222no—
335#95—112no—
336#95—222no—
337C2×C11—82no—
338C2×C11#241711yescharacteristic
339C2×C11C2×#46011yescharacteristic
340C2×C11#304611yescharacteristic
341C2×C11#329811yescharacteristic
342C2×C11#333211yescharacteristic
343C2×C11Q8×SD1611yescharacteristic
344C2×C11#338611yescharacteristic
345C24—21no—
346C2×Q8—112no—
347C2×Q8—112no—
348C2×Q8—112no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×Q8—442no—
353C2×Q8—442no—
354C2×Q8—442no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4Q8×D1112yes—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—222no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—228no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—112no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—81no—
390C4⋊C4—114no—
391C4⋊C4—112no—
392C4⋊C4—224no—
393C4⋊C4—222no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—444no—
398C4⋊C4—444no—
399C4⋊C4—444no—
400C4⋊C4—442no—
401C4⋊C4—882no—
402C22⋊C4—42no—
403C22⋊C4—444no—
404C22⋊C4—444no—
405C42—224no—
406C42—222no—
407C42—222no—
408C42—444no—
409C42#433912yes—
410C42D4×D1112yes—
411C11#2481311yescharacteristic, complemented, Sylow
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23C2×D4×D1111yescharacteristic
420Q8—114no—
421Q8—222no—
422Q8—222no—
423Q8—222no—
424Q8—884no—
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—84no—
438C2×C4—114no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4#6693712yes—
454C2×C4#6693712yes—
455C2×C4#6696412yes—
456C2×C4SD16×D1112yes—
457C2×C4C2×#433911yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#6703711yescharacteristic
460C2×C4C2×Q8×D1111yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#6704311yescharacteristic
463C8—42no—
464C8—222no—
465C8—441no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C2×#6693711yescharacteristic
474C22#1062314311yescharacteristic
475C22#1062316311yescharacteristic
476C22C2×#6696411yescharacteristic
477C22C2×SD16×D1111yescharacteristic
478C22#1062330611yescharacteristic
479C22#1062331011yescharacteristic
480C4—22no—
481C4—81no—
482C4—82no—
483C4—224no—
484C4—224no—
485C4—442no—
486C4—442no—
487C4—882no—
488C4#1062237514yes—
489C4#1062304211yescharacteristic
490C4#1062306011yescharacteristic
491C4#1062313911yescharacteristic
492C4D11×C22⋊Q811yescharacteristic
493C2—82no—
494C2#1307206911yescharacteristic
495C2C2×#1062237511yescharacteristic
496C2#1307816511yescharacteristic
497C2#1308048411yescharacteristic
498C2#1308094611yescharacteristic
499C2#1308147111yescharacteristic
500C2#1308154111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1802D11
hypocenterC11#24813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
4. #13071528C2semidirect
5. #13070096C2semidirect
7. #13069576C2semidirect
8. #13069332C2semidirect
10. #13068620C2semidirect
60. C2×#4324Q8semidirect
145. C4⋊Dic11SD16semidirect
223. Dic22C22⋊Q8semidirect
411. C11#24813semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C2×C4×#43242
#130735692
#130715282
#130700962
#130699882
#130695762
#130693322
#130689682
#130686202
C11×#18022
#2481311