Finite Group Databasebeta

← #14814894

Subgroups — #14814894

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622335C212yesmaximal, complemented
2#13073569C211yesmaximal, characteristic
3D4×C4⋊Dic11C211yesmaximal, characteristic
4#13069820C212yesmaximal, complemented
5#13069820C212yesmaximal, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13068921C212yesmaximal, complemented
10C4×#66882C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11—21no—
14C22×C4⋊Dic11C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2212yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622834—21no—
23#10622825C2212yes—
24C2×#66882C2212yes—
25C2×#66882C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31#10622598—21no—
32#10622589—21no—
33#10622563—22no—
34#10622562—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38#10622335—28no—
39#10622189C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11C2312yes—
44C23×Dic11—22no—
45C22×Dic22C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57D4×Dic11—44no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—42no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70#66977—24no—
71#66977—24no—
72#66977—42no—
73#66977—42no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78#66922—22no—
79#66922—22no—
80C11×C4⋊C8—22no—
81C11×C22⋊C8—24no—
82C11×C22⋊C8—42no—
83C4×C8×C11—22no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87#66882—24no—
88#66882—22no—
89#66882D414yescomplemented
90#66880—24no—
91#66880—24no—
92#66880—42no—
93#66880—42no—
94#26236—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11Q1614yes—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—44no—
116C22×Dic11—44no—
117C22×Dic11—82no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11C2×D412yes—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—24no—
135C42×C11#4112yes—
136C42×C11#4112yes—
137C22⋊Dic11—44no—
138C22⋊Dic11—44no—
139C22⋊Dic11—44no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—44no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11—81no—
152C4⋊Dic11C2×D412yes—
153C4⋊Dic11C2×D412yes—
154C4⋊Dic11#4112yes—
155Dic11⋊C4—44no—
156Dic11⋊C4—44no—
157C4×Dic11—42no—
158C4×Dic11—42no—
159C2×#484—112no—
160#2542—111no—
161D4×C4⋊C4—111no—
162#2036—112no—
163#2036—112no—
164#1981—111no—
165#1956—111no—
166#1954D1111yescharacteristic
167#1947—111no—
168#1872—112no—
169C4×#107—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11C2×Q1614yes—
177C23×C11C22×D411yescharacteristic
178D4×C11—28no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11#12312yes—
189C2×C4×C11#12312yes—
190C2×C4×C11C2×Q1612yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—88no—
217Dic22—42no—
218Dic22—42no—
219Dic22—42no—
220Dic22—42no—
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—42no—
224C2×C4⋊Q8—111no—
225C2×C22⋊Q8—112no—
226C2×C22⋊Q8—112no—
227C2×C4×D4—221no—
228C2×C4×D4C2×D1111yescharacteristic
229C22×C4⋊C4—112no—
230#484—228no—
231C2×#107—111no—
232C2×#107—112no—
233C2×#107—111no—
234C2×C4⋊C8C2×D1111yescharacteristic
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#103—112no—
239C2×C22⋊C8C2×D1112yes—
240C2×C22⋊C8C2×D1112yes—
241C2×C4×C8C2×D1111yescharacteristic
242#399—222no—
243#390—221no—
244#389—221no—
245#385—222no—
246#384—111no—
247#384—221no—
248#380—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—111no—
251#340—111no—
252#340—112no—
253#340—111no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12311yescharacteristic
262C22×C11D4211yescharacteristic
263C22×C11#54611yescharacteristic
264C22×C11C22×Q1611yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—42no—
270C4×C11#48414yescomplemented
271C4×C11#53211yescharacteristic
272C4×C11#54011yescharacteristic
273C4×C11#55011yescharacteristic
274C4×C11#55911yescharacteristic
275Dic11—42no—
276Dic11—42no—
277Dic11—42no—
278Dic11—81no—
279Dic11—82no—
280Dic11—82no—
281C22×Q8—112no—
282C22×D4D4411yescharacteristic
283C23×C4—222no—
284C23×C4C22×D1112yes—
285C22×C8C22×D1111yescharacteristic
286C22×C8C22×D1112yes—
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—222no—
289C4⋊Q8—222no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—442no—
293C22⋊Q8—442no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—444no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—224no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—442no—
311C2×C4⋊C4D4411yescharacteristic
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4D4412yes—
316C2×C42—221no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#107—114no—
320#107—222no—
321#107—224no—
322C4⋊C8—22no—
323#103—224no—
324#103—224no—
325#103—442no—
326#103—442no—
327C22⋊C8—24no—
328C22⋊C8—42no—
329C4×C8—22no—
330#95—221no—
331#95—221no—
332#95—222no—
333C2×C11—44no—
334C2×C11#244511yescharacteristic
335C2×C11C2×#48411yescharacteristic
336C2×C11#309711yescharacteristic
337C2×C11#327211yescharacteristic
338C2×C11D4×Q1611yescharacteristic
339C2×C11#329911yescharacteristic
340C2×C11#333011yescharacteristic
341C24C2×D4412yes—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4Dic4414yes—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—444no—
364C22×C4—444no—
365C22×C4—882no—
366C22×C4C2×D4412yes—
367C22×C4C2×D4411yescharacteristic
368C22×C4C2×D4411yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8D4×D1112yes—
379C4⋊C4—22no—
380C4⋊C4—112no—
381C4⋊C4—112no—
382C4⋊C4—112no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—444no—
391C4⋊C4—444no—
392C4⋊C4—444no—
393C4⋊C4—442no—
394C4⋊C4—442no—
395C4⋊C4—442no—
396C4⋊C4—881no—
397C22⋊C4—24no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—444no—
401C42—442no—
402C42—442no—
403C42#434112yes—
404C42#434112yes—
405C11#2623611yescharacteristic, complemented, Sylow
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23C2×Dic4414yes—
413C23C22×D4411yescharacteristic
414Q8—442no—
415Q8—442no—
416Q8—442no—
417Q8—442no—
418D4—28no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—888no—
447C2×C4#6693912yes—
448C2×C4#6693912yes—
449C2×C4C2×Dic4412yes—
450C2×C4#6696112yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4#6703711yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—22no—
458C8—42no—
459C8—41no—
460C22—24no—
461C22—24no—
462C22—24no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×#6693911yescharacteristic
468C22D4×D4411yescharacteristic
469C22#1062308511yescharacteristic
470C22C22×Dic4411yescharacteristic
471C22C2×#6696111yescharacteristic
472C22#1062328211yescharacteristic
473C22#1062328411yescharacteristic
474C4—22no—
475C4—42no—
476C4—442no—
477C4—442no—
478C4—442no—
479C4—881no—
480C4—882no—
481C4—882no—
482C4#1062233514yescomplemented
483C4#1062312711yescharacteristic
484C4#1062315011yescharacteristic
485C4#1062321211yescharacteristic
486C4#1062324911yescharacteristic
487C2—44no—
488C2#1307237911yescharacteristic
489C2C2×#1062233511yescharacteristic
490C2#1307858611yescharacteristic
491C2#1308021811yescharacteristic
492C2D4×Dic4411yescharacteristic
493C2#1308049311yescharacteristic
494C2#1308092211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#26236
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622335C2semidirect
4. #13069820C2semidirect
5. #13069820C2semidirect
6. #13069538C2semidirect
7. #13069418C2semidirect
8. #13069375C2semidirect
9. #13068921C2semidirect
10. C4×#66882C2semidirect
89. #66882D4semidirect
270. C4×C11#484semidirect
405. C11#26236semidirect
482. C4#10622335semidirect

Maximal subgroups

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

subgroupindex
C2×#106223352
#130735692
D4×C4⋊Dic112
#130698202
#130695382
#130694182
#130693752
#130689212
C4×#668822
C11×#19542
#2623611