Finite Group Databasebeta

← #14803638

Subgroups — #14803638

Order 2816.

894 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×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3#13073569C211yesmaximal, characteristic
4#13071674C211yesmaximal, characteristic, complemented
5#13070028C212yesmaximal, complemented
6#13069932C212yesmaximal
7#13069568C211yesmaximal, characteristic, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13068968C212yesmaximal
10#13068620C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324C2212yes—
14C2×#66977—21no—
15C2×#66977—21no—
16C2×#66940C2212yes—
17C2×#66922C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834C2212yes—
24C2×#66880C2212yes—
25C2×#66880C2212yes—
26C2×Dic11⋊C8C2212yes—
27#10622632—24no—
28#10622589C2212yes—
29#10622587C2212yes—
30C2×#66874C2212yes—
31#10622562—22no—
32C4×C4⋊Dic11—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622294—24no—
37#10622266—22no—
38C11×#340C2211yescharacteristic
39C11×#340C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×Dic22—21no—
46C22×Dic22C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×#4324—24no—
60C2×#4324—24no—
61C2×#4324—42no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2312yes—
68#66977—44no—
69#66977—44no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76#66940—24no—
77#66940—42no—
78#66922—22no—
79#66922—22no—
80#66922—22no—
81#66922D414yes—
82C11×#102—22no—
83C11×#102—22no—
84C4×C8×C11—22no—
85C11×#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89#66880—24no—
90#66880—24no—
91Dic11⋊C8—42no—
92#66874—24no—
93C4⋊(C11⋊C8)—22no—
94#25320—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11#4112yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
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—22no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C2×Dic22C2×D414yes—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4#4112yes—
136C11×C22⋊C4—42no—
137C42×C11—42no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140C22⋊Dic11—44no—
141C22⋊Dic11—44no—
142#4324—48no—
143C4⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11SD1614yescomplemented
150Dic11⋊C4—44no—
151Dic11⋊C4—44no—
152Dic11⋊C4—44no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—44no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×#487—111no—
160C2×#461—111no—
161#2542—111no—
162#2365—111no—
163#2072—112no—
164#2055—112no—
165#1988—111no—
166#1939—111no—
167#1880—112no—
168#1803—112no—
169C4×#102D1111yescharacteristic
170C23×C11—22no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11C22×D411yescharacteristic
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
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—24no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C2×SD1614yes—
216Dic22—24no—
217Dic22—24no—
218Dic22—42no—
219Dic22—42no—
220Dic22—84no—
221C8×C11—41no—
222C8×C11—41no—
223C11⋊C8—42no—
224C22×SD16—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8—111no—
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—221no—
229C2×C4×Q8—112no—
230C2×C4×D4C2×D1111yescharacteristic
231#487—224no—
232#461—224no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—112no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#102C2×D1111yescharacteristic
239C2×#102C2×D1111yescharacteristic
240C2×C4×C8C2×D1111yescharacteristic
241#399—222no—
242#391—112no—
243#390—112no—
244#389—221no—
245#387—222no—
246#384—112no—
247C4×C4⋊C4—111no—
248C4×C4⋊C4—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—112no—
251#340—112no—
252#340C2×D1111yescharacteristic
253#340C2×D1111yescharacteristic
254#336—112no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11C2×#12111yescharacteristic
263C22×C11#54611yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11C22×SD1611yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11#57811yescharacteristic
268C22×C11#57811yescharacteristic
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11#46014yes—
274C4×C11#52911yescharacteristic
275C4×C11#54211yescharacteristic
276C4×C11#54611yescharacteristic
277C4×C11#54711yescharacteristic
278Dic11—24no—
279Dic11—42no—
280Dic11—44no—
281Dic11—82no—
282C22×Q8—112no—
283C22×Q8—221no—
284C22×D4C22×D1111yescharacteristic
285C23×C4—21no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—114no—
293C4⋊Q8—222no—
294C4⋊Q8—222no—
295C4⋊Q8—222no—
296C22⋊Q8—444no—
297C22⋊Q8—444no—
298C4×Q8—224no—
299C4×Q8—442no—
300C4×D4—22no—
301C4×D4—22no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C42—21no—
318C2×C42—112no—
319C2×C42—222no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322C4⋊C8—442no—
323#103—224no—
324#103—224no—
325#103—224no—
326#102—22no—
327#102—22no—
328C4×C8—22no—
329#95—21no—
330#95—112no—
331#95—222no—
332#95—222no—
333C2×C11—82no—
334C2×C11#242711yescharacteristic
335C2×C11C2×#46011yescharacteristic
336C2×C11#304411yescharacteristic
337C2×C11#329811yescharacteristic
338C2×C11#333011yescharacteristic
339C2×C11#335911yescharacteristic
340C2×C11#336711yescharacteristic
341C24—21no—
342C2×Q8—114no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4#433912yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370SD16—448no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—114no—
386C4⋊C4—224no—
387C4⋊C4—224no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—444no—
392C4⋊C4—444no—
393C4⋊C4—444no—
394C4⋊C4—442no—
395C4⋊C4#433912yes—
396C22⋊C4—42no—
397C22⋊C4—444no—
398C22⋊C4—444no—
399C42—42no—
400C42—222no—
401C42—222no—
402C42—444no—
403C42#433912yes—
404C42D4×D1112yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—22no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23C2×D4×D1111yescharacteristic
414Q8—224no—
415Q8—224no—
416Q8—442no—
417Q8—442no—
418Q8—884no—
419D4—22no—
420D4—22no—
421D4—41no—
422D4—41no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—84no—
435C2×C4—114no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—224no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4#6693712yes—
448C2×C4#6693712yes—
449C2×C4#6696412yes—
450C2×C4SD16×D1112yes—
451C2×C4C2×#433911yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4#6704211yescharacteristic
456C2×C4#6704311yescharacteristic
457C8—41no—
458C8—41no—
459C8—442no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×#6693711yescharacteristic
468C22#1062308111yescharacteristic
469C22#1062308311yescharacteristic
470C22C2×#6696411yescharacteristic
471C22C2×SD16×D1111yescharacteristic
472C22#1062330211yescharacteristic
473C22#1062330211yescharacteristic
474C4—22no—
475C4—42no—
476C4—81no—
477C4—81no—
478C4—224no—
479C4—444no—
480C4—442no—
481C4—882no—
482C4#1062237514yes—
483C4#1062301011yescharacteristic
484C4#1062306511yescharacteristic
485C4#1062308111yescharacteristic
486C4#1062308211yescharacteristic
487C2—82no—
488C2#1307219311yescharacteristic
489C2C2×#1062237511yescharacteristic
490C2#1307814911yescharacteristic
491C2#1308048311yescharacteristic
492C2#1308092311yescharacteristic
493C2#1308125611yescharacteristic
494C2#1308133211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC4×#102D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
4. #13071674C2semidirect
5. #13070028C2semidirect
7. #13069568C2semidirect
8. #13069334C2semidirect
10. #13068620C2semidirect
149. C4⋊Dic11SD16semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106226322
#130735692
#130716742
#130700282
#130699322
#130695682
#130693342
#130689682
#130686202
C4×C11×#1022
#2532011