Finite Group Databasebeta

← #14803281

Subgroups — #14803281

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2#13073832C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic
4#13069995C212yesmaximal, complemented
5#13069929C212yesmaximal
6#13069472C212yesmaximal
7#13069419C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069289C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#461C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66977—21no—
16C2×C4×Dic22C2211yescharacteristic
17C11×#461—24no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20#10622843C2212yes—
21#10622843C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24#10622834C2212yes—
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622825—21no—
28C2×#66881C2212yes—
29C2×Dic11⋊C8C2212yes—
30C2×C8×Dic11C2212yes—
31#10622595—22no—
32#10622590—21no—
33#10622587—21no—
34#10622586C2212yes—
35#10622561—22no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622443—24no—
40#10622189C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11C2312yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C2×C11×SD16—24no—
48C2×C11×SD16—24no—
49C2×C11×SD16—42no—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68#66977—44no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4D412yes—
71C2×C4×Dic11—21no—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×C4⋊C8D414yes—
78C11×#103—24no—
79#66899—24no—
80#66899—42no—
81#66896—22no—
82#66896—22no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66881—42no—
90Dic11⋊C8—24no—
91C8×Dic11—24no—
92C4×C11⋊C8—22no—
93#25293—111nomaximal, Sylow
94C24×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11#4112yes—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22SD1614yescomplemented
123C11×SD16—48no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C2×D414yes—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C22⋊C4—42no—
132C42×C11C2×D412yes—
133C42×C11#4112yes—
134C22⋊Dic11—44no—
135C22⋊Dic11—82no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—42no—
144C4⋊Dic11—81no—
145Dic11⋊C4—24no—
146Dic11⋊C4—44no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—42no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8#4112yes—
156C2×#461D1111yescharacteristic
157C2×C8×Q8—111no—
158#2568—111no—
159#2538—111no—
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956—111no—
164#1948—111no—
165#1933—112no—
166C4×#102—111no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11C22×D411yescharacteristic
175Q8×C11—42no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—42no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—41no—
182D4×C11—41no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—84no—
192C2×C4×C11#12112yes—
193C2×C4×C11#12112yes—
194C2×C4×C11C2×SD1612yes—
195C2×C4×C11#13512yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11C2×SD1614yes—
217Dic22—28no—
218C8×C11—24no—
219C11⋊C8—22no—
220C11⋊C8—41no—
221C22×SD16C2×D1112yes—
222C2×C4⋊Q8C2×D1111yescharacteristic
223C2×C22⋊Q8—221no—
224C2×C4×Q8—111no—
225C2×C4×D4C2×D1111yescharacteristic
226#461—24no—
227C8×Q8—224no—
228C2×#106—112no—
229C2×C4⋊C8—112no—
230C2×C4⋊C8C2×D1111yescharacteristic
231C2×#103—112no—
232C2×#103—112no—
233C2×#103C2×D1112yes—
234C2×#102—111no—
235C2×#102—111no—
236C2×C4×C8—112no—
237C2×C4×C8—111no—
238#400—222no—
239#396—222no—
240#391—112no—
241#391—112no—
242#391—221no—
243#390—112no—
244#389—112no—
245#384—111no—
246#382—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249#340—112no—
250#340—111no—
251#340—111no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11C2×#12111yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11#55011yescharacteristic
262C22×C11C22×SD1611yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11#57711yescharacteristic
265C22×C11#57811yescharacteristic
266C4×C11—22no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#46514yes—
270C4×C11#52911yescharacteristic
271C4×C11#54211yescharacteristic
272C4×C11#54611yescharacteristic
273C4×C11#54811yescharacteristic
274Dic11—24no—
275Dic11—42no—
276Dic11—81no—
277Dic11—82no—
278Dic11—81no—
279C22×Q8—111no—
280C22×Q8C22×D1112yes—
281C22×D4C22×D1111yescharacteristic
282C23×C4—21no—
283C2×SD16—24no—
284C2×SD16—24no—
285C2×SD16—42no—
286C22×C8—111no—
287C22×C8—111no—
288C22×C8C22×D1112yes—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C22⋊Q8—444no—
292C4×Q8—222no—
293C4×Q8—222no—
294C4×D4—22no—
295C4×D4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—112no—
311C2×C42—221no—
312C2×C42C22×D1111yescharacteristic
313#106—442no—
314C4⋊C8—224no—
315C4⋊C8C22⋊D1114yes—
316#103—24no—
317#103—224no—
318#103—442no—
319#102—222no—
320#102—222no—
321C4×C8—224no—
322C4×C8—222no—
323#95—222no—
324#95—222no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—221no—
329C2×C11—82no—
330C2×C11#242611yescharacteristic
331C2×C11C2×#46511yescharacteristic
332C2×C11#306311yescharacteristic
333C2×C11#335911yescharacteristic
334C2×C11#336011yescharacteristic
335C2×C11#339211yescharacteristic
336C2×C11#339311yescharacteristic
337C24—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—114no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4#434112yes—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—48no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—112no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8C2×C22⋊D1114yes—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—224no—
381C4⋊C4—222no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—221no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—881no—
391C22⋊C4—42no—
392C22⋊C4—444no—
393C22⋊C4—882no—
394C42—222no—
395C42—222no—
396C42—442no—
397C42#434112yes—
398C42C2×C22⋊D1112yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C2×D4×D1111yescharacteristic
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—228no—
413D4—22no—
414D4—22no—
415D4—41no—
416D4—41no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—84no—
426C2×C4—114no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—442no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4SD16×D1112yes—
442C2×C4#6696912yes—
443C2×C4#6699112yes—
444C2×C4#6699112yes—
445C2×C4C2×#434111yescharacteristic
446C2×C4C2×#434111yescharacteristic
447C2×C4#6703711yescharacteristic
448C2×C4#41×D1111yescharacteristic
449C2×C4#6704311yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—24no—
452C8—222no—
453C8—441no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1062312911yescharacteristic
462C22#1062313011yescharacteristic
463C22C2×SD16×D1111yescharacteristic
464C22C2×#6696911yescharacteristic
465C22#1062330911yescharacteristic
466C22#1062331011yescharacteristic
467C22C2×#6699111yescharacteristic
468C4—22no—
469C4—82no—
470C4—81no—
471C4—224no—
472C4—442no—
473C4—881no—
474C4—881no—
475C4—882no—
476C4#1062278414yes—
477C4#1062313111yescharacteristic
478C4#1062313411yescharacteristic
479C4#1062333711yescharacteristic
480C4#1062336211yescharacteristic
481C2—82no—
482C2#1307217811yescharacteristic
483C2C2×#1062278411yescharacteristic
484C2#1307830111yescharacteristic
485C2#1308125311yescharacteristic
486C2#1308126911yescharacteristic
487C2#1308159211yescharacteristic
488C2#1308160311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#461D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
2. #13073832C2semidirect
4. #13069995C2semidirect
7. #13069419C2semidirect
8. #13069380C2semidirect
9. #13069289C2semidirect
122. C2×Dic22SD16semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130738322
#130735382
#130699952
#130699292
#130694722
#130694192
#130693802
#130692892
C4×#668962
C2×C11×#4612
#2529311