Finite Group Databasebeta

← #14803286

Subgroups — #14803286

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×#10622696C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073832C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13069993C212yesmaximal, complemented
6#13069930C212yesmaximal
7#13069467C212yesmaximal
8#13069377C211yesmaximal, characteristic, complemented
9#13069294C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C22×#4325C2212yes—
14C2×#66950—21no—
15C2×C4×D44C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#103C2212yes—
18C2×C11×#103C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#384C2211yescharacteristic
21#10622843C2212yes—
22#10622843C2212yes—
23C2×#66899C2212yes—
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622696—24no—
29#10622607—22no—
30#10622601C2212yes—
31#10622600—21no—
32#10622598C2212yes—
33#10622595—22no—
34#10622590—21no—
35#10622587—21no—
36C2×#66872C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C8×Dic22—24no—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11C2312yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×#4325—24no—
58C2×#4325—24no—
59C2×#4325—42no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4D412yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72#66950—44no—
73C4×D44—22no—
74C4×D44—22no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×#103—24no—
78C11×#103—42no—
79C4×C8×C11—22no—
80#66899—24no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—22no—
88#66885—22no—
89Dic11⋊C8—24no—
90C8×Dic11—24no—
91#66872—42no—
92C4⋊(C11⋊C8)D414yes—
93#25293—111nomaximal, Sylow
94C23×D11—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—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44#4112yes—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22SD1614yescomplemented
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—81no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137#4325—48no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—44no—
149Dic11⋊C4—24no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—42no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8C2×D414yes—
156C2×#461—111no—
157C2×C8×Q8—111no—
158#2568—111no—
159#2538—111no—
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956D1111yescharacteristic, complemented
164#1948—111no—
165#1933—112no—
166C4×#102—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—42no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—42no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11#12112yes—
188C2×C4×C11#12112yes—
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11C2×SD1614yes—
212D44—22no—
213D44—22no—
214D44—41no—
215D44—41no—
216C4×D11—84no—
217Dic22—28no—
218C8×C11—22no—
219C8×C11—41no—
220C11⋊C8—24no—
221C22×SD16—112no—
222C2×C4⋊Q8C2×D1111yescharacteristic
223C2×C22⋊Q8—221no—
224C2×C4×Q8—111no—
225C2×C4×D4—111no—
226#461—224no—
227C8×Q8—224no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8—112no—
231C2×#103—112no—
232C2×#103C2×D1112yes—
233C2×#103C2×D1112yes—
234C2×#102—111no—
235C2×#102—111no—
236C2×C4×C8—112no—
237C2×C4×C8C2×D1111yescharacteristic
238#400—222no—
239#396—222no—
240#391—112no—
241#391—112no—
242#391—221no—
243#390—112no—
244#389—112no—
245#384C2×D1111yescharacteristic
246#382—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249#340—111no—
250#340—111no—
251#340—112no—
252C22×C11C2×#12111yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11#55011yescharacteristic
255C22×C11C22×SD1611yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C4×C11—22no—
267C4×C11—82no—
268C4×C11—82no—
269C4×C11#46514yes—
270C4×C11#52911yescharacteristic
271C4×C11#54211yescharacteristic
272C4×C11#54611yescharacteristic
273C4×C11#54811yescharacteristic
274Dic11—24no—
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C22×Q8—111no—
280C22×Q8C22×D1112yes—
281C22×D4—111no—
282C23×C4—221no—
283C2×SD16—224no—
284C2×SD16—224no—
285C2×SD16—442no—
286C22×C8—112no—
287C22×C8C22×D1111yescharacteristic
288C22×C8C22×D1111yescharacteristic
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C22⋊Q8—444no—
292C4×Q8—222no—
293C4×Q8—222no—
294C4×D4—222no—
295C4×D4—222no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4C22×D1112yes—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—222no—
310C2×C42—112no—
311C2×C42—221no—
312C2×C42C22×D1111yescharacteristic
313#106—442no—
314C4⋊C8—114no—
315C4⋊C8—224no—
316#103—24no—
317#103—42no—
318#103—224no—
319#102—222no—
320#102—222no—
321C4×C8—22no—
322C4×C8—224no—
323#95—222no—
324#95—222no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—221no—
329C2×C11#242611yescharacteristic
330C2×C11C2×#46511yescharacteristic
331C2×C11#306311yescharacteristic
332C2×C11#335911yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#339211yescharacteristic
335C2×C11#339311yescharacteristic
336D11—82no—
337C24—221no—
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—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—112no—
356C22×C4—112no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—442no—
361C22×C4—442no—
362C22×C4—442no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—448no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—114no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8#434112yes—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—81no—
382C4⋊C4—224no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—442no—
393C22⋊C4—882no—
394C42—222no—
395C42—222no—
396C42—442no—
397C42#433912yes—
398C42D4×D1112yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—222no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23C2×D4×D1111yescharacteristic
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—228no—
413D4—222no—
414D4—222no—
415D4—441no—
416D4—441no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—114no—
426C2×C4—222no—
427C2×C4—222no—
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—441no—
439C2×C4—441no—
440C2×C4—884no—
441C2×C4#6693712yes—
442C2×C4#6693712yes—
443C2×C4SD16×D1112yes—
444C2×C4#6697212yes—
445C2×C4C2×#433911yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C2×#434111yescharacteristic
448C2×C4#6703711yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—22no—
452C8—41no—
453C8—224no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×#6693711yescharacteristic
462C22#1062320811yescharacteristic
463C22#1062324911yescharacteristic
464C22C2×SD16×D1111yescharacteristic
465C22#1062329311yescharacteristic
466C22C2×#6697211yescharacteristic
467C22#1062329711yescharacteristic
468C4—22no—
469C4—82no—
470C4—82no—
471C4—224no—
472C4—442no—
473C4—881no—
474C4—881no—
475C4—881no—
476C4#1062242014yes—
477C4#1062308811yescharacteristic
478C4#1062309211yescharacteristic
479C4#1062312911yescharacteristic
480C4#1062314311yescharacteristic
481C2—882no—
482C2#1307218311yescharacteristic
483C2C2×#1062242011yescharacteristic
484C2#1307830511yescharacteristic
485C2#1308125511yescharacteristic
486C2#1308127011yescharacteristic
487C2#1308159411yescharacteristic
488C2#1308160611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1956D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073832C2semidirect
5. #13069993C2semidirect
8. #13069377C2semidirect
9. #13069294C2semidirect
11. C11×#1956C2semidirect
122. C2×Dic22SD16semidirect
163. #1956D11semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×C8×Dic222
#130738322
#130735392
#130699932
#130699302
#130694672
#130693772
#130692942
C4×#668852
C11×#19562
#2529311