Finite Group Databasebeta

← #14814844

Subgroups — #14814844

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622427C212yesmaximal, complemented
2#13073570C211yesmaximal, characteristic
3#13071567C211yesmaximal, characteristic
4#13069818C212yesmaximal, complemented
5#13069810C212yesmaximal, complemented
6#13069540C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic
8#13069377C211yesmaximal, characteristic, complemented
9#13068925C212yesmaximal, complemented
10C4×#66882C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×#66999C2212yes—
15C2×#66945C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C11×#103C2212yes—
18C2×C11×#103C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C2×#66899C2212yes—
22C2×#66899C2212yes—
23C2×(C2×D11)⋊C8C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66882C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27#10622605—22no—
28#10622603—22no—
29#10622601—21no—
30#10622601—21no—
31#10622600C2212yes—
32#10622589—21no—
33C4⋊C4×Dic11—21no—
34C2×#66872C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622427—28no—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×D44D411yescharacteristic
44C22×C4×D11C2312yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11C2311yescharacteristic
55#66999—24no—
56#66999—24no—
57#66999—42no—
58#66999—42no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4D412yes—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C22×C11⋊C8C2312yes—
75#66945—24no—
76#66945—42no—
77C4×D44—22no—
78C4×D44—22no—
79C11×#103—24no—
80C11×#103—42no—
81C4×C8×C11—22no—
82#66899—24no—
83#66899—42no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87(C2×D11)⋊C8—24no—
88(C2×D11)⋊C8—42no—
89#66882—22no—
90#66882D414yescomplemented
91#66872—24no—
92C4⋊(C11⋊C8)—22no—
93#26231—111nomaximal, Sylow
94C23×D11C2×D412yes—
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×Dic11—21no—
110C22×Dic11C2×D412yes—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C2×D412yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—81no—
132C42×C11#4112yes—
133C42×C11#4112yes—
134(C2×D11)⋊C4—24no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—82no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11C2×D412yes—
146C4⋊Dic11C2×D412yes—
147C4⋊Dic11#4112yes—
148Dic11⋊C4—44no—
149Dic11⋊C4—44no—
150C4×Dic11—44no—
151C4×Dic11—42no—
152C4×Dic11—42no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×#485—112no—
157#2542—111no—
158#2354—111no—
159#2036—112no—
160#2035—112no—
161#1981—111no—
162#1956D1111yescharacteristic, complemented
163#1954—111no—
164#1948—111no—
165#1873—112no—
166C4×#107—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
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#12312yes—
188C2×C4×C11#12312yes—
189C2×C4×C11#13512yes—
190C2×C4×C11#13712yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
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×Dic11—41no—
212D44—44no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—42no—
217C8×C11—22no—
218C8×C11—41no—
219C11⋊C8—42no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×C22⋊Q8—112no—
222C2×C22⋊Q8—112no—
223C2×C4×D4—111no—
224C2×#117—112no—
225#485—228no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
230C2×#103—112no—
231C2×#103—112no—
232C2×#103C2×D1112yes—
233C2×#103C2×D1112yes—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—112no—
236C2×C4×C8C2×D1111yescharacteristic
237#399—222no—
238#390—221no—
239#390—221no—
240#388—222no—
241#384—221no—
242#384C2×D1111yescharacteristic
243#380—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—111no—
246C4×C4⋊C4—221no—
247#340—111no—
248#340—111no—
249#340—112no—
250C22×C11C2×#12311yescharacteristic
251C22×C11D4211yescharacteristic
252C22×C11#54611yescharacteristic
253C22×C11C2×#13511yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C22×C11#57711yescharacteristic
256C22×C11#57811yescharacteristic
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C4×C11—22no—
265C4×C11—82no—
266C4×C11—82no—
267C4×C11#48514yescomplemented
268C4×C11#53211yescharacteristic
269C4×C11#54011yescharacteristic
270C4×C11#55011yescharacteristic
271C4×C11#55911yescharacteristic
272Dic11—42no—
273Dic11—42no—
274Dic11—42no—
275Dic11—42no—
276Dic11—81no—
277C22×Q8C22×D1112yes—
278C22×D4—111no—
279C23×C4—112no—
280C22×C8—112no—
281C22×C8C22×D1111yescharacteristic
282C22×C8C22×D1111yescharacteristic
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285C22⋊Q8—224no—
286C22⋊Q8—224no—
287C22⋊Q8—442no—
288C22⋊Q8—442no—
289C4×D4—222no—
290C4×D4—222no—
291#117—224no—
292#117—442no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4C22×D1112yes—
305C2×C22⋊C4—112no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—222no—
311C2×C42—221no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314#107—114no—
315#107—222no—
316#106—224no—
317C4⋊C8—222no—
318#103—24no—
319#103—42no—
320#103—224no—
321#103—442no—
322C22⋊C8—224no—
323C22⋊C8—442no—
324C4×C8—22no—
325#95—222no—
326#95—221no—
327#95—221no—
328C2×C11#244511yescharacteristic
329C2×C11C2×#48511yescharacteristic
330C2×C11#309711yescharacteristic
331C2×C11#327811yescharacteristic
332C2×C11#328311yescharacteristic
333C2×C11#330311yescharacteristic
334C2×C11#332811yescharacteristic
335D11—82no—
336C24—112no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—112no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8D4×D1112yes—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—81no—
377C4⋊C4—112no—
378C4⋊C4—112no—
379C4⋊C4—112no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—444no—
387C4⋊C4—444no—
388C22⋊C4—224no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—882no—
393C42—444no—
394C42—442no—
395C42—442no—
396C42#433912yes—
397C42#434112yes—
398C11#2623111yescharacteristic, complemented, Sylow
399C23—222no—
400C23—222no—
401C23—222no—
402C23—222no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23C2×D4×D1111yescharacteristic
407Q8—42no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411D4—444no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4#6693612yes—
440C2×C4#6693612yes—
441C2×C4#6696812yes—
442C2×C4#6697212yes—
443C2×C4C2×#433911yescharacteristic
444C2×C4C2×D4×D1111yescharacteristic
445C2×C4C2×#434111yescharacteristic
446C2×C4#6703711yescharacteristic
447C2×C4#41×D1111yescharacteristic
448C2×C4#6704211yescharacteristic
449C8—22no—
450C8—41no—
451C8—442no—
452C22—442no—
453C22—442no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22C2×#6693611yescharacteristic
460C22#1062320711yescharacteristic
461C22#1062324811yescharacteristic
462C22C2×#6696811yescharacteristic
463C22#1062329311yescharacteristic
464C22C2×#6697211yescharacteristic
465C22#1062329711yescharacteristic
466C4—22no—
467C4—82no—
468C4—82no—
469C4—442no—
470C4—442no—
471C4—442no—
472C4—442no—
473C4—881no—
474C4#1062242714yescomplemented
475C4#1062308411yescharacteristic
476C4#1062309011yescharacteristic
477C4#1062312711yescharacteristic
478C4#1062315011yescharacteristic
479C2—882no—
480C2#1307238411yescharacteristic
481C2C2×#1062242711yescharacteristic
482C2#1307858111yescharacteristic
483C2#1308028111yescharacteristic
484C2#1308033611yescharacteristic
485C2#1308054311yescharacteristic
486C2#1308089811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1956D11
hypocenterC11#26231
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
1. C2×#10622427C2semidirect
4. #13069818C2semidirect
5. #13069810C2semidirect
6. #13069540C2semidirect
8. #13069377C2semidirect
9. #13068925C2semidirect
10. C4×#66882C2semidirect
11. C11×#1956C2semidirect
90. #66882D4semidirect
162. #1956D11semidirect
267. C4×C11#485semidirect
398. C11#26231semidirect
474. C4#10622427semidirect

Maximal subgroups

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

subgroupindex
C2×#106224272
#130735702
#130715672
#130698182
#130698102
#130695402
#130694102
#130693772
#130689252
C4×#668822
C11×#19562
#2623111