Finite Group Databasebeta

← #14814843

Subgroups — #14814843

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×#10622480C212yesmaximal, complemented
2#13073565C211yesmaximal, characteristic
3#13071567C211yesmaximal, characteristic
4#13069822C212yesmaximal, complemented
5#13069814C212yesmaximal, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic
9#13068927C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C2×#66950C2212yes—
13C2×#66950C2212yes—
14C2×#66945C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C8C2212yes—
22C2×(C2×D11)⋊C8C2212yes—
23C2×#66880C2212yes—
24C2×#66880C2212yes—
25#10622603—22no—
26#10622601—21no—
27#10622600C2212yes—
28C4⋊C4×Dic11—21no—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66871C2211yescharacteristic
32C2×#66871C2211yescharacteristic
33#10622552—21no—
34#10622548—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622480—28no—
38#10622290—22no—
39C11×#340C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D44D411yescharacteristic
43C22×C4×D11C2312yes—
44C22×Dic22C2312yes—
45C22×C8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D412yes—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69#66950—24no—
70#66950—24no—
71#66950—42no—
72#66950—42no—
73#66945—24no—
74#66945—42no—
75C4×D44—22no—
76C4×D44—22no—
77#66922—22no—
78#66922—22no—
79C11×#106—24no—
80C11×C4⋊C8—22no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84(C2×D11)⋊C8—24no—
85(C2×D11)⋊C8—42no—
86#66880—24no—
87#66880—42no—
88#66874—24no—
89#66874—42no—
90#66871—22no—
91#66871D414yescomplemented
92C4×C11⋊C8—22no—
93#26231—111nomaximal, Sylow
94C23×D11C2×D412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D412yes—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4C2×D412yes—
130C11×C4⋊C4#4112yes—
131C42×C11—42no—
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—44no—
144C4⋊Dic11—44no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147C4⋊Dic11C2×D412yes—
148C4×Dic11—44no—
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⋊C8C2×D412yes—
156C2×#485—112no—
157#2542—111no—
158#2354—111no—
159#2036—112no—
160#2035—112no—
161#1981—111no—
162#1956—111no—
163#1954—111no—
164#1948D1111yescharacteristic, complemented
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—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11#12312yes—
187C2×C4×C11#12312yes—
188C2×C4×C11#13512yes—
189C2×C4×C11#13712yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208D44—44no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—42no—
213Dic22—42no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217C8×C11—42no—
218C11⋊C8—22no—
219C11⋊C8—41no—
220C2×C4⋊Q8—111no—
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×#106C2×D1112yes—
229C2×C4⋊C8C2×D1111yescharacteristic
230C2×#103—112no—
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—112no—
236C2×C4×C8—111no—
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—221no—
246C4×C4⋊C4C2×D1111yescharacteristic
247#340—111no—
248#340—111no—
249#340C2×D1112yes—
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—42no—
266C4×C11—42no—
267C4×C11—82no—
268C4×C11#48514yescomplemented
269C4×C11#53211yescharacteristic
270C4×C11#54011yescharacteristic
271C4×C11#55011yescharacteristic
272C4×C11#55911yescharacteristic
273Dic11—42no—
274Dic11—42no—
275Dic11—82no—
276Dic11—81no—
277C22×Q8—112no—
278C22×D4—111no—
279C23×C4—112no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8C22×D1112yes—
283C4⋊Q8—222no—
284C4⋊Q8—222no—
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—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22×D1112yes—
303C2×C4⋊C4C22×D1111yescharacteristic
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C22⋊C4—112no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—21no—
311C2×C42—222no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314#107—114no—
315#107—222no—
316#106—24no—
317C4⋊C8—22no—
318#103—224no—
319#103—224no—
320#103—442no—
321#103—442no—
322C22⋊C8—224no—
323C22⋊C8—442no—
324C4×C8—222no—
325#95—21no—
326#95—222no—
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—222no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—112no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—112no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—221no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—81no—
377C4⋊C4—112no—
378C4⋊C4—222no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—444no—
383C4⋊C4—444no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4D4×D1112yes—
387C4⋊C4#434312yes—
388C22⋊C4—224no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—882no—
393C42—42no—
394C42—444no—
395C42—442no—
396C42#433912yes—
397C42#434312yes—
398C11#2623111yescharacteristic, complemented, Sylow
399C23—222no—
400C23—222no—
401C23—222no—
402C23—222no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23C2×D4×D1111yescharacteristic
407Q8—442no—
408Q8—442no—
409Q8—442no—
410Q8—442no—
411D4—444no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4#6694712yes—
440C2×C4#6694712yes—
441C2×C4#6696812yes—
442C2×C4#6696912yes—
443C2×C4C2×#433911yescharacteristic
444C2×C4C2×D4×D1111yescharacteristic
445C2×C4C2×#434311yescharacteristic
446C2×C4C2×#434311yescharacteristic
447C2×C4#6704211yescharacteristic
448C2×C4#6704211yescharacteristic
449C8—42no—
450C8—222no—
451C8—441no—
452C22—442no—
453C22—442no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22C2×#6694711yescharacteristic
460C22#1062314011yescharacteristic
461C22#1062316111yescharacteristic
462C22C2×#6696811yescharacteristic
463C22C2×#6696911yescharacteristic
464C22#1062330611yescharacteristic
465C22#1062331011yescharacteristic
466C4—22no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—442no—
471C4—442no—
472C4—881no—
473C4—882no—
474C4#1062248014yescomplemented
475C4#1062308411yescharacteristic
476C4#1062311611yescharacteristic
477C4#1062322911yescharacteristic
478C4#1062325611yescharacteristic
479C2—882no—
480C2#1307238311yescharacteristic
481C2C2×#1062248011yescharacteristic
482C2#1307858711yescharacteristic
483C2#1308028511yescharacteristic
484C2#1308033311yescharacteristic
485C2#1308054111yescharacteristic
486C2#1308089611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1948D11
hypocenterC11#26231
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#10622480C2semidirect
4. #13069822C2semidirect
5. #13069814C2semidirect
6. #13069538C2semidirect
7. #13069417C2semidirect
9. #13068927C2semidirect
10. C4×#66871C2semidirect
11. C11×#1948C2semidirect
91. #66871D4semidirect
164. #1948D11semidirect
268. C4×C11#485semidirect
398. C11#26231semidirect
474. C4#10622480semidirect

Maximal subgroups

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

subgroupindex
C2×#106224802
#130735652
#130715672
#130698222
#130698142
#130695382
#130694172
#130694092
#130689272
C4×#668712
C11×#19482
#2623111