Finite Group Databasebeta

← #14814839

Subgroups — #14814839

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×#10622336C212yesmaximal, complemented
2#13073569C211yesmaximal, characteristic
3#13071565C211yesmaximal, characteristic
4#13069820C212yesmaximal, complemented
5#13069813C212yesmaximal, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13068926C212yesmaximal, complemented
10C4×#66882C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66979C2212yes—
14C2×#66977C2212yes—
15C2×#66977C2212yes—
16C2×#66922C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2212yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21#10622834—21no—
22#10622834—21no—
23#10622825C2212yes—
24C2×#66882C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66881C2212yes—
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31#10622589—21no—
32C4⋊C4×Dic11—21no—
33#10622564—22no—
34#10622562—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38#10622336—28no—
39#10622189C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11C2312yes—
44C22×Dic22C2312yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2311yescharacteristic
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57#66979—24no—
58#66979—42no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68#66977—24no—
69#66977—24no—
70#66977—42no—
71#66977—42no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77#66922—22no—
78#66922—22no—
79C11×C4⋊C8—22no—
80C11×C22⋊C8—24no—
81C11×C22⋊C8—42no—
82C4×C8×C11—22no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86#66882—22no—
87#66882D414yescomplemented
88#66881—24no—
89#66880—24no—
90#66880—24no—
91#66880—42no—
92#66880—42no—
93#26231—111nomaximal, Sylow
94C24×C11C2×D412yes—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—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—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D412yes—
129C11×C4⋊C4—22no—
130C11×C22⋊C4—24no—
131C42×C11#4112yes—
132C42×C11#4112yes—
133C22⋊Dic11—44no—
134C22⋊Dic11—44no—
135C22⋊Dic11—44no—
136C22⋊Dic11—82no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147C4⋊Dic11—81no—
148C4⋊Dic11C2×D412yes—
149C4⋊Dic11C2×D412yes—
150C4⋊Dic11#4112yes—
151Dic11⋊C4—44no—
152Dic11⋊C4—44no—
153C4×Dic11—44no—
154C4×Dic11—42no—
155C4×Dic11—42no—
156C2×#485—112no—
157#2542—111no—
158#2354—111no—
159#2036—112no—
160#2035—112no—
161#1981—111no—
162#1956—111no—
163#1954D1111yescharacteristic
164#1948—111no—
165#1873—112no—
166C4×#107—111no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C22×D411yescharacteristic
175D4×C11—44no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11#12312yes—
186C2×C4×C11#12312yes—
187C2×C4×C11#13512yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213Dic22—42no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217C8×C11—22no—
218C8×C11—41no—
219C8×C11—42no—
220C2×C4⋊Q8—111no—
221C2×C22⋊Q8—112no—
222C2×C22⋊Q8—112no—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#117—112no—
225#485—228no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—112no—
229C2×C4⋊C8C2×D1111yescharacteristic
230C2×#103—112no—
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×C22⋊C8C2×D1112yes—
235C2×C22⋊C8C2×D1112yes—
236C2×C4×C8C2×D1111yescharacteristic
237#399—222no—
238#390—221no—
239#390—221no—
240#388—222no—
241#384—111no—
242#384—221no—
243#380—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—111no—
246C4×C4⋊C4—221no—
247#340—111no—
248#340—112no—
249#340—111no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11C2×#12311yescharacteristic
258C22×C11D4211yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11C2×#13511yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11#57711yescharacteristic
263C22×C11#57811yescharacteristic
264C4×C11—22no—
265C4×C11—42no—
266C4×C11#48514yescomplemented
267C4×C11#53211yescharacteristic
268C4×C11#54011yescharacteristic
269C4×C11#55011yescharacteristic
270C4×C11#55911yescharacteristic
271Dic11—42no—
272Dic11—42no—
273Dic11—42no—
274Dic11—82no—
275Dic11—82no—
276Dic11—81no—
277C22×Q8—112no—
278C22×D4D4411yescharacteristic
279C23×C4C22×D1112yes—
280C22×C8C22×D1111yescharacteristic
281C22×C8C22×D1112yes—
282C22×C8C22×D1111yescharacteristic
283C4⋊Q8—222no—
284C4⋊Q8—222no—
285C22⋊Q8—224no—
286C22⋊Q8—224no—
287C22⋊Q8—442no—
288C22⋊Q8—442no—
289C4×D4—22no—
290C4×D4—22no—
291#117—224no—
292#117—442no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4D4411yescharacteristic
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4D4412yes—
310C2×C42—222no—
311C2×C42—221no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314#107—114no—
315#107—222no—
316#106—224no—
317C4⋊C8—22no—
318#103—224no—
319#103—224no—
320#103—442no—
321#103—442no—
322C22⋊C8—24no—
323C22⋊C8—42no—
324C4×C8—22no—
325#95—221no—
326#95—221no—
327#95—222no—
328C2×C11—82no—
329C2×C11#244511yescharacteristic
330C2×C11C2×#48511yescharacteristic
331C2×C11#309711yescharacteristic
332C2×C11#327811yescharacteristic
333C2×C11#328311yescharacteristic
334C2×C11#330311yescharacteristic
335C2×C11#332811yescharacteristic
336C24C2×D4412yes—
337C2×Q8—222no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4C2×D4412yes—
359C22×C4C2×D4411yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—21no—
370C2×C8D4×D1112yes—
371C4⋊C4—22no—
372C4⋊C4—112no—
373C4⋊C4—112no—
374C4⋊C4—112no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—222no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—222no—
382C4⋊C4—444no—
383C4⋊C4—444no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4—442no—
387C4⋊C4—881no—
388C22⋊C4—24no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C22⋊C4—882no—
393C42—444no—
394C42—442no—
395C42—442no—
396C42#434112yes—
397C42#434112yes—
398C11#2623111yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23C22×D4411yescharacteristic
407Q8—442no—
408Q8—442no—
409Q8—442no—
410Q8—442no—
411D4—44no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4#6693912yes—
440C2×C4#6693912yes—
441C2×C4#6695712yes—
442C2×C4#6696212yes—
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4C2×#434111yescharacteristic
446C2×C4#6703711yescharacteristic
447C2×C4#41×D1111yescharacteristic
448C2×C4#6704211yescharacteristic
449C8—22no—
450C8—42no—
451C8—41no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22C2×#6693911yescharacteristic
460C22D4×D4411yescharacteristic
461C22#1062308511yescharacteristic
462C22C2×#6695711yescharacteristic
463C22C2×#6696211yescharacteristic
464C22#1062328211yescharacteristic
465C22#1062328411yescharacteristic
466C4—22no—
467C4—42no—
468C4—442no—
469C4—442no—
470C4—442no—
471C4—882no—
472C4—881no—
473C4—882no—
474C4#1062233614yescomplemented
475C4#1062312711yescharacteristic
476C4#1062315011yescharacteristic
477C4#1062321211yescharacteristic
478C4#1062324911yescharacteristic
479C2—82no—
480C2#1307237911yescharacteristic
481C2C2×#1062233611yescharacteristic
482C2#1307858611yescharacteristic
483C2#1308028411yescharacteristic
484C2#1308033811yescharacteristic
485C2#1308054511yescharacteristic
486C2#1308090011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#26231
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622336C2semidirect
4. #13069820C2semidirect
5. #13069813C2semidirect
6. #13069538C2semidirect
7. #13069418C2semidirect
8. #13069380C2semidirect
9. #13068926C2semidirect
10. C4×#66882C2semidirect
87. #66882D4semidirect
266. C4×C11#485semidirect
398. C11#26231semidirect
474. C4#10622336semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
#130735692
#130715652
#130698202
#130698132
#130695382
#130694182
#130693802
#130689262
C4×#668822
C11×#19542
#2623111