Finite Group Databasebeta

← #14814835

Subgroups — #14814835

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×#10622609C212yesmaximal, complemented
2#13073569C211yesmaximal, characteristic
3#13069819C212yesmaximal, complemented
4#13069812C212yesmaximal, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13069377C211yesmaximal, characteristic, complemented
9#13068928C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#2354C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×C11×#117C2212yes—
14C2×#66977C2212yes—
15C2×#66977C2212yes—
16C2×#66922C2211yescharacteristic
17C11×#390—21no—
18C11×#388—22no—
19C11×#384C2211yescharacteristic
20C11×#380C2212yes—
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834—21no—
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622609—28no—
27#10622589—21no—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33C2×#66871C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35#10622562—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11C2312yes—
44C22×Dic22C2312yes—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C11×#117—24no—
48C11×#117—42no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11—22no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—24no—
68#66977—24no—
69#66977—42no—
70#66977—42no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77#66922—22no—
78#66922—22no—
79C11×#95—22no—
80C11×#95—21no—
81C11⋊#95—21no—
82C22⋊(C11⋊C8)—24no—
83C22⋊(C11⋊C8)—42no—
84#66874—24no—
85#66874—24no—
86#66874—42no—
87#66874—42no—
88#66872—24no—
89#66871—22no—
90#66871D414yescomplemented
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—22no—
93#26231—111nomaximal, Sylow
94C24×C11C2×D412yes—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—81no—
128C11×C4⋊C4C2×D412yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—82no—
132C42×C11—44no—
133C42×C11—42no—
134C42×C11#4112yes—
135C42×C11#4112yes—
136C22⋊Dic11—44no—
137C22⋊Dic11—44no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—42no—
141C4⋊Dic11—42no—
142C4⋊Dic11C2×D412yes—
143C4⋊Dic11#4112yes—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146C4×Dic11—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8C2×D412yes—
156C2×#485—112no—
157#2542—111no—
158#2354D1111yescharacteristic
159#2036—112no—
160#2035—112no—
161#1981—111no—
162#1956—111no—
163#1954—111no—
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—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11#12312yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#13512yes—
197C2×C4×C11#13712yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213Dic22—42no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217C11⋊C8—22no—
218C11⋊C8—41no—
219C11⋊C8—42no—
220C2×C4⋊Q8—111no—
221C2×C22⋊Q8—112no—
222C2×C22⋊Q8—112no—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#117C2×D1112yes—
225#485—228no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
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—21no—
239#390—221no—
240#388—22no—
241#384—221no—
242#384C2×D1111yescharacteristic
243#380C2×D1112yes—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—111no—
246C4×C4⋊C4C2×D1111yescharacteristic
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—42no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#48514yescomplemented
270C4×C11#53211yescharacteristic
271C4×C11#54011yescharacteristic
272C4×C11#55011yescharacteristic
273C4×C11#55911yescharacteristic
274Dic11—42no—
275Dic11—42no—
276Dic11—82no—
277C22×Q8—112no—
278C22×D4C22⋊D1111yescharacteristic
279C23×C4C22×D1112yes—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—112no—
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—24no—
292#117—42no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4C22⋊D1111yescharacteristic
302C2×C4⋊C4C22×D1112yes—
303C2×C4⋊C4C22×D1111yescharacteristic
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4C22⋊D1112yes—
310C2×C42—22no—
311C2×C42—21no—
312C2×C42—221no—
313C2×C42C22×D1111yescharacteristic
314#107—114no—
315#107—222no—
316#106—224no—
317C4⋊C8—222no—
318#103—224no—
319#103—224no—
320#103—442no—
321#103—442no—
322C22⋊C8—224no—
323C22⋊C8—442no—
324C4×C8—222no—
325#95—22no—
326#95—21no—
327#95—221no—
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×C22⋊D1112yes—
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—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—112no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—222no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—42no—
378C4⋊C4—81no—
379C4⋊C4—112no—
380C4⋊C4—112no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—444no—
384C4⋊C4—444no—
385C4⋊C4—442no—
386C4⋊C4—442no—
387C4⋊C4D4×D1112yes—
388C22⋊C4—24no—
389C22⋊C4—44no—
390C22⋊C4—82no—
391C22⋊C4—444no—
392C22⋊C4—444no—
393C42—44no—
394C42—42no—
395C42—442no—
396C42#433912yes—
397C42#433912yes—
398C11#2623111yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23C22×C22⋊D1111yescharacteristic
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—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4#6698212yes—
440C2×C4#6698212yes—
441C2×C4#6700312yes—
442C2×C4#6700412yes—
443C2×C4C2×#433911yescharacteristic
444C2×C4C2×#433911yescharacteristic
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4#6703711yescharacteristic
447C2×C4#41×D1111yescharacteristic
448C2×C4#6704211yescharacteristic
449C8—222no—
450C8—442no—
451C8—441no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22C2×#6698211yescharacteristic
460C22D4×C22⋊D1111yescharacteristic
461C22C2×#6700311yescharacteristic
462C22C2×#6700411yescharacteristic
463C22#1062336011yescharacteristic
464C22#1062336711yescharacteristic
465C22#1062336911yescharacteristic
466C4—22no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—81no—
471C4—442no—
472C4—442no—
473C4—882no—
474C4#1062260914yescomplemented
475C4#1062307911yescharacteristic
476C4#1062308411yescharacteristic
477C4#1062309011yescharacteristic
478C4#1062309311yescharacteristic
479C2—82no—
480C2#1307237511yescharacteristic
481C2C2×#1062260911yescharacteristic
482C2#1307858511yescharacteristic
483C2#1308028211yescharacteristic
484C2#1308033411yescharacteristic
485C2#1308053811yescharacteristic
486C2#1308089311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2354D11
hypocenterC11#26231
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. C2×#10622609C2semidirect
3. #13069819C2semidirect
4. #13069812C2semidirect
5. #13069539C2semidirect
6. #13069417C2semidirect
8. #13069377C2semidirect
9. #13068928C2semidirect
10. C4×#66871C2semidirect
90. #66871D4semidirect
269. C4×C11#485semidirect
398. C11#26231semidirect
474. C4#10622609semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
#130735692
#130698192
#130698122
#130695392
#130694172
#130694112
#130693772
#130689282
C4×#668712
C11×#23542
#2623111