Finite Group Databasebeta

← C4×#10622583 #14760913

Subgroups — C4×#10622583 #14760913

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622583C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic
3#13069257C212yesmaximal, complemented
4#13069208C212yesmaximal, complemented
5#13068923C211yesmaximal, characteristic
6#13068804C211yesmaximal, characteristic
7#13068706C211yesmaximal, characteristic
8C4×#66871C212yesmaximal, complemented
9C4×#66874C212yesmaximal, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11—21no—
15C22×C42×C11C2211yescharacteristic
16C2×#66977C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C4×C11×C4⋊C4—21no—
19C4×C11×C4⋊C4—21no—
20C4×C11×C4⋊C4C2212yes—
21C4×C11×C4⋊C4C2212yes—
22C2×C11×#95—21no—
23#10622825C2211yescharacteristic
24#10622823—21no—
25C4×C22⋊Dic11—21no—
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622583C418yesdirect product factor
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66871C2212yes—
32C2×#66871C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622546—21no—
35C4×Dic11⋊C4—21no—
36#10622542C2211yescharacteristic
37#10622541C2211yescharacteristic
38C2×C4×C11⋊C8C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11—24no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—44no—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70#66977—22no—
71#66977C2×C414yes—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2312yes—
79C4×Dic22—24no—
80C11×#95—22no—
81C11×#95—22no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)C2×C414yes—
89#66874—24no—
90#66874C2×C418yescomplemented
91#66871—24no—
92#66871C2×C418yescomplemented
93C4×C11⋊C8—24no—
94C4×#484—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—41no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11Q1614yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—21no—
127C2×Dic22C22×C412yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C22×C414yes—
133C11×C4⋊C4#4114yes—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—44no—
138C42×C11—44no—
139C42×C11#4114yes—
140C22⋊Dic11—24no—
141C22⋊Dic11—42no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C412yes—
146Dic11⋊C4—24no—
147Dic11⋊C4—42no—
148Dic11⋊C4—42no—
149C4×Dic11—42no—
150C4×Dic11—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8C22×C414yes—
157C2×#484—111no—
158C4×C22⋊Q8—111no—
159C2×C4×C4⋊C4D1111yescharacteristic
160#1928—112no—
161#1921—112no—
162#1872—111no—
163#1852—111no—
164#1824—111no—
165C4×#107—112no—
166C4×#103—112no—
167C4×C22⋊C8—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11C4×D412yes—
173C23×C11C2×Q1612yes—
174C23×C11#13512yes—
175C23×C11C22×D411yescharacteristic
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—28no—
185C2×C4×C11—24no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—44no—
191C2×C4×C11—48no—
192C2×C4×C11—48no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C4×D412yes—
198C2×C4×C11#12312yes—
199C2×C4×C11#12312yes—
200C2×C4×C11C2×Q1612yes—
201C2×C4×C11C2×Q1612yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11C23×C411yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C11C2×#4112yes—
206C2×C4×C11C2×#4111yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219Dic22—24no—
220Dic22—42no—
221C11⋊C8—24no—
222C11⋊C8—42no—
223C2×C22⋊Q8—111no—
224C2×C4×Q8—111no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C42—21no—
228C22×C42C2×D1111yescharacteristic
229#484—118no—
230C2×#107—112no—
231C2×#107—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8—111no—
236C2×C4×C8—112no—
237#391—111no—
238#389—111no—
239#387—221no—
240#385—221no—
241#380—111no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246C4×C4⋊C4C2×D1112yes—
247C4×C4⋊C4C2×D1112yes—
248C4×C22⋊C4—221no—
249C2×#95—21no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#336—112no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11C4×Q1614yes—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11C2×#12311yescharacteristic
264C22×C11#52511yescharacteristic
265C22×C11C22×Q1611yescharacteristic
266C22×C11C2×#13511yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—41no—
273C4×C11—44no—
274C4×C11—44no—
275C4×C11#48414yescomplemented
276C4×C11C4×#4112yes—
277C4×C11#52912yes—
278Dic11—42no—
279Dic11—42no—
280Dic11—81no—
281Dic11—81no—
282C22×Q8—111no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C22⋊D1111yescharacteristic
286C23×C4C22⋊D1111yescharacteristic
287C23×C4C22×D1111yescharacteristic
288C22×C8—112no—
289C22×C8—112no—
290C22⋊Q8—114no—
291C22⋊Q8—222no—
292C4×Q8—224no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4C4×D1114yes—
304C2×C4⋊C4C22×D1112yes—
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C42—24no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—44no—
312C2×C42—221no—
313C2×C42—221no—
314C2×C42C22⋊D1111yescharacteristic
315C2×C42C22⋊D1111yescharacteristic
316C2×C42C22×D1111yescharacteristic
317C2×C42C22×D1111yescharacteristic
318#107—118no—
319#107—224no—
320#103—118no—
321#103—224no—
322C22⋊C8—114no—
323C22⋊C8—222no—
324C4×C8—224no—
325#95—22no—
326#95—22no—
327#95—221no—
328#95—221no—
329#95—221no—
330#95—221no—
331#95—221no—
332C2×C11—24no—
333C2×C11C4×#12311yescharacteristic
334C2×C11C2×C4×Q1611yescharacteristic
335C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
336C2×C11C2×#48411yescharacteristic
337C2×C11#309111yescharacteristic
338C2×C11#310411yescharacteristic
339C2×C11#310511yescharacteristic
340C24C2×C22⋊D1111yescharacteristic
341C2×Q8—112no—
342C2×Q8—221no—
343C2×Q8—222no—
344C2×Q8—222no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4#432614yes—
365C22×C4C2×C4×D1112yes—
366C22×C4#433912yes—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373C2×C8—114no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—112no—
384C4⋊C4—224no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4C2×C4×D1114yes—
391C4⋊C4#433914yes—
392C22⋊C4—224no—
393C22⋊C4—442no—
394C42—22no—
395C42—22no—
396C42—22no—
397C42—44no—
398C42—44no—
399C42—442no—
400C42—442no—
401C42#433914yes—
402C11C4×#48411yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23C4×C22⋊D1112yes—
408C23C2×#432612yes—
409C23#6700312yes—
410C23C22×C22⋊D1111yescharacteristic
411Q8—224no—
412Q8—442no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—28no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—24no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—44no—
428C2×C4—48no—
429C2×C4—48no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4C4×C22⋊D1112yes—
447C2×C4#6698212yes—
448C2×C4#6698212yes—
449C2×C4#6698512yes—
450C2×C4C2×#432612yes—
451C2×C4C2×#432612yes—
452C2×C4C22×C4×D1111yescharacteristic
453C2×C4C2×#433912yes—
454C2×C4C2×#433912yes—
455C2×C4C2×#433911yescharacteristic
456C8—224no—
457C8—442no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22C4×#432614yes—
465C22C2×C4×C22⋊D1111yescharacteristic
466C22C2×#6698211yescharacteristic
467C22#1062332211yescharacteristic
468C22C2×#6698511yescharacteristic
469C22C22×#432611yescharacteristic
470C22C2×#6700311yescharacteristic
471C22#1062335311yescharacteristic
472C4—22no—
473C4—22no—
474C4—22no—
475C4—41no—
476C4—44no—
477C4—44no—
478C4—442no—
479C4—442no—
480C4—881no—
481C4—881no—
482C4#1062258314yesdirect product factor
483C4C4×#433912yes—
484C4#1062301012yes—
485C2—24no—
486C2C4×#6698211yescharacteristic
487C2C2×C4×#432611yescharacteristic
488C2C4×#6698511yescharacteristic
489C2C2×#1062258311yescharacteristic
490C2#1307852911yescharacteristic
491C2#1307865511yescharacteristic
492C2#1307866311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4×#484
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069257C2semidirect
4. #13069208C2semidirect
8. C4×#66871C2semidirect
9. C4×#66874C2semidirect
28. #10622583C4direct (N × H)
90. #66874C2×C4semidirect
92. #66871C2×C4semidirect
275. C4×C11#484semidirect
402. C11C4×#484semidirect
482. C4#10622583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225832
C4×#669772
#130692572
#130692082
#130689232
#130688042
#130687062
C4×#668712
C4×#668742
C4×C22⋊(C11⋊C8)2
C2×C4×C11×C4⋊C42
C4×#48411