Finite Group Databasebeta

← C2×#13070032 #14782511

Subgroups — C2×#13070032 #14782511

Order 2816.

1278 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66896C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622590C211yesmaximal, characteristic, complemented
4#13070032C218yesmaximal, direct product factor
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C22⋊Dic11—21no—
13C22×C22⋊Dic11—21no—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×C11×#102—24no—
19C2×C11×#102C2214yes—
20#10622834—22no—
21#10622834C2214yes—
22C2×#66896—24no—
23C2×#66896C2214yes—
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26#10622590—22no—
27#10622590C2214yescomplemented
28#10622189C2214yescomplemented
29#10622188C2214yescomplemented
30#10622167C2214yescomplemented
31C25×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11D414yes—
39C22×D4×C11C2312yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—44no—
57C2×C22⋊Dic11—44no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D412yes—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8—22no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8C2312yes—
74C11×#102—28no—
75#66896—28no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C2×#2073—111nomaximal, Sylow
79C24×C11—24no—
80C24×C11—22no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11C2×D411yescharacteristic
88C2×D4×C11—24no—
89C2×D4×C11—28no—
90C2×D4×C11—28no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—44no—
99C2×D4×C11—44no—
100C2×D4×C11C2×D414yes—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—44no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C22⋊Dic11—48no—
137C22⋊Dic11—48no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—42no—
143C4⋊Dic11—42no—
144C4×Dic11—24no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—44no—
151C22×#102—111no—
152C22×#102D1111yescharacteristic
153C2×#390—111no—
154C2×#382—111no—
155#2073—118no—
156C2×#340—111no—
157C2×#340—111no—
158C2×#336—111no—
159C23×C11—24no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—48no—
167C23×C11—48no—
168C23×C11—48no—
169C23×C11—84no—
170C23×C11—84no—
171C23×C11—84no—
172C23×C11—84no—
173C23×C11#12112yes—
174C23×C11#12312yes—
175C23×C11#12412yes—
176C23×C11#13512yes—
177C23×C11#13512yes—
178C23×C11AGL(1,ℤ/8)12yes—
179C23×C11AGL(1,ℤ/8)12yes—
180C23×C11C22×D411yescharacteristic
181D4×C11—24no—
182D4×C11—24no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—48no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—84no—
190C2×C4×C11#12112yes—
191C2×C4×C11#12312yes—
192C2×C4×C11#12314yes—
193C2×C4×C11#12314yes—
194C2×C4×C11#12412yes—
195C2×C4×C11#12614yes—
196C2×C4×C11#12614yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—84no—
218C2×Dic11—84no—
219C8×C11—42no—
220C11⋊C8—42no—
221C23×D4C2×D1111yescharacteristic
222C23×C8—111no—
223C23×C8C2×D1111yescharacteristic
224C22×C4⋊C4—111no—
225C22×C4⋊C4—111no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C22⋊C4—221no—
228C22×C22⋊C4—221no—
229C22×C42—111no—
230C2×#102—24no—
231C2×#102—114no—
232C2×#102—224no—
233C2×#102C2×D1114yes—
234#390—114no—
235#390—222no—
236#382—114no—
237#382—222no—
238C2×#95—221no—
239C2×#95—221no—
240#340—114no—
241#340—114no—
242#336—114no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—816no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11#39714yes—
252C22×C11#46314yes—
253C22×C11#46314yes—
254C22×C11#48214yes—
255C22×C11#48214yes—
256C22×C11#48814yes—
257C22×C11#49014yes—
258C22×C11C2×#12111yescharacteristic
259C22×C11C2×#12311yescharacteristic
260C22×C11C2×#12411yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11—82no—
266C4×C11#39714yes—
267C4×C11C2×#12311yescharacteristic
268C4×C11C2×#12311yescharacteristic
269C4×C11C2×#12611yescharacteristic
270C4×C11C2×#12611yescharacteristic
271Dic11—42no—
272Dic11—42no—
273Dic11—82no—
274Dic11—82no—
275C25—21no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4C22⋊D1114yes—
283C22×D4C22×D1112yes—
284C23×C4—21no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—221no—
288C23×C4—221no—
289C23×C4C22×D1111yescharacteristic
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—112no—
294C22×C8—222no—
295C22×C8—222no—
296C22×C8—222no—
297C22×C8C22×D1112yes—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1112yes—
310C2×C22⋊C4—224no—
311C2×C22⋊C4—224no—
312C2×C22⋊C4—444no—
313C2×C22⋊C4—444no—
314C2×C42—112no—
315C2×C42—112no—
316C2×C42—222no—
317C2×C42—222no—
318#102—28no—
319#102—228no—
320#95—224no—
321#95—224no—
322C2×C11—84no—
323C2×C11#207318yescomplemented
324C2×C11C2×#39711yescharacteristic
325C2×C11C2×#46311yescharacteristic
326C2×C11C2×#46311yescharacteristic
327C2×C11C2×#48211yescharacteristic
328C2×C11C2×#48211yescharacteristic
329C2×C11C2×#48811yescharacteristic
330C2×C11C2×#49011yescharacteristic
331C24—24no—
332C24—22no—
333C24—42no—
334C24—42no—
335C24—42no—
336C24—42no—
337C24—42no—
338C24—42no—
339C24D4×D1111yescharacteristic
340C2×D4—28no—
341C2×D4—28no—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—44no—
349C2×D4—44no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4C2×C22⋊D1114yes—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—442no—
373C22×C4#433912yes—
374C22×C4#433912yes—
375C22×C4D4×D1111yescharacteristic
376C22×C4#434112yes—
377C22×C4#434112yes—
378C22×C4#434112yes—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C23×D1111yescharacteristic
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—44no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—444no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—442no—
398C22⋊C4—448no—
399C22⋊C4—448no—
400C42—224no—
401C42—222no—
402C42—222no—
403C11C2×#207311yescharacteristic, complemented, Sylow
404C23—24no—
405C23—42no—
406C23—48no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—48no—
411C23—42no—
412C23—42no—
413C23—48no—
414C23—84no—
415C23—84no—
416C23—84no—
417C23—84no—
418C23#6693612yes—
419C23#6693812yes—
420C23#6696412yes—
421C23#6696512yes—
422C23#6696712yes—
423C23#6696912yes—
424C23#6699212yes—
425C23C2×D4×D1111yescharacteristic
426D4—24no—
427D4—24no—
428D4—42no—
429D4—42no—
430D4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—84no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—444no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—884no—
450C2×C4—884no—
451C2×C4#6693214yes—
452C2×C4#6693214yes—
453C2×C4#6693612yes—
454C2×C4#6693812yes—
455C2×C4#6698214yes—
456C2×C4#6698814yes—
457C2×C4#6699212yes—
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C8—42no—
465C8—442no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—82no—
470C22—82no—
471C22—816no—
472C22—82no—
473C22—82no—
474C22#1062237714yes—
475C22#1062238114yes—
476C22#1062239214yes—
477C22#1062239714yes—
478C22#1062256514yes—
479C22#1062276614yes—
480C22#1062277814yes—
481C22C2×#6693611yescharacteristic
482C22C2×#6693811yescharacteristic
483C22C2×#6696411yescharacteristic
484C22C2×#6696511yescharacteristic
485C22C2×#6696711yescharacteristic
486C22C2×#6696911yescharacteristic
487C22C2×#6699211yescharacteristic
488C4—82no—
489C4—442no—
490C4—442no—
491C4—882no—
492C4—882no—
493C4#1062256514yes—
494C4C2×#6693211yescharacteristic
495C4C2×#6693211yescharacteristic
496C4C2×#6698211yescharacteristic
497C4C2×#6698811yescharacteristic
498C2—84no—
499C2#1307003218yesdirect product factor
500C2C2×#1062256511yescharacteristic
501C2C2×#1062276611yescharacteristic
502C2C2×#1062277811yescharacteristic
503C2C2×#1062239711yescharacteristic
504C2C2×#1062239211yescharacteristic
505C2C2×#1062238111yescharacteristic
506C2C2×#1062237711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2073
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#10622590C2semidirect
4. #13070032C2direct (N × H)
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
27. #10622590C22semidirect
28. #10622189C22semidirect
29. #10622188C22semidirect
30. #10622167C22semidirect
323. C2×C11#2073semidirect
403. C11C2×#2073semidirect
499. C2#13070032direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668962
C2×#106228342
C2×#106225902
#130700322
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1022
C2×#207311