Finite Group Databasebeta

← C2×#13067729 #14729520

Subgroups — C2×#13067729 #14729520

Order 2816.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10622307C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4C2×#10622456C211yesmaximal, characteristic
5#13067729C218yesmaximal, direct product factor
6C2×#10622120C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999—21no—
11C22×#4325—21no—
12C22×D88—21no—
13#10623115—22no—
14#10623115—22no—
15#10623115—22no—
16#10623115C2214yescomplemented
17C2×#66951—22no—
18C2×#66945—21no—
19C2×#66928—21no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66885—21no—
27C2×#66885—22no—
28#10622640—22no—
29#10622640C2214yescomplemented
30C2×#66873—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622456—22no—
33#10622456C2214yes—
34#10622307—22no—
35#10622307C2214yescomplemented
36C11×Q8⋊C8C2214yescomplemented
37#10622120C2214yescomplemented
38#10622097C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44D411yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11D412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#66999—24no—
57#66999—24no—
58C2×#4325—24no—
59C2×#4325—44no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D412yes—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C22×C11⋊C8—21no—
69C2×D88—24no—
70C2×D88—44no—
71#66951—28no—
72#66951—28no—
73#66945—24no—
74#66945—24no—
75#66928—24no—
76#66928—24no—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927C2312yes—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C4×Dic22—24no—
90C4×Dic22—24no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C4×C8×C11—21no—
94C4×C8×C11C2312yes—
95#66885—28no—
96#66885—24no—
97#66873—24no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C2×#1628—111nomaximal, Sylow
101C23×D11—21no—
102C23×D11—41no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C2×D412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×D44—21no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—44no—
121C2×D44—41no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—42no—
128C2×D44C2×D412yes—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—42no—
140C2×C8×C11—42no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2×D412yes—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2411yescharacteristic
151#4325—48no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—22no—
155(C2×D11)⋊C4—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11C2×D414yes—
162Dic11⋊C4—28no—
163C4×Dic11—28no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—42no—
166D88—48no—
167C2×#556—111no—
168C2×#486—111no—
169C2×#460—111no—
170C2×#459—111no—
171#1628—118no—
172C2×#332—111no—
173C2×Q8⋊C8D1111yescharacteristic, complemented
174C2×D4⋊C8—111no—
175C23×C11#12011yescharacteristic
176C22×D11—22no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—82no—
182C22×D11—82no—
183C22×D11—82no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#13512yes—
196C2×C4×C11#13512yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—44no—
205C2×Dic11—42no—
206D44—22no—
207D44—22no—
208D44—44no—
209D44—42no—
210D44—42no—
211D44—42no—
212D44—42no—
213D44—42no—
214D44—82no—
215D44—82no—
216D44—82no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—44no—
220Dic22—42no—
221Dic22—42no—
222Dic22—44no—
223C8×C11—42no—
224C8×C11—42no—
225C11⋊C8—42no—
226C22×SD16—221no—
227C22×D8—221no—
228#556—114no—
229#556—222no—
230#556—222no—
231#556—222no—
232C2×C4⋊Q8—111no—
233C2×#127—111no—
234C2×#126—222no—
235C2×#124—221no—
236C2×C22⋊Q8—221no—
237C2×C4×Q8—221no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4—111no—
240C2×#117—221no—
241#486—114no—
242#486—222no—
243#460—114no—
244#460—222no—
245#459—114no—
246#459—222no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#102—222no—
250C2×#102—221no—
251C2×#102—221no—
252C2×C4×C8C2×D1111yescharacteristic
253#332—114no—
254Q8⋊C8C2×D1114yescomplemented
255D4⋊C8—114no—
256C22×C11#44912yes—
257C22×C11#44912yes—
258C22×C11#45412yes—
259C22×C11C2×#12011yescharacteristic
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—84no—
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—164no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11#44912yes—
273C4×C11#44912yes—
274C4×C11C2×#13511yescharacteristic
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278Dic11—44no—
279Dic11—42no—
280C22×Q8—221no—
281C22×Q8D4411yescharacteristic
282C22×D4—111no—
283C22×D4—221no—
284C22×D4—221no—
285C22×D4—221no—
286C23×C4—221no—
287C2×SD16—224no—
288C2×SD16—444no—
289C2×D8—224no—
290C2×D8—444no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—221no—
294C4⋊Q8—112no—
295C4⋊Q8—112no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298#127—112no—
299#127—221no—
300#127—221no—
301#127—221no—
302#126—228no—
303#126—228no—
304#124—224no—
305#124—224no—
306C22⋊Q8—224no—
307C22⋊Q8—224no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—224no—
311C4×Q8—224no—
312C4×Q8D4412yes—
313C4×Q8C22×D1112yes—
314C4×D4—112no—
315C4×D4—112no—
316C4×D4—221no—
317C4×D4—221no—
318#117—224no—
319#117—224no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4D4411yescharacteristic
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—221no—
329C2×C42—21no—
330C2×C42—222no—
331C2×C42C22×D1111yescharacteristic
332C4⋊C8—21no—
333C4⋊C8—112no—
334C4⋊C8—221no—
335C4⋊C8C22×D1112yes—
336#102—224no—
337#102—228no—
338#102—224no—
339C4×C8—21no—
340C4×C8C22×D1112yes—
341C2×C11#162814yescomplemented
342C2×C11C2×#44911yescharacteristic
343C2×C11C2×#44911yescharacteristic
344C2×C11C2×#45411yescharacteristic
345D11—82no—
346D11—162no—
347C24—221no—
348C24—441no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—222no—
353C2×Q8—222no—
354C2×Q8—442no—
355C2×Q8—442no—
356C2×Q8C2×D4412yes—
357C2×D4—112no—
358C2×D4—221no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—444no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—442no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—442no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4C2×D4411yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383SD16—448no—
384D8—448no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—42no—
389C2×C8—222no—
390C2×C8—442no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—112no—
395C4⋊C4—114no—
396C4⋊C4—228no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4C2×D4412yes—
402C22⋊C4—228no—
403C22⋊C4—228no—
404C22⋊C4—222no—
405C22⋊C4—222no—
406C42—22no—
407C42—22no—
408C42—228no—
409C42C2×D4411yescharacteristic
410C42D4×D1111yescharacteristic
411C42D4×D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11C2×#162811yescharacteristic, complemented, Sylow
414C23—222no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—882no—
420C23—882no—
421C23—882no—
422C23#6693511yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—42no—
426Q8—442no—
427Q8—442no—
428Q8—444no—
429D4—222no—
430D4—222no—
431D4—444no—
432D4—442no—
433D4—442no—
434D4—442no—
435D4—442no—
436D4—442no—
437D4—882no—
438D4—882no—
439D4—882no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—222no—
446C2×C4—224no—
447C2×C4—442no—
448C2×C4—444no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—444no—
452C2×C4#6693511yescharacteristic
453C2×C4#6693511yescharacteristic
454C2×C4#6693511yescharacteristic
455C2×C4#6695712yes—
456C2×C4#6696112yes—
457C2×C4#6696712yes—
458C2×C4#6697212yes—
459C2×C4C22×D4411yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×D4×D1111yescharacteristic
462C8—42no—
463C8—42no—
464C8—442no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22—884no—
469C22—882no—
470C22—882no—
471C22—882no—
472C22—1764no—
473C22#1062234712yes—
474C22#1062242412yes—
475C22#1062244012yes—
476C22C2×#6693511yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—442no—
482C4—444no—
483C4#1062234712yes—
484C4#1062242412yes—
485C4C2×#6695711yescharacteristic
486C4C2×#6696111yescharacteristic
487C4C2×#6696711yescharacteristic
488C4C2×#6697211yescharacteristic
489C2—882no—
490C2—1762no—
491C2#1306772914yesdirect product factor
492C2C2×#1062234711yescharacteristic
493C2C2×#1062242411yescharacteristic
494C2C2×#1062244011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#10622456C2
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1628
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. C2×#10622307C2semidirect
3. C2×#10622640C2semidirect
5. #13067729C2direct (N × H)
6. C2×#10622120C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
16. #10623115C22semidirect
29. #10622640C22semidirect
35. #10622307C22semidirect
36. C11×Q8⋊C8C22semidirect
37. #10622120C22semidirect
38. #10622097C22semidirect
173. C2×Q8⋊C8D11semidirect
254. Q8⋊C8C2×D11semidirect
341. C2×C11#1628semidirect
413. C11C2×#1628semidirect
491. C2#13067729direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106223072
C2×#106226402
C2×#106224562
#130677292
C2×#106221202
C2×#106220972
C2×C11×Q8⋊C82
C2×#162811