Finite Group Databasebeta

← C2×#13070580 #14907712

Subgroups — C2×#13070580 #14907712

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C22×#66892C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic, complemented
4#13070580C218yesmaximal, direct product factor
5C2×#10622203C211yesmaximal, characteristic, complemented
6C2×#10622205C211yesmaximal, characteristic, complemented
7C2×#10622199C211yesmaximal, characteristic, complemented
8C2×C11×#578C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4—21no—
10C11×#578—22no—
11C11×#578—22no—
12C11×#578—22no—
13C11×#578C2214yescomplemented
14C2×C11×#137—22no—
15C2×C11×#137—21no—
16C2×C11×#135—21no—
17C2×C11×#135C2211yescharacteristic
18C22×C11×Q16—21no—
19C22×C11×Q16C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×#67002—21no—
22C22×D88C2211yescharacteristic
23#10622806—22no—
24#10622806C2214yescomplemented
25C2×#66892—22no—
26C2×#66892—22no—
27C2×#66892—21no—
28C2×#66892C2214yescomplemented
29C2×#66890—21no—
30#10622755—22no—
31#10622755C2214yescomplemented
32C2×#66887—21no—
33C2×#66883C2211yescharacteristic
34C2×#66876C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36#10622205C2214yescomplemented
37#10622203C2214yescomplemented
38#10622199C2214yescomplemented
39C11×2−1+4—24no—
40C11×2−1+4—24no—
41C11×2−1+4—42no—
42C11×2−1+4—42no—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—42no—
46C2×C11×#41—41no—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—41no—
51C22×D44—21no—
52C11×#137—28no—
53C11×#137—24no—
54C11×#137—28no—
55C11×#137—24no—
56C11×#135—24no—
57C11×#135—24no—
58C11×#135—21no—
59C11×#135—21no—
60C11×#135D412yes—
61C11×#135C2312yes—
62C2×C11×Q16—22no—
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×Q16—21no—
66C2×C11×Q16—21no—
67C2×C11×Q16—21no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×Q16D412yes—
70C2×C11×Q16D412yes—
71C2×C11×Q16C2312yes—
72C2×C11×SD16—22no—
73C2×C11×SD16—21no—
74C2×C11×D8D411yescharacteristic
75C11×#131—21no—
76C11×#131—21no—
77C11×#131D412yes—
78C11×#131C2312yes—
79C2×C11×M16—21no—
80C2×C11×M16D411yescharacteristic
81C22×C8×C11—21no—
82C22×C8×C11C2311yescharacteristic
83#67002—24no—
84#67002—42no—
85C2×#4325—41no—
86C2×#4323—41no—
87C2×#4318—21no—
88C2×D88—21no—
89C2×D88—21no—
90C2×D88—21no—
91C2×D88—21no—
92C2×D88—21no—
93C2×D88C2312yes—
94#66892—28no—
95#66892—24no—
96#66890—24no—
97#66887—24no—
98#66883—21no—
99#66883C2312yes—
100#66876—21no—
101#66876C2312yes—
102C2×C11⋊C16—21no—
103C2×C11⋊C16—21no—
104C2×C11⋊C16—21no—
105C2×C11⋊C16C2312yes—
106C2×#2193—111nomaximal, Sylow
107C23×D11—41no—
108C11×#41—21no—
109C11×#41—21no—
110C11×#41—28no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—44no—
114C11×#41—48no—
115C11×#41—48no—
116C11×#41—44no—
117C11×#41—44no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41D812yes—
121C11×#41C2×D412yes—
122C2×Q8×C11—28no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—42no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11—41no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11D811yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—41no—
139C2×D4×C11D811yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C2×D44—22no—
147C2×D44—41no—
148C2×D44—41no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C11×Q16—28no—
153C11×Q16—21no—
154C11×Q16—22no—
155C11×Q16—22no—
156C11×Q16—22no—
157C11×Q16C2×D412yes—
158C11×Q16C2×D414yes—
159C11×SD16—28no—
160C11×SD16—22no—
161C11×SD16—22no—
162C11×D8—21no—
163C11×D8C2×D412yes—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—21no—
167C11×M16C2×D412yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2411yescharacteristic
177#4325—44no—
178#4323—44no—
179#4318—22no—
180#4318—41no—
181C2×C11⋊C8—41no—
182D88—22no—
183D88—22no—
184D88—41no—
185D88—41no—
186C11⋊C16—22no—
187C11⋊C16—22no—
188C2×#578D1111yescharacteristic, complemented
189C2×#509—111no—
190C22×SD32—111no—
191C2×#472—111no—
192#2193—118no—
193C2×#362—111no—
194C2×#359—111no—
195C2×#350—111no—
196C23×C11—21no—
197C23×C11—41no—
198C23×C11AGL(1,ℤ/8)11yescharacteristic
199C22×D11—42no—
200C22×D11—81no—
201C22×D11—81no—
202C22×D11—162no—
203Q8×C11—21no—
204Q8×C11—24no—
205Q8×C11—22no—
206Q8×C11—48no—
207Q8×C11—42no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11C2×D812yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—21no—
216D4×C11—48no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—41no—
220D4×C11C2×D812yes—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—48no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11C2×D811yescharacteristic
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238D44—42no—
239D44—42no—
240D44—81no—
241D44—81no—
242C8×C11—22no—
243C8×C11#12011yescharacteristic
244C8×C11#12011yescharacteristic
245C8×C11C22×D411yescharacteristic
246C8×C11C22×D411yescharacteristic
247C11⋊C8—42no—
248C2×2−1+4—21no—
249#578—22no—
250#578—22no—
251#578—22no—
252#578C2×D1114yescomplemented
253C2×#137—22no—
254C2×#137—21no—
255C2×AGL(1,ℤ/8)—221no—
256C2×#135—21no—
257C2×#135C2×D1111yescharacteristic
258C22×Q16—21no—
259C22×Q16C2×D1111yescharacteristic
260C22×D8—111no—
261C2×#131C2×D1111yescharacteristic
262#509—114no—
263#509—222no—
264C2×SD32—114no—
265C2×SD32—222no—
266C2×SD32—222no—
267C2×SD32—221no—
268C2×D16—221no—
269C2×M32—111no—
270C22×C16—111no—
271#472—114no—
272#472—222no—
273C2×#108—111no—
274C2×#100—221no—
275#362—114no—
276#359—114no—
277#350—114no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—82no—
283C22×C11#44711yescharacteristic
284C22×C11#44711yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C2×D11—82no—
287C2×D11—162no—
288C2×D11—162no—
289C2×D11—162no—
290C4×C11—22no—
291C4×C11—44no—
292C4×C11—42no—
293C4×C11#44711yescharacteristic
294C4×C11#44711yescharacteristic
295C4×C11C2×#12011yescharacteristic
296C4×C11C22×D811yescharacteristic
2972−1+4—24no—
2982−1+4—24no—
2992−1+4—42no—
3002−1+4—42no—
301C2×#41—22no—
302C2×#41—21no—
303C2×#41—42no—
304C2×#41—41no—
305C2×#41C22⋊D1111yescharacteristic
306C22×Q8—22no—
307C22×Q8—21no—
308C22×Q8—41no—
309C22×D4—221no—
310#137—24no—
311#137—28no—
312#137—28no—
313#137—24no—
314AGL(1,ℤ/8)—224no—
315AGL(1,ℤ/8)—442no—
316#135—24no—
317#135—24no—
318#135—21no—
319#135—21no—
320#135C22⋊D1112yes—
321#135C22×D1112yes—
322C2×Q16—22no—
323C2×Q16—24no—
324C2×Q16—24no—
325C2×Q16—21no—
326C2×Q16—21no—
327C2×Q16—21no—
328C2×Q16C22⋊D1111yescharacteristic
329C2×Q16C22⋊D1112yes—
330C2×Q16C22⋊D1112yes—
331C2×Q16C22×D1112yes—
332C2×SD16—22no—
333C2×SD16—21no—
334C2×SD16—441no—
335C2×D8—112no—
336C2×D8—221no—
337C2×D8—221no—
338C2×D8—221no—
339C2×D8—221no—
340C2×D8—221no—
341C2×D8—441no—
342C2×D8C22⋊D1111yescharacteristic
343#131—21no—
344#131—21no—
345#131C22⋊D1112yes—
346#131C22×D1112yes—
347C2×M16—21no—
348C2×M16—221no—
349C2×M16C22⋊D1111yescharacteristic
350C22×C8—21no—
351C22×C8C22×D1111yescharacteristic
352SD32—228no—
353SD32—224no—
354D16—224no—
355M32—112no—
356M32—221no—
357C2×C16—112no—
358C2×C16—221no—
359C2×C16—221no—
360C2×C16—221no—
361#108—112no—
362#108—221no—
363#100—224no—
364C2×C11—21no—
365C2×C11—21no—
366C2×C11—42no—
367C2×C11—82no—
368C2×C11#219312yescomplemented
369C2×C11C2×#44711yescharacteristic
370D11—162no—
371C24—441no—
372#41—21no—
373#41—21no—
374#41—28no—
375#41—22no—
376#41—22no—
377#41—44no—
378#41—48no—
379#41—48no—
380#41—44no—
381#41—44no—
382#41—41no—
383#41—41no—
384#41#432312yes—
385#41C2×C22⋊D1112yes—
386C2×Q8—28no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—42no—
392C2×Q8—44no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8#432311yescharacteristic
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—222no—
404C2×D4—441no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C2×D4#432311yescharacteristic
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4C2×C22⋊D1111yescharacteristic
416Q16—28no—
417Q16—21no—
418Q16—22no—
419Q16—22no—
420Q16—22no—
421Q16C2×C22⋊D1112yes—
422Q16C2×C22⋊D1114yes—
423SD16—28no—
424SD16—22no—
425SD16—22no—
426SD16—444no—
427D8—21no—
428D8—222no—
429D8—222no—
430D8—444no—
431D8—441no—
432D8—441no—
433D8C2×C22⋊D1112yes—
434M16—21no—
435M16—22no—
436M16—22no—
437M16—222no—
438M16—441no—
439M16C2×C22⋊D1112yes—
440C2×C8—21no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—441no—
444C2×C8C2×C22⋊D1111yescharacteristic
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C2×C22⋊D1111yescharacteristic
449C2×C8C23×D1111yescharacteristic
450C16—222no—
451C16—222no—
452C11C2×#219311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—41no—
455C23—442no—
456C23—881no—
457C23—881no—
458C23—1762no—
459C23#6698511yescharacteristic
460Q8—21no—
461Q8—24no—
462Q8—22no—
463Q8—48no—
464Q8—42no—
465Q8—41no—
466Q8—42no—
467Q8—42no—
468Q8C2×#432312yes—
469D4—22no—
470D4—22no—
471D4—21no—
472D4—22no—
473D4—48no—
474D4—42no—
475D4—42no—
476D4—41no—
477D4—442no—
478D4—442no—
479D4—881no—
480D4—881no—
481D4C2×#432312yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—48no—
486C2×C4—48no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4C2×#432311yescharacteristic
494C2×C4C2×#432311yescharacteristic
495C2×C4#6698511yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4#6700611yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—22no—
500C8—442no—
501C8#6700611yescharacteristic
502C8#6700611yescharacteristic
503C8C22×C22⋊D1111yescharacteristic
504C8C22×C22⋊D1111yescharacteristic
505C22—22no—
506C22—22no—
507C22—42no—
508C22—42no—
509C22—82no—
510C22—882no—
511C22—1762no—
512C22—1762no—
513C22—1762no—
514C22#1062283011yescharacteristic
515C22#1062283011yescharacteristic
516C22C2×#6698511yescharacteristic
517C4—22no—
518C4—44no—
519C4—42no—
520C4#1062283011yescharacteristic
521C4#1062283011yescharacteristic
522C4C22×#432311yescharacteristic
523C4C2×#6700611yescharacteristic
524C2—21no—
525C2—21no—
526C2—42no—
527C2—82no—
528C2—1762no—
529C2#1307058012yesdirect product factor
530C2C2×#1062283011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#578C2
socleC22×C11#447
hypercenterC2×#578D11
hypocenterC11C2×#2193
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C22×#66892C2semidirect
3. C2×#10622755C2semidirect
4. #13070580C2direct (N × H)
5. C2×#10622203C2semidirect
6. C2×#10622205C2semidirect
7. C2×#10622199C2semidirect
8. C2×C11×#578C2semidirect
13. C11×#578C22semidirect
24. #10622806C22semidirect
28. C2×#66892C22semidirect
31. #10622755C22semidirect
36. #10622205C22semidirect
37. #10622203C22semidirect
38. #10622199C22semidirect
188. C2×#578D11semidirect
252. #578C2×D11semidirect
368. C2×C11#2193semidirect
452. C11C2×#2193semidirect
529. C2#13070580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228062
C22×#668922
C2×#106227552
#130705802
C2×#106222032
C2×#106222052
C2×#106221992
C2×C11×#5782
C2×#219311