Finite Group Databasebeta

← C2×#13070585 #14907702

Subgroups — C2×#13070585 #14907702

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623283C211yesmaximal, characteristic
2C2×#10622792C211yesmaximal, characteristic, complemented
3C22×#66892C211yesmaximal, characteristic, complemented
4#13070585C218yesmaximal, direct product factor
5C2×#10622133C211yesmaximal, characteristic, complemented
6C2×#10622135C211yesmaximal, characteristic, complemented
7C2×#10622199C211yesmaximal, characteristic, complemented
8C2×C11×#473C211yesmaximal, characteristic, complemented
9C2×#67042—21no—
10C2×C11×#137—21no—
11C22×C11×Q16C2211yescharacteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623283—22no—
14#10623283—22no—
15#10623283—22no—
16#10623283C2214yes—
17C2×#66961—21no—
18C2×#66961—22no—
19C2×#66957—21no—
20C2×#66957C2211yescharacteristic
21C22×D88—21no—
22C22×D88C2211yescharacteristic
23C11×#473—22no—
24C11×#473C2214yescomplemented
25C2×C11×#108C2211yescharacteristic, complemented
26C2×C11×#101—21no—
27C2×#66893—21no—
28#10622792—22no—
29#10622792C2214yescomplemented
30C2×#66892—22no—
31C2×#66892—22no—
32C2×#66892—21no—
33C2×#66892C2214yescomplemented
34C2×#66876C2211yescharacteristic, complemented
35C22×C11⋊C16C2211yescharacteristic, complemented
36#10622199C2214yescomplemented
37#10622135C2214yescomplemented
38#10622133C2214yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×Q8×C11—21no—
41#67042—24no—
42#67042—24no—
43#67042—42no—
44#67042—42no—
45C2×#4343—41no—
46C2×D4×D11—42no—
47C2×D4×D11—41no—
48C2×#4339—22no—
49C2×#4339—21no—
50C22×D44—22no—
51C22×D44—21no—
52C11×#137—24no—
53C11×#137—42no—
54C2×C11×Q16—21no—
55C2×C11×Q16—21no—
56C2×C11×Q16—21no—
57C2×C11×Q16—21no—
58C2×C11×Q16—21no—
59C2×C11×Q16—41no—
60C2×C11×Q16C2312yescomplemented
61C2×C11×SD16—41no—
62C11×#131—21no—
63C11×#131—21no—
64C11×#131D412yes—
65C11×#131C2312yes—
66C2×C11×M16—21no—
67C2×C11×M16—21no—
68C2×C11×M16D411yescharacteristic
69C22×C8×C11—21no—
70C22×C8×C11C2311yescharacteristic
71#66961—24no—
72#66961—28no—
73#66961—24no—
74#66961—28no—
75C2×Dic44D411yescharacteristic
76#66957—24no—
77#66957—21no—
78#66957—21no—
79#66957—24no—
80#66957D412yes—
81#66957C2312yes—
82C2×D88—22no—
83C2×D88—24no—
84C2×D88—21no—
85C2×D88—21no—
86C2×D88—21no—
87C2×D88—24no—
88C2×D88D411yescharacteristic
89C2×D88D412yes—
90C2×D88D412yes—
91C2×D88C2312yes—
92C2×#4314—22no—
93C2×#4314—21no—
94C11×#108—21no—
95C11×#108C2312yescomplemented
96C11×#101—24no—
97#66893—24no—
98#66892—28no—
99#66892—24no—
100#66876—21no—
101#66876C2312yescomplemented
102C2×C11⋊C16—21no—
103C2×C11⋊C16—21no—
104C2×C11⋊C16—21no—
105C2×C11⋊C16C2312yescomplemented
106C2×#2194—111nomaximal, Sylow
107C23×D11—42no—
108C23×D11—41no—
109C11×#41—21no—
110C11×#41—21no—
111C11×#41D812yes—
112C11×#41C2×D412yes—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11D811yescharacteristic
120C2×D4×C11—21no—
121C2×D4×C11D811yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—42no—
126C2×C22⋊D11—41no—
127#4343—44no—
128#4343—44no—
129D4×D11—48no—
130D4×D11—48no—
131D4×D11—44no—
132D4×D11—44no—
133#4339—28no—
134#4339—22no—
135#4339—22no—
136#4339—44no—
137#4339—41no—
138#4339—41no—
139C2×D44—28no—
140C2×D44—22no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—42no—
145C2×D44—44no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44—41no—
149C2×C4×D11—42no—
150C2×C4×D11—41no—
151C2×Dic22—21no—
152C11×Q16—22no—
153C11×Q16—22no—
154C11×Q16—41no—
155C11×Q16—41no—
156C11×Q16—44no—
157C11×SD16—44no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—21no—
161C11×M16—22no—
162C11×M16—41no—
163C11×M16C2×D412yes—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—21no—
167C2×C8×C11—41no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2411yescharacteristic
174Dic44—21no—
175Dic44C2×D412yes—
176D88—28no—
177D88—21no—
178D88—22no—
179D88—22no—
180D88—22no—
181D88C2×D412yes—
182D88C2×D414yes—
183#4314—28no—
184#4314—22no—
185#4314—22no—
186C11⋊C16—22no—
187C11⋊C16—22no—
188C2×#576—111no—
189C2×#510—111no—
190C22×SD32—111no—
191C2×#473D1111yescharacteristic, complemented
192#2194—118no—
193C2×#361—111no—
194C2×#359—111no—
195C2×#350—111no—
196C23×C11—21no—
197C23×C11AGL(1,ℤ/8)11yescharacteristic
198C22×D11—42no—
199C22×D11—41no—
200C22×D11—48no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—162no—
204C22×D11—164no—
205Q8×C11—21no—
206Q8×C11—42no—
207Q8×C11—42no—
208Q8×C11—81no—
209Q8×C11—81no—
210Q8×C11C2×D812yes—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—21no—
214D4×C11C2×D812yes—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—81no—
220C2×C4×C11—81no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C22⋊D11—48no—
228C22⋊D11—42no—
229C22⋊D11—42no—
230C2×Dic11—41no—
231D44—24no—
232D44—22no—
233D44—48no—
234D44—42no—
235D44—41no—
236D44—42no—
237D44—42no—
238C4×D11—48no—
239C4×D11—42no—
240C4×D11—42no—
241Dic22—22no—
242Dic22—41no—
243C8×C11—22no—
244C8×C11—42no—
245C8×C11#12011yescharacteristic
246C8×C11#12011yescharacteristic
247C8×C11C22×D411yescharacteristic
248C8×C11C22×D411yescharacteristic
249C2×H(5,𝔽2)—221no—
250#576—114no—
251#576—222no—
252#576—222no—
253#576—222no—
254C2×#137—21no—
255C2×AGL(1,ℤ/8)—222no—
256C2×AGL(1,ℤ/8)—221no—
257C2×#135—111no—
258C2×#135—221no—
259C22×Q16C2×D1111yescharacteristic, complemented
260C22×D8—111no—
261C22×D8—221no—
262C2×#131C2×D1111yescharacteristic
263#510—114no—
264#510—222no—
265C2×Q32—221no—
266C2×SD32—114no—
267C2×SD32—222no—
268C2×SD32—222no—
269C2×SD32—221no—
270C2×M32—111no—
271C22×C16—111no—
272#473—22no—
273#473C2×D1114yescomplemented
274C2×#108C2×D1111yescharacteristic, complemented
275C2×#101—21no—
276#361—114no—
277#359—114no—
278#350—114no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—42no—
282C22×C11#44711yescharacteristic
283C22×C11#44711yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C2×D11—42no—
286C2×D11—44no—
287C2×D11—84no—
288C2×D11—82no—
289C2×D11—162no—
290C2×D11—162no—
291C2×D11—168no—
292C4×C11—22no—
293C4×C11—82no—
294C4×C11#44711yescharacteristic
295C4×C11#44711yescharacteristic
296C4×C11C2×#12011yescharacteristic
297C4×C11C22×D811yescharacteristic
298Dic11—42no—
299H(5,𝔽2)—224no—
300H(5,𝔽2)—224no—
301H(5,𝔽2)—442no—
302H(5,𝔽2)—442no—
303C2×#41—222no—
304C2×#41—221no—
305C2×#41—441no—
306C2×#41C22⋊D1111yescharacteristic
307C22×Q8—21no—
308C22×D4—222no—
309C22×D4—221no—
310C22×D4—442no—
311C22×D4—441no—
312#137—24no—
313#137—42no—
314AGL(1,ℤ/8)—228no—
315AGL(1,ℤ/8)—224no—
316AGL(1,ℤ/8)—228no—
317AGL(1,ℤ/8)—224no—
318#135—112no—
319#135—112no—
320#135—224no—
321#135—224no—
322#135—221no—
323#135—221no—
324C2×Q16—21no—
325C2×Q16—21no—
326C2×Q16—21no—
327C2×Q16—21no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16—111no—
331C2×Q16C22×D1112yescomplemented
332C2×SD16—41no—
333C2×SD16—222no—
334C2×SD16—221no—
335C2×D8—112no—
336C2×D8—112no—
337C2×D8—111no—
338C2×D8—112no—
339C2×D8—224no—
340C2×D8—222no—
341C2×D8—224no—
342C2×D8—221no—
343C2×D8—221no—
344C2×D8—221no—
345#131—21no—
346#131—21no—
347#131C22⋊D1112yes—
348#131C22×D1112yes—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16C22⋊D1111yescharacteristic
352C22×C8—21no—
353C22×C8C22×D1111yescharacteristic
354Q32—224no—
355SD32—228no—
356SD32—224no—
357M32—112no—
358M32—221no—
359C2×C16—112no—
360C2×C16—221no—
361C2×C16—221no—
362C2×C16—221no—
363#108—21no—
364#108C22×D1112yescomplemented
365#101—24no—
366C2×C11—21no—
367C2×C11—21no—
368C2×C11—42no—
369C2×C11#219412yescomplemented
370C2×C11C2×#44711yescharacteristic
371D11—84no—
372D11—82no—
373C24—442no—
374C24—441no—
375#41—21no—
376#41—21no—
377#41—228no—
378#41—222no—
379#41—222no—
380#41—444no—
381#41—444no—
382#41—444no—
383#41—441no—
384#41—441no—
385#41#432312yes—
386#41C2×C22⋊D1112yes—
387C2×Q8—22no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—221no—
394C2×Q8#432311yescharacteristic
395C2×D4—21no—
396C2×D4—228no—
397C2×D4—222no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—442no—
402C2×D4—444no—
403C2×D4—448no—
404C2×D4—448no—
405C2×D4—444no—
406C2×D4—442no—
407C2×D4—441no—
408C2×D4—444no—
409C2×D4—441no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4#432311yescharacteristic
413C22×C4—21no—
414C22×C4—41no—
415C22×C4—442no—
416C22×C4—441no—
417C22×C4C2×C22⋊D1111yescharacteristic
418Q16—22no—
419Q16—22no—
420Q16—44no—
421Q16—41no—
422Q16—41no—
423Q16—112no—
424Q16—221no—
425SD16—44no—
426SD16—228no—
427SD16—222no—
428SD16—222no—
429D8—114no—
430D8—112no—
431D8—228no—
432D8—222no—
433D8—221no—
434D8—222no—
435D8—222no—
436M16—21no—
437M16—22no—
438M16—22no—
439M16—22no—
440M16—41no—
441M16C2×C22⋊D1112yes—
442C2×C8—21no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—41no—
446C2×C8D4×D1111yescharacteristic
447C2×C8D4×D1111yescharacteristic
448C2×C8D4×D1111yescharacteristic
449C2×C8D4×D1111yescharacteristic
450C2×C8C2×C22⋊D1111yescharacteristic
451C2×C8C23×D1111yescharacteristic
452C16—222no—
453C16—222no—
454C11C2×#219411yescharacteristic, complemented, Sylow
455C23—21no—
456C23—448no—
457C23—442no—
458C23—441no—
459C23—442no—
460C23—442no—
461C23—1762no—
462C23—1764no—
463C23#6700211yescharacteristic
464Q8—21no—
465Q8—42no—
466Q8—42no—
467Q8—81no—
468Q8—81no—
469Q8—222no—
470Q8—441no—
471Q8C2×#432312yes—
472D4—22no—
473D4—22no—
474D4—21no—
475D4—224no—
476D4—222no—
477D4—448no—
478D4—448no—
479D4—442no—
480D4—442no—
481D4—442no—
482D4—441no—
483D4—442no—
484D4—442no—
485D4C2×#432312yes—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—448no—
493C2×C4—441no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4C2×#432311yescharacteristic
497C2×C4C2×#432311yescharacteristic
498C2×C4#6699011yescharacteristic
499C2×C4#6699011yescharacteristic
500C2×C4#6700211yescharacteristic
501C2×C4C22×C22⋊D1111yescharacteristic
502C8—22no—
503C8—42no—
504C8#6699011yescharacteristic
505C8#6699011yescharacteristic
506C8C2×D4×D1111yescharacteristic
507C8C2×D4×D1111yescharacteristic
508C22—22no—
509C22—22no—
510C22—42no—
511C22—444no—
512C22—442no—
513C22—884no—
514C22—882no—
515C22—1762no—
516C22—1762no—
517C22—1768no—
518C22#1062264911yescharacteristic
519C22#1062264911yescharacteristic
520C22C2×#6700211yescharacteristic
521C4—22no—
522C4—82no—
523C4—442no—
524C4#1062264911yescharacteristic
525C4#1062264911yescharacteristic
526C4C22×#432311yescharacteristic
527C4C2×#6699011yescharacteristic
528C2—21no—
529C2—21no—
530C2—42no—
531C2—884no—
532C2—882no—
533C2#1307058512yesdirect product factor
534C2C2×#1062264911yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#473C2
socleC22×C11#447
prime radicalC2×#10623283C2
hypercenterC2×#473D11
hypocenterC11C2×#2194
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
2. C2×#10622792C2semidirect
3. C22×#66892C2semidirect
4. #13070585C2direct (N × H)
5. C2×#10622133C2semidirect
6. C2×#10622135C2semidirect
7. C2×#10622199C2semidirect
8. C2×C11×#473C2semidirect
11. C22×C11×Q16C22semidirect
24. C11×#473C22semidirect
25. C2×C11×#108C22semidirect
29. #10622792C22semidirect
33. C2×#66892C22semidirect
34. C2×#66876C22semidirect
35. C22×C11⋊C16C22semidirect
36. #10622199C22semidirect
37. #10622135C22semidirect
38. #10622133C22semidirect
60. C2×C11×Q16C23semidirect
95. C11×#108C23semidirect
101. #66876C23semidirect
105. C2×C11⋊C16C23semidirect
191. C2×#473D11semidirect
259. C22×Q16C2×D11semidirect
273. #473C2×D11semidirect
274. C2×#108C2×D11semidirect
331. C2×Q16C22×D11semidirect
364. #108C22×D11semidirect
369. C2×C11#2194semidirect
454. C11C2×#2194semidirect
533. C2#13070585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232832
C2×#106227922
C22×#668922
#130705852
C2×#106221332
C2×#106221352
C2×#106221992
C2×C11×#4732
C2×#219411