Finite Group Databasebeta

← C2×#13070571 #14907694

Subgroups — C2×#13070571 #14907694

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623283C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic, complemented
3C22×#66890C211yesmaximal, characteristic, complemented
4#13070571C218yesmaximal, direct product factor
5C2×#10622133C211yesmaximal, characteristic, complemented
6C2×#10622135C211yesmaximal, characteristic, complemented
7C2×#10622199C211yesmaximal, characteristic, complemented
8C2×C11×#472C211yesmaximal, characteristic, complemented
9C2×#67042—21no—
10C2×C11×AGL(1,ℤ/8)—21no—
11C22×C11×D8C2211yescharacteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623283—22no—
14#10623283—22no—
15#10623283—22no—
16#10623283C2214yescomplemented
17C2×#66961—21no—
18C2×#66961—22no—
19C2×#66957—21no—
20C2×#66957C2211yescharacteristic
21C22×D88—21no—
22C22×D88C2211yescharacteristic
23C11×#472—22no—
24C11×#472C2214yescomplemented
25C2×C11×#108C2211yescharacteristic, complemented
26C2×C11×#100—21no—
27C2×#66891—21no—
28#10622760—22no—
29#10622760C2214yescomplemented
30C2×#66890—22no—
31C2×#66890—22no—
32C2×#66890—21no—
33C2×#66890C2214yescomplemented
34C2×#66876C2211yescharacteristic, complemented
35C22×C11⋊C16C2211yescharacteristic, complemented
36#10622199C2214yescomplemented
37#10622135C2214yescomplemented
38#10622133C2214yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×D4×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×AGL(1,ℤ/8)—24no—
53C11×AGL(1,ℤ/8)—42no—
54C2×C11×SD16—41no—
55C2×C11×D8—21no—
56C2×C11×D8—21no—
57C2×C11×D8—21no—
58C2×C11×D8—21no—
59C2×C11×D8—21no—
60C2×C11×D8—41no—
61C2×C11×D8C2312yescomplemented
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×#100—24no—
97#66891—24no—
98#66890—28no—
99#66890—24no—
100#66876—21no—
101#66876C2312yescomplemented
102C2×C11⋊C16—21no—
103C2×C11⋊C16—21no—
104C2×C11⋊C16—21no—
105C2×C11⋊C16C2312yescomplemented
106C2×#2192—111nomaximal, Sylow
107C24×C11—41no—
108C23×D11—42no—
109C23×D11—41no—
110C11×#41—21no—
111C11×#41—21no—
112C11×#41D812yes—
113C11×#41C2×D412yes—
114C2×Q8×C11D811yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11D811yescharacteristic
123C22×C4×C11—21no—
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×SD16—44no—
153C11×D8—22no—
154C11×D8—22no—
155C11×D8—41no—
156C11×D8—41no—
157C11×D8—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×#509—111no—
190C22×D16—111no—
191C2×#472D1111yescharacteristic, complemented
192#2192—118no—
193C2×#361—111no—
194C2×#359—111no—
195C2×#350—111no—
196C23×C11—21no—
197C23×C11—42no—
198C23×C11—81no—
199C23×C11—81no—
200C23×C11—162no—
201C23×C11AGL(1,ℤ/8)11yescharacteristic
202C22×D11—42no—
203C22×D11—41no—
204C22×D11—48no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—162no—
208C22×D11—164no—
209Q8×C11—21no—
210Q8×C11C2×D812yes—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—21no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—81no—
217D4×C11—81no—
218D4×C11C2×D812yes—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—48no—
229C22⋊D11—42no—
230C22⋊D11—42no—
231C2×Dic11—41no—
232D44—24no—
233D44—22no—
234D44—48no—
235D44—42no—
236D44—41no—
237D44—42no—
238D44—42no—
239C4×D11—48no—
240C4×D11—42no—
241C4×D11—42no—
242Dic22—22no—
243Dic22—41no—
244C8×C11—22no—
245C8×C11—42no—
246C8×C11#12011yescharacteristic
247C8×C11#12011yescharacteristic
248C8×C11C22×D411yescharacteristic
249C8×C11C22×D411yescharacteristic
250C2×H(5,𝔽2)—221no—
251#576—114no—
252#576—222no—
253#576—222no—
254#576—222no—
255C2×AGL(1,ℤ/8)—21no—
256C2×AGL(1,ℤ/8)—222no—
257C2×AGL(1,ℤ/8)—221no—
258C2×#135—111no—
259C2×#135—221no—
260C22×D8—111no—
261C22×D8—221no—
262C22×D8C2×D1111yescharacteristic, complemented
263C2×#131C2×D1111yescharacteristic
264#509—114no—
265#509—222no—
266C2×SD32—221no—
267C2×D16—114no—
268C2×D16—222no—
269C2×D16—222no—
270C2×D16—221no—
271C2×M32—111no—
272C22×C16—111no—
273#472—22no—
274#472C2×D1114yescomplemented
275C2×#108C2×D1111yescharacteristic, complemented
276C2×#100—21no—
277#361—114no—
278#359—114no—
279#350—114no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—82no—
284C22×C11—162no—
285C22×C11—162no—
286C22×C11—162no—
287C22×C11#44711yescharacteristic
288C22×C11#44711yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C2×D11—42no—
291C2×D11—44no—
292C2×D11—84no—
293C2×D11—82no—
294C2×D11—162no—
295C2×D11—162no—
296C2×D11—168no—
297C4×C11—22no—
298C4×C11#44711yescharacteristic
299C4×C11#44711yescharacteristic
300C4×C11C2×#12011yescharacteristic
301C4×C11C22×D811yescharacteristic
302Dic11—42no—
303H(5,𝔽2)—224no—
304H(5,𝔽2)—224no—
305H(5,𝔽2)—442no—
306H(5,𝔽2)—442no—
307C2×#41—222no—
308C2×#41—221no—
309C2×#41—441no—
310C2×#41C22⋊D1111yescharacteristic
311C22×D4—21no—
312C22×D4—222no—
313C22×D4—221no—
314C22×D4—442no—
315C22×D4—441no—
316AGL(1,ℤ/8)—24no—
317AGL(1,ℤ/8)—42no—
318AGL(1,ℤ/8)—228no—
319AGL(1,ℤ/8)—224no—
320AGL(1,ℤ/8)—228no—
321AGL(1,ℤ/8)—224no—
322#135—112no—
323#135—112no—
324#135—224no—
325#135—224no—
326#135—221no—
327#135—221no—
328C2×Q16—111no—
329C2×SD16—41no—
330C2×SD16—222no—
331C2×SD16—221no—
332C2×D8—21no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—21no—
336C2×D8—21no—
337C2×D8—41no—
338C2×D8—112no—
339C2×D8—112no—
340C2×D8—111no—
341C2×D8—112no—
342C2×D8—224no—
343C2×D8—222no—
344C2×D8—224no—
345C2×D8—221no—
346C2×D8—221no—
347C2×D8—221no—
348C2×D8C22×D1112yescomplemented
349#131—21no—
350#131—21no—
351#131C22⋊D1112yes—
352#131C22×D1112yes—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—21no—
357C22×C8C22×D1111yescharacteristic
358SD32—224no—
359D16—228no—
360D16—224no—
361M32—112no—
362M32—221no—
363C2×C16—112no—
364C2×C16—221no—
365C2×C16—221no—
366C2×C16—221no—
367#108—21no—
368#108C22×D1112yescomplemented
369#100—24no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—42no—
373C2×C11—162no—
374C2×C11#219212yescomplemented
375C2×C11C2×#44711yescharacteristic
376D11—84no—
377D11—82no—
378C24—41no—
379C24—442no—
380C24—441no—
381#41—21no—
382#41—21no—
383#41—228no—
384#41—222no—
385#41—222no—
386#41—444no—
387#41—444no—
388#41—444no—
389#41—441no—
390#41—441no—
391#41#432312yes—
392#41C2×C22⋊D1112yes—
393C2×Q8—221no—
394C2×Q8#432311yescharacteristic
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—228no—
403C2×D4—222no—
404C2×D4—221no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—442no—
408C2×D4—444no—
409C2×D4—448no—
410C2×D4—448no—
411C2×D4—444no—
412C2×D4—442no—
413C2×D4—441no—
414C2×D4—444no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4#432311yescharacteristic
419C22×C4—21no—
420C22×C4—442no—
421C22×C4—441no—
422C22×C4C2×C22⋊D1111yescharacteristic
423Q16—112no—
424Q16—221no—
425SD16—44no—
426SD16—228no—
427SD16—222no—
428SD16—222no—
429D8—22no—
430D8—22no—
431D8—44no—
432D8—41no—
433D8—41no—
434D8—114no—
435D8—112no—
436D8—228no—
437D8—222no—
438D8—221no—
439D8—222no—
440D8—222no—
441M16—21no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—41no—
446M16C2×C22⋊D1112yes—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—41no—
451C2×C8D4×D1111yescharacteristic
452C2×C8D4×D1111yescharacteristic
453C2×C8D4×D1111yescharacteristic
454C2×C8D4×D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C16—222no—
458C16—222no—
459C11C2×#219211yescharacteristic, complemented, Sylow
460C23—21no—
461C23—42no—
462C23—81no—
463C23—81no—
464C23—162no—
465C23—448no—
466C23—442no—
467C23—441no—
468C23—442no—
469C23—442no—
470C23—1762no—
471C23—1764no—
472C23#6700211yescharacteristic
473Q8—21no—
474Q8—222no—
475Q8—441no—
476Q8C2×#432312yes—
477D4—22no—
478D4—22no—
479D4—21no—
480D4—42no—
481D4—42no—
482D4—81no—
483D4—81no—
484D4—224no—
485D4—222no—
486D4—448no—
487D4—448no—
488D4—442no—
489D4—442no—
490D4—442no—
491D4—441no—
492D4—442no—
493D4—442no—
494D4C2×#432312yes—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—448no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4C2×#432311yescharacteristic
503C2×C4C2×#432311yescharacteristic
504C2×C4#6699011yescharacteristic
505C2×C4#6699011yescharacteristic
506C2×C4#6700211yescharacteristic
507C2×C4C22×C22⋊D1111yescharacteristic
508C8—22no—
509C8—42no—
510C8#6699011yescharacteristic
511C8#6699011yescharacteristic
512C8C2×D4×D1111yescharacteristic
513C8C2×D4×D1111yescharacteristic
514C22—22no—
515C22—22no—
516C22—42no—
517C22—82no—
518C22—162no—
519C22—162no—
520C22—162no—
521C22—444no—
522C22—442no—
523C22—884no—
524C22—882no—
525C22—1762no—
526C22—1762no—
527C22—1768no—
528C22#1062264911yescharacteristic
529C22#1062264911yescharacteristic
530C22C2×#6700211yescharacteristic
531C4—22no—
532C4—442no—
533C4#1062264911yescharacteristic
534C4#1062264911yescharacteristic
535C4C22×#432311yescharacteristic
536C4C2×#6699011yescharacteristic
537C2—21no—
538C2—21no—
539C2—42no—
540C2—162no—
541C2—884no—
542C2—882no—
543C2#1307057112yesdirect product factor
544C2C2×#1062264911yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#472C2
socleC22×C11#447
hypercenterC2×#472D11
hypocenterC11C2×#2192
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#10623283C2semidirect
2. C2×#10622760C2semidirect
3. C22×#66890C2semidirect
4. #13070571C2direct (N × H)
5. C2×#10622133C2semidirect
6. C2×#10622135C2semidirect
7. C2×#10622199C2semidirect
8. C2×C11×#472C2semidirect
11. C22×C11×D8C22semidirect
16. #10623283C22semidirect
24. C11×#472C22semidirect
25. C2×C11×#108C22semidirect
29. #10622760C22semidirect
33. C2×#66890C22semidirect
34. C2×#66876C22semidirect
35. C22×C11⋊C16C22semidirect
36. #10622199C22semidirect
37. #10622135C22semidirect
38. #10622133C22semidirect
61. C2×C11×D8C23semidirect
95. C11×#108C23semidirect
101. #66876C23semidirect
105. C2×C11⋊C16C23semidirect
191. C2×#472D11semidirect
262. C22×D8C2×D11semidirect
274. #472C2×D11semidirect
275. C2×#108C2×D11semidirect
348. C2×D8C22×D11semidirect
368. #108C22×D11semidirect
374. C2×C11#2192semidirect
459. C11C2×#2192semidirect
543. C2#13070571direct (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×#106227602
C22×#668902
#130705712
C2×#106221332
C2×#106221352
C2×#106221992
C2×C11×#4722
C2×#219211