Finite Group Databasebeta

← C2×#13070573 #14907696

Subgroups — C2×#13070573 #14907696

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×#10622806C211yesmaximal, characteristic, complemented
2C22×#66890C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic, complemented
4#13070573C218yesmaximal, direct product factor
5C2×#10622201C211yesmaximal, characteristic, complemented
6C2×#10622205C211yesmaximal, characteristic, complemented
7C2×#10622199C211yesmaximal, characteristic, complemented
8C2×C11×#576C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)—21no—
10C11×#576—22no—
11C11×#576—22no—
12C11×#576—22no—
13C11×#576C2214yescomplemented
14C2×C11×AGL(1,ℤ/8)—22no—
15C2×C11×AGL(1,ℤ/8)—21no—
16C2×C11×#135—21no—
17C2×C11×#135C2211yescharacteristic
18C22×C11×D8—21no—
19C22×C11×D8C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×#67002—21no—
22C22×D88C2211yescharacteristic, complemented
23#10622806—22no—
24#10622806C2214yescomplemented
25C2×#66892—21no—
26C2×#66890—22no—
27C2×#66890—22no—
28C2×#66890—21no—
29C2×#66890C2214yescomplemented
30#10622755—22no—
31#10622755C2214yescomplemented
32C2×#66887—21no—
33C2×#66883C2211yescharacteristic, complemented
34C2×#66876C2211yescharacteristic, complemented
35C22×C11⋊C16C2211yescharacteristic, complemented
36#10622205C2214yescomplemented
37#10622201C2214yescomplemented
38#10622199C2214yescomplemented
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—24no—
41C11×H(5,𝔽2)—42no—
42C11×H(5,𝔽2)—42no—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—41no—
46C2×C11×#41D411yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—42no—
50C22×D4×C11—41no—
51C22×D44—21no—
52C11×AGL(1,ℤ/8)—28no—
53C11×AGL(1,ℤ/8)—24no—
54C11×AGL(1,ℤ/8)—28no—
55C11×AGL(1,ℤ/8)—24no—
56C11×#135—24no—
57C11×#135—24no—
58C11×#135—21no—
59C11×#135—21no—
60C11×#135D412yes—
61C11×#135C2312yes—
62C2×C11×Q16D411yescharacteristic
63C2×C11×SD16—22no—
64C2×C11×SD16—21no—
65C2×C11×D8—22no—
66C2×C11×D8—24no—
67C2×C11×D8—24no—
68C2×C11×D8—21no—
69C2×C11×D8—21no—
70C2×C11×D8—21no—
71C2×C11×D8D411yescharacteristic
72C2×C11×D8D412yes—
73C2×C11×D8D412yes—
74C2×C11×D8C2312yes—
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×D88C2312yescomplemented
94#66892—24no—
95#66890—28no—
96#66890—24no—
97#66887—24no—
98#66883—21no—
99#66883C2312yescomplemented
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—42no—
108C24×C11—41no—
109C23×D11—41no—
110C11×#41—21no—
111C11×#41—21no—
112C11×#41—28no—
113C11×#41—22no—
114C11×#41—22no—
115C11×#41—44no—
116C11×#41—44no—
117C11×#41—44no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41D812yes—
121C11×#41C2×D412yes—
122C2×Q8×C11—21no—
123C2×Q8×C11D811yescharacteristic
124C2×D4×C11—21no—
125C2×D4×C11—28no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—42no—
131C2×D4×C11—44no—
132C2×D4×C11—48no—
133C2×D4×C11—48no—
134C2×D4×C11—44no—
135C2×D4×C11—42no—
136C2×D4×C11—41no—
137C2×D4×C11—44no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11D811yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—42no—
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—21no—
153C11×Q16C2×D412yes—
154C11×SD16—28no—
155C11×SD16—22no—
156C11×SD16—22no—
157C11×D8—28no—
158C11×D8—21no—
159C11×D8—22no—
160C11×D8—22no—
161C11×D8—22no—
162C11×D8C2×D412yes—
163C11×D8C2×D414yes—
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×#576D1111yescharacteristic, complemented
189C2×#509—111no—
190C22×D16—111no—
191C2×#472—111no—
192#2192—118no—
193C2×#361—111no—
194C2×#359—111no—
195C2×#350—111no—
196C23×C11—21no—
197C23×C11—48no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—162no—
203C23×C11—164no—
204C23×C11AGL(1,ℤ/8)11yescharacteristic
205C22×D11—42no—
206C22×D11—81no—
207C22×D11—81no—
208C22×D11—162no—
209Q8×C11—21no—
210Q8×C11—22no—
211Q8×C11—41no—
212Q8×C11C2×D812yes—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—24no—
217D4×C11—21no—
218D4×C11—48no—
219D4×C11—48no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11C2×D812yes—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—48no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240D44—42no—
241D44—42no—
242D44—81no—
243D44—81no—
244C8×C11—22no—
245C8×C11#12011yescharacteristic
246C8×C11#12011yescharacteristic
247C8×C11C22×D411yescharacteristic
248C8×C11C22×D411yescharacteristic
249C11⋊C8—42no—
250C2×H(5,𝔽2)—21no—
251#576—22no—
252#576—22no—
253#576—22no—
254#576C2×D1114yescomplemented
255C2×AGL(1,ℤ/8)—22no—
256C2×AGL(1,ℤ/8)—21no—
257C2×AGL(1,ℤ/8)—221no—
258C2×#135—21no—
259C2×#135C2×D1111yescharacteristic
260C22×D8—21no—
261C22×D8—111no—
262C22×D8C2×D1111yescharacteristic
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—114no—
274#472—222no—
275C2×#108—111no—
276C2×#100—221no—
277#361—114no—
278#359—114no—
279#350—114no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—84no—
286C22×C11—82no—
287C22×C11—162no—
288C22×C11—162no—
289C22×C11—168no—
290C22×C11#44711yescharacteristic
291C22×C11#44711yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C2×D11—82no—
294C2×D11—162no—
295C2×D11—162no—
296C2×D11—162no—
297C4×C11—22no—
298C4×C11—42no—
299C4×C11#44711yescharacteristic
300C4×C11#44711yescharacteristic
301C4×C11C2×#12011yescharacteristic
302C4×C11C22×D811yescharacteristic
303H(5,𝔽2)—24no—
304H(5,𝔽2)—24no—
305H(5,𝔽2)—42no—
306H(5,𝔽2)—42no—
307C2×#41—22no—
308C2×#41—21no—
309C2×#41—41no—
310C2×#41C22⋊D1111yescharacteristic
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—42no—
314C22×D4—41no—
315C22×D4—221no—
316AGL(1,ℤ/8)—24no—
317AGL(1,ℤ/8)—28no—
318AGL(1,ℤ/8)—28no—
319AGL(1,ℤ/8)—24no—
320AGL(1,ℤ/8)—224no—
321AGL(1,ℤ/8)—442no—
322#135—24no—
323#135—24no—
324#135—21no—
325#135—21no—
326#135C22⋊D1112yes—
327#135C22×D1112yes—
328C2×Q16C22⋊D1111yescharacteristic
329C2×SD16—22no—
330C2×SD16—21no—
331C2×SD16—441no—
332C2×D8—22no—
333C2×D8—24no—
334C2×D8—24no—
335C2×D8—21no—
336C2×D8—21no—
337C2×D8—21no—
338C2×D8—112no—
339C2×D8—221no—
340C2×D8—221no—
341C2×D8—221no—
342C2×D8—221no—
343C2×D8—221no—
344C2×D8—441no—
345C2×D8C22⋊D1111yescharacteristic
346C2×D8C22⋊D1112yes—
347C2×D8C22⋊D1112yes—
348C2×D8C22×D1112yes—
349#131—21no—
350#131—21no—
351#131C22⋊D1112yes—
352#131C22×D1112yes—
353C2×M16—21no—
354C2×M16—221no—
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—112no—
368#108—221no—
369#100—224no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—42no—
373C2×C11—84no—
374C2×C11—82no—
375C2×C11#219212yescomplemented
376C2×C11C2×#44711yescharacteristic
377D11—162no—
378C24—42no—
379C24—41no—
380C24—441no—
381#41—21no—
382#41—21no—
383#41—28no—
384#41—22no—
385#41—22no—
386#41—44no—
387#41—44no—
388#41—44no—
389#41—41no—
390#41—41no—
391#41#432312yes—
392#41C2×C22⋊D1112yes—
393C2×Q8—21no—
394C2×Q8#432311yescharacteristic
395C2×D4—21no—
396C2×D4—28no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—44no—
403C2×D4—48no—
404C2×D4—48no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—44no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—222no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4#432311yescharacteristic
419C22×C4—21no—
420C22×C4—42no—
421C22×C4—41no—
422C22×C4C2×C22⋊D1111yescharacteristic
423Q16—21no—
424Q16C2×C22⋊D1112yes—
425SD16—28no—
426SD16—22no—
427SD16—22no—
428SD16—444no—
429D8—28no—
430D8—21no—
431D8—22no—
432D8—22no—
433D8—22no—
434D8—222no—
435D8—222no—
436D8—444no—
437D8—441no—
438D8—441no—
439D8C2×C22⋊D1112yes—
440D8C2×C22⋊D1114yes—
441M16—21no—
442M16—22no—
443M16—22no—
444M16—222no—
445M16—441no—
446M16C2×C22⋊D1112yes—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—441no—
451C2×C8C2×C22⋊D1111yescharacteristic
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C16—222no—
458C16—222no—
459C11C2×#219211yescharacteristic, complemented, Sylow
460C23—21no—
461C23—48no—
462C23—42no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—162no—
467C23—164no—
468C23—442no—
469C23—881no—
470C23—881no—
471C23—1762no—
472C23#6698511yescharacteristic
473Q8—21no—
474Q8—22no—
475Q8—41no—
476Q8C2×#432312yes—
477D4—22no—
478D4—22no—
479D4—21no—
480D4—22no—
481D4—24no—
482D4—48no—
483D4—48no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—41no—
488D4—42no—
489D4—42no—
490D4—442no—
491D4—442no—
492D4—881no—
493D4—881no—
494D4C2×#432312yes—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—48no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4C2×#432311yescharacteristic
503C2×C4C2×#432311yescharacteristic
504C2×C4#6698511yescharacteristic
505C2×C4#6700611yescharacteristic
506C2×C4#6700611yescharacteristic
507C2×C4C22×C22⋊D1111yescharacteristic
508C8—22no—
509C8—442no—
510C8#6700611yescharacteristic
511C8#6700611yescharacteristic
512C8C22×C22⋊D1111yescharacteristic
513C8C22×C22⋊D1111yescharacteristic
514C22—22no—
515C22—22no—
516C22—42no—
517C22—44no—
518C22—42no—
519C22—84no—
520C22—82no—
521C22—162no—
522C22—162no—
523C22—168no—
524C22—882no—
525C22—1762no—
526C22—1762no—
527C22—1762no—
528C22#1062283011yescharacteristic
529C22#1062283011yescharacteristic
530C22C2×#6698511yescharacteristic
531C4—22no—
532C4—42no—
533C4#1062283011yescharacteristic
534C4#1062283011yescharacteristic
535C4C22×#432311yescharacteristic
536C4C2×#6700611yescharacteristic
537C2—21no—
538C2—21no—
539C2—42no—
540C2—84no—
541C2—82no—
542C2—1762no—
543C2#1307057312yesdirect product factor
544C2C2×#1062283011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#576C2
socleC22×C11#447
hypercenterC2×#576D11
hypocenterC11C2×#2192
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C22×#66890C2semidirect
3. C2×#10622755C2semidirect
4. #13070573C2direct (N × H)
5. C2×#10622201C2semidirect
6. C2×#10622205C2semidirect
7. C2×#10622199C2semidirect
8. C2×C11×#576C2semidirect
13. C11×#576C22semidirect
22. C22×D88C22semidirect
24. #10622806C22semidirect
29. C2×#66890C22semidirect
31. #10622755C22semidirect
33. C2×#66883C22semidirect
34. C2×#66876C22semidirect
35. C22×C11⋊C16C22semidirect
36. #10622205C22semidirect
37. #10622201C22semidirect
38. #10622199C22semidirect
93. C2×D88C23semidirect
99. #66883C23semidirect
101. #66876C23semidirect
105. C2×C11⋊C16C23semidirect
188. C2×#576D11semidirect
254. #576C2×D11semidirect
375. C2×C11#2192semidirect
459. C11C2×#2192semidirect
543. C2#13070573direct (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×#668902
C2×#106227552
#130705732
C2×#106222012
C2×#106222052
C2×#106221992
C2×C11×#5762
C2×#219211