Finite Group Databasebeta

← C2×#13070562 #14907657

Subgroups — C2×#13070562 #14907657

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C212yesmaximal, complemented
2C2×#10622748C211yesmaximal, characteristic, complemented
3#13070562C218yesmaximal, direct product factor
4C2×#10622204C212yesmaximal, complemented
5C2×#10622191C211yesmaximal, characteristic, complemented
6C2×C11×#575C211yesmaximal, characteristic, complemented
7C22×C11×#41—21no—
8C11×#575—24no—
9C11×#575—22no—
10C11×#575C2214yescomplemented
11C2×C11×#137—22no—
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×#135—21no—
14C2×C11×#135C2212yes—
15C22×C11×M16C2211yescharacteristic
16C2×#66983—21no—
17C22×D88C2211yescharacteristic, complemented
18#10622806—24no—
19#10622806C2218yescomplemented
20C2×#66892—22no—
21C2×#66890—22no—
22#10622748—22no—
23#10622748C2214yescomplemented
24C2×#66885—21no—
25C2×#66881C2211yescharacteristic, complemented
26C2×#66876C2212yescomplemented
27#10622204C2218yescomplemented
28#10622191C2214yescomplemented
29C2×C11×#41—22no—
30C2×C11×#41—24no—
31C2×C11×#41—22no—
32C2×C11×#41—24no—
33C2×C11×#41—41no—
34C2×C11×#41—42no—
35C2×C11×#41—41no—
36C2×C11×#41—42no—
37C22×Q8×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—41no—
40C23×C4×C11—41no—
41C23×C4×C11D411yescharacteristic
42C22×C22⋊D11—41no—
43C22×D44—21no—
44C11×#137—28no—
45C11×#137—28no—
46C11×AGL(1,ℤ/8)—28no—
47C11×AGL(1,ℤ/8)—28no—
48C11×#135—24no—
49C11×#135—24no—
50C11×#135—22no—
51C11×#135—22no—
52C11×#135D414yescomplemented
53C11×#135C2314yes—
54C2×C11×Q16—21no—
55C2×C11×Q16D412yescomplemented
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C2×C11×D8—21no—
59C2×C11×D8D412yescomplemented
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16D412yes—
63C2×C11×M16C2312yes—
64C22×C8×C11D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66#66983—24no—
67#66983—42no—
68C2×(C2×D11)⋊C4—41no—
69C2×C4⋊Dic11—21no—
70C2×D88—22no—
71C2×D88—22no—
72C2×D88—21no—
73C2×D88C2312yescomplemented
74#66892—28no—
75#66890—28no—
76#66885—24no—
77#66881—21no—
78#66881C2312yescomplemented
79#66876—22no—
80#66876C2314yescomplemented
81C2×C11⋊C16—22no—
82C2×#2190—111nomaximal, Sylow
83C24×C11—41no—
84C24×C11D811yescharacteristic
85C23×D11—41no—
86C11×#41—28no—
87C11×#41—24no—
88C11×#41—24no—
89C11×#41—44no—
90C11×#41—44no—
91C11×#41—44no—
92C11×#41—44no—
93C11×#41—44no—
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—41no—
99C2×Q8×C11—42no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—41no—
103C2×D4×C11—42no—
104C2×D4×C11—44no—
105C2×D4×C11—42no—
106C2×D4×C11—44no—
107C2×D4×C11—42no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—41no—
116C22×C4×C11—42no—
117C22×C4×C11D811yescharacteristic
118C22×C4×C11D812yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—44no—
122C2×C22⋊D11—84no—
123C22×Dic11—41no—
124C2×D44—22no—
125C2×D44—41no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C11×Q16—24no—
131C11×Q16—22no—
132C11×Q16C2×D414yescomplemented
133C11×SD16—28no—
134C11×SD16—24no—
135C11×SD16—24no—
136C11×D8—24no—
137C11×D8—22no—
138C11×D8C2×D414yescomplemented
139C11×M16—24no—
140C11×M16—24no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148(C2×D11)⋊C4—44no—
149C4⋊Dic11—22no—
150C4⋊Dic11—41no—
151D88—24no—
152D88—42no—
153C11⋊C16—24no—
154C2×#575D1111yescharacteristic, complemented
155C2×#509—112no—
156C2×#469—111no—
157#2190—118no—
158C2×#360—112no—
159C2×#349—111no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—42no—
165C23×C11—84no—
166C23×C11C2×D811yescharacteristic
167C23×C11C2×D812yes—
168C22×D11—42no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11—81no—
172C22×D11—81no—
173Q8×C11—24no—
174Q8×C11—44no—
175Q8×C11—42no—
176D4×C11—24no—
177D4×C11—44no—
178D4×C11—48no—
179D4×C11—44no—
180D4×C11—44no—
181D4×C11—42no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—48no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11C2×D812yes—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—88no—
201C2×Dic11—42no—
202C2×Dic11—82no—
203D44—42no—
204D44—42no—
205D44—81no—
206D44—81no—
207C8×C11—22no—
208C8×C11#12012yes—
209C8×C11C22×D412yes—
210C22×#41—21no—
211#575—24no—
212#575—22no—
213#575C2×D1114yescomplemented
214C2×#137—22no—
215C2×AGL(1,ℤ/8)—22no—
216C2×#135—21no—
217C2×#135C2×D1112yes—
218C22×D8—111no—
219C22×M16C2×D1111yescharacteristic
220C2×#121—221no—
221#509—118no—
222#509—224no—
223C2×SD32—222no—
224C2×D16—222no—
225C2×M32—112no—
226#469—114no—
227#469—222no—
228C2×#106—111no—
229C2×#102—221no—
230#360—118no—
231#349—114no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—81no—
238C22×C11—88no—
239C22×C11—84no—
240C22×C11#44711yescharacteristic
241C22×C11#44711yescharacteristic
242C22×C11C22×D811yescharacteristic
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—82no—
246C2×D11—162no—
247C2×D11—162no—
248C4×C11—22no—
249C4×C11—44no—
250C4×C11#44711yescharacteristic
251C4×C11#44711yescharacteristic
252C4×C11C2×#12011yescharacteristic
253C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
254Dic11—82no—
255C2×#41—22no—
256C2×#41—24no—
257C2×#41—24no—
258C2×#41—22no—
259C2×#41—41no—
260C2×#41—42no—
261C2×#41—41no—
262C2×#41—42no—
263C22×Q8—21no—
264C22×D4—21no—
265C22×D4—41no—
266C22×D4—221no—
267C22×D4—441no—
268C23×C4—41no—
269C23×C4C22⋊D1111yescharacteristic
270#137—28no—
271#137—28no—
272AGL(1,ℤ/8)—28no—
273AGL(1,ℤ/8)—28no—
274#135—24no—
275#135—24no—
276#135—22no—
277#135—22no—
278#135C22⋊D1114yescomplemented
279#135C22×D1114yes—
280C2×Q16—21no—
281C2×Q16C22⋊D1112yescomplemented
282C2×SD16—22no—
283C2×SD16—22no—
284C2×D8—21no—
285C2×D8—112no—
286C2×D8—222no—
287C2×D8—222no—
288C2×D8—221no—
289C2×D8C22⋊D1112yescomplemented
290C2×M16—22no—
291C2×M16—22no—
292C2×M16C22⋊D1112yes—
293C2×M16C22×D1112yes—
294C22×C8C22⋊D1111yescharacteristic
295C22×C8C22×D1111yescharacteristic
296#121—224no—
297#121—442no—
298C2×C4⋊C4—221no—
299C2×C22⋊C4—441no—
300SD32—228no—
301D16—228no—
302M32—114no—
303M32—222no—
304C2×C16—222no—
305#106—112no—
306#106—221no—
307#102—224no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—42no—
311C2×C11—84no—
312C2×C11#219012yescomplemented
313C2×C11C2×#44711yescharacteristic
314D11—162no—
315C24—41no—
316C24—441no—
317C24#432311yescharacteristic
318#41—28no—
319#41—24no—
320#41—24no—
321#41—44no—
322#41—44no—
323#41—44no—
324#41—44no—
325#41—44no—
326#41—42no—
327#41—42no—
328C2×Q8—24no—
329C2×Q8—22no—
330C2×Q8—41no—
331C2×Q8—42no—
332C2×D4—24no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—42no—
340C2×D4—222no—
341C2×D4—444no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—884no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—441no—
358C22×C4#432311yescharacteristic
359C22×C4#432312yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1111yescharacteristic
362Q16—24no—
363Q16—22no—
364Q16C2×C22⋊D1114yescomplemented
365SD16—28no—
366SD16—24no—
367SD16—24no—
368D8—24no—
369D8—22no—
370D8—224no—
371D8—442no—
372D8C2×C22⋊D1114yescomplemented
373M16—24no—
374M16—24no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×C22⋊D1112yes—
378C2×C8C2×C22⋊D1111yescharacteristic
379C2×C8C2×C22⋊D1112yes—
380C2×C8C2×C22⋊D1112yes—
381C2×C8C23×D1111yescharacteristic
382C4⋊C4—222no—
383C4⋊C4—441no—
384C22⋊C4—444no—
385C16—224no—
386C11C2×#219011yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—42no—
390C23—44no—
391C23—42no—
392C23—84no—
393C23—442no—
394C23—882no—
395C23—882no—
396C23—881no—
397C23—881no—
398C23C2×#432311yescharacteristic
399C23C2×#432312yes—
400Q8—24no—
401Q8—44no—
402Q8—42no—
403D4—24no—
404D4—44no—
405D4—48no—
406D4—44no—
407D4—44no—
408D4—42no—
409D4—442no—
410D4—442no—
411D4—888no—
412D4—881no—
413D4—881no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—48no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—442no—
426C2×C4—882no—
427C2×C4C2×#432312yes—
428C2×C4C2×#432311yescharacteristic
429C2×C4#6698511yescharacteristic
430C2×C4#6698511yescharacteristic
431C2×C4#6700611yescharacteristic
432C2×C4#6700611yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—22no—
435C8#6700612yes—
436C8C22×C22⋊D1112yes—
437C22—22no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—44no—
442C22—81no—
443C22—88no—
444C22—84no—
445C22—882no—
446C22—882no—
447C22—882no—
448C22—1762no—
449C22—1762no—
450C22#1062283011yescharacteristic
451C22#1062283011yescharacteristic
452C22C22×#432311yescharacteristic
453C4—22no—
454C4—44no—
455C4—882no—
456C4#1062283011yescharacteristic
457C4#1062283011yescharacteristic
458C4C2×#6698511yescharacteristic
459C4C2×#6700611yescharacteristic
460C2—21no—
461C2—21no—
462C2—42no—
463C2—84no—
464C2—1762no—
465C2#1307056212yesdirect product factor
466C2C2×#1062283011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#575C2
socleC22×C11#447
hypercenterC2×#575D11
hypocenterC11C2×#2190
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×#10622748C2semidirect
3. #13070562C2direct (N × H)
4. C2×#10622204C2semidirect
5. C2×#10622191C2semidirect
6. C2×C11×#575C2semidirect
10. C11×#575C22semidirect
17. C22×D88C22semidirect
19. #10622806C22semidirect
23. #10622748C22semidirect
25. C2×#66881C22semidirect
26. C2×#66876C22semidirect
27. #10622204C22semidirect
28. #10622191C22semidirect
52. C11×#135D4semidirect
55. C2×C11×Q16D4semidirect
59. C2×C11×D8D4semidirect
73. C2×D88C23semidirect
78. #66881C23semidirect
80. #66876C23semidirect
132. C11×Q16C2×D4semidirect
138. C11×D8C2×D4semidirect
154. C2×#575D11semidirect
213. #575C2×D11semidirect
278. #135C22⋊D11semidirect
281. C2×Q16C22⋊D11semidirect
289. C2×D8C22⋊D11semidirect
312. C2×C11#2190semidirect
364. Q16C2×C22⋊D11semidirect
372. D8C2×C22⋊D11semidirect
386. C11C2×#2190semidirect
465. C2#13070562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106227482
#130705622
C2×#106222042
C2×#106221912
C2×C11×#5752
C2×#219011