Finite Group Databasebeta

← C2×#13078080 #15620603

Subgroups — C2×#13078080 #15620603

Order 2816.

3242 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C212yesmaximal, complemented
2C2×#10623008C211yesmaximal, characteristic, complemented
3#13078080C2116yesmaximal, direct product factor
4C2×#10622629C214yesmaximal, complemented
5C2×#10622632C212yesmaximal, complemented
6C2×#10622628C212yesmaximal, complemented
7C2×#10622537C211yesmaximal, characteristic, complemented
8C2×#10622579C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11—21no—
12C22×#4339C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—24no—
16C2×C4×D4×C11C2212yes—
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C22×C42×C11C2211yescharacteristic
22C22×#4324C2214yes—
23C2×#66985—216no—
24C2×#66985C22116yescomplemented
25C22×#4323C2214yes—
26C2×#66983—21no—
27C2×#66983—21no—
28C22×#4318C2212yes—
29#10623008—24no—
30#10623008C2218yescomplemented
31C2×#66928C2212yescomplemented
32C2×#66927C2211yescharacteristic, complemented
33C2×C4×D44—21no—
34C2×C4×D44—21no—
35C2×#66922C2211yescharacteristic, complemented
36#10622632C22116yescomplemented
37#10622629C22132yescomplemented
38#10622628C22116yescomplemented
39C2×#66874C2214yescomplemented
40#10622579C22116yescomplemented
41C2×#66873C2214yescomplemented
42#10622537C2218yescomplemented
43C2×C4⋊(C11⋊C8)C2212yescomplemented
44C2×C4⋊(C11⋊C8)C2212yescomplemented
45C25×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—24no—
49C22×D4×C11D418yescomplemented
50C22×D4×C11C2312yes—
51C22×D4×C11C2314yes—
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—28no—
56C23×C4×C11—48no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—22no—
61C2×#4339—24no—
62C2×#4339—28no—
63C2×#4339—28no—
64C2×#4339C2318yes—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2312yes—
68C22×C4×D11—22no—
69C22×Dic22C2312yes—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C4×D4×C11—28no—
73C4×D4×C11—28no—
74C4×D4×C11C2318yes—
75C4×D4×C11C2318yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—28no—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D414yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2314yes—
89C2×#4324—216no—
90C2×#4324C23116yes—
91#66985—264no—
92C2×#4323—216no—
93C2×#4323C23116yes—
94#66983—28no—
95#66983—28no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×#4318—28no—
101C2×#4318C2318yes—
102C22×C11⋊C8C2314yes—
103#66928—24no—
104#66928C2318yescomplemented
105#66927—22no—
106#66927C2314yescomplemented
107C4×D44—28no—
108C4×D44—28no—
109#66922—22no—
110#66922C2314yescomplemented
111#66874C23116yescomplemented
112#66873C23116yescomplemented
113C4⋊(C11⋊C8)C2318yescomplemented
114C4⋊(C11⋊C8)C2318yescomplemented
115C2×#3036—111nomaximal, Sylow
116C24×C11—28no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—44no—
120C24×C11—44no—
121C24×C11C2×D411yescharacteristic
122C23×D11—22no—
123C2×D4×C11—28no—
124C2×D4×C11—216no—
125C2×D4×C11—22no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—28no—
129C2×D4×C11C2×D418yes—
130C2×D4×C11C2×D4116yescomplemented
131C2×D4×C11C2414yes—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—28no—
137C22×C4×C11—42no—
138C22×C4×C11—48no—
139C22×C4×C11—432no—
140C22×C4×C11—44no—
141C22×C4×C11—48no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4114yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—48no—
156C22×Dic11—22no—
157#4339—216no—
158#4339—216no—
159#4339—416no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—44no—
166C2×D44—44no—
167C2×D44C2414yes—
168C2×C4×D11—28no—
169C2×C4×D11—48no—
170C2×Dic22—24no—
171C2×Dic22—22no—
172C2×Dic22—24no—
173C2×Dic22C2414yes—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4C2414yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C42×C11C2×D412yes—
180C42×C11C2×D414yes—
181C42×C11C2×D414yes—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C42×C11C2412yes—
185#4324—232no—
186#4323—232no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191#4318—216no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8C2418yes—
194C22×AGL(1,ℤ/8)—112no—
195C2×#532—111no—
196C22×C4×D4D1111yescharacteristic, complemented
197#3036—1116no—
198C2×#463—114no—
199C2×#461—112no—
200C2×#459—112no—
201C2×#423—111no—
202C2×#417—112no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—24no—
208C23×C11—48no—
209C23×C11—432no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11#12114yes—
214C23×C11C22×D412yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—24no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—44no—
220D4×C11—28no—
221D4×C11—216no—
222D4×C11—24no—
223D4×C11C22×D418yes—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—28no—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11—416no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—416no—
234C2×C4×C11#12114yes—
235C2×C4×C11#12118yes—
236C2×C4×C11AGL(1,ℤ/8)14yescomplemented
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11C2×#4114yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—416no—
249C2×Dic11—24no—
250C2×Dic11—44no—
251D44—24no—
252D44—24no—
253D44—48no—
254D44—44no—
255D44—48no—
256C4×D11—416no—
257Dic22—24no—
258Dic22—24no—
259Dic22—44no—
260C11⋊C8—28no—
261C22×#41—112no—
262C23×D4C2×D1111yescharacteristic
263C24×C4—21no—
264C2×AGL(1,ℤ/8)—1116no—
265C2×AGL(1,ℤ/8)—2216no—
266C22×SD16—114no—
267C22×D8—114no—
268C22×M16—112no—
269#532—118no—
270#532—224no—
271C2×C4⋊Q8—111no—
272C2×#127—111no—
273C2×#124—112no—
274C2×#121—221no—
275C2×#121—221no—
276C2×C4×D4—21no—
277C2×C4×D4—21no—
278C2×C4×D4—24no—
279C2×C4×D4—221no—
280C2×C4×D4—221no—
281C2×C4×D4C2×D1112yes—
282C2×C4×D4C2×D1112yes—
283C2×C4×D4C2×D1118yescomplemented
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4—21no—
286C22×C42C2×D1111yescharacteristic
287#463—1132no—
288#461—1116no—
289#459—1116no—
290#423—118no—
291C2×C4⋊C8—112no—
292C2×C4⋊C8—112no—
293#417—1116no—
294C2×#103—114no—
295C2×#102—114no—
296C22×C11—28no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—28no—
300C22×C11—432no—
301C22×C11—416no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11C2×#12114yes—
305C22×C11C2×#12112yes—
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11#57512yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—44no—
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—88no—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11C2×#12112yes—
318C4×C11C2×#12114yes—
319C4×C11C2×AGL(1,ℤ/8)14yescomplemented
320C4×C11C23×D411yescharacteristic
321C4×C11C22×#4111yescharacteristic
322Dic11—44no—
323C25—21no—
324C2×#41—118no—
325C2×#41—224no—
326C2×#41—228no—
327C2×#41—228no—
328C22×Q8—112no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—112no—
333C22×D4—222no—
334C22×D4—221no—
335C22×D4—221no—
336C22×D4D4418yescomplemented
337C22×D4C22×D1112yes—
338C22×D4C22×D1114yes—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—28no—
343C23×C4—48no—
344C23×C4—222no—
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348AGL(1,ℤ/8)—2264no—
349C2×SD16—1116no—
350C2×SD16—2216no—
351C2×D8—1116no—
352C2×D8—2216no—
353C2×M16—118no—
354C2×M16—228no—
355C22×C8—114no—
356C4⋊Q8—114no—
357C4⋊Q8—222no—
358#127—114no—
359#127—222no—
360#124—118no—
361#124—224no—
362#121—228no—
363#121—228no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—28no—
367C4×D4—28no—
368C4×D4—228no—
369C4×D4—228no—
370C4×D4C22×D1118yes—
371C4×D4C22×D1118yes—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1112yes—
377C2×C4⋊C4C22×D1114yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C42C22⋊D1111yescharacteristic
384C2×C42C22⋊D1111yescharacteristic
385C2×C42C22⋊D1114yes—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1114yes—
389C4⋊C8—118no—
390C4⋊C8—118no—
391#103—1116no—
392#102—1116no—
393C2×C11—24no—
394C2×C11—48no—
395C2×C11#303614yescomplemented
396C2×C11C22×#12111yescharacteristic
397C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C11C2×#57511yescharacteristic
399D11—84no—
400C24—28no—
401C24—24no—
402C24—22no—
403C24—44no—
404C24—44no—
405C24—222no—
406C24C2×C22⋊D1111yescharacteristic
407#41—2216no—
408#41—2216no—
409#41—4416no—
410C2×Q8—114no—
411C2×Q8—222no—
412C2×Q8—224no—
413C2×Q8—224no—
414C2×D4—28no—
415C2×D4—216no—
416C2×D4—24no—
417C2×D4—28no—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—114no—
421C2×D4—228no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—224no—
426C2×D4—222no—
427C2×D4—444no—
428C2×D4—448no—
429C2×D4—444no—
430C2×D4C2×D4418yes—
431C2×D4C2×D44116yescomplemented
432C2×D4C23×D1114yes—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—42no—
439C22×C4—48no—
440C22×C4—432no—
441C22×C4—44no—
442C22×C4—48no—
443C22×C4—222no—
444C22×C4—228no—
445C22×C4—448no—
446C22×C4C2×D4414yes—
447C22×C4#433914yes—
448C22×C4C2×C22⋊D1114yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1112yes—
457C22×C4C23×D1111yescharacteristic
458SD16—2232no—
459D8—2232no—
460M16—2216no—
461C2×C8—118no—
462C2×C8—228no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4C23×D1114yes—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C42C2×C22⋊D1114yes—
473C42C2×C22⋊D1114yes—
474C42C2×C22⋊D1112yes—
475C42C2×C22⋊D1112yes—
476C42C23×D1112yes—
477C42C23×D1112yes—
478C11C2×#303611yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—28no—
482C23—216no—
483C23—24no—
484C23—48no—
485C23—432no—
486C23—48no—
487C23—44no—
488C23—44no—
489C23—224no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23#6698314yes—
494C23C22×C22⋊D1112yes—
495C23C22×C22⋊D1111yescharacteristic
496Q8—224no—
497Q8—224no—
498Q8—444no—
499D4—28no—
500D4—216no—
501D4—24no—
502D4—224no—
503D4—224no—
504D4—448no—
505D4—4416no—
506D4—444no—
507D4—448no—
508D4C22×D4418yes—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—28no—
513C2×C4—24no—
514C2×C4—44no—
515C2×C4—416no—
516C2×C4—48no—
517C2×C4—44no—
518C2×C4—416no—
519C2×C4—224no—
520C2×C4—444no—
521C2×C4—4416no—
522C2×C4#6698314yes—
523C2×C4#6698318yes—
524C2×C4#6698514yescomplemented
525C2×C4C22×D4412yes—
526C2×C4C22×D4414yes—
527C2×C4C2×#433912yes—
528C2×C4C2×#433914yes—
529C2×C4C22×C22⋊D1112yes—
530C2×C4C22×C22⋊D1112yes—
531C2×C4C22×C22⋊D1112yes—
532C2×C4C22×C22⋊D1112yes—
533C2×C4C22×C22⋊D1111yescharacteristic
534C2×C4C22×C22⋊D1112yes—
535C2×C4C24×D1111yescharacteristic
536C8—228no—
537C22—28no—
538C22—22no—
539C22—22no—
540C22—28no—
541C22—432no—
542C22—416no—
543C22—44no—
544C22—44no—
545C22—444no—
546C22—444no—
547C22—444no—
548C22—888no—
549C22C2×#6698314yes—
550C22C2×#6698312yes—
551C22C2×#6698512yes—
552C22#1062335312yes—
553C22C23×C22⋊D1111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—44no—
558C4—444no—
559C4C2×#6698314yes—
560C4C2×#6698312yes—
561C4C2×#6698514yescomplemented
562C4C23×D4411yescharacteristic
563C4C22×#433911yescharacteristic
564C2—24no—
565C2—48no—
566C2—884no—
567C2#1307808014yesdirect product factor
568C2C22×#6698311yescharacteristic
569C2C22×#6698511yescharacteristic
570C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C4×D4×C11C2
socleC23×C11C22×D4
hypercenterC22×C4×D4D11
hypocenterC11C2×#3036
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C2×#10623008C2semidirect
3. #13078080C2direct (N × H)
4. C2×#10622629C2semidirect
5. C2×#10622632C2semidirect
6. C2×#10622628C2semidirect
7. C2×#10622537C2semidirect
8. C2×#10622579C2semidirect
9. C22×C4×D4×C11C2semidirect
18. C2×C4×D4×C11C22semidirect
24. C2×#66985C22semidirect
30. #10623008C22semidirect
31. C2×#66928C22semidirect
32. C2×#66927C22semidirect
35. C2×#66922C22semidirect
36. #10622632C22semidirect
37. #10622629C22semidirect
38. #10622628C22semidirect
39. C2×#66874C22semidirect
40. #10622579C22semidirect
41. C2×#66873C22semidirect
42. #10622537C22semidirect
43. C2×C4⋊(C11⋊C8)C22semidirect
44. C2×C4⋊(C11⋊C8)C22semidirect
49. C22×D4×C11D4semidirect
104. #66928C23semidirect
106. #66927C23semidirect
110. #66922C23semidirect
111. #66874C23semidirect
112. #66873C23semidirect
113. C4⋊(C11⋊C8)C23semidirect
114. C4⋊(C11⋊C8)C23semidirect
130. C2×D4×C11C2×D4semidirect
196. C22×C4×D4D11semidirect
236. C2×C4×C11AGL(1,ℤ/8)semidirect
283. C2×C4×D4C2×D11semidirect
319. C4×C11C2×AGL(1,ℤ/8)semidirect
336. C22×D4D44semidirect
395. C2×C11#3036semidirect
431. C2×D4C2×D44semidirect
478. C11C2×#3036semidirect
524. C2×C4#66985semidirect
561. C4C2×#66985semidirect
567. C2#13078080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106230082
#130780802
C2×#106226292
C2×#106226322
C2×#106226282
C2×#106225372
C2×#106225792
C22×C4×D4×C112
C2×#303611