Finite Group Databasebeta

← C2×#13079422 #15624364

Subgroups — C2×#13079422 #15624364

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2#13079422C2116yesmaximal, direct product factor
3C2×#10622583C212yesmaximal, complemented
4C2×#10622646C212yesmaximal, complemented
5C2×#10622655C214yesmaximal, complemented
6C2×#10622653C212yesmaximal, complemented
7C2×#10622831C212yesmaximal, complemented
8C2×#10622820C211yesmaximal, characteristic, complemented
9C22×C11×#121C211yesmaximal, characteristic
10C23×D4×C11—21no—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic, complemented
14C2×C11×#121—21no—
15C2×C11×#121—21no—
16C2×C11×#121—24no—
17C2×C11×#121C2212yes—
18C2×C11×#121C2218yes—
19C2×C11×#121C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C22×C22⋊Dic11—21no—
23C22×#4324C2214yescomplemented
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C2×#66977—21no—
26C2×#66977—24no—
27C2×#66977—21no—
28C2×#66977C2212yes—
29C2×#66977C2218yescomplemented
30C2×#66977C2212yescomplemented
31C22×Dic11⋊C4—21no—
32C22×#4318C2212yescomplemented
33#10622831C22116yescomplemented
34C2×#66896C2214yescomplemented
35#10622820C2218yescomplemented
36C2×C22⋊(C11⋊C8)C2212yes—
37C2×C22⋊(C11⋊C8)C2212yescomplemented
38#10622655C22132yescomplemented
39#10622653C22116yescomplemented
40#10622646C22116yescomplemented
41#10622583C22116yescomplemented
42C2×#66874C2214yescomplemented
43C2×#66871C2214yescomplemented
44C25×C11—21no—
45C25×C11D411yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—28no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—44no—
52C22×D4×C11—48no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—21no—
56C23×C4×C11—44no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D414yes—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22—22no—
68C22×Dic22—21no—
69C22×Dic22—44no—
70C22×Dic22C2312yes—
71C22×Dic22C2314yescomplemented
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—28no—
75C11×#121—28no—
76C11×#121C2318yes—
77C11×#121C2318yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—28no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—22no—
88C2×#4324—48no—
89C2×#4324C23116yescomplemented
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yescomplemented
94#66977—24no—
95#66977—28no—
96#66977—24no—
97#66977—28no—
98#66977C2318yes—
99#66977C2318yescomplemented
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4—22no—
103C2×#4318—44no—
104C2×#4318C2318yescomplemented
105C22×C11⋊C8C2314yes—
106#66896C23116yescomplemented
107C22⋊(C11⋊C8)C2318yes—
108C22⋊(C11⋊C8)C2318yescomplemented
109#66874C23116yescomplemented
110#66871C23116yescomplemented
111C2×#3193—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—42no—
117C24×C11—44no—
118C24×C11—44no—
119C24×C11—44no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D414yes—
122C24×C11C2×D411yescharacteristic
123C24×C11C2×D411yescharacteristic
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—24no—
127C2×D4×C11—22no—
128C2×D4×C11—28no—
129C2×D4×C11—48no—
130C2×D4×C11—44no—
131C2×D4×C11—48no—
132C2×D4×C11—432no—
133C2×D4×C11—48no—
134C2×D4×C11—48no—
135C2×D4×C11C2414yes—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—48no—
142C22×C4×C11—48no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—44no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—44no—
165C22×Dic11—44no—
166C2×Dic22—22no—
167C2×Dic22—24no—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—44no—
171C2×Dic22—48no—
172C2×Dic22C2414yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2414yes—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C22⋊Dic11—28no—
179C22⋊Dic11—28no—
180#4324—416no—
181C4⋊Dic11—22no—
182C4⋊Dic11—24no—
183C4⋊Dic11C2414yes—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186#4318—48no—
187C2×C11⋊C8—28no—
188C2×C11⋊C8C2418yes—
189C22×C22⋊Q8—111no—
190C22×#121D1111yescharacteristic
191#3193—1116no—
192C2×#484—112no—
193C2×#480—112no—
194C2×#468—114no—
195C2×#448—112no—
196C2×#450—112no—
197C2×#407—111no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—28no—
204C23×C11—22no—
205C23×C11—28no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—44no—
209C23×C11—416no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—48no—
215C23×C11—44no—
216C23×C11—816no—
217C23×C11AGL(1,ℤ/8)14yes—
218C23×C11#13714yes—
219C23×C11C22×D412yes—
220C23×C11C22×D412yes—
221C23×C11C22×D412yes—
222C23×C11C22×D411yescharacteristic
223D4×C11—28no—
224D4×C11—48no—
225D4×C11—416no—
226D4×C11—416no—
227D4×C11—44no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—48no—
242C2×C4×C11—44no—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11H(5,𝔽2)14yes—
248C2×C4×C11C2511yescharacteristic
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—48no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254C2×Dic11—44no—
255Dic22—28no—
256Dic22—48no—
257Dic22—44no—
258C11⋊C8—28no—
259C23×Q8—111no—
260C23×D4—21no—
261C23×D4C2×D1111yescharacteristic
262C24×C4C2×D1111yescharacteristic
263C22×SD16—114no—
264C22×M16—112no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—118no—
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8—224no—
270C2×C22⋊Q8—221no—
271C2×#121—21no—
272C2×#121—24no—
273C2×#121—21no—
274C2×#121C2×D1112yes—
275C2×#121C2×D1118yes—
276C2×#121C2×D1112yes—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—221no—
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C22⋊C4—21no—
281C22×C22⋊C4—221no—
282#484—1116no—
283#480—1116no—
284#468—1132no—
285#450—1116no—
286#448—1116no—
287C2×#107—114no—
288C2×#103—114no—
289C2×#102—114no—
290#407—118no—
291C2×C22⋊C8—112no—
292C2×C22⋊C8—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—416no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—816no—
308C22×C11—88no—
309C22×C11#53412yes—
310C22×C11C2×AGL(1,ℤ/8)14yes—
311C22×C11C2×AGL(1,ℤ/8)12yes—
312C22×C11C2×#13714yes—
313C22×C11C2×#13712yes—
314C22×C11C23×D411yescharacteristic
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—44no—
319C4×C11#53412yes—
320C4×C11C2×H(5,𝔽2)12yes—
321Dic11—44no—
322Dic11—44no—
323C25—21no—
324C25C22⋊D1111yescharacteristic
325C22×Q8—112no—
326C22×Q8—114no—
327C22×Q8—222no—
328C22×Q8—221no—
329C22×Q8—444no—
330C22×D4—28no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—44no—
336C22×D4—48no—
337C22×D4C22×D1112yes—
338C22×D4C22×D1114yes—
339C23×C4—21no—
340C23×C4—44no—
341C23×C4—221no—
342C23×C4—221no—
343C23×C4C22⋊D1111yescharacteristic
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22⋊D1114yes—
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1114yes—
351C2×SD16—1116no—
352C2×SD16—448no—
353C2×M16—118no—
354C2×M16—444no—
355C22×C8—114no—
356C22⋊Q8—118no—
357C22⋊Q8—118no—
358C22⋊Q8—224no—
359C22⋊Q8—224no—
360C22⋊Q8—228no—
361C22⋊Q8—228no—
362#121—24no—
363#121—24no—
364#121—28no—
365#121—28no—
366#121C22×D1118yes—
367#121C22×D1118yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—228no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4C22×D1112yes—
378C2×C4⋊C4C22×D1114yes—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—228no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385#107—1116no—
386#103—1116no—
387#102—1116no—
388C22⋊C8—118no—
389C22⋊C8—118no—
390C2×C11—24no—
391C2×C11—24no—
392C2×C11—42no—
393C2×C11—84no—
394C2×C11#319314yescomplemented
395C2×C11C2×#53411yescharacteristic
396C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C11C22×#13711yescharacteristic
398C24—24no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—42no—
403C24—44no—
404C24—44no—
405C24—44no—
406C24C2×C22⋊D1111yescharacteristic
407C24C2×C22⋊D1114yes—
408C24C2×C22⋊D1111yescharacteristic
409C24C2×C22⋊D1111yescharacteristic
410C2×Q8—114no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×Q8—228no—
414C2×Q8—448no—
415C2×Q8—444no—
416C2×Q8—448no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—432no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4C23×D1114yes—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1114yes—
455C22×C4C23×D1112yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1111yescharacteristic
459SD16—4416no—
460M16—448no—
461C2×C8—118no—
462C2×C8—228no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—114no—
466C4⋊C4—224no—
467C4⋊C4—222no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4C23×D1114yes—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C11C2×#319311yescharacteristic, complemented, Sylow
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—28no—
481C23—22no—
482C23—22no—
483C23—28no—
484C23—22no—
485C23—24no—
486C23—44no—
487C23—416no—
488C23—48no—
489C23—48no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—44no—
494C23—816no—
495C23#6698514yes—
496C23#6700414yes—
497C23C22×C22⋊D1112yes—
498C23C22×C22⋊D1112yes—
499C23C22×C22⋊D1112yes—
500C23C22×C22⋊D1111yescharacteristic
501Q8—228no—
502Q8—448no—
503Q8—444no—
504D4—28no—
505D4—48no—
506D4—416no—
507D4—416no—
508D4—44no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—44no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—448no—
527C2×C4—448no—
528C2×C4—444no—
529C2×C4—444no—
530C2×C4#6703714yes—
531C2×C4C22×C22⋊D1112yes—
532C2×C4C22×C22⋊D1112yes—
533C2×C4C22×C22⋊D1112yes—
534C2×C4C22×C22⋊D1111yescharacteristic
535C2×C4C24×D1111yescharacteristic
536C8—228no—
537C22—22no—
538C22—22no—
539C22—28no—
540C22—28no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—416no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—44no—
551C22—816no—
552C22—88no—
553C22C2×#6698514yes—
554C22C2×#6698512yes—
555C22#1062333512yes—
556C22C2×#6700414yes—
557C22C2×#6700412yes—
558C22C23×C22⋊D1111yescharacteristic
559C4—22no—
560C4—22no—
561C4—22no—
562C4—44no—
563C4—444no—
564C4—444no—
565C4#1062333512yes—
566C4C2×#6703712yes—
567C2—24no—
568C2—24no—
569C2—42no—
570C2—84no—
571C2#1307942214yesdirect product factor
572C2C2×#1062333511yescharacteristic
573C2C22×#6698511yescharacteristic
574C2C22×#6700411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C22×D4
hypercenterC22×#121D11
hypocenterC11C2×#3193
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
2. #13079422C2direct (N × H)
3. C2×#10622583C2semidirect
4. C2×#10622646C2semidirect
5. C2×#10622655C2semidirect
6. C2×#10622653C2semidirect
7. C2×#10622831C2semidirect
8. C2×#10622820C2semidirect
13. C23×Dic22C22semidirect
23. C22×#4324C22semidirect
24. C22×C4⋊Dic11C22semidirect
29. C2×#66977C22semidirect
30. C2×#66977C22semidirect
32. C22×#4318C22semidirect
33. #10622831C22semidirect
34. C2×#66896C22semidirect
35. #10622820C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
38. #10622655C22semidirect
39. #10622653C22semidirect
40. #10622646C22semidirect
41. #10622583C22semidirect
42. C2×#66874C22semidirect
43. C2×#66871C22semidirect
71. C22×Dic22C23semidirect
89. C2×#4324C23semidirect
93. C2×C4⋊Dic11C23semidirect
99. #66977C23semidirect
104. C2×#4318C23semidirect
106. #66896C23semidirect
108. C22⋊(C11⋊C8)C23semidirect
109. #66874C23semidirect
110. #66871C23semidirect
394. C2×C11#3193semidirect
475. C11C2×#3193semidirect
571. C2#13079422direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
#130794222
C2×#106225832
C2×#106226462
C2×#106226552
C2×#106226532
C2×#106228312
C2×#106228202
C22×C11×#1212
C2×#319311