Finite Group Databasebeta

← C2×#13074331 #14920102

Subgroups — C2×#13074331 #14920102

Order 2816.

7946 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D11C211yesmaximal, characteristic, complemented
2C22×#66939C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic, complemented
4C22×#67006C211yesmaximal, characteristic, complemented
5#13074331C2116yesmaximal, direct product factor
6C2×#10622574C214yesmaximal, complemented
7C2×#10622573C214yesmaximal, complemented
8C2×#10622556C211yesmaximal, characteristic, complemented
9C2×#10622568C211yesmaximal, characteristic, complemented
10C2×C11×#379C211yesmaximal, characteristic, complemented
11C26×C11C2211yescharacteristic
12C25×D11C2211yescharacteristic
13C23×C22⋊D11—28no—
14C23×C22⋊D11—28no—
15C23×C22⋊D11—28no—
16C23×C22⋊D11C2214yes—
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2218yescomplemented
19C23×C22⋊D11C2212yescomplemented
20C24×Dic11C2211yescharacteristic
21C23×D44C2212yescomplemented
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2214yescomplemented
25C2×#67006—28no—
26C2×#67006C2218yescomplemented
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2212yescomplemented
29C22×(C2×D11)⋊C4C2212yescomplemented
30C22×(C2×D11)⋊C4C2212yescomplemented
31C22×(C2×D11)⋊C4C2214yescomplemented
32C22×C4⋊Dic11C2212yescomplemented
33C2×#66939—28no—
34C2×#66939C2218yescomplemented
35C2×#66935—28no—
36C2×#66935C2218yescomplemented
37C11×#379C2218yescomplemented
38C2×C11⋊#95C2214yescomplemented
39#10622574C22132yescomplemented
40#10622573C22132yescomplemented
41#10622568C2218yescomplemented
42#10622556C2218yescomplemented
43C25×C11—24no—
44C25×C11—24no—
45C25×C11—48no—
46C25×C11D418yescomplemented
47C25×C11C2312yes—
48C25×C11C2311yescharacteristic
49C25×C11C2314yes—
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—48no—
53C24×D11D418yescomplemented
54C24×D11C2311yescharacteristic
55C24×D11C2312yes—
56C24×D11C2314yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C22×C22⋊D11—2128no—
60C22×C22⋊D11—216no—
61C22×C22⋊D11—232no—
62C22×C22⋊D11—216no—
63C22×C22⋊D11—232no—
64C22×C22⋊D11—24no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—216no—
69C22×C22⋊D11—232no—
70C22×C22⋊D11—48no—
71C22×C22⋊D11C2314yes—
72C22×C22⋊D11C23116yes—
73C22×C22⋊D11C2318yescomplemented
74C23×Dic11—24no—
75C23×Dic11—24no—
76C23×Dic11D418yescomplemented
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2312yes—
80C23×Dic11C2314yes—
81C22×D44—28no—
82C22×D44—48no—
83C22×D44C2318yescomplemented
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—48no—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C23116yescomplemented
90#67006—232no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—28no—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2318yescomplemented
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—48no—
98C2×(C2×D11)⋊C4C2318yescomplemented
99C2×(C2×D11)⋊C4C2318yescomplemented
100C2×(C2×D11)⋊C4C23116yescomplemented
101C2×C4⋊Dic11—28no—
102C2×C4⋊Dic11C2318yescomplemented
103#66939—232no—
104#66935—232no—
105C11⋊#95C23116yescomplemented
106C2×#2613—111nomaximal, Sylow
107C24×C11—28no—
108C24×C11—232no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—28no—
112C24×C11—28no—
113C24×C11—28no—
114C24×C11—28no—
115C24×C11—432no—
116C24×C11—416no—
117C24×C11—432no—
118C24×C11—432no—
119C24×C11C2×D418yes—
120C24×C11C2×D414yes—
121C24×C11C2×D414yes—
122C24×C11C2×D414yes—
123C24×C11C2×D4116yescomplemented
124C24×C11C2414yes—
125C24×C11C2412yes—
126C24×C11C2411yescharacteristic
127C23×D11—232no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—28no—
131C23×D11—28no—
132C23×D11—28no—
133C23×D11—28no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—28no—
138C23×D11—432no—
139C23×D11—416no—
140C23×D11—432no—
141C23×D11—432no—
142C23×D11C2×D418yes—
143C23×D11C2×D4116yescomplemented
144C23×D11C2412yes—
145C23×D11C2414yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—28no—
149C22×C4×C11—28no—
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C2×C22⋊D11—2128no—
153C2×C22⋊D11—2256no—
154C2×C22⋊D11—232no—
155C2×C22⋊D11—232no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—232no—
161C2×C22⋊D11—416no—
162C2×C22⋊D11—432no—
163C2×C22⋊D11—416no—
164C22×Dic11—232no—
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11—28no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—28no—
174C22×Dic11C2×D418yes—
175C22×Dic11C2×D4116yescomplemented
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2414yes—
179C2×D44—216no—
180C2×D44—416no—
181C2×D44—432no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—416no—
185C22⋊Dic11—28no—
186C22⋊Dic11—216no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—416no—
190C4⋊Dic11—216no—
191C24×D4—111no—
192C22×#123—111no—
193C22×#120—111no—
194C22×#120—111no—
195#2613—1116no—
196C2×#394—114no—
197C2×#392—114no—
198C2×#381—111no—
199C2×#379—111no—
200C2×#379D1111yescharacteristic, complemented
201C23×C11—216no—
202C23×C11—216no—
203C23×C11—216no—
204C23×C11—28no—
205C23×C11—216no—
206C23×C11—232no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—28no—
212C23×C11—28no—
213C23×C11—432no—
214C23×C11—4128no—
215C23×C11—432no—
216C23×C11—432no—
217C23×C11—416no—
218C23×C11—416no—
219C23×C11#120116yes—
220C23×C11C22×D418yes—
221C23×C11C22×D414yes—
222C23×C11C22×D412yes—
223C23×C11C22×D414yes—
224C23×C11C22×D414yes—
225C23×C11C22×D412yes—
226C23×C11C22×D412yes—
227C23×C11H(5,𝔽2)18yes—
228C23×C11C2511yescharacteristic
229C22×D11—216no—
230C22×D11—232no—
231C22×D11—216no—
232C22×D11—216no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—28no—
241C22×D11—432no—
242C22×D11—4128no—
243C22×D11—432no—
244C22×D11—432no—
245C22×D11—416no—
246C22×D11—416no—
247C22×D11—44no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11C22×D418yes—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—48no—
257C2×C4×C11—48no—
258C22⋊D11—2128no—
259C22⋊D11—432no—
260C22⋊D11—416no—
261C2×Dic11—216no—
262C2×Dic11—232no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—28no—
270C2×Dic11—44no—
271C2×Dic11—48no—
272C2×Dic11C22×D418yes—
273D44—432no—
274C26—111no—
275C26C2×D1111yescharacteristic
276C23×D4—118no—
277C23×D4—114no—
278C23×D4—111no—
279C23×D4—112no—
280C23×D4—112no—
281C23×D4—228no—
282C23×D4—228no—
283C23×D4—228no—
284C24×C4—111no—
285C2×#123—118no—
286C2×#123—228no—
287C2×#120—118no—
288C2×#120—118no—
289C2×#120—228no—
290C2×#120—228no—
291C22×C4⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—114no—
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1114yescomplemented
300#394—1132no—
301#392—1132no—
302#381—118no—
303#379—118no—
304#379C2×D1118yescomplemented
305C2×#95—114no—
306C22×C11—232no—
307C22×C11—28no—
308C22×C11—28no—
309C22×C11—28no—
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—464no—
314C22×C11—432no—
315C22×C11—48no—
316C22×C11—48no—
317C22×C11C2×#12018yes—
318C22×C11C2×#12014yes—
319C22×C11#53418yes—
320C22×C11#53418yes—
321C22×C11#53518yes—
322C22×C11C23×D411yescharacteristic
323C22×C11C23×D411yescharacteristic
324C22×C11C23×D411yescharacteristic
325C22×C11C2×H(5,𝔽2)14yes—
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—28no—
329C2×D11—464no—
330C2×D11—432no—
331C2×D11—48no—
332C2×D11—48no—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—88no—
338C4×C11—44no—
339C4×C11—44no—
340Dic11—28no—
341Dic11—42no—
342Dic11—44no—
343C25—24no—
344C25—24no—
345C25—48no—
346C25—112no—
347C25—118no—
348C25—114no—
349C25—111no—
350C25—224no—
351C25—224no—
352C25—448no—
353C25D4418yescomplemented
354C25C22×D1112yes—
355C25C22×D1111yescharacteristic
356C25C22×D1114yes—
357C22×D4—114no—
358C22×D4—1116no—
359C22×D4—118no—
360C22×D4—118no—
361C22×D4—228no—
362C22×D4—2216no—
363C22×D4—2232no—
364C22×D4—2216no—
365C22×D4—2232no—
366C22×D4—22128no—
367C22×D4—2216no—
368C22×D4—2232no—
369C22×D4—228no—
370C22×D4—224no—
371C22×D4—224no—
372C22×D4—224no—
373C22×D4—448no—
374C22×D4—448no—
375C23×C4—118no—
376C23×C4—114no—
377C23×C4—112no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4—224no—
381C23×C4—224no—
382C23×C4C22×D1112yes—
383C23×C4C22×D1112yes—
384#123—2232no—
385#120—2232no—
386#120—2232no—
387C2×C4⋊C4—118no—
388C2×C4⋊C4—228no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—48no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—1116no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—448no—
402C2×C22⋊C4C22×D1114yes—
403C2×C22⋊C4C22×D1114yes—
404C2×C22⋊C4C22×D11116yescomplemented
405#95—1116no—
406C2×C11—28no—
407C2×C11—48no—
408C2×C11#261318yescomplemented
409C2×C11C22×#12011yescharacteristic
410C2×C11C2×#53412yes—
411C2×C11C2×#53412yes—
412C2×C11C2×#53512yes—
413D11—48no—
414D11—82no—
415C24—28no—
416C24—232no—
417C24—24no—
418C24—24no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—416no—
424C24—432no—
425C24—432no—
426C24—432no—
427C24—118no—
428C24—114no—
429C24—1116no—
430C24—112no—
431C24—2232no—
432C24—228no—
433C24—224no—
434C24—228no—
435C24—224no—
436C24—228no—
437C24—228no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—228no—
442C24—4432no—
443C24—4416no—
444C24—4432no—
445C24—4432no—
446C24C2×D4418yes—
447C24C2×D4414yes—
448C24C2×D44116yescomplemented
449C24D4×D1114yes—
450C24D4×D1114yes—
451C24C23×D1114yes—
452C24C23×D1112yes—
453C24C23×D1111yescharacteristic
454C2×D4—2216no—
455C2×D4—2232no—
456C2×D4—2232no—
457C2×D4—22128no—
458C2×D4—22256no—
459C2×D4—2232no—
460C2×D4—2216no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—4416no—
465C2×D4—4432no—
466C2×D4—4416no—
467C2×D4—4432no—
468C2×D4—4416no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—118no—
474C22×C4—1116no—
475C22×C4—114no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—2232no—
479C22×C4—228no—
480C22×C4—224no—
481C22×C4—228no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—228no—
488C22×C4C23×D1114yes—
489C22×C4C23×D1114yes—
490C4⋊C4—2216no—
491C22⋊C4—28no—
492C22⋊C4—28no—
493C22⋊C4—416no—
494C22⋊C4—2216no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—228no—
498C22⋊C4—4416no—
499C11C2×#261311yescharacteristic, complemented, Sylow
500C23—216no—
501C23—216no—
502C23—216no—
503C23—28no—
504C23—216no—
505C23—232no—
506C23—216no—
507C23—216no—
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—432no—
513C23—432no—
514C23—432no—
515C23—4128no—
516C23—416no—
517C23—416no—
518C23—118no—
519C23—2232no—
520C23—2216no—
521C23—2216no—
522C23—2216no—
523C23—224no—
524C23—224no—
525C23—228no—
526C23—228no—
527C23—222no—
528C23—222no—
529C23—222no—
530C23—228no—
531C23—4432no—
532C23—4432no—
533C23—4432no—
534C23—44128no—
535C23—4416no—
536C23—4416no—
537C23—444no—
538C23—448no—
539C23—448no—
540C23—448no—
541C23#66935116yes—
542C23C22×D4418yes—
543C23C22×D4414yes—
544C23C22×D4412yes—
545C23C2×D4×D1114yes—
546C23C2×D4×D1114yes—
547C23C2×D4×D1112yes—
548C23C2×D4×D1112yes—
549C23#6703718yes—
550C23C24×D1111yescharacteristic
551D4—22128no—
552D4—4432no—
553D4—4432no—
554D4—4416no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—48no—
560C2×C4—48no—
561C2×C4—118no—
562C2×C4—2232no—
563C2×C4—2216no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—228no—
571C2×C4—444no—
572C2×C4—448no—
573C22—28no—
574C22—28no—
575C22—28no—
576C22—232no—
577C22—28no—
578C22—28no—
579C22—28no—
580C22—464no—
581C22—48no—
582C22—48no—
583C22—432no—
584C22—228no—
585C22—228no—
586C22—228no—
587C22—4464no—
588C22—448no—
589C22—448no—
590C22—4432no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—442no—
595C22—888no—
596C22C2×#6693518yes—
597C22C2×#6693514yes—
598C22#1062302418yes—
599C22#1062312018yes—
600C22#1062312318yes—
601C22C23×D4411yescharacteristic
602C22C22×D4×D1111yescharacteristic
603C22C22×D4×D1111yescharacteristic
604C22C2×#6703714yes—
605C4—44no—
606C4—44no—
607C4—228no—
608C4—444no—
609C4—442no—
610C2—28no—
611C2—48no—
612C2—448no—
613C2—882no—
614C2#1307433118yesdirect product factor
615C2C22×#6693511yescharacteristic
616C2C2×#1062312012yes—
617C2C2×#1062302412yes—
618C2C2×#1062312312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
hypercenterC2×#379D11
hypocenterC11C2×#2613
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊D11C2semidirect
2. C22×#66939C2semidirect
3. C22×#66935C2semidirect
4. C22×#67006C2semidirect
5. #13074331C2direct (N × H)
6. C2×#10622574C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622556C2semidirect
9. C2×#10622568C2semidirect
10. C2×C11×#379C2semidirect
18. C23×C22⋊D11C22semidirect
19. C23×C22⋊D11C22semidirect
21. C23×D44C22semidirect
24. C22×C11×C22⋊C4C22semidirect
26. C2×#67006C22semidirect
28. C22×C22⋊Dic11C22semidirect
29. C22×(C2×D11)⋊C4C22semidirect
30. C22×(C2×D11)⋊C4C22semidirect
31. C22×(C2×D11)⋊C4C22semidirect
32. C22×C4⋊Dic11C22semidirect
34. C2×#66939C22semidirect
36. C2×#66935C22semidirect
37. C11×#379C22semidirect
38. C2×C11⋊#95C22semidirect
39. #10622574C22semidirect
40. #10622573C22semidirect
41. #10622568C22semidirect
42. #10622556C22semidirect
46. C25×C11D4semidirect
53. C24×D11D4semidirect
73. C22×C22⋊D11C23semidirect
76. C23×Dic11D4semidirect
83. C22×D44C23semidirect
89. C2×C11×C22⋊C4C23semidirect
94. C2×C22⋊Dic11C23semidirect
98. C2×(C2×D11)⋊C4C23semidirect
99. C2×(C2×D11)⋊C4C23semidirect
100. C2×(C2×D11)⋊C4C23semidirect
102. C2×C4⋊Dic11C23semidirect
105. C11⋊#95C23semidirect
123. C24×C11C2×D4semidirect
143. C23×D11C2×D4semidirect
175. C22×Dic11C2×D4semidirect
200. C2×#379D11semidirect
299. C22×C22⋊C4C2×D11semidirect
304. #379C2×D11semidirect
353. C25D44semidirect
404. C2×C22⋊C4C22×D11semidirect
408. C2×C11#2613semidirect
448. C24C2×D44semidirect
499. C11C2×#2613semidirect
614. C2#13074331direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊D112
C22×#669392
C22×#669352
C22×#670062
#130743312
C2×#106225742
C2×#106225732
C2×#106225562
C2×#106225682
C2×C11×#3792
C2×#261311