Finite Group Databasebeta

← C2×#13071966 #14921570

Subgroups — C2×#13071966 #14921570

Order 2816.

8622 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C212yesmaximal, complemented
2C22×#67006C212yesmaximal, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071966C2116yesmaximal, direct product factor
5C2×#10622835C212yesmaximal, complemented
6C2×#10622836C212yesmaximal, complemented
7C2×#10622834C212yesmaximal, complemented
8C2×#10622825C211yesmaximal, characteristic, complemented
9C2×#10622860C212yesmaximal, complemented
10C24×D4×C11C211yesmaximal, characteristic, complemented
11C26×C11C2212yes—
12C23×D4×C11—216no—
13C23×D4×C11—28no—
14C23×D4×C11C2212yes—
15C23×D4×C11C2212yes—
16C23×D4×C11C2218yescomplemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2214yescomplemented
20C23×C4×D11C2211yescharacteristic, complemented
21C2×#67006—216no—
22C2×#67006C22116yescomplemented
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2214yescomplemented
26C22×C22⋊Dic11C2214yescomplemented
27C22×C22⋊Dic11C2214yescomplemented
28C2×#66991—216no—
29C2×#66991C22116yescomplemented
30C2×C4×C22⋊D11—28no—
31C2×C4×C22⋊D11C2218yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
33C22×C4⋊Dic11C2212yescomplemented
34C22×Dic11⋊C4C2211yescharacteristic, complemented
35C22×C4×Dic11C2211yescharacteristic, complemented
36#10622860C22116yescomplemented
37#10622836C22116yescomplemented
38#10622835C22116yescomplemented
39#10622834C22116yescomplemented
40#10622825C2218yescomplemented
41C2×C11⋊#95C2212yescomplemented
42C25×C11—216no—
43C25×C11—28no—
44C25×C11—28no—
45C25×C11—28no—
46C25×C11—48no—
47C25×C11C2314yes—
48C25×C11C2318yes—
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×D4×C11—2128no—
52C22×D4×C11—216no—
53C22×D4×C11—264no—
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11—28no—
57C22×D4×C11—232no—
58C22×D4×C11D4116yescomplemented
59C22×D4×C11C2318yes—
60C22×D4×C11C2318yes—
61C23×C4×C11—28no—
62C23×C4×C11D418yescomplemented
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—24no—
67C22×C22⋊D11—24no—
68C22×C22⋊D11—216no—
69C22×C22⋊D11—216no—
70C22×C22⋊D11—48no—
71C22×C22⋊D11D418yescomplemented
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C23116yescomplemented
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2314yes—
77C23×Dic11C2311yescharacteristic
78C22×C4×D11—24no—
79C22×C4×D11—28no—
80C22×C4×D11C2314yescomplemented
81#67006—264no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—216no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—216no—
86C2×C22⋊Dic11—48no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C23116yescomplemented
90C2×C22⋊Dic11C23116yescomplemented
91C2×C22⋊Dic11C23116yescomplemented
92#66991—264no—
93C4×C22⋊D11—232no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4C2314yescomplemented
96C2×C4⋊Dic11—28no—
97C2×C4⋊Dic11C2318yescomplemented
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4C2314yescomplemented
100C2×C4×Dic11—24no—
101C2×C4×Dic11C2314yescomplemented
102C11⋊#95C2318yescomplemented
103C2×#2408—111nomaximal, Sylow
104C24×C11—24no—
105C24×C11—24no—
106C24×C11—264no—
107C24×C11—28no—
108C24×C11—232no—
109C24×C11—216no—
110C24×C11—28no—
111C24×C11—28no—
112C24×C11—28no—
113C24×C11—28no—
114C24×C11—28no—
115C24×C11—216no—
116C24×C11—216no—
117C24×C11—416no—
118C24×C11—464no—
119C24×C11—464no—
120C24×C11—432no—
121C24×C11—432no—
122C24×C11C2×D4116yes—
123C24×C11C2×D414yes—
124C24×C11C2×D414yes—
125C24×C11#4114yes—
126C24×C11C2418yes—
127C24×C11C2412yes—
128C24×C11C2411yescharacteristic
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—22no—
132C23×D11—24no—
133C23×D11C2×D414yescomplemented
134C23×D11C2412yes—
135C2×D4×C11—264no—
136C2×D4×C11—2256no—
137C2×D4×C11—232no—
138C2×D4×C11—264no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—216no—
142C2×D4×C11C2×D4132yescomplemented
143C22×C4×C11—24no—
144C22×C4×C11—232no—
145C22×C4×C11—216no—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D418yes—
149C22×C4×C11C2×D4116yescomplemented
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C2×C22⋊D11—232no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—232no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—232no—
157C2×C22⋊D11—416no—
158C2×C22⋊D11—464no—
159C2×C22⋊D11C2×D4116yescomplemented
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—28no—
164C22×Dic11—24no—
165C22×Dic11—28no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—28no—
169C22×Dic11C2×D414yescomplemented
170C22×Dic11C2418yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C2×C4×D11—28no—
175C2×C4×D11—216no—
176C2×C4×D11—416no—
177C22⋊Dic11—232no—
178C22⋊Dic11—28no—
179C22⋊Dic11—232no—
180C22⋊Dic11—216no—
181C22⋊Dic11—416no—
182(C2×D11)⋊C4—28no—
183C4⋊Dic11—216no—
184Dic11⋊C4—28no—
185C4×Dic11—28no—
186C24×D4D1111yescharacteristic, complemented
187C22×#121—112no—
188C22×#120—112no—
189C22×C4×D4—111no—
190#2408—1116no—
191C2×#394—112no—
192C2×#392—112no—
193C2×#390—112no—
194C2×#380—111no—
195C2×#379—112no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—264no—
203C23×C11—232no—
204C23×C11—232no—
205C23×C11—232no—
206C23×C11—28no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—28no—
212C23×C11—464no—
213C23×C11—464no—
214C23×C11—4256no—
215C23×C11—432no—
216C23×C11—416no—
217C23×C11—432no—
218C23×C11—416no—
219C23×C11—416no—
220C23×C11—416no—
221C23×C11#121116yescomplemented
222C23×C11C22×D414yes—
223C23×C11C22×D412yes—
224C23×C11C22×D4116yes—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11C22×D414yes—
228C23×C11C2×#4114yes—
229C23×C11C2×#4112yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11C2511yescharacteristic
232C22×D11—28no—
233C22×D11—216no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—48no—
241C22×D11C22×D414yescomplemented
242D4×C11—264no—
243D4×C11—264no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—232no—
247C2×C4×C11#120116yescomplemented
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D418yes—
251C22⋊D11—232no—
252C22⋊D11—464no—
253C2×Dic11—28no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—28no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11—416no—
266C2×Dic11C22×D414yescomplemented
267C4×D11—416no—
268C26C2×D1112yes—
269C23×D4—216no—
270C23×D4—28no—
271C23×D4—111no—
272C23×D4—114no—
273C23×D4C2×D1112yes—
274C23×D4C2×D1112yes—
275C23×D4C2×D1118yescomplemented
276C24×C4—111no—
277C24×C4C2×D1111yescharacteristic
278C2×#121—1116no—
279C2×#121—2216no—
280C2×#120—1116no—
281C2×#120—2216no—
282C2×C4×D4—118no—
283C2×C4×D4—228no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C22⋊C4—114no—
287C22×C22⋊C4—114no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—114no—
292C22×C42—111no—
293#394—1116no—
294#392—1116no—
295#390—1116no—
296#380—118no—
297#379—1116no—
298C2×#95—112no—
299C22×C11—24no—
300C22×C11—232no—
301C22×C11—24no—
302C22×C11—28no—
303C22×C11—28no—
304C22×C11—216no—
305C22×C11—216no—
306C22×C11—216no—
307C22×C11—4128no—
308C22×C11—464no—
309C22×C11—48no—
310C22×C11—48no—
311C22×C11—48no—
312C22×C11—48no—
313C22×C11C2×#12014yes—
314C22×C11C2×#12114yes—
315C22×C11C2×#12118yescomplemented
316C22×C11#53514yes—
317C22×C11D4218yes—
318C22×C11#54618yes—
319C22×C11C23×D411yescharacteristic
320C22×C11C23×D411yescharacteristic
321C22×C11C23×D412yes—
322C22×C11C22×#4111yescharacteristic
323C22×C11C2×H(5,𝔽2)12yes—
324C2×D11—24no—
325C2×D11—28no—
326C2×D11—42no—
327C2×D11—416no—
328C2×D11—42no—
329C2×D11—44no—
330C4×C11—24no—
331C4×C11C2×#12018yescomplemented
332Dic11—24no—
333Dic11—42no—
334Dic11—42no—
335Dic11—48no—
336C25—216no—
337C25—28no—
338C25—28no—
339C25—28no—
340C25—48no—
341C25—111no—
342C25C22×D1114yes—
343C25C22×D1118yes—
344C25C22×D1111yescharacteristic
345C22×D4—2128no—
346C22×D4—216no—
347C22×D4—264no—
348C22×D4—28no—
349C22×D4—28no—
350C22×D4—28no—
351C22×D4—232no—
352C22×D4—118no—
353C22×D4—114no—
354C22×D4—1116no—
355C22×D4—224no—
356C22×D4—224no—
357C22×D4—2216no—
358C22×D4—2216no—
359C22×D4—448no—
360C22×D4C22⋊D11116yescomplemented
361C22×D4C22×D1118yes—
362C22×D4C22×D1118yes—
363C23×C4—28no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—114no—
368C23×C4—114no—
369C23×C4—224no—
370C23×C4—228no—
371C23×C4C22⋊D1118yescomplemented
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1114yes—
374C23×C4C22×D1111yescharacteristic
375#121—2264no—
376#120—2264no—
377C4×D4—2232no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—118no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4—228no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—1116no—
385C2×C22⋊C4—1116no—
386C2×C22⋊C4—114no—
387C2×C22⋊C4—1116no—
388C2×C22⋊C4—2216no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—2216no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—448no—
394C2×C42—114no—
395C2×C42—224no—
396#95—118no—
397C2×C11—28no—
398C2×C11—416no—
399C2×C11#240818yescomplemented
400C2×C11C22×#12011yescharacteristic
401C2×C11C22×#12111yescharacteristic
402C2×C11C2×#53511yescharacteristic
403C2×C11C2×D4212yes—
404C2×C11C2×#54612yes—
405D11—44no—
406C24—24no—
407C24—24no—
408C24—264no—
409C24—28no—
410C24—28no—
411C24—28no—
412C24—28no—
413C24—232no—
414C24—216no—
415C24—28no—
416C24—28no—
417C24—216no—
418C24—216no—
419C24—416no—
420C24—464no—
421C24—464no—
422C24—432no—
423C24—432no—
424C24—114no—
425C24—112no—
426C24—222no—
427C24—224no—
428C24—222no—
429C24—224no—
430C24D4×D1114yes—
431C24#434114yes—
432C24C2×C22⋊D11116yes—
433C24C2×C22⋊D1114yes—
434C24C23×D1118yes—
435C24C23×D1112yes—
436C24C23×D1111yescharacteristic
437C2×D4—264no—
438C2×D4—2256no—
439C2×D4—232no—
440C2×D4—264no—
441C2×D4—216no—
442C2×D4—216no—
443C2×D4—216no—
444C2×D4—1116no—
445C2×D4—2232no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—2232no—
449C2×D4—2232no—
450C2×D4—4416no—
451C2×D4—4464no—
452C2×D4C2×C22⋊D11132yescomplemented
453C22×C4—24no—
454C22×C4—232no—
455C22×C4—216no—
456C22×C4—114no—
457C22×C4—112no—
458C22×C4—118no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—228no—
464C22×C4—224no—
465C22×C4—228no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—228no—
470C22×C4—228no—
471C22×C4—2216no—
472C22×C4—4416no—
473C22×C4C2×C22⋊D1114yes—
474C22×C4C2×C22⋊D1114yes—
475C22×C4C2×C22⋊D1118yes—
476C22×C4C2×C22⋊D11116yescomplemented
477C22×C4C23×D1112yes—
478C22×C4C23×D1112yes—
479C4⋊C4—228no—
480C4⋊C4—2216no—
481C22⋊C4—2232no—
482C22⋊C4—2216no—
483C22⋊C4—228no—
484C22⋊C4—2232no—
485C22⋊C4—228no—
486C22⋊C4—4416no—
487C42—228no—
488C11C2×#240811yescharacteristic, complemented, Sylow
489C23—216no—
490C23—28no—
491C23—216no—
492C23—28no—
493C23—24no—
494C23—24no—
495C23—264no—
496C23—232no—
497C23—232no—
498C23—232no—
499C23—28no—
500C23—28no—
501C23—28no—
502C23—28no—
503C23—28no—
504C23—28no—
505C23—464no—
506C23—464no—
507C23—432no—
508C23—4256no—
509C23—416no—
510C23—432no—
511C23—416no—
512C23—416no—
513C23—416no—
514C23—114no—
515C23—228no—
516C23—2216no—
517C23—222no—
518C23—224no—
519C23—222no—
520C23—224no—
521C23—444no—
522C23—448no—
523C23—444no—
524C23#66991116yescomplemented
525C23C2×D4×D1114yes—
526C23C2×D4×D1112yes—
527C23C2×#434114yes—
528C23C2×#434112yes—
529C23#6703714yes—
530C23C22×C22⋊D11116yes—
531C23C22×C22⋊D1114yes—
532C23C22×C22⋊D1112yes—
533C23C22×C22⋊D1114yes—
534C23C24×D1111yescharacteristic
535D4—264no—
536D4—264no—
537D4—2232no—
538D4—4464no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—232no—
542C2×C4—114no—
543C2×C4—228no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—228no—
553C2×C4—4416no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—4416no—
557C2×C4#67006116yescomplemented
558C2×C4C22×C22⋊D1114yes—
559C2×C4C22×C22⋊D1114yes—
560C2×C4C22×C22⋊D1118yes—
561C22—24no—
562C22—232no—
563C22—28no—
564C22—28no—
565C22—24no—
566C22—216no—
567C22—216no—
568C22—216no—
569C22—4128no—
570C22—48no—
571C22—464no—
572C22—48no—
573C22—48no—
574C22—48no—
575C22—228no—
576C22—224no—
577C22—442no—
578C22—4416no—
579C22—444no—
580C22—442no—
581C22C2×#6699114yes—
582C22C2×#6699118yescomplemented
583C22D4×C22⋊D1118yes—
584C22#1062333614yes—
585C22#1062333718yes—
586C22C2×#6700614yes—
587C22C22×D4×D1111yescharacteristic
588C22C22×#434111yescharacteristic
589C22C2×#6703712yes—
590C22C23×C22⋊D1111yescharacteristic
591C22C23×C22⋊D1112yes—
592C4—24no—
593C4—224no—
594C4—442no—
595C4—448no—
596C4—442no—
597C4C2×#6700618yescomplemented
598C2—28no—
599C2—416no—
600C2—444no—
601C2#1307196618yesdirect product factor
602C2C22×#6700611yescharacteristic
603C2C22×#6699111yescharacteristic
604C2C2×#1062333611yescharacteristic
605C2C2×D4×C22⋊D1112yes—
606C2C2×#1062333712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC24×D4×C11C2
socleC24×C11C24
hypercenterC24×D4D11
hypocenterC11C2×#2408
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66991C2semidirect
2. C22×#67006C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071966C2direct (N × H)
5. C2×#10622835C2semidirect
6. C2×#10622836C2semidirect
7. C2×#10622834C2semidirect
8. C2×#10622825C2semidirect
9. C2×#10622860C2semidirect
10. C24×D4×C11C2semidirect
16. C23×D4×C11C22semidirect
19. C23×C22⋊D11C22semidirect
20. C23×C4×D11C22semidirect
22. C2×#67006C22semidirect
25. C22×C22⋊Dic11C22semidirect
26. C22×C22⋊Dic11C22semidirect
27. C22×C22⋊Dic11C22semidirect
29. C2×#66991C22semidirect
31. C2×C4×C22⋊D11C22semidirect
32. C22×(C2×D11)⋊C4C22semidirect
33. C22×C4⋊Dic11C22semidirect
34. C22×Dic11⋊C4C22semidirect
35. C22×C4×Dic11C22semidirect
36. #10622860C22semidirect
37. #10622836C22semidirect
38. #10622835C22semidirect
39. #10622834C22semidirect
40. #10622825C22semidirect
41. C2×C11⋊#95C22semidirect
58. C22×D4×C11D4semidirect
62. C23×C4×C11D4semidirect
71. C22×C22⋊D11D4semidirect
73. C22×C22⋊D11C23semidirect
80. C22×C4×D11C23semidirect
89. C2×C22⋊Dic11C23semidirect
90. C2×C22⋊Dic11C23semidirect
91. C2×C22⋊Dic11C23semidirect
95. C2×(C2×D11)⋊C4C23semidirect
97. C2×C4⋊Dic11C23semidirect
99. C2×Dic11⋊C4C23semidirect
101. C2×C4×Dic11C23semidirect
102. C11⋊#95C23semidirect
133. C23×D11C2×D4semidirect
142. C2×D4×C11C2×D4semidirect
149. C22×C4×C11C2×D4semidirect
159. C2×C22⋊D11C2×D4semidirect
169. C22×Dic11C2×D4semidirect
186. C24×D4D11semidirect
221. C23×C11#121semidirect
241. C22×D11C22×D4semidirect
247. C2×C4×C11#120semidirect
266. C2×Dic11C22×D4semidirect
275. C23×D4C2×D11semidirect
315. C22×C11C2×#121semidirect
331. C4×C11C2×#120semidirect
360. C22×D4C22⋊D11semidirect
371. C23×C4C22⋊D11semidirect
399. C2×C11#2408semidirect
452. C2×D4C2×C22⋊D11semidirect
476. C22×C4C2×C22⋊D11semidirect
488. C11C2×#2408semidirect
524. C23#66991semidirect
557. C2×C4#67006semidirect
582. C22C2×#66991semidirect
597. C4C2×#67006semidirect
601. C2#13071966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×#670062
C22×C4×C22⋊D112
#130719662
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106228252
C2×#106228602
C24×D4×C112
C2×#240811