Finite Group Databasebeta

← C2×#13071853 #14919992

Subgroups — C2×#13071853 #14919992

Order 2816.

4134 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C212yesmaximal, complemented
3C22×#66930C211yesmaximal, characteristic, complemented
4#13071853C2116yesmaximal, direct product factor
5C2×#10622593C211yesmaximal, characteristic, complemented
6C2×#10622289C212yesmaximal, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622572C212yesmaximal, complemented
9C2×#10622573C211yesmaximal, characteristic
10C2×#10622262C211yesmaximal, characteristic, complemented
11C2×#10622279C212yesmaximal, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2212yes—
14C24×Dic11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C2×#66946—28no—
33C2×#66946C2218yescomplemented
34C2×(C22⋊D11)⋊C4—216no—
35C2×(C22⋊D11)⋊C4C22116yescomplemented
36C2×#66930—28no—
37C2×#66930C2218yescomplemented
38C11×#397C2218yescomplemented
39C2×C11×#95C2212yes—
40C2×C11×#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2211yescharacteristic
43#10622593C2218yescomplemented
44#10622573C2218yes—
45#10622572C22116yescomplemented
46#10622289C22116yescomplemented
47#10622285C2218yescomplemented
48#10622279C22116yescomplemented
49#10622262C2218yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—28no—
57C22×C22⋊D11—28no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11C2318yes—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11D418yescomplemented
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2314yes—
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C22×D44—28no—
70C22×D44—24no—
71C22×D44C2314yes—
72C22×C4×D11—28no—
73C22×C4×D11—28no—
74C22×C4×D11—28no—
75C22×C4×D11C2318yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11C2314yes—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—28no—
102C2×C4×Dic11D418yescomplemented
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2318yes—
105C2×C4×Dic11C2314yes—
106#66946—232no—
107(C22⋊D11)⋊C4—264no—
108#66930—232no—
109C11×#95C2314yes—
110C11×#95C2318yes—
111C11⋊#95C2314yes—
112C11⋊#95C2318yes—
113C2×#2392—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11C2×D414yes—
119C24×C11C2412yes—
120C24×C11C2411yescharacteristic
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11#4118yes—
128C23×D11C2414yes—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C2×C22⋊D11—264no—
144C2×C22⋊D11—216no—
145C2×C22⋊D11—216no—
146C2×C22⋊D11—216no—
147C22×Dic11—232no—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2×D414yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×D4116yescomplemented
162C22×Dic11#4118yes—
163C22×Dic11#4114yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C2×D44—232no—
170C2×D44—216no—
171C2×D44—28no—
172C2×C4×D11—216no—
173C2×C4×D11—216no—
174C2×C4×D11—216no—
175C2×C4×D11—432no—
176C11×C4⋊C4—28no—
177C11×C22⋊C4—216no—
178C11×C22⋊C4—28no—
179C22⋊Dic11—28no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184Dic11⋊C4—28no—
185Dic11⋊C4—216no—
186Dic11⋊C4—216no—
187Dic11⋊C4—28no—
188C4×Dic11—28no—
189C4×Dic11—216no—
190C4×Dic11C2×D4116yescomplemented
191C22×C4×D4—111no—
192C22×C4×D4—112no—
193C22×#117—111no—
194#2392—1116no—
195C2×#398—111no—
196C2×#397D1111yescharacteristic, complemented
197C2×#396—112no—
198C2×#394—111no—
199C2×#394—112no—
200C2×#392—111no—
201C2×C4×C4⋊C4—111no—
202C2×C4×C22⋊C4—112no—
203C23×C11—28no—
204C23×C11—216no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11C22×D414yes—
213C23×C11C22×D412yes—
214C23×C11C22×D412yes—
215C23×C11C2×#4112yes—
216C23×C11C2×#4114yes—
217C23×C11C2×#4114yes—
218C23×C11C2511yescharacteristic
219C22×D11—216no—
220C22×D11—216no—
221C22×D11—216no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11C2×#4118yes—
233C2×C4×C11—28no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—48no—
244C2×C4×C11—48no—
245C2×C4×C11—44no—
246C2×C4×C11C22×D414yes—
247C22⋊D11—264no—
248C2×Dic11—28no—
249C2×Dic11—216no—
250C2×Dic11—28no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—232no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11#121116yes—
261C2×Dic11C22×D414yes—
262C2×Dic11C22×D414yes—
263C2×Dic11C22×D414yes—
264C2×Dic11C22×D414yes—
265C2×Dic11C2×#4118yes—
266C2×Dic11C2×#4114yes—
267D44—232no—
268C4×D11—432no—
269C23×D4—112no—
270C23×D4—111no—
271C24×C4—111no—
272C24×C4—112no—
273C2×C4×D4—118no—
274C2×C4×D4—1116no—
275C2×C4×D4—228no—
276C2×C4×D4—2216no—
277C2×#117—118no—
278C2×#117—228no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4C2×D1112yes—
291C22×C42—111no—
292C22×C42—111no—
293C22×C42—112no—
294#398—118no—
295#397C2×D1118yescomplemented
296#396—1116no—
297#394—1116no—
298#394—118no—
299#392—118no—
300C4×C4⋊C4—118no—
301C4×C22⋊C4—1116no—
302C2×#95—111no—
303C2×#95—112no—
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1112yes—
306C22×C11—24no—
307C22×C11—28no—
308C22×C11—416no—
309C22×C11—42no—
310C22×C11—44no—
311C22×C11—42no—
312C22×C11C2×#12114yes—
313C22×C11#52514yes—
314C22×C11#52518yes—
315C22×C11#52918yes—
316C22×C11#53214yes—
317C22×C11C23×D411yescharacteristic
318C22×C11C23×D411yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C22×#4112yes—
321C22×C11C22×#4112yes—
322C2×D11—28no—
323C2×D11—28no—
324C2×D11—28no—
325C2×D11—432no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C4×C11—24no—
331C4×C11—44no—
332C4×C11—44no—
333C4×C11—42no—
334Dic11—24no—
335Dic11—28no—
336Dic11—24no—
337Dic11—42no—
338Dic11C2×#12118yes—
339C25—112no—
340C25C22×D1111yescharacteristic
341C22×D4—118no—
342C22×D4—114no—
343C22×D4—228no—
344C22×D4—228no—
345C22×D4—228no—
346C22×D4—228no—
347C22×D4—224no—
348C23×C4—111no—
349C23×C4—118no—
350C23×C4—114no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—112no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—228no—
357C23×C4—228no—
358C23×C4—228no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C4×D4—2232no—
366C4×D4—2264no—
367#117—2232no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—228no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4C22×D1114yes—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4C22×D1114yes—
391C2×C22⋊C4C22×D1118yes—
392C2×C42—118no—
393C2×C42—114no—
394C2×C42—114no—
395C2×C42—118no—
396C2×C42—224no—
397C2×C42—228no—
398#95—118no—
399#95—114no—
400#95C22×D1118yes—
401#95C22×D1114yes—
402C2×C11—44no—
403C2×C11#239218yescomplemented
404C2×C11C22×#12111yescharacteristic
405C2×C11C2×#52512yes—
406C2×C11C2×#52511yescharacteristic
407C2×C11C2×#52912yes—
408C2×C11C2×#53211yescharacteristic
409D11—48no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24—118no—
415C24—114no—
416C24—224no—
417C24—224no—
418C24—224no—
419C24—224no—
420C24—224no—
421C24—224no—
422C24D4×D1114yes—
423C24C23×D1112yes—
424C24C23×D1111yescharacteristic
425C2×D4—2216no—
426C2×D4—2232no—
427C2×D4—2216no—
428C2×D4—2216no—
429C2×D4—2264no—
430C2×D4—2216no—
431C2×D4—228no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—1116no—
448C22×C4—118no—
449C22×C4—114no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—2216no—
454C22×C4—2216no—
455C22×C4—2216no—
456C22×C4—228no—
457C22×C4—2232no—
458C22×C4—228no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—4432no—
467C22×C4D4×D1114yes—
468C22×C4C23×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1112yes—
472C4⋊C4—28no—
473C4⋊C4—228no—
474C4⋊C4—2216no—
475C4⋊C4—2216no—
476C4⋊C4—228no—
477C22⋊C4—216no—
478C22⋊C4—28no—
479C22⋊C4—2216no—
480C22⋊C4—2216no—
481C22⋊C4—2216no—
482C22⋊C4—2216no—
483C22⋊C4—228no—
484C42—1116no—
485C42—228no—
486C42—2216no—
487C11C2×#239211yescharacteristic, complemented, Sylow
488C23—28no—
489C23—216no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—48no—
495C23—44no—
496C23—44no—
497C23—118no—
498C23—2216no—
499C23—2216no—
500C23—2216no—
501C23—224no—
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—448no—
508C23—448no—
509C23—448no—
510C23—448no—
511C23C2×D4×D1114yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1112yes—
514C23#41×D1112yes—
515C23#41×D1114yes—
516C23#41×D1114yes—
517C23C24×D1111yescharacteristic
518D4—2232no—
519D4—2264no—
520C2×C4—28no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4—44no—
533C2×C4—1116no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—118no—
540C2×C4—2232no—
541C2×C4—228no—
542C2×C4—2216no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—4432no—
552C2×C4—444no—
553C2×C4C2×D4×D1114yes—
554C22—24no—
555C22—28no—
556C22—44no—
557C22—42no—
558C22—416no—
559C22—42no—
560C22—228no—
561C22—228no—
562C22—228no—
563C22—444no—
564C22—444no—
565C22—444no—
566C22—4432no—
567C22—444no—
568C22D11×#12114yes—
569C22#1062318714yes—
570C22#1062318718yes—
571C22#1062319914yes—
572C22#1062323718yes—
573C22C22×D4×D1111yescharacteristic
574C22C22×D4×D1111yescharacteristic
575C22C2×#41×D1111yescharacteristic
576C22C2×#41×D1112yes—
577C22C2×#41×D1112yes—
578C4—24no—
579C4—42no—
580C4—44no—
581C4—44no—
582C4—118no—
583C4—224no—
584C4—224no—
585C4—228no—
586C4—442no—
587C2—44no—
588C2—448no—
589C2#1307185318yesdirect product factor
590C2C2×D11×#12111yescharacteristic
591C2C2×#1062318711yescharacteristic
592C2C2×#1062318712yes—
593C2C2×#1062323712yes—
594C2C2×#1062319911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#397D11
hypocenterC11C2×#2392
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66946C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. C22×#66930C2semidirect
4. #13071853C2direct (N × H)
5. C2×#10622593C2semidirect
6. C2×#10622289C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622572C2semidirect
10. C2×#10622262C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#397C2semidirect
33. C2×#66946C22semidirect
35. C2×(C22⋊D11)⋊C4C22semidirect
37. C2×#66930C22semidirect
38. C11×#397C22semidirect
43. #10622593C22semidirect
45. #10622572C22semidirect
46. #10622289C22semidirect
47. #10622285C22semidirect
48. #10622279C22semidirect
49. #10622262C22semidirect
62. C23×Dic11D4semidirect
102. C2×C4×Dic11D4semidirect
161. C22×Dic11C2×D4semidirect
190. C4×Dic11C2×D4semidirect
196. C2×#397D11semidirect
295. #397C2×D11semidirect
403. C2×C11#2392semidirect
487. C11C2×#2392semidirect
589. C2#13071853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
C22×(C22⋊D11)⋊C42
C22×#669302
#130718532
C2×#106225932
C2×#106222892
C2×#106222852
C2×#106225722
C2×#106225732
C2×#106222622
C2×#106222792
C2×C11×#3972
C2×#239211