Finite Group Databasebeta

← C2×#13076639 #14959897

Subgroups — C2×#13076639 #14959897

Order 2816.

3774 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3#13076639C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622284C211yesmaximal, characteristic, complemented
7C2×#10622284C212yesmaximal, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×D44C2212yes—
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2212yes—
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C2×#66948—28no—
32C2×#66948C2218yescomplemented
33C2×#66937—28no—
34C2×#66937C2218yescomplemented
35C11×#397C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622573C22116yescomplemented
43#10622573C2218yescomplemented
44#10622573C22116yescomplemented
45#10622288C22116yescomplemented
46#10622284C2218yescomplemented
47#10622284C22116yescomplemented
48#10622277C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—24no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2314yes—
65C22×C22⋊D11C2314yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C22×D44—24no—
71C22×D44—28no—
72C22×D44—24no—
73C22×D44—44no—
74C22×D44—44no—
75C22×D44—44no—
76C22×D44—44no—
77C22×D44—44no—
78C22×D44—44no—
79C22×D44—44no—
80C22×D44C2314yes—
81C22×D44C2318yes—
82C22×D44C2314yes—
83C22×D44C2318yes—
84C22×C4×D11—44no—
85C22×C4×D11D418yescomplemented
86C22×C4×D11C2314yes—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2318yes—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4—44no—
98C2×(C2×D11)⋊C4—44no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4C2314yes—
107#66948—232no—
108#66937—232no—
109C11×#95C2314yes—
110C11×#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2314yes—
113C11⋊#95C2318yes—
114C2×#2815—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—22no—
120C24×C11C2412yes—
121C24×C11C2411yescharacteristic
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—22no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11—24no—
138C23×D11C2×D414yes—
139C23×D11C2414yes—
140C23×D11C2412yes—
141C23×D11C2412yes—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—416no—
164C2×C22⋊D11—416no—
165C2×C22⋊D11—432no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11C2×D414yes—
173C22×Dic11C2414yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C2×D44—28no—
177C2×D44—216no—
178C2×D44—28no—
179C2×D44—48no—
180C2×D44—48no—
181C2×D44—48no—
182C2×D44—48no—
183C2×D44—48no—
184C2×D44—48no—
185C2×D44—48no—
186C2×D44—416no—
187C2×D44—432no—
188C2×D44—416no—
189C2×D44—432no—
190C2×C4×D11—416no—
191C2×C4×D11—48no—
192C2×C4×D11C2×D4116yescomplemented
193C11×C4⋊C4—28no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—48no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202Dic11⋊C4—28no—
203C22×#121—111no—
204C22×#121—111no—
205#2815—1116no—
206C2×#397—112no—
207C2×#397—111no—
208C2×#397D1111yescharacteristic, complemented
209C2×#392—111no—
210C2×#392—112no—
211C2×#392—112no—
212C2×#392—111no—
213C2×#392—112no—
214C2×#381—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11C22×D412yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C11H(5,𝔽2)14yes—
228C23×C11H(5,𝔽2)12yes—
229C23×C11H(5,𝔽2)14yes—
230C23×C11C2511yescharacteristic
231C22×D11—28no—
232C22×D11—28no—
233C22×D11—28no—
234C22×D11—24no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—44no—
254C22×D11—48no—
255C22×D11—44no—
256C22×D11—44no—
257C22×D11—48no—
258C22×D11—48no—
259C22×D11—48no—
260C22×D11—48no—
261C22×D11—48no—
262C22×D11—48no—
263C22×D11—48no—
264C22×D11C22×D414yes—
265C2×C4×C11—28no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—48no—
276C2×C4×C11—44no—
277C2×C4×C11—48no—
278C2×C4×C11C22×D414yes—
279C22⋊D11—416no—
280C22⋊D11—416no—
281C22⋊D11—432no—
282C2×Dic11—28no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—44no—
290C2×Dic11—48no—
291C2×Dic11C22×D414yes—
292D44—416no—
293D44—432no—
294D44—416no—
295D44—432no—
296C4×D11—416no—
297C23×D4—111no—
298C23×D4—111no—
299C23×D4—112no—
300C23×D4—111no—
301C23×D4—112no—
302C23×D4—111no—
303C23×D4—112no—
304C24×C4—111no—
305C2×#121—118no—
306C2×#121—118no—
307C2×#121—228no—
308C2×#121—228no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—112no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—112no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4C2×D1111yescharacteristic
318C22×C22⋊C4C2×D1112yes—
319#397—118no—
320#397—1116no—
321#397C2×D1118yescomplemented
322#392—1116no—
323#392—118no—
324#392—1116no—
325#392—118no—
326#392—1116no—
327#381—118no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95—111no—
331C2×#95C2×D1112yes—
332C2×#95C2×D1111yescharacteristic
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—88no—
339C22×C11#53414yes—
340C22×C11#53514yes—
341C22×C11#53514yes—
342C22×C11#56018yes—
343C22×C11#56018yes—
344C22×C11C23×D411yescharacteristic
345C22×C11C2×H(5,𝔽2)11yescharacteristic
346C22×C11C2×H(5,𝔽2)12yes—
347C22×C11C2×H(5,𝔽2)11yescharacteristic
348C22×C11C2×H(5,𝔽2)12yes—
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—24no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—416no—
355C2×D11—44no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—42no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—44no—
367C2×D11—816no—
368C2×D11—88no—
369C4×C11—24no—
370C4×C11—44no—
371C4×C11—42no—
372C4×C11—44no—
373Dic11—24no—
374Dic11—42no—
375Dic11—44no—
376C25—111no—
377C25—111no—
378C25—112no—
379C25C22×D1111yescharacteristic
380C22×D4—114no—
381C22×D4—114no—
382C22×D4—118no—
383C22×D4—118no—
384C22×D4—114no—
385C22×D4—114no—
386C22×D4—118no—
387C22×D4—224no—
388C22×D4—228no—
389C22×D4—224no—
390C22×D4—224no—
391C22×D4—224no—
392C22×D4—444no—
393C22×D4—444no—
394C22×D4—444no—
395C22×D4—444no—
396C22×D4—444no—
397C22×D4—444no—
398C22×D4—444no—
399C22×D4—444no—
400C22×D4—444no—
401C22×D4—444no—
402C22×D4—444no—
403C22×D4—444no—
404C23×C4—111no—
405C23×C4—118no—
406C23×C4—114no—
407C23×C4—111no—
408C23×C4—112no—
409C23×C4—444no—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1112yes—
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#121—2232no—
415#121—2232no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—224no—
419C2×C4⋊C4C22×D1114yes—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—118no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—118no—
425C2×C22⋊C4—118no—
426C2×C22⋊C4—118no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4—228no—
429C2×C22⋊C4—224no—
430C2×C22⋊C4—444no—
431C2×C22⋊C4—444no—
432C2×C22⋊C4—444no—
433C2×C22⋊C4—444no—
434C2×C22⋊C4C22×D1114yes—
435C2×C22⋊C4C22×D1118yes—
436#95—118no—
437#95—114no—
438#95—118no—
439#95C22×D1114yes—
440#95C22×D1118yes—
441C2×C11—82no—
442C2×C11#281518yescomplemented
443C2×C11C2×#53411yescharacteristic
444C2×C11C2×#53511yescharacteristic
445C2×C11C2×#53511yescharacteristic
446C2×C11C2×#56012yes—
447C2×C11C2×#56012yes—
448D11—44no—
449D11—84no—
450D11—82no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—114no—
457C24—112no—
458C24—112no—
459C24—114no—
460C24—222no—
461C24—224no—
462C24—222no—
463C24—224no—
464C24—224no—
465C24—222no—
466C24—224no—
467C24—222no—
468C24—222no—
469C24—224no—
470C24—224no—
471C24—224no—
472C24—224no—
473C24—224no—
474C24—224no—
475C24—224no—
476C24C23×D1112yes—
477C24C23×D1111yescharacteristic
478C2×D4—228no—
479C2×D4—2216no—
480C2×D4—228no—
481C2×D4—228no—
482C2×D4—228no—
483C2×D4—448no—
484C2×D4—448no—
485C2×D4—448no—
486C2×D4—448no—
487C2×D4—448no—
488C2×D4—448no—
489C2×D4—448no—
490C2×D4—4416no—
491C2×D4—4432no—
492C2×D4—4416no—
493C2×D4—4432no—
494C2×D4—448no—
495C2×D4—448no—
496C2×D4—448no—
497C2×D4—448no—
498C2×D4—448no—
499C2×D4—4416no—
500C2×D4—4416no—
501C2×D4—4432no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—114no—
512C22×C4—112no—
513C22×C4—1116no—
514C22×C4—114no—
515C22×C4—112no—
516C22×C4—224no—
517C22×C4—222no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—224no—
521C22×C4—224no—
522C22×C4—4416no—
523C22×C4—448no—
524C22×C4D4×D1114yes—
525C22×C4C23×D1114yes—
526C22×C4C23×D1114yes—
527C22×C4C23×D1112yes—
528C22×C4C23×D1112yes—
529C4⋊C4—28no—
530C4⋊C4—228no—
531C22⋊C4—28no—
532C22⋊C4—48no—
533C22⋊C4—2216no—
534C22⋊C4—228no—
535C22⋊C4—448no—
536C22⋊C4—448no—
537C22⋊C4—448no—
538C22⋊C4—448no—
539C11C2×#281511yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—24no—
543C23—22no—
544C23—24no—
545C23—48no—
546C23—44no—
547C23—44no—
548C23—48no—
549C23—44no—
550C23—114no—
551C23—228no—
552C23—228no—
553C23—222no—
554C23—224no—
555C23—222no—
556C23—224no—
557C23—228no—
558C23—224no—
559C23—222no—
560C23—224no—
561C23—222no—
562C23—222no—
563C23—224no—
564C23—224no—
565C23—224no—
566C23—224no—
567C23—224no—
568C23—224no—
569C23—224no—
570C23—448no—
571C23—448no—
572C23—448no—
573C23—448no—
574C23—448no—
575C23—448no—
576C23—444no—
577C23—448no—
578C23—444no—
579C23—448no—
580C23—448no—
581C23—448no—
582C23—444no—
583C23—448no—
584C23C2×D4×D1112yes—
585C23#6703712yes—
586C23#6704212yes—
587C23#6704214yes—
588C23#6704214yes—
589C23C24×D1111yescharacteristic
590D4—4416no—
591D4—4432no—
592D4—4416no—
593D4—4432no—
594D4—4416no—
595D4—4416no—
596D4—4432no—
597C2×C4—28no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—48no—
608C2×C4—48no—
609C2×C4—44no—
610C2×C4—114no—
611C2×C4—228no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—4416no—
619C2×C4—448no—
620C2×C4—444no—
621C2×C4C2×D4×D1114yes—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—44no—
626C22—44no—
627C22—88no—
628C22—224no—
629C22—224no—
630C22—224no—
631C22—444no—
632C22—444no—
633C22—4416no—
634C22—444no—
635C22—442no—
636C22—444no—
637C22—442no—
638C22—442no—
639C22—444no—
640C22—444no—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—8816no—
647C22—888no—
648C22#1062313814yes—
649C22#1062318414yes—
650C22#1062319718yes—
651C22#1062320514yes—
652C22#1062324218yes—
653C22C22×D4×D1111yescharacteristic
654C22C2×#6703711yescharacteristic
655C22C2×#6704212yes—
656C22C2×#6704211yescharacteristic
657C22C2×#6704212yes—
658C4—24no—
659C4—44no—
660C4—42no—
661C4—44no—
662C4—224no—
663C4—442no—
664C4—444no—
665C2—82no—
666C2—444no—
667C2—884no—
668C2—882no—
669C2#1307663918yesdirect product factor
670C2C2×#1062318411yescharacteristic
671C2C2×#1062313811yescharacteristic
672C2C2×#1062320511yescharacteristic
673C2C2×#1062319712yes—
674C2C2×#1062324212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2815
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66937C2semidirect
3. #13076639C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622284C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#397C2semidirect
32. C2×#66948C22semidirect
34. C2×#66937C22semidirect
35. C11×#397C22semidirect
41. #10622606C22semidirect
42. #10622573C22semidirect
43. #10622573C22semidirect
44. #10622573C22semidirect
45. #10622288C22semidirect
46. #10622284C22semidirect
47. #10622284C22semidirect
48. #10622277C22semidirect
85. C22×C4×D11D4semidirect
192. C2×C4×D11C2×D4semidirect
208. C2×#397D11semidirect
321. #397C2×D11semidirect
442. C2×C11#2815semidirect
539. C11C2×#2815semidirect
669. C2#13076639direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669372
#130766392
C2×#106222882
C2×#106226062
C2×#106222842
C2×#106225732
C2×#106222772
C2×C11×#3972
C2×#281511