Finite Group Databasebeta

← C2×#13069025 #14755387

Subgroups — C2×#13069025 #14755387

Order 2816.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623329C211yesmaximal, characteristic, complemented
2C22×#66898C211yesmaximal, characteristic, complemented
3C2×#10622860C212yesmaximal, complemented
4#13069025C218yesmaximal, direct product factor
5C2×#10622165C212yesmaximal, complemented
6C22×C11×#120C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C23×D4×C11—21no—
9C23×D4×C11C2211yescharacteristic
10C2×C11×#120—24no—
11C2×C11×#120—22no—
12C2×C11×#120C418yescomplemented
13C2×C11×#120C2214yes—
14C22×C11×C22⋊C4—21no—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11—21no—
17C22×C22⋊Dic11—24no—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20#10623329—22no—
21#10623329—24no—
22#10623329C2214yescomplemented
23C2×D4×Dic11—24no—
24C2×#66979—21no—
25#10622860—24no—
26#10622860C2218yescomplemented
27C2×#66898—24no—
28C2×#66898C2214yescomplemented
29#10622165C2218yescomplemented
30C25×C11—22no—
31C25×C11—21no—
32C25×C11—22no—
33C25×C11—22no—
34C25×C11—21no—
35C25×C11—24no—
36C25×C11—48no—
37C25×C11C2×C414yescomplemented
38C25×C11D411yescharacteristic
39C25×C11C2312yes—
40C25×C11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11—28no—
45C22×D4×C11—24no—
46C22×D4×C11—48no—
47C22×D4×C11C2×C414yes—
48C22×D4×C11D414yes—
49C22×D4×C11D412yes—
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11D414yescomplemented
56C11×#120—216no—
57C11×#120—28no—
58C11×#120C2×C4116yescomplemented
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—28no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4C2×C414yescomplemented
64C2×C11×C22⋊C4C2312yes—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—216no—
76C2×C22⋊Dic11—416no—
77C2×C22⋊Dic11D414yescomplemented
78C2×C22⋊Dic11C2314yes—
79C2×C22⋊Dic11C2314yes—
80D4×Dic11—216no—
81D4×Dic11—216no—
82#66979—24no—
83#66979—24no—
84C2×C4⋊Dic11—22no—
85C2×C4×Dic11—22no—
86#66898—28no—
87C2×#1889—111nomaximal, Sylow
88C24×C11—216no—
89C24×C11—28no—
90C24×C11—24no—
91C24×C11—28no—
92C24×C11—21no—
93C24×C11—24no—
94C24×C11—22no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—24no—
98C24×C11—28no—
99C24×C11—22no—
100C24×C11—24no—
101C24×C11—416no—
102C24×C11—44no—
103C24×C11—48no—
104C24×C11—48no—
105C24×C11—44no—
106C24×C11—416no—
107C24×C11—416no—
108C24×C11—48no—
109C24×C11—432no—
110C24×C11—44no—
111C24×C11—41no—
112C24×C11—42no—
113C24×C11—41no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11C22⋊C414yescomplemented
119C24×C11C22×C412yes—
120C24×C11C22×C414yescomplemented
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D411yescharacteristic
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4114yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—28no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—216no—
138C2×D4×C11—432no—
139C2×D4×C11—416no—
140C2×D4×C11C22⋊C418yescomplemented
141C2×D4×C11C22×C414yes—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—44no—
149C22×C4×C11C22⋊C414yescomplemented
150C22×C4×C11C2×D412yes—
151C22×Dic11—28no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—48no—
156C22×Dic11—48no—
157C22×Dic11—44no—
158C22×Dic11—84no—
159C22×Dic11C2×D418yescomplemented
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—216no—
163C11×C22⋊C4C22×C414yescomplemented
164C22⋊Dic11—28no—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—432no—
172C22⋊Dic11—44no—
173C4⋊Dic11—28no—
174C4×Dic11—28no—
175C22×#120D1111yescharacteristic
176C2×#518—111no—
177C22×#99—111no—
178C2×#379—112no—
179#1889—118no—
180C2×#342—112no—
181C23×C11—28no—
182C23×C11—24no—
183C23×C11—216no—
184C23×C11—216no—
185C23×C11—28no—
186C23×C11—232no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—44no—
194C23×C11—48no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—42no—
198C23×C11—48no—
199C23×C11—42no—
200C23×C11—48no—
201C23×C11—416no—
202C23×C11—416no—
203C23×C11—432no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—416no—
208C23×C11—416no—
209C23×C11—48no—
210C23×C11—432no—
211C23×C11—416no—
212C23×C11—48no—
213C23×C11—44no—
214C23×C11—432no—
215C23×C11—416no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—48no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—84no—
225C23×C11—82no—
226C23×C11C2×C22⋊C412yes—
227C23×C11C2×C22⋊C412yes—
228C23×C11C2×C22⋊C414yescomplemented
229C23×C11C4×D414yes—
230C23×C11C4×D414yes—
231C23×C11#12011yescharacteristic
232C23×C11#12012yes—
233C23×C11#12011yescharacteristic
234C23×C11#12114yes—
235C23×C11#12114yes—
236C23×C11#12312yes—
237C23×C11#12312yes—
238C23×C11C23×C411yescharacteristic
239C23×C11C22×D412yes—
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C2×#4112yes—
243D4×C11—28no—
244D4×C11—28no—
245D4×C11—216no—
246D4×C11—432no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—48no—
253C2×C4×C11—44no—
254C2×C4×C11C2×C22⋊C414yescomplemented
255C2×Dic11—28no—
256C2×Dic11—48no—
257C2×Dic11—48no—
258C2×Dic11—48no—
259C2×Dic11—44no—
260C2×Dic11—84no—
261C2×Dic11—88no—
262C2×Dic11—88no—
263C26C2×D1111yescharacteristic
264C23×D4—21no—
265C23×D4C2×D1111yescharacteristic
266C2×#120—24no—
267C2×#120—22no—
268C2×#120Dic1118yescomplemented
269C2×#120C2×D1114yes—
270#518—114no—
271#518—224no—
272#518—222no—
273C2×C4×D4—224no—
274C2×#117—221no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—221no—
279C22×C22⋊C4—224no—
280C22×C22⋊C4C2×D1111yescharacteristic
281C2×#99—114no—
282C2×#99—224no—
283#379—118no—
284#379—224no—
285#342—118no—
286C22×C11—24no—
287C22×C11—28no—
288C22×C11—24no—
289C22×C11—28no—
290C22×C11—22no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—24no—
294C22×C11—28no—
295C22×C11—216no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—416no—
306C22×C11—44no—
307C22×C11—48no—
308C22×C11—48no—
309C22×C11—416no—
310C22×C11—432no—
311C22×C11—416no—
312C22×C11—48no—
313C22×C11—48no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—82no—
317C22×C11—84no—
318C22×C11#38612yes—
319C22×C11#38614yes—
320C22×C11#38612yes—
321C22×C11B(4,𝔽2)14yes—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×C4×D412yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12112yes—
326C22×C11C2×#12311yescharacteristic
327C4×C11—24no—
328C4×C11—44no—
329Dic11—48no—
330Dic11—84no—
331C25—22no—
332C25—21no—
333C25—22no—
334C25—24no—
335C25—22no—
336C25—21no—
337C25—48no—
338C25C2×Dic1114yescomplemented
339C25C22⋊D1111yescharacteristic
340C25C22×D1112yes—
341C25C22×D1111yescharacteristic
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—28no—
346C22×D4—24no—
347C22×D4—48no—
348C22×D4C2×Dic1114yes—
349C22×D4C22⋊D1114yes—
350C22×D4C22⋊D1112yes—
351C22×D4C22×D1112yes—
352C23×C4—21no—
353C23×C4—114no—
354C23×C4—222no—
355C23×C4—222no—
356C23×C4C22⋊D1111yescharacteristic
357#120—216no—
358#120—28no—
359#120C2×Dic11116yescomplemented
360C4×D4—2216no—
361C4×D4—2216no—
362#117—224no—
363#117—224no—
364C2×C4⋊C4—222no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—2216no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—4416no—
384C2×C22⋊C4C2×Dic1114yescomplemented
385C2×C22⋊C4C22×D1112yes—
386C2×C42—222no—
387#99—228no—
388C2×C11—22no—
389C2×C11—21no—
390C2×C11—22no—
391C2×C11—21no—
392C2×C11—22no—
393C2×C11—24no—
394C2×C11—48no—
395C2×C11—44no—
396C2×C11#188914yescomplemented
397C2×C11C2×#38611yescharacteristic
398C2×C11C2×B(4,𝔽2)12yes—
399C24—216no—
400C24—28no—
401C24—28no—
402C24—21no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—21no—
408C24—28no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—48no—
413C24—44no—
414C24—416no—
415C24—44no—
416C24—48no—
417C24—416no—
418C24—416no—
419C24—48no—
420C24—432no—
421C24—44no—
422C24—42no—
423C24—42no—
424C24—41no—
425C24—42no—
426C24—41no—
427C24—44no—
428C24—44no—
429C24C22⋊Dic1114yescomplemented
430C24D4×D1112yes—
431C24D4×D1112yes—
432C24#434114yes—
433C24C22×Dic1112yes—
434C24C22×Dic1114yescomplemented
435C24C2×C22⋊D1111yescharacteristic
436C24C2×C22⋊D1112yes—
437C24C2×C22⋊D1111yescharacteristic
438C24C2×C22⋊D1112yes—
439C24C23×D1111yescharacteristic
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—216no—
449C2×D4—432no—
450C2×D4—416no—
451C2×D4C22⋊Dic1118yescomplemented
452C2×D4C22×Dic1114yes—
453C2×D4C2×C22⋊D1114yes—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—118no—
461C22×C4—224no—
462C22×C4—228no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—448no—
466C22×C4—448no—
467C22×C4—444no—
468C22×C4—884no—
469C22×C4C22⋊Dic1114yescomplemented
470C22×C4C2×C22⋊D1112yes—
471C4⋊C4—228no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—216no—
475C22⋊C4—228no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—4432no—
483C22⋊C4—444no—
484C22⋊C4C22×Dic1114yescomplemented
485C42—228no—
486C11C2×#188911yescharacteristic, complemented, Sylow
487C23—24no—
488C23—28no—
489C23—216no—
490C23—216no—
491C23—28no—
492C23—232no—
493C23—28no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—48no—
503C23—44no—
504C23—42no—
505C23—42no—
506C23—48no—
507C23—432no—
508C23—416no—
509C23—416no—
510C23—44no—
511C23—48no—
512C23—416no—
513C23—48no—
514C23—416no—
515C23—48no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—44no—
520C23—416no—
521C23—432no—
522C23—42no—
523C23—42no—
524C23—44no—
525C23—44no—
526C23—48no—
527C23—44no—
528C23—44no—
529C23—48no—
530C23—84no—
531C23—82no—
532C23D4×Dic1114yes—
533C23D4×Dic1114yes—
534C23#6698812yes—
535C23#6698812yes—
536C23#6699011yescharacteristic
537C23#6699012yes—
538C23#6699011yescharacteristic
539C23#6699214yes—
540C23#6699214yes—
541C23C2×C22⋊Dic1112yes—
542C23C2×C22⋊Dic1112yes—
543C23C2×C22⋊Dic1114yescomplemented
544C23C2×D4×D1112yes—
545C23C2×#434112yes—
546C23C23×Dic1111yescharacteristic
547C23C22×C22⋊D1111yescharacteristic
548C23C22×C22⋊D1111yescharacteristic
549D4—28no—
550D4—28no—
551D4—216no—
552D4—432no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—48no—
559C2×C4—44no—
560C2×C4—228no—
561C2×C4—448no—
562C2×C4—448no—
563C2×C4—448no—
564C2×C4—444no—
565C2×C4—884no—
566C2×C4—888no—
567C2×C4—888no—
568C2×C4C2×C22⋊Dic1114yescomplemented
569C22—24no—
570C22—28no—
571C22—28no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—28no—
578C22—216no—
579C22—24no—
580C22—44no—
581C22—42no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—41no—
586C22—41no—
587C22—44no—
588C22—44no—
589C22—416no—
590C22—48no—
591C22—48no—
592C22—416no—
593C22—432no—
594C22—44no—
595C22—416no—
596C22—48no—
597C22—44no—
598C22—48no—
599C22—82no—
600C22—84no—
601C22#1062264514yes—
602C22#1062283312yes—
603C22#1062283314yes—
604C22#1062283312yes—
605C22C2×D4×Dic1112yes—
606C22C2×#6698811yescharacteristic
607C22C2×#6699011yescharacteristic
608C22C2×#6699212yes—
609C22C22×C22⋊Dic1111yescharacteristic
610C4—24no—
611C4—44no—
612C4—448no—
613C4—884no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—21no—
618C2—22no—
619C2—24no—
620C2—48no—
621C2—44no—
622C2#1306902514yesdirect product factor
623C2C2×#1062283311yescharacteristic
624C2C2×#1062264512yes—
subgroupG/H
centerC23#66990
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC22×C11×#120C2
socleC23×C11#120
cosocleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C2×#1889
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623329C2semidirect
2. C22×#66898C2semidirect
3. C2×#10622860C2semidirect
4. #13069025C2direct (N × H)
5. C2×#10622165C2semidirect
12. C2×C11×#120C4semidirect
22. #10623329C22semidirect
26. #10622860C22semidirect
28. C2×#66898C22semidirect
29. #10622165C22semidirect
37. C25×C11C2×C4semidirect
55. C23×Dic11D4semidirect
58. C11×#120C2×C4semidirect
63. C2×C11×C22⋊C4C2×C4semidirect
77. C2×C22⋊Dic11D4semidirect
118. C24×C11C22⋊C4semidirect
120. C24×C11C22×C4semidirect
140. C2×D4×C11C22⋊C4semidirect
149. C22×C4×C11C22⋊C4semidirect
159. C22×Dic11C2×D4semidirect
163. C11×C22⋊C4C22×C4semidirect
228. C23×C11C2×C22⋊C4semidirect
254. C2×C4×C11C2×C22⋊C4semidirect
268. C2×#120Dic11semidirect
338. C25C2×Dic11semidirect
359. #120C2×Dic11semidirect
384. C2×C22⋊C4C2×Dic11semidirect
396. C2×C11#1889semidirect
429. C24C22⋊Dic11semidirect
434. C24C22×Dic11semidirect
451. C2×D4C22⋊Dic11semidirect
469. C22×C4C22⋊Dic11semidirect
484. C22⋊C4C22×Dic11semidirect
486. C11C2×#1889semidirect
543. C23C2×C22⋊Dic11semidirect
568. C2×C4C2×C22⋊Dic11semidirect
622. C2#13069025direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233292
C22×#668982
C2×#106228602
#130690252
C2×#106221652
C22×C11×#1202
C2×#188911