Finite Group Databasebeta

← C2×#13077878 #15620159

Subgroups — C2×#13077878 #15620159

Order 2816.

5078 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C22×#66962C212yesmaximal, complemented
3C22×#66977C211yesmaximal, characteristic, complemented
4#13077878C2116yesmaximal, direct product factor
5C2×#10622346C214yesmaximal, complemented
6C2×#10622352C212yesmaximal, complemented
7C2×#10622344C212yesmaximal, complemented
8C2×#10622746C212yesmaximal, complemented
9C2×C11×#407C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11—21no—
12C22×#4339—21no—
13C22×#4339—21no—
14C22×#4339—24no—
15C22×#4339—216no—
16C22×#4339C2212yes—
17C22×#4339C2218yes—
18C22×#4339C2212yes—
19C23×D44C2211yescharacteristic
20C23×C4×D11—21no—
21C23×Dic22C2211yescharacteristic
22C23×Dic22C2211yescharacteristic, complemented
23C22×C11×M16C2212yescomplemented
24C22×C22⋊Dic11—21no—
25C22×C4⋊Dic11C2211yescharacteristic, complemented
26C2×#66977—21no—
27C2×#66977—24no—
28C2×#66977—21no—
29C2×#66977C2212yes—
30C2×#66977C2218yescomplemented
31C2×#66977C2212yescomplemented
32C22×Dic11⋊C4—21no—
33C2×#66962—216no—
34C2×#66962C22116yescomplemented
35C22×Dic44C2214yescomplemented
36C22×#4314C2214yescomplemented
37C11×#407C2218yescomplemented
38C2×C11×C22⋊C8C2212yes—
39C2×C11×C22⋊C8C2212yescomplemented
40#10622746C22116yescomplemented
41C2×#66885C2214yescomplemented
42C2×#66880C2214yescomplemented
43#10622352C22116yescomplemented
44#10622346C22132yescomplemented
45#10622344C22116yescomplemented
46C25×C11D411yescharacteristic
47C24×D11—21no—
48C23×C4×C11—28no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D414yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—216no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—22no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C2×#4339—216no—
65C2×#4339—264no—
66C2×#4339—216no—
67C2×#4339—28no—
68C2×#4339—24no—
69C2×#4339—28no—
70C2×#4339—24no—
71C2×#4339—28no—
72C2×#4339—264no—
73C2×#4339—28no—
74C2×#4339—28no—
75C2×#4339D4116yes—
76C2×#4339C2318yes—
77C2×#4339C2318yes—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—28no—
81C22×D44C2314yes—
82C22×D44C2312yes—
83C22×C4×D11—216no—
84C22×C4×D11—22no—
85C22×C4×D11—28no—
86C22×C4×D11—22no—
87C22×Dic22—21no—
88C22×Dic22—22no—
89C22×Dic22—28no—
90C22×Dic22—28no—
91C22×Dic22—22no—
92C22×Dic22—21no—
93C22×Dic22C2312yes—
94C22×Dic22C2314yes—
95C22×Dic22C2312yes—
96C22×Dic22C2314yescomplemented
97C2×C11×M16—28no—
98C2×C11×M16C2318yescomplemented
99C22×C8×C11C2314yes—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—28no—
102C2×C22⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yescomplemented
107#66977—24no—
108#66977—28no—
109#66977—24no—
110#66977—28no—
111#66977C2318yes—
112#66977C2318yescomplemented
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—28no—
115C2×Dic11⋊C4—22no—
116#66962—264no—
117C2×Dic44—216no—
118C2×Dic44C23116yescomplemented
119C2×#4314—216no—
120C2×#4314C23116yescomplemented
121C11×C22⋊C8C2318yes—
122C11×C22⋊C8C2318yescomplemented
123#66885C23116yescomplemented
124#66880C23116yescomplemented
125C2×#3007—111nomaximal, Sylow
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—42no—
129C24×C11C2×D411yescharacteristic
130C24×C11C2×D414yes—
131C24×C11C2×D411yescharacteristic
132C24×C11C2×D411yescharacteristic
133C23×D11—28no—
134C23×D11—24no—
135C23×D11—22no—
136C23×D11—44no—
137C23×D11—44no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—216no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—216no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D418yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2412yes—
159C2×C22⋊D11—264no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C22×Dic11—28no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—44no—
172C22×Dic11—44no—
173#4339—264no—
174#4339—264no—
175#4339—232no—
176#4339—216no—
177#4339—216no—
178#4339—232no—
179#4339—216no—
180#4339C2×D4132yes—
181C2×D44—28no—
182C2×D44—216no—
183C2×D44—216no—
184C2×D44—24no—
185C2×D44—22no—
186C2×D44—24no—
187C2×D44C2×D418yes—
188C2×D44C2414yes—
189C2×C4×D11—216no—
190C2×C4×D11—264no—
191C2×C4×D11—216no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×Dic22—28no—
195C2×Dic22—216no—
196C2×Dic22—216no—
197C2×Dic22—24no—
198C2×Dic22—22no—
199C2×Dic22—24no—
200C2×Dic22—28no—
201C2×Dic22—216no—
202C2×Dic22—22no—
203C2×Dic22—24no—
204C2×Dic22—44no—
205C2×Dic22—48no—
206C2×Dic22C2×D418yes—
207C2×Dic22C2414yes—
208C2×Dic22C2414yes—
209C11×M16—216no—
210C2×C8×C11—28no—
211C2×C8×C11C2418yes—
212C22⋊Dic11—28no—
213C22⋊Dic11—28no—
214C4⋊Dic11—22no—
215C4⋊Dic11—24no—
216C4⋊Dic11C2414yes—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic44—232no—
220#4314—232no—
221C23×#41—111no—
222C22×#137—112no—
223C22×C22⋊Q8—111no—
224#3007—1116no—
225C2×#452—114no—
226C2×#451—112no—
227C2×#450—112no—
228C2×#417—112no—
229C2×#407D1111yescharacteristic, complemented
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—28no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—28no—
238C23×C11—22no—
239C23×C11—44no—
240C23×C11—416no—
241C23×C11#12014yes—
242C23×C11#13714yescomplemented
243C23×C11C22×D412yes—
244C23×C11C22×D412yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—216no—
248C22×D11—28no—
249C22×D11—24no—
250C22×D11—432no—
251C22×D11—48no—
252C22×D11—44no—
253C22×D11—48no—
254C22×D11—44no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—28no—
258C2×C4×C11—24no—
259C2×C4×C11—28no—
260C2×C4×C11—28no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11#12014yes—
265C2×C4×C11#12018yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C22×D418yes—
272C2×C4×C11C2511yescharacteristic
273C22⋊D11—232no—
274C22⋊D11—232no—
275C2×Dic11—216no—
276C2×Dic11—28no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281C2×Dic11—48no—
282C2×Dic11—44no—
283C2×Dic11—44no—
284D44—216no—
285D44—28no—
286D44—24no—
287D44C22×D418yes—
288C4×D11—232no—
289C4×D11—232no—
290Dic22—216no—
291Dic22—28no—
292Dic22—24no—
293Dic22—28no—
294Dic22—44no—
295Dic22—48no—
296Dic22C22×D418yes—
297C8×C11—28no—
298C22×#41—112no—
299C22×#41—112no—
300C22×#41—118no—
301C22×#41—2216no—
302C22×#41—221no—
303C22×#41—224no—
304C22×#41—221no—
305C23×Q8—111no—
306C23×Q8—111no—
307C23×D4—111no—
308C23×D4—221no—
309C24×C4—221no—
310C24×C4C2×D1111yescharacteristic
311C2×#137—1116no—
312C2×#137—2216no—
313C22×Q16—114no—
314C22×SD16—114no—
315C22×M16C2×D1112yescomplemented
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—118no—
319C2×C22⋊Q8—221no—
320C2×C22⋊Q8—224no—
321C2×C22⋊Q8—221no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—221no—
324C22×C22⋊C4—221no—
325#452—1132no—
326#451—1116no—
327#450—1116no—
328#417—1116no—
329C2×#103—114no—
330C2×#102—114no—
331#407C2×D1118yescomplemented
332C2×C22⋊C8C2×D1112yes—
333C2×C22⋊C8C2×D1112yescomplemented
334C22×C11—22no—
335C22×C11—28no—
336C22×C11—28no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—416no—
344C22×C11—44no—
345C22×C11C2×#12014yes—
346C22×C11C2×#12012yes—
347C22×C11C2×#13712yes—
348C22×C11C2×#13714yescomplemented
349C22×C11#57512yes—
350C22×C11C23×D411yescharacteristic
351C2×D11—28no—
352C2×D11—432no—
353C2×D11—416no—
354C2×D11—44no—
355C2×D11—44no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11C2×#12012yes—
359C4×C11C2×#12014yes—
360C4×C11C23×D412yes—
361Dic11—28no—
362Dic11—44no—
363Dic11—44no—
364C25—221no—
365C25D4411yescharacteristic
366C2×#41—1116no—
367C2×#41—118no—
368C2×#41—118no—
369C2×#41—228no—
370C2×#41—228no—
371C2×#41—2264no—
372C2×#41—2216no—
373C2×#41—2264no—
374C2×#41—2216no—
375C2×#41—228no—
376C2×#41—224no—
377C2×#41—228no—
378C2×#41—224no—
379C2×#41—228no—
380C22×Q8—112no—
381C22×Q8—112no—
382C22×Q8—114no—
383C22×Q8—114no—
384C22×Q8—228no—
385C22×Q8—222no—
386C22×Q8—221no—
387C22×Q8—222no—
388C22×Q8—221no—
389C22×Q8—228no—
390C22×D4—112no—
391C22×D4—114no—
392C22×D4—228no—
393C22×D4—2216no—
394C22×D4—228no—
395C22×D4—222no—
396C22×D4—222no—
397C22×D4—222no—
398C22×D4—221no—
399C23×C4—28no—
400C23×C4—2216no—
401C23×C4—221no—
402C23×C4—228no—
403C23×C4—222no—
404C23×C4—222no—
405C23×C4—221no—
406C23×C4—221no—
407C23×C4D4411yescharacteristic
408C23×C4D4411yescharacteristic
409C23×C4D4414yes—
410C23×C4D4411yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1111yescharacteristic
413C23×C4C22×D1114yes—
414C23×C4C22×D1111yescharacteristic
415#137—2264no—
416C2×Q16—1116no—
417C2×Q16—2216no—
418C2×SD16—1116no—
419C2×SD16—2216no—
420C2×M16—28no—
421C2×M16C22×D1118yescomplemented
422C22×C8C22×D1114yes—
423C22⋊Q8—118no—
424C22⋊Q8—118no—
425C22⋊Q8—228no—
426C22⋊Q8—224no—
427C22⋊Q8—224no—
428C22⋊Q8—228no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—228no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—222no—
436C2×C22⋊C4—228no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439#103—1116no—
440#102—1116no—
441C22⋊C8C22×D1118yes—
442C22⋊C8C22×D1118yescomplemented
443C2×C11—24no—
444C2×C11—24no—
445C2×C11—42no—
446C2×C11#300714yescomplemented
447C2×C11C22×#12011yescharacteristic
448C2×C11C22×#13711yescharacteristic
449C2×C11C2×#57511yescharacteristic
450D11—48no—
451C24—24no—
452C24—24no—
453C24—42no—
454C24—228no—
455C24—224no—
456C24—222no—
457C24—444no—
458C24—444no—
459C24C2×D4411yescharacteristic
460C24C2×D4414yes—
461C24C2×D4411yescharacteristic
462C24C2×D4411yescharacteristic
463#41—1132no—
464#41—2216no—
465#41—2216no—
466#41—2264no—
467#41—2232no—
468#41—2264no—
469#41—2232no—
470#41—2216no—
471C2×Q8—118no—
472C2×Q8—114no—
473C2×Q8—114no—
474C2×Q8—2216no—
475C2×Q8—228no—
476C2×Q8—2216no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×Q8—224no—
480C2×Q8—222no—
481C2×Q8—224no—
482C2×Q8—228no—
483C2×Q8—2216no—
484C2×Q8—444no—
485C2×Q8—448no—
486C2×D4—118no—
487C2×D4—114no—
488C2×D4—2216no—
489C2×D4—228no—
490C2×D4—2216no—
491C2×D4—2264no—
492C2×D4—2216no—
493C2×D4—2216no—
494C2×D4—228no—
495C2×D4—228no—
496C2×D4—224no—
497C2×D4—222no—
498C2×D4—224no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—216no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—216no—
506C22×C4—2216no—
507C22×C4—2264no—
508C22×C4—228no—
509C22×C4—224no—
510C22×C4—222no—
511C22×C4—2216no—
512C22×C4—228no—
513C22×C4—228no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—444no—
519C22×C4—444no—
520C22×C4C2×D4414yes—
521C22×C4C2×D4414yes—
522C22×C4C2×D4412yes—
523C22×C4C2×D4412yes—
524C22×C4C2×D4414yes—
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4412yes—
528C22×C4C2×D4411yescharacteristic
529C22×C4D4×D1118yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1112yes—
533C22×C4C23×D1111yescharacteristic
534Q16—2232no—
535SD16—2232no—
536M16—216no—
537C2×C8—28no—
538C2×C8C23×D1118yes—
539C4⋊C4—114no—
540C4⋊C4—224no—
541C4⋊C4—222no—
542C4⋊C4—228no—
543C4⋊C4—228no—
544C22⋊C4—228no—
545C22⋊C4—228no—
546C11C2×#300711yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—28no—
552C23—22no—
553C23—22no—
554C23—28no—
555C23—22no—
556C23—44no—
557C23—416no—
558C23—2216no—
559C23—228no—
560C23—224no—
561C23—4432no—
562C23—448no—
563C23—444no—
564C23—448no—
565C23—444no—
566C23#6693514yes—
567C23#6696214yescomplemented
568C23C22×D4412yes—
569C23C22×D4412yes—
570C23C22×D4412yes—
571C23C22×D4411yescharacteristic
572Q8—118no—
573Q8—2216no—
574Q8—228no—
575Q8—224no—
576Q8—228no—
577Q8—448no—
578Q8—444no—
579D4—118no—
580D4—2216no—
581D4—2232no—
582D4—2232no—
583D4—228no—
584D4—224no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—28no—
588C2×C4—28no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—28no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—2232no—
595C2×C4—2216no—
596C2×C4—228no—
597C2×C4—224no—
598C2×C4—2232no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—448no—
602C2×C4—448no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4#6693514yes—
606C2×C4#6693518yes—
607C2×C4C22×D4412yes—
608C2×C4C22×D4412yes—
609C2×C4C22×D4412yes—
610C2×C4C22×D4411yescharacteristic
611C2×C4C2×D4×D1114yes—
612C2×C4C2×D4×D1118yes—
613C2×C4C24×D1111yescharacteristic
614C8—28no—
615C22—28no—
616C22—28no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—416no—
625C22—44no—
626C22—228no—
627C22—4432no—
628C22—4416no—
629C22—444no—
630C22—444no—
631C22C2×#6693514yes—
632C22C2×#6693512yes—
633C22C2×#6696212yes—
634C22C2×#6696214yescomplemented
635C22#1062327912yes—
636C22C23×D4411yescharacteristic
637C4—22no—
638C4—22no—
639C4—228no—
640C4—444no—
641C4—444no—
642C4C2×#6693514yes—
643C4C2×#6693512yes—
644C4C22×D4×D1112yes—
645C2—24no—
646C2—24no—
647C2—42no—
648C2—448no—
649C2#1307787814yesdirect product factor
650C2C22×#6693511yescharacteristic
651C2C22×#6696211yescharacteristic
652C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC23×C11C22×D4
prime radicalC23×#4339C2
hypercenterC2×#407D11
hypocenterC11C2×#3007
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#66962C2semidirect
3. C22×#66977C2semidirect
4. #13077878C2direct (N × H)
5. C2×#10622346C2semidirect
6. C2×#10622352C2semidirect
7. C2×#10622344C2semidirect
8. C2×#10622746C2semidirect
9. C2×C11×#407C2semidirect
22. C23×Dic22C22semidirect
23. C22×C11×M16C22semidirect
25. C22×C4⋊Dic11C22semidirect
30. C2×#66977C22semidirect
31. C2×#66977C22semidirect
34. C2×#66962C22semidirect
35. C22×Dic44C22semidirect
36. C22×#4314C22semidirect
37. C11×#407C22semidirect
39. C2×C11×C22⋊C8C22semidirect
40. #10622746C22semidirect
41. C2×#66885C22semidirect
42. C2×#66880C22semidirect
43. #10622352C22semidirect
44. #10622346C22semidirect
45. #10622344C22semidirect
96. C22×Dic22C23semidirect
98. C2×C11×M16C23semidirect
106. C2×C4⋊Dic11C23semidirect
112. #66977C23semidirect
118. C2×Dic44C23semidirect
120. C2×#4314C23semidirect
122. C11×C22⋊C8C23semidirect
123. #66885C23semidirect
124. #66880C23semidirect
229. C2×#407D11semidirect
242. C23×C11#137semidirect
315. C22×M16C2×D11semidirect
331. #407C2×D11semidirect
333. C2×C22⋊C8C2×D11semidirect
348. C22×C11C2×#137semidirect
421. C2×M16C22×D11semidirect
442. C22⋊C8C22×D11semidirect
446. C2×C11#3007semidirect
546. C11C2×#3007semidirect
567. C23#66962semidirect
634. C22C2×#66962semidirect
649. C2#13077878direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669622
C22×#669772
#130778782
C2×#106223462
C2×#106223522
C2×#106223442
C2×#106227462
C2×C11×#4072
C2×#300711