Finite Group Databasebeta

← C2×#13078165 #15620709

Subgroups — C2×#13078165 #15620709

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic
3C2×#10623356C211yesmaximal, characteristic, complemented
4C2×#10623035C211yesmaximal, characteristic, complemented
5#13078165C2116yesmaximal, direct product factor
6C2×#10622380C212yesmaximal, complemented
7C2×#10622406C212yesmaximal, complemented
8C2×#10622400C212yesmaximal, complemented
9C2×#10622431C212yesmaximal, complemented
10C2×#10622732C211yesmaximal, characteristic, complemented
11C22×#66874C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18#10623356—24no—
19#10623356C2218yescomplemented
20C2×#67003—28no—
21C2×#67003C2218yes—
22C2×#66997C2212yes—
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66989C2212yes—
26C2×#66988—22no—
27C22×#4324C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×C4×C22⋊D11—22no—
30C2×#66979C2211yescharacteristic
31C2×#66977—21no—
32C2×#66977—21no—
33C23×C11⋊C8C2211yescharacteristic
34C2×#66962—28no—
35C2×#66962C2218yescomplemented
36C22×Dic44C2212yes—
37C22×#4314C2212yes—
38#10623035—24no—
39#10623035C2218yescomplemented
40C2×#66946C2212yes—
41C2×#66945—21no—
42C2×C4⋊C4×D11—21no—
43C2×#66940C2212yes—
44C11×#417C2218yescomplemented
45C2×C11×#103C2212yes—
46C2×C11×#102C2212yes—
47#10622732C2218yescomplemented
48C2×Dic11⋊C8C2212yes—
49C2×Dic11⋊C8C2212yes—
50C2×#66874C2212yes—
51C2×#66874C2212yes—
52C2×#66874C2218yescomplemented
53#10622431C22116yescomplemented
54#10622406C22116yescomplemented
55#10622400C22116yescomplemented
56#10622380C22116yescomplemented
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C2×#4339—22no—
70C2×#4339—24no—
71C2×#4339D418yes—
72C2×#4339C2314yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×Dic22—24no—
77C22×Dic22—24no—
78C22×Dic22—21no—
79C22×Dic22—22no—
80C22×Dic22C2312yes—
81C22×Dic22C2314yes—
82C22×Dic22C2311yescharacteristic
83C2×C11×M16—24no—
84C2×C11×M16C2314yes—
85C22×C8×C11C2312yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11D412yes—
93#67003—232no—
94#66997—24no—
95#66997C2318yes—
96C2×#4326—24no—
97C2×#4326C2314yes—
98C2×#4325—24no—
99C2×#4325C2314yes—
100#66989—24no—
101#66989C2318yes—
102#66988—216no—
103C2×#4324—24no—
104C2×#4324C2314yes—
105C2×#4323—24no—
106C2×#4323C2314yes—
107C4×C22⋊D11—216no—
108C2×(C2×D11)⋊C4—22no—
109#66979D414yes—
110#66979C2314yes—
111C2×C4⋊Dic11D411yescharacteristic
112C2×C4⋊Dic11D411yescharacteristic
113#66977—28no—
114#66977—28no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11C2312yes—
120C22×C11⋊C8—24no—
121C22×C11⋊C8C2314yes—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66962—232no—
125C2×Dic44—28no—
126C2×Dic44C2318yes—
127C2×#4314—28no—
128C2×#4314C2318yes—
129#66946—24no—
130#66946C2318yes—
131#66945—28no—
132C4⋊C4×D11—28no—
133#66940—24no—
134#66940C2318yes—
135C11×#103C2318yes—
136C11×#102C2318yes—
137Dic11⋊C8C2318yes—
138Dic11⋊C8C2318yes—
139#66874C2318yes—
140#66874C2318yes—
141C2×#3046—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—48no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11C2412yes—
152C2×D4×C11—24no—
153C2×D4×C11—22no—
154C2×D4×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11—44no—
157C2×D4×C11C2412yes—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—44no—
163C22×C4×C11—82no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11#4114yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2412yes—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—24no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—44no—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178#4339—216no—
179#4339—28no—
180#4339C2×D4116yes—
181C2×D44—21no—
182C2×D44—22no—
183C2×D44C2×D414yes—
184C2×D44C2412yes—
185C2×C4×D11—28no—
186C2×C4×D11—28no—
187C2×C4×D11—24no—
188C2×C4×D11—84no—
189C2×Dic22—21no—
190C2×Dic22—24no—
191C2×Dic22—28no—
192C2×Dic22—24no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—24no—
196C2×Dic22—28no—
197C2×Dic22—44no—
198C2×Dic22—48no—
199C2×Dic22C2×D414yes—
200C2×Dic22C2414yes—
201C2×Dic22C2412yes—
202C11×M16—28no—
203C2×C8×C11—24no—
204C2×C8×C11C2414yes—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4C2414yes—
208C22⋊Dic11—28no—
209C22⋊Dic11—28no—
210C22⋊Dic11C2×D418yes—
211#4326—28no—
212#4325—28no—
213#4324—28no—
214#4323—28no—
215(C2×D11)⋊C4—28no—
216C4⋊Dic11C2×D414yes—
217C4⋊Dic11C2×D414yes—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221C4×Dic11—28no—
222C4×Dic11C2×D414yes—
223C4×Dic11C2414yes—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—28no—
227C2×C11⋊C8C2412yes—
228C2×C11⋊C8C2412yes—
229Dic44—216no—
230#4314—216no—
231C22×#137—111no—
232C22×#135—111no—
233C2×#536—111no—
234C2×#520—111no—
235#3046—1116no—
236C2×#464—112no—
237C2×#462—112no—
238C2×#463—112no—
239C2×#461—112no—
240C2×#424—111no—
241C2×#417D1111yescharacteristic, complemented
242C22×#103—111no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11#12114yes—
250C23×C11C22×D412yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—42no—
255C22×D11—42no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—42no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—48no—
262D4×C11—42no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—42no—
266C2×C4×C11—44no—
267C2×C4×C11—48no—
268C2×C4×C11—84no—
269C2×C4×C11#12114yes—
270C2×C4×C11#12118yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C22×D414yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4114yes—
277C2×C4×C11C2511yescharacteristic
278C22⋊D11—216no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—48no—
285C2×Dic11—44no—
286C2×Dic11C22×D414yes—
287C2×Dic11C22×D414yes—
288D44—24no—
289D44—22no—
290D44C22×D414yes—
291C4×D11—216no—
292C4×D11—88no—
293Dic22—24no—
294Dic22—22no—
295Dic22—24no—
296Dic22—24no—
297Dic22—48no—
298Dic22—44no—
299Dic22C22×D414yes—
300C8×C11—24no—
301C11⋊C8—22no—
302C11⋊C8—22no—
303C22×#41—111no—
304C22×#41C2×D1111yescharacteristic
305C23×Q8—111no—
306C2×#137—118no—
307C2×#137—228no—
308C2×#135—118no—
309C2×#135—228no—
310C22×Q16—111no—
311C22×Q16—112no—
312C22×SD16—111no—
313C22×SD16—111no—
314C22×SD16—112no—
315C22×D8—111no—
316C22×M16C2×D1111yescharacteristic
317C23×C8—111no—
318#536—118no—
319#536—224no—
320C2×C4⋊Q8—112no—
321C2×#124—112no—
322C2×#123—222no—
323C2×C22⋊Q8—221no—
324C2×C22⋊Q8—221no—
325#520—118no—
326#520—224no—
327C2×C4×Q8—112no—
328C2×C4×D4—112no—
329C2×C4×D4—222no—
330C2×#117—111no—
331C2×#117—221no—
332C22×C4⋊C4—221no—
333C22×C4⋊C4C2×D1111yescharacteristic
334#464—1116no—
335#463—1116no—
336#462—1116no—
337#461—1116no—
338#424—118no—
339C2×C4⋊C8—112no—
340C2×C4⋊C8—112no—
341#417C2×D1118yescomplemented
342C2×#103—112no—
343C2×#103—112no—
344C2×#103—118no—
345C2×#103C2×D1112yes—
346C2×#102C2×D1112yes—
347C22×C11—28no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—84no—
354C22×C11C2×#12114yes—
355C22×C11C2×#12112yes—
356C22×C11#57712yes—
357C22×C11#57812yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—24no—
360C2×D11—48no—
361C2×D11—42no—
362C2×D11—42no—
363C4×C11—42no—
364C4×C11—44no—
365C4×C11C2×#12114yes—
366C4×C11C2×#12112yes—
367C4×C11C23×D411yescharacteristic
368C4×C11C22×#4111yescharacteristic
369Dic11—24no—
370Dic11—24no—
371Dic11—24no—
372Dic11—44no—
373C2×#41—22no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—118no—
377C2×#41—114no—
378C2×#41—224no—
379C2×#41—222no—
380C2×#41C22×D1114yes—
381C22×Q8—111no—
382C22×Q8—112no—
383C22×Q8—114no—
384C22×Q8—221no—
385C22×Q8—222no—
386C22×Q8—224no—
387C22×Q8—224no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—21no—
390C22×D4—111no—
391C22×D4—221no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—222no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399#137—2232no—
400#135—2232no—
401C2×Q16—114no—
402C2×Q16—118no—
403C2×Q16—228no—
404C2×Q16—224no—
405C2×SD16—114no—
406C2×SD16—114no—
407C2×SD16—118no—
408C2×SD16—228no—
409C2×SD16—224no—
410C2×SD16—224no—
411C2×D8—114no—
412C2×D8—224no—
413C2×M16—24no—
414C2×M16C22×D1114yes—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—114no—
418C22×C8—224no—
419C22×C8C22×D1112yes—
420C4⋊Q8—118no—
421C4⋊Q8—224no—
422#124—118no—
423#124—224no—
424#123—2216no—
425C22⋊Q8—228no—
426C22⋊Q8—228no—
427C4×Q8—118no—
428C4×Q8—224no—
429C4×D4—118no—
430C4×D4—224no—
431C4×D4—2216no—
432#117—114no—
433#117—114no—
434#117—228no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—228no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4C22×D1112yes—
444C2×C4⋊C4C22×D1114yes—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C42—112no—
450C2×C42—222no—
451C4⋊C8—118no—
452C4⋊C8—118no—
453#103—118no—
454#103—118no—
455#103C22×D1118yes—
456#102C22×D1118yes—
457C2×C11—24no—
458C2×C11—82no—
459C2×C11#304614yescomplemented
460C2×C11C22×#12111yescharacteristic
461C2×C11C2×#57711yescharacteristic
462C2×C11C2×#57811yescharacteristic
463D11—44no—
464C24—21no—
465C24—221no—
466C24D4×D1111yescharacteristic
467#41—28no—
468#41—28no—
469#41—48no—
470#41—1116no—
471#41—2216no—
472#41—228no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—114no—
477C2×Q8—112no—
478C2×Q8—114no—
479C2×Q8—222no—
480C2×Q8—221no—
481C2×Q8—224no—
482C2×Q8—222no—
483C2×Q8—224no—
484C2×Q8—228no—
485C2×Q8—224no—
486C2×Q8—228no—
487C2×Q8—444no—
488C2×Q8—448no—
489C2×Q8C23×D1112yes—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—44no—
495C2×D4—114no—
496C2×D4—112no—
497C2×D4—228no—
498C2×D4—224no—
499C2×D4—222no—
500C2×D4—221no—
501C2×D4C23×D1112yes—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—44no—
507C22×C4—82no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—228no—
511C22×C4—221no—
512C22×C4—228no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—444no—
517C22×C4—884no—
518C22×C4#433914yes—
519C22×C4D4×D1112yes—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1114yes—
522C22×C4C23×D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—2216no—
525Q16—228no—
526SD16—2216no—
527SD16—228no—
528SD16—228no—
529D8—228no—
530M16—28no—
531C2×C8—24no—
532C2×C8—112no—
533C2×C8—112no—
534C2×C8—222no—
535C2×C8—222no—
536C2×C8—228no—
537C2×C8C23×D1114yes—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—114no—
541C4⋊C4—114no—
542C4⋊C4—228no—
543C4⋊C4—228no—
544C4⋊C4—228no—
545C4⋊C4C23×D1114yes—
546C22⋊C4—118no—
547C22⋊C4—228no—
548C22⋊C4—228no—
549C22⋊C4—228no—
550C42—114no—
551C42—114no—
552C42—228no—
553C11C2×#304611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—224no—
561C23—222no—
562C23—442no—
563C23—442no—
564C23#6693714yes—
565C23C2×D4×D1112yes—
566C23C2×D4×D1111yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—42no—
570Q8—114no—
571Q8—224no—
572Q8—222no—
573Q8—224no—
574Q8—224no—
575Q8—448no—
576Q8—444no—
577D4—22no—
578D4—22no—
579D4—48no—
580D4—42no—
581D4—114no—
582D4—2216no—
583D4—224no—
584D4—222no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—48no—
590C2×C4—84no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—2216no—
598C2×C4—224no—
599C2×C4—448no—
600C2×C4—444no—
601C2×C4—888no—
602C2×C4#6693714yes—
603C2×C4#6693718yes—
604C2×C4C2×#433912yes—
605C2×C4C2×#433914yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×D4×D1112yes—
608C2×C4C2×D4×D1112yes—
609C2×C4C2×D4×D1114yes—
610C2×C4C24×D1111yescharacteristic
611C8—24no—
612C8—222no—
613C8—222no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—84no—
621C22—224no—
622C22—448no—
623C22—442no—
624C22—442no—
625C22C2×#6693714yes—
626C22C2×#6693712yes—
627C22#1062330612yes—
628C22#1062331012yes—
629C22C22×D4×D1111yescharacteristic
630C4—42no—
631C4—44no—
632C4—224no—
633C4—224no—
634C4—224no—
635C4—444no—
636C4C2×#6693714yes—
637C4C2×#6693712yes—
638C4C22×#433911yescharacteristic
639C4C22×D4×D1111yescharacteristic
640C2—24no—
641C2—82no—
642C2—444no—
643C2#1307816514yesdirect product factor
644C2C22×#6693711yescharacteristic
645C2C2×#1062330611yescharacteristic
646C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
hypercenterC2×#417D11
hypocenterC11C2×#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×#66962C2semidirect
3. C2×#10623356C2semidirect
4. C2×#10623035C2semidirect
5. #13078165C2direct (N × H)
6. C2×#10622380C2semidirect
7. C2×#10622406C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622431C2semidirect
10. C2×#10622732C2semidirect
11. C22×#66874C2semidirect
12. C2×C11×#417C2semidirect
19. #10623356C22semidirect
35. C2×#66962C22semidirect
39. #10623035C22semidirect
44. C11×#417C22semidirect
47. #10622732C22semidirect
52. C2×#66874C22semidirect
53. #10622431C22semidirect
54. #10622406C22semidirect
55. #10622400C22semidirect
56. #10622380C22semidirect
241. C2×#417D11semidirect
341. #417C2×D11semidirect
459. C2×C11#3046semidirect
553. C11C2×#3046semidirect
643. C2#13078165direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#670032
C2×#106233562
C2×#106230352
#130781652
C2×#106223802
C2×#106224062
C2×#106224002
C2×#106224312
C2×#106227322
C22×#668742
C2×C11×#4172
C2×#304611