Finite Group Databasebeta

← C2×#13069636 #14780663

Subgroups — C2×#13069636 #14780663

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C22×#67000C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C22×#66900C211yesmaximal, characteristic, complemented
6#13069636C218yesmaximal, direct product factor
7C2×#10622170C211yesmaximal, characteristic, complemented
8C2×C11×#536C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C11×#536—22no—
13C11×#536—22no—
14C11×#536—22no—
15C11×#536C2214yescomplemented
16C2×C11×C4⋊Q8—21no—
17C2×C11×#124—21no—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×#67002—22no—
22C2×#67002—24no—
23C2×#67002—24no—
24C2×#67002C2214yes—
25C2×#67000—22no—
26C2×#67000—24no—
27C2×#67000—24no—
28C2×#67000C2214yescomplemented
29C22×#4325—21no—
30C22×#4323—21no—
31C22×(C2×D11)⋊C4—22no—
32C22×C4×Dic11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66901—24no—
36C2×#66901C2214yescomplemented
37C2×#66900—24no—
38C2×#66900C2214yescomplemented
39#10622614—22no—
40#10622614C2214yescomplemented
41C2×#66873—22no—
42#10622170C2214yescomplemented
43C24×D11—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41D412yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11—22no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11D411yescharacteristic
61C22×Q8×C11D412yes—
62C22×Q8×C11C2312yes—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11D412yes—
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44—22no—
72C22×D44—21no—
73C22×D44—21no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44D414yes—
78C22×D44C2312yes—
79C11×C4⋊Q8—24no—
80C11×C4⋊Q8—24no—
81C11×#124—24no—
82C11×#124—24no—
83C11×#123—28no—
84C11×#123—28no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—28no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117D412yes—
90C11×#117C2312yes—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96#67002—216no—
97#67002—28no—
98#67002—28no—
99#67000—216no—
100#67000—28no—
101#67000—28no—
102C2×#4325—28no—
103C2×#4325—24no—
104C2×#4323—28no—
105C2×#4323—24no—
106C2×(C2×D11)⋊C4—216no—
107C2×(C2×D11)⋊C4—28no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11D414yes—
111C2×C4×Dic11C2312yes—
112C2×#4318—22no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318D414yes—
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66900—28no—
124#66873—28no—
125C2×#2003—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—48no—
131C23×D11—41no—
132C23×D11—41no—
133C23×D11—42no—
134C11×#41—24no—
135C11×#41—24no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—42no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—42no—
144C2×Q8×C11—24no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—24no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11—22no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—42no—
160C2×Q8×C11—42no—
161C2×Q8×C11—42no—
162C2×Q8×C11—42no—
163C2×Q8×C11—42no—
164C2×Q8×C11—42no—
165C2×Q8×C11C2×D412yes—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—21no—
170C2×D4×C11—22no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11C2×D412yes—
174C22×C4×C11—24no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4112yes—
194C22×C4×C11C2411yescharacteristic
195C22×Dic11—24no—
196C22×Dic11—22no—
197C22×Dic11—44no—
198C2×D44—24no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—41no—
209C2×D44—41no—
210C2×D44—42no—
211C2×D44—42no—
212C2×D44—42no—
213C2×D44—42no—
214C2×D44—42no—
215C2×D44C2×D414yes—
216C11×C4⋊C4—216no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4C2×D414yes—
219C11×C22⋊C4—216no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C42×C11—22no—
223C42×C11—22no—
224#4325—216no—
225#4323—216no—
226(C2×D11)⋊C4—232no—
227C4×Dic11—24no—
228C4×Dic11—22no—
229C4×Dic11C2×D414yes—
230#4318—24no—
231#4318—22no—
232#4318—22no—
233#4318—22no—
234#4318—42no—
235#4318C2×D414yes—
236C2×C11⋊C8—24no—
237C2×C11⋊C8—22no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—42no—
240C22×AGL(1,ℤ/8)—111no—
241C2×#536D1111yescharacteristic, complemented
242C22×#124—111no—
243C22×#104—111no—
244C2×#418—111no—
245C22×#101—111no—
246#2003—118no—
247C2×#339—111no—
248C23×C11—24no—
249C23×C11—22no—
250C23×C11—42no—
251C23×C11—44no—
252C23×C11#12012yes—
253C23×C11#12011yescharacteristic
254C23×C11#12011yescharacteristic
255C23×C11#12112yes—
256C23×C11C22×D411yescharacteristic
257C22×D11—24no—
258C22×D11—48no—
259C22×D11—416no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—44no—
263C22×D11—44no—
264C22×D11—84no—
265C22×D11—88no—
266C22×D11—84no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—42no—
270Q8×C11—42no—
271Q8×C11—42no—
272Q8×C11—42no—
273Q8×C11—44no—
274Q8×C11—44no—
275Q8×C11—42no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—42no—
279D4×C11—42no—
280D4×C11—44no—
281D4×C11—42no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—42no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—44no—
294C2×C4×C11#12012yes—
295C2×C4×C11#12012yes—
296C2×C4×C11#12012yes—
297C2×C4×C11#12011yescharacteristic
298C2×C4×C11#12011yescharacteristic
299C2×C4×C11#12112yes—
300C2×C4×C11#12112yes—
301C2×C4×C11#12112yes—
302C2×C4×C11#12112yes—
303C2×C4×C11#12112yes—
304C2×C4×C11#12712yes—
305C2×C4×C11#12712yes—
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×Dic11—24no—
313C2×Dic11—44no—
314C2×Dic11—48no—
315D44—24no—
316D44—24no—
317D44—42no—
318D44—42no—
319D44—44no—
320D44—44no—
321C11⋊C8—24no—
322C11⋊C8—42no—
323C22×#41C2×D1111yescharacteristic
324C23×Q8C2×D1111yescharacteristic
325C23×D4—111no—
326C2×AGL(1,ℤ/8)—114no—
327C2×AGL(1,ℤ/8)—224no—
328C2×AGL(1,ℤ/8)—224no—
329C2×AGL(1,ℤ/8)—222no—
330C22×SD16—221no—
331C22×D8—221no—
332C22×M16—111no—
333C22×M16—111no—
334#536—22no—
335#536—22no—
336#536—22no—
337#536C2×D1114yescomplemented
338C2×C4⋊Q8—21no—
339C2×#124—21no—
340C2×#124—114no—
341C2×#124—224no—
342C2×#124—224no—
343C2×#124—222no—
344C2×#123—22no—
345C2×C22⋊Q8—22no—
346C2×#117C2×D1111yescharacteristic
347C22×C22⋊C4—222no—
348C22×C42—111no—
349C2×#104—114no—
350C2×#104—224no—
351#418—114no—
352#418—222no—
353C2×#102—222no—
354C2×#101—114no—
355C2×#101—224no—
356#339—114no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—44no—
363C22×C11—84no—
364C22×C11#39212yes—
365C22×C11#39212yes—
366C22×C11#45414yes—
367C22×C11C2×#12011yescharacteristic
368C22×C11C2×#12011yescharacteristic
369C22×C11C2×#12111yescharacteristic
370C2×D11—48no—
371C2×D11—44no—
372C2×D11—84no—
373C2×D11—88no—
374C2×D11—84no—
375C2×D11—88no—
376C4×C11—44no—
377C4×C11—42no—
378C4×C11—44no—
379C4×C11#39212yes—
380C4×C11#39212yes—
381C4×C11C2×#12011yescharacteristic
382C4×C11C2×#12111yescharacteristic
383C4×C11C2×#12111yescharacteristic
384C4×C11C2×#12711yescharacteristic
385Dic11—44no—
386C25—221no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41C22⋊D1112yes—
394C2×#41C22×D1112yes—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8C22⋊D1111yescharacteristic
404C22×Q8C22⋊D1112yes—
405C22×Q8C22×D1112yes—
406C22×D4—21no—
407C22×D4—114no—
408C22×D4—112no—
409C22×D4—222no—
410C22×D4—222no—
411C22×D4—222no—
412C22×D4—221no—
413C22×D4—221no—
414C22×D4—221no—
415C22×D4—221no—
416C22×D4—221no—
417C22×D4C22⋊D1111yescharacteristic
418C23×C4—21no—
419C23×C4—221no—
420C23×C4C22⋊D1112yes—
421C23×C4C22×D1111yescharacteristic
422AGL(1,ℤ/8)—228no—
423AGL(1,ℤ/8)—228no—
424AGL(1,ℤ/8)—2216no—
425C2×SD16—228no—
426C2×SD16—224no—
427C2×D8—228no—
428C2×D8—224no—
429C2×M16—114no—
430C2×M16—112no—
431C2×M16—112no—
432C2×M16—222no—
433C2×M16—221no—
434C2×M16—221no—
435C2×M16—222no—
436C2×M16—222no—
437C22×C8—221no—
438C22×C8—221no—
439C4⋊Q8—24no—
440C4⋊Q8—24no—
441#124—24no—
442#124—24no—
443#124—228no—
444#124—228no—
445#124—2216no—
446#123—28no—
447#123—28no—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450#117—21no—
451#117—21no—
452#117C22⋊D1112yes—
453#117C22×D1112yes—
454C2×C4⋊C4—24no—
455C2×C4⋊C4C22⋊D1112yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—2216no—
459C2×C22⋊C4—228no—
460C2×C42—21no—
461C2×C42—114no—
462C2×C42—112no—
463C2×C42—222no—
464C2×C42—221no—
465#104—228no—
466#102—228no—
467#101—228no—
468C2×C11—21no—
469C2×C11—21no—
470C2×C11—22no—
471C2×C11—82no—
472C2×C11#200314yescomplemented
473C2×C11C2×#39211yescharacteristic
474C2×C11C2×#45412yes—
475D11—84no—
476C24—21no—
477C24—224no—
478C24—222no—
479C24—448no—
480C24—442no—
481C24—441no—
482C24—441no—
483C24C2×C22⋊D1111yescharacteristic
484#41—24no—
485#41—24no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—42no—
491#41—42no—
492#41—42no—
493#41—42no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—21no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8C2×C22⋊D1112yes—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—114no—
524C2×D4—224no—
525C2×D4—224no—
526C2×D4—224no—
527C2×D4—224no—
528C2×D4—224no—
529C2×D4—222no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—442no—
535C2×D4—442no—
536C2×D4—442no—
537C2×D4—442no—
538C2×D4—442no—
539C2×D4—441no—
540C2×D4—441no—
541C2×D4C2×C22⋊D1112yes—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—224no—
553C22×C4—222no—
554C22×C4—444no—
555C22×C4D4×D1112yes—
556C22×C4D4×D1112yes—
557C22×C4D4×D1112yes—
558C22×C4#434112yes—
559C22×C4C2×C22⋊D1114yes—
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C23×D1111yescharacteristic
566SD16—2216no—
567D8—2216no—
568M16—114no—
569M16—224no—
570M16—222no—
571M16—222no—
572M16—222no—
573M16—442no—
574C2×C8—224no—
575C2×C8—222no—
576C2×C8—222no—
577C2×C8—442no—
578C4⋊C4—216no—
579C4⋊C4—22no—
580C4⋊C4C2×C22⋊D1114yes—
581C22⋊C4—216no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—2232no—
585C42—22no—
586C42—22no—
587C42—114no—
588C42—224no—
589C42—222no—
590C11C2×#200311yescharacteristic, complemented, Sylow
591C23—24no—
592C23—22no—
593C23—42no—
594C23—44no—
595C23—224no—
596C23—4416no—
597C23—448no—
598C23—442no—
599C23—444no—
600C23—444no—
601C23—442no—
602C23—888no—
603C23—884no—
604C23—884no—
605C23#6699012yes—
606C23#6699212yes—
607C23#6700611yescharacteristic
608C23#6700611yescharacteristic
609C23C22×C22⋊D1111yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—42no—
613Q8—42no—
614Q8—42no—
615Q8—42no—
616Q8—44no—
617Q8—44no—
618Q8—42no—
619D4—22no—
620D4—22no—
621D4—42no—
622D4—42no—
623D4—44no—
624D4—42no—
625D4—224no—
626D4—224no—
627D4—442no—
628D4—442no—
629D4—444no—
630D4—444no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—224no—
644C2×C4—448no—
645C2×C4—444no—
646C2×C4#6699012yes—
647C2×C4#6699012yes—
648C2×C4#6699012yes—
649C2×C4#6699112yes—
650C2×C4#6699112yes—
651C2×C4#6699212yes—
652C2×C4#6699212yes—
653C2×C4#6699212yes—
654C2×C4#6699312yes—
655C2×C4#6699312yes—
656C2×C4#6700611yescharacteristic
657C2×C4#6700611yescharacteristic
658C2×C4C2×D4×D1111yescharacteristic
659C2×C4C2×D4×D1111yescharacteristic
660C2×C4C2×D4×D1111yescharacteristic
661C2×C4C2×#434111yescharacteristic
662C2×C4C22×C22⋊D1111yescharacteristic
663C2×C4C22×C22⋊D1111yescharacteristic
664C8—224no—
665C8—442no—
666C22—24no—
667C22—24no—
668C22—22no—
669C22—22no—
670C22—44no—
671C22—42no—
672C22—84no—
673C22—448no—
674C22—444no—
675C22—884no—
676C22—888no—
677C22—888no—
678C22—884no—
679C22#1062283612yes—
680C22#1062283612yes—
681C22#1062285814yes—
682C22C2×#6699011yescharacteristic
683C22C2×#6699211yescharacteristic
684C22C2×#6700611yescharacteristic
685C4—44no—
686C4—44no—
687C4—42no—
688C4—444no—
689C4#1062283612yes—
690C4#1062283612yes—
691C4C2×#6699011yescharacteristic
692C4C2×#6699111yescharacteristic
693C4C2×#6699211yescharacteristic
694C4C2×#6699311yescharacteristic
695C2—21no—
696C2—21no—
697C2—22no—
698C2—82no—
699C2—884no—
700C2#1306963614yesdirect product factor
701C2C2×#1062283611yescharacteristic
702C2C2×#1062285812yes—
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11#120
prime radicalC22×#67002C2
hypercenterC2×#536D11
hypocenterC11C2×#2003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C22×#67000C2semidirect
3. C22×#66901C2semidirect
4. C2×#10622614C2semidirect
5. C22×#66900C2semidirect
6. #13069636C2direct (N × H)
7. C2×#10622170C2semidirect
8. C2×C11×#536C2semidirect
15. C11×#536C22semidirect
28. C2×#67000C22semidirect
36. C2×#66901C22semidirect
38. C2×#66900C22semidirect
40. #10622614C22semidirect
42. #10622170C22semidirect
241. C2×#536D11semidirect
337. #536C2×D11semidirect
472. C2×C11#2003semidirect
590. C11C2×#2003semidirect
700. C2#13069636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#670002
C22×#669012
C2×#106226142
C22×#669002
#130696362
C2×#106221702
C2×C11×#5362
C2×#200311