Finite Group Databasebeta

← C2×#13069643 #14780655

Subgroups — C2×#13069643 #14780655

Order 2816.

2190 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C22×#66989C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4C2×#10622617C211yesmaximal, characteristic, complemented
5C22×#66897C211yesmaximal, characteristic, complemented
6#13069643C218yesmaximal, direct product factor
7C2×#10622170C211yesmaximal, characteristic, complemented
8C2×C11×#535C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C11×#535—22no—
13C11×#535—22no—
14C11×#535—22no—
15C11×#535C2214yes—
16C2×C11×#127—21no—
17C2×C11×#124—21no—
18C2×C11×#121—22no—
19C2×C11×#120—22no—
20C2×C11×#117C2211yescharacteristic
21C22×C22⋊Dic11—22no—
22C2×#67004—22no—
23C2×#67004—24no—
24C2×#67004—24no—
25C2×#67004C2214yescomplemented
26C22×#4326—21no—
27C2×#66989—22no—
28C2×#66989—24no—
29C2×#66989—24no—
30C2×#66989C2214yescomplemented
31C22×#4324—21no—
32C22×C4×Dic11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66901—24no—
36C2×#66901C2214yescomplemented
37C2×#66897—24no—
38C2×#66897C2214yescomplemented
39#10622617—22no—
40#10622617C2214yescomplemented
41C2×#66874—22no—
42#10622170C2214yescomplemented
43C25×C11D412yes—
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×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—24no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11D412yes—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2312yes—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C23×Dic11—21no—
70C22×Dic22—21no—
71C22×Dic22—21no—
72C22×Dic22—22no—
73C22×Dic22—21no—
74C22×Dic22—21no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22—21no—
78C22×Dic22D414yescomplemented
79C22×Dic22C2312yes—
80C11×#127—24no—
81C11×#127—24no—
82C11×#124—24no—
83C11×#124—24no—
84C11×#121—28no—
85C11×#121—28no—
86C11×#120—28no—
87C11×#120—28no—
88C11×#117—21no—
89C11×#117—21no—
90C11×#117D412yes—
91C11×#117C2312yes—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96C2×C22⋊Dic11—216no—
97C2×C22⋊Dic11—28no—
98#67004—216no—
99#67004—28no—
100#67004—28no—
101C2×#4326—28no—
102C2×#4326—24no—
103#66989—216no—
104#66989—28no—
105#66989—28no—
106C2×#4324—28no—
107C2×#4324—24no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11D414yescomplemented
111C2×C4×Dic11C2312yes—
112C2×#4318—22no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318D414yescomplemented
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66897—28no—
124#66874—28no—
125C2×#2004—111nomaximal, Sylow
126C24×C11—24no—
127C24×C11—22no—
128C24×C11—21no—
129C24×C11—22no—
130C24×C11—24no—
131C24×C11—48no—
132C24×C11C2×D411yescharacteristic
133C24×C11C2×D414yes—
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—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11C2×D412yes—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—216no—
151C2×D4×C11—22no—
152C2×D4×C11—24no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—22no—
157C2×D4×C11—24no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—88no—
175C2×D4×C11C2×D412yes—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
192C22×Dic11—24no—
193C22×Dic11—24no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—44no—
197C22×Dic11—41no—
198C22×Dic11—41no—
199C22×Dic11—42no—
200C2×Dic22—24no—
201C2×Dic22—24no—
202C2×Dic22—24no—
203C2×Dic22—24no—
204C2×Dic22—24no—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22—22no—
208C2×Dic22—22no—
209C2×Dic22—22no—
210C2×Dic22—41no—
211C2×Dic22—41no—
212C2×Dic22—42no—
213C2×Dic22—42no—
214C2×Dic22—42no—
215C2×Dic22—42no—
216C2×Dic22—42no—
217C2×Dic22C2×D414yescomplemented
218C11×C4⋊C4—22no—
219C11×C4⋊C4C2×D414yes—
220C11×C22⋊C4—216no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C42×C11—22no—
224C42×C11—22no—
225C22⋊Dic11—232no—
226#4326—216no—
227#4324—216no—
228C4×Dic11—24no—
229C4×Dic11—22no—
230C4×Dic11C2×D414yescomplemented
231#4318—24no—
232#4318—22no—
233#4318—22no—
234#4318—22no—
235#4318—42no—
236#4318C2×D414yescomplemented
237C2×C11⋊C8—24no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—22no—
240C2×C11⋊C8—42no—
241C22×#137—111no—
242C2×#535D1111yescharacteristic
243C22×#124—111no—
244C22×#104—111no—
245C2×#419—111no—
246C22×#100—111no—
247#2004—118no—
248C2×#339—111no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—22no—
253C23×C11—24no—
254C23×C11—48no—
255C23×C11—416no—
256C23×C11—42no—
257C23×C11—44no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—48no—
261C23×C11—84no—
262C23×C11—88no—
263C23×C11#12012yes—
264C23×C11#12011yescharacteristic
265C23×C11#12011yescharacteristic
266C23×C11#12112yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—42no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—42no—
274D4×C11—42no—
275D4×C11—44no—
276D4×C11—42no—
277D4×C11—42no—
278D4×C11—42no—
279D4×C11—42no—
280D4×C11—44no—
281D4×C11—44no—
282D4×C11—42no—
283D4×C11—816no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—42no—
287C2×C4×C11—44no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—44no—
291C2×C4×C11#12012yes—
292C2×C4×C11#12012yes—
293C2×C4×C11#12012yes—
294C2×C4×C11#12011yescharacteristic
295C2×C4×C11#12011yescharacteristic
296C2×C4×C11#12112yes—
297C2×C4×C11#12112yes—
298C2×C4×C11#12112yes—
299C2×C4×C11#12112yes—
300C2×C4×C11#12112yes—
301C2×C4×C11#12712yes—
302C2×C4×C11#12712yes—
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—44no—
312C2×Dic11—48no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—44no—
316C2×Dic11—44no—
317Dic22—24no—
318Dic22—24no—
319Dic22—42no—
320Dic22—42no—
321Dic22—44no—
322Dic22—44no—
323C11⋊C8—24no—
324C11⋊C8—42no—
325C22×#41C2×D1111yescharacteristic
326C23×Q8—111no—
327C23×D4C2×D1111yescharacteristic
328C2×#137—114no—
329C2×#137—224no—
330C2×#137—224no—
331C2×#137—222no—
332C22×Q16—221no—
333C22×SD16—221no—
334C22×M16—111no—
335C22×M16—111no—
336#535—22no—
337#535—22no—
338#535—22no—
339#535C2×D1114yes—
340C2×#127—21no—
341C2×#124—21no—
342C2×#124—114no—
343C2×#124—224no—
344C2×#124—224no—
345C2×#124—222no—
346C2×#121—22no—
347C2×#120—22no—
348C2×#117C2×D1111yescharacteristic
349C22×C22⋊C4—222no—
350C22×C42—111no—
351C2×#104—114no—
352C2×#104—224no—
353#419—114no—
354#419—222no—
355C2×#103—222no—
356C2×#100—114no—
357C2×#100—224no—
358#339—114no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—48no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—48no—
368C22×C11—84no—
369C22×C11—88no—
370C22×C11—84no—
371C22×C11—88no—
372C22×C11#39212yes—
373C22×C11#39212yes—
374C22×C11#45514yes—
375C22×C11C2×#12011yescharacteristic
376C22×C11C2×#12011yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C4×C11—42no—
379C4×C11—44no—
380C4×C11#39212yes—
381C4×C11#39212yes—
382C4×C11C2×#12011yescharacteristic
383C4×C11C2×#12111yescharacteristic
384C4×C11C2×#12111yescharacteristic
385C4×C11C2×#12711yescharacteristic
386Dic11—44no—
387Dic11—44no—
388C25C22⋊D1112yes—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41C22⋊D1112yes—
396C2×#41C22×D1112yes—
397C22×Q8—114no—
398C22×Q8—112no—
399C22×Q8—222no—
400C22×Q8—221no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—221no—
404C22×Q8—221no—
405C22×Q8—221no—
406C22×Q8—221no—
407C22×Q8C22⋊D1111yescharacteristic
408C22×D4—21no—
409C22×D4—24no—
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C22⋊D1112yes—
419C22×D4C22⋊D1111yescharacteristic
420C22×D4C22×D1112yes—
421C23×C4—21no—
422C23×C4—221no—
423C23×C4—221no—
424C23×C4C22×D1111yescharacteristic
425#137—228no—
426#137—228no—
427#137—2216no—
428C2×Q16—228no—
429C2×Q16—224no—
430C2×SD16—228no—
431C2×SD16—224no—
432C2×M16—114no—
433C2×M16—112no—
434C2×M16—112no—
435C2×M16—222no—
436C2×M16—221no—
437C2×M16—221no—
438C2×M16—222no—
439C2×M16—222no—
440C22×C8—221no—
441C22×C8—221no—
442#127—24no—
443#127—24no—
444#124—24no—
445#124—24no—
446#124—228no—
447#124—228no—
448#124—2216no—
449#121—28no—
450#121—28no—
451#120—28no—
452#120—28no—
453#117—21no—
454#117—21no—
455#117C22⋊D1112yes—
456#117C22×D1112yes—
457C2×C4⋊C4C22⋊D1112yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—2216no—
461C2×C22⋊C4—228no—
462C2×C42—21no—
463C2×C42—114no—
464C2×C42—112no—
465C2×C42—222no—
466C2×C42—221no—
467#104—228no—
468#103—228no—
469#100—228no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—22no—
473C2×C11—84no—
474C2×C11—82no—
475C2×C11#200414yescomplemented
476C2×C11C2×#39211yescharacteristic
477C2×C11C2×#45512yes—
478C24—24no—
479C24—22no—
480C24—21no—
481C24—24no—
482C24—22no—
483C24—48no—
484C24C2×C22⋊D1111yescharacteristic
485C24C2×C22⋊D1114yes—
486#41—24no—
487#41—24no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—42no—
493#41—42no—
494#41—42no—
495#41—42no—
496C2×Q8—21no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—114no—
500C2×Q8—224no—
501C2×Q8—222no—
502C2×Q8—224no—
503C2×Q8—224no—
504C2×Q8—224no—
505C2×Q8—224no—
506C2×Q8—222no—
507C2×Q8—222no—
508C2×Q8—222no—
509C2×Q8—222no—
510C2×Q8—442no—
511C2×Q8—442no—
512C2×Q8—442no—
513C2×Q8—442no—
514C2×Q8—442no—
515C2×Q8—441no—
516C2×Q8—441no—
517C2×Q8C2×C22⋊D1112yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—216no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—88no—
545C2×D4C2×C22⋊D1112yes—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—444no—
557C22×C4—442no—
558C22×C4—441no—
559C22×C4—441no—
560C22×C4D4×D1112yes—
561C22×C4D4×D1112yes—
562C22×C4D4×D1112yes—
563C22×C4#434112yes—
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C23×D1111yescharacteristic
570Q16—2216no—
571SD16—2216no—
572M16—114no—
573M16—224no—
574M16—222no—
575M16—222no—
576M16—222no—
577M16—442no—
578C2×C8—224no—
579C2×C8—222no—
580C2×C8—222no—
581C2×C8—442no—
582C4⋊C4—22no—
583C4⋊C4C2×C22⋊D1114yes—
584C22⋊C4—216no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—2232no—
588C42—22no—
589C42—22no—
590C42—114no—
591C42—224no—
592C42—222no—
593C11C2×#200411yescharacteristic, complemented, Sylow
594C23—24no—
595C23—24no—
596C23—24no—
597C23—22no—
598C23—24no—
599C23—48no—
600C23—416no—
601C23—42no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—48no—
606C23—84no—
607C23—88no—
608C23#6699012yes—
609C23#6699212yes—
610C23#6700611yescharacteristic
611C23#6700611yescharacteristic
612C23C22×C22⋊D1111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—42no—
616Q8—224no—
617Q8—224no—
618Q8—442no—
619Q8—442no—
620Q8—444no—
621Q8—444no—
622D4—22no—
623D4—22no—
624D4—42no—
625D4—42no—
626D4—44no—
627D4—42no—
628D4—42no—
629D4—42no—
630D4—42no—
631D4—44no—
632D4—44no—
633D4—42no—
634D4—816no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—448no—
645C2×C4—444no—
646C2×C4—442no—
647C2×C4—444no—
648C2×C4—444no—
649C2×C4—442no—
650C2×C4#6699012yes—
651C2×C4#6699012yes—
652C2×C4#6699012yes—
653C2×C4#6699112yes—
654C2×C4#6699112yes—
655C2×C4#6699212yes—
656C2×C4#6699212yes—
657C2×C4#6699212yes—
658C2×C4#6699312yes—
659C2×C4#6699312yes—
660C2×C4#6700611yescharacteristic
661C2×C4#6700611yescharacteristic
662C2×C4C2×D4×D1111yescharacteristic
663C2×C4C2×D4×D1111yescharacteristic
664C2×C4C2×D4×D1111yescharacteristic
665C2×C4C2×#434111yescharacteristic
666C2×C4C22×C22⋊D1111yescharacteristic
667C2×C4C22×C22⋊D1111yescharacteristic
668C8—224no—
669C8—442no—
670C22—24no—
671C22—24no—
672C22—22no—
673C22—22no—
674C22—48no—
675C22—44no—
676C22—48no—
677C22—42no—
678C22—44no—
679C22—84no—
680C22—88no—
681C22—88no—
682C22—84no—
683C22#1062283612yes—
684C22#1062283612yes—
685C22#1062285514yes—
686C22C2×#6699011yescharacteristic
687C22C2×#6699211yescharacteristic
688C22C2×#6700611yescharacteristic
689C4—44no—
690C4—42no—
691C4—444no—
692C4—444no—
693C4#1062283612yes—
694C4#1062283612yes—
695C4C2×#6699011yescharacteristic
696C4C2×#6699111yescharacteristic
697C4C2×#6699211yescharacteristic
698C4C2×#6699311yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—84no—
703C2—82no—
704C2#1306964314yesdirect product factor
705C2C2×#1062283611yescharacteristic
706C2C2×#1062285512yes—
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11#120
hypercenterC2×#535D11
hypocenterC11C2×#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×#66989C2semidirect
3. C22×#66901C2semidirect
4. C2×#10622617C2semidirect
5. C22×#66897C2semidirect
6. #13069643C2direct (N × H)
7. C2×#10622170C2semidirect
25. C2×#67004C22semidirect
30. C2×#66989C22semidirect
36. C2×#66901C22semidirect
38. C2×#66897C22semidirect
40. #10622617C22semidirect
42. #10622170C22semidirect
78. C22×Dic22D4semidirect
110. C2×C4×Dic11D4semidirect
117. C2×#4318D4semidirect
217. C2×Dic22C2×D4semidirect
230. C4×Dic11C2×D4semidirect
236. #4318C2×D4semidirect
475. C2×C11#2004semidirect
593. C11C2×#2004semidirect
704. C2#13069643direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669892
C22×#669012
C2×#106226172
C22×#668972
#130696432
C2×#106221702
C2×C11×#5352
C2×#200411