Finite Group Databasebeta

← C2×#21446821 #29706802

Subgroups — C2×#21446821 #29706802

Order 15616.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758201C211yesmaximal, characteristic, complemented
2C22×#14519753C211yesmaximal, characteristic, complemented
3C22×#14519752C211yesmaximal, characteristic
4C22×#14519699C211yesmaximal, characteristic, complemented
5C22×#14519689C211yesmaximal, characteristic, complemented
6#21446821C218yesmaximal, direct product factor
7C2×#16839524C211yesmaximal, characteristic, complemented
8C22×#103×C61C211yesmaximal, characteristic, complemented
9C23×D244—21no—
10C23×D244C2211yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C22×#11758201—24no—
13C22×#11758201—24no—
14C22×#11758201—24no—
15C22×#11758201C2214yescomplemented
16C23×#92418C2211yescharacteristic
17C2×#14519753—24no—
18C2×#14519753—24no—
19C2×#14519753—22no—
20C2×#14519753C2214yescomplemented
21C2×#14519752—24no—
22C2×#14519752—24no—
23C2×#14519752—22no—
24C2×#14519752C2214yes—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196—21no—
27C22×#11758198—21no—
28C22×#11758198—21no—
29C2×#14519699—24no—
30C2×#14519699C2214yescomplemented
31C2×#14519689—24no—
32C2×#14519689C2214yescomplemented
33#16839524C2214yescomplemented
34C23×Q8×C61C2211yescharacteristic
35C23×C8×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C2×#103×C61—24no—
38C2×#103×C61C2214yescomplemented
39C24×D61—21no—
40C24×D61D411yescharacteristic
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—28no—
46C22×D244—24no—
47C22×D244—21no—
48C22×D244—22no—
49C22×D244—44no—
50C22×D244—44no—
51C22×D244D414yes—
52C22×D244C2312yes—
53C23×Dic61—21no—
54C23×Dic61D411yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61D412yes—
62C22×C4×D61C2312yes—
63C2×#11758201—232no—
64C2×#11758201—28no—
65C2×#11758201—28no—
66C2×#11758201—28no—
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418D414yescomplemented
70C22×#92418C2312yes—
71#14519753—216no—
72#14519753—28no—
73#14519753—28no—
74#14519752—216no—
75#14519752—28no—
76#14519752—28no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61D414yescomplemented
80C2×C4⋊Dic61C2312yes—
81C2×#11758196—28no—
82C2×#11758196—24no—
83C2×#11758198—28no—
84C2×#11758198—28no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87#14519699—28no—
88#14519689—28no—
89C22×Q8×C61—22no—
90C22×Q8×C61—21no—
91C22×Q8×C61—22no—
92C22×Q8×C61—22no—
93C22×Q8×C61—22no—
94C22×Q8×C61—22no—
95C22×Q8×C61D414yescomplemented
96C22×Q8×C61C2312yes—
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C22×C8×C61—22no—
101C22×C8×C61—22no—
102C22×C8×C61—22no—
103C22×C8×C61C2312yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61D414yes—
107C2×C4⋊C4×C61C2312yes—
108#103×C61—28no—
109C24×C61C2×D411yescharacteristic
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—24no—
117C23×D61—22no—
118C23×D61—42no—
119C23×D61—42no—
120C23×D61—42no—
121C23×D61—42no—
122C23×D61—42no—
123C23×D61—42no—
124C23×D61SD1614yescomplemented
125C23×D61C2×D412yes—
126C2×Q8×C61—24no—
127C2×Q8×C61—22no—
128C2×Q8×C61—28no—
129C2×Q8×C61—28no—
130C2×Q8×C61—22no—
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61—42no—
135C2×Q8×C61—42no—
136C2×Q8×C61—44no—
137C2×Q8×C61—44no—
138C2×Q8×C61C2×D414yescomplemented
139C22×C4×C61—24no—
140C22×C4×C61—24no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61#4112yes—
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—24no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—42no—
161C22×Dic61—42no—
162C22×Dic61C2×D412yes—
163C2×D244—28no—
164C2×D244—28no—
165C2×D244—22no—
166C2×D244—22no—
167C2×D244—22no—
168C2×D244—22no—
169C2×D244—216no—
170C2×D244—24no—
171C2×D244—22no—
172C2×D244—48no—
173C2×D244—432no—
174C2×D244—48no—
175C2×D244—42no—
176C2×D244—44no—
177C2×D244—42no—
178C2×D244—44no—
179C2×D244C2×D414yes—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—44no—
190C2×C4×D61—44no—
191C2×C4×D61—44no—
192C2×C4×D61—44no—
193C2×C8×C61—22no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C2×C8×C61—44no—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61C2×D414yes—
200#11758201—232no—
201#11758198—216no—
202#11758198—216no—
203C4⋊Dic61—24no—
204C4⋊Dic61—22no—
205C4⋊Dic61C2×D414yescomplemented
206#11758196—216no—
207C2×#92418—28no—
208C2×#92418—22no—
209C2×#92418—22no—
210C2×#92418C2×D414yescomplemented
211C23×C61#12012yes—
212C23×C61#12012yes—
213C23×C61#12112yes—
214C23×C61C2×SD1612yes—
215C23×C61#13512yes—
216C23×C61AGL(1,ℤ/8)12yes—
217C23×C61#13712yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—28no—
226C22×D61—28no—
227C22×D61—28no—
228C22×D61—24no—
229C22×D61—44no—
230C22×D61—44no—
231C22×D61—44no—
232C22×D61—44no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—48no—
240C22×D61—48no—
241C22×D61—48no—
242C22×D61—84no—
243C22×D61—84no—
244C22×D61—84no—
245C22×D61—84no—
246C22×D61C2×SD1614yescomplemented
247Q8×C61—24no—
248Q8×C61—24no—
249Q8×C61—42no—
250Q8×C61—42no—
251Q8×C61—48no—
252C2×C4×C61—24no—
253C2×C4×C61—24no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—48no—
259C2×C4×C61—48no—
260C2×C4×C61#12014yes—
261C2×C4×C61#12012yes—
262C2×C4×C61#12012yes—
263C2×C4×C61#12114yes—
264C2×C4×C61#12114yes—
265C2×C4×C61#12112yes—
266C2×C4×C61#12714yes—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×Dic61—22no—
274C2×Dic61—24no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—44no—
280C2×Dic61—48no—
281D244—24no—
282D244—24no—
283D244—432no—
284D244—42no—
285D244—42no—
286D244—48no—
287C4×D61—42no—
288C4×D61—42no—
289C4×D61—42no—
290C4×D61—42no—
291C4×D61—48no—
292C8×C61—42no—
293#92418—24no—
294C2×#2000—611nomaximal, Sylow
295C22×C61#39214yes—
296C22×C61#44814yes—
297C22×C61#44914yes—
298C22×C61#45014yes—
299C22×C61#45214yes—
300C22×C61#46514yes—
301C22×C61#46814yes—
302C22×C61C2×#12011yescharacteristic
303C22×C61C2×#12011yescharacteristic
304C22×C61C2×#12111yescharacteristic
305C22×C61C22×SD1611yescharacteristic
306C22×C61C2×#13511yescharacteristic
307C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C61C2×#13711yescharacteristic
309C2×D61—24no—
310C2×D61—24no—
311C2×D61—24no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61—416no—
316C2×D61—42no—
317C2×D61—44no—
318C2×D61—44no—
319C2×D61—44no—
320C2×D61—82no—
321C2×D61—82no—
322C2×D61—816no—
323C2×D61—82no—
324C2×D61—82no—
325C4×C61—44no—
326C4×C61—44no—
327C4×C61#39214yes—
328C4×C61C2×#12011yescharacteristic
329C4×C61C2×#12111yescharacteristic
330C4×C61C2×#12111yescharacteristic
331C4×C61C2×#12711yescharacteristic
332Dic61—42no—
333Dic61—44no—
334C23×SD16—611no—
335C22×C22⋊Q8—611no—
336C22×#121—611no—
337C22×#103D6111yescharacteristic, complemented
338C22×#102—611no—
339C22×C22⋊C8—611no—
340#2000—618no—
341C2×#340—611no—
342C2×C61#200018yescomplemented
343C2×C61C2×#39211yescharacteristic
344C2×C61C2×#45011yescharacteristic
345C2×C61C2×#44811yescharacteristic
346C2×C61C2×#44911yescharacteristic
347C2×C61C2×#45211yescharacteristic
348C2×C61C2×#46511yescharacteristic
349C2×C61C2×#46811yescharacteristic
350D61—44no—
351D61—84no—
352C23×Q8C2×D6111yescharacteristic
353C23×D4—611no—
354C23×D4—1221no—
355C24×C4—611no—
356C22×SD16—614no—
357C22×SD16—1224no—
358C22×SD16—1224no—
359C22×SD16—1224no—
360C23×C8—611no—
361C23×C8C2×D6111yescharacteristic
362C2×C22⋊Q8—614no—
363C2×C22⋊Q8—1224no—
364C2×C22⋊Q8—1222no—
365C2×C22⋊Q8—1224no—
366C2×#121—614no—
367C2×#121—1222no—
368C2×#121—1224no—
369C2×#121—1224no—
370C22×C4⋊C4—611no—
371C22×C4⋊C4—1221no—
372C22×C4⋊C4C2×D6111yescharacteristic
373C22×C22⋊C4—1221no—
374C22×C22⋊C4—1221no—
375C2×#103—24no—
376C2×#103C2×D6114yescomplemented
377C2×#102—614no—
378C2×#102—1224no—
379C2×C22⋊C8—614no—
380C2×C22⋊C8—1224no—
381#340—614no—
382C61C2×#200011yescharacteristic, complemented, Sylow
383C25—611no—
384C25—1221no—
385C22×Q8—21no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8D24414yescomplemented
392C22×Q8C22×D6112yes—
393C22×D4—614no—
394C22×D4—612no—
395C22×D4—1224no—
396C22×D4—1228no—
397C22×D4—1222no—
398C22×D4—1222no—
399C22×D4—1222no—
400C22×D4—1222no—
401C22×D4—1221no—
402C22×D4—1222no—
403C22×D4—2444no—
404C22×D4—2444no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—611no—
408C23×C4—612no—
409C23×C4—612no—
410C23×C4—1221no—
411C23×C4—1222no—
412C23×C4—1222no—
413C23×C4—1222no—
414C23×C4—1222no—
415C23×C4—1222no—
416C23×C4—1222no—
417C23×C4C22×D6111yescharacteristic
418C2×SD16—1228no—
419C2×SD16—1228no—
420C2×SD16—12232no—
421C2×SD16—1228no—
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—22no—
425C22×C8—614no—
426C22×C8—612no—
427C22×C8—1222no—
428C22×C8—1222no—
429C22×C8C22×D6112yes—
430C22⋊Q8—1228no—
431C22⋊Q8—12216no—
432C22⋊Q8—1228no—
433#121—1228no—
434#121—12216no—
435#121—1228no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—614no—
439C2×C4⋊C4—612no—
440C2×C4⋊C4—1224no—
441C2×C4⋊C4—1228no—
442C2×C4⋊C4—1222no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4C22⋊D6114yes—
445C2×C4⋊C4C22×D6112yes—
446C2×C22⋊C4—1224no—
447C2×C22⋊C4—1224no—
448C2×C22⋊C4—1228no—
449C2×C22⋊C4—1228no—
450#103—28no—
451#102—1228no—
452C22⋊C8—1228no—
453C24—612no—
454C24—614no—
455C24—1222no—
456C24—1222no—
457C24—1222no—
458C24—1222no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24—1224no—
463C24—2442no—
464C24—2442no—
465C24—2442no—
466C24—2442no—
467C24—2442no—
468C24—2442no—
469C24D4×D6111yescharacteristic
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8C2×D24414yescomplemented
483C2×D4—614no—
484C2×D4—12216no—
485C2×D4—1222no—
486C2×D4—1222no—
487C2×D4—1222no—
488C2×D4—1222no—
489C2×D4—1222no—
490C2×D4—1224no—
491C2×D4—1228no—
492C2×D4—1228no—
493C2×D4—2448no—
494C2×D4—2448no—
495C2×D4—24432no—
496C2×D4—2442no—
497C2×D4—2442no—
498C2×D4—2444no—
499C2×D4—2444no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—612no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1224no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1224no—
521C22×C4—1224no—
522C22×C4—1224no—
523C22×C4—2442no—
524C22×C4—2442no—
525C22×C4—2444no—
526C22×C4—2444no—
527C22×C4—2444no—
528C22×C4—2444no—
529C22×C4C2×D24412yes—
530C22×C4#1175822212yes—
531C22×C4D4×D6112yes—
532C22×C4D4×D6112yes—
533C22×C4D4×D6112yes—
534C22×C4D4×D6111yescharacteristic
535C22×C4C2×C22⋊D6112yes—
536C22×C4C23×D6111yescharacteristic
537SD16—12232no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—44no—
542C2×C8—614no—
543C2×C8—1222no—
544C2×C8—1222no—
545C2×C8—1228no—
546C4⋊C4—22no—
547C4⋊C4—24no—
548C4⋊C4—614no—
549C4⋊C4—12216no—
550C4⋊C4—1222no—
551C4⋊C4—1224no—
552C4⋊C4C2×C22⋊D6114yes—
553C22⋊C4—12216no—
554C22⋊C4—12216no—
555C23—614no—
556C23—1222no—
557C23—1222no—
558C23—1228no—
559C23—1222no—
560C23—1222no—
561C23—1222no—
562C23—1222no—
563C23—1228no—
564C23—1228no—
565C23—1224no—
566C23—4884no—
567C23—4884no—
568C23—4884no—
569C23—4884no—
570C23—2442no—
571C23—2442no—
572C23—2442no—
573C23—2442no—
574C23—2442no—
575C23—2442no—
576C23—2448no—
577C23—2448no—
578C23—2448no—
579C23—2444no—
580C23—2444no—
581C23—2444no—
582C23—2444no—
583C23#1451974512yes—
584C23#1451974712yes—
585C23#1451975012yes—
586C23SD16×D6112yes—
587C23#1451980012yes—
588C23#1451980412yes—
589C23#1451980912yes—
590C23C2×D4×D6111yescharacteristic
591Q8—24no—
592Q8—24no—
593Q8—42no—
594Q8—42no—
595Q8—48no—
596D4—1224no—
597D4—1224no—
598D4—24432no—
599D4—2442no—
600D4—2442no—
601D4—2448no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—48no—
609C2×C4—48no—
610C2×C4—1222no—
611C2×C4—1224no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2448no—
617C2×C4—2444no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2448no—
623C2×C4#1451974512yes—
624C2×C4#1451974714yes—
625C2×C4#1451974712yes—
626C2×C4#1451975014yes—
627C2×C4#1451975012yes—
628C2×C4#1451975114yes—
629C2×C4#1451977314yes—
630C2×C4C2×D4×D6111yescharacteristic
631C2×C4C2×D4×D6111yescharacteristic
632C2×C4C2×D4×D6111yescharacteristic
633C2×C4C22×C22⋊D6111yescharacteristic
634C2×C4C22×D24411yescharacteristic
635C2×C4C2×#1175822211yescharacteristic
636C8—42no—
637C8—1224no—
638C22—1224no—
639C22—1224no—
640C22—1224no—
641C22—4882no—
642C22—4882no—
643C22—4882no—
644C22—48816no—
645C22—4882no—
646C22—2444no—
647C22—2444no—
648C22—2444no—
649C22—2442no—
650C22—2442no—
651C22—24416no—
652C22—2442no—
653C22—2442no—
654C22#1683967114yes—
655C22#1683990214yes—
656C22#1683991014yes—
657C22#1683991114yes—
658C22#1683992314yes—
659C22#1683999414yes—
660C22#1684001114yes—
661C22C2×#1451974511yescharacteristic
662C22C2×#1451974711yescharacteristic
663C22C2×#1451975011yescharacteristic
664C22C2×SD16×D6111yescharacteristic
665C22C2×#1451980011yescharacteristic
666C22C2×#1451980411yescharacteristic
667C22C2×#1451980911yescharacteristic
668C4—44no—
669C4—44no—
670C4—2442no—
671C4—2444no—
672C4#1683967114yes—
673C4C2×#1451974711yescharacteristic
674C4C2×#1451975011yescharacteristic
675C4C2×#1451975111yescharacteristic
676C4C2×#1451977311yescharacteristic
677C2—4884no—
678C2—2444no—
679C2#2144682118yesdirect product factor
680C2C2×#1683967111yescharacteristic
681C2C2×#1683991111yescharacteristic
682C2C2×#1683990211yescharacteristic
683C2C2×#1683991011yescharacteristic
684C2C2×#1683992311yescharacteristic
685C2C2×#1683999411yescharacteristic
686C2C2×#1684001111yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519752C2
hypercenterC22×#103D61
hypocenterC61C2×#2000
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#11758201C2semidirect
2. C22×#14519753C2semidirect
4. C22×#14519699C2semidirect
5. C22×#14519689C2semidirect
6. #21446821C2direct (N × H)
7. C2×#16839524C2semidirect
8. C22×#103×C61C2semidirect
15. C22×#11758201C22semidirect
20. C2×#14519753C22semidirect
30. C2×#14519699C22semidirect
32. C2×#14519689C22semidirect
33. #16839524C22semidirect
38. C2×#103×C61C22semidirect
69. C22×#92418D4semidirect
79. C2×C4⋊Dic61D4semidirect
95. C22×Q8×C61D4semidirect
124. C23×D61SD16semidirect
138. C2×Q8×C61C2×D4semidirect
205. C4⋊Dic61C2×D4semidirect
210. C2×#92418C2×D4semidirect
246. C22×D61C2×SD16semidirect
337. C22×#103D61semidirect
342. C2×C61#2000semidirect
376. C2×#103C2×D61semidirect
382. C61C2×#2000semidirect
391. C22×Q8D244semidirect
482. C2×Q8C2×D244semidirect
679. C2#21446821direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117582012
C22×#145197532
C22×#145197522
C22×#145196992
C22×#145196892
#214468212
C2×#168395242
C22×#103×C612
C2×#200061