Finite Group Databasebeta

← C2×#21449149 #29848699

Subgroups — C2×#21449149 #29848699

Order 15616.

5718 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758224C211yesmaximal, characteristic
2C22×#14519759C212yesmaximal, complemented
3C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21449149C2116yesmaximal, direct product factor
5C2×#16839683C211yesmaximal, characteristic, complemented
6C2×#16839682C211yesmaximal, characteristic, complemented
7C2×#16839676C211yesmaximal, characteristic, complemented
8C2×#16839638C212yesmaximal, complemented
9C2×#16839637C212yesmaximal, complemented
10C2×#16839634C212yesmaximal, complemented
11C2×#16839624C211yesmaximal, characteristic, complemented
12C2×C61×#394C211yesmaximal, characteristic, complemented
13C22×#11758224—216no—
14C22×#11758224—28no—
15C22×#11758224C2218yes—
16C23×Dic122C2211yescharacteristic
17C23×C22⋊D61C2212yes—
18C24×Dic61C2212yes—
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519759—216no—
23C2×#14519759C22116yescomplemented
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2212yes—
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2212yes—
29C2×C4⋊C4×D61—28no—
30C2×C4⋊C4×D61C2218yescomplemented
31C22×C22⋊Dic61C2212yes—
32C22×C22⋊Dic61C2212yes—
33C22×#11758198C2212yes—
34#16839683C2218yescomplemented
35#16839682C2218yescomplemented
36#16839676C2218yescomplemented
37#16839638C22116yescomplemented
38#16839637C22116yescomplemented
39#16839634C22116yescomplemented
40#16839624C2218yescomplemented
41C2×#14519684C2212yes—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2212yes—
44C2×#14519684C2212yes—
45C23×D4×C61C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2212yes—
48C22×C22⋊C4×C61C2212yes—
49C61×#394C2218yescomplemented
50C2×#95×C61C2211yescharacteristic
51C24×D61C2311yescharacteristic
52C2×#11758224—2128no—
53C2×#11758224—264no—
54C2×#11758224—232no—
55C22×Dic122—24no—
56C22×Dic122—28no—
57C22×Dic122C2314yes—
58C22×C22⋊D61—28no—
59C22×C22⋊D61—28no—
60C22×C22⋊D61D4116yes—
61C22×C22⋊D61C2318yes—
62C23×Dic61—28no—
63C23×Dic61—28no—
64C23×Dic61—28no—
65C23×Dic61C2312yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2318yes—
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2312yes—
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—24no—
72C22×C4×D61—28no—
73C22×C4×D61—24no—
74C22×C4×D61—24no—
75C22×C4×D61—24no—
76C22×C4×D61—28no—
77C22×C4×D61D418yes—
78C22×C4×D61C2314yes—
79C22×C4×D61C2314yes—
80C22×C4×D61C2314yes—
81#14519759—264no—
82C2×C4⋊Dic61—24no—
83C2×C4⋊Dic61—28no—
84C2×C4⋊Dic61C2318yes—
85C2×C4⋊Dic61C2314yes—
86C2×#11758196—24no—
87C2×#11758196—24no—
88C2×#11758196—28no—
89C2×#11758196C2318yes—
90C2×#11758196C2314yes—
91C2×#11758196C2314yes—
92C4⋊C4×D61—232no—
93C2×C22⋊Dic61—28no—
94C2×C22⋊Dic61—28no—
95C2×C22⋊Dic61C2318yes—
96C2×C22⋊Dic61C2318yes—
97C2×#11758198—28no—
98C2×#11758198C2318yes—
99#14519684C2314yes—
100#14519684C2318yes—
101#14519684C2318yes—
102#14519684C2318yes—
103C25×C61C2312yes—
104C22×D4×C61—28no—
105C22×D4×C61—24no—
106C22×D4×C61C2314yes—
107C23×C4×C61C2312yes—
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61—24no—
112C2×C4⋊C4×C61C2314yes—
113C2×C22⋊C4×C61—28no—
114C2×C22⋊C4×C61—28no—
115C2×C22⋊C4×C61C2318yes—
116C2×C22⋊C4×C61C2318yes—
117#95×C61C2314yes—
118C24×C61—24no—
119C24×C61—24no—
120C24×C61—24no—
121C24×C61—24no—
122C24×C61—24no—
123C24×C61—24no—
124C24×C61C2×D418yes—
125C24×C61C2414yes—
126C24×C61C2411yescharacteristic
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—24no—
130C23×D61C2×D414yes—
131C23×D61C2×D418yes—
132C23×D61C2412yes—
133C2×D4×C61—232no—
134C2×D4×C61—216no—
135C2×D4×C61—28no—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—24no—
140C22×C4×C61—22no—
141C22×C4×C61—24no—
142C22×C4×C61—24no—
143C22×C4×C61—24no—
144C22×C4×C61C2×D414yes—
145C22×C4×C61#4114yescomplemented
146C22×C4×C61C2412yes—
147C22×C4×C61C2414yes—
148C22×C4×C61C2412yes—
149C22×C4×C61C2412yes—
150C2×C22⋊D61—264no—
151C2×C22⋊D61—216no—
152C2×C22⋊D61—216no—
153C2×C22⋊D61C2×D4132yes—
154C22×Dic61—264no—
155C22×Dic61—24no—
156C22×Dic61—22no—
157C22×Dic61—24no—
158C22×Dic61—24no—
159C22×Dic61—216no—
160C22×Dic61—22no—
161C22×Dic61—216no—
162C22×Dic61—216no—
163C22×Dic61—24no—
164C22×Dic61—22no—
165C22×Dic61—24no—
166C22×Dic61—24no—
167C22×Dic61—24no—
168C22×Dic61C2×D414yes—
169C22×Dic61C2×D418yes—
170C22×Dic61#4114yescomplemented
171C22×Dic61C2412yes—
172C22×Dic61C2414yes—
173C22×Dic61C2412yes—
174C22×Dic61C2414yes—
175C22×Dic61C2412yes—
176#11758224—2256no—
177C2×C4×D61—232no—
178C2×C4×D61—232no—
179C2×C4×D61—216no—
180C2×C4×D61—28no—
181C2×C4×D61—28no—
182C2×C4×D61—28no—
183C2×C4×D61—28no—
184C2×C4×D61—216no—
185C2×C4×D61—416no—
186C2×C4×D61C2×D4116yes—
187C2×Dic122—232no—
188C2×Dic122—28no—
189C2×Dic122—216no—
190C4⋊C4×C61—28no—
191C22⋊C4×C61—216no—
192C22⋊C4×C61—216no—
193C22⋊Dic61—216no—
194C22⋊Dic61—216no—
195#11758198—216no—
196C4⋊Dic61—28no—
197C4⋊Dic61—216no—
198#11758196—28no—
199#11758196—28no—
200#11758196—216no—
201C23×C61—216no—
202C23×C61—216no—
203C23×C61—216no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—48no—
211C23×C61—48no—
212C23×C61—48no—
213C23×C61—48no—
214C23×C61C22×D418yes—
215C23×C61C22×D412yes—
216C23×C61C22×D414yes—
217C23×C61C2×#4112yes—
218C23×C61C2×#4112yes—
219C23×C612−1+414yes—
220C23×C61C2511yescharacteristic
221C22×D61—28no—
222C22×D61—28no—
223C22×D61—216no—
224C22×D61—216no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—24no—
228C22×D61#120116yes—
229C22×D61C22×D418yes—
230C22×D61C22×D414yes—
231D4×C61—232no—
232C2×C4×C61—28no—
233C2×C4×C61—28no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—22no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—44no—
243C2×C4×C61—48no—
244C2×C4×C61C22×D414yes—
245C2×C4×C61C2×#4114yescomplemented
246C22⋊D61—264no—
247C2×Dic61—264no—
248C2×Dic61—216no—
249C2×Dic61—28no—
250C2×Dic61—28no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—44no—
262C2×Dic61—48no—
263C2×Dic61C22×D418yes—
264C2×Dic61C22×D414yes—
265C2×Dic61C2×#4114yescomplemented
266C4×D61—232no—
267C4×D61—232no—
268C4×D61—416no—
269Dic122—232no—
270C2×#2406—611nomaximal, Sylow
271C22×C61—28no—
272C22×C61—28no—
273C22×C61—28no—
274C22×C61—432no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61—44no—
278C22×C61—44no—
279C22×C61C2×#12014yes—
280C22×C61#52514yes—
281C22×C61#53614yes—
282C22×C61#54718yes—
283C22×C61#54718yes—
284C22×C61C23×D411yescharacteristic
285C22×C61C23×D412yes—
286C22×C61C22×#4111yescharacteristic
287C22×C61C22×#4111yescharacteristic
288C22×C61C2×2−1+412yes—
289C2×D61—232no—
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—28no—
293C2×D61—28no—
294C2×D61C2×#12018yes—
295C4×C61—24no—
296C4×C61—24no—
297C4×C61—42no—
298C4×C61—44no—
299Dic61—28no—
300Dic61—24no—
301Dic61—24no—
302Dic61—42no—
303Dic61—44no—
304C23×#41—611no—
305C22×#123—612no—
306C23×C4⋊C4—611no—
307#2406—6116no—
308C2×#395—611no—
309C2×#395—611no—
310C2×#394—611no—
311C2×#394D6111yescharacteristic, complemented
312C2×#386—612no—
313C2×#385—612no—
314C2×#385—612no—
315C2×#381—611no—
316C2×C61—48no—
317C2×C61#240618yescomplemented
318C2×C61C22×#12011yescharacteristic
319C2×C61C2×#52511yescharacteristic
320C2×C61C2×#53611yescharacteristic
321C2×C61C2×#54712yes—
322C2×C61C2×#54712yes—
323D61—28no—
324C22×#41—618no—
325C22×#41—1228no—
326C22×#41—12216no—
327C23×Q8—611no—
328C23×D4—612no—
329C23×D4C2×D6111yescharacteristic
330C24×C4—611no—
331C24×C4—612no—
332C24×C4—611no—
333C24×C4—611no—
334C2×#123—6116no—
335C2×#123—12216no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—612no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4—612no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—618no—
342C22×C4⋊C4—1228no—
343C22×C4⋊C4C2×D6111yescharacteristic
344C22×C22⋊C4—612no—
345C22×C22⋊C4—612no—
346C22×C22⋊C4—612no—
347C22×C22⋊C4C2×D6112yes—
348C22×C22⋊C4C2×D6112yes—
349#395—618no—
350#395—618no—
351#394—618no—
352#394C2×D6118yescomplemented
353#386—6116no—
354#385—6116no—
355#385—6116no—
356#381—618no—
357C2×#95—611no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—612no—
361C2×#95C2×D6111yescharacteristic
362C61C2×#240611yescharacteristic, complemented, Sylow
363C25—611no—
364C25C22×D6112yes—
365C2×#41—12232no—
366C2×#41—12264no—
367C2×#41—122128no—
368C22×Q8—614no—
369C22×Q8—1228no—
370C22×Q8—1224no—
371C22×D4—28no—
372C22×D4—24no—
373C22×D4—6116no—
374C22×D4—618no—
375C22×D4—1228no—
376C22×D4—1228no—
377C22×D4C22×D6114yes—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—612no—
381C23×C4—618no—
382C23×C4—614no—
383C23×C4—618no—
384C23×C4—612no—
385C23×C4—611no—
386C23×C4—614no—
387C23×C4—614no—
388C23×C4—1224no—
389C23×C4—1224no—
390C23×C4—1228no—
391C23×C4—1224no—
392C23×C4—1228no—
393C23×C4—1228no—
394C23×C4—1228no—
395C23×C4—1228no—
396C23×C4—1224no—
397C23×C4C22×D6112yes—
398C23×C4C22×D6111yescharacteristic
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401#123—12264no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—614no—
404C2×C4⋊C4—614no—
405C2×C4⋊C4—614no—
406C2×C4⋊C4—618no—
407C2×C4⋊C4—618no—
408C2×C4⋊C4—12232no—
409C2×C4⋊C4—1224no—
410C2×C4⋊C4—1224no—
411C2×C4⋊C4—1228no—
412C2×C4⋊C4—1228no—
413C2×C4⋊C4—1224no—
414C2×C4⋊C4C22×D6114yes—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—618no—
418C2×C22⋊C4—618no—
419C2×C22⋊C4—618no—
420C2×C22⋊C4—1228no—
421C2×C22⋊C4—1228no—
422C2×C22⋊C4—1228no—
423C2×C22⋊C4C22×D6118yes—
424C2×C22⋊C4C22×D6118yes—
425#95—618no—
426#95—614no—
427#95—618no—
428#95—618no—
429#95C22×D6114yes—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—618no—
437C24—614no—
438C24—612no—
439C24—1222no—
440C24—1222no—
441C24—1224no—
442C24D4×D6118yes—
443C24C23×D6114yes—
444C24C23×D6111yescharacteristic
445#41—122256no—
446C2×Q8—12216no—
447C2×Q8—12232no—
448C2×Q8—1228no—
449C2×D4—232no—
450C2×D4—216no—
451C2×D4—28no—
452C2×D4—6132no—
453C2×D4—12264no—
454C2×D4—12216no—
455C2×D4—12216no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—614no—
465C22×C4—618no—
466C22×C4—614no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—614no—
470C22×C4—6116no—
471C22×C4—614no—
472C22×C4—612no—
473C22×C4—1228no—
474C22×C4—1228no—
475C22×C4—12232no—
476C22×C4—12216no—
477C22×C4—12232no—
478C22×C4—1228no—
479C22×C4—12216no—
480C22×C4—12216no—
481C22×C4—12216no—
482C22×C4—12264no—
483C22×C4—1222no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—1224no—
487C22×C4—12216no—
488C22×C4—1222no—
489C22×C4—1228no—
490C22×C4—1224no—
491C22×C4—1224no—
492C22×C4—1222no—
493C22×C4—1224no—
494C22×C4—1224no—
495C22×C4—24416no—
496C22×C4D4×D6114yes—
497C22×C4#1175822414yescomplemented
498C22×C4C23×D6114yes—
499C22×C4C23×D6112yes—
500C22×C4C23×D6112yes—
501C22×C4C23×D6112yes—
502C4⋊C4—28no—
503C4⋊C4—1228no—
504C4⋊C4—1228no—
505C4⋊C4—12216no—
506C4⋊C4—12216no—
507C4⋊C4—1228no—
508C22⋊C4—216no—
509C22⋊C4—216no—
510C22⋊C4—12216no—
511C22⋊C4—12216no—
512C22⋊C4—12216no—
513C23—216no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—216no—
521C23—216no—
522C23—48no—
523C23—48no—
524C23—48no—
525C23—48no—
526C23—6116no—
527C23—618no—
528C23—614no—
529C23—1228no—
530C23—1222no—
531C23—1228no—
532C23—1222no—
533C23—1224no—
534C23—12216no—
535C23—12216no—
536C23C2×D4×D6118yes—
537C23C2×D4×D6112yes—
538C23C2×D4×D6114yes—
539C23#41×D6112yes—
540C23C2×#1175822412yes—
541C23#1451982414yes—
542C23C24×D6111yescharacteristic
543Q8—12232no—
544D4—232no—
545D4—12264no—
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—44no—
557C2×C4—48no—
558C2×C4—614no—
559C2×C4—618no—
560C2×C4—614no—
561C2×C4—12232no—
562C2×C4—12232no—
563C2×C4—12264no—
564C2×C4—1228no—
565C2×C4—12216no—
566C2×C4—1228no—
567C2×C4—1222no—
568C2×C4—1224no—
569C2×C4—1224no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1224no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—24416no—
578C2×C4—2444no—
579C2×C4—2448no—
580C2×C4C2×D4×D6114yes—
581C2×C4C2×#1175822414yescomplemented
582C22—28no—
583C22—28no—
584C22—28no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—432no—
590C22—618no—
591C22—1228no—
592C22—1228no—
593C22—1224no—
594C22—1224no—
595C22—12232no—
596C22#120×D6114yes—
597C22#1684027214yes—
598C22#1684033214yes—
599C22#1684041018yes—
600C22#1684041218yes—
601C22C22×D4×D6112yes—
602C22C22×D4×D6111yescharacteristic
603C22C2×#41×D6111yescharacteristic
604C22C22×#1175822411yescharacteristic
605C22C2×#1451982412yes—
606C4—24no—
607C4—24no—
608C4—44no—
609C4—42no—
610C4—1224no—
611C4—1228no—
612C4—1224no—
613C4—2444no—
614C4—2442no—
615C2—48no—
616C2—1228no—
617C2#2144914918yesdirect product factor
618C2C2×#120×D6111yescharacteristic
619C2C2×#1684027211yescharacteristic
620C2C2×#1684033211yescharacteristic
621C2C2×#1684041012yes—
622C2C2×#1684041212yes—
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#394C2
socleC24×C61C24
prime radicalC23×#11758224C2
hypercenterC2×#394D61
hypocenterC61C2×#2406
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#14519759C2semidirect
3. C22×C4⋊C4×D61C2semidirect
4. #21449149C2direct (N × H)
5. C2×#16839683C2semidirect
6. C2×#16839682C2semidirect
7. C2×#16839676C2semidirect
8. C2×#16839638C2semidirect
9. C2×#16839637C2semidirect
10. C2×#16839634C2semidirect
11. C2×#16839624C2semidirect
12. C2×C61×#394C2semidirect
23. C2×#14519759C22semidirect
30. C2×C4⋊C4×D61C22semidirect
34. #16839683C22semidirect
35. #16839682C22semidirect
36. #16839676C22semidirect
37. #16839638C22semidirect
38. #16839637C22semidirect
39. #16839634C22semidirect
40. #16839624C22semidirect
49. C61×#394C22semidirect
145. C22×C4×C61#41semidirect
170. C22×Dic61#41semidirect
245. C2×C4×C61C2×#41semidirect
265. C2×Dic61C2×#41semidirect
311. C2×#394D61semidirect
317. C2×C61#2406semidirect
352. #394C2×D61semidirect
362. C61C2×#2406semidirect
497. C22×C4#11758224semidirect
581. C2×C4C2×#11758224semidirect
617. C2#21449149direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117582242
C22×#145197592
C22×C4⋊C4×D612
#214491492
C2×#168396832
C2×#168396822
C2×#168396762
C2×#168396382
C2×#168396372
C2×#168396342
C2×#168396242
C2×C61×#3942
C2×#240661