Finite Group Databasebeta

← C2×#21449329 #29847883

Subgroups — C2×#21449329 #29847883

Order 15616.

3830 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×#14519758C212yesmaximal, complemented
2C22×D4×Dic61C211yesmaximal, characteristic, complemented
3#21449329C2116yesmaximal, direct product factor
4C2×#16839690C212yesmaximal, complemented
5C2×#16839676C212yesmaximal, complemented
6C2×#16839665C211yesmaximal, characteristic, complemented
7C2×#16839658C211yesmaximal, characteristic, complemented
8C2×#16839634C212yesmaximal, complemented
9C2×#16839631C211yesmaximal, characteristic, complemented
10C2×#16839622C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
12C22×#121×C61C211yesmaximal, characteristic
13C24×Dic61C2212yes—
14C2×#14519758—216no—
15C2×#14519758C22116yescomplemented
16C2×D4×Dic61—28no—
17C2×D4×Dic61C2218yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758196C2212yes—
22C22×#11758196C2212yes—
23C22×C22⋊Dic61C2212yes—
24C22×C22⋊Dic61C2212yes—
25C22×C22⋊Dic61C2212yes—
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2212yes—
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839690C22116yescomplemented
32#16839676C22116yescomplemented
33#16839665C2218yescomplemented
34#16839658C2218yescomplemented
35#16839634C22116yescomplemented
36#16839631C2218yescomplemented
37#16839622C2218yescomplemented
38C4×C22⋊Dic61C2218yescomplemented
39C2×#14519684C2212yes—
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2212yes—
42C2×#14519684C2211yescharacteristic
43C23×D4×C61C2212yes—
44C23×D4×C61C2211yescharacteristic
45C24×C4×C61C2211yescharacteristic
46C2×#121×C61—28no—
47C2×#121×C61C2218yes—
48C22×C4⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2212yes—
50C23×Dic61—28no—
51C23×Dic61—28no—
52C23×Dic61—44no—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C23×Dic61C2318yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60#14519758—264no—
61D4×Dic61—232no—
62C2×C4⋊Dic61—24no—
63C2×C4⋊Dic61—24no—
64C2×C4⋊Dic61C2314yes—
65C2×C4⋊Dic61C2314yes—
66C2×#11758196—28no—
67C2×#11758196—28no—
68C2×#11758196—44no—
69C2×#11758196C2318yes—
70C2×#11758196C2318yes—
71C2×#11758196C2318yes—
72C2×C22⋊Dic61—28no—
73C2×C22⋊Dic61—28no—
74C2×C22⋊Dic61—28no—
75C2×C22⋊Dic61—28no—
76C2×C22⋊Dic61—24no—
77C2×C22⋊Dic61D418yescomplemented
78C2×C22⋊Dic61C2318yes—
79C2×C22⋊Dic61C2318yes—
80C2×C22⋊Dic61C2318yes—
81C2×C22⋊Dic61C2314yes—
82C2×C22⋊Dic61C2318yes—
83C2×C22⋊Dic61C2314yes—
84C2×C4×Dic61—24no—
85C2×C4×Dic61—24no—
86C2×C4×Dic61C2314yes—
87C2×C4×Dic61C2314yes—
88#14519684C2314yes—
89#14519684C2318yes—
90#14519684C2318yes—
91#14519684C2314yes—
92C25×C61C2311yescharacteristic
93C25×C61C2312yes—
94C22×D4×C61—28no—
95C22×D4×C61—28no—
96C22×D4×C61—24no—
97C22×D4×C61—24no—
98C22×D4×C61—44no—
99C22×D4×C61D418yes—
100C22×D4×C61C2318yes—
101C22×D4×C61C2314yes—
102C23×C4×C61—24no—
103C23×C4×C61—24no—
104C23×C4×C61—24no—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2314yes—
108C23×C4×C61C2311yescharacteristic
109#121×C61—232no—
110C2×C4⋊C4×C61—24no—
111C2×C4⋊C4×C61C2314yes—
112C2×C22⋊C4×C61—28no—
113C2×C22⋊C4×C61C2318yes—
114C24×C61—24no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—24no—
119C24×C61—24no—
120C24×C61—22no—
121C24×C61—24no—
122C24×C61—24no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—24no—
126C24×C61C2×D414yes—
127C24×C61C2×D418yes—
128C24×C61C2414yes—
129C24×C61C2412yes—
130C24×C61C2411yescharacteristic
131C2×D4×C61—216no—
132C2×D4×C61—216no—
133C2×D4×C61—232no—
134C2×D4×C61—28no—
135C2×D4×C61—28no—
136C2×D4×C61—48no—
137C2×D4×C61—432no—
138C2×D4×C61C2×D4116yes—
139C22×C4×C61—22no—
140C22×C4×C61—24no—
141C22×C4×C61—24no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—24no—
145C22×C4×C61—28no—
146C22×C4×C61—28no—
147C22×C4×C61—28no—
148C22×C4×C61—416no—
149C22×C4×C61C2×D414yes—
150C22×C4×C61#4114yes—
151C22×C4×C61#4114yes—
152C22×C4×C61C2412yes—
153C22×C4×C61C2414yes—
154C22×C4×C61C2412yes—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—24no—
162C22×Dic61—24no—
163C22×Dic61—216no—
164C22×Dic61—22no—
165C22×Dic61—24no—
166C22×Dic61—24no—
167C22×Dic61—22no—
168C22×Dic61—24no—
169C22×Dic61—24no—
170C22×Dic61—22no—
171C22×Dic61—216no—
172C22×Dic61—48no—
173C22×Dic61—432no—
174C22×Dic61C2×D414yes—
175C22×Dic61C2×D414yes—
176C22×Dic61#4114yes—
177C22×Dic61C2414yes—
178C22×Dic61C2412yes—
179C22×Dic61C2414yes—
180C22×Dic61C2412yes—
181C22×Dic61C2412yes—
182C22×Dic61C2412yes—
183C4⋊C4×C61—28no—
184C22⋊C4×C61—216no—
185C22⋊Dic61—216no—
186C22⋊Dic61—216no—
187C22⋊Dic61—216no—
188C22⋊Dic61—28no—
189C22⋊Dic61—216no—
190C22⋊Dic61C2×D4116yescomplemented
191C4⋊Dic61—28no—
192C4⋊Dic61—28no—
193#11758196—216no—
194#11758196—216no—
195#11758196—48no—
196C4×Dic61—28no—
197C4×Dic61—28no—
198C23×C61—216no—
199C23×C61—28no—
200C23×C61—216no—
201C23×C61—28no—
202C23×C61—216no—
203C23×C61—28no—
204C23×C61—24no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—24no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—22no—
214C23×C61—24no—
215C23×C61—22no—
216C23×C61—44no—
217C23×C61—48no—
218C23×C61—44no—
219C23×C61—48no—
220C23×C61—44no—
221C23×C61—48no—
222C23×C61—44no—
223C23×C61—48no—
224C23×C61C22×D414yes—
225C23×C61C22×D418yes—
226C23×C61C22×D412yes—
227C23×C61C22×D412yes—
228C23×C61C2×#4112yes—
229C23×C61C2×#4112yes—
230C23×C61C2×#4112yes—
231C23×C61H(5,𝔽2)12yes—
232C23×C612−1+412yes—
233C23×C61C2511yescharacteristic
234D4×C61—232no—
235D4×C61—432no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—24no—
242C2×C4×C61—44no—
243C2×C4×C61—48no—
244C2×C4×C61—416no—
245C2×C4×C61#123116yescomplemented
246C2×C4×C61C22×D414yes—
247C2×C4×C61C2×#4114yes—
248C2×C4×C61C2×#4114yes—
249C2×Dic61—28no—
250C2×Dic61—28no—
251C2×Dic61—28no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—22no—
265C2×Dic61—24no—
266C2×Dic61—22no—
267C2×Dic61—432no—
268C2×Dic61—48no—
269C2×Dic61—48no—
270C2×Dic61—44no—
271C2×Dic61C22×D414yes—
272C2×Dic61C22×D414yes—
273C2×Dic61C2×#4114yes—
274C2×#2422—611nomaximal, Sylow
275C22×C61—28no—
276C22×C61—24no—
277C22×C61—28no—
278C22×C61—24no—
279C22×C61—28no—
280C22×C61—24no—
281C22×C61—42no—
282C22×C61—44no—
283C22×C61—432no—
284C22×C61—416no—
285C22×C61—42no—
286C22×C61—44no—
287C22×C61—42no—
288C22×C61—44no—
289C22×C61—42no—
290C22×C61—44no—
291C22×C61C2×#12314yes—
292C22×C61#53214yes—
293C22×C61#54214yes—
294C22×C61D4214yes—
295C22×C61#54714yes—
296C22×C61#54714yes—
297C22×C61#55314yes—
298C22×C61C23×D411yescharacteristic
299C22×C61C23×D411yescharacteristic
300C22×C61C22×#4111yescharacteristic
301C22×C61C22×#4111yescharacteristic
302C22×C61C22×#4111yescharacteristic
303C22×C61C2×H(5,𝔽2)11yescharacteristic
304C22×C61C2×2−1+411yescharacteristic
305C4×C61—42no—
306C4×C61—44no—
307C4×C61C2×#12318yescomplemented
308Dic61—24no—
309Dic61—24no—
310Dic61—24no—
311Dic61—44no—
312Dic61—44no—
313Dic61—42no—
314C22×#123—612no—
315C22×#121D6111yescharacteristic
316C22×C4×D4—611no—
317#2422—6116no—
318C2×#397—612no—
319C2×#394—612no—
320C2×#390—611no—
321C2×#389—611no—
322C2×#385—612no—
323C2×#384—611no—
324C2×#380—611no—
325C2×C4×C22⋊C4—611no—
326C2×C61—48no—
327C2×C61—44no—
328C2×C61#242218yescomplemented
329C2×C61C22×#12311yescharacteristic
330C2×C61C2×#53211yescharacteristic
331C2×C61C2×#54211yescharacteristic
332C2×C61C2×D4211yescharacteristic
333C2×C61C2×#54711yescharacteristic
334C2×C61C2×#54711yescharacteristic
335C2×C61C2×#55311yescharacteristic
336C23×D4C2×D6112yes—
337C23×D4C2×D6111yescharacteristic
338C24×C4—612no—
339C24×C4C2×D6111yescharacteristic
340C2×#123—6116no—
341C2×#123—12216no—
342C2×#121—28no—
343C2×#121C2×D6118yes—
344C2×C4×D4—618no—
345C2×C4×D4—1228no—
346C22×C4⋊C4—612no—
347C22×C4⋊C4—612no—
348C22×C4⋊C4—611no—
349C22×C4⋊C4—611no—
350C22×C4⋊C4—612no—
351C22×C4⋊C4C2×D6111yescharacteristic
352C22×C22⋊C4—611no—
353C22×C22⋊C4—611no—
354C22×C22⋊C4—612no—
355C22×C22⋊C4—612no—
356C22×C22⋊C4—612no—
357C22×C22⋊C4—612no—
358C22×C22⋊C4C2×D6112yes—
359C22×C42—611no—
360C22×C42—611no—
361#397—6116no—
362#394—6116no—
363#390—618no—
364#389—618no—
365#385—6116no—
366#384—618no—
367#380—618no—
368C4×C22⋊C4—618no—
369C2×#95—612no—
370C2×#95—611no—
371C2×#95—612no—
372C2×#95—611no—
373C61C2×#242211yescharacteristic, complemented, Sylow
374C25C22×D6111yescharacteristic
375C25C22×D6112yes—
376C22×D4—28no—
377C22×D4—28no—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4—44no—
381C22×D4C22⋊D6118yes—
382C22×D4C22×D6118yes—
383C22×D4C22×D6114yes—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—612no—
391C23×C4—611no—
392C23×C4—612no—
393C23×C4—618no—
394C23×C4—1228no—
395C23×C4—1228no—
396C23×C4—2444no—
397C23×C4C22×D6114yes—
398C23×C4C22×D6111yescharacteristic
399C23×C4C22×D6112yes—
400C23×C4C22×D6111yescharacteristic
401#123—12264no—
402#121—232no—
403C4×D4—12232no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—614no—
406C2×C4⋊C4—618no—
407C2×C4⋊C4—618no—
408C2×C4⋊C4—614no—
409C2×C4⋊C4—618no—
410C2×C4⋊C4—1228no—
411C2×C4⋊C4—1228no—
412C2×C4⋊C4—1224no—
413C2×C4⋊C4—1224no—
414C2×C4⋊C4—2444no—
415C2×C4⋊C4C22×D6114yes—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—618no—
418C2×C22⋊C4—614no—
419C2×C22⋊C4—618no—
420C2×C22⋊C4—618no—
421C2×C22⋊C4—618no—
422C2×C22⋊C4—614no—
423C2×C22⋊C4—618no—
424C2×C22⋊C4—1228no—
425C2×C22⋊C4—1224no—
426C2×C22⋊C4—1228no—
427C2×C22⋊C4—1228no—
428C2×C22⋊C4—1228no—
429C2×C22⋊C4C22×D6118yes—
430C2×C42—614no—
431C2×C42—614no—
432C2×C42—1224no—
433C2×C42—1224no—
434#95—614no—
435#95—614no—
436#95—618no—
437#95—618no—
438C24—24no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24D4×D6114yes—
451C24C2×C22⋊D6118yes—
452C24C23×D6112yes—
453C24C23×D6114yes—
454C24C23×D6111yescharacteristic
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—232no—
460C2×D4—48no—
461C2×D4—432no—
462C2×D4C2×C22⋊D61116yes—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—416no—
473C22×C4—614no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—614no—
481C22×C4—614no—
482C22×C4—12216no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4—1222no—
492C22×C4—1224no—
493C22×C4—12216no—
494C22×C4—1224no—
495C22×C4—1222no—
496C22×C4—1224no—
497C22×C4—1224no—
498C22×C4—1222no—
499C22×C4—2448no—
500C22×C4—24432no—
501C22×C4#1175822414yes—
502C22×C4#1175822414yes—
503C22×C4C2×C22⋊D6114yes—
504C22×C4C23×D6112yes—
505C22×C4C23×D6114yes—
506C22×C4C23×D6112yes—
507C4⋊C4—28no—
508C4⋊C4—12216no—
509C4⋊C4—12216no—
510C4⋊C4—1228no—
511C4⋊C4—1228no—
512C4⋊C4—2448no—
513C22⋊C4—216no—
514C22⋊C4—6116no—
515C22⋊C4—12216no—
516C22⋊C4—1228no—
517C22⋊C4—12216no—
518C22⋊C4—12216no—
519C22⋊C4—12216no—
520C42—1228no—
521C42—1228no—
522C23—216no—
523C23—28no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—22no—
534C23—24no—
535C23—22no—
536C23—216no—
537C23—28no—
538C23—216no—
539C23—28no—
540C23—44no—
541C23—48no—
542C23—44no—
543C23—48no—
544C23—44no—
545C23—48no—
546C23—44no—
547C23—48no—
548C23C2×D4×D6114yes—
549C23C2×D4×D6112yes—
550C23C22×C22⋊D6118yes—
551C23C22×C22⋊D6112yes—
552C23#41×D6112yes—
553C23C2×#1175822412yes—
554C23C2×#1175822412yes—
555C23#1451982212yes—
556C23#1451982412yes—
557C23C24×D6111yescharacteristic
558D4—232no—
559D4—432no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—416no—
569C2×C4—614no—
570C2×C4—614no—
571C2×C4—614no—
572C2×C4—1228no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1228no—
580C2×C4—1228no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—1224no—
589C2×C4—1222no—
590C2×C4—24432no—
591C2×C4—2448no—
592C2×C4—2448no—
593C2×C4—2444no—
594C2×C4#14519758116yescomplemented
595C2×C4C22×C22⋊D6114yes—
596C2×C4C2×#1175822414yes—
597C2×C4C2×#1175822414yes—
598C22—28no—
599C22—24no—
600C22—28no—
601C22—24no—
602C22—28no—
603C22—24no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—432no—
608C22—416no—
609C22—42no—
610C22—44no—
611C22—44no—
612C22—42no—
613C22—44no—
614C22C2×#1451975814yes—
615C22#1684030714yes—
616C22#1684037914yes—
617C22D4×C22⋊D6114yes—
618C22#1684041114yes—
619C22#1684041214yes—
620C22#1684045914yes—
621C22C22×D4×D6111yescharacteristic
622C22C23×C22⋊D6111yescharacteristic
623C22C2×#41×D6111yescharacteristic
624C22C22×#1175822411yescharacteristic
625C22C22×#1175822411yescharacteristic
626C22C2×#1451982211yescharacteristic
627C22C2×#1451982411yescharacteristic
628C4—44no—
629C4—42no—
630C4—1224no—
631C4—1224no—
632C4—1224no—
633C4—2444no—
634C4—2442no—
635C4—2444no—
636C4C2×#1451975818yescomplemented
637C2—48no—
638C2—44no—
639C2#2144932918yesdirect product factor
640C2C22×#1451975811yescharacteristic
641C2C2×#1684030711yescharacteristic
642C2C2×#1684037911yescharacteristic
643C2C2×D4×C22⋊D6111yescharacteristic
644C2C2×#1684041111yescharacteristic
645C2C2×#1684041211yescharacteristic
646C2C2×#1684045911yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
Fitting, prime radicalC22×#121×C61C2
socleC24×C61C24
hypercenterC22×#121D61
hypocenterC61C2×#2422
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14519758C2semidirect
2. C22×D4×Dic61C2semidirect
3. #21449329C2direct (N × H)
4. C2×#16839690C2semidirect
5. C2×#16839676C2semidirect
6. C2×#16839665C2semidirect
7. C2×#16839658C2semidirect
8. C2×#16839634C2semidirect
9. C2×#16839631C2semidirect
10. C2×#16839622C2semidirect
11. C2×C4×C22⋊Dic61C2semidirect
15. C2×#14519758C22semidirect
17. C2×D4×Dic61C22semidirect
31. #16839690C22semidirect
32. #16839676C22semidirect
33. #16839665C22semidirect
34. #16839658C22semidirect
35. #16839634C22semidirect
36. #16839631C22semidirect
37. #16839622C22semidirect
38. C4×C22⋊Dic61C22semidirect
77. C2×C22⋊Dic61D4semidirect
190. C22⋊Dic61C2×D4semidirect
245. C2×C4×C61#123semidirect
307. C4×C61C2×#123semidirect
328. C2×C61#2422semidirect
373. C61C2×#2422semidirect
594. C2×C4#14519758semidirect
636. C4C2×#14519758semidirect
639. C2#21449329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197582
C22×D4×Dic612
#214493292
C2×#168396902
C2×#168396762
C2×#168396652
C2×#168396582
C2×#168396342
C2×#168396312
C2×#168396222
C2×C4×C22⋊Dic612
C22×#121×C612
C2×#242261