Finite Group Databasebeta

← C4×#16839689 #29601833

Subgroups — C4×#16839689 #29601833

Order 15616.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839689C211yesmaximal, characteristic
2C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
3C2×C4×#11758198C211yesmaximal, characteristic
4C2×C4×#11758198C212yesmaximal
5#21444088C211yesmaximal, characteristic, complemented
6#21444079C212yesmaximal, complemented
7#21444076C211yesmaximal, characteristic, complemented
8#21444067C212yesmaximal
9#21444065C211yesmaximal, characteristic
10C4×#14519684C212yesmaximal, complemented
11C4×#95×C61C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×#11758198C2212yes—
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2211yescharacteristic
18C22×#11758198C2212yes—
19C22×C4×Dic61C2211yescharacteristic
20C22×C4×Dic61C2212yes—
21#16839689C418yesdirect product factor
22C4×C4⋊Dic61—24no—
23C4×#11758198—24no—
24C4×#11758198—28no—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C22×C42×C61C2212yes—
35C22×C42×C61C2211yescharacteristic
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C24×D61C2311yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C23×Dic61C2311yescharacteristic
45C22×C4×D61—22no—
46C22×C4×D61—24no—
47C22×C4×D61—24no—
48C22×C4×D61—22no—
49C22×C4×D61D414yes—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—24no—
54C2×C4⋊Dic61C2×C414yescomplemented
55C2×#11758198—24no—
56C2×#11758198—24no—
57C2×#11758198—22no—
58C2×#11758198—24no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—24no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×#11758198—24no—
65C2×#11758198C2×C418yes—
66C2×#11758198C2×C414yes—
67C2×C4×Dic61—22no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—24no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—24no—
72#14519684—22no—
73#14519684—22no—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—24no—
78#14519684—24no—
79#14519684—24no—
80#14519684C2×C418yescomplemented
81C23×C4×C61C2312yes—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2312yes—
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×C42×C61—24no—
87C2×C42×C61—24no—
88C2×C42×C61—24no—
89C2×C42×C61—24no—
90C2×C42×C61D414yes—
91#95×C61—24no—
92#95×C61—22no—
93#95×C61C2×C414yescomplemented
94C24×C61C2411yescharacteristic
95C23×D61—21no—
96C23×D61—21no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—21no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—21no—
103C23×D61C22×C412yes—
104C23×D61C2×D412yes—
105C23×D61#4112yes—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61C22×C414yes—
125C22×C4×C61C22×C412yes—
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2×D412yes—
130C22×C4×C61#4114yes—
131C22×C4×C61#4112yes—
132C22×C4×C61#4112yes—
133C22×C4×C61#4114yes—
134C22×C4×C61#4114yes—
135C22×Dic61—21no—
136C22×Dic61—22no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—21no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C414yes—
161C22×Dic61C2×D412yes—
162C22×Dic61#4112yes—
163C22×Dic61#4114yes—
164C2×C4×D61—28no—
165C2×C4×D61—216no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—48no—
169C42×C61—28no—
170C42×C61—48no—
171#11758198—28no—
172#11758198—216no—
173#11758198—216no—
174#11758198—28no—
175C4⋊Dic61—28no—
176C4⋊Dic61—28no—
177C4×Dic61—48no—
178C4×Dic61—44no—
179C23×C61C23×C411yescharacteristic
180C23×C61C22×D411yescharacteristic
181C23×C61C22×D411yescharacteristic
182C23×C61C2×#4111yescharacteristic
183C23×C61C2×#4111yescharacteristic
184C23×C61C2×#4111yescharacteristic
185C23×C61C2×#4112yes—
186C23×C61C2×#4112yes—
187C23×C61C2×#4112yes—
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4112yes—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—22no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61C4×D414yes—
213C2×C4×C61—24no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—22no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61C4×D414yes—
237C2×C4×C61#12114yes—
238C2×C4×C61#12318yes—
239C2×C4×C61#12314yes—
240C2×C4×C61#12414yes—
241C2×C4×C61#12618yes—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—41no—
259C2×Dic61—42no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—41no—
271C4×D61—416no—
272C4×#397—611nomaximal, Sylow
273C22×C61C2×C4×D411yescharacteristic
274C22×C61C2×C4×D411yescharacteristic
275C22×C61C4×#4112yes—
276C22×C61C4×#4112yes—
277C22×C61C4×#4111yescharacteristic
278C22×C61C2×#12111yescharacteristic
279C22×C61C2×#12312yes—
280C22×C61C2×#12311yescharacteristic
281C22×C61#52512yes—
282C22×C61#52511yescharacteristic
283C22×C61#52511yescharacteristic
284C22×C61C2×#12411yescharacteristic
285C22×C61C2×#12612yes—
286C22×C61#52912yes—
287C22×C61#52912yes—
288C22×C61#52912yes—
289C22×C61#52912yes—
290C22×C61#52912yes—
291C22×C61#52912yes—
292C22×C61#52912yes—
293C22×C61#52911yescharacteristic
294C22×C61#53211yescharacteristic
295C22×C61#53211yescharacteristic
296C2×D61—24no—
297C2×D61—28no—
298C2×D61—44no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—44no—
303C2×D61—42no—
304C2×D61—44no—
305C2×D61—42no—
306C2×D61—42no—
307C4×C61—24no—
308C4×C61—42no—
309C4×C61—44no—
310C4×C61—44no—
311C4×C61#39718yescomplemented
312Dic61—42no—
313Dic61—44no—
314Dic61—42no—
315Dic61—44no—
316Dic61—42no—
317C2×#397—611no—
318C2×C4×C4⋊C4—611no—
319C2×C4×C22⋊C4—611no—
320C2×C4×C22⋊C4—612no—
321#1445—611no—
322#1443—612no—
323#1442—611no—
324#1440—612no—
325#1439—611no—
326C4×#95—612no—
327C4×#95D6111yescharacteristic, complemented
328C2×C61C4×#12111yescharacteristic
329C2×C61C4×#12312yes—
330C2×C61C4×#12311yescharacteristic
331C2×C61C4×#12411yescharacteristic
332C2×C61C4×#12612yes—
333C2×C61C2×#39711yescharacteristic
334C2×C61#239211yescharacteristic
335C2×C61#239511yescharacteristic
336C2×C61#239512yes—
337C2×C61#239811yescharacteristic
338C2×C61#240112yes—
339D61—44no—
340C24×C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C22⋊C4—611no—
344C22×C22⋊C4—612no—
345C22×C22⋊C4—612no—
346C22×C22⋊C4—611no—
347C22×C42—611no—
348C22×C42—612no—
349C22×C42C2×D6112yes—
350C22×C42C2×D6111yescharacteristic
351#397—618no—
352C4×C4⋊C4—1224no—
353C4×C22⋊C4—1228no—
354C4×C22⋊C4—1224no—
355C2×#95—612no—
356C2×#95—612no—
357C2×#95—612no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—612no—
361C2×#95—611no—
362C2×#95—611no—
363C2×#95—612no—
364C2×#95C2×D6111yescharacteristic
365C2×#95C2×D6112yes—
366C2×#95C2×D6111yescharacteristic
367C61C4×#39711yescharacteristic, complemented, Sylow
368C25—611no—
369C23×C4—612no—
370C23×C4—612no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—614no—
375C23×C4—1222no—
376C23×C4—1224no—
377C23×C4—1224no—
378C23×C4—1222no—
379C23×C4C22×D6112yes—
380C23×C4C22×D6111yescharacteristic
381C23×C4C22×D6112yes—
382C23×C4C22×D6111yescharacteristic
383C23×C4C22×D6111yescharacteristic
384C2×C4⋊C4—614no—
385C2×C4⋊C4—1224no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C22⋊C4—618no—
390C2×C22⋊C4—614no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1224no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1224no—
396C2×C22⋊C4—1222no—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1222no—
399C2×C22⋊C4—1224no—
400C2×C22⋊C4—1222no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—1222no—
406C2×C42—1224no—
407C2×C42—1224no—
408C2×C42—1224no—
409C2×C42—1224no—
410C2×C42D24414yes—
411#95—24no—
412#95—22no—
413#95—618no—
414#95—1224no—
415#95—1224no—
416#95—1224no—
417#95—1224no—
418#95—1222no—
419#95—1222no—
420#95—1224no—
421#95—1224no—
422#95C4×D6114yescomplemented
423C24—612no—
424C24—612no—
425C24—612no—
426C24—1221no—
427C24—1222no—
428C24—1221no—
429C24—1222no—
430C24—1221no—
431C24—1222no—
432C24—1222no—
433C24—1221no—
434C24C23×D6111yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—612no—
454C22×C4—614no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—614no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1221no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1228no—
483C22×C4—12216no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4—2448no—
487C22×C4C2×C4×D6114yes—
488C22×C4C2×C4×D6112yes—
489C22×C4C2×D24412yes—
490C22×C4C2×D24412yes—
491C22×C4C2×D24412yes—
492C22×C4#1175822214yes—
493C22×C4#1175822212yes—
494C22×C4#1175822214yes—
495C22×C4D4×D6112yes—
496C22×C4#1175822414yes—
497C22×C4#1175822612yes—
498C4⋊C4—1228no—
499C4⋊C4—1228no—
500C22⋊C4—12216no—
501C22⋊C4—12216no—
502C22⋊C4—1228no—
503C22⋊C4—1228no—
504C42—28no—
505C42—48no—
506C42—2448no—
507C42—2444no—
508C23—614no—
509C23—1222no—
510C23—1224no—
511C23—1224no—
512C23—1222no—
513C23—1222no—
514C23—1224no—
515C23—1224no—
516C23—1222no—
517C23—1224no—
518C23—1224no—
519C23—1222no—
520C23—1222no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23—2441no—
531C23C22×C4×D6111yescharacteristic
532C23C2×D4×D6111yescharacteristic
533C23C22×D24411yescharacteristic
534C23#41×D6111yescharacteristic
535C23#41×D6112yes—
536C23#41×D6111yescharacteristic
537C23C2×#1175822412yes—
538C23C2×#1175822211yescharacteristic
539C23C2×#1175822212yes—
540C23C2×#1175822212yes—
541C23C2×#1175822611yescharacteristic
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1224no—
570C2×C4—1222no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—1222no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2441no—
594C2×C4—24416no—
595C2×C4C4×D24414yes—
596C2×C4#1451975214yes—
597C2×C4#1451975918yes—
598C2×C4#1451976114yes—
599C2×C4#1451976514yes—
600C2×C4#1451977218yes—
601C22—1224no—
602C22—1228no—
603C22—2442no—
604C22—2442no—
605C22—2442no—
606C22—2444no—
607C22—2442no—
608C22—2442no—
609C22—2444no—
610C22—2442no—
611C22—2444no—
612C22C4×D4×D6111yescharacteristic
613C22C2×C4×D24411yescharacteristic
614C22C4×#1175822412yes—
615C22C4×#1175822212yes—
616C22C4×#1175822611yescharacteristic
617C22C2×#1451975211yescharacteristic
618C22C2×#1451975912yes—
619C22C2×#1451976111yescharacteristic
620C22#1684027112yes—
621C22#1684027411yescharacteristic
622C22#1684027411yescharacteristic
623C22C2×#1451976511yescharacteristic
624C22C2×#1451977212yes—
625C22#1684029012yes—
626C22#1684029012yes—
627C22#1684029212yes—
628C22#1684029212yes—
629C22#1684029412yes—
630C22#1684029612yes—
631C22#1684029912yes—
632C22#1684029911yescharacteristic
633C22#1684030911yescharacteristic
634C22#1684031211yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—2442no—
640C4—2444no—
641C4—2444no—
642C4—2442no—
643C4—2442no—
644C4#1683968918yesdirect product factor
645C2—2444no—
646C2C4×#1451975211yescharacteristic
647C2C4×#1451975912yes—
648C2C4×#1451976111yescharacteristic
649C2C4×#1451976511yescharacteristic
650C2C4×#1451977212yes—
651C2C2×#1683968911yescharacteristic
652C2#2144905911yescharacteristic
653C2#2144907911yescharacteristic
654C2#2144908012yes—
655C2#2144910511yescharacteristic
656C2#2144912012yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4×#95D61
hypocenterC61C4×#397
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic61C2semidirect
5. #21444088C2semidirect
6. #21444079C2semidirect
7. #21444076C2semidirect
10. C4×#14519684C2semidirect
11. C4×#95×C61C2semidirect
21. #16839689C4direct (N × H)
54. C2×C4⋊Dic61C2×C4semidirect
80. #14519684C2×C4semidirect
93. #95×C61C2×C4semidirect
311. C4×C61#397semidirect
327. C4×#95D61semidirect
367. C61C4×#397semidirect
422. #95C4×D61semidirect
644. C4#16839689direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168396892
C2×C4×C4⋊Dic612
C2×C4×#117581982
#214440882
#214440792
#214440762
#214440672
#214440652
C4×#145196842
C4×#95×C612
C4×#39761