Finite Group Databasebeta

← C4×#16839765 #29677787

Subgroups — C4×#16839765 #29677787

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#16839765C212yesmaximal
3C2×C4×#11758189C211yesmaximal, characteristic, complemented
4C4×#14519735C211yesmaximal, characteristic, complemented
5#21445646C212yesmaximal, complemented
6#21445643C212yesmaximal, complemented
7C4×#14519697C211yesmaximal, characteristic, complemented
8C4×#14519699C211yesmaximal, characteristic, complemented
9C4×#14519698C211yesmaximal, characteristic, complemented
10#21445537C212yesmaximal, complemented
11C4×#102×C61C211yesmaximal, characteristic, complemented
12C22×D4×D61C2211yescharacteristic
13C23×C4×D61—21no—
14C22×#11758189C2212yes—
15C2×C4×D244C2211yescharacteristic
16C2×D4×Dic61C2211yescharacteristic
17C2×#14519739C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×#14519737—21no—
20C4×D4×D61—24no—
21C4×D4×D61C418yescomplemented
22C2×#14519735C2212yes—
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25C2×C42×D61C2211yescharacteristic
26#16839765C4116yesdirect product factor
27C2×#14519699C2212yes—
28C2×#14519698C2212yes—
29C2×#14519697C2212yes—
30C4×#11758189—24no—
31C2×#14519687C2212yescomplemented
32C2×C4×#92418C2211yescharacteristic, complemented
33C4⋊C4×Dic61C2212yescomplemented
34C4×C4⋊Dic61C2211yescharacteristic, complemented
35C4×#11758198—21no—
36#16839609—21no—
37#16839607—21no—
38C42×Dic61—21no—
39#16839525C2212yescomplemented
40#16839524C2212yescomplemented
41#16839524C2212yescomplemented
42C2×C4×D4×C61C2211yescharacteristic
43C2×#102×C61C2212yes—
44C2×C4×C8×C61C2211yescharacteristic, complemented
45C4×C4⋊C4×C61C2211yescharacteristic, complemented
46C61×#340C2212yescomplemented
47C24×D61—21no—
48C22×D244C2311yescharacteristic
49C22×C22⋊D61—21no—
50C2×D4×D61—22no—
51C2×D4×D61—24no—
52C2×D4×D61C2×C414yes—
53C2×D4×D61C2×C418yes—
54C23×Dic61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—28no—
59C22×C4×D61—44no—
60C22×C4×D61—44no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758189—24no—
65C2×#11758189—24no—
66C2×#11758189C2×C418yescomplemented
67C22×#92418C2312yes—
68C4×D244—22no—
69C4×D244C2×C414yes—
70D4×Dic61—22no—
71D4×Dic61C2×C414yes—
72#14519739—22no—
73#14519739C2×C414yes—
74C4×C22⋊D61—28no—
75#14519737—28no—
76#14519735—24no—
77#14519735C2×C418yescomplemented
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2312yes—
80C2×#11758196—21no—
81C4⋊C4×D61—22no—
82C4⋊C4×D61C2×C414yes—
83C2×C22⋊Dic61—21no—
84C2×#11758198—22no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C22⋊C4×D61—28no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C42×D61C2×C414yes—
95C42×D61D414yes—
96#14519699C2×C418yescomplemented
97#14519698C2×C418yescomplemented
98#14519697C2×C418yescomplemented
99#14519687—24no—
100C4×#92418—22no—
101#14519684—21no—
102#14519684—22no—
103C22×D4×C61C2311yescharacteristic
104C23×C4×C61—21no—
105C22×C8×C61C2312yes—
106C4×D4×C61—22no—
107C4×D4×C61C2×C414yes—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2312yes—
110C2×C22⋊C4×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#102×C61C2×C418yescomplemented
114C4×C8×C61—22no—
115#95×C61—21no—
116C24×C61—21no—
117C23×D61—21no—
118C23×D61—24no—
119C23×D61—28no—
120C23×D61—42no—
121C23×D61—42no—
122C23×D61—44no—
123C23×D61C2×D411yescharacteristic
124C2×D4×C61—21no—
125C2×D4×C61—22no—
126C2×D4×C61C22×C414yes—
127C2×D4×C61C22×C412yes—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—24no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—28no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—24no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146D4×D61—28no—
147D4×D61—216no—
148D4×D61C42116yescomplemented
149C2×D244—21no—
150C2×D244—22no—
151C2×D244C22×C414yes—
152C2×D244C22×C412yes—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—24no—
156C2×C4×D61—24no—
157C2×C4×D61—24no—
158C2×C4×D61—432no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C414yes—
167C2×C4×D61C22⋊C414yes—
168C2×C4×D61C22×C412yes—
169C2×C4×D61C22×C414yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61#4114yes—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61C22×C414yescomplemented
175C4⋊C4×C61—21no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61C22×C412yes—
178C4⋊C4×C61C22×C414yescomplemented
179C22⋊C4×C61—24no—
180C42×C61—42no—
181C42×C61C22×C412yes—
182C42×C61C2×D412yes—
183C22⋊Dic61—24no—
184#11758198—28no—
185#11758198—24no—
186#11758198—24no—
187C4⋊Dic61—21no—
188C4⋊Dic61—22no—
189C4⋊Dic61C22×C412yes—
190C4⋊Dic61C22×C414yescomplemented
191#11758196—24no—
192C4×Dic61—28no—
193C4×Dic61—44no—
194C4×Dic61—42no—
195C4×Dic61C22⋊C414yes—
196C4×Dic61C22⋊C414yes—
197C4×Dic61C22×C412yes—
198C4×Dic61C2×D412yes—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418C22×C414yescomplemented
202#11758189—216no—
203C23×C61—22no—
204C23×C61—24no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—42no—
208C23×C61C22×D411yescharacteristic
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—216no—
215C22×D61—48no—
216C22×D61—48no—
217C22×D61—416no—
218C22×D61—416no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—42no—
222C22×D61C2×C22⋊C412yes—
223C22×D61C4×D414yes—
224D4×C61—22no—
225D4×C61—24no—
226D4×C61C2×C4214yes—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—42no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—42no—
234C2×C4×C61—48no—
235C2×C4×C61C2×C22⋊C412yes—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61AGL(1,ℤ/8)12yes—
238C2×C4×C61AGL(1,ℤ/8)12yes—
239C2×C4×C61C23×C411yescharacteristic
240C2×C4×C61C23×C412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4112yes—
243C22⋊D61—216no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—48no—
250C2×Dic61—42no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—42no—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C4×D414yes—
258D244—22no—
259D244—24no—
260D244C2×C4214yes—
261C4×D61—28no—
262C4×D61—44no—
263C4×D61—48no—
264C4×D61—48no—
265C4×D61—48no—
266C4×D61C2×C4214yes—
267C4×D61#11714yes—
268C4×D61C4×D418yes—
269C8×C61—24no—
270#92418—24no—
271C4×#418—611nomaximal, Sylow
272C22×C61—24no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61C22×C22⋊C411yescharacteristic
278C22×C61C2×C4×D412yes—
279C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C61#57512yes—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—24no—
285C2×D61—24no—
286C2×D61—24no—
287C2×D61—432no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—44no—
291C2×D61—44no—
292C2×D61C4×C22⋊C414yes—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61#41814yescomplemented
297C4×C61C22×C4211yescharacteristic
298C4×C61C2×#11711yescharacteristic
299C4×C61C2×C4×D412yes—
300Dic61—22no—
301Dic61—22no—
302Dic61—42no—
303Dic61—44no—
304Dic61C4×C22⋊C414yes—
305C22×C4×D4—611no—
306C2×#418—612no—
307C2×C4×M16—611no—
308C4×#117—611no—
309#1762—612no—
310#1762—612no—
311C4×#102—611no—
312C4×#102—611no—
313C4×#102—611no—
314C4×#102D6111yescharacteristic, complemented
315#1736—612no—
316C2×C61—44no—
317C2×C61C2×C4×C22⋊C411yescharacteristic
318C2×C61C2×#41811yescharacteristic
319C2×C61#289611yescharacteristic
320C2×C61C4×AGL(1,ℤ/8)12yes—
321C2×C61C4×AGL(1,ℤ/8)12yes—
322D61—24no—
323D61—44no—
324C23×D4—611no—
325C24×C4—1221no—
326C22×M16—612no—
327C2×C4×D4—611no—
328C2×C4×D4—618no—
329C2×C4×D4—611no—
330C2×C4×D4—611no—
331C2×C4×D4—1221no—
332C2×C4×D4—1224no—
333C2×C4×D4—1221no—
334C2×C4×D4C2×D6111yescharacteristic
335C2×#117—612no—
336C22×C4⋊C4—611no—
337C22×C22⋊C4—1221no—
338C22×C42—611no—
339#418—6116no—
340C2×#102—612no—
341C2×#102—612no—
342C2×#102—612no—
343C2×#102C2×D6112yes—
344C4×M16—1224no—
345C2×#97—612no—
346C2×C4×C8—611no—
347C2×C4×C8C2×D6111yescharacteristic, complemented
348C4×C4⋊C4—612no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4C2×D6111yescharacteristic, complemented
351C4×C22⋊C4—1221no—
352C4×C22⋊C4—1221no—
353#376—1221no—
354C43—1221no—
355#340—612no—
356#340—612no—
357#340—612no—
358#340C2×D6112yescomplemented
359C61C4×#41811yescharacteristic, complemented, Sylow
360C25—1221no—
361C22×D4—614no—
362C22×D4—618no—
363C22×D4—611no—
364C22×D4—1222no—
365C22×D4—1224no—
366C22×D4—1221no—
367C22×D4C22×D6111yescharacteristic
368C23×C4—21no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1228no—
374C23×C4—1221no—
375C23×C4—1221no—
376C23×C4—1221no—
377C23×C4—2444no—
378C23×C4—2444no—
379C2×M16—618no—
380C2×M16—1224no—
381C2×M16—1224no—
382C22×C8—612no—
383C22×C8C22×D6112yes—
384C4×D4—22no—
385C4×D4—614no—
386C4×D4—614no—
387C4×D4—614no—
388C4×D4—1228no—
389C4×D4—1222no—
390C4×D4—1228no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4C4×D6114yes—
394#117—618no—
395#117—1224no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—614no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—1228no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1222no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C42—21no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—614no—
414C2×C42—614no—
415C2×C42—1222no—
416C2×C42—1222no—
417C2×C42—1221no—
418C2×C42C22×D6111yescharacteristic
419#102—618no—
420#102—618no—
421#102—618no—
422#102C4×D6118yescomplemented
423#97—1224no—
424C4×C8—22no—
425C4×C8—1222no—
426#95—21no—
427#95—1222no—
428#95—1221no—
429C24—21no—
430C24—611no—
431C24—1224no—
432C24—1228no—
433C24—1221no—
434C24—2442no—
435C24—2442no—
436C24—2444no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—6116no—
440C2×D4—614no—
441C2×D4—612no—
442C2×D4—1228no—
443C2×D4—12216no—
444C2×D4—1224no—
445C2×D4—1228no—
446C2×D4—1221no—
447C2×D4—1222no—
448C2×D4C2×C4×D6114yes—
449C2×D4C2×C4×D6112yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—614no—
458C22×C4—612no—
459C22×C4—614no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—614no—
463C22×C4—614no—
464C22×C4—1224no—
465C22×C4—1224no—
466C22×C4—1224no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1221no—
471C22×C4—1224no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—24432no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4D4×D6111yescharacteristic
483C22×C4D4×D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485M16—12216no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—614no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8C2×C4×D6114yescomplemented
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—614no—
495C4⋊C4—612no—
496C4⋊C4—1224no—
497C4⋊C4—1221no—
498C4⋊C4—1222no—
499C4⋊C4C2×C4×D6112yes—
500C4⋊C4C2×C4×D6114yescomplemented
501C22⋊C4—24no—
502C22⋊C4—1224no—
503C22⋊C4—1228no—
504C22⋊C4—1224no—
505C22⋊C4—1224no—
506C42—42no—
507C42—612no—
508C42—612no—
509C42—614no—
510C42—614no—
511C42—1228no—
512C42—2444no—
513C42—2442no—
514C42C2×C4×D6112yes—
515C42D4×D6112yes—
516C23—22no—
517C23—24no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—612no—
522C23—614no—
523C23—12216no—
524C23—1221no—
525C23—1221no—
526C23—1222no—
527C23—1222no—
528C23—1224no—
529C23—2448no—
530C23—24416no—
531C23—24416no—
532C23—2448no—
533C23—2441no—
534C23—2441no—
535C23—2442no—
536C23C2×D4×D6111yescharacteristic
537D4—22no—
538D4—24no—
539D4—614no—
540D4—12216no—
541D4—1222no—
542D4—1224no—
543D4C42×D6114yes—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—48no—
552C2×C4—612no—
553C2×C4—614no—
554C2×C4—614no—
555C2×C4—614no—
556C2×C4—618no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1222no—
562C2×C4—1228no—
563C2×C4—1222no—
564C2×C4—1224no—
565C2×C4—2444no—
566C2×C4—2448no—
567C2×C4—2448no—
568C2×C4—2448no—
569C2×C4—2441no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2448no—
574C2×C4C22⋊C4×D6112yes—
575C2×C4C22⋊C4×D6112yes—
576C2×C4#1451980112yes—
577C2×C4#1451980412yes—
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C22×C4×D6112yes—
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4#41×D6112yes—
582C8—24no—
583C8—1224no—
584C22—24no—
585C22—44no—
586C22—44no—
587C22—42no—
588C22—42no—
589C22—614no—
590C22—1224no—
591C22—1224no—
592C22—1222no—
593C22—1222no—
594C22—1224no—
595C22—24432no—
596C22—2444no—
597C22—2444no—
598C22—2442no—
599C22—2442no—
600C22C2×C22⋊C4×D6111yescharacteristic
601C22C4×D4×D6112yes—
602C22C2×#1451980111yescharacteristic
603C22C2×#1451980411yescharacteristic
604C22#1684055912yes—
605C4—22no—
606C4—44no—
607C4—42no—
608C4—614no—
609C4—1222no—
610C4—1222no—
611C4—2444no—
612C4—2442no—
613C4#1683976514yesdirect product factor
614C4C2×C42×D6111yescharacteristic
615C4#117×D6111yescharacteristic
616C4C4×D4×D6112yes—
617C2—44no—
618C2—1224no—
619C2—2444no—
620C2C4×C22⋊C4×D6111yescharacteristic
621C2C2×#1683976511yescharacteristic
622C2#2145433411yescharacteristic
623C2C4×#1451980112yes—
624C2C4×#1451980412yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61C4×#418
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758189C2semidirect
4. C4×#14519735C2semidirect
5. #21445646C2semidirect
6. #21445643C2semidirect
7. C4×#14519697C2semidirect
8. C4×#14519699C2semidirect
9. C4×#14519698C2semidirect
10. #21445537C2semidirect
11. C4×#102×C61C2semidirect
21. C4×D4×D61C4semidirect
26. #16839765C4direct (N × H)
31. C2×#14519687C22semidirect
32. C2×C4×#92418C22semidirect
33. C4⋊C4×Dic61C22semidirect
34. C4×C4⋊Dic61C22semidirect
39. #16839525C22semidirect
40. #16839524C22semidirect
41. #16839524C22semidirect
44. C2×C4×C8×C61C22semidirect
45. C4×C4⋊C4×C61C22semidirect
46. C61×#340C22semidirect
66. C2×#11758189C2×C4semidirect
77. #14519735C2×C4semidirect
96. #14519699C2×C4semidirect
97. #14519698C2×C4semidirect
98. #14519697C2×C4semidirect
113. #102×C61C2×C4semidirect
148. D4×D61C42semidirect
174. C2×C8×C61C22×C4semidirect
178. C4⋊C4×C61C22×C4semidirect
190. C4⋊Dic61C22×C4semidirect
201. C2×#92418C22×C4semidirect
296. C4×C61#418semidirect
314. C4×#102D61semidirect
347. C2×C4×C8C2×D61semidirect
350. C4×C4⋊C4C2×D61semidirect
358. #340C2×D61semidirect
359. C61C4×#418semidirect
422. #102C4×D61semidirect
491. C2×C8C2×C4×D61semidirect
500. C4⋊C4C2×C4×D61semidirect
613. C4#16839765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#168397652
C2×C4×#117581892
C4×#145197352
#214456462
#214456432
C4×#145196972
C4×#145196992
C4×#145196982
#214455372
C4×#102×C612
C4×#41861