Finite Group Databasebeta

← C4×#16839958 #29686191

Subgroups — C4×#16839958 #29686191

Order 15616.

1272 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839958C211yesmaximal, characteristic
2C2×C4×D488C212yesmaximal, complemented
3C4×#14519774C211yesmaximal, characteristic, complemented
4C42×D244C211yesmaximal, characteristic, complemented
5#21446745C211yesmaximal, characteristic, complemented
6#21446578C211yesmaximal, characteristic, complemented
7#21446440C212yesmaximal, complemented
8#21446166C212yesmaximal, complemented
9#21445820C211yesmaximal, characteristic, complemented
10C4×#14519699C212yesmaximal, complemented
11C4×C4⋊C8×C61C211yesmaximal, characteristic, complemented
12C22×D488C2212yes—
13C2×#14519774C2211yescharacteristic
14C2×C4×D244—21no—
15C2×C4×D244—21no—
16C2×C4×D244C2212yes—
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C42×D61—21no—
21#16839958C418yesdirect product factor
22C4×D488—28no—
23C2×#14519711C2212yes—
24C2×#14519699C2212yes—
25C2×#14519699C2212yes—
26C2×#14519699C2212yes—
27C2×#14519699C2212yes—
28#16839664—21no—
29#16839664—21no—
30#16839664C2212yes—
31#16839632C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33C4×C4⋊Dic61C2211yescharacteristic
34C4×C4⋊Dic61C2211yescharacteristic
35C4×#11758198—21no—
36C4×#11758198—21no—
37C4×#11758198—21no—
38#16839525C2212yes—
39#16839525C2212yes—
40C2×C4⋊C8×C61C2211yescharacteristic
41C2×C4⋊C8×C61C2211yescharacteristic
42C2×C4×C8×C61C2212yes—
43C43×C61C2211yescharacteristic
44C61×#336C2212yes—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244C2312yes—
48C22×D244C2311yescharacteristic
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61—22no—
53C2×D488—24no—
54C2×D488—24no—
55C2×D488C2×C418yescomplemented
56#14519774—22no—
57#14519774C2×C414yescomplemented
58C4×D244—22no—
59C4×D244—22no—
60C4×D244—22no—
61C4×D244—24no—
62C4×D244—24no—
63C4×D244—22no—
64C4×D244—44no—
65C4×D244—44no—
66C4×D244C2×C414yescomplemented
67C4×D244D414yescomplemented
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2312yes—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C42×D61—44no—
84#14519711—24no—
85#14519699—24no—
86#14519699—24no—
87#14519699—24no—
88#14519699C2×C418yescomplemented
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92C22×C8×C61C2312yes—
93C22×C8×C61C2312yes—
94C2×C42×C61D411yescharacteristic
95C2×C42×C61D411yescharacteristic
96C2×C42×C61D411yescharacteristic
97C2×C42×C61D411yescharacteristic
98C2×C42×C61C2311yescharacteristic
99C2×C42×C61C2311yescharacteristic
100C2×C42×C61C2311yescharacteristic
101C4⋊C8×C61—22no—
102C4⋊C8×C61C2×C414yescomplemented
103C4×C8×C61—24no—
104C23×D61—21no—
105C23×D61—22no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—22no—
117C2×D244—21no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—24no—
125C2×D244—24no—
126C2×D244—22no—
127C2×D244—42no—
128C2×D244—42no—
129C2×D244—42no—
130C2×D244—42no—
131C2×D244C22×C414yes—
132C2×D244C22×C412yes—
133C2×D244C2×D412yes—
134C2×D244#4112yes—
135C2×C4×D61—24no—
136C2×C4×D61—24no—
137C2×C4×D61—24no—
138C2×C4×D61—42no—
139C2×C4×D61—42no—
140C2×C4×D61—42no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C4×D61—42no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—22no—
152C2×C8×C61C22×C414yes—
153C42×C61—22no—
154C42×C61—22no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61—41no—
158C42×C61D814yescomplemented
159C42×C61C22×C412yes—
160C42×C61C2×D412yes—
161C42×C61#4112yes—
162C42×C61#4112yes—
163#11758198—24no—
164#11758198—24no—
165#11758198—24no—
166#11758198—44no—
167#11758198—44no—
168#11758198—44no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—22no—
173C4⋊Dic61—22no—
174C4⋊Dic61—42no—
175C4⋊Dic61—42no—
176C4⋊Dic61C22×C412yes—
177C4⋊Dic61C2×D412yes—
178C4⋊Dic61#4112yes—
179C4×Dic61—42no—
180C4×Dic61—42no—
181C4×Dic61—42no—
182D488—216no—
183C23×C61C22×D411yescharacteristic
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—24no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61C4×D412yes—
208C2×C4×C61C4×D412yes—
209C2×C4×C61#12112yes—
210C2×C4×C61#12112yes—
211C2×C4×C61C2×D812yes—
212C2×C4×C61C2×D812yes—
213C2×C4×C61C2×D812yes—
214C2×C4×C61#13512yes—
215C2×C4×C61AGL(1,ℤ/8)12yes—
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234D244—24no—
235D244—22no—
236D244—24no—
237D244—22no—
238D244—22no—
239D244—48no—
240D244—42no—
241D244—42no—
242D244—48no—
243D244C4×D414yescomplemented
244C4×D61—48no—
245C4×D61—48no—
246C4×D61—48no—
247C4×D61—88no—
248C8×C61—24no—
249C8×C61—42no—
250C4×#459—611nomaximal, Sylow
251C22×C61C2×C4×D411yescharacteristic
252C22×C61C2×#12111yescharacteristic
253C22×C61#52511yescharacteristic
254C22×C61C22×D811yescharacteristic
255C22×C61C2×#13511yescharacteristic
256C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C61#57511yescharacteristic
258C2×D61—24no—
259C2×D61—42no—
260C2×D61—42no—
261C2×D61—42no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—42no—
265C2×D61—44no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61—82no—
269C2×D61—82no—
270C2×D61—82no—
271C2×D61—82no—
272C4×C61—22no—
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—41no—
276C4×C61C4×D814yescomplemented
277C4×C61#45914yescomplemented
278C4×C61C2×C4×D411yescharacteristic
279C4×C61C4×#4111yescharacteristic
280C4×C61#52911yescharacteristic
281C4×C61#53211yescharacteristic
282Dic61—42no—
283Dic61—42no—
284Dic61—42no—
285Dic61—82no—
286C2×#459—611no—
287C2×C4×D8—612no—
288C4×#127—611no—
289C42×D4—611no—
290#1982—611no—
291#1947—611no—
292#1925—612no—
293#1879—612no—
294#1802—611no—
295C4×C4⋊C8D6111yescharacteristic, complemented
296C4×#102—612no—
297C2×C61C4×#12111yescharacteristic
298C2×C61C2×C4×D811yescharacteristic
299C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
300C2×C61C2×#45911yescharacteristic
301C2×C61#303511yescharacteristic
302C2×C61#310011yescharacteristic
303C2×C61#310611yescharacteristic
304D61—44no—
305D61—84no—
306C22×D8—612no—
307C2×#127—611no—
308C2×C4×D4—611no—
309C2×C4×D4—611no—
310C2×C4×D4—612no—
311C2×C4×D4—611no—
312C2×C4×D4—1221no—
313C2×C4×D4—1221no—
314C22×C42—1221no—
315#459—618no—
316C4×D8—1228no—
317C2×#107—612no—
318C2×C4⋊C8C2×D6111yescharacteristic
319C2×C4⋊C8C2×D6111yescharacteristic
320C2×#102—612no—
321C2×#102—612no—
322C2×#102—612no—
323C2×#102—612no—
324C2×C4×C8C2×D6112yes—
325#390—612no—
326#390—1221no—
327#390—1221no—
328#384—611no—
329C4×C4⋊C4—611no—
330C4×C4⋊C4—611no—
331C4×C4⋊C4—611no—
332C4×C22⋊C4—1221no—
333C4×C22⋊C4—1221no—
334C4×C22⋊C4—1221no—
335C43C2×D6111yescharacteristic
336#340—612no—
337#340—612no—
338#336C2×D6112yes—
339C61C4×#45911yescharacteristic, complemented, Sylow
340C22×D4—611no—
341C22×D4—612no—
342C22×D4—1221no—
343C22×D4—1221no—
344C23×C4—1221no—
345C23×C4—1221no—
346C23×C4—1221no—
347C23×C4—1222no—
348C2×D8—618no—
349C2×D8—1224no—
350C2×D8—1224no—
351C22×C8C22×D6112yes—
352C22×C8C22×D6112yes—
353#127—614no—
354#127—1222no—
355C4×D4—614no—
356C4×D4—614no—
357C4×D4—1222no—
358C4×D4—1222no—
359C4×D4—1222no—
360C4×D4—1224no—
361C4×D4—1222no—
362C4×D4—1224no—
363C4×D4—2444no—
364C4×D4—2444no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—612no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1221no—
371C2×C22⋊C4—1221no—
372C2×C22⋊C4—1221no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C42—1221no—
378C2×C42—1221no—
379C2×C42—1221no—
380C2×C42—2444no—
381C2×C42D24411yescharacteristic
382C2×C42D24411yescharacteristic
383C2×C42D24411yescharacteristic
384C2×C42D24411yescharacteristic
385C2×C42C22×D6111yescharacteristic
386C2×C42C22×D6111yescharacteristic
387C2×C42C22×D6111yescharacteristic
388#107—1224no—
389C4⋊C8—22no—
390C4⋊C8C4×D6114yescomplemented
391#102—618no—
392#102—1224no—
393#102—1224no—
394#102—1224no—
395C4×C8—24no—
396#95—1221no—
397#95—1221no—
398#95—1221no—
399C24—1221no—
400C24—1222no—
401C2×D4—612no—
402C2×D4—614no—
403C2×D4—612no—
404C2×D4—612no—
405C2×D4—1222no—
406C2×D4—1221no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1221no—
410C2×D4—1222no—
411C2×D4—1221no—
412C2×D4—1222no—
413C2×D4—1224no—
414C2×D4—1224no—
415C2×D4—2442no—
416C2×D4—2442no—
417C2×D4—2442no—
418C2×D4—2442no—
419C22×C4—1224no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1224no—
424C22×C4—1224no—
425C22×C4—1222no—
426C22×C4—2442no—
427C22×C4—2444no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4C2×D24411yescharacteristic
436C22×C4C2×D24411yescharacteristic
437C22×C4C2×D24411yescharacteristic
438C22×C4C2×D24411yescharacteristic
439C22×C4C2×D24411yescharacteristic
440C22×C4C2×D24411yescharacteristic
441C22×C4C23×D6111yescharacteristic
442D8—12216no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8C2×C4×D6114yes—
449C4⋊C4—612no—
450C4⋊C4—612no—
451C4⋊C4—612no—
452C4⋊C4—1221no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1222no—
456C4⋊C4—1222no—
457C4⋊C4—2442no—
458C4⋊C4—2442no—
459C22⋊C4—1224no—
460C22⋊C4—1224no—
461C22⋊C4—1224no—
462C22⋊C4—2444no—
463C22⋊C4—2444no—
464C22⋊C4—2444no—
465C42—21no—
466C42—21no—
467C42—22no—
468C42—22no—
469C42—41no—
470C42—2442no—
471C42—2442no—
472C42—2442no—
473C42D48814yescomplemented
474C42C2×C4×D6112yes—
475C42#1175822212yes—
476C42D4×D6112yes—
477C42#1175822612yes—
478C23—1222no—
479C23—1222no—
480C23—1222no—
481C23—1224no—
482C23—2442no—
483C23—2442no—
484C23—2442no—
485C23—2442no—
486C23—2442no—
487C23—2442no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23C22×D24411yescharacteristic
493D4—614no—
494D4—1224no—
495D4—1222no—
496D4—1224no—
497D4—1222no—
498D4—1222no—
499D4—2448no—
500D4—2442no—
501D4—2442no—
502D4—2448no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—4888no—
516C2×C4—2448no—
517C2×C4—2442no—
518C2×C4—2442no—
519C2×C4—2442no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2448no—
527C2×C4—2448no—
528C2×C4C4×D24412yes—
529C2×C4C4×D24412yes—
530C2×C4#1451975212yes—
531C2×C4#1451975212yes—
532C2×C4C2×D48812yes—
533C2×C4C2×D48812yes—
534C2×C4C2×D48812yes—
535C2×C4#1451979912yes—
536C2×C4#1451980512yes—
537C2×C4C22×C4×D6111yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C2×C4#41×D6111yescharacteristic
541C2×C4C2×#1175822211yescharacteristic
542C2×C4C2×#1175822611yescharacteristic
543C8—24no—
544C8—42no—
545C22—1224no—
546C22—4882no—
547C22—4882no—
548C22—4882no—
549C22—4882no—
550C22—2444no—
551C22—2444no—
552C22—2444no—
553C22—2442no—
554C22—2442no—
555C22—2442no—
556C22—2442no—
557C22—2442no—
558C22—2442no—
559C22C2×C4×D24411yescharacteristic
560C22C2×#1451975211yescharacteristic
561C22#1684027411yescharacteristic
562C22C22×D48811yescharacteristic
563C22C2×#1451979911yescharacteristic
564C22C2×#1451980511yescharacteristic
565C22#1684056211yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—41no—
570C4—4882no—
571C4—2442no—
572C4—2442no—
573C4—2442no—
574C4C4×D48814yescomplemented
575C4#1683995814yesdirect product factor
576C4C4×D4×D6111yescharacteristic
577C4C4×#1175822611yescharacteristic
578C4#1684029911yescharacteristic
579C4#1684030911yescharacteristic
580C2—4884no—
581C2—2444no—
582C2C4×#1451975211yescharacteristic
583C2C2×C4×D48811yescharacteristic
584C2C4×#1451980511yescharacteristic
585C2C2×#1683995811yescharacteristic
586C2#2145527611yescharacteristic
587C2#2145582011yescharacteristic
588C2#2145588011yescharacteristic
subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×C4⋊C8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839958C2
cosocleC22×C4×C61C24
hypercenterC4×C4⋊C8D61
hypocenterC61C4×#459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C4×D488C2semidirect
3. C4×#14519774C2semidirect
4. C42×D244C2semidirect
5. #21446745C2semidirect
6. #21446578C2semidirect
7. #21446440C2semidirect
8. #21446166C2semidirect
9. #21445820C2semidirect
10. C4×#14519699C2semidirect
11. C4×C4⋊C8×C61C2semidirect
21. #16839958C4direct (N × H)
55. C2×D488C2×C4semidirect
57. #14519774C2×C4semidirect
66. C4×D244C2×C4semidirect
67. C4×D244D4semidirect
88. #14519699C2×C4semidirect
102. C4⋊C8×C61C2×C4semidirect
158. C42×C61D8semidirect
243. D244C4×D4semidirect
276. C4×C61C4×D8semidirect
277. C4×C61#459semidirect
295. C4×C4⋊C8D61semidirect
339. C61C4×#459semidirect
390. C4⋊C8C4×D61semidirect
473. C42D488semidirect
574. C4C4×D488semidirect
575. C4#16839958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399582
C2×C4×D4882
C4×#145197742
C42×D2442
#214467452
#214465782
#214464402
#214461662
#214458202
C4×#145196992
C4×C4⋊C8×C612
C4×#45961