Finite Group Databasebeta

← C4×#16840123 #29688077

Subgroups — C4×#16840123 #29688077

Order 15616.

886 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840123C211yesmaximal, characteristic
2C4×#14519776C211yesmaximal, characteristic, complemented
3C4×#14519766C211yesmaximal, characteristic
4#21446790C211yesmaximal, characteristic, complemented
5#21446632C211yesmaximal, characteristic
6#21446517C211yesmaximal, characteristic
7#21446514C211yesmaximal, characteristic
8#21446511C211yesmaximal, characteristic, complemented
9#21446506C211yesmaximal, characteristic, complemented
10#21445951C211yesmaximal, characteristic, complemented
11C4×#14519701C211yesmaximal, characteristic, complemented
12C4×#14519697C211yesmaximal, characteristic
13C4×#14519699C211yesmaximal, characteristic
14C4×#14519687C211yesmaximal, characteristic, complemented
15C4×#103×C61C211yesmaximal, characteristic, complemented
16C2×#14519776C2211yescharacteristic
17C2×#14519766C2211yescharacteristic
18C2×C4×Dic122—21no—
19C2×C4×D244C2211yescharacteristic
20#16840123C418yesdirect product factor
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839669C2211yescharacteristic
33#16839666—21no—
34#16839663C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839659—21no—
37#16839658C2211yescharacteristic
38#16839652—21no—
39#16839652—21no—
40#16839631C2211yescharacteristic
41#16839627C2211yescharacteristic
42C4×#11758196—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×#11758198—21no—
45C4×#11758198—21no—
46C42×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×Dic122—21no—
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519776—22no—
66#14519776C2×C414yescomplemented
67#14519766—22no—
68#14519766C2×C414yes—
69C4×Dic122—44no—
70C4×D244—22no—
71C4×D244—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519701—22no—
93#14519701C2×C414yescomplemented
94#14519699—22no—
95#14519699C2×C414yes—
96#14519697—22no—
97#14519697C2×C414yes—
98#14519687—22no—
99#14519687—22no—
100#14519687—22no—
101#14519687C2×C414yescomplemented
102C4×#92418—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×Q8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4×Q8×C61—22no—
114C4×Q8×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#103×C61—22no—
123#103×C61C2×C414yescomplemented
124C4×C8×C61—22no—
125#95×C61—21no—
126C23×D61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244C22×C412yes—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×Dic122—24no—
157C2×Dic122—42no—
158C2×Dic122—42no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C22×C412yes—
164C2×C8×C61#4112yes—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—42no—
171C4⋊C4×C61C22×C412yes—
172C42×C61—42no—
173C42×C61—42no—
174C42×C61#4112yes—
175C42×C61#4112yes—
176#11758198—24no—
177#11758198—24no—
178#11758198—42no—
179#11758198—42no—
180#11758198—42no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—42no—
187C4⋊Dic61C22×C412yes—
188#11758196—24no—
189#11758196—42no—
190#11758196—42no—
191#11758196—42no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—41no—
197C4×Dic61—41no—
198C4×Dic61—42no—
199C4×Dic61C22×C412yes—
200C4×Dic61#4112yes—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C22×C412yes—
206C2×#92418#4112yes—
207C23×C61C22×D411yescharacteristic
208C22×D61—22no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215Q8×C61—22no—
216Q8×C61—22no—
217Q8×C61—41no—
218Q8×C61—41no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61#12412yes—
234C2×C4×C61#12412yes—
235C2×C4×C61AGL(1,ℤ/8)12yes—
236C2×C4×C61#13712yes—
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61C4×D412yes—
263C2×Dic61C4×D412yes—
264D244—22no—
265D244—22no—
266D244—41no—
267D244—41no—
268C4×D61—84no—
269Dic122—48no—
270C8×C61—22no—
271C8×C61—22no—
272#92418—22no—
273#92418—22no—
274C4×#489—611nomaximal, Sylow
275C22×C61C2×C4×D411yescharacteristic
276C22×C61C2×#12411yescharacteristic
277C22×C61#53211yescharacteristic
278C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C61C2×#13711yescharacteristic
280C22×C61#57511yescharacteristic
281C22×C61#57511yescharacteristic
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C4×C61—22no—
290C4×C61—42no—
291C4×C61—42no—
292C4×C61—81no—
293C4×C61—81no—
294C4×C61#48914yescomplemented
295C4×C61C4×#4111yescharacteristic
296C4×C61C4×#4111yescharacteristic
297C4×C61#52911yescharacteristic
298C4×C61#52911yescharacteristic
299Dic61—22no—
300Dic61—22no—
301Dic61—41no—
302Dic61—41no—
303Dic61—42no—
304Dic61—81no—
305Dic61—81no—
306C2×#489—611no—
307C4×C4⋊Q8—611no—
308C4×#124—611no—
309#1993—611no—
310#1959—611no—
311#1936—611no—
312#1936—611no—
313#1935—611no—
314#1935—611no—
315#1836—611no—
316C4×#103—611no—
317C4×#103D6111yescharacteristic, complemented
318C4×#102—611no—
319C4×#102—611no—
320C4×#97—611no—
321C2×C61C4×#12411yescharacteristic
322C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
323C2×C61C4×#13711yescharacteristic
324C2×C61C2×#48911yescharacteristic
325C2×C61#313511yescharacteristic
326C2×C61#317111yescharacteristic
327C2×C61#317211yescharacteristic
328D61—82no—
329C2×C4⋊Q8—611no—
330C2×#124—611no—
331C2×C4×Q8—1221no—
332C2×C4×Q8C2×D6111yescharacteristic
333C2×C4×D4—611no—
334#489—618no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103C2×D6111yescharacteristic
338C2×#103C2×D6111yescharacteristic
339C2×#102—611no—
340C2×#102—611no—
341C2×#102—611no—
342C2×#102—611no—
343C2×#97—611no—
344C2×#97—611no—
345C2×#97—611no—
346C2×#97—611no—
347C2×C4×C8—611no—
348C2×C4×C8C2×D6111yescharacteristic
349#391—611no—
350#391—1221no—
351#390—611no—
352#389—611no—
353#389—611no—
354#389—1221no—
355#388—1221no—
356#388—1221no—
357#384—611no—
358#382—611no—
359C4×C4⋊C4—611no—
360C4×C4⋊C4—1221no—
361C4×C4⋊C4C2×D6111yescharacteristic
362C4×C22⋊C4—1221no—
363C4×C22⋊C4—1221no—
364C43—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340C2×D6111yescharacteristic
372#340C2×D6111yescharacteristic
373C61C4×#48911yescharacteristic, complemented, Sylow
374C22×Q8—1221no—
375C22×Q8C22×D6111yescharacteristic
376C22×D4—611no—
377C23×C4—1221no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8C22×D6111yescharacteristic
381C22×C8C22×D6111yescharacteristic
382C4⋊Q8—614no—
383C4⋊Q8—1222no—
384#124—614no—
385#124—1222no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—2444no—
389C4×D4—1222no—
390C4×D4—1222no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—1221no—
417C2×C42C22×D6111yescharacteristic
418#103—22no—
419#103—614no—
420#103—1222no—
421#103C4×D6114yescomplemented
422#102—614no—
423#102—614no—
424#102—1222no—
425#102—1222no—
426#97—614no—
427#97—1222no—
428#97—1222no—
429#97—1222no—
430C4×C8—22no—
431C4×C8—1222no—
432#95—21no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440C24—1221no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—1224no—
447C2×Q8—2442no—
448C2×Q8—2442no—
449C2×Q8C2×C4×D6112yes—
450C2×D4—612no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—612no—
478C2×C8—612no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8C2×C4×D6112yes—
484C2×C8#1175822212yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—612no—
492C4⋊C4—1224no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—2442no—
499C4⋊C4—2442no—
500C4⋊C4—2442no—
501C4⋊C4—2442no—
502C4⋊C4C2×C4×D6112yes—
503C22⋊C4—1224no—
504C22⋊C4—1224no—
505C22⋊C4—2442no—
506C22⋊C4—2442no—
507C22⋊C4—2442no—
508C42—42no—
509C42—42no—
510C42—612no—
511C42—612no—
512C42—1222no—
513C42—1221no—
514C42—1221no—
515C42—1222no—
516C42—2441no—
517C42—2441no—
518C42—2442no—
519C42#1175822212yes—
520C42#1175822412yes—
521C23—1222no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23C2×D4×D6111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—2448no—
534D4—1222no—
535D4—1222no—
536D4—2441no—
537D4—2441no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1222no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—4884no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4#1451976312yes—
575C2×C4#1451976312yes—
576C2×C4#1451980412yes—
577C2×C4#1451980912yes—
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4#41×D6111yescharacteristic
580C2×C4#41×D6111yescharacteristic
581C2×C4C2×#1175822411yescharacteristic
582C2×C4C2×#1175822211yescharacteristic
583C2×C4C2×#1175822211yescharacteristic
584C8—22no—
585C8—22no—
586C8—1222no—
587C8—1222no—
588C22—4881no—
589C22—4881no—
590C22—4881no—
591C22—4881no—
592C22—2442no—
593C22—2442no—
594C22—2442no—
595C22C4×D4×D6111yescharacteristic
596C22C2×#1451976311yescharacteristic
597C22#1684030911yescharacteristic
598C22C2×#1451980411yescharacteristic
599C22C2×#1451980911yescharacteristic
600C22#1684055911yescharacteristic
601C22#1684055911yescharacteristic
602C4—22no—
603C4—42no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—1222no—
608C4—1222no—
609C4—4881no—
610C4—4881no—
611C4—2441no—
612C4—2442no—
613C4—2441no—
614C4#1684012314yesdirect product factor
615C4C4×#1175822411yescharacteristic
616C4C4×#1175822211yescharacteristic
617C4#1684029011yescharacteristic
618C4#1684029211yescharacteristic
619C2—4882no—
620C2C4×#1451976311yescharacteristic
621C2C4×#1451980411yescharacteristic
622C2C4×#1451980911yescharacteristic
623C2C2×#1684012311yescharacteristic
624C2#2145616211yescharacteristic
625C2#2145641011yescharacteristic
626C2#2145642311yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenterC4×#103D61
hypocenterC61C4×#489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C4×#14519776C2semidirect
4. #21446790C2semidirect
8. #21446511C2semidirect
9. #21446506C2semidirect
10. #21445951C2semidirect
11. C4×#14519701C2semidirect
14. C4×#14519687C2semidirect
15. C4×#103×C61C2semidirect
20. #16840123C4direct (N × H)
66. #14519776C2×C4semidirect
93. #14519701C2×C4semidirect
101. #14519687C2×C4semidirect
123. #103×C61C2×C4semidirect
294. C4×C61#489semidirect
317. C4×#103D61semidirect
373. C61C4×#489semidirect
421. #103C4×D61semidirect
614. C4#16840123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401232
C4×#145197762
C4×#145197662
#214467902
#214466322
#214465172
#214465142
#214465112
#214465062
#214459512
C4×#145197012
C4×#145196972
C4×#145196992
C4×#145196872
C4×#103×C612
C4×#48961