Finite Group Databasebeta

← C4×#16840120 #29688071

Subgroups — C4×#16840120 #29688071

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×#16840120C211yesmaximal, characteristic
2C4×#14519776C211yesmaximal, characteristic, complemented
3C4×#14519764C211yesmaximal, characteristic
4#21446790C211yesmaximal, characteristic, complemented
5#21446634C211yesmaximal, characteristic
6#21446518C211yesmaximal, characteristic
7#21446513C211yesmaximal, characteristic
8#21446510C211yesmaximal, characteristic, complemented
9#21446507C211yesmaximal, characteristic, complemented
10#21445951C211yesmaximal, characteristic, complemented
11C4×#14519700C211yesmaximal, characteristic, complemented
12C4×#14519702C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic
14C4×#14519687C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519764C2211yescharacteristic
18C2×C4×Dic122—21no—
19C2×C4×Dic122C2211yescharacteristic
20#16840120C418yesdirect product factor
21C2×#14519702C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839667C2211yescharacteristic
33#16839666—21no—
34#16839665C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839659—21no—
37#16839658C2211yescharacteristic
38#16839656—21no—
39#16839656—21no—
40#16839631C2211yescharacteristic
41#16839627C2211yescharacteristic
42C4×#11758196—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×C22⋊Dic61—21no—
45C4×C22⋊Dic61—21no—
46C42×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×Dic122—21no—
61C22×Dic122C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519776—22no—
65#14519776C2×C414yescomplemented
66#14519764—22no—
67#14519764C2×C414yes—
68C4×Dic122—22no—
69C4×Dic122—22no—
70C4×Dic122—44no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519702—22no—
93#14519702C2×C414yescomplemented
94#14519700—22no—
95#14519700C2×C414yescomplemented
96#14519698—22no—
97#14519698C2×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×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#102×C61—22no—
123#102×C61C2×C414yes—
124C4×C8×C61—22no—
125#95×C61—21no—
126C24×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—42no—
137C22×C4×C61—42no—
138C22×C4×C61—42no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—24no—
156C2×Dic122—42no—
157C2×Dic122—42no—
158C2×Dic122C22×C412yes—
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×C61C22×C412yes—
171C22⋊C4×C61—42no—
172C42×C61—42no—
173C42×C61#4112yes—
174C42×C61#4112yes—
175C22⋊Dic61—24no—
176C22⋊Dic61—24no—
177C22⋊Dic61—42no—
178C22⋊Dic61—42no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—42no—
185C4⋊Dic61C22×C412yes—
186#11758196—24no—
187#11758196—42no—
188#11758196—42no—
189#11758196—42no—
190#11758196—42no—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196C4×Dic61—41no—
197C4×Dic61—42no—
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×C61—22no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61C22×D411yescharacteristic
215D4×C61—22no—
216D4×C61—22no—
217D4×C61—41no—
218D4×C61—41no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
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—84no—
231C2×C4×C61#12412yes—
232C2×C4×C61#12412yes—
233C2×C4×C61AGL(1,ℤ/8)12yes—
234C2×C4×C61#13712yes—
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—41no—
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×Dic61—41no—
263C2×Dic61C4×D412yes—
264C2×Dic61C4×D412yes—
265Dic122—22no—
266Dic122—22no—
267Dic122—48no—
268Dic122—41no—
269Dic122—41no—
270C8×C61—22no—
271C8×C61—22no—
272#92418—22no—
273#92418—22no—
274C4×#489—611nomaximal, Sylow
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61C2×C4×D411yescharacteristic
283C22×C61C2×#12411yescharacteristic
284C22×C61#53211yescharacteristic
285C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C61C2×#13711yescharacteristic
287C22×C61#57511yescharacteristic
288C22×C61#57511yescharacteristic
289C4×C61—22no—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61#48914yescomplemented
294C4×C61C4×#4111yescharacteristic
295C4×C61C4×#4111yescharacteristic
296C4×C61#52911yescharacteristic
297C4×C61#52911yescharacteristic
298Dic61—22no—
299Dic61—22no—
300Dic61—41no—
301Dic61—41no—
302Dic61—42no—
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×#103—611no—
318C4×#102—611no—
319C4×#102D6111yescharacteristic
320C4×#97—611no—
321C2×C61—82no—
322C2×C61C4×#12411yescharacteristic
323C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
324C2×C61C4×#13711yescharacteristic
325C2×C61C2×#48911yescharacteristic
326C2×C61#313511yescharacteristic
327C2×C61#317111yescharacteristic
328C2×C61#317211yescharacteristic
329C2×C4⋊Q8—611no—
330C2×#124—611no—
331C2×C4×Q8—611no—
332C2×C4×Q8—1221no—
333C2×C4×D4C2×D6111yescharacteristic
334#489—618no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#103—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102C2×D6111yescharacteristic
342C2×#102C2×D6111yescharacteristic
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—611no—
375C22×Q8—1221no—
376C22×D4C22×D6111yescharacteristic
377C23×C4—21no—
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—1222no—
387C4×Q8—1222no—
388C4×Q8—2444no—
389C4×D4—22no—
390C4×D4—22no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—1221no—
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—21no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C42—21no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42C22×D6111yescharacteristic
418#103—614no—
419#103—614no—
420#103—1222no—
421#103—1222no—
422#102—22no—
423#102—614no—
424#102—1222no—
425#102C4×D6114yes—
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—21no—
441C2×Q8—612no—
442C2×Q8—1224no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—2442no—
449C2×Q8—2442no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4C2×C4×D6112yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
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—612no—
491C4⋊C4—1224no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—2442no—
498C4⋊C4—2442no—
499C4⋊C4—2442no—
500C4⋊C4—2442no—
501C4⋊C4—2442no—
502C4⋊C4C2×C4×D6112yes—
503C22⋊C4—42no—
504C22⋊C4—1224no—
505C22⋊C4—1224no—
506C22⋊C4—2442no—
507C22⋊C4—2442no—
508C42—42no—
509C42—612no—
510C42—612no—
511C42—1221no—
512C42—1221no—
513C42—1222no—
514C42—1222no—
515C42—2441no—
516C42—2441no—
517C42—2442no—
518C42—2442no—
519C42#1175822212yes—
520C42#1175822412yes—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D6111yescharacteristic
529Q8—1222no—
530Q8—1222no—
531Q8—2448no—
532Q8—2441no—
533Q8—2441no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—84no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—2441no—
565C2×C4—2441no—
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#1451980112yes—
577C2×C4#1451980612yes—
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—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C4×D4×D6111yescharacteristic
596C22C2×#1451976311yescharacteristic
597C22#1684030911yescharacteristic
598C22C2×#1451980111yescharacteristic
599C22C2×#1451980611yescharacteristic
600C22#1684055911yescharacteristic
601C22#1684055911yescharacteristic
602C4—22no—
603C4—42no—
604C4—81no—
605C4—81no—
606C4—1222no—
607C4—1222no—
608C4—4881no—
609C4—4881no—
610C4—2441no—
611C4—2442no—
612C4—2441no—
613C4—2442no—
614C4#1684012014yesdirect product factor
615C4C4×#1175822411yescharacteristic
616C4C4×#1175822211yescharacteristic
617C4#1684029011yescharacteristic
618C4#1684029211yescharacteristic
619C2—82no—
620C2C4×#1451976311yescharacteristic
621C2C4×#1451980111yescharacteristic
622C2C4×#1451980611yescharacteristic
623C2C2×#1684012011yescharacteristic
624C2#2145616211yescharacteristic
625C2#2145641211yescharacteristic
626C2#2145642111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61C4×#489
LCSG ▷ C2×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
2. C4×#14519776C2semidirect
4. #21446790C2semidirect
8. #21446510C2semidirect
9. #21446507C2semidirect
10. #21445951C2semidirect
11. C4×#14519700C2semidirect
12. C4×#14519702C2semidirect
14. C4×#14519687C2semidirect
20. #16840120C4direct (N × H)
65. #14519776C2×C4semidirect
93. #14519702C2×C4semidirect
95. #14519700C2×C4semidirect
101. #14519687C2×C4semidirect
293. C4×C61#489semidirect
373. C61C4×#489semidirect
614. C4#16840120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401202
C4×#145197762
C4×#145197642
#214467902
#214466342
#214465182
#214465132
#214465102
#214465072
#214459512
C4×#145197002
C4×#145197022
C4×#145196982
C4×#145196872
C4×#102×C612
C4×#48961