Finite Group Databasebeta

← C4×#16840503 #29842703

Subgroups — C4×#16840503 #29842703

Order 15616.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840503C211yesmaximal, characteristic
2#21449011C211yesmaximal, characteristic, complemented
3#21449008C211yesmaximal, characteristic, complemented
4#21448995C211yesmaximal, characteristic, complemented
5#21448974C213yesmaximal, complemented
6#21448972C213yesmaximal, complemented
7#21448966C213yesmaximal, complemented
8#21448959C213yesmaximal, complemented
9C4×#14519774C211yesmaximal, characteristic, complemented
10C4×#14519771C211yesmaximal, characteristic, complemented
11C4×#14519762C213yesmaximal, complemented
12C4×#14519752C213yesmaximal, complemented
13C4×#14519750C213yesmaximal, complemented
14C4×#14519747C213yesmaximal, complemented
15C4×#126×C61C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17#16840503C4116yesdirect product factor
18C2×#14519774C2211yescharacteristic
19C2×#14519771C2211yescharacteristic
20C2×#14519762C2213yes—
21C2×#14519752C2213yes—
22C2×#14519750C2213yes—
23C2×#14519747C2213yes—
24C2×C4×D244C2213yes—
25C2×C4×D244C2213yes—
26C2×C4×D244C2213yescomplemented
27C2×C4×C22⋊D61C2213yes—
28C2×C42×D61C2213yescomplemented
29#16839664C2213yes—
30#16839664C2213yescomplemented
31#16839663C2213yes—
32#16839662C2213yes—
33#16839661C2213yescomplemented
34#16839659C2213yescomplemented
35#16839655C2213yes—
36#16839654C2213yes—
37#16839654C2213yescomplemented
38#16839653C2213yes—
39#16839652C2213yes—
40#16839651C2213yes—
41#16839651C2213yescomplemented
42#16839649C2213yescomplemented
43#16839648C2213yescomplemented
44#16839646C2213yescomplemented
45#16839640C2213yes—
46#16839640C2213yes—
47#16839640C2213yes—
48#16839640C2213yes—
49#16839640C2213yescomplemented
50#16839640C2213yescomplemented
51#16839639C2213yes—
52#16839638C2213yes—
53#16839637C2213yes—
54#16839636C2213yes—
55#16839636C2213yes—
56#16839633C2213yescomplemented
57#16839632C2211yescharacteristic, complemented
58#16839630C2211yescharacteristic, complemented
59#16839624C2213yescomplemented
60#16839621C2213yescomplemented
61#16839619C2213yescomplemented
62#16839617C2213yes—
63C4×#11758196C2213yescomplemented
64C4×#11758198C2213yes—
65C4×#11758198C2213yes—
66C4×#11758198C2213yescomplemented
67C2×#126×C61C2211yescharacteristic
68C61×#388C2213yes—
69C61×#387C2213yescomplemented
70C61×#383C2211yescharacteristic, complemented
71C4×C4⋊C4×C61C2213yescomplemented
72C4×C22⋊C4×C61C2213yes—
73C43×C61C2211yescharacteristic, complemented
74C24×D61C2311yescharacteristic
75C22×D244C2313yes—
76C22×D244C2313yes—
77C22×D244C2313yes—
78C22×C22⋊D61C2313yes—
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—46no—
81C22×C4×D61C2313yes—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2313yes—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2313yes—
88#14519774C2×C418yescomplemented
89#14519771C2×C418yescomplemented
90#14519762C2×C4124yescomplemented
91#14519752C2×C4124yescomplemented
92#14519750C2×C4124yescomplemented
93#14519747C2×C4124yescomplemented
94C4×D244—46no—
95C4×D244—46no—
96C4×D244—46no—
97C4×C22⋊D61—46no—
98C2×C4⋊Dic61C2313yes—
99C2×C4⋊Dic61C2313yes—
100C2×C4⋊Dic61C2313yes—
101C2×#11758196C2313yes—
102C2×#11758196C2313yes—
103C2×#11758196C2313yes—
104C2×C22⋊Dic61C2313yes—
105C2×#11758198C2313yes—
106C2×#11758198C2313yes—
107C2×#11758198C2313yes—
108C2×#11758198C2313yes—
109C2×#11758198C2313yes—
110C2×#11758198C2313yes—
111C2×#11758198C2313yes—
112C2×#11758198C2313yes—
113C2×#11758198C2313yes—
114C2×#11758198C2313yes—
115C2×#11758198C2313yes—
116C2×#11758198C2313yes—
117C2×#11758198C2313yes—
118C2×C4×Dic61C2313yes—
119C2×C4×Dic61C2313yes—
120C2×C4×Dic61C2313yes—
121C42×D61—46no—
122#14519684C2313yes—
123#14519684C2313yes—
124#14519684C2313yes—
125#14519684C2313yes—
126#14519684C2313yes—
127#14519684C2313yes—
128#14519684C2313yes—
129#14519684C2313yes—
130C23×C4×C61C2311yescharacteristic
131#126×C61C2×C418yescomplemented
132C2×C4⋊C4×C61C2313yes—
133C2×C4⋊C4×C61C2313yes—
134C2×C22⋊C4×C61C2313yes—
135C2×C22⋊C4×C61C2313yes—
136C2×C42×C61C2313yes—
137C2×C42×C61C2313yes—
138C2×C42×C61C2313yes—
139C2×C42×C61C2311yescharacteristic
140#95×C61C2313yes—
141#95×C61C2313yes—
142#95×C61C2313yes—
143#95×C61C2313yes—
144C24×C61C2411yescharacteristic
145C23×D61—43no—
146C23×D61—43no—
147C23×D61C22×C414yes—
148C23×D61C2413yes—
149C23×D61C2411yescharacteristic
150C23×D61C2411yescharacteristic
151C22×C4×C61—26no—
152C22×C4×C61C2411yescharacteristic
153C22×C4×C61C2413yes—
154C22×C4×C61C2413yes—
155C22×C4×C61C2413yes—
156C22×C4×C61C2413yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—43no—
159C2×C22⋊D61—43no—
160C2×C22⋊D61C22×C4112yes—
161C22×Dic61—43no—
162C22×Dic61C2411yescharacteristic
163C22×Dic61C2411yescharacteristic
164C22×Dic61C2413yes—
165C22×Dic61C2413yes—
166C22×Dic61C2413yes—
167C2×D244—43no—
168C2×D244—43no—
169C2×D244—43no—
170C2×D244—43no—
171C2×D244—43no—
172C2×D244—43no—
173C2×D244C22×C4112yes—
174C2×D244C22×C4112yes—
175C2×D244C22×C4112yescomplemented
176C2×C4×D61—26no—
177C2×C4×D61—26no—
178C2×C4×D61—26no—
179C2×C4×D61—26no—
180C2×C4×D61—26no—
181C2×C4×D61—43no—
182C2×C4×D61—43no—
183C2×C4×D61—43no—
184C2×C4×D61—43no—
185C2×C4×D61—43no—
186C2×C4×D61—43no—
187C2×C4×D61—43no—
188C2×C4×D61—416no—
189C2×C4×D61C22×C4112yescomplemented
190C4⋊C4×C61—43no—
191C4⋊C4×C61C22×C4112yescomplemented
192C22⋊C4×C61—43no—
193C22⋊C4×C61C22×C4112yes—
194C42×C61—26no—
195C42×C61—26no—
196C42×C61—43no—
197C42×C61C22×C414yescomplemented
198C22⋊Dic61—43no—
199#11758198—43no—
200#11758198—43no—
201#11758198—43no—
202#11758198—43no—
203#11758198—43no—
204#11758198—43no—
205#11758198—43no—
206#11758198—43no—
207#11758198—43no—
208#11758198—43no—
209#11758198C22×C4112yes—
210#11758198C22×C4112yes—
211#11758198C22×C4112yescomplemented
212C4⋊Dic61—43no—
213C4⋊Dic61—43no—
214C4⋊Dic61—43no—
215#11758196—43no—
216#11758196—43no—
217#11758196C22×C4112yescomplemented
218C4×Dic61—26no—
219C4×Dic61—43no—
220C4×Dic61—43no—
221C23×C61—23no—
222C23×C61—23no—
223C23×C61C23×C412yes—
224C23×C61C2511yescharacteristic
225C22×D61—23no—
226C22×D61—23no—
227C22×D61—23no—
228C22×D61—23no—
229C22×D61—23no—
230C22×D61—23no—
231C22×D61—23no—
232C22×D61—23no—
233C22×D61—23no—
234C22×D61—23no—
235C22×D61—412no—
236C22×D61—44no—
237C22×D61—412no—
238C22×D61C23×C412yes—
239C22×D61C23×C412yes—
240C22×D61C23×C416yes—
241C2×C4×C61—23no—
242C2×C4×C61—23no—
243C2×C4×C61—23no—
244C2×C4×C61—23no—
245C2×C4×C61—23no—
246C2×C4×C61—23no—
247C2×C4×C61—23no—
248C2×C4×C61—23no—
249C2×C4×C61—23no—
250C2×C4×C61—23no—
251C2×C4×C61—23no—
252C2×C4×C61—44no—
253C2×C4×C61C23×C416yes—
254C2×C4×C61C23×C416yes—
255C2×C4×C61H(5,𝔽2)16yes—
256C22⋊D61—412no—
257C2×Dic61—23no—
258C2×Dic61—23no—
259C2×Dic61—23no—
260C2×Dic61—23no—
261C2×Dic61—23no—
262C2×Dic61—23no—
263C2×Dic61—23no—
264C2×Dic61—23no—
265C2×Dic61—23no—
266C2×Dic61—23no—
267C2×Dic61—44no—
268C2×Dic61C23×C416yes—
269D244—412no—
270D244—412no—
271D244—412no—
272C4×D61—412no—
273C4×D61—412no—
274C4×D61—44no—
275C4×D61—44no—
276C4×D61—412no—
277C4×D61—44no—
278C4×D61—44no—
279C4×#560—611nomaximal, Sylow
280C22×C61—26no—
281C22×C61—41no—
282C22×C61—43no—
283C22×C61C24×C411yescharacteristic
284C22×C61C2×H(5,𝔽2)13yes—
285C22×C61#58513yes—
286C2×D61—26no—
287C2×D61—26no—
288C2×D61—26no—
289C2×D61—26no—
290C2×D61—26no—
291C2×D61—416no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—43no—
295C2×D61—43no—
296C2×D61—43no—
297C2×D61—43no—
298C2×D61—43no—
299C2×D61—43no—
300C4×C61—26no—
301C4×C61—26no—
302C4×C61—41no—
303C4×C61—43no—
304C4×C61—43no—
305C4×C61#56014yescomplemented
306Dic61—26no—
307Dic61—41no—
308Dic61—41no—
309Dic61—43no—
310Dic61—43no—
311C2×#560—611no—
312#2383—611no—
313#2383—611no—
314#2380—611no—
315#2377—613no—
316#2377—613no—
317#2376—613no—
318#2375—613no—
319C4×#127—611no—
320C4×#126—611no—
321C4×#126D6111yescharacteristic, complemented
322C4×#123—613no—
323C4×#121—613no—
324C4×#121—613no—
325C4×#120—613no—
326C2×C61—42no—
327C2×C61C4×H(5,𝔽2)13yes—
328C2×C61C2×#56011yescharacteristic
329C2×C61#352913yes—
330D61—46no—
331D61—42no—
332D61—42no—
333C24×C4—611no—
334#560—6116no—
335C2×#127—611no—
336C2×#126—611no—
337C2×#126C2×D6111yescharacteristic
338C2×#123—613no—
339C2×#121—613no—
340C2×#121—613no—
341C2×#120—613no—
342C2×C4×D4—613no—
343C2×C4×D4—613no—
344C2×C4×D4—613no—
345C2×C4×D4—613no—
346C22×C42—613no—
347#390—613no—
348#390—613no—
349#390—613no—
350#390—613no—
351#389—613no—
352#389—613no—
353#388—613no—
354#388—613no—
355#388—613no—
356#388—613no—
357#388—613no—
358#388—613no—
359#388—613no—
360#388C2×D6113yes—
361#387—613no—
362#387—613no—
363#387—613no—
364#387C2×D6113yescomplemented
365#386—613no—
366#386—613no—
367#386—613no—
368#386—613no—
369#386—613no—
370#386—613no—
371#386—613no—
372#386—613no—
373#385—613no—
374#385—613no—
375#385—613no—
376#385—613no—
377#384—611no—
378#383—611no—
379#383C2×D6111yescharacteristic, complemented
380#381—613no—
381#380—613no—
382#380—613no—
383#379—613no—
384C4×C4⋊C4—613no—
385C4×C4⋊C4C2×D6113yescomplemented
386C4×C22⋊C4—613no—
387C4×C22⋊C4—613no—
388C4×C22⋊C4—613no—
389C4×C22⋊C4C2×D6113yes—
390C43C2×D6111yescharacteristic, complemented
391C61C4×#56011yescharacteristic, complemented, Sylow
392C25—611no—
393C22×D4—613no—
394C22×D4—613no—
395C22×D4—613no—
396C22×D4—613no—
397C23×C4—613no—
398C23×C4—611no—
399C23×C4—613no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—613no—
405C23×C4—2446no—
406C23×C4C22×D6111yescharacteristic
407#127—618no—
408#126—618no—
409#126C4×D6118yescomplemented
410#123—6124no—
411#121—6124no—
412#121—6124no—
413#120—6124no—
414C4×D4—2446no—
415C4×D4—2446no—
416C4×D4—2446no—
417C4×D4—2446no—
418C2×C4⋊C4—613no—
419C2×C4⋊C4—613no—
420C2×C4⋊C4—613no—
421C2×C4⋊C4—613no—
422C2×C4⋊C4—613no—
423C2×C4⋊C4—613no—
424C2×C4⋊C4C22×D6113yes—
425C2×C4⋊C4C22×D6113yes—
426C2×C22⋊C4—613no—
427C2×C22⋊C4—613no—
428C2×C22⋊C4—613no—
429C2×C22⋊C4—613no—
430C2×C22⋊C4—613no—
431C2×C22⋊C4—613no—
432C2×C22⋊C4—613no—
433C2×C22⋊C4—613no—
434C2×C22⋊C4—613no—
435C2×C22⋊C4—613no—
436C2×C22⋊C4—613no—
437C2×C22⋊C4—613no—
438C2×C22⋊C4—613no—
439C2×C22⋊C4—613no—
440C2×C22⋊C4C22×D6113yes—
441C2×C22⋊C4C22×D6113yes—
442C2×C42—613no—
443C2×C42—613no—
444C2×C42—613no—
445C2×C42—2446no—
446C2×C42C22×D6113yes—
447C2×C42C22×D6113yes—
448C2×C42C22×D6113yes—
449C2×C42C22×D6111yescharacteristic
450#95—613no—
451#95—613no—
452#95—613no—
453#95—613no—
454#95—613no—
455#95—613no—
456#95—613no—
457#95—613no—
458#95C22×D6113yes—
459#95C22×D6113yes—
460#95C22×D6113yes—
461#95C22×D6113yes—
462C24—611no—
463C24—611no—
464C24—613no—
465C24—614no—
466C24—2443no—
467C24—2443no—
468C24C23×D6111yescharacteristic
469C2×D4—6112no—
470C2×D4—6112no—
471C2×D4—6112no—
472C2×D4—6112no—
473C2×D4—2443no—
474C2×D4—2443no—
475C2×D4—2443no—
476C2×D4—2443no—
477C2×D4—2443no—
478C2×D4—2443no—
479C2×D4—2443no—
480C2×D4—2443no—
481C22×C4—26no—
482C22×C4—613no—
483C22×C4—6112no—
484C22×C4—613no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—613no—
488C22×C4—1226no—
489C22×C4—1226no—
490C22×C4—1226no—
491C22×C4—1226no—
492C22×C4—1226no—
493C22×C4—2443no—
494C22×C4—2443no—
495C22×C4—2443no—
496C22×C4—2443no—
497C22×C4—2443no—
498C22×C4—2443no—
499C22×C4—2443no—
500C22×C4—24416no—
501C22×C4—2443no—
502C22×C4C23×D6113yes—
503C22×C4C23×D6113yes—
504C22×C4C23×D6111yescharacteristic
505C22×C4C23×D6113yes—
506C22×C4C23×D6113yes—
507C22×C4C23×D6111yescharacteristic
508C4⋊C4—43no—
509C4⋊C4—6112no—
510C4⋊C4—2443no—
511C4⋊C4—2443no—
512C4⋊C4—2443no—
513C4⋊C4—2443no—
514C4⋊C4—2443no—
515C4⋊C4C2×C4×D61112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—6112no—
518C22⋊C4—6112no—
519C22⋊C4—6112no—
520C22⋊C4—2443no—
521C22⋊C4—2443no—
522C22⋊C4—2443no—
523C22⋊C4—2443no—
524C22⋊C4—2443no—
525C22⋊C4—2443no—
526C22⋊C4—2443no—
527C22⋊C4—2443no—
528C22⋊C4—2443no—
529C22⋊C4—2443no—
530C22⋊C4—2443no—
531C22⋊C4C2×C4×D61112yes—
532C42—26no—
533C42—26no—
534C42—43no—
535C42—1226no—
536C42—2443no—
537C42—2443no—
538C42C2×C4×D6114yescomplemented
539C23—23no—
540C23—23no—
541C23—612no—
542C23—612no—
543C23—616no—
544C23—1223no—
545C23—1223no—
546C23—1223no—
547C23—1223no—
548C23—1223no—
549C23—1223no—
550C23—1223no—
551C23—1223no—
552C23—1223no—
553C23—1223no—
554C23—24412no—
555C23—2444no—
556C23—24412no—
557C23C22×C4×D6112yes—
558C23C24×D6111yescharacteristic
559D4—24412no—
560D4—24412no—
561D4—24412no—
562D4—24412no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—44no—
575C2×C4—616no—
576C2×C4—1223no—
577C2×C4—1223no—
578C2×C4—1223no—
579C2×C4—1223no—
580C2×C4—1223no—
581C2×C4—1223no—
582C2×C4—1223no—
583C2×C4—1223no—
584C2×C4—1223no—
585C2×C4—1223no—
586C2×C4—24412no—
587C2×C4—24412no—
588C2×C4—2444no—
589C2×C4—2444no—
590C2×C4—2444no—
591C2×C4—24412no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4C22×C4×D6116yes—
595C2×C4C22×C4×D6116yes—
596C2×C4#1451982316yes—
597C22—26no—
598C22—41no—
599C22—43no—
600C22—1226no—
601C22—1226no—
602C22—1226no—
603C22—1226no—
604C22—1226no—
605C22—24416no—
606C22—2441no—
607C22—2441no—
608C22—2443no—
609C22—2443no—
610C22—2443no—
611C22—2443no—
612C22—2443no—
613C22—2443no—
614C22C23×C4×D6111yescharacteristic
615C22C2×#1451982313yes—
616C22#1684059813yes—
617C4—26no—
618C4—26no—
619C4—41no—
620C4—43no—
621C4—43no—
622C4—1226no—
623C4—2443no—
624C4—2441no—
625C4—2441no—
626C4—2443no—
627C4#1684050314yesdirect product factor
628C2—42no—
629C2—2442no—
630C2—2442no—
631C2—2446no—
632C2C4×#1451982313yes—
633C2C2×#1684050311yescharacteristic
634C2#2145995813yes—
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC4×#126×C61C2
socle, cosocleC23×C61C25
prime radicalC2×#16840503C2
hypercenterC4×#126D61
hypocenterC61C4×#560
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #21449011C2semidirect
3. #21449008C2semidirect
4. #21448995C2semidirect
5. #21448974C2semidirect
6. #21448972C2semidirect
7. #21448966C2semidirect
8. #21448959C2semidirect
9. C4×#14519774C2semidirect
10. C4×#14519771C2semidirect
11. C4×#14519762C2semidirect
12. C4×#14519752C2semidirect
13. C4×#14519750C2semidirect
14. C4×#14519747C2semidirect
15. C4×#126×C61C2semidirect
17. #16840503C4direct (N × H)
26. C2×C4×D244C22semidirect
28. C2×C42×D61C22semidirect
30. #16839664C22semidirect
33. #16839661C22semidirect
34. #16839659C22semidirect
37. #16839654C22semidirect
41. #16839651C22semidirect
42. #16839649C22semidirect
43. #16839648C22semidirect
44. #16839646C22semidirect
49. #16839640C22semidirect
50. #16839640C22semidirect
56. #16839633C22semidirect
57. #16839632C22semidirect
58. #16839630C22semidirect
59. #16839624C22semidirect
60. #16839621C22semidirect
61. #16839619C22semidirect
63. C4×#11758196C22semidirect
66. C4×#11758198C22semidirect
69. C61×#387C22semidirect
70. C61×#383C22semidirect
71. C4×C4⋊C4×C61C22semidirect
73. C43×C61C22semidirect
88. #14519774C2×C4semidirect
89. #14519771C2×C4semidirect
90. #14519762C2×C4semidirect
91. #14519752C2×C4semidirect
92. #14519750C2×C4semidirect
93. #14519747C2×C4semidirect
131. #126×C61C2×C4semidirect
175. C2×D244C22×C4semidirect
189. C2×C4×D61C22×C4semidirect
191. C4⋊C4×C61C22×C4semidirect
197. C42×C61C22×C4semidirect
211. #11758198C22×C4semidirect
217. #11758196C22×C4semidirect
305. C4×C61#560semidirect
321. C4×#126D61semidirect
364. #387C2×D61semidirect
379. #383C2×D61semidirect
385. C4×C4⋊C4C2×D61semidirect
390. C43C2×D61semidirect
391. C61C4×#560semidirect
409. #126C4×D61semidirect
515. C4⋊C4C2×C4×D61semidirect
538. C42C2×C4×D61semidirect
627. C4#16840503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405032
#214490112
#214490082
#214489952
#214489742
#214489722
#214489662
#214489592
C4×#145197742
C4×#145197712
C4×#145197622
C4×#145197522
C4×#145197502
C4×#145197472
C4×#126×C612
C4×#56061