Finite Group Databasebeta

← C2×C4×#14519839 #30614124

Subgroups — C2×C4×#14519839 #30614124

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519839C212yesmaximal
2C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4C4×#14519839C218yesmaximal, direct product factor
5C2×#16840635C212yesmaximal, complemented
6C2×C4×D4×D61C211yesmaximal, characteristic
7C22×D61⋊C8C2212yes—
8C22×C4⋊#6923C2212yes—
9C22×C4×#6923—21no—
10C2×#14519839C4116yesdirect product factor
11C2×#14519839C2218yes—
12C4×D61⋊C8—22no—
13C4×D61⋊C8C2214yescomplemented
14C2×C4×#92420—21no—
15C2×C4×#92420—21no—
16C4×C4⋊#6923—22no—
17C4×C4⋊#6923C2214yescomplemented
18C2×(C2×#6923)⋊C4—21no—
19#16840635C2218yescomplemented
20C22×D4×D61C2211yescharacteristic
21C23×C4×D61—21no—
22C2×C4×D244C411yescharacteristic, complemented
23C2×D4×Dic61C411yescharacteristic, complemented
24C2×#14519739C411yescharacteristic, complemented
25C2×C4×C22⋊D61—21no—
26C2×#14519737—21no—
27C4×D4×D61—22no—
28C4×D4×D61—22no—
29C4×D4×D61C414yescomplemented
30C4×D4×D61C2214yes—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C22⋊C4×D61—21no—
33C2×C42×D61C2211yescharacteristic
34C2×C4×D4×C61C411yescharacteristic, complemented
35C23×#6923—22no—
36C2×D61⋊C8—22no—
37C2×D61⋊C8—24no—
38C2×D61⋊C8C2×C418yescomplemented
39C2×D61⋊C8C2314yes—
40C22×#92420—22no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—24no—
43C2×C4⋊#6923C2×C418yescomplemented
44C2×C4⋊#6923C2314yes—
45C2×C4×#6923—24no—
46C2×C4×#6923—44no—
47#14519839C2×C4132yesdirect product factor
48C4×#92420—24no—
49C4×#92420—24no—
50(C2×#6923)⋊C4—24no—
51C24×D61—21no—
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61—21no—
54C2×D4×D61—21no—
55C2×D4×D61—21no—
56C2×D4×D61—24no—
57C2×D4×D61C2×C418yes—
58C2×D4×D61C2×C412yes—
59C2×D4×D61C2312yes—
60C23×Dic61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61—44no—
67C22×C4×D61—44no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C4×D244—22no—
72C4×D244C2×C414yescomplemented
73D4×Dic61—22no—
74D4×Dic61C2×C414yescomplemented
75#14519739—22no—
76#14519739C2×C414yescomplemented
77C4×C22⋊D61—24no—
78C4×C22⋊D61—24no—
79#14519737—24no—
80#14519737—24no—
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196—21no—
83C4⋊C4×D61—21no—
84C4⋊C4×D61—21no—
85C4⋊C4×D61C2×C412yes—
86C4⋊C4×D61C2312yes—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C22⋊C4×D61—24no—
91C22⋊C4×D61—24no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C42×D61C2×C412yes—
96C42×D61D412yes—
97C42×D61D412yes—
98C42×D61C2312yes—
99C22×D4×C61C2×C411yescharacteristic
100C23×C4×C61—21no—
101C4×D4×C61—22no—
102C4×D4×C61C2×C414yescomplemented
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C42×C61C2×C411yescharacteristic
106C24×C61—21no—
107C23×D61—21no—
108C23×D61—22no—
109C23×D61—28no—
110C23×D61—22no—
111C23×D61—42no—
112C23×D61—42no—
113C23×D61—44no—
114C23×D61C2×D411yescharacteristic
115C22×#6923—28no—
116C22×#6923—24no—
117C22×#6923—44no—
118C22×#6923—44no—
119C2×D4×C61—21no—
120C2×D4×C61—22no—
121C2×D4×C61C4214yescomplemented
122C2×D4×C61C22×C412yes—
123C22×C4×C61—21no—
124C22×C4×C61—24no—
125C22×C4×C61—44no—
126C22×C4×C61C22⋊C411yescharacteristic
127C22×C4×C61C22⋊C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C2×C22⋊D61—22no—
130C2×C22⋊D61—28no—
131C2×C22⋊D61—22no—
132C22×Dic61—21no—
133C22×Dic61—24no—
134C22×Dic61—44no—
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C22⋊C411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138D4×D61—24no—
139D4×D61—28no—
140D4×D61—28no—
141D4×D61—24no—
142D4×D61C4218yescomplemented
143D4×D61C22×C418yes—
144C2×D244—21no—
145C2×D244—22no—
146C2×D244C4214yescomplemented
147C2×D244C22×C412yes—
148C2×C4×D61—24no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—44no—
156C2×C4×D61—44no—
157C2×C4×D61—416no—
158C2×C4×D61—48no—
159C2×C4×D61—48no—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22⋊C412yes—
162C2×C4×D61D814yes—
163C2×C4×D61SD1614yes—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C414yes—
166C2×C4×D61C2×D412yes—
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D412yes—
170C2×C4×D61#4114yes—
171C2×C4×D61C2411yescharacteristic
172C2×#92420—28no—
173C2×#92420—24no—
174C4⋊#6923—28no—
175C4⋊#6923—24no—
176C4⋊#6923C22×C418yescomplemented
177C4×#6923—48no—
178D61⋊C8—28no—
179D61⋊C8—24no—
180D61⋊C8C22×C418yescomplemented
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C412yes—
183C22⋊C4×C61—24no—
184C42×C61C22⋊C412yes—
185C42×C61C22×C412yes—
186C22⋊Dic61—24no—
187#11758198—24no—
188#11758198—24no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22×C412yes—
191#11758196—22no—
192#11758196—22no—
193C4×Dic61C22⋊C412yes—
194C4×Dic61C22⋊C412yes—
195C4×Dic61C22⋊C412yes—
196C4×Dic61C22×C412yes—
197C4×Dic61C2×D412yes—
198C4×Dic61C2×D412yes—
199C23×C61—22no—
200C23×C61—24no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61C2×C22⋊C411yescharacteristic
204C22×D61—22no—
205C22×D61—24no—
206C22×D61—28no—
207C22×D61—28no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—44no—
213C22×D61—44no—
214C22×D61—44no—
215C22×D61—416no—
216C22×D61—416no—
217C22×D61C2×C22⋊C411yescharacteristic
218C22×D61C4×D414yes—
219C22×D61C2×D812yes—
220C22×D61C2×SD1612yes—
221C22×D61#13514yes—
222C22×D61C22×D411yescharacteristic
223C2×#6923—28no—
224C2×#6923—44no—
225C2×#6923—44no—
226C2×#6923—416no—
227D4×C61—22no—
228D4×C61—24no—
229D4×C61C2×C4214yescomplemented
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—42no—
233C2×C4×C61—48no—
234C2×C4×C61#10214yescomplemented
235C2×C4×C61C2×C4212yes—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C412yes—
239C2×C4×C61#11712yes—
240C2×C4×C61C23×C411yescharacteristic
241C22⋊D61—28no—
242C22⋊D61—28no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—42no—
246C2×Dic61—48no—
247C2×Dic61#10214yescomplemented
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C4×D414yes—
252C2×Dic61C22×D411yescharacteristic
253D244—22no—
254D244—24no—
255D244C2×C4214yescomplemented
256C4×D61—24no—
257C4×D61—24no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—44no—
261C4×D61—48no—
262C4×D61—48no—
263C4×D61#10218yescomplemented
264C4×D61C2×C4212yes—
265C4×D61#11712yes—
266C4×D61C4×D414yes—
267C4×D61C4×D414yes—
268C4×D61C2×D814yes—
269C4×D61C2×SD1614yes—
270C4×D61C23×C412yes—
271C4×D61C2×#4112yes—
272#92420—28no—
273C2×C4×#102—611nomaximal, Sylow
274C22×C61—24no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—48no—
278C22×C61C4×C22⋊C412yes—
279C22×C61C2×#10212yes—
280C22×C61#41612yes—
281C22×C61C22×C22⋊C411yescharacteristic
282C2×D61—24no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—48no—
286C2×D61—48no—
287C2×D61—48no—
288C2×D61—416no—
289C2×D61C4×C22⋊C412yes—
290C2×D61C2×#10212yes—
291C2×D61#41612yes—
292C2×D61C4×D818yes—
293C2×D61C4×SD1618yes—
294C2×D61C2×C4×D412yes—
295C2×D61C22×D811yescharacteristic
296C2×D61C22×SD1611yescharacteristic
297C2×D61C2×#13512yes—
298#6923—48no—
299C4×C61—22no—
300C4×C61—42no—
301C4×C61C4×C22⋊C412yes—
302C4×C61C2×#10214yescomplemented
303C4×C61C22×C4211yescharacteristic
304C4×C61C2×#11711yescharacteristic
305Dic61—22no—
306Dic61—42no—
307Dic61C4×C22⋊C412yes—
308Dic61C2×#10214yescomplemented
309Dic61C2×C4×D412yes—
310C22×C4×D4—611no—
311C22×#102—612no—
312C22×C4×C8—611no—
313C2×C4×C4⋊C4—611no—
314C4×#102—618no—
315C2×#340—612no—
316C2×C61—44no—
317C2×C61C4×#10214yescomplemented
318C2×C61C2×C4×C22⋊C411yescharacteristic
319C2×C61C22×#10211yescharacteristic
320C2×C61C2×#41611yescharacteristic
321D61—44no—
322D61C4×#10214yescomplemented
323D61C2×C4×D812yes—
324D61C2×C4×SD1612yes—
325C23×D4—611no—
326C24×C4—1221no—
327C23×C8—612no—
328C2×C4×D4—611no—
329C2×C4×D4—614no—
330C2×C4×D4—614no—
331C2×C4×D4—611no—
332C2×C4×D4—611no—
333C2×C4×D4—1221no—
334C2×C4×D4—1222no—
335C2×C4×D4—1222no—
336C2×C4×D4—1221no—
337C2×C4×D4#692311yescharacteristic, complemented
338C22×C4⋊C4—612no—
339C22×C4⋊C4—611no—
340C22×C22⋊C4—1221no—
341C22×C42—611no—
342C22×C42—1221no—
343C2×#102—6116no—
344C2×#102—618no—
345C2×C4×C8—614no—
346C2×C4×C8—1221no—
347C2×C4×C8—1221no—
348C2×C4×C8—1222no—
349C4×C4⋊C4—614no—
350C4×C4⋊C4—1222no—
351C2×#95—1221no—
352#340—618no—
353C61C2×C4×#10211yescharacteristic, complemented, Sylow
354C25—1221no—
355C22×D4—618no—
356C22×D4—612no—
357C22×D4—612no—
358C22×D4—611no—
359C22×D4—1221no—
360C22×D4—1221no—
361C22×D4—1224no—
362C22×D4—1221no—
363C22×D4C2×#692311yescharacteristic
364C23×C4—21no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—1221no—
369C23×C4—1224no—
370C23×C4—1224no—
371C23×C4—1221no—
372C23×C4—1221no—
373C23×C4—1222no—
374C23×C4—1221no—
375C23×C4—2444no—
376C23×C4—2444no—
377C22×C8—618no—
378C22×C8—614no—
379C22×C8—1222no—
380C22×C8—1224no—
381C22×C8—1222no—
382C4×D4—22no—
383C4×D4—614no—
384C4×D4—614no—
385C4×D4—614no—
386C4×D4—1224no—
387C4×D4—1224no—
388C4×D4—1222no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4C2×#692314yescomplemented
394C2×C4⋊C4—618no—
395C2×C4⋊C4—614no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1224no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4C2×#692311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—612no—
415C2×C42—612no—
416C2×C42—612no—
417C2×C42—612no—
418C2×C42—1224no—
419C2×C42—2444no—
420C2×C42C2×#692311yescharacteristic
421#102—6132no—
422C4×C8—1224no—
423C4×C8—1224no—
424#95—1224no—
425C24—21no—
426C24—611no—
427C24—1222no—
428C24—1222no—
429C24—1228no—
430C24—1221no—
431C24—2442no—
432C24—2442no—
433C24—2444no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—618no—
437C2×D4—618no—
438C2×D4—614no—
439C2×D4—612no—
440C2×D4—1224no—
441C2×D4—1224no—
442C2×D4—1228no—
443C2×D4—1228no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1228no—
447C2×D4—1221no—
448C2×D4—1222no—
449C2×D4C4×#692314yescomplemented
450C2×D4C22×#692312yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—44no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—614no—
457C22×C4—614no—
458C22×C4—614no—
459C22×C4—612no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—612no—
463C22×C4—614no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—1224no—
470C22×C4—1224no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1224no—
474C22×C4—1224no—
475C22×C4—1228no—
476C22×C4—1221no—
477C22×C4—1224no—
478C22×C4—2444no—
479C22×C4—24416no—
480C22×C4—2448no—
481C22×C4—2448no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4—2444no—
487C22×C4—2444no—
488C22×C4C22⋊#692311yescharacteristic
489C22×C4C22⋊#692311yescharacteristic
490C22×C4C22×#692311yescharacteristic
491C2×C8—618no—
492C2×C8—1224no—
493C2×C8—1224no—
494C2×C8—1228no—
495C2×C8—1228no—
496C4⋊C4—21no—
497C4⋊C4—618no—
498C4⋊C4—612no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1224no—
502C4⋊C4—1228no—
503C4⋊C4—1221no—
504C4⋊C4C22×#692312yes—
505C22⋊C4—24no—
506C22⋊C4—1224no—
507C22⋊C4—1224no—
508C22⋊C4—1224no—
509C42—612no—
510C42—612no—
511C42—612no—
512C42—612no—
513C42—612no—
514C42—612no—
515C42—2448no—
516C42C22⋊#692312yes—
517C42C22×#692312yes—
518C23—22no—
519C23—24no—
520C23—42no—
521C23—42no—
522C23—612no—
523C23—612no—
524C23—614no—
525C23—611no—
526C23—611no—
527C23—614no—
528C23—1228no—
529C23—1228no—
530C23—1222no—
531C23—1224no—
532C23—2442no—
533C23—2442no—
534C23—2444no—
535C23—24416no—
536C23—24416no—
537C23—2444no—
538C23—2444no—
539C23—2442no—
540C23—2442no—
541C23C2×C22⋊#692311yescharacteristic
542D4—22no—
543D4—24no—
544D4—614no—
545D4—1228no—
546D4—1228no—
547D4—1222no—
548D4—1224no—
549D4C2×C4×#692314yescomplemented
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—42no—
553C2×C4—48no—
554C2×C4—614no—
555C2×C4—611no—
556C2×C4—612no—
557C2×C4—611no—
558C2×C4—614no—
559C2×C4—618no—
560C2×C4—614no—
561C2×C4—614no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—614no—
567C2×C4—614no—
568C2×C4—612no—
569C2×C4—1224no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1228no—
573C2×C4—1222no—
574C2×C4—2448no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2444no—
578C2×C4—2448no—
579C2×C4—2444no—
580C2×C4—24416no—
581C2×C4—2444no—
582C2×C4—2442no—
583C2×C4—2448no—
584C2×C4#1451983914yesdirect product factor
585C2×C4C2×C4×#692312yes—
586C2×C4C2×C22⋊#692312yes—
587C2×C4C2×C22⋊#692312yes—
588C2×C4C2×C22⋊#692311yescharacteristic
589C2×C4#1451985612yes—
590C2×C4C23×#692311yescharacteristic
591C8—1228no—
592C22—24no—
593C22—48no—
594C22—42no—
595C22—42no—
596C22—618no—
597C22—618no—
598C22—611no—
599C22—611no—
600C22—612no—
601C22—612no—
602C22—612no—
603C22—612no—
604C22—612no—
605C22—1224no—
606C22—2448no—
607C22—2448no—
608C22—24416no—
609C22—2448no—
610C22—2442no—
611C22—2442no—
612C22C4×C22⋊#692312yes—
613C22C2×#1451983912yes—
614C22#1684075212yes—
615C22C22×C22⋊#692311yescharacteristic
616C4—22no—
617C4—42no—
618C4—614no—
619C4—612no—
620C4—612no—
621C4—1222no—
622C4—2448no—
623C4—2442no—
624C4C4×C22⋊#692312yes—
625C4C2×#1451983914yesdirect product factor
626C4C22×C4×#692311yescharacteristic
627C4C2×#1451985611yescharacteristic
628C2—44no—
629C2—612no—
630C2—612no—
631C2—614no—
632C2—2444no—
633C2C4×#1451983914yesdirect product factor
634C2C2×C4×C22⋊#692311yescharacteristic
635C2C22×#1451983911yescharacteristic
636C2C2×#1684075211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×C4×#102
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D61⋊C8C2semidirect
3. C2×C4×C4⋊#6923C2semidirect
4. C4×#14519839C2direct (N × H)
5. C2×#16840635C2semidirect
10. C2×#14519839C4direct (N × H)
13. C4×D61⋊C8C22semidirect
17. C4×C4⋊#6923C22semidirect
19. #16840635C22semidirect
22. C2×C4×D244C4semidirect
23. C2×D4×Dic61C4semidirect
24. C2×#14519739C4semidirect
29. C4×D4×D61C4semidirect
34. C2×C4×D4×C61C4semidirect
38. C2×D61⋊C8C2×C4semidirect
43. C2×C4⋊#6923C2×C4semidirect
47. #14519839C2×C4direct (N × H)
72. C4×D244C2×C4semidirect
74. D4×Dic61C2×C4semidirect
76. #14519739C2×C4semidirect
102. C4×D4×C61C2×C4semidirect
121. C2×D4×C61C42semidirect
142. D4×D61C42semidirect
146. C2×D244C42semidirect
176. C4⋊#6923C22×C4semidirect
180. D61⋊C8C22×C4semidirect
229. D4×C61C2×C42semidirect
234. C2×C4×C61#102semidirect
247. C2×Dic61#102semidirect
255. D244C2×C42semidirect
263. C4×D61#102semidirect
302. C4×C61C2×#102semidirect
308. Dic61C2×#102semidirect
317. C2×C61C4×#102semidirect
322. D61C4×#102semidirect
337. C2×C4×D4#6923semidirect
353. C61C2×C4×#102semidirect
393. C4×D4C2×#6923semidirect
449. C2×D4C4×#6923semidirect
549. D4C2×C4×#6923semidirect
584. C2×C4#14519839direct (N × H)
625. C4C2×#14519839direct (N × H)
633. C2C4×#14519839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198392
C2×C4×D61⋊C82
C2×C4×C4⋊#69232
C4×#145198392
C2×#168406352
C2×C4×D4×D612
C2×C4×#10261