Finite Group Databasebeta

← C2×C4×#14519840 #30614126

Subgroups — C2×C4×#14519840 #30614126

Order 15616.

1726 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519840C212yesmaximal
2C2×C4×D61⋊C8C211yesmaximal, characteristic
3C2×C4×C4⋊#6923C211yesmaximal, characteristic
4C4×#14519840C218yesmaximal, direct product factor
5C2×#16840635C212yesmaximal
6C2×C4×Q8×D61C211yesmaximal, characteristic
7C22×D61⋊C8C2212yes—
8C22×C4⋊#6923C2212yes—
9C22×C4×#6923—21no—
10C2×#14519840C4116yesdirect product factor
11C2×#14519840C2218yes—
12C4×D61⋊C8—22no—
13C4×D61⋊C8C2214yes—
14C2×C4×#92420—21no—
15C2×C4×#92420—21no—
16C4×C4⋊#6923—22no—
17C4×C4⋊#6923C2214yes—
18C2×(C2×#6923)⋊C4—21no—
19#16840635C2218yes—
20C22×Q8×D61C2211yescharacteristic
21C2×Q8×Dic61C411yescharacteristic, complemented
22C2×C4×Dic122—21no—
23C2×C4×Dic122C411yescharacteristic, complemented
24C2×#14519742—21no—
25C2×#14519742C411yescharacteristic, complemented
26C4×Q8×D61—22no—
27C4×Q8×D61—22no—
28C4×Q8×D61C414yescomplemented
29C4×Q8×D61C2214yes—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C42×D61—21no—
33C2×C42×D61C2211yescharacteristic
34C2×C4×Q8×C61C411yescharacteristic, complemented
35C23×#6923—22no—
36C2×D61⋊C8—22no—
37C2×D61⋊C8—24no—
38C2×D61⋊C8C2×C418yes—
39C2×D61⋊C8C2314yes—
40C22×#92420—22no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—24no—
43C2×C4⋊#6923C2×C418yes—
44C2×C4⋊#6923C2314yes—
45C2×C4×#6923—24no—
46C2×C4×#6923—44no—
47#14519840C2×C4132yesdirect product factor
48C4×#92420—24no—
49C4×#92420—24no—
50(C2×#6923)⋊C4—24no—
51C22×Dic122—21no—
52C22×Dic122C2×C411yescharacteristic
53C2×Q8×D61—21no—
54C2×Q8×D61—21no—
55C2×Q8×D61—24no—
56C2×Q8×D61C2×C418yes—
57C2×Q8×D61C2×C412yes—
58C2×Q8×D61C2312yes—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64Q8×Dic61—22no—
65Q8×Dic61C2×C414yescomplemented
66C4×Dic122—22no—
67C4×Dic122—24no—
68C4×Dic122—24no—
69C4×Dic122C2×C414yescomplemented
70#14519742—22no—
71#14519742—24no—
72#14519742—24no—
73#14519742C2×C414yescomplemented
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—21no—
82C4⋊C4×D61—21no—
83C4⋊C4×D61C2×C412yes—
84C4⋊C4×D61C2312yes—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C42×D61—24no—
92C42×D61—24no—
93C42×D61C2×C412yes—
94C42×D61D412yes—
95C42×D61D412yes—
96C42×D61C2312yes—
97C22×Q8×C61C2×C411yescharacteristic
98C4×Q8×C61—22no—
99C4×Q8×C61C2×C414yescomplemented
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C42×C61—21no—
103C2×C42×C61C2×C411yescharacteristic
104C23×D61C2×D411yescharacteristic
105C22×#6923—28no—
106C22×#6923—24no—
107C22×#6923—44no—
108C22×#6923—44no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61C4214yescomplemented
112C2×Q8×C61C22×C412yes—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22⋊C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C2×D411yescharacteristic
123Q8×D61—24no—
124Q8×D61—28no—
125Q8×D61—28no—
126Q8×D61—24no—
127Q8×D61C4218yescomplemented
128Q8×D61C22×C418yes—
129C2×C4×D61—22no—
130C2×C4×D61—28no—
131C2×C4×D61—24no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—44no—
136C2×C4×D61C22⋊C412yes—
137C2×C4×D61C22⋊C412yes—
138C2×C4×D61SD1614yes—
139C2×C4×D61Q1614yes—
140C2×C4×D61C22×C411yescharacteristic
141C2×C4×D61C22×C414yes—
142C2×C4×D61C2×D412yes—
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2×D411yescharacteristic
145C2×C4×D61C2×D412yes—
146C2×C4×D61#4114yes—
147C2×C4×D61C2411yescharacteristic
148C2×Dic122—21no—
149C2×Dic122—22no—
150C2×Dic122—22no—
151C2×Dic122—28no—
152C2×Dic122—22no—
153C2×Dic122C4214yescomplemented
154C2×Dic122C22×C412yes—
155C2×#92420—28no—
156C2×#92420—24no—
157C4⋊#6923—28no—
158C4⋊#6923—24no—
159C4⋊#6923C22×C418yes—
160C4×#6923—48no—
161D61⋊C8—28no—
162D61⋊C8—24no—
163D61⋊C8C22×C418yes—
164C4⋊C4×C61—24no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61C22×C412yes—
167C42×C61—24no—
168C42×C61C22⋊C412yes—
169C42×C61C22×C412yes—
170C4⋊Dic61—21no—
171C4⋊Dic61—24no—
172C4⋊Dic61C22×C412yes—
173#11758196—24no—
174#11758196—24no—
175#11758196—22no—
176#11758196—22no—
177C4×Dic61—24no—
178C4×Dic61—24no—
179C4×Dic61—24no—
180C4×Dic61C22⋊C412yes—
181C4×Dic61C22⋊C412yes—
182C4×Dic61C22⋊C412yes—
183C4×Dic61C22×C412yes—
184C4×Dic61C2×D412yes—
185C4×Dic61C2×D412yes—
186C23×C61C2×C22⋊C411yescharacteristic
187C22×D61C2×C22⋊C411yescharacteristic
188C22×D61C4×D414yes—
189C22×D61C2×SD1612yes—
190C22×D61C2×Q1612yes—
191C22×D61#13514yes—
192C22×D61C22×D411yescharacteristic
193C2×#6923—28no—
194C2×#6923—44no—
195C2×#6923—44no—
196C2×#6923—416no—
197Q8×C61—22no—
198Q8×C61—24no—
199Q8×C61C2×C4214yescomplemented
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61#10314yescomplemented
206C2×C4×C61C2×C4212yes—
207C2×C4×C61C2×C22⋊C412yes—
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C2×C22⋊C412yes—
210C2×C4×C61#11712yes—
211C2×C4×C61C23×C411yescharacteristic
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—42no—
217C2×Dic61#10314yescomplemented
218C2×Dic61C2×C22⋊C412yes—
219C2×Dic61C2×C22⋊C411yescharacteristic
220C2×Dic61C2×C22⋊C412yes—
221C2×Dic61C4×D414yes—
222C2×Dic61C22×D411yescharacteristic
223C4×D61—28no—
224C4×D61—24no—
225C4×D61—28no—
226C4×D61—24no—
227C4×D61—44no—
228C4×D61—44no—
229C4×D61#10318yescomplemented
230C4×D61C2×C4212yes—
231C4×D61#11712yes—
232C4×D61C4×D414yes—
233C4×D61C4×D414yes—
234C4×D61C2×SD1614yes—
235C4×D61C2×Q1614yes—
236C4×D61C23×C412yes—
237C4×D61C2×#4112yes—
238Dic122—22no—
239Dic122—24no—
240Dic122—28no—
241Dic122—28no—
242Dic122C2×C4214yescomplemented
243#92420—28no—
244C2×C4×#103—611nomaximal, Sylow
245C22×C61C4×C22⋊C412yes—
246C22×C61C2×#10312yes—
247C22×C61#41612yes—
248C22×C61C22×C22⋊C411yescharacteristic
249C2×D61C4×C22⋊C412yes—
250C2×D61C2×#10312yes—
251C2×D61#41612yes—
252C2×D61C4×SD1618yes—
253C2×D61C4×Q1618yes—
254C2×D61C2×C4×D412yes—
255C2×D61C22×SD1611yescharacteristic
256C2×D61C22×Q1611yescharacteristic
257C2×D61C2×#13512yes—
258#6923—48no—
259C4×C61—22no—
260C4×C61—24no—
261C4×C61—42no—
262C4×C61C4×C22⋊C412yes—
263C4×C61C2×#10314yescomplemented
264C4×C61C22×C4211yescharacteristic
265C4×C61C2×#11711yescharacteristic
266Dic61—22no—
267Dic61—24no—
268Dic61—42no—
269Dic61C4×C22⋊C412yes—
270Dic61C2×#10314yescomplemented
271Dic61C2×C4×D412yes—
272C22×C4×Q8—611no—
273C22×#103—612no—
274C22×C4×C8—611no—
275C2×C4×C4⋊C4—611no—
276C4×#103—618no—
277C2×#340—612no—
278C2×C61C4×#10314yescomplemented
279C2×C61C2×C4×C22⋊C411yescharacteristic
280C2×C61C22×#10311yescharacteristic
281C2×C61C2×#41611yescharacteristic
282D61C4×#10314yescomplemented
283D61C2×C4×SD1612yes—
284D61C2×C4×Q1612yes—
285C23×Q8—611no—
286C23×C8—612no—
287C2×C4×Q8—611no—
288C2×C4×Q8—614no—
289C2×C4×Q8—614no—
290C2×C4×Q8—611no—
291C2×C4×Q8—611no—
292C2×C4×Q8—1221no—
293C2×C4×Q8—1221no—
294C2×C4×Q8—1222no—
295C2×C4×Q8—1222no—
296C2×C4×Q8#692311yescharacteristic, complemented
297C22×C4⋊C4—612no—
298C22×C4⋊C4—611no—
299C22×C4⋊C4—1221no—
300C22×C42—611no—
301C22×C42—1221no—
302C22×C42—1221no—
303C2×#103—6116no—
304C2×#103—618no—
305C2×C4×C8—614no—
306C2×C4×C8—1221no—
307C2×C4×C8—1221no—
308C2×C4×C8—1222no—
309C4×C4⋊C4—614no—
310C4×C4⋊C4—1222no—
311C2×#95—1221no—
312#340—618no—
313C61C2×C4×#10311yescharacteristic, complemented, Sylow
314C22×Q8—618no—
315C22×Q8—612no—
316C22×Q8—612no—
317C22×Q8—611no—
318C22×Q8—1221no—
319C22×Q8—1221no—
320C22×Q8—1221no—
321C22×Q8—1224no—
322C22×Q8C2×#692311yescharacteristic
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—1221no—
327C23×C4—1221no—
328C23×C4—1222no—
329C22×C8—618no—
330C22×C8—614no—
331C22×C8—1222no—
332C22×C8—1224no—
333C22×C8—1222no—
334C4×Q8—22no—
335C4×Q8—614no—
336C4×Q8—614no—
337C4×Q8—614no—
338C4×Q8—1224no—
339C4×Q8—1224no—
340C4×Q8—1224no—
341C4×Q8—1224no—
342C4×Q8—1222no—
343C4×Q8—1222no—
344C4×Q8—1222no—
345C4×Q8C2×#692314yescomplemented
346C2×C4⋊C4—21no—
347C2×C4⋊C4—618no—
348C2×C4⋊C4—614no—
349C2×C4⋊C4—611no—
350C2×C4⋊C4—612no—
351C2×C4⋊C4—612no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1224no—
355C2×C4⋊C4—1224no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C2×#692311yescharacteristic
363C2×C42—21no—
364C2×C42—611no—
365C2×C42—611no—
366C2×C42—611no—
367C2×C42—612no—
368C2×C42—612no—
369C2×C42—612no—
370C2×C42—612no—
371C2×C42—1224no—
372C2×C42—1224no—
373C2×C42—1221no—
374C2×C42—1221no—
375C2×C42—1221no—
376C2×C42—1224no—
377C2×C42—2444no—
378C2×C42C2×#692311yescharacteristic
379#103—6132no—
380C4×C8—1224no—
381C4×C8—1224no—
382#95—1224no—
383C24—611no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—618no—
387C2×Q8—618no—
388C2×Q8—614no—
389C2×Q8—612no—
390C2×Q8—1222no—
391C2×Q8—1222no—
392C2×Q8—1228no—
393C2×Q8—1224no—
394C2×Q8—1224no—
395C2×Q8—1228no—
396C2×Q8—1228no—
397C2×Q8—1221no—
398C2×Q8—1222no—
399C2×Q8C4×#692314yescomplemented
400C2×Q8C22×#692312yes—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—614no—
406C22×C4—614no—
407C22×C4—614no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—614no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1224no—
421C22×C4—1228no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1221no—
425C22×C4—1224no—
426C22×C4—1228no—
427C22×C4—1221no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4—2444no—
431C22×C4C22⋊#692311yescharacteristic
432C22×C4C22⋊#692311yescharacteristic
433C22×C4C22×#692311yescharacteristic
434C2×C8—618no—
435C2×C8—1224no—
436C2×C8—1224no—
437C2×C8—1228no—
438C2×C8—1228no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—618no—
442C4⋊C4—612no—
443C4⋊C4—1222no—
444C4⋊C4—1222no—
445C4⋊C4—1224no—
446C4⋊C4—1224no—
447C4⋊C4—1224no—
448C4⋊C4—1228no—
449C4⋊C4—1221no—
450C4⋊C4—1224no—
451C4⋊C4C22×#692312yes—
452C42—24no—
453C42—612no—
454C42—612no—
455C42—612no—
456C42—612no—
457C42—612no—
458C42—612no—
459C42—1224no—
460C42—1224no—
461C42—1224no—
462C42—2448no—
463C42C22⋊#692312yes—
464C42C22×#692312yes—
465C23—612no—
466C23—612no—
467C23—614no—
468C23—611no—
469C23—611no—
470C23—614no—
471C23C2×C22⋊#692311yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—614no—
475Q8—1228no—
476Q8—1228no—
477Q8—1222no—
478Q8—1224no—
479Q8C2×C4×#692314yescomplemented
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—614no—
486C2×C4—612no—
487C2×C4—611no—
488C2×C4—611no—
489C2×C4—614no—
490C2×C4—618no—
491C2×C4—614no—
492C2×C4—614no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—614no—
498C2×C4—614no—
499C2×C4—612no—
500C2×C4—1224no—
501C2×C4—1224no—
502C2×C4—1228no—
503C2×C4—1228no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1224no—
507C2×C4—1228no—
508C2×C4—1222no—
509C2×C4—2444no—
510C2×C4—2444no—
511C2×C4—2444no—
512C2×C4—24416no—
513C2×C4—2444no—
514C2×C4—2442no—
515C2×C4#1451984014yesdirect product factor
516C2×C4C2×C4×#692312yes—
517C2×C4C2×C22⋊#692312yes—
518C2×C4C2×C22⋊#692312yes—
519C2×C4C2×C22⋊#692311yescharacteristic
520C2×C4#1451985612yes—
521C2×C4C23×#692311yescharacteristic
522C8—1228no—
523C22—618no—
524C22—618no—
525C22—611no—
526C22—611no—
527C22—612no—
528C22—612no—
529C22—612no—
530C22—612no—
531C22—612no—
532C22C4×C22⋊#692312yes—
533C22C2×#1451984012yes—
534C22#1684075212yes—
535C22C22×C22⋊#692311yescharacteristic
536C4—22no—
537C4—24no—
538C4—42no—
539C4—614no—
540C4—612no—
541C4—612no—
542C4—1222no—
543C4—1224no—
544C4—2448no—
545C4—2442no—
546C4C4×C22⋊#692312yes—
547C4C2×#1451984014yesdirect product factor
548C4C22×C4×#692311yescharacteristic
549C4C2×#1451985611yescharacteristic
550C2—612no—
551C2—612no—
552C2—614no—
553C2C4×#1451984014yesdirect product factor
554C2C2×C4×C22⋊#692311yescharacteristic
555C2C22×#1451984011yescharacteristic
556C2C2×#1684075211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×C4×#103
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
4. C4×#14519840C2direct (N × H)
10. C2×#14519840C4direct (N × H)
21. C2×Q8×Dic61C4semidirect
23. C2×C4×Dic122C4semidirect
25. C2×#14519742C4semidirect
28. C4×Q8×D61C4semidirect
34. C2×C4×Q8×C61C4semidirect
47. #14519840C2×C4direct (N × H)
65. Q8×Dic61C2×C4semidirect
69. C4×Dic122C2×C4semidirect
73. #14519742C2×C4semidirect
99. C4×Q8×C61C2×C4semidirect
111. C2×Q8×C61C42semidirect
127. Q8×D61C42semidirect
153. C2×Dic122C42semidirect
199. Q8×C61C2×C42semidirect
205. C2×C4×C61#103semidirect
217. C2×Dic61#103semidirect
229. C4×D61#103semidirect
242. Dic122C2×C42semidirect
263. C4×C61C2×#103semidirect
270. Dic61C2×#103semidirect
278. C2×C61C4×#103semidirect
282. D61C4×#103semidirect
296. C2×C4×Q8#6923semidirect
313. C61C2×C4×#103semidirect
345. C4×Q8C2×#6923semidirect
399. C2×Q8C4×#6923semidirect
479. Q8C2×C4×#6923semidirect
515. C2×C4#14519840direct (N × H)
547. C4C2×#14519840direct (N × H)
553. C2C4×#14519840direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198402
C2×C4×D61⋊C82
C2×C4×C4⋊#69232
C4×#145198402
C2×#168406352
C2×C4×Q8×D612
C2×C4×#10361