Finite Group Databasebeta

← C2×C4×#14519835 #30614050

Subgroups — C2×C4×#14519835 #30614050

Order 15616.

2242 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519835C212yesmaximal
2C2×C4×C22⋊#6923C212yesmaximal, complemented
3C4×#14519835C218yesmaximal, direct product factor
4C2×#16840640C212yesmaximal, complemented
5C22×C4×C22⋊D61C211yesmaximal, characteristic
6C22×C22⋊#6923C2214yes—
7C22×C4×#6923—22no—
8C2×#14519835C4116yesdirect product factor
9C2×#14519835C2218yes—
10C4×C22⋊#6923—24no—
11C4×C22⋊#6923C2218yescomplemented
12C2×(C2×#6923)⋊C4—22no—
13#16840640C2218yescomplemented
14C23×C22⋊D61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×C4×C22⋊D61—22no—
17C2×C4×C22⋊D61—22no—
18C2×C4×C22⋊D61—24no—
19C2×C4×C22⋊D61C414yescomplemented
20C2×C4×C22⋊D61C2214yes—
21C22×#11758196C411yescharacteristic, complemented
22C22×C22⋊Dic61C411yescharacteristic, complemented
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C411yescharacteristic, complemented
25C24×C4×C61C411yescharacteristic, complemented
26C23×#6923—24no—
27C2×C22⋊#6923—24no—
28C2×C22⋊#6923—28no—
29C2×C22⋊#6923C2×C4116yescomplemented
30C2×C22⋊#6923C2318yes—
31C2×C4×#6923—28no—
32C2×C4×#6923—48no—
33#14519835C2×C4132yesdirect product factor
34(C2×#6923)⋊C4—28no—
35C24×D61C2311yescharacteristic
36C22×C22⋊D61—22no—
37C22×C22⋊D61—22no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61C2×C418yes—
40C22×C22⋊D61C2×C412yes—
41C22×C22⋊D61C2312yes—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C22×C4×D61—44no—
46C22×C4×D61C2×C412yes—
47C22×C4×D61D412yes—
48C22×C4×D61D412yes—
49C22×C4×D61D414yes—
50C22×C4×D61C2312yes—
51C4×C22⋊D61—28no—
52C4×C22⋊D61—28no—
53C4×C22⋊D61—28no—
54C4×C22⋊D61—28no—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196C2×C414yescomplemented
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61C2×C414yescomplemented
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×#11758198C2×C412yes—
64C2×#11758198C2312yes—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61C2×C414yescomplemented
69C25×C61C2×C411yescharacteristic
70C23×C4×C61—22no—
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61—44no—
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61C2×C411yescharacteristic
76C23×C4×C61C2×C414yescomplemented
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—22no—
80C24×C61—42no—
81C24×C61—42no—
82C24×C61C4214yescomplemented
83C24×C61C22×C411yescharacteristic
84C24×C61C22×C412yes—
85C23×D61—42no—
86C23×D61—42no—
87C23×D61C22×C411yescharacteristic
88C23×D61C22×C414yes—
89C23×D61C2×D412yes—
90C23×D61C2×D412yes—
91C23×D61#4114yes—
92C23×D61C2411yescharacteristic
93C22×#6923—216no—
94C22×#6923—28no—
95C22×#6923—48no—
96C22×#6923—48no—
97C22×C4×C61—24no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—24no—
101C22×C4×C61—24no—
102C22×C4×C61—44no—
103C22×C4×C61—48no—
104C22×C4×C61—48no—
105C22×C4×C61—44no—
106C22×C4×C61—42no—
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22⋊C412yes—
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22×C412yes—
111C22×C4×C61C22×C412yes—
112C2×C22⋊D61—24no—
113C2×C22⋊D61—24no—
114C2×C22⋊D61—216no—
115C2×C22⋊D61—216no—
116C2×C22⋊D61—24no—
117C2×C22⋊D61—24no—
118C2×C22⋊D61C4218yescomplemented
119C2×C22⋊D61C22×C418yes—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—22no—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61C4214yescomplemented
128C22×Dic61C22⋊C412yes—
129C22×Dic61C22⋊C412yes—
130C22×Dic61C22×C412yes—
131C22×Dic61C22×C412yes—
132C22×Dic61C22×C412yes—
133C2×C4×D61—28no—
134C2×C4×D61—44no—
135C2×C4×D61—48no—
136C2×C4×D61—44no—
137C2×C4×D61—44no—
138C2×C4×D61C22⋊C414yes—
139C2×C4×D61C22⋊C414yes—
140C2×C4×D61C2×D414yes—
141C2×C4×D61C2×D414yes—
142C22⋊#6923—216no—
143C22⋊#6923—28no—
144C22⋊#6923C22×C4116yescomplemented
145C4×#6923—416no—
146C22⋊Dic61—28no—
147#11758198—24no—
148#11758198—24no—
149#11758196—28no—
150C4×Dic61—24no—
151C4×Dic61—24no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—24no—
157C23×C61—24no—
158C23×C61—42no—
159C23×C61—42no—
160C23×C61—48no—
161C23×C61—42no—
162C23×C61—48no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61C2×C4212yes—
167C23×C61C2×C4214yescomplemented
168C23×C61C2×C22⋊C411yescharacteristic
169C23×C61C2×C22⋊C411yescharacteristic
170C23×C61#11712yes—
171C23×C61C23×C411yescharacteristic
172C22×D61—24no—
173C22×D61—24no—
174C22×D61—41no—
175C22×D61—42no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—48no—
179C22×D61—42no—
180C22×D61—48no—
181C22×D61—41no—
182C22×D61C2×C4212yes—
183C22×D61C2×C22⋊C412yes—
184C22×D61#11712yes—
185C22×D61C4×D418yes—
186C22×D61C4×D418yes—
187C22×D61C23×C412yes—
188C22×D61C22×D412yes—
189C22×D61C2×#4112yes—
190C2×#6923—216no—
191C2×#6923—48no—
192C2×#6923—48no—
193C2×#6923—432no—
194C2×C4×C61—22no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—22no—
198C2×C4×C61—48no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—48no—
202C2×C4×C61—42no—
203C2×C4×C61#9914yescomplemented
204C2×C4×C61C2×C22⋊C412yes—
205C2×C4×C61C2×C22⋊C412yes—
206C22⋊D61—216no—
207C22⋊D61—216no—
208C2×Dic61—22no—
209C2×Dic61—22no—
210C2×Dic61—24no—
211C2×Dic61—24no—
212C2×Dic61—24no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61C2×C4214yescomplemented
220C2×Dic61C2×C22⋊C414yes—
221C4×D61—28no—
222C4×D61—28no—
223C4×D61—44no—
224C4×D61—44no—
225C2×C4×#99—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—24no—
231C22×C61—24no—
232C22×C61—24no—
233C22×C61—44no—
234C22×C61—44no—
235C22×C61—48no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—48no—
239C22×C61C4×C22⋊C412yes—
240C22×C61C4×C22⋊C412yes—
241C22×C61C2×#9912yes—
242C22×C61#41012yes—
243C22×C61C22×C4211yescharacteristic
244C22×C61C22×C22⋊C411yescharacteristic
245C22×C61C2×#11711yescharacteristic
246C2×D61—22no—
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—216no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61—48no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61C4×C22⋊C414yes—
257C2×D61C2×C4×D414yes—
258#6923—416no—
259C4×C61—22no—
260C4×C61—42no—
261C4×C61C2×#9914yescomplemented
262Dic61—24no—
263Dic61—24no—
264Dic61—42no—
265C22×C4×D4—611no—
266C22×#99—612no—
267C2×C4×C22⋊C4—612no—
268C4×#99—618no—
269C2×#342—612no—
270C2×C61—21no—
271C2×C61—22no—
272C2×C61—21no—
273C2×C61—44no—
274C2×C61C4×#9914yescomplemented
275C2×C61C2×C4×C22⋊C411yescharacteristic
276C2×C61C22×#9911yescharacteristic
277C2×C61C2×#41011yescharacteristic
278D61—24no—
279D61—24no—
280C23×D4—611no—
281C24×C4—611no—
282C24×C4#692311yescharacteristic, complemented
283C2×C4×D4—614no—
284C2×C4×D4—614no—
285C2×C4×D4—1222no—
286C2×C4×D4—1224no—
287C2×C4×D4—1222no—
288C22×C4⋊C4—611no—
289C22×C22⋊C4—614no—
290C22×C22⋊C4—611no—
291C22×C22⋊C4—611no—
292C22×C42—611no—
293C22×C42—1222no—
294C2×#99—6116no—
295C2×#99—618no—
296C4×C22⋊C4—618no—
297C4×C22⋊C4—1224no—
298C2×#95—1222no—
299#342—618no—
300C61C2×C4×#9911yescharacteristic, complemented, Sylow
301C25—611no—
302C25C2×#692311yescharacteristic
303C22×D4—618no—
304C22×D4—612no—
305C22×D4—612no—
306C22×D4—1222no—
307C22×D4—1222no—
308C22×D4—1224no—
309C23×C4—22no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—44no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—612no—
316C23×C4—612no—
317C23×C4—614no—
318C23×C4—612no—
319C23×C4—612no—
320C23×C4—611no—
321C23×C4—1224no—
322C23×C4—2444no—
323C23×C4C2×#692311yescharacteristic
324C23×C4C2×#692311yescharacteristic
325C23×C4C2×#692314yescomplemented
326C4×D4—1228no—
327C4×D4—1228no—
328C4×D4—1228no—
329C4×D4—1228no—
330C2×C4⋊C4—614no—
331C2×C4⋊C4—1222no—
332C2×C4⋊C4—1222no—
333C2×C22⋊C4—6116no—
334C2×C22⋊C4—618no—
335C2×C22⋊C4—614no—
336C2×C22⋊C4—612no—
337C2×C22⋊C4—612no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1228no—
343C2×C22⋊C4—1224no—
344C2×C42—614no—
345C2×C42—1221no—
346C2×C42—1222no—
347C2×C42—1221no—
348C2×C42—1228no—
349C2×C42—2448no—
350#99—6132no—
351#95—1228no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—42no—
356C24—42no—
357C24—612no—
358C24—614no—
359C24—612no—
360C24—614no—
361C24—611no—
362C24—611no—
363C24—2442no—
364C24—2442no—
365C24C4×#692314yescomplemented
366C24C22×#692311yescharacteristic
367C24C22×#692312yes—
368C2×D4—618no—
369C2×D4—618no—
370C2×D4—1224no—
371C2×D4—1224no—
372C2×D4—1224no—
373C2×D4—1224no—
374C2×D4—12216no—
375C2×D4—12216no—
376C22×C4—24no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—44no—
382C22×C4—48no—
383C22×C4—48no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—614no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—614no—
392C22×C4—614no—
393C22×C4—614no—
394C22×C4—614no—
395C22×C4—612no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1222no—
399C22×C4—1228no—
400C22×C4—1228no—
401C22×C4—12216no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—2448no—
405C22×C4—2444no—
406C22×C4—2444no—
407C22×C4—2444no—
408C22×C4—2442no—
409C22×C4—2448no—
410C22×C4—2448no—
411C22×C4—2442no—
412C22×C4C22⋊#692311yescharacteristic
413C22×C4C22⋊#692312yes—
414C22×C4C22⋊#692311yescharacteristic
415C22×C4C22×#692312yes—
416C22×C4C22×#692312yes—
417C4⋊C4—1228no—
418C22⋊C4—6116no—
419C22⋊C4—1224no—
420C22⋊C4—1224no—
421C22⋊C4—1228no—
422C22⋊C4—1228no—
423C22⋊C4—12216no—
424C42—1224no—
425C42—1224no—
426C42—24416no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—24no—
432C23—24no—
433C23—42no—
434C23—48no—
435C23—42no—
436C23—42no—
437C23—48no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—612no—
442C23—612no—
443C23—618no—
444C23—612no—
445C23—612no—
446C23—612no—
447C23—612no—
448C23—618no—
449C23—1224no—
450C23—1224no—
451C23—2442no—
452C23—2441no—
453C23—2441no—
454C23—2448no—
455C23—2448no—
456C23—2442no—
457C23—2441no—
458C23—2441no—
459C23C2×C4×#692312yes—
460C23C2×C4×#692314yescomplemented
461C23C2×C22⋊#692311yescharacteristic
462C23C2×C22⋊#692311yescharacteristic
463C23#1451985612yes—
464C23C23×#692311yescharacteristic
465D4—12216no—
466D4—12216no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—48no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—48no—
475C2×C4—42no—
476C2×C4—614no—
477C2×C4—614no—
478C2×C4—1224no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1224no—
482C2×C4—1224no—
483C2×C4—1228no—
484C2×C4—1228no—
485C2×C4—12216no—
486C2×C4—1222no—
487C2×C4—2444no—
488C2×C4—2444no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2448no—
493C2×C4—24432no—
494C2×C4—2448no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4#1451983514yesdirect product factor
498C2×C4C2×C22⋊#692312yes—
499C2×C4C2×C22⋊#692312yes—
500C22—24no—
501C22—24no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—24no—
507C22—44no—
508C22—44no—
509C22—48no—
510C22—48no—
511C22—42no—
512C22—42no—
513C22—614no—
514C22—614no—
515C22—12216no—
516C22—1222no—
517C22—1222no—
518C22—1222no—
519C22—1222no—
520C22—2442no—
521C22—2442no—
522C22—2442no—
523C22—2442no—
524C22—2448no—
525C22C4×C22⋊#692312yes—
526C22C4×C22⋊#692312yes—
527C22C2×#1451983512yes—
528C22#1684074112yes—
529C22C22×C4×#692311yescharacteristic
530C22C22×C22⋊#692311yescharacteristic
531C22C2×#1451985611yescharacteristic
532C4—22no—
533C4—42no—
534C4—1224no—
535C4—1224no—
536C4—24416no—
537C4—2442no—
538C4C2×#1451983514yesdirect product factor
539C2—21no—
540C2—21no—
541C2—22no—
542C2—44no—
543C2—1224no—
544C2—1224no—
545C2C4×#1451983514yesdirect product factor
546C2C2×C4×C22⋊#692311yescharacteristic
547C2C22×#1451983511yescharacteristic
548C2C2×#1684074111yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC22×C61C22×C42
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC23×D61C24
hypercenterC24×C4#6923
hypocenterC61C2×C4×#99
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊#6923C2semidirect
3. C4×#14519835C2direct (N × H)
4. C2×#16840640C2semidirect
8. C2×#14519835C4direct (N × H)
11. C4×C22⋊#6923C22semidirect
13. #16840640C22semidirect
19. C2×C4×C22⋊D61C4semidirect
21. C22×#11758196C4semidirect
22. C22×C22⋊Dic61C4semidirect
24. C22×C4×Dic61C4semidirect
25. C24×C4×C61C4semidirect
29. C2×C22⋊#6923C2×C4semidirect
33. #14519835C2×C4direct (N × H)
57. C2×#11758196C2×C4semidirect
60. C2×C22⋊Dic61C2×C4semidirect
68. C2×C4×Dic61C2×C4semidirect
76. C23×C4×C61C2×C4semidirect
82. C24×C61C42semidirect
118. C2×C22⋊D61C42semidirect
127. C22×Dic61C42semidirect
144. C22⋊#6923C22×C4semidirect
167. C23×C61C2×C42semidirect
203. C2×C4×C61#99semidirect
219. C2×Dic61C2×C42semidirect
261. C4×C61C2×#99semidirect
274. C2×C61C4×#99semidirect
282. C24×C4#6923semidirect
300. C61C2×C4×#99semidirect
325. C23×C4C2×#6923semidirect
365. C24C4×#6923semidirect
460. C23C2×C4×#6923semidirect
497. C2×C4#14519835direct (N × H)
538. C4C2×#14519835direct (N × H)
545. C2C4×#14519835direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198352
C2×C4×C22⋊#69232
C4×#145198352
C2×#168406402
C22×C4×C22⋊D612
C2×C4×#9961