Finite Group Databasebeta

← C2×#21461065 #30609937

Subgroups — C2×#21461065 #30609937

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C212yesmaximal, complemented
2#21461065C218yesmaximal, direct product factor
3C2×#16840606C212yesmaximal, complemented
4C2×#16840605C212yesmaximal, complemented
5C22×C22⋊C4×D61C211yesmaximal, characteristic
6C22×#11758213—22no—
7#16840733—24no—
8#16840733C2218yescomplemented
9C2×#14519834—22no—
10C2×C22⋊#92420C2214yescomplemented
11#16840606C2218yescomplemented
12#16840605C2218yescomplemented
13C25×D61C411yescharacteristic
14C23×C4×D61C411yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×#11758198C411yescharacteristic
18C22×#11758198C2211yescharacteristic
19C2×C22⋊C4×D61—22no—
20C2×C22⋊C4×D61—22no—
21C2×C22⋊C4×D61—24no—
22C2×C22⋊C4×D61C414yes—
23C2×C22⋊C4×D61C2214yes—
24C22×C22⋊C4×C61C411yescharacteristic
25C2×#11758213—28no—
26C2×#11758213—48no—
27C22×#92420—24no—
28#14519834—28no—
29C22⋊#92420—24no—
30C22⋊#92420C2318yescomplemented
31C24×D61—24no—
32C24×D61—22no—
33C24×D61—21no—
34C24×D61—21no—
35C24×D61—24no—
36C24×D61—44no—
37C24×D61—44no—
38C24×D61C2×C411yescharacteristic
39C24×D61C2×C414yes—
40C24×D61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2311yescharacteristic
43C22×C4×D61—22no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—44no—
47C22×C4×D61—44no—
48C22×C4×D61C2×C414yes—
49C22×C4×D61C2×C412yes—
50C22×C4×D61D412yes—
51C22×C4×D61D412yes—
52C22×C4×D61D414yes—
53C22×C4×D61C2312yes—
54C2×C22⋊Dic61—22no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61C2×C412yes—
57C2×C22⋊Dic61C2312yes—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—22no—
62C2×#11758198C2×C412yes—
63C2×#11758198C2×C414yes—
64C2×#11758198C2312yes—
65C22⋊C4×D61—28no—
66C22⋊C4×D61—28no—
67C22⋊C4×D61—28no—
68C22⋊C4×D61—28no—
69C25×C61C2×C411yescharacteristic
70C23×C4×C61C2×C411yescharacteristic
71C23×C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61C2×C414yes—
75C24×C61—21no—
76C24×C61—21no—
77C24×C61—22no—
78C24×C61—42no—
79C24×C61—42no—
80C24×C61M1614yescomplemented
81C24×C61C22×C411yescharacteristic
82C24×C61C22×C412yes—
83C23×D61—22no—
84C23×D61—22no—
85C23×D61—24no—
86C23×D61—24no—
87C23×D61—216no—
88C23×D61—28no—
89C23×D61—28no—
90C23×D61—21no—
91C23×D61—21no—
92C23×D61—22no—
93C23×D61—28no—
94C23×D61—24no—
95C23×D61—24no—
96C23×D61—28no—
97C23×D61—432no—
98C23×D61—432no—
99C23×D61—44no—
100C23×D61—44no—
101C23×D61—48no—
102C23×D61—48no—
103C23×D61—48no—
104C23×D61—48no—
105C23×D61—44no—
106C23×D61—44no—
107C23×D61—42no—
108C23×D61—42no—
109C23×D61C22⋊C412yes—
110C23×D61C22⋊C411yescharacteristic
111C23×D61C22⋊C411yescharacteristic
112C23×D61M1614yescomplemented
113C23×D61C22×C412yes—
114C23×D61C22×C412yes—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—42no—
118C22×C4×C61—42no—
119C22×C4×C61C22⋊C412yes—
120C22×C4×C61C22⋊C412yes—
121C22×C4×C61C22×C412yes—
122C22×C4×C61C22×C412yes—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61C22×C412yes—
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C2×D412yes—
130C22×Dic61C2×D412yes—
131C22×Dic61C2411yescharacteristic
132C2×C4×D61—28no—
133C2×C4×D61—24no—
134C2×C4×D61—24no—
135C2×C4×D61—44no—
136C2×C4×D61—48no—
137C2×C4×D61—44no—
138C2×C4×D61—44no—
139C2×C4×D61—44no—
140C2×C4×D61—48no—
141C2×C4×D61—44no—
142C2×C4×D61—48no—
143C2×C4×D61C22⋊C414yes—
144C2×C4×D61C22⋊C414yes—
145C2×C4×D61C2×D414yes—
146C2×C4×D61C2×D414yes—
147C2×#92420—28no—
148C2×#92420—48no—
149#11758213—416no—
150C22⋊C4×C61—28no—
151C22⋊Dic61—24no—
152C22⋊Dic61—24no—
153#11758198—28no—
154#11758198—24no—
155#11758198—24no—
156C23×C61—22no—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—24no—
161C23×C61—24no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—48no—
165C23×C61—48no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61C2×C22⋊C411yescharacteristic
171C23×C61C2×C22⋊C411yescharacteristic
172C23×C61C2×M1612yes—
173C23×C61C2×M1612yes—
174C23×C61C2×M1614yescomplemented
175C23×C61C23×C411yescharacteristic
176C22×D61—216no—
177C22×D61—216no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—24no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—24no—
186C22×D61—24no—
187C22×D61—24no—
188C22×D61—24no—
189C22×D61—216no—
190C22×D61—216no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—432no—
196C22×D61—464no—
197C22×D61—432no—
198C22×D61—48no—
199C22×D61—48no—
200C22×D61—432no—
201C22×D61—432no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—48no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—48no—
208C22×D61—48no—
209C22×D61—48no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61#9914yes—
213C22×D61#10014yes—
214C22×D61C2×C22⋊C412yes—
215C22×D61C2×C22⋊C412yes—
216C22×D61C2×M1614yescomplemented
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61C2×C22⋊C414yes—
225C2×Dic61—24no—
226C2×Dic61—22no—
227C2×Dic61—41no—
228C2×Dic61—42no—
229C2×Dic61—41no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C22×D412yes—
235C4×D61—28no—
236C4×D61—28no—
237C4×D61—44no—
238C4×D61—44no—
239C4×D61—48no—
240C4×D61—48no—
241#92420—48no—
242C2×#1462—611nomaximal, Sylow
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—24no—
248C22×C61—24no—
249C22×C61—24no—
250C22×C61—44no—
251C22×C61—44no—
252C22×C61—48no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—48no—
256C22×C61#40712yes—
257C22×C61#40712yes—
258C22×C61C2×#9912yes—
259C22×C61C2×#10012yes—
260C22×C61C22×C22⋊C411yescharacteristic
261C22×C61C22×M1611yescharacteristic
262C22×C61C22×M1611yescharacteristic
263C2×D61—28no—
264C2×D61—28no—
265C2×D61—216no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—28no—
271C2×D61—28no—
272C2×D61—24no—
273C2×D61—432no—
274C2×D61—432no—
275C2×D61—44no—
276C2×D61—48no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—48no—
280C2×D61—44no—
281C2×D61C2×#9914yes—
282C2×D61C2×#10014yes—
283C4×C61—24no—
284C4×C61—42no—
285Dic61—22no—
286Dic61—22no—
287Dic61—42no—
288C23×C22⋊C4—611no—
289C2×#407—612no—
290#1462—618no—
291C2×#323—612no—
292C2×#323—612no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—22no—
296C2×C61—44no—
297C2×C61#146214yescomplemented
298C2×C61C2×#40711yescharacteristic
299C2×C61C22×#9911yescharacteristic
300C2×C61C22×#10011yescharacteristic
301D61—24no—
302D61—24no—
303D61—44no—
304C26—611no—
305C24×C4—611no—
306C24×C4—611no—
307C22×M16—1222no—
308C22×C22⋊C4—611no—
309C22×C22⋊C4—611no—
310C22×C22⋊C4—611no—
311C22×C22⋊C4—614no—
312C22×C22⋊C4—614no—
313C22×C22⋊C4—1222no—
314C22×C22⋊C4—1222no—
315C22×C22⋊C4—1224no—
316C22×C22⋊C4#692311yescharacteristic
317#407—618no—
318#407—1224no—
319C2×C22⋊C8—614no—
320C2×C22⋊C8—1222no—
321#323—618no—
322#323—618no—
323C61C2×#146211yescharacteristic, complemented, Sylow
324C25—611no—
325C25—611no—
326C25—614no—
327C25—1222no—
328C25—1221no—
329C25—1221no—
330C25—1224no—
331C25—1224no—
332C25—2444no—
333C25—2444no—
334C25C2×#692311yescharacteristic
335C23×C4—611no—
336C23×C4—612no—
337C23×C4—612no—
338C23×C4—614no—
339C23×C4—612no—
340C23×C4—612no—
341C23×C4—611no—
342C23×C4—614no—
343C23×C4—1222no—
344C23×C4—1221no—
345C23×C4—1221no—
346C23×C4—2444no—
347C23×C4—2444no—
348C23×C4C2×#692311yescharacteristic
349C23×C4C2×#692311yescharacteristic
350C2×M16—1228no—
351C2×M16—2448no—
352C22×C8—1224no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—612no—
356C2×C22⋊C4—612no—
357C2×C22⋊C4—612no—
358C2×C22⋊C4—612no—
359C2×C22⋊C4—614no—
360C2×C22⋊C4—1228no—
361C2×C22⋊C4—1228no—
362C2×C22⋊C4—1228no—
363C2×C22⋊C4—1228no—
364C2×C22⋊C4—1222no—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1222no—
368C2×C22⋊C4—1222no—
369C2×C22⋊C4—1222no—
370C2×C22⋊C4C2×#692314yes—
371C22⋊C8—618no—
372C22⋊C8—1224no—
373C22⋊C8—1228no—
374C24—21no—
375C24—21no—
376C24—22no—
377C24—42no—
378C24—42no—
379C24—611no—
380C24—611no—
381C24—612no—
382C24—612no—
383C24—614no—
384C24—612no—
385C24—1224no—
386C24—1224no—
387C24—1224no—
388C24—1224no—
389C24—1228no—
390C24—12216no—
391C24—1228no—
392C24—1228no—
393C24—1222no—
394C24—1222no—
395C24—1221no—
396C24—1221no—
397C24—1222no—
398C24—1228no—
399C24—2442no—
400C24—2442no—
401C24—2444no—
402C24—2444no—
403C24—2448no—
404C24—2448no—
405C24—24432no—
406C24—2448no—
407C24—2448no—
408C24—24432no—
409C24—2444no—
410C24—2444no—
411C24#1175821314yescomplemented
412C24C22×#692311yescharacteristic
413C24C22×#692312yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—612no—
419C22×C4—612no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—614no—
423C22×C4—614no—
424C22×C4—614no—
425C22×C4—614no—
426C22×C4—612no—
427C22×C4—1228no—
428C22×C4—1224no—
429C22×C4—1224no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—2444no—
433C22×C4—2448no—
434C22×C4—2444no—
435C22×C4—2444no—
436C22×C4—2444no—
437C22×C4—2448no—
438C22×C4—2444no—
439C22×C4—2448no—
440C22×C4—2442no—
441C22×C4—2442no—
442C22×C4C22⋊#692312yes—
443C22×C4C22⋊#692312yes—
444C22×C4C22×#692312yes—
445C22×C4C22×#692312yes—
446M16—24416no—
447C2×C8—1228no—
448C2×C8—2448no—
449C22⋊C4—28no—
450C22⋊C4—1224no—
451C22⋊C4—1224no—
452C22⋊C4—1224no—
453C22⋊C4—1224no—
454C22⋊C4—1228no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—22no—
461C23—48no—
462C23—42no—
463C23—42no—
464C23—48no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—614no—
470C23—614no—
471C23—612no—
472C23—612no—
473C23—614no—
474C23—1224no—
475C23—1224no—
476C23—1224no—
477C23—1224no—
478C23—12216no—
479C23—12216no—
480C23—12216no—
481C23—12216no—
482C23—1224no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—1222no—
487C23—1222no—
488C23—1222no—
489C23—1224no—
490C23—1224no—
491C23—1222no—
492C23—1222no—
493C23—2448no—
494C23—2442no—
495C23—2442no—
496C23—2448no—
497C23—2442no—
498C23—2442no—
499C23—2448no—
500C23—2448no—
501C23—24432no—
502C23—24432no—
503C23—24464no—
504C23—24432no—
505C23—24432no—
506C23—2448no—
507C23—2448no—
508C23—2442no—
509C23—2442no—
510C23C2×C22⋊#692311yescharacteristic
511C23C2×C22⋊#692311yescharacteristic
512C23D61⋊M1612yes—
513C23C2×#1175821312yes—
514C23C2×#1175821314yescomplemented
515C23C23×#692311yescharacteristic
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—1228no—
526C2×C4—1228no—
527C2×C4—1224no—
528C2×C4—1222no—
529C2×C4—2444no—
530C2×C4—2444no—
531C2×C4—2448no—
532C2×C4—2448no—
533C2×C4—2441no—
534C2×C4—2442no—
535C2×C4—2441no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4C2×C22⋊#692314yes—
540C8—2448no—
541C22—24no—
542C22—24no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—24no—
548C22—44no—
549C22—48no—
550C22—44no—
551C22—48no—
552C22—42no—
553C22—42no—
554C22—614no—
555C22—614no—
556C22—12216no—
557C22—1228no—
558C22—1228no—
559C22—1228no—
560C22—1228no—
561C22—1222no—
562C22—1222no—
563C22—1222no—
564C22—1222no—
565C22—1224no—
566C22—2444no—
567C22—2448no—
568C22—2444no—
569C22—24432no—
570C22—24432no—
571C22—2448no—
572C22—2442no—
573C22—2442no—
574C22#1684073312yes—
575C22#1684073312yes—
576C22D61⋊#9912yes—
577C22D61⋊#10012yes—
578C22C22×C22⋊#692311yescharacteristic
579C22C2×D61⋊M1611yescharacteristic
580C22C22×#1175821311yescharacteristic
581C4—24no—
582C4—42no—
583C4—1222no—
584C4—1222no—
585C4—2442no—
586C2—22no—
587C2—21no—
588C2—21no—
589C2—44no—
590C2—1224no—
591C2—1224no—
592C2—2444no—
593C2#2146106514yesdirect product factor
594C2C2×#1684073311yescharacteristic
595C2C2×D61⋊#9911yescharacteristic
596C2C2×D61⋊#10011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×D61C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1462
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840733C2semidirect
2. #21461065C2direct (N × H)
3. C2×#16840606C2semidirect
4. C2×#16840605C2semidirect
8. #16840733C22semidirect
10. C2×C22⋊#92420C22semidirect
11. #16840606C22semidirect
12. #16840605C22semidirect
30. C22⋊#92420C23semidirect
80. C24×C61M16semidirect
112. C23×D61M16semidirect
174. C23×C61C2×M16semidirect
216. C22×D61C2×M16semidirect
297. C2×C61#1462semidirect
323. C61C2×#1462semidirect
411. C24#11758213semidirect
514. C23C2×#11758213semidirect
593. C2#21461065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407332
#214610652
C2×#168406062
C2×#168406052
C22×C22⋊C4×D612
C2×#146261