Finite Group Databasebeta

← C2×#21455744 #30547793

Subgroups — C2×#21455744 #30547793

Order 15616.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C23×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#21455744C2116yesmaximal, direct product factor
4C2×#16840098C212yesmaximal, complemented
5C2×#16840081C212yesmaximal, complemented
6C2×#16840093C212yesmaximal, complemented
7C2×#16840076C212yesmaximal, complemented
8C2×#16839804C212yesmaximal, complemented
9C2×#16839764C212yesmaximal, complemented
10C2×C61×#407C211yesmaximal, characteristic, complemented
11C22×#11758222C2211yescharacteristic
12C24×Dic61—21no—
13#16840273—24no—
14#16840273C2218yes—
15C2×#14519760—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519746—21no—
21C2×C4×C22⋊D61—21no—
22C2×C4×C22⋊D61—21no—
23C2×#14519736C2211yescharacteristic
24C22×C4⋊Dic61—21no—
25C22×C4⋊Dic61—21no—
26C22×C4⋊Dic61—21no—
27C22×C4⋊Dic61—24no—
28C22×C4⋊Dic61C2212yes—
29C22×C4⋊Dic61C2212yes—
30C22×C4⋊Dic61C2212yes—
31C22×C4⋊Dic61C2218yescomplemented
32#16840098C22116yescomplemented
33#16840093C22116yescomplemented
34#16840081C22116yescomplemented
35#16840076C22116yescomplemented
36#16839804C22116yescomplemented
37C2×#14519711C2214yescomplemented
38C2×#14519709C2214yescomplemented
39#16839764C22116yescomplemented
40C2×#14519702C2214yescomplemented
41C2×#14519699C2214yescomplemented
42C24×C4×C61C2211yescharacteristic
43C22×M16×C61C2212yes—
44C61×#407C2218yescomplemented
45C2×C22⋊C8×C61C2212yes—
46C2×C22⋊C8×C61C2212yes—
47C2×#11758222—22no—
48C2×#11758222—28no—
49C2×#11758222C2314yes—
50C22×Dic122C2311yescharacteristic
51C22×D244C2311yescharacteristic
52C22×C22⋊D61—21no—
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C23×Dic61—22no—
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—28no—
59C23×Dic61—48no—
60C22×C4×D61—21no—
61#14519760—28no—
62#14519756—22no—
63#14519756—22no—
64#14519756C2314yes—
65#14519756C2314yes—
66#14519751—22no—
67#14519751—22no—
68#14519751C2314yes—
69#14519751C2314yes—
70#14519746—28no—
71C4×C22⋊D61—28no—
72C4×C22⋊D61—28no—
73#14519736—22no—
74#14519736C2314yes—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—24no—
78C2×C4⋊Dic61—24no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—28no—
82C2×C4⋊Dic61—28no—
83C2×C4⋊Dic61—28no—
84C2×C4⋊Dic61C2314yes—
85C2×C4⋊Dic61C2318yes—
86C2×C4⋊Dic61C2318yes—
87C2×C4⋊Dic61C2318yes—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98#14519711C23116yescomplemented
99#14519709C23116yescomplemented
100#14519702C23116yescomplemented
101#14519699C23116yescomplemented
102C25×C61D411yescharacteristic
103C23×C4×C61—28no—
104C23×C4×C61D411yescharacteristic
105C23×C4×C61D411yescharacteristic
106C23×C4×C61D411yescharacteristic
107C23×C4×C61D414yes—
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2314yes—
111C23×C4×C61C2311yescharacteristic
112C2×M16×C61—28no—
113C2×M16×C61C2318yes—
114C22×C8×C61C2314yes—
115C22⋊C8×C61C2318yes—
116C22⋊C8×C61C2318yes—
117C24×C61—24no—
118C24×C61—24no—
119C24×C61—24no—
120C24×C61C2×D414yes—
121C24×C61C2×D411yescharacteristic
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D411yescharacteristic
124C23×D61—21no—
125C22×C4×C61—24no—
126C22×C4×C61—24no—
127C22×C4×C61—24no—
128C22×C4×C61—216no—
129C22×C4×C61—24no—
130C22×C4×C61—24no—
131C22×C4×C61—216no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D414yes—
135C22×C4×C61C2×D414yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D414yes—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D412yes—
141C22×C4×C61#4118yes—
142C22×C4×C61C2412yes—
143C22×C4×C61C2412yes—
144C22×C4×C61C2411yescharacteristic
145C22×C4×C61C2412yes—
146C2×C22⋊D61—24no—
147C2×C22⋊D61—24no—
148C2×C22⋊D61—24no—
149C2×C22⋊D61—44no—
150C2×C22⋊D61—44no—
151C2×C22⋊D61—44no—
152C22×Dic61—21no—
153C22×Dic61—28no—
154C22×Dic61—28no—
155C22×Dic61—28no—
156C22×Dic61—24no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—48no—
160C22×Dic61—48no—
161C22×Dic61—432no—
162C22×Dic61—48no—
163#11758222—216no—
164#11758222—48no—
165C2×D244—24no—
166C2×D244—21no—
167C2×D244C2412yes—
168C2×C4×D61—24no—
169C2×C4×D61—44no—
170C2×Dic122—24no—
171C2×Dic122—21no—
172C2×Dic122C2412yes—
173M16×C61—216no—
174C2×C8×C61—28no—
175C2×C8×C61C2418yes—
176C22⋊Dic61—24no—
177C22⋊Dic61—24no—
178C22⋊Dic61—24no—
179#11758198—24no—
180#11758198—24no—
181C4⋊Dic61—28no—
182C4⋊Dic61—28no—
183C4⋊Dic61—28no—
184C4⋊Dic61—24no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C2418yes—
188C4⋊Dic61C2412yes—
189C4⋊Dic61C2412yes—
190#11758196—24no—
191#11758196—24no—
192C4×Dic61—24no—
193C23×C61—232no—
194C23×C61—28no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—28no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—28no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61#12314yes—
204C23×C61AGL(1,ℤ/8)14yes—
205C23×C61#13714yes—
206C23×C61C22×D412yes—
207C23×C61C22×D412yes—
208C23×C61C22×D412yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C2×C4×C61—28no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—28no—
220C2×C4×C61—28no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61#12314yes—
224C2×C4×C61#12318yes—
225C2×C4×C61C22×D412yes—
226C2×C4×C61C22×D412yes—
227C2×C4×C61C22×D412yes—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4114yes—
230C2×C4×C61C2×#4118yes—
231C2×C4×C61C2511yescharacteristic
232C22⋊D61—48no—
233C22⋊D61—48no—
234C22⋊D61—48no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—28no—
239C2×Dic61—416no—
240C2×Dic61—416no—
241C2×Dic61—42no—
242C2×Dic61—416no—
243C2×Dic61—48no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246D244—24no—
247D244—42no—
248C4×D61—48no—
249Dic122—24no—
250Dic122—42no—
251C8×C61—28no—
252C2×#3092—611nomaximal, Sylow
253C22×C61—232no—
254C22×C61—28no—
255C22×C61—28no—
256C22×C61—28no—
257C22×C61—22no—
258C22×C61—22no—
259C22×C61—22no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—22no—
263C22×C61C2×#12314yes—
264C22×C61C2×#12312yes—
265C22×C61C2×AGL(1,ℤ/8)14yes—
266C22×C61C2×AGL(1,ℤ/8)12yes—
267C22×C61C2×#13714yes—
268C22×C61C2×#13712yes—
269C22×C61C23×D411yescharacteristic
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—84no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61C2×#12312yes—
277C4×C61C2×#12314yes—
278C4×C61C22×#4112yes—
279Dic61—42no—
280Dic61—48no—
281Dic61—42no—
282Dic61—42no—
283C2×#525—611no—
284C23×C4⋊C4—611no—
285#3092—6116no—
286C2×#484—612no—
287C2×#481—612no—
288C2×#483—612no—
289C2×#480—612no—
290C2×#428—612no—
291C2×#417—612no—
292C2×#407D6111yescharacteristic, complemented
293C2×C61—24no—
294C2×C61—24no—
295C2×C61—24no—
296C2×C61#309214yescomplemented
297C2×C61C22×#12311yescharacteristic
298C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
299C2×C61C22×#13711yescharacteristic
300D61—82no—
301C22×#41—611no—
302C24×C4—1221no—
303C24×C4C2×D6111yescharacteristic
304C22×M16C2×D6112yes—
305#525—618no—
306#525—1224no—
307C2×#123—1221no—
308C2×C22⋊Q8—611no—
309C2×C22⋊Q8—611no—
310C2×#121—611no—
311C2×#121—611no—
312C2×#120—1221no—
313C2×C4×D4—1221no—
314C2×C4×D4—1221no—
315C2×#117—611no—
316C22×C4⋊C4—612no—
317C22×C4⋊C4—612no—
318C22×C4⋊C4—618no—
319C22×C4⋊C4—612no—
320C22×C4⋊C4—1221no—
321C22×C4⋊C4—1221no—
322C22×C4⋊C4—1221no—
323C22×C4⋊C4—1224no—
324#484—6116no—
325#483—6116no—
326#481—6116no—
327#480—6116no—
328#428—6116no—
329C2×#107—614no—
330C2×#106—614no—
331#417—6116no—
332C2×#103—614no—
333C2×#102—614no—
334#407C2×D6118yescomplemented
335C2×C22⋊C8C2×D6112yes—
336C2×C22⋊C8C2×D6112yes—
337C61C2×#309211yescharacteristic, complemented, Sylow
338C25D24411yescharacteristic
339C2×#41—614no—
340C2×#41—1222no—
341C2×#41—1228no—
342C22×Q8—611no—
343C22×D4—611no—
344C22×D4—1221no—
345C22×D4—1221no—
346C22×D4—1221no—
347C23×C4—28no—
348C23×C4—1228no—
349C23×C4—1222no—
350C23×C4—1222no—
351C23×C4—1222no—
352C23×C4—1221no—
353C23×C4—2448no—
354C23×C4D24411yescharacteristic
355C23×C4D24411yescharacteristic
356C23×C4D24411yescharacteristic
357C23×C4D24414yes—
358C23×C4C22×D6111yescharacteristic
359C23×C4C22×D6111yescharacteristic
360C23×C4C22×D6114yes—
361C23×C4C22×D6111yescharacteristic
362C2×M16—28no—
363C2×M16C22×D6118yes—
364C22×C8C22×D6114yes—
365#123—1228no—
366C22⋊Q8—614no—
367C22⋊Q8—614no—
368C22⋊Q8—1222no—
369C22⋊Q8—1222no—
370#121—614no—
371#121—614no—
372#121—1222no—
373#121—1222no—
374#120—1228no—
375C4×D4—1228no—
376C4×D4—1228no—
377#117—614no—
378#117—1222no—
379C2×C4⋊C4—614no—
380C2×C4⋊C4—618no—
381C2×C4⋊C4—618no—
382C2×C4⋊C4—618no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1228no—
386C2×C4⋊C4—1228no—
387C2×C4⋊C4—1224no—
388C2×C4⋊C4—1224no—
389C2×C4⋊C4—1228no—
390C2×C4⋊C4—1224no—
391C2×C4⋊C4—1222no—
392C2×C4⋊C4—1222no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C42—1221no—
402#107—6116no—
403#106—6116no—
404#103—6116no—
405#102—6116no—
406C22⋊C8C22×D6118yes—
407C22⋊C8C22×D6118yes—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—1221no—
412C24C2×D24414yes—
413C24C2×D24411yescharacteristic
414C24C2×D24411yescharacteristic
415C24C2×D24411yescharacteristic
416#41—12216no—
417#41—2448no—
418C2×Q8—612no—
419C2×Q8—1221no—
420C2×Q8—1224no—
421C2×D4—612no—
422C2×D4—1224no—
423C2×D4—1224no—
424C2×D4—1224no—
425C2×D4—1221no—
426C2×D4—1224no—
427C2×D4—2444no—
428C2×D4—2444no—
429C2×D4—2444no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—216no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—216no—
437C22×C4—1228no—
438C22×C4—1228no—
439C22×C4—1228no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1224no—
444C22×C4—1224no—
445C22×C4—24432no—
446C22×C4—2448no—
447C22×C4—2448no—
448C22×C4—2448no—
449C22×C4—2444no—
450C22×C4C2×D24414yes—
451C22×C4C2×D24414yes—
452C22×C4C2×D24412yes—
453C22×C4C2×D24412yes—
454C22×C4C2×D24414yes—
455C22×C4C2×D24411yescharacteristic
456C22×C4C2×D24411yescharacteristic
457C22×C4C2×D24412yes—
458C22×C4C2×D24411yescharacteristic
459C22×C4#1175822418yes—
460C22×C4C23×D6112yes—
461C22×C4C23×D6112yes—
462C22×C4C23×D6112yes—
463C22×C4C23×D6111yescharacteristic
464M16—216no—
465C2×C8—28no—
466C2×C8C23×D6118yes—
467C4⋊C4—618no—
468C4⋊C4—612no—
469C4⋊C4—612no—
470C4⋊C4—1228no—
471C4⋊C4—1228no—
472C4⋊C4—1228no—
473C4⋊C4—1224no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1224no—
477C4⋊C4—1224no—
478C22⋊C4—1224no—
479C22⋊C4—1224no—
480C22⋊C4—1224no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C42—1224no—
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—1222no—
495C23—2442no—
496C23—2442no—
497C23—2442no—
498C23#1451976114yes—
499C23#1451980514yes—
500C23#1451981014yes—
501C23C22×D24412yes—
502C23C22×D24412yes—
503C23C22×D24412yes—
504C23C22×D24411yescharacteristic
505Q8—1224no—
506Q8—2442no—
507D4—1224no—
508D4—2448no—
509D4—2448no—
510D4—2448no—
511D4—2442no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1228no—
525C2×C4—24416no—
526C2×C4—24416no—
527C2×C4—2442no—
528C2×C4—24416no—
529C2×C4—2448no—
530C2×C4—2442no—
531C2×C4—2442no—
532C2×C4—2448no—
533C2×C4#1451976114yes—
534C2×C4#1451976118yes—
535C2×C4C22×D24412yes—
536C2×C4C22×D24412yes—
537C2×C4C22×D24412yes—
538C2×C4C22×D24411yescharacteristic
539C2×C4C2×#1175822414yes—
540C2×C4C2×#1175822418yes—
541C2×C4C24×D6111yescharacteristic
542C8—28no—
543C22—232no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—4884no—
554C22—2442no—
555C22—2442no—
556C22—2442no—
557C22C2×#1451976114yes—
558C22C2×#1451976112yes—
559C22C2×#1451980514yes—
560C22C2×#1451980512yes—
561C22C2×#1451981014yes—
562C22C2×#1451981012yes—
563C22C23×D24411yescharacteristic
564C4—22no—
565C4—22no—
566C4—2448no—
567C4—2442no—
568C4—2442no—
569C4—2442no—
570C4C2×#1451976114yes—
571C4C2×#1451976112yes—
572C4C22×#1175822412yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—4882no—
577C2#2145574414yesdirect product factor
578C2C22×#1451976111yescharacteristic
579C2C22×#1451980511yescharacteristic
580C2C22×#1451981011yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#407C2
socleC23×C61C22×D4
prime radicalC2×#16840273C2
hypercenterC2×#407D61
hypocenterC61C2×#3092
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic61C2semidirect
3. #21455744C2direct (N × H)
4. C2×#16840098C2semidirect
5. C2×#16840081C2semidirect
6. C2×#16840093C2semidirect
7. C2×#16840076C2semidirect
8. C2×#16839804C2semidirect
9. C2×#16839764C2semidirect
10. C2×C61×#407C2semidirect
31. C22×C4⋊Dic61C22semidirect
32. #16840098C22semidirect
33. #16840093C22semidirect
34. #16840081C22semidirect
35. #16840076C22semidirect
36. #16839804C22semidirect
37. C2×#14519711C22semidirect
38. C2×#14519709C22semidirect
39. #16839764C22semidirect
40. C2×#14519702C22semidirect
41. C2×#14519699C22semidirect
44. C61×#407C22semidirect
98. #14519711C23semidirect
99. #14519709C23semidirect
100. #14519702C23semidirect
101. #14519699C23semidirect
292. C2×#407D61semidirect
296. C2×C61#3092semidirect
334. #407C2×D61semidirect
337. C61C2×#3092semidirect
577. C2#21455744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402732
C23×C4⋊Dic612
#214557442
C2×#168400982
C2×#168400812
C2×#168400932
C2×#168400762
C2×#168398042
C2×#168397642
C2×C61×#4072
C2×#309261