Finite Group Databasebeta

← C2×#21455863 #30548057

Subgroups — C2×#21455863 #30548057

Order 15616.

2602 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic, complemented
2C22×#14519739C211yesmaximal, characteristic, complemented
3#21455863C2116yesmaximal, direct product factor
4C2×#16840097C211yesmaximal, characteristic, complemented
5C2×#16840061C212yesmaximal, complemented
6C2×#16839976C212yesmaximal, complemented
7C2×#16839915C211yesmaximal, characteristic, complemented
8C2×#16839895C211yesmaximal, characteristic
9C2×#16839849C212yesmaximal, complemented
10C2×#16839842C212yesmaximal, complemented
11C2×#16839812C211yesmaximal, characteristic, complemented
12C2×C61×#481C211yesmaximal, characteristic, complemented
13C23×D244C2211yescharacteristic
14C23×C4×D61—21no—
15C22×#11758190C2212yes—
16C22×#11758199C2212yes—
17#16840293—24no—
18#16840293C2218yescomplemented
19C2×#14519770—21no—
20C2×#14519768C2211yescharacteristic, complemented
21C2×#14519764C2211yescharacteristic, complemented
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519742C2211yescharacteristic, complemented
25C2×D4×Dic61—21no—
26C2×D4×Dic61C2211yescharacteristic, complemented
27C2×#14519739—21no—
28C2×#14519739—21no—
29C2×#14519739—24no—
30C2×#14519739C2212yes—
31C2×#14519739C2212yes—
32C2×#14519739C2218yescomplemented
33C2×#14519733—21no—
34C22×#11758198—21no—
35C22×C4×Dic61C2211yescharacteristic
36#16840097C2218yescomplemented
37#16840061C22116yescomplemented
38#16839976C22116yescomplemented
39#16839915C2218yescomplemented
40#16839895C2218yes—
41#16839849C22116yescomplemented
42#16839842C22116yescomplemented
43#16839812C2218yescomplemented
44C2×#14519710C2212yescomplemented
45C2×#14519706C2212yescomplemented
46C2×#14519700C2212yescomplemented
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×C8×Dic61C2212yescomplemented
51C2×#121×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#481C2218yescomplemented
54C2×#106×C61C2212yescomplemented
55C2×#102×C61C2212yescomplemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C24×D61—21no—
58C22×Dic122C2311yescharacteristic
59C22×D244—21no—
60C22×D244—22no—
61C22×D244—28no—
62C22×D244C2314yes—
63C22×D244C2312yes—
64C23×Dic61—21no—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—28no—
70C22×C4×D61—48no—
71C2×#11758190—28no—
72C2×#11758190C2318yes—
73C2×#11758199—28no—
74C2×#11758199C2318yes—
75C22×#92418C2312yes—
76#14519770—28no—
77#14519768—22no—
78#14519768C2314yescomplemented
79#14519764—22no—
80#14519764C2314yescomplemented
81#14519758—28no—
82#14519756—22no—
83#14519756C2314yes—
84#14519742—22no—
85#14519742C2314yescomplemented
86D4×Dic61—28no—
87D4×Dic61—22no—
88D4×Dic61C2314yescomplemented
89#14519739—24no—
90#14519739—24no—
91#14519739—28no—
92#14519739—28no—
93#14519739C2318yes—
94#14519739C2318yes—
95#14519733—28no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—28no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D414yes—
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2314yes—
115#14519710C2318yescomplemented
116#14519706C2318yescomplemented
117#14519700C2318yescomplemented
118#14519699C2318yes—
119#14519697C2318yes—
120C22⋊#92418C2314yes—
121C8×Dic61C2318yescomplemented
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61C2312yes—
127#121×C61—22no—
128#121×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2314yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#106×C61C2318yescomplemented
136#102×C61C2318yescomplemented
137C22⋊C8×C61C2314yes—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—28no—
141C23×D61—24no—
142C23×D61—22no—
143C23×D61—44no—
144C23×D61—44no—
145C2×D4×C61—24no—
146C2×D4×C61—21no—
147C2×D4×C61—24no—
148C2×D4×C61—44no—
149C2×D4×C61C2412yes—
150C22×C4×C61—24no—
151C22×C4×C61—24no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—44no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2412yes—
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—24no—
160C22×Dic61—24no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—24no—
164C22×Dic61—44no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D414yes—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D414yes—
170C22×Dic61C2×D411yescharacteristic
171C2×D244—28no—
172C2×D244—216no—
173C2×D244—24no—
174C2×D244—22no—
175C2×D244—24no—
176C2×D244—216no—
177C2×D244#4118yes—
178C2×D244C2414yes—
179C2×C4×D61—28no—
180C2×C4×D61—28no—
181C2×C4×D61—48no—
182C2×C4×D61—432no—
183C2×C4×D61—48no—
184C2×Dic122—24no—
185C2×Dic122—21no—
186C2×Dic122C2412yes—
187C2×C8×C61—24no—
188C2×C8×C61C2414yes—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61C2414yes—
193C4⋊C4×C61C2412yes—
194C22⋊C4×C61—24no—
195C22⋊Dic61—24no—
196C22⋊Dic61—24no—
197C22⋊Dic61—24no—
198C22⋊Dic61—24no—
199#11758199—216no—
200#11758198—28no—
201#11758198—28no—
202C4⋊Dic61—21no—
203C4⋊Dic61—24no—
204C4⋊Dic61C2412yes—
205#11758196—24no—
206#11758196—24no—
207#11758196—24no—
208C4×Dic61—24no—
209C4×Dic61C2×D414yes—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
217#11758190—216no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61#13514yes—
225C23×C61C22×D412yes—
226C23×C61C22×D411yescharacteristic
227C22×D61—216no—
228C22×D61—28no—
229C22×D61—24no—
230C22×D61—48no—
231C22×D61—432no—
232C22×D61—48no—
233C22×D61—44no—
234C22×D61—44no—
235D4×C61—24no—
236D4×C61—48no—
237D4×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—48no—
244C2×C4×C61—42no—
245C2×C4×C61—44no—
246C2×C4×C61C22×D412yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4114yes—
249C2×C4×C61C2511yescharacteristic
250C2×Dic61—28no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—28no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—48no—
260C2×Dic61AGL(1,ℤ/8)14yes—
261C2×Dic61C22×D412yes—
262C2×Dic61C22×D412yes—
263C2×Dic61C22×D412yes—
264C2×Dic61C22×D412yes—
265D244—216no—
266D244—28no—
267D244—24no—
268D244C2×#4118yes—
269C4×D61—416no—
270C4×D61—416no—
271Dic122—24no—
272Dic122—42no—
273C8×C61—24no—
274#92418—24no—
275C2×#3105—611nomaximal, Sylow
276C22×C61—28no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—84no—
283C22×C61#52512yes—
284C22×C61C2×#13514yes—
285C22×C61C2×#13512yes—
286C22×C61C2×AGL(1,ℤ/8)12yes—
287C22×C61C23×D411yescharacteristic
288C2×D61—28no—
289C2×D61—432no—
290C2×D61—416no—
291C2×D61—44no—
292C2×D61—44no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61#52512yes—
297C4×C61C22×#4112yes—
298Dic61—22no—
299Dic61—22no—
300Dic61—22no—
301Dic61—42no—
302Dic61—42no—
303Dic61C2×AGL(1,ℤ/8)14yes—
304C2×#529—611no—
305C22×C4×D4—611no—
306#3105—6116no—
307C2×#484—611no—
308C2×#481D6111yescharacteristic, complemented
309C2×#478—612no—
310C2×#463—612no—
311C2×#450—611no—
312C2×#447—611no—
313C2×C4×SD16—612no—
314C2×C4×D8—612no—
315C2×#431—611no—
316C2×C61—24no—
317C2×C61—82no—
318C2×C61#310514yescomplemented
319C2×C61C2×#52511yescharacteristic
320C2×C61C22×#13511yescharacteristic
321C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
322D61—48no—
323C23×D4—611no—
324C24×C4—1221no—
325C22×SD16—612no—
326C22×D8—612no—
327#529—618no—
328#529—1224no—
329C2×#126—1221no—
330C2×#125—611no—
331C2×#124—611no—
332C2×#123—1221no—
333C2×C22⋊Q8—611no—
334C2×#121C2×D6111yescharacteristic
335C2×C4×Q8—611no—
336C2×C4×D4—611no—
337C2×C4×D4—612no—
338C2×C4×D4—612no—
339C2×C4×D4—618no—
340C2×C4×D4—1221no—
341C2×C4×D4—1221no—
342C2×C4×D4—1224no—
343C2×C4×D4—1221no—
344C2×#117—1221no—
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C22⋊C4—1221no—
347C22×C42—611no—
348#484—618no—
349#481C2×D6118yescomplemented
350#478—6116no—
351#463—6116no—
352#450—618no—
353#447—618no—
354C4×SD16—6116no—
355C4×D8—6116no—
356#431—618no—
357C2×#107—612no—
358C2×#106C2×D6112yescomplemented
359C2×C4⋊C8—612no—
360C2×#103—612no—
361C2×#102—612no—
362C2×#102—612no—
363C2×#102C2×D6112yescomplemented
364C2×C22⋊C8—611no—
365C2×C22⋊C8C2×D6111yescharacteristic
366C2×C4×C8—612no—
367C61C2×#310511yescharacteristic, complemented, Sylow
368C25—1221no—
369C22×Q8—611no—
370C22×D4—21no—
371C22×D4—612no—
372C22×D4—614no—
373C22×D4—1228no—
374C22×D4—1222no—
375C22×D4—1221no—
376C22×D4C22×D6111yescharacteristic
377C23×C4—21no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—1228no—
381C23×C4—1222no—
382C23×C4—1222no—
383C23×C4—1221no—
384C23×C4—2448no—
385C23×C4C22×D6111yescharacteristic
386C2×SD16—618no—
387C2×SD16—1228no—
388C2×D8—618no—
389C2×D8—1228no—
390C22×C8—612no—
391C22×C8C22×D6112yes—
392#126—1228no—
393#125—614no—
394#125—1222no—
395#124—614no—
396#124—1222no—
397#123—1228no—
398C22⋊Q8—614no—
399C22⋊Q8—1222no—
400#121—22no—
401#121C22×D6114yes—
402C4×Q8—614no—
403C4×Q8—1222no—
404C4×D4—614no—
405C4×D4—618no—
406C4×D4—618no—
407C4×D4—1228no—
408C4×D4—1224no—
409C4×D4—1224no—
410C4×D4—1228no—
411C4×D4—1222no—
412C4×D4—1228no—
413#117—1228no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4C22×D6112yes—
422C2×C4⋊C4C22×D6114yes—
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—1228no—
426C2×C22⋊C4—1222no—
427C2×C22⋊C4—1222no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—614no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—614no—
438C2×C42—1221no—
439#107—618no—
440#106C22×D6118yescomplemented
441C4⋊C8—618no—
442#103—618no—
443#102—618no—
444#102—618no—
445#102C22×D6118yescomplemented
446C22⋊C8—614no—
447C22⋊C8C22×D6114yes—
448C4×C8—618no—
449C24—21no—
450C24—1228no—
451C24—1224no—
452C24—1222no—
453C24—2444no—
454C24—2444no—
455C24D4×D6111yescharacteristic
456C2×Q8—612no—
457C2×Q8—1221no—
458C2×Q8—1224no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—24no—
462C2×D4—44no—
463C2×D4—618no—
464C2×D4—614no—
465C2×D4—12216no—
466C2×D4—1228no—
467C2×D4—12216no—
468C2×D4—1224no—
469C2×D4—1222no—
470C2×D4—1224no—
471C2×D4C23×D6112yes—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—611no—
478C22×C4—614no—
479C22×C4—614no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—1228no—
484C22×C4—1228no—
485C22×C4—1224no—
486C22×C4—1224no—
487C22×C4—1224no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—2448no—
491C22×C4—24432no—
492C22×C4—2448no—
493C22×C4—2444no—
494C22×C4D4×D6112yes—
495C22×C4D4×D6111yescharacteristic
496C22×C4C23×D6112yes—
497C22×C4C23×D6111yescharacteristic
498SD16—12216no—
499D8—12216no—
500C2×C8—24no—
501C2×C8—614no—
502C2×C8—1224no—
503C2×C8C23×D6114yes—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—612no—
508C4⋊C4—1224no—
509C4⋊C4—1224no—
510C4⋊C4—1224no—
511C4⋊C4—1221no—
512C4⋊C4—1224no—
513C4⋊C4C23×D6112yes—
514C4⋊C4C23×D6114yes—
515C22⋊C4—24no—
516C22⋊C4—1228no—
517C22⋊C4—1228no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C42—614no—
523C42—612no—
524C42—612no—
525C42—614no—
526C42—612no—
527C42—612no—
528C42—1224no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—12216no—
536C23—1228no—
537C23—1224no—
538C23—2448no—
539C23—24432no—
540C23—2448no—
541C23—2444no—
542C23—2444no—
543C23#1451979814yes—
544C23C2×D4×D6112yes—
545C23C2×D4×D6111yescharacteristic
546Q8—1224no—
547Q8—2442no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—618no—
552D4—12216no—
553D4—1228no—
554D4—1224no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—614no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—1228no—
569C2×C4—1228no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—24416no—
576C2×C4—24416no—
577C2×C4—2448no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6111yescharacteristic
582C2×C4#41×D6114yes—
583C2×C4C24×D6111yescharacteristic
584C8—24no—
585C8—1224no—
586C22—22no—
587C22—22no—
588C22—28no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—84no—
593C22—1228no—
594C22—24432no—
595C22—2444no—
596C22—2444no—
597C22—24416no—
598C22#1684027012yes—
599C22C2×#1451979814yes—
600C22C2×#1451979812yes—
601C22AGL(1,ℤ/8)×D6112yes—
602C22C22×D4×D6111yescharacteristic
603C4—22no—
604C4—42no—
605C4—44no—
606C4—614no—
607C4—1222no—
608C4—1222no—
609C4—1222no—
610C4—2442no—
611C4—2442no—
612C4#1684027012yes—
613C4C2×#41×D6112yes—
614C2—24no—
615C2—82no—
616C2—2448no—
617C2#2145586314yesdirect product factor
618C2C2×#1684027011yescharacteristic
619C2C22×#1451979811yescharacteristic
620C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
hypercenterC2×#481D61
hypocenterC61C2×#3105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16840293C2semidirect
2. C22×#14519739C2semidirect
3. #21455863C2direct (N × H)
4. C2×#16840097C2semidirect
5. C2×#16840061C2semidirect
6. C2×#16839976C2semidirect
7. C2×#16839915C2semidirect
9. C2×#16839849C2semidirect
10. C2×#16839842C2semidirect
11. C2×#16839812C2semidirect
12. C2×C61×#481C2semidirect
18. #16840293C22semidirect
20. C2×#14519768C22semidirect
21. C2×#14519764C22semidirect
24. C2×#14519742C22semidirect
26. C2×D4×Dic61C22semidirect
32. C2×#14519739C22semidirect
36. #16840097C22semidirect
37. #16840061C22semidirect
38. #16839976C22semidirect
39. #16839915C22semidirect
41. #16839849C22semidirect
42. #16839842C22semidirect
43. #16839812C22semidirect
44. C2×#14519710C22semidirect
45. C2×#14519706C22semidirect
46. C2×#14519700C22semidirect
50. C2×C8×Dic61C22semidirect
53. C61×#481C22semidirect
54. C2×#106×C61C22semidirect
55. C2×#102×C61C22semidirect
78. #14519768C23semidirect
80. #14519764C23semidirect
85. #14519742C23semidirect
88. D4×Dic61C23semidirect
115. #14519710C23semidirect
116. #14519706C23semidirect
117. #14519700C23semidirect
121. C8×Dic61C23semidirect
135. #106×C61C23semidirect
136. #102×C61C23semidirect
308. C2×#481D61semidirect
318. C2×C61#3105semidirect
349. #481C2×D61semidirect
358. C2×#106C2×D61semidirect
363. C2×#102C2×D61semidirect
367. C61C2×#3105semidirect
440. #106C22×D61semidirect
445. #102C22×D61semidirect
617. C2#21455863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402932
C22×#145197392
#214558632
C2×#168400972
C2×#168400612
C2×#168399762
C2×#168399152
C2×#168398952
C2×#168398492
C2×#168398422
C2×#168398122
C2×C61×#4812
C2×#310561