Finite Group Databasebeta

← C2×#21457147 #30552808

Subgroups — C2×#21457147 #30552808

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic, complemented
2C2×#16840294C211yesmaximal, characteristic, complemented
3#21457147C2116yesmaximal, direct product factor
4C2×#16840054C211yesmaximal, characteristic, complemented
5C2×#16840061C212yesmaximal, complemented
6C2×#16839997C212yesmaximal, complemented
7C2×#16839992C212yesmaximal, complemented
8C2×#16839963C211yesmaximal, characteristic, complemented
9C2×#16839976C212yesmaximal, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
12C2×C61×#476C211yesmaximal, characteristic, complemented
13C22×#11758226—21no—
14C22×#11758190C2212yes—
15C22×#11758199C2212yes—
16C22×C8×D61C2212yes—
17#16840313—24no—
18#16840313C2218yescomplemented
19C2×#14519774C2211yescharacteristic
20#16840294—24no—
21#16840294C2218yescomplemented
22C2×#14519770—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519766—21no—
25C2×#14519764C2211yescharacteristic
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519752C2212yes—
30C2×#14519748C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519739—21no—
33C2×#14519739C2212yes—
34C2×C4×C22⋊D61—21no—
35C2×#14519736—21no—
36C2×C42×D61C2211yescharacteristic
37#16840061C22116yescomplemented
38#16840054C2218yescomplemented
39#16839997C22116yescomplemented
40#16839992C22116yescomplemented
41#16839976C22116yescomplemented
42#16839963C2218yescomplemented
43#16839957C2218yescomplemented
44C2×#14519710C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519706C2212yes—
47C4⋊C8×D61C2218yescomplemented
48C2×#14519700C2212yes—
49C2×#14519699C2212yes—
50C2×#14519697C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#476C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758226—28no—
58C2×#11758226—48no—
59C22×Dic122C2311yescharacteristic
60C22×D244—22no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244C2312yes—
64C22×C22⋊D61—21no—
65C22×C4×D61—22no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758190—44no—
70C2×#11758190C2318yes—
71C2×#11758199—44no—
72C2×#11758199C2318yes—
73C22×#92418C2312yes—
74C2×C8×D61—44no—
75C2×C8×D61C2318yes—
76#14519774—22no—
77#14519774C2314yes—
78#14519770—28no—
79#14519768—22no—
80#14519768C2314yes—
81#14519766—28no—
82#14519764—22no—
83#14519764C2314yes—
84#14519759—28no—
85#14519757—22no—
86#14519757C2314yes—
87#14519752—28no—
88#14519752—24no—
89#14519752C2318yes—
90#14519748—22no—
91#14519748C2314yes—
92C4×Dic122—22no—
93C4×Dic122C2314yes—
94#14519739—28no—
95#14519739—24no—
96#14519739C2318yes—
97C4×C22⋊D61—28no—
98#14519736—28no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C42×D61D414yes—
115C42×D61C2314yes—
116#14519710C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519700C2318yes—
120#14519699C2318yes—
121#14519697C2318yes—
122C22×Q8×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128C4×D4×C61—22no—
129C4×D4×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#106×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#102×C61C2318yes—
138C24×C61—21no—
139C23×D61—22no—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—24no—
142C2×Q8×C61—44no—
143C2×D4×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61C2412yes—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—24no—
150C22×C4×C61—44no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—44no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161#11758226—432no—
162C2×D244—24no—
163C2×D244—24no—
164C2×D244—28no—
165C2×D244—24no—
166C2×D244—24no—
167C2×D244—22no—
168C2×D244—44no—
169C2×D244—48no—
170C2×D244—44no—
171C2×D244C2414yes—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—28no—
177C2×C4×D61—48no—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2×D414yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2412yes—
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122—21no—
185C2×Dic122C2412yes—
186C2×C8×C61—24no—
187C2×C8×C61C2414yes—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61C2414yes—
192C4⋊C4×C61C2412yes—
193C22⋊C4×C61—24no—
194C42×C61C2×D412yes—
195C42×C61C2412yes—
196C22⋊Dic61—24no—
197C22⋊Dic61—24no—
198C22⋊Dic61—24no—
199#11758199—48no—
200#11758198—24no—
201#11758198—28no—
202#11758198—28no—
203C4⋊Dic61—21no—
204C4⋊Dic61—24no—
205C4⋊Dic61—24no—
206C4⋊Dic61C2412yes—
207#11758196—24no—
208#11758196—24no—
209C4×Dic61—24no—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216#11758190—48no—
217C8×D61—48no—
218C23×C61—22no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61C22×D411yescharacteristic
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—24no—
226C22×D61—44no—
227C22×D61—44no—
228C22×D61—44no—
229C22×D61AGL(1,ℤ/8)14yes—
230C22×D61C22×D412yes—
231Q8×C61—48no—
232D4×C61—22no—
233D4×C61—22no—
234D4×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—42no—
239C2×C4×C61—44no—
240C2×C4×C61—48no—
241C2×C4×C61#13514yes—
242C2×C4×C61C22×D412yes—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D412yes—
245C2×C4×C61H(5,𝔽2)12yes—
246C2×C4×C612−1+412yes—
247C2×C4×C61C2511yescharacteristic
248C22⋊D61—48no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258C2×Dic61C22×D412yes—
259D244—24no—
260D244—24no—
261D244—48no—
262D244—416no—
263D244—44no—
264D244—48no—
265C4×D61—28no—
266C4×D61—24no—
267C4×D61—28no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—416no—
271Dic122—22no—
272Dic122—22no—
273Dic122—42no—
274C8×C61—24no—
275#92418—24no—
276C2×#3247—611nomaximal, Sylow
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—84no—
281C22×C61#53712yes—
282C22×C61C2×#13512yes—
283C22×C61C2×AGL(1,ℤ/8)12yes—
284C22×C61C23×D411yescharacteristic
285C2×D61—22no—
286C2×D61—28no—
287C2×D61—22no—
288C2×D61—44no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—88no—
292C2×D61C2×AGL(1,ℤ/8)14yes—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61#53712yes—
297C4×C61C2×#13514yes—
298C4×C61C2×H(5,𝔽2)11yescharacteristic
299C4×C61C2×2−1+411yescharacteristic
300Dic61—22no—
301Dic61—22no—
302Dic61—22no—
303Dic61—42no—
304Dic61—42no—
305C2×#532—611no—
306C2×#529—611no—
307#3247—6116no—
308C2×#477—611no—
309C2×#478—612no—
310C2×#476D6111yescharacteristic, complemented
311C2×#466—612no—
312C2×#465—612no—
313C2×#460—611no—
314C2×#463—612no—
315C2×#459—611no—
316C22×C4⋊C8—611no—
317C2×C61—82no—
318C2×C61#324714yescomplemented
319C2×C61C2×#53711yescharacteristic
320C2×C61C22×#13511yescharacteristic
321C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
322D61—24no—
323D61—84no—
324C22×#41—1221no—
325C22×SD16—612no—
326C22×D8—612no—
327C23×C8—612no—
328#532—618no—
329#532—1224no—
330C2×C4⋊Q8C2×D6111yescharacteristic
331C2×#127—611no—
332#529—618no—
333#529—1224no—
334C2×#126—1221no—
335C2×#125—611no—
336C2×#124—611no—
337C2×#124—1221no—
338C2×#123—1221no—
339C2×C22⋊Q8—611no—
340C2×#121—611no—
341C2×#121—612no—
342C2×#121—1221no—
343C2×C4×Q8—611no—
344C2×C4×D4—612no—
345C2×C4×D4—1221no—
346C2×C4×D4—1221no—
347C2×C4×D4C2×D6111yescharacteristic
348C2×#117—1221no—
349C22×C42—611no—
350#478—6116no—
351#477—618no—
352#476C2×D6118yescomplemented
353#466—6116no—
354#465—6116no—
355#463—6116no—
356#460—618no—
357#459—618no—
358C2×#107—612no—
359C2×#106C2×D6112yes—
360C2×C4⋊C8—612no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—618no—
363C2×C4⋊C8C2×D6111yescharacteristic
364C2×#103—612no—
365C2×#102—612no—
366C2×#102—612no—
367C2×#102C2×D6112yes—
368C61C2×#324711yescharacteristic, complemented, Sylow
369C2×#41—1228no—
370C2×#41—2448no—
371C22×Q8—21no—
372C22×Q8—611no—
373C22×D4—612no—
374C22×D4—1222no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4—1221no—
378C22×D4C22×D6111yescharacteristic
379C23×C4—21no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1222no—
384C2×SD16—618no—
385C2×SD16—2444no—
386C2×D8—618no—
387C2×D8—2444no—
388C22×C8—612no—
389C22×C8—618no—
390C22×C8—2444no—
391C22×C8C22×D6112yes—
392C4⋊Q8—22no—
393C4⋊Q8C22×D6114yes—
394#127—614no—
395#127—1222no—
396#126—1228no—
397#125—614no—
398#125—1222no—
399#124—614no—
400#124—1222no—
401#124—1228no—
402#123—1228no—
403C22⋊Q8—614no—
404C22⋊Q8—1222no—
405#121—614no—
406#121—618no—
407#121—1224no—
408#121—1228no—
409#121—1222no—
410C4×Q8—614no—
411C4×Q8—1222no—
412C4×D4—22no—
413C4×D4—618no—
414C4×D4—1224no—
415C4×D4—1228no—
416C4×D4—1228no—
417C4×D4C22×D6114yes—
418#117—1228no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C22×D6112yes—
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1222no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—614no—
438C2×C42—614no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441#107—618no—
442#106C22×D6118yes—
443C4⋊C8—618no—
444C4⋊C8—614no—
445C4⋊C8C22×D6114yes—
446#103—618no—
447#102—618no—
448#102—618no—
449#102C22×D6118yes—
450C24—21no—
451C24—611no—
452C24—1222no—
453#41—24432no—
454C2×Q8—24no—
455C2×Q8—44no—
456C2×Q8—612no—
457C2×Q8—1221no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—614no—
464C2×D4—1228no—
465C2×D4—1224no—
466C2×D4—1224no—
467C2×D4—1222no—
468C2×D4—1224no—
469C2×D4—1224no—
470C2×D4—1224no—
471C2×D4—2444no—
472C2×D4—2448no—
473C2×D4—2444no—
474C2×D4—2444no—
475C2×D4C23×D6112yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—44no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—614no—
484C22×C4—612no—
485C22×C4—614no—
486C22×C4—612no—
487C22×C4—1228no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1224no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—2448no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498SD16—2448no—
499D8—2448no—
500C2×C8—24no—
501C2×C8—614no—
502C2×C8—1224no—
503C2×C8—2448no—
504C2×C8C23×D6114yes—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—612no—
509C4⋊C4—1224no—
510C4⋊C4—1224no—
511C4⋊C4—1224no—
512C4⋊C4—1221no—
513C4⋊C4—1224no—
514C4⋊C4C23×D6112yes—
515C4⋊C4C23×D6114yes—
516C22⋊C4—24no—
517C22⋊C4—1228no—
518C22⋊C4—1228no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1224no—
523C42—614no—
524C42—612no—
525C42—614no—
526C42—612no—
527C42—1224no—
528C42D4×D6112yes—
529C42C23×D6112yes—
530C23—22no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—614no—
535C23—612no—
536C23—1222no—
537C23—1222no—
538C23—1224no—
539C23—2444no—
540C23—2444no—
541C23—2444no—
542C23C2×D4×D6111yescharacteristic
543Q8—48no—
544Q8—1222no—
545Q8—1222no—
546Q8—2442no—
547D4—22no—
548D4—22no—
549D4—42no—
550D4—1224no—
551D4—1224no—
552D4—2448no—
553D4—24416no—
554D4—2448no—
555D4—2448no—
556D4—2444no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—612no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—1228no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1228no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—24416no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4#1451979814yes—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6112yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#1451982312yes—
584C2×C4#1451982512yes—
585C2×C4C24×D6111yescharacteristic
586C8—24no—
587C8—1224no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—84no—
592C22—614no—
593C22—1222no—
594C22—1222no—
595C22—1228no—
596C22—4888no—
597C22—2444no—
598C22—2444no—
599C22—2444no—
600C22#1684034212yes—
601C22C2×#1451979812yes—
602C22AGL(1,ℤ/8)×D6112yes—
603C22C22×D4×D6111yescharacteristic
604C4—22no—
605C4—42no—
606C4—44no—
607C4—1222no—
608C4—1222no—
609C4—1222no—
610C4—2442no—
611C4—2442no—
612C4#1684034212yes—
613C4C2×#1451979814yes—
614C4C2×#1451982311yescharacteristic
615C4C2×#1451982511yescharacteristic
616C2—82no—
617C2—1224no—
618C2—4884no—
619C2#2145714714yesdirect product factor
620C2C2×#1684034211yescharacteristic
621C2C22×#1451979811yescharacteristic
622C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
hypercenterC2×#476D61
hypocenterC61C2×#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16840313C2semidirect
2. C2×#16840294C2semidirect
3. #21457147C2direct (N × H)
4. C2×#16840054C2semidirect
5. C2×#16840061C2semidirect
6. C2×#16839997C2semidirect
7. C2×#16839992C2semidirect
8. C2×#16839963C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839957C2semidirect
11. C2×C4⋊C8×D61C2semidirect
12. C2×C61×#476C2semidirect
18. #16840313C22semidirect
21. #16840294C22semidirect
37. #16840061C22semidirect
38. #16840054C22semidirect
39. #16839997C22semidirect
40. #16839992C22semidirect
41. #16839976C22semidirect
42. #16839963C22semidirect
43. #16839957C22semidirect
47. C4⋊C8×D61C22semidirect
53. C61×#476C22semidirect
310. C2×#476D61semidirect
318. C2×C61#3247semidirect
352. #476C2×D61semidirect
368. C61C2×#3247semidirect
619. C2#21457147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403132
C2×#168402942
#214571472
C2×#168400542
C2×#168400612
C2×#168399972
C2×#168399922
C2×#168399632
C2×#168399762
C2×#168399572
C2×C4⋊C8×D612
C2×C61×#4762
C2×#324761