Finite Group Databasebeta

← C2×#21455938 #30548204

Subgroups — C2×#21455938 #30548204

Order 15616.

2398 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×#16840307C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3#21455938C2116yesmaximal, direct product factor
4C2×#16840075C211yesmaximal, characteristic, complemented
5C2×#16840056C212yesmaximal, complemented
6C2×#16839961C212yesmaximal, complemented
7C2×#16839903C211yesmaximal, characteristic, complemented
8C2×#16839900C211yesmaximal, characteristic, complemented
9C2×#16839861C212yesmaximal, complemented
10C2×#16839859C212yesmaximal, complemented
11C2×#16839816C211yesmaximal, characteristic, complemented
12C2×C61×#480C211yesmaximal, characteristic, complemented
13C22×#11758224—21no—
14C23×Dic122C2211yescharacteristic
15C22×#11758190C2212yes—
16C22×#11758200C2212yes—
17#16840307—24no—
18#16840307C2218yes—
19C2×#14519776C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21C2×#14519763—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519742—21no—
25C2×#14519742—21no—
26C2×#14519742—24no—
27C2×#14519742C2212yes—
28C2×#14519742C2212yes—
29C2×#14519742C2218yescomplemented
30C2×D4×Dic61C2211yescharacteristic
31C2×#14519739C2211yescharacteristic
32C2×#14519737—21no—
33C22×#11758196—21no—
34C22×C4×Dic61—21no—
35C22×C4×Dic61C2211yescharacteristic
36#16840075C2218yescomplemented
37#16840056C22116yescomplemented
38#16839961C22116yescomplemented
39#16839903C2218yescomplemented
40#16839900C2218yescomplemented
41#16839861C22116yescomplemented
42#16839859C22116yescomplemented
43#16839816C2218yescomplemented
44C2×#14519710C2212yes—
45C2×#14519706C2212yes—
46C2×#14519702C2212yes—
47C2×#14519700C2212yes—
48C2×#14519697C2212yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519687C2212yes—
51C2×#121×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#480C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×#102×C61C2212yes—
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#11758224—28no—
58C2×#11758224—48no—
59C22×Dic122—21no—
60C22×Dic122—22no—
61C22×Dic122—28no—
62C22×Dic122—21no—
63C22×Dic122C2314yes—
64C22×Dic122C2312yes—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C23×Dic61—21no—
70C23×Dic61—21no—
71C23×Dic61D411yescharacteristic
72C23×Dic61D411yescharacteristic
73C22×C4×D61—21no—
74C2×#11758190—28no—
75C2×#11758190C2318yes—
76C2×#11758200—28no—
77C2×#11758200C2318yes—
78C22×#92418C2312yes—
79#14519776—22no—
80#14519776C2314yes—
81#14519773—22no—
82#14519773C2314yes—
83#14519763—28no—
84#14519751—22no—
85#14519751C2314yes—
86#14519749—28no—
87#14519742—24no—
88#14519742—24no—
89#14519742—28no—
90#14519742—28no—
91#14519742C2318yes—
92#14519742C2318yes—
93D4×Dic61—22no—
94D4×Dic61C2314yes—
95#14519739—22no—
96#14519739C2314yes—
97#14519737—28no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—28no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—28no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D414yes—
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2314yes—
115#14519710C2318yes—
116#14519706C2318yes—
117#14519702C2318yes—
118#14519700C2318yes—
119#14519697C2318yes—
120C22⋊#92418C2314yes—
121#14519687C2318yes—
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×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2312yes—
133C2×C4⋊C4×C61C2314yes—
134C2×C22⋊C4×C61—21no—
135#107×C61C2318yes—
136#102×C61C2318yes—
137C22⋊C8×C61C2314yes—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C2×D4×C61—24no—
142C2×D4×C61—21no—
143C2×D4×C61—24no—
144C2×D4×C61—44no—
145C2×D4×C61C2412yes—
146C22×C4×C61—24no—
147C22×C4×C61—21no—
148C22×C4×C61—24no—
149C22×C4×C61—22no—
150C22×C4×C61—44no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2412yes—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—24no—
156C2×C22⋊D61—24no—
157C2×C22⋊D61—24no—
158C2×C22⋊D61—44no—
159C2×C22⋊D61—44no—
160C2×C22⋊D61—44no—
161C22×Dic61—28no—
162C22×Dic61—24no—
163C22×Dic61—24no—
164C22×Dic61—22no—
165C22×Dic61—24no—
166C22×Dic61—21no—
167C22×Dic61—24no—
168C22×Dic61—44no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D414yes—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D414yes—
174C22×Dic61C2×D411yescharacteristic
175#11758224—432no—
176C2×D244—24no—
177C2×D244—21no—
178C2×D244C2412yes—
179C2×C4×D61—24no—
180C2×C4×D61—44no—
181C2×Dic122—28no—
182C2×Dic122—216no—
183C2×Dic122—24no—
184C2×Dic122—22no—
185C2×Dic122—24no—
186C2×Dic122—216no—
187C2×Dic122—24no—
188C2×Dic122—44no—
189C2×Dic122#4118yescomplemented
190C2×Dic122C2414yes—
191C2×C8×C61—24no—
192C2×C8×C61C2414yes—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61C2414yes—
197C4⋊C4×C61C2412yes—
198C22⋊C4×C61—24no—
199C22⋊Dic61—24no—
200#11758200—216no—
201#11758198—24no—
202#11758198—24no—
203C4⋊Dic61—21no—
204C4⋊Dic61C2412yes—
205#11758196—28no—
206#11758196—28no—
207#11758196—24no—
208C4×Dic61—28no—
209C4×Dic61—28no—
210C4×Dic61C2×D414yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2×D412yes—
214C4×Dic61C2412yes—
215C4×Dic61C2412yes—
216C2×#92418—24no—
217C2×#92418C2414yes—
218#11758190—216no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61AGL(1,ℤ/8)14yes—
226C23×C61C22×D412yes—
227C23×C61C22×D411yescharacteristic
228C22×D61—22no—
229C22×D61—42no—
230C22×D61—42no—
231C22×D61—42no—
232D4×C61—24no—
233D4×C61—48no—
234D4×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—42no—
241C2×C4×C61—48no—
242C2×C4×C61—44no—
243C2×C4×C61C22×D412yes—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4114yes—
246C2×C4×C61C2511yescharacteristic
247C22⋊D61—48no—
248C22⋊D61—48no—
249C22⋊D61—48no—
250C2×Dic61—216no—
251C2×Dic61—28no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—28no—
255C2×Dic61—22no—
256C2×Dic61—24no—
257C2×Dic61—28no—
258C2×Dic61—22no—
259C2×Dic61—48no—
260C2×Dic61—42no—
261C2×Dic61#13714yes—
262C2×Dic61C22×D412yes—
263C2×Dic61C22×D412yes—
264C2×Dic61C22×D412yes—
265C2×Dic61C22×D412yes—
266D244—24no—
267D244—42no—
268C4×D61—48no—
269Dic122—216no—
270Dic122—28no—
271Dic122—24no—
272Dic122—48no—
273Dic122C2×#4118yescomplemented
274C8×C61—24no—
275#92418—24no—
276C2×#3112—611nomaximal, Sylow
277C22×C61—28no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—84no—
284C22×C61#52512yes—
285C22×C61C2×AGL(1,ℤ/8)14yes—
286C22×C61C2×AGL(1,ℤ/8)12yes—
287C22×C61C2×#13712yes—
288C22×C61C23×D411yescharacteristic
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—84no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61#52512yes—
297C4×C61C22×#4112yes—
298Dic61—28no—
299Dic61—22no—
300Dic61—22no—
301Dic61—22no—
302Dic61—42no—
303Dic61C2×#13714yes—
304C2×#532—611no—
305C22×C4×Q8—611no—
306#3112—6116no—
307C2×#480—611no—
308C2×#480D6111yescharacteristic, complemented
309C2×#477—612no—
310C2×#460—612no—
311C2×#448—611no—
312C2×#448—611no—
313C2×#440—612no—
314C2×#440—612no—
315C2×#432—611no—
316C2×C61—24no—
317C2×C61—82no—
318C2×C61#311214yescomplemented
319C2×C61C2×#52511yescharacteristic
320C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
321C2×C61C22×#13711yescharacteristic
322D61—82no—
323C22×#41—1221no—
324C23×Q8—611no—
325C22×SD16—612no—
326C22×SD16—612no—
327#532—618no—
328#532—1224no—
329C2×C4⋊Q8—611no—
330C2×#127—611no—
331C2×#124—1221no—
332C2×#121—611no—
333C2×#121—1221no—
334C2×#121C2×D6111yescharacteristic
335C2×C4×Q8—612no—
336C2×C4×Q8—612no—
337C2×C4×Q8—618no—
338C2×C4×Q8—1221no—
339C2×C4×Q8—1221no—
340C2×C4×Q8—1224no—
341C2×C4×D4—611no—
342C2×C4×D4—611no—
343C2×C4×D4—1221no—
344C22×C4⋊C4—1221no—
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C42—611no—
347C22×C42—1221no—
348#480—618no—
349#480C2×D6118yescomplemented
350#477—6116no—
351#460—6116no—
352#448—618no—
353#448—618no—
354#440—6116no—
355#440—6116no—
356#432—618no—
357C2×#107—612no—
358C2×#107C2×D6112yes—
359C2×C4⋊C8—612no—
360C2×#103—612no—
361C2×#103—612no—
362C2×#102—612no—
363C2×#102C2×D6112yes—
364C2×C22⋊C8—611no—
365C2×C22⋊C8C2×D6111yescharacteristic
366C2×#97—612no—
367C61C2×#311211yescharacteristic, complemented, Sylow
368C2×#41—1228no—
369C2×#41—2448no—
370C22×Q8—612no—
371C22×Q8—614no—
372C22×Q8—1221no—
373C22×Q8—1228no—
374C22×Q8—1222no—
375C22×Q8—1221no—
376C22×D4—21no—
377C22×D4—611no—
378C22×D4—1221no—
379C22×D4—1221no—
380C22×D4—1221no—
381C22×D4C22×D6111yescharacteristic
382C23×C4—21no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—1221no—
386C23×C4—1221no—
387C23×C4—1221no—
388C23×C4C22×D6111yescharacteristic
389C2×SD16—618no—
390C2×SD16—618no—
391C2×SD16—1228no—
392C2×SD16—1228no—
393C22×C8—612no—
394C22×C8C22×D6112yes—
395C4⋊Q8—614no—
396C4⋊Q8—1222no—
397#127—614no—
398#127—1222no—
399#124—1228no—
400#121—22no—
401#121—614no—
402#121—1228no—
403#121—1222no—
404#121C22×D6114yes—
405C4×Q8—618no—
406C4×Q8—618no—
407C4×Q8—1224no—
408C4×Q8—1228no—
409C4×Q8—1228no—
410C4×Q8—1224no—
411C4×D4—614no—
412C4×D4—614no—
413C4×D4—1228no—
414C4×D4—1222no—
415C4×D4—1222no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—1228no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1222no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C22×D6112yes—
424C2×C4⋊C4C22×D6114yes—
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—614no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—614no—
436C2×C42—1228no—
437C2×C42—1222no—
438C2×C42—1222no—
439#107—618no—
440#107C22×D6118yes—
441C4⋊C8—618no—
442#103—618no—
443#103—618no—
444#102—618no—
445#102C22×D6118yes—
446C22⋊C8—614no—
447C22⋊C8C22×D6114yes—
448#97—618no—
449C24—21no—
450C24—1221no—
451C24D4×D6111yescharacteristic
452#41—24432no—
453C2×Q8—618no—
454C2×Q8—614no—
455C2×Q8—1224no—
456C2×Q8—12216no—
457C2×Q8—1228no—
458C2×Q8—12216no—
459C2×Q8—1224no—
460C2×Q8—1222no—
461C2×Q8—1224no—
462C2×Q8—2444no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—24no—
466C2×D4—44no—
467C2×D4—612no—
468C2×D4—1224no—
469C2×D4—1224no—
470C2×D4—1224no—
471C2×D4—1221no—
472C2×D4—1224no—
473C2×D4—2444no—
474C2×D4—2444no—
475C2×D4—2444no—
476C2×D4C23×D6112yes—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—44no—
482C22×C4—611no—
483C22×C4—614no—
484C22×C4—614no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4—1228no—
492C22×C4—1224no—
493C22×C4—1222no—
494C22×C4—1224no—
495C22×C4—1221no—
496C22×C4—2444no—
497C22×C4—2444no—
498C22×C4D4×D6112yes—
499C22×C4D4×D6111yescharacteristic
500C22×C4C23×D6112yes—
501C22×C4C23×D6111yescharacteristic
502SD16—12216no—
503SD16—12216no—
504C2×C8—24no—
505C2×C8—614no—
506C2×C8—1224no—
507C2×C8C23×D6114yes—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—1228no—
513C4⋊C4—1228no—
514C4⋊C4—1224no—
515C4⋊C4—1221no—
516C4⋊C4C23×D6114yes—
517C4⋊C4C23×D6112yes—
518C22⋊C4—24no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C42—614no—
523C42—612no—
524C42—614no—
525C42—612no—
526C42—612no—
527C42—612no—
528C42—1228no—
529C42—1228no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—1222no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23#1451980114yes—
541C23C2×D4×D6112yes—
542C23C2×D4×D6111yescharacteristic
543Q8—618no—
544Q8—12216no—
545Q8—1228no—
546Q8—1224no—
547Q8—2448no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—1224no—
552D4—2448no—
553D4—2448no—
554D4—2448no—
555D4—2442no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—614no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—1228no—
570C2×C4—12216no—
571C2×C4—1228no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1228no—
575C2×C4—1222no—
576C2×C4—1224no—
577C2×C4—1222no—
578C2×C4—2448no—
579C2×C4—2448no—
580C2×C4—2442no—
581C2×C4C2×D4×D6112yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#41×D6114yes—
584C2×C4C24×D6111yescharacteristic
585C8—24no—
586C8—1224no—
587C22—28no—
588C22—22no—
589C22—22no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—84no—
594C22—4884no—
595C22—2442no—
596C22—2442no—
597C22—2442no—
598C22#1684027012yes—
599C22C2×#1451980114yes—
600C22C2×#1451980112yes—
601C22#137×D6112yes—
602C22C22×D4×D6111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—614no—
607C4—1222no—
608C4—1222no—
609C4—1222no—
610C4—1228no—
611C4—2442no—
612C4#1684027012yes—
613C4C2×#41×D6112yes—
614C2—24no—
615C2—82no—
616C2—4882no—
617C2#2145593814yesdirect product factor
618C2C2×#1684027011yescharacteristic
619C2C22×#1451980111yescharacteristic
620C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#480C2
socleC23×C61C22×D4
prime radicalC2×#16840307C2
hypercenterC2×#480D61
hypocenterC61C2×#3112
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
3. #21455938C2direct (N × H)
4. C2×#16840075C2semidirect
5. C2×#16840056C2semidirect
6. C2×#16839961C2semidirect
7. C2×#16839903C2semidirect
8. C2×#16839900C2semidirect
9. C2×#16839861C2semidirect
10. C2×#16839859C2semidirect
11. C2×#16839816C2semidirect
12. C2×C61×#480C2semidirect
29. C2×#14519742C22semidirect
36. #16840075C22semidirect
37. #16840056C22semidirect
38. #16839961C22semidirect
39. #16839903C22semidirect
40. #16839900C22semidirect
41. #16839861C22semidirect
42. #16839859C22semidirect
43. #16839816C22semidirect
53. C61×#480C22semidirect
189. C2×Dic122#41semidirect
273. Dic122C2×#41semidirect
308. C2×#480D61semidirect
318. C2×C61#3112semidirect
349. #480C2×D61semidirect
367. C61C2×#3112semidirect
617. C2#21455938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403072
C22×#145197422
#214559382
C2×#168400752
C2×#168400562
C2×#168399612
C2×#168399032
C2×#168399002
C2×#168398612
C2×#168398592
C2×#168398162
C2×C61×#4802
C2×#311261