Finite Group Databasebeta

← C2×#21456859 #30551319

Subgroups — C2×#21456859 #30551319

Order 15616.

2198 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×#16840297C211yesmaximal, characteristic, complemented
3#21456859C2116yesmaximal, direct product factor
4C2×#16840154C211yesmaximal, characteristic, complemented
5C2×#16840151C211yesmaximal, characteristic, complemented
6C2×#16840128C211yesmaximal, characteristic, complemented
7C2×#16839987C212yesmaximal, complemented
8C2×#16839980C212yesmaximal, complemented
9C2×#16839927C212yesmaximal, complemented
10C2×#16839910C212yesmaximal, complemented
11C2×#16839817C211yesmaximal, characteristic, complemented
12C2×C61×#491C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×#11758202C2212yes—
15C22×#11758190C2212yes—
16C22×#11758201C2212yes—
17C22×D488C2212yes—
18#16840313—24no—
19#16840313C2218yescomplemented
20C2×#14519774C2211yescharacteristic
21#16840297—24no—
22#16840297C2218yescomplemented
23C2×#14519772—21no—
24C2×#14519766C2212yes—
25C2×#14519765C2211yescharacteristic
26C2×#14519762—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519752—21no—
30C2×#14519752C2211yescharacteristic
31C2×#14519742C2211yescharacteristic
32C2×#14519739—21no—
33C2×#14519739—21no—
34C2×#14519739—21no—
35C2×#14519739C2211yescharacteristic
36C2×#14519735—21no—
37C2×C42×D61C2211yescharacteristic
38#16840154C2218yescomplemented
39#16840151C2218yescomplemented
40#16840128C2218yescomplemented
41#16839987C22116yescomplemented
42#16839980C22116yescomplemented
43#16839927C22116yescomplemented
44#16839910C22116yescomplemented
45#16839817C2218yescomplemented
46C2×#14519706C2212yes—
47C2×#14519697C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519688C2211yescharacteristic
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#125×C61C2211yescharacteristic
53C61×#491C2218yescomplemented
54C2×#103×C61C2212yes—
55C2×#103×C61C2212yes—
56C2×#97×C61C2211yescharacteristic
57C2×#11758226—24no—
58C2×#11758226—44no—
59C2×#11758226—44no—
60C2×#11758226C2318yes—
61C22×Dic122C2311yescharacteristic
62C22×D244—21no—
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244C2311yescharacteristic
67C22×D244C2312yes—
68C22×C4×D61—21no—
69C22×C4×D61—22no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758202—44no—
74C2×#11758202C2318yes—
75C2×#11758190—44no—
76C2×#11758190C2318yes—
77C2×#11758201—44no—
78C2×#11758201C2318yes—
79C2×D488—44no—
80C2×D488C2318yes—
81C22×#92418C2312yes—
82#14519774—22no—
83#14519774C2314yes—
84#14519772—28no—
85#14519766—24no—
86#14519766C2318yes—
87#14519765—22no—
88#14519765C2314yes—
89#14519762—28no—
90#14519757—22no—
91#14519757C2314yes—
92#14519752—28no—
93#14519752—28no—
94#14519752—22no—
95#14519752C2314yes—
96#14519742—22no—
97#14519742C2314yes—
98#14519739—28no—
99#14519739—28no—
100#14519739—28no—
101#14519739—22no—
102#14519739C2314yes—
103#14519735—28no—
104C2×C4⋊Dic61—21no—
105C2×#11758196—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C42×D61D414yes—
118C42×D61C2314yes—
119#14519706C2318yes—
120#14519697C2318yes—
121#14519697C2318yes—
122#14519689C2318yes—
123#14519688C2314yes—
124C22×Q8×C61C2312yes—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128#125×C61—22no—
129#125×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#103×C61C2318yes—
138#103×C61C2318yes—
139#97×C61C2314yes—
140C23×D61—22no—
141C23×D61—21no—
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—22no—
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
146C2×Q8×C61C2414yes—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758226—48no—
158#11758226—48no—
159#11758226—416no—
160C2×D244—24no—
161C2×D244—24no—
162C2×D244—24no—
163C2×D244—28no—
164C2×D244—24no—
165C2×D244—24no—
166C2×D244—24no—
167C2×D244—22no—
168C2×D244—21no—
169C2×D244—44no—
170C2×D244—44no—
171C2×D244—44no—
172C2×D244—48no—
173C2×D244C2414yes—
174C2×D244C2412yes—
175C2×C4×D61—24no—
176C2×C4×D61—28no—
177C2×C4×D61—24no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—44no—
181C2×C4×D61—48no—
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D414yes—
184C2×C4×D61C2×D414yes—
185C2×C4×D61C2412yes—
186C2×Dic122—24no—
187C2×Dic122—21no—
188C2×Dic122C2412yes—
189C2×C8×C61—24no—
190C2×C8×C61C2414yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—24no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C2412yes—
198C4⋊C4×C61C2412yes—
199C42×C61C2×D412yes—
200C42×C61C2412yes—
201#11758202—48no—
202#11758201—48no—
203#11758198—24no—
204#11758198—24no—
205#11758198—24no—
206#11758198—24no—
207#11758198—28no—
208#11758198—28no—
209#11758198—24no—
210C4⋊Dic61—24no—
211#11758196—24no—
212C4×Dic61—24no—
213C4×Dic61C2×D412yes—
214C4×Dic61C2×D414yes—
215C4×Dic61C2×D414yes—
216C4×Dic61C2412yes—
217C2×#92418—24no—
218C2×#92418C2414yes—
219D488—48no—
220#11758190—48no—
221C23×C61C22×D411yescharacteristic
222C22×D61—22no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—24no—
227C22×D61—44no—
228C22×D61—42no—
229C22×D61—42no—
230C22×D61—44no—
231C22×D61—44no—
232C22×D61—42no—
233C22×D61C22×D412yes—
234Q8×C61—24no—
235Q8×C61—24no—
236Q8×C61—44no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—24no—
242C2×C4×C61—44no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61C22×D412yes—
246C2×C4×C61C22×D412yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61H(5,𝔽2)14yes—
249C2×C4×C61C2511yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—42no—
255C2×Dic61C22×D412yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258D244—24no—
259D244—24no—
260D244—24no—
261D244—48no—
262D244—48no—
263D244—48no—
264D244—416no—
265D244—42no—
266D244—44no—
267C4×D61—24no—
268C4×D61—24no—
269C4×D61—44no—
270C4×D61—44no—
271C4×D61—48no—
272C4×D61—416no—
273Dic122—24no—
274Dic122—42no—
275C8×C61—24no—
276#92418—24no—
277C2×#3219—611nomaximal, Sylow
278C22×C61#53512yes—
279C22×C61#57512yes—
280C22×C61#57512yes—
281C22×C61C23×D411yescharacteristic
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—22no—
285C2×D61—44no—
286C2×D61—44no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—42no—
292C2×D61—88no—
293C2×D61—84no—
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—44no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61#53512yes—
300C4×C61C2×H(5,𝔽2)12yes—
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—42no—
305C2×#532—611no—
306C2×#529—611no—
307#3219—6116no—
308C2×#497—611no—
309C2×#496—611no—
310C2×#491D6111yescharacteristic, complemented
311C2×#490—611no—
312C2×#464—612no—
313C2×#463—612no—
314C2×#452—612no—
315C2×#449—612no—
316C2×#432—611no—
317C2×C61#321914yescomplemented
318C2×C61C2×#53511yescharacteristic
319C2×C61C2×#57511yescharacteristic
320C2×C61C2×#57511yescharacteristic
321D61—42no—
322D61—84no—
323D61—82no—
324C22×#41—612no—
325C22×Q16—612no—
326C22×SD16—612no—
327C22×SD16—612no—
328C22×D8—612no—
329#532—618no—
330#532—1224no—
331C2×C4⋊Q8C2×D6111yescharacteristic
332C2×#127—611no—
333#529—618no—
334#529—1224no—
335C2×#126—1221no—
336C2×#125C2×D6111yescharacteristic
337C2×#124—612no—
338C2×#124—611no—
339C2×#123—1221no—
340C2×C22⋊Q8—611no—
341C2×#121—611no—
342C2×#121—1221no—
343C2×#121—1221no—
344C2×C4×Q8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—1221no—
347C2×C4×D4—1221no—
348C2×C4×D4—1221no—
349C2×#117—1221no—
350C22×C42—611no—
351#497—618no—
352#496—618no—
353#491C2×D6118yescomplemented
354#490—618no—
355#464—6116no—
356#463—6116no—
357#452—6116no—
358#449—6116no—
359#432—618no—
360C2×C4⋊C8—612no—
361C2×#103C2×D6112yes—
362C2×#103C2×D6112yes—
363C2×#102—612no—
364C2×#102—612no—
365C2×C22⋊C8—612no—
366C2×#97—611no—
367C2×#97C2×D6111yescharacteristic
368C61C2×#321911yescharacteristic, complemented, Sylow
369C2×#41—618no—
370C2×#41—1224no—
371C2×#41—2444no—
372C2×#41—2444no—
373C22×Q8—611no—
374C22×Q8C22×D6112yes—
375C22×D4—611no—
376C22×D4—612no—
377C22×D4—1221no—
378C22×D4—1222no—
379C22×D4—1221no—
380C22×D4—1221no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—1221no—
385C23×C4—1222no—
386C2×Q16—618no—
387C2×Q16—2444no—
388C2×SD16—618no—
389C2×SD16—618no—
390C2×SD16—2444no—
391C2×SD16—2444no—
392C2×D8—618no—
393C2×D8—2444no—
394C22×C8—612no—
395C22×C8C22×D6112yes—
396C4⋊Q8—22no—
397C4⋊Q8C22×D6114yes—
398#127—614no—
399#127—1222no—
400#126—1228no—
401#125—22no—
402#125C22×D6114yes—
403#124—618no—
404#124—614no—
405#124—1224no—
406#124—1222no—
407#123—1228no—
408C22⋊Q8—614no—
409C22⋊Q8—1222no—
410#121—614no—
411#121—1222no—
412#121—1228no—
413#121—1228no—
414C4×Q8—614no—
415C4×Q8—1222no—
416C4×D4—614no—
417C4×D4—1222no—
418C4×D4—1228no—
419C4×D4—1228no—
420C4×D4—1228no—
421#117—1228no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4C22×D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1222no—
433C2×C22⋊C4—1222no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—614no—
441C2×C42—614no—
442C2×C42—1221no—
443C2×C42C22×D6111yescharacteristic
444C4⋊C8—618no—
445#103C22×D6118yes—
446#103C22×D6118yes—
447#102—618no—
448#102—618no—
449C22⋊C8—618no—
450#97—614no—
451#97C22×D6114yes—
452C24—611no—
453C24—1221no—
454C24—1222no—
455#41—2448no—
456#41—2448no—
457#41—24416no—
458C2×Q8—22no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—612no—
462C2×Q8—1221no—
463C2×Q8—1224no—
464C2×Q8C23×D6114yes—
465C2×D4—614no—
466C2×D4—612no—
467C2×D4—1224no—
468C2×D4—1228no—
469C2×D4—1221no—
470C2×D4—1224no—
471C2×D4—1224no—
472C2×D4—1222no—
473C2×D4—1224no—
474C2×D4—1224no—
475C2×D4—1224no—
476C2×D4—2444no—
477C2×D4—2444no—
478C2×D4—2448no—
479C2×D4—2444no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—614no—
489C22×C4—614no—
490C22×C4—1224no—
491C22×C4—1228no—
492C22×C4—1224no—
493C22×C4—1221no—
494C22×C4—2442no—
495C22×C4—2442no—
496C22×C4—2444no—
497C22×C4—2448no—
498C22×C4D4×D6111yescharacteristic
499C22×C4D4×D6111yescharacteristic
500C22×C4C23×D6111yescharacteristic
501Q16—2448no—
502SD16—2448no—
503SD16—2448no—
504D8—2448no—
505C2×C8—24no—
506C2×C8—614no—
507C2×C8—1224no—
508C2×C8C23×D6114yes—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—1224no—
516C4⋊C4—1224no—
517C4⋊C4C23×D6112yes—
518C4⋊C4C23×D6112yes—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1228no—
522C22⋊C4—1228no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C22⋊C4—1224no—
526C42—614no—
527C42—614no—
528C42—612no—
529C42—612no—
530C42—1224no—
531C42D4×D6112yes—
532C42C23×D6112yes—
533C23—612no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23—1222no—
538C23—1224no—
539C23—2442no—
540C23—2444no—
541C23—2444no—
542C23—2442no—
543C23—2444no—
544C23—2442no—
545C23C2×D4×D6111yescharacteristic
546Q8—24no—
547Q8—24no—
548Q8—44no—
549Q8—1224no—
550Q8—2442no—
551D4—1224no—
552D4—1224no—
553D4—1224no—
554D4—2448no—
555D4—2448no—
556D4—2448no—
557D4—24416no—
558D4—2442no—
559D4—2444no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—2444no—
578C2×C4—2444no—
579C2×C4—2448no—
580C2×C4—24416no—
581C2×C4—2442no—
582C2×C4C2×D4×D6112yes—
583C2×C4C2×D4×D6112yes—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4#1451982314yes—
586C2×C4C24×D6111yescharacteristic
587C8—24no—
588C8—1224no—
589C22—1222no—
590C22—1222no—
591C22—1222no—
592C22—4884no—
593C22—4888no—
594C22—2442no—
595C22—2444no—
596C22—2444no—
597C22—2442no—
598C22—2444no—
599C22—2442no—
600C22—2444no—
601C22#1684033012yes—
602C22#1684056112yes—
603C22#1684056112yes—
604C22C22×D4×D6111yescharacteristic
605C4—22no—
606C4—22no—
607C4—42no—
608C4—42no—
609C4—44no—
610C4—1222no—
611C4—1222no—
612C4—1222no—
613C4—2442no—
614C4#1684033012yes—
615C4C2×#1451982312yes—
616C2—4882no—
617C2—4884no—
618C2—2442no—
619C2#2145685914yesdirect product factor
620C2C2×#1684033011yescharacteristic
621C2C2×#1684056111yescharacteristic
622C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#491C2
socleC23×C61C22×D4
hypercenterC2×#491D61
hypocenterC61C2×#3219
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#16840313C2semidirect
2. C2×#16840297C2semidirect
3. #21456859C2direct (N × H)
4. C2×#16840154C2semidirect
5. C2×#16840151C2semidirect
6. C2×#16840128C2semidirect
7. C2×#16839987C2semidirect
8. C2×#16839980C2semidirect
9. C2×#16839927C2semidirect
10. C2×#16839910C2semidirect
11. C2×#16839817C2semidirect
12. C2×C61×#491C2semidirect
19. #16840313C22semidirect
22. #16840297C22semidirect
38. #16840154C22semidirect
39. #16840151C22semidirect
40. #16840128C22semidirect
41. #16839987C22semidirect
42. #16839980C22semidirect
43. #16839927C22semidirect
44. #16839910C22semidirect
45. #16839817C22semidirect
53. C61×#491C22semidirect
310. C2×#491D61semidirect
317. C2×C61#3219semidirect
353. #491C2×D61semidirect
368. C61C2×#3219semidirect
619. C2#21456859direct (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×#168402972
#214568592
C2×#168401542
C2×#168401512
C2×#168401282
C2×#168399872
C2×#168399802
C2×#168399272
C2×#168399102
C2×#168398172
C2×C61×#4912
C2×#321961