Finite Group Databasebeta

← C2×#21458231 #30558496

Subgroups — C2×#21458231 #30558496

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840486C211yesmaximal, characteristic, complemented
2C2×#16840478C211yesmaximal, characteristic
3#21458231C2116yesmaximal, direct product factor
4C2×#16840106C212yesmaximal, complemented
5C2×#16840088C212yesmaximal, complemented
6C2×#16840054C211yesmaximal, characteristic, complemented
7C2×#16840039C211yesmaximal, characteristic, complemented
8C2×#16839992C212yesmaximal, complemented
9C2×C4×#11758190C211yesmaximal, characteristic, complemented
10C2×C8×D244C211yesmaximal, characteristic, complemented
11C2×#16839797C212yesmaximal, complemented
12C2×C61×#498C211yesmaximal, characteristic, complemented
13C22×#11758190C2211yescharacteristic
14C22×C8×D61C2212yes—
15#16840486—24no—
16#16840486C2218yescomplemented
17#16840478—24no—
18#16840478C2218yes—
19C2×#14519772—22no—
20C2×#14519766—22no—
21C2×#14519766—21no—
22C2×#14519757C2212yes—
23C2×#14519752—21no—
24C2×#14519752C2212yes—
25C2×Q8×Dic61—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519735—21no—
30C2×#14519735C2212yes—
31C2×#14519735C2212yes—
32#16840106C22116yescomplemented
33#16840088C22116yescomplemented
34#16840054C2218yescomplemented
35#16840039C2218yescomplemented
36#16839992C22116yescomplemented
37C4×#11758190C2218yescomplemented
38C8×D244C2218yescomplemented
39#16839797C22116yescomplemented
40C2×#14519710C2212yes—
41C2×#14519710C2212yes—
42C2×#14519709C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44C2×#14519702C2211yescharacteristic
45C2×#14519700C2212yes—
46C2×#14519699C2211yescharacteristic
47C2×#14519697C2212yes—
48C2×#14519689C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4⋊Q8×C61C2211yescharacteristic
51C61×#498C2218yescomplemented
52C2×#106×C61C2212yes—
53C2×#106×C61C2212yes—
54C2×C4×C8×C61C2211yescharacteristic
55C22×Dic122C2311yescharacteristic
56C22×D244—22no—
57C22×D244D411yescharacteristic
58C22×D244C2311yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61C2312yes—
61C2×#11758190—24no—
62C2×#11758190C2314yes—
63C22×#92418C2312yes—
64C2×C8×D61—28no—
65C2×C8×D61C2318yes—
66#14519772—216no—
67#14519766—28no—
68#14519766—216no—
69#14519757—24no—
70#14519757C2318yes—
71#14519752—28no—
72#14519752—24no—
73#14519752C2318yes—
74Q8×Dic61—28no—
75C4×Dic122—22no—
76C4×Dic122C2314yes—
77C4×D244—22no—
78C4×D244D414yes—
79C4×D244C2314yes—
80C4×D244C2314yes—
81#14519735—24no—
82#14519735—24no—
83#14519735—28no—
84#14519735C2318yes—
85#14519735C2318yes—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—21no—
95C2×#11758198—22no—
96C2×#11758198D412yes—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100#14519710C2318yes—
101#14519710C2318yes—
102#14519709C2314yes—
103C4⋊#92418C2314yes—
104#14519702C2314yes—
105#14519700C2318yes—
106#14519699C2314yes—
107#14519697C2318yes—
108#14519689C2318yes—
109C22×Q8×C61—21no—
110C22×Q8×C61—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61—22no—
115C4⋊Q8×C61C2314yes—
116C4⋊Q8×C61C2314yes—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61C2312yes—
120C2×C4⋊C4×C61C2312yes—
121C2×C42×C61C2311yescharacteristic
122#106×C61C2318yes—
123#106×C61C2318yes—
124C4×C8×C61C2314yes—
125C23×D61—21no—
126C23×D61C2×D412yes—
127C2×Q8×C61—24no—
128C2×Q8×C61—24no—
129C2×Q8×C61—44no—
130C2×Q8×C61—82no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61C2×D412yes—
140C2×D244—24no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—21no—
144C2×D244—28no—
145C2×D244—84no—
146C2×D244C2×D414yes—
147C2×D244C2412yes—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—24no—
151C2×C4×D61—44no—
152C2×C4×D61C2×D414yes—
153C2×C4×D61C2414yes—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—21no—
157C2×Dic122C2412yes—
158C2×C8×C61—22no—
159C2×C8×C61#4114yes—
160C2×C8×C61C2412yes—
161C2×C8×C61C2412yes—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61C2414yes—
167C4⋊C4×C61C2414yes—
168C42×C61C2×D412yes—
169C42×C61C2412yes—
170#11758198—28no—
171#11758198—28no—
172#11758198—28no—
173#11758198—24no—
174#11758198—28no—
175#11758198C2×D418yes—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—28no—
179C4⋊Dic61C2×D414yes—
180C4⋊Dic61C2412yes—
181C4⋊Dic61C2412yes—
182#11758196—24no—
183C4×Dic61—24no—
184C4×Dic61—28no—
185C4×Dic61—28no—
186C2×#92418—24no—
187C2×#92418C2414yes—
188#11758190—28no—
189C8×D61—216no—
190C23×C61C22×D411yescharacteristic
191C22×D61—24no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—22no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61C22×D414yes—
199Q8×C61—48no—
200Q8×C61—84no—
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—44no—
205C2×C4×C61—44no—
206C2×C4×C61#13514yes—
207C2×C4×C61C22×D412yes—
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C22×D412yes—
210C2×C4×C61C2×#4112yes—
211C2×C4×C612−1+412yes—
212C2×C4×C61C2511yescharacteristic
213C2×Dic61—24no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61C22×D414yes—
221D244—28no—
222D244—22no—
223D244—22no—
224D244—42no—
225D244—88no—
226C4×D61—28no—
227C4×D61—24no—
228C4×D61—24no—
229C4×D61—48no—
230Dic122—22no—
231Dic122—22no—
232Dic122—42no—
233C8×C61—22no—
234C8×C61C2×#4114yes—
235#92418—24no—
236C2×#3340—611nomaximal, Sylow
237C22×C61#54712yes—
238C22×C61C2×#13512yes—
239C22×C61#57712yes—
240C22×C61C23×D411yescharacteristic
241C2×D61—24no—
242C2×D61—24no—
243C2×D61—24no—
244C2×D61—48no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—84no—
249C4×C61—22no—
250C4×C61—44no—
251C4×C61—44no—
252C4×C61#54712yes—
253C4×C61C2×#13514yes—
254C4×C61C22×#4111yescharacteristic
255C4×C61C2×2−1+411yescharacteristic
256Dic61—24no—
257Dic61—42no—
258Dic61—42no—
259Dic61—42no—
260C2×#556—611no—
261C2×#555—611no—
262#3340—6116no—
263C2×#498D6111yescharacteristic, complemented
264C2×#485—612no—
265C2×#482—612no—
266C2×#477—611no—
267C2×#474—611no—
268C2×#465—612no—
269C2×C4×SD16—611no—
270C2×C8×D4—611no—
271C2×#427—612no—
272C2×C61#334014yescomplemented
273C2×C61C2×#54711yescharacteristic
274C2×C61C22×#13511yescharacteristic
275C2×C61C2×#57711yescharacteristic
276D61—44no—
277D61—82no—
278C22×SD16—611no—
279C23×C8—612no—
280#556—618no—
281#556—1224no—
282#555—618no—
283#555—1224no—
284C2×C4⋊Q8C2×D6111yescharacteristic
285C2×C4⋊Q8C2×D6111yescharacteristic
286C2×#126—1222no—
287C2×#124—1222no—
288C2×#124—1221no—
289C2×C22⋊Q8—612no—
290C2×#121—612no—
291C2×#121—1221no—
292C2×C4×Q8—611no—
293C2×C4×Q8—1221no—
294C2×C4×D4—611no—
295C2×C4×D4—611no—
296C2×#117—612no—
297C2×#117—612no—
298C2×#117—1221no—
299#498C2×D6118yescomplemented
300#485—6116no—
301#482—6116no—
302#477—618no—
303#474—618no—
304#465—6116no—
305C4×SD16—618no—
306C8×D4—618no—
307#427—6116no—
308C2×#107—612no—
309C2×#107—612no—
310C2×#106—611no—
311C2×#106C2×D6112yes—
312C2×#106C2×D6112yes—
313C2×C4⋊C8—611no—
314C2×#103—611no—
315C2×#103—612no—
316C2×#102—611no—
317C2×#102—612no—
318C2×C22⋊C8—612no—
319C2×C4×C8C2×D6111yescharacteristic
320C61C2×#334011yescharacteristic, complemented, Sylow
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—611no—
324C22×D4—611no—
325C22×D4—611no—
326C22×D4—1222no—
327C23×C4—612no—
328C23×C4—1221no—
329C2×SD16—614no—
330C2×SD16—1224no—
331C22×C8—612no—
332C22×C8—618no—
333C22×C8—1228no—
334C22×C8C22×D6111yescharacteristic
335C22×C8C22×D6111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C22×D6114yes—
339C4⋊Q8C22×D6114yes—
340#126—12216no—
341#124—12216no—
342#124—1228no—
343C22⋊Q8—618no—
344C22⋊Q8—1224no—
345#121—618no—
346#121—1224no—
347#121—1228no—
348C4×Q8—614no—
349C4×Q8—1228no—
350C4×Q8—1222no—
351C4×D4—614no—
352C4×D4—614no—
353C4×D4—614no—
354C4×D4—1222no—
355#117—618no—
356#117—618no—
357#117—1228no—
358#117—1224no—
359#117—1224no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—1222no—
366C2×C4⋊C4—1221no—
367C2×C4⋊C4C22×D6112yes—
368C2×C4⋊C4C22×D6112yes—
369C2×C22⋊C4—612no—
370C2×C22⋊C4—1222no—
371C2×C22⋊C4—1222no—
372C2×C22⋊C4—1222no—
373C2×C22⋊C4—1222no—
374C2×C22⋊C4—1221no—
375C2×C42—1222no—
376C2×C42—1222no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—618no—
380#107—618no—
381#106—614no—
382#106C22×D6118yes—
383#106C22×D6118yes—
384C4⋊C8—614no—
385#103—614no—
386#103—618no—
387#102—614no—
388#102—618no—
389C22⋊C8—618no—
390C4×C8C22×D6114yes—
391C24—612no—
392C24—1221no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—44no—
396C2×Q8—82no—
397C2×Q8—612no—
398C2×Q8—1221no—
399C2×Q8—1222no—
400C2×Q8—1222no—
401C2×D4—614no—
402C2×D4—612no—
403C2×D4—1228no—
404C2×D4—1221no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1224no—
408C2×D4—4884no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—612no—
412C22×C4—614no—
413C22×C4—614no—
414C22×C4—1224no—
415C22×C4—1224no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1224no—
420C22×C4—2444no—
421C22×C4D4×D6111yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4C23×D6111yescharacteristic
424SD16—1228no—
425C2×C8—22no—
426C2×C8—614no—
427C2×C8—1224no—
428C2×C8—12216no—
429C2×C8#1175822614yes—
430C2×C8C23×D6112yes—
431C2×C8C23×D6112yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—614no—
437C4⋊C4—612no—
438C4⋊C4—612no—
439C4⋊C4—1228no—
440C4⋊C4—1221no—
441C4⋊C4—1221no—
442C4⋊C4—1224no—
443C4⋊C4C23×D6114yes—
444C4⋊C4C23×D6114yes—
445C22⋊C4—618no—
446C22⋊C4—1228no—
447C22⋊C4—1228no—
448C22⋊C4—1228no—
449C22⋊C4—1228no—
450C22⋊C4—1224no—
451C42—1228no—
452C42—1228no—
453C42—1224no—
454C42D4×D6112yes—
455C42C23×D6112yes—
456C23—614no—
457C23—1224no—
458C23—1224no—
459C23—1224no—
460C23—1222no—
461C23—2442no—
462C23—2442no—
463C23—2442no—
464C23C2×D4×D6111yescharacteristic
465Q8—48no—
466Q8—84no—
467Q8—1222no—
468Q8—1222no—
469Q8—2442no—
470D4—1228no—
471D4—1222no—
472D4—1222no—
473D4—4888no—
474D4—2442no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—614no—
481C2×C4—1224no—
482C2×C4—1224no—
483C2×C4—1224no—
484C2×C4—1228no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2448no—
492C2×C4#1451979814yes—
493C2×C4C2×D4×D6112yes—
494C2×C4C2×D4×D6112yes—
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4C2×#1175822612yes—
497C2×C4#1451982512yes—
498C2×C4C24×D6111yescharacteristic
499C8—22no—
500C8—1224no—
501C8C2×#1175822614yes—
502C22—1224no—
503C22—1224no—
504C22—1224no—
505C22—4884no—
506C22—2442no—
507C22—2442no—
508C22—2442no—
509C22—2448no—
510C22#1684041512yes—
511C22C2×#1451979812yes—
512C22#1684056812yes—
513C22C22×D4×D6111yescharacteristic
514C4—22no—
515C4—44no—
516C4—44no—
517C4—1224no—
518C4—2442no—
519C4—2442no—
520C4—2442no—
521C4#1684041512yes—
522C4C2×#1451979814yes—
523C4C22×#1175822611yescharacteristic
524C4C2×#1451982511yescharacteristic
525C2—4882no—
526C2—2444no—
527C2#2145823114yesdirect product factor
528C2C2×#1684041511yescharacteristic
529C2C22×#1451979811yescharacteristic
530C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#498C2
socleC23×C61C22×D4
prime radicalC2×#16840478C2
hypercenterC2×#498D61
hypocenterC61C2×#3340
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#16840486C2semidirect
3. #21458231C2direct (N × H)
4. C2×#16840106C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840054C2semidirect
7. C2×#16840039C2semidirect
8. C2×#16839992C2semidirect
9. C2×C4×#11758190C2semidirect
10. C2×C8×D244C2semidirect
11. C2×#16839797C2semidirect
12. C2×C61×#498C2semidirect
16. #16840486C22semidirect
32. #16840106C22semidirect
33. #16840088C22semidirect
34. #16840054C22semidirect
35. #16840039C22semidirect
36. #16839992C22semidirect
37. C4×#11758190C22semidirect
38. C8×D244C22semidirect
39. #16839797C22semidirect
51. C61×#498C22semidirect
263. C2×#498D61semidirect
272. C2×C61#3340semidirect
299. #498C2×D61semidirect
320. C61C2×#3340semidirect
527. C2#21458231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404862
C2×#168404782
#214582312
C2×#168401062
C2×#168400882
C2×#168400542
C2×#168400392
C2×#168399922
C2×C4×#117581902
C2×C8×D2442
C2×#168397972
C2×C61×#4982
C2×#334061