Finite Group Databasebeta

← C2×#21458444 #30558762

Subgroups — C2×#21458444 #30558762

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840478C211yesmaximal, characteristic
2C2×#16840473C211yesmaximal, characteristic, complemented
3#21458444C2116yesmaximal, direct product factor
4C2×#16840105C212yesmaximal, complemented
5C2×#16840077C212yesmaximal, complemented
6C2×#16840054C211yesmaximal, characteristic, complemented
7C2×#16840049C211yesmaximal, characteristic, complemented
8C2×#16840009C212yesmaximal, complemented
9C2×C4×#11758190C211yesmaximal, characteristic, complemented
10C2×#16839841C211yesmaximal, characteristic, complemented
11C2×#16839803C212yesmaximal, complemented
12C2×C61×#500C211yesmaximal, characteristic, complemented
13C22×#11758190C2211yescharacteristic
14C22×#11758189C2212yes—
15#16840478—24no—
16#16840478C2218yes—
17#16840473—24no—
18#16840473C2218yescomplemented
19C2×#14519768—21no—
20C2×#14519766—22no—
21C2×#14519757C2212yes—
22C2×#14519753—22no—
23C2×#14519752—21no—
24C2×#14519752C2212yes—
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519739—21no—
29C2×#14519735—21no—
30C2×#14519735C2212yes—
31C2×C4⋊C4×D61C2212yes—
32#16840105C22116yescomplemented
33#16840077C22116yescomplemented
34#16840054C2218yescomplemented
35#16840049C2218yescomplemented
36#16840009C22116yescomplemented
37C4×#11758190C2218yescomplemented
38#16839841C2218yescomplemented
39#16839803C22116yescomplemented
40C2×#14519710C2212yes—
41C2×#14519709C2211yescharacteristic
42C2×#14519708C2212yes—
43C2×C4⋊#92418C2211yescharacteristic
44C2×#14519702C2211yescharacteristic
45C2×#14519700C2212yes—
46C2×#14519699C2211yescharacteristic
47C2×#14519697C2212yes—
48C2×#14519689C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4⋊Q8×C61C2211yescharacteristic
51C61×#500C2218yescomplemented
52C2×#107×C61C2212yes—
53C2×#107×C61C2212yes—
54C2×C4×C8×C61C2211yescharacteristic
55C22×Dic122C2311yescharacteristic
56C22×D244—22no—
57C22×D244D411yescharacteristic
58C22×D244C2311yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C22×C4×D61C2312yes—
62C2×#11758190—24no—
63C2×#11758190C2314yes—
64C2×#11758189—28no—
65C2×#11758189C2318yes—
66C22×#92418C2312yes—
67#14519768—28no—
68#14519766—216no—
69#14519757—24no—
70#14519757C2318yes—
71#14519753—216no—
72#14519752—28no—
73#14519752—24no—
74#14519752C2318yes—
75C4×Dic122—22no—
76C4×Dic122C2314yes—
77C4×D244—22no—
78C4×D244D414yes—
79C4×D244C2314yes—
80C4×D244C2314yes—
81#14519739—28no—
82#14519735—24no—
83#14519735—28no—
84#14519735C2318yes—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—22no—
91C4⋊C4×D61—24no—
92C4⋊C4×D61C2318yes—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—21no—
96C2×#11758198—22no—
97C2×#11758198D412yes—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—22no—
100#14519710C2318yes—
101#14519709C2314yes—
102#14519708C2318yes—
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#107×C61C2318yes—
123#107×C61C2318yes—
124C4×C8×C61C2314yes—
125C23×D61—21no—
126C23×D61C2×D412yes—
127C2×Q8×C61—24no—
128C2×Q8×C61—24no—
129C2×Q8×C61—82no—
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—28no—
152C2×C4×D61—44no—
153C2×C4×D61—84no—
154C2×C4×D61C2×D414yes—
155C2×C4×D61C2414yes—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—21no—
159C2×Dic122C2412yes—
160C2×C8×C61—22no—
161C2×C8×C61#4114yes—
162C2×C8×C61C2412yes—
163C2×C8×C61C2412yes—
164C4⋊C4×C61—24no—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61C2414yes—
169C4⋊C4×C61C2414yes—
170C42×C61C2×D412yes—
171C42×C61C2412yes—
172#11758198—28no—
173#11758198—28no—
174#11758198—24no—
175#11758198—28no—
176#11758198C2×D418yes—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—28no—
180C4⋊Dic61C2×D414yes—
181C4⋊Dic61C2412yes—
182C4⋊Dic61C2412yes—
183#11758196—24no—
184#11758196—28no—
185C4×Dic61—24no—
186C4×Dic61—28no—
187C2×#92418—24no—
188C2×#92418C2414yes—
189#11758190—28no—
190#11758189—216no—
191C23×C61C22×D411yescharacteristic
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—22no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61C22×D414yes—
200Q8×C61—84no—
201Q8×C61—84no—
202C2×C4×C61—22no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—44no—
206C2×C4×C61—44no—
207C2×C4×C61#13714yes—
208C2×C4×C61C22×D412yes—
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×D412yes—
211C2×C4×C61C2×#4112yes—
212C2×C4×C612−1+412yes—
213C2×C4×C61C2511yescharacteristic
214C2×Dic61—24no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61C22×D414yes—
222D244—28no—
223D244—22no—
224D244—22no—
225D244—42no—
226D244—88no—
227C4×D61—28no—
228C4×D61—24no—
229C4×D61—24no—
230C4×D61—48no—
231C4×D61—88no—
232Dic122—22no—
233Dic122—22no—
234Dic122—42no—
235C8×C61—22no—
236C8×C61C2×#4114yes—
237#92418—24no—
238C2×#3357—611nomaximal, Sylow
239C22×C61#54712yes—
240C22×C61C2×#13712yes—
241C22×C61#57612yes—
242C22×C61C23×D411yescharacteristic
243C2×D61—24no—
244C2×D61—24no—
245C2×D61—24no—
246C2×D61—48no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—84no—
251C4×C61—22no—
252C4×C61—44no—
253C4×C61—44no—
254C4×C61#54712yes—
255C4×C61C2×#13714yes—
256C4×C61C22×#4111yescharacteristic
257C4×C61C2×2−1+411yescharacteristic
258Dic61—24no—
259Dic61—42no—
260Dic61—42no—
261Dic61—42no—
262C2×#555—611no—
263C2×#554—611no—
264#3357—6116no—
265C2×#500D6111yescharacteristic, complemented
266C2×#485—612no—
267C2×#480—612no—
268C2×#477—611no—
269C2×#476—611no—
270C2×#468—612no—
271C2×C4×SD16—611no—
272C2×#436—611no—
273C2×#428—612no—
274C2×C61#335714yescomplemented
275C2×C61C2×#54711yescharacteristic
276C2×C61C22×#13711yescharacteristic
277C2×C61C2×#57611yescharacteristic
278D61—44no—
279D61—82no—
280C22×SD16—611no—
281C22×M16—612no—
282#555—618no—
283#555—1224no—
284#554—618no—
285#554—1224no—
286C2×C4⋊Q8C2×D6111yescharacteristic
287C2×C4⋊Q8C2×D6111yescharacteristic
288C2×#125—1221no—
289C2×#124—1222no—
290C2×C22⋊Q8—612no—
291C2×C22⋊Q8—1222no—
292C2×#121—612no—
293C2×#121—1221no—
294C2×C4×Q8—611no—
295C2×C4×D4—611no—
296C2×C4×D4—611no—
297C2×C4×D4—1221no—
298C2×#117—612no—
299C2×#117—1221no—
300C22×C4⋊C4—612no—
301#500C2×D6118yescomplemented
302#485—6116no—
303#480—6116no—
304#477—618no—
305#476—618no—
306#468—6116no—
307C4×SD16—618no—
308#436—618no—
309#428—6116no—
310C2×#107—612no—
311C2×#107C2×D6112yes—
312C2×#107C2×D6112yes—
313C2×#106—611no—
314C2×#106—612no—
315C2×C4⋊C8—611no—
316C2×#103—611no—
317C2×#103—612no—
318C2×#102—611no—
319C2×#102—612no—
320C2×C22⋊C8—612no—
321C2×C4×C8C2×D6111yescharacteristic
322C61C2×#335711yescharacteristic, complemented, Sylow
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—611no—
326C22×D4—611no—
327C22×D4—611no—
328C22×D4—1222no—
329C23×C4—612no—
330C23×C4—1222no—
331C23×C4—1221no—
332C2×SD16—614no—
333C2×SD16—1224no—
334C2×M16—618no—
335C2×M16—1228no—
336C22×C8—612no—
337C22×C8C22×D6111yescharacteristic
338C22×C8C22×D6111yescharacteristic
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8C22×D6114yes—
342C4⋊Q8C22×D6114yes—
343#125—1228no—
344#124—12216no—
345C22⋊Q8—618no—
346C22⋊Q8—12216no—
347C22⋊Q8—1224no—
348#121—618no—
349#121—1224no—
350#121—1228no—
351C4×Q8—614no—
352C4×Q8—1222no—
353C4×D4—614no—
354C4×D4—614no—
355C4×D4—614no—
356C4×D4—1228no—
357C4×D4—1222no—
358#117—618no—
359#117—1228no—
360#117—1224no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—618no—
367C2×C4⋊C4—1224no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—1222no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4C22×D6112yes—
372C2×C4⋊C4C22×D6112yes—
373C2×C22⋊C4—612no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1221no—
378C2×C42—1222no—
379C2×C42—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—618no—
382#107C22×D6118yes—
383#107C22×D6118yes—
384#106—614no—
385#106—618no—
386C4⋊C8—614no—
387#103—614no—
388#103—618no—
389#102—614no—
390#102—618no—
391C22⋊C8—618no—
392C4×C8C22×D6114yes—
393C24—612no—
394C24—1221no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—82no—
398C2×Q8—82no—
399C2×Q8—612no—
400C2×Q8—1221no—
401C2×Q8—1222no—
402C2×Q8—1222no—
403C2×D4—614no—
404C2×D4—612no—
405C2×D4—1228no—
406C2×D4—1224no—
407C2×D4—1221no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—4884no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—612no—
414C22×C4—614no—
415C22×C4—614no—
416C22×C4—1228no—
417C22×C4—1224no—
418C22×C4—1224no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1224no—
423C22×C4—4884no—
424C22×C4—2444no—
425C22×C4D4×D6111yescharacteristic
426C22×C4D4×D6111yescharacteristic
427C22×C4C23×D6111yescharacteristic
428SD16—1228no—
429M16—12216no—
430C2×C8—22no—
431C2×C8—614no—
432C2×C8—1224no—
433C2×C8#1175822614yes—
434C2×C8C23×D6112yes—
435C2×C8C23×D6112yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—614no—
441C4⋊C4—612no—
442C4⋊C4—612no—
443C4⋊C4—1228no—
444C4⋊C4—1228no—
445C4⋊C4—1221no—
446C4⋊C4—1221no—
447C4⋊C4—1224no—
448C4⋊C4C23×D6114yes—
449C4⋊C4C23×D6114yes—
450C22⋊C4—618no—
451C22⋊C4—1228no—
452C22⋊C4—1228no—
453C22⋊C4—1228no—
454C22⋊C4—1224no—
455C42—1228no—
456C42—1224no—
457C42D4×D6112yes—
458C42C23×D6112yes—
459C23—614no—
460C23—1224no—
461C23—1224no—
462C23—1224no—
463C23—1222no—
464C23—2442no—
465C23—2442no—
466C23—2442no—
467C23C2×D4×D6111yescharacteristic
468Q8—84no—
469Q8—84no—
470Q8—1222no—
471Q8—1222no—
472Q8—2442no—
473D4—1228no—
474D4—1222no—
475D4—1222no—
476D4—4888no—
477D4—2442no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—614no—
484C2×C4—1224no—
485C2×C4—1224no—
486C2×C4—1224no—
487C2×C4—1228no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—4888no—
492C2×C4—2442no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2448no—
496C2×C4#1451980914yes—
497C2×C4C2×D4×D6112yes—
498C2×C4C2×D4×D6112yes—
499C2×C4C2×D4×D6111yescharacteristic
500C2×C4C2×#1175822612yes—
501C2×C4#1451982512yes—
502C2×C4C24×D6111yescharacteristic
503C8—22no—
504C8—1224no—
505C8C2×#1175822614yes—
506C22—1224no—
507C22—1224no—
508C22—1224no—
509C22—4884no—
510C22—2442no—
511C22—2442no—
512C22—2442no—
513C22—2448no—
514C22#1684041512yes—
515C22C2×#1451980912yes—
516C22#1684056312yes—
517C22C22×D4×D6111yescharacteristic
518C4—22no—
519C4—44no—
520C4—44no—
521C4—1224no—
522C4—2442no—
523C4—2442no—
524C4—2442no—
525C4#1684041512yes—
526C4C2×#1451980914yes—
527C4C22×#1175822611yescharacteristic
528C4C2×#1451982511yescharacteristic
529C2—4882no—
530C2—2444no—
531C2#2145844414yesdirect product factor
532C2C2×#1684041511yescharacteristic
533C2C22×#1451980911yescharacteristic
534C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#500C2
socleC23×C61C22×D4
prime radicalC2×#16840478C2
hypercenterC2×#500D61
hypocenterC61C2×#3357
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. C2×#16840473C2semidirect
3. #21458444C2direct (N × H)
4. C2×#16840105C2semidirect
5. C2×#16840077C2semidirect
6. C2×#16840054C2semidirect
7. C2×#16840049C2semidirect
8. C2×#16840009C2semidirect
9. C2×C4×#11758190C2semidirect
10. C2×#16839841C2semidirect
11. C2×#16839803C2semidirect
12. C2×C61×#500C2semidirect
18. #16840473C22semidirect
32. #16840105C22semidirect
33. #16840077C22semidirect
34. #16840054C22semidirect
35. #16840049C22semidirect
36. #16840009C22semidirect
37. C4×#11758190C22semidirect
38. #16839841C22semidirect
39. #16839803C22semidirect
51. C61×#500C22semidirect
265. C2×#500D61semidirect
274. C2×C61#3357semidirect
301. #500C2×D61semidirect
322. C61C2×#3357semidirect
531. C2#21458444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404782
C2×#168404732
#214584442
C2×#168401052
C2×#168400772
C2×#168400542
C2×#168400492
C2×#168400092
C2×C4×#117581902
C2×#168398412
C2×#168398032
C2×C61×#5002
C2×#335761