Finite Group Databasebeta

← C2×#21457060 #30552175

Subgroups — C2×#21457060 #30552175

Order 15616.

1790 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C2×#16840297C211yesmaximal, characteristic
3#21457060C2116yesmaximal, direct product factor
4C2×#16840172C211yesmaximal, characteristic, complemented
5C2×#16840124C211yesmaximal, characteristic, complemented
6C2×#16840122C211yesmaximal, characteristic, complemented
7C2×#16840105C212yesmaximal, complemented
8C2×#16840088C212yesmaximal
9C2×#16840072C212yesmaximal, complemented
10C2×#16840065C212yesmaximal, complemented
11C2×#16839817C211yesmaximal, characteristic, complemented
12C2×C61×#501C211yesmaximal, characteristic, complemented
13#16840317—24no—
14#16840317C2218yescomplemented
15C2×#14519777C2211yescharacteristic
16#16840297—24no—
17#16840297C2218yes—
18C2×#14519772—21no—
19C2×#14519768C2212yes—
20C2×#14519765C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519757—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519753—21no—
25C2×#14519752C2211yescharacteristic
26C2×Q8×Dic61—21no—
27C2×#14519742—21no—
28C2×#14519742C2211yescharacteristic
29C2×#14519739—21no—
30C2×#14519739C2211yescharacteristic
31C2×#14519735—21no—
32C2×#14519735C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16840172C2218yescomplemented
35#16840124C2218yescomplemented
36#16840122C2218yescomplemented
37#16840105C22116yescomplemented
38#16840088C22116yes—
39#16840072C22116yescomplemented
40#16840065C22116yescomplemented
41#16839817C2218yescomplemented
42C2×#14519710C2212yes—
43C2×#14519708C2212yes—
44C2×#14519706C2212yes—
45C2×#14519702C2212yes—
46C2×#14519700C2212yes—
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519688C2211yescharacteristic
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#125×C61C2211yescharacteristic
53C61×#501C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×#106×C61C2212yes—
56C2×#97×C61C2211yescharacteristic
57C22×Dic122—21no—
58C22×Dic122C2311yescharacteristic
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2312yes—
66#14519777—22no—
67#14519777C2314yes—
68#14519772—28no—
69#14519768—24no—
70#14519768C2318yes—
71#14519765—22no—
72#14519765C2314yes—
73#14519762—28no—
74#14519757—28no—
75#14519757—22no—
76#14519757C2314yes—
77#14519753—28no—
78#14519752—22no—
79#14519752C2314yes—
80Q8×Dic61—28no—
81#14519742—28no—
82#14519742—22no—
83#14519742C2314yes—
84#14519739—28no—
85#14519739—22no—
86#14519739C2314yes—
87#14519735—24no—
88#14519735—28no—
89#14519735C2318yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61C2312yes—
94C2×#11758196—22no—
95C2×#11758196—21no—
96C2×#11758198—22no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C42×D61D414yes—
108C42×D61C2314yes—
109#14519710C2318yes—
110#14519708C2318yes—
111#14519706C2318yes—
112#14519702C2318yes—
113#14519700C2318yes—
114#14519699C2318yes—
115#14519697C2318yes—
116#14519689C2318yes—
117#14519688C2314yes—
118C22×Q8×C61—21no—
119C22×C8×C61C2312yes—
120C4⋊Q8×C61—22no—
121C4⋊Q8×C61C2314yes—
122#125×C61—22no—
123#125×C61C2314yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2312yes—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#107×C61C2318yes—
132#106×C61C2318yes—
133#97×C61C2314yes—
134C23×D61—21no—
135C23×D61C2×D411yescharacteristic
136C2×Q8×C61—24no—
137C2×Q8×C61—44no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—22no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C2×D244—24no—
150C2×D244—24no—
151C2×D244—21no—
152C2×D244—44no—
153C2×D244C2412yes—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—44no—
159C2×C4×D61C2×D412yes—
160C2×C4×D61C2×D414yes—
161C2×C4×D61C2×D414yes—
162C2×C4×D61C2412yes—
163C2×Dic122—24no—
164C2×Dic122—24no—
165C2×Dic122—21no—
166C2×Dic122—44no—
167C2×Dic122C2412yes—
168C2×C8×C61—24no—
169C2×C8×C61C2414yes—
170C4⋊C4×C61—24no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—24no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61C2412yes—
177C4⋊C4×C61C2414yes—
178C4⋊C4×C61C2412yes—
179C42×C61C2×D412yes—
180C42×C61C2412yes—
181#11758198—28no—
182#11758198—24no—
183#11758198—24no—
184#11758198—24no—
185#11758198—24no—
186#11758198—24no—
187C4⋊Dic61—24no—
188C4⋊Dic61—22no—
189C4⋊Dic61—24no—
190C4⋊Dic61—28no—
191C4⋊Dic61C2414yes—
192#11758196—28no—
193#11758196—24no—
194C4×Dic61—24no—
195C4×Dic61—28no—
196C4×Dic61C2×D412yes—
197C4×Dic61C2×D414yes—
198C4×Dic61C2×D414yes—
199C4×Dic61C2412yes—
200C2×#92418—24no—
201C2×#92418C2414yes—
202C23×C61C22×D411yescharacteristic
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61C22×D412yes—
211Q8×C61—48no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—44no—
220C2×C4×C61C22×D412yes—
221C2×C4×C61C22×D412yes—
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C612−1+414yes—
224C2×C4×C61C2511yescharacteristic
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—24no—
229C2×Dic61—22no—
230C2×Dic61—42no—
231C2×Dic61—44no—
232C2×Dic61C22×D412yes—
233C2×Dic61C22×D412yes—
234C2×Dic61C22×D412yes—
235D244—24no—
236D244—48no—
237D244—42no—
238C4×D61—24no—
239C4×D61—24no—
240C4×D61—44no—
241C4×D61—44no—
242C4×D61—48no—
243Dic122—24no—
244Dic122—48no—
245Dic122—42no—
246C8×C61—24no—
247#92418—24no—
248C2×#3240—611nomaximal, Sylow
249C22×C61#53612yes—
250C22×C61#57512yes—
251C22×C61#57512yes—
252C22×C61C23×D411yescharacteristic
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—44no—
257C2×D61—42no—
258C2×D61—42no—
259C2×D61—42no—
260C2×D61—84no—
261C4×C61—22no—
262C4×C61—22no—
263C4×C61—42no—
264C4×C61—42no—
265C4×C61—44no—
266C4×C61#53612yes—
267C4×C61C2×2−1+412yes—
268Dic61—22no—
269Dic61—22no—
270Dic61—22no—
271Dic61—42no—
272Dic61—44no—
273C2×#533—611no—
274C2×#529—611no—
275#3240—6116no—
276C2×#501—611no—
277C2×#501D6111yescharacteristic, complemented
278C2×#489—611no—
279C2×#489—611no—
280C2×#485—612no—
281C2×#482—612no—
282C2×#479—612no—
283C2×#478—612no—
284C2×#432—611no—
285C2×C61#324014yescomplemented
286C2×C61C2×#53611yescharacteristic
287C2×C61C2×#57511yescharacteristic
288C2×C61C2×#57511yescharacteristic
289D61—42no—
290D61—82no—
291#533—618no—
292#533—1224no—
293C2×C4⋊Q8—611no—
294C2×C4⋊Q8C2×D6111yescharacteristic
295#529—618no—
296#529—1224no—
297C2×#126—1221no—
298C2×#125—612no—
299C2×#125C2×D6111yescharacteristic
300C2×#124—611no—
301C2×#123—1221no—
302C2×C22⋊Q8—611no—
303C2×C22⋊Q8—1221no—
304C2×C22⋊Q8—1221no—
305C2×#121—611no—
306C2×C4×Q8—611no—
307C2×C4×Q8—1221no—
308C2×C4×Q8—1221no—
309C2×C4×D4—611no—
310C2×C4×D4—1221no—
311C2×#117—612no—
312C2×#117—1221no—
313C22×C42—611no—
314#501—618no—
315#501C2×D6118yescomplemented
316#489—618no—
317#489—618no—
318#485—6116no—
319#482—6116no—
320#479—6116no—
321#478—6116no—
322#432—618no—
323C2×#107—612no—
324C2×#107C2×D6112yes—
325C2×#106—612no—
326C2×#106C2×D6112yes—
327C2×C4⋊C8—612no—
328C2×#103—612no—
329C2×#103—612no—
330C2×#102—612no—
331C2×#102—612no—
332C2×C22⋊C8—612no—
333C2×#97—611no—
334C2×#97C2×D6111yescharacteristic
335C61C2×#324011yescharacteristic, complemented, Sylow
336C22×Q8—21no—
337C22×Q8—611no—
338C22×Q8—1221no—
339C22×D4—611no—
340C22×D4—1221no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—1221no—
345C22×C8—612no—
346C22×C8C22×D6112yes—
347C4⋊Q8—22no—
348C4⋊Q8—614no—
349C4⋊Q8—1222no—
350C4⋊Q8C22×D6114yes—
351#126—1228no—
352#125—22no—
353#125—618no—
354#125—1224no—
355#125C22×D6114yes—
356#124—614no—
357#124—1222no—
358#123—1228no—
359C22⋊Q8—614no—
360C22⋊Q8—1222no—
361C22⋊Q8—1228no—
362C22⋊Q8—1228no—
363#121—614no—
364#121—1222no—
365C4×Q8—614no—
366C4×Q8—1222no—
367C4×Q8—1228no—
368C4×Q8—1228no—
369C4×D4—614no—
370C4×D4—1222no—
371C4×D4—1228no—
372#117—618no—
373#117—1228no—
374#117—1224no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1222no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4C22×D6112yes—
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—614no—
397C2×C42—614no—
398C2×C42—1222no—
399C2×C42—1221no—
400C2×C42C22×D6111yescharacteristic
401#107—618no—
402#107C22×D6118yes—
403#106—618no—
404#106C22×D6118yes—
405C4⋊C8—618no—
406#103—618no—
407#103—618no—
408#102—618no—
409#102—618no—
410C22⋊C8—618no—
411#97—614no—
412#97C22×D6114yes—
413C24—611no—
414C24—1221no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—612no—
418C2×Q8—1221no—
419C2×Q8—1224no—
420C2×Q8—1224no—
421C2×Q8—2444no—
422C2×D4—612no—
423C2×D4—1224no—
424C2×D4—1221no—
425C2×D4—1224no—
426C2×D4—2444no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—614no—
436C22×C4—614no—
437C22×C4—1224no—
438C22×C4—1224no—
439C22×C4—1221no—
440C22×C4—1222no—
441C22×C4—2442no—
442C22×C4—2442no—
443C22×C4—2444no—
444C22×C4D4×D6111yescharacteristic
445C22×C4D4×D6111yescharacteristic
446C22×C4C23×D6111yescharacteristic
447C2×C8—24no—
448C2×C8—614no—
449C2×C8—1224no—
450C2×C8C23×D6114yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—614no—
458C4⋊C4—1224no—
459C4⋊C4—1228no—
460C4⋊C4—1224no—
461C4⋊C4—1228no—
462C4⋊C4—1222no—
463C4⋊C4—1224no—
464C4⋊C4C23×D6114yes—
465C4⋊C4C23×D6112yes—
466C4⋊C4C23×D6112yes—
467C22⋊C4—1224no—
468C22⋊C4—1224no—
469C22⋊C4—1228no—
470C22⋊C4—1224no—
471C22⋊C4—1224no—
472C22⋊C4—1224no—
473C42—614no—
474C42—612no—
475C42—614no—
476C42—612no—
477C42—1228no—
478C42—1224no—
479C42D4×D6112yes—
480C42C23×D6112yes—
481C23—612no—
482C23—1222no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—2442no—
487C23—2442no—
488C23—2442no—
489C23C2×D4×D6111yescharacteristic
490Q8—48no—
491Q8—1224no—
492Q8—2448no—
493Q8—2442no—
494D4—1224no—
495D4—2448no—
496D4—2442no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—612no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1224no—
512C2×C4—1224no—
513C2×C4—1222no—
514C2×C4—1224no—
515C2×C4—2444no—
516C2×C4—2444no—
517C2×C4—2448no—
518C2×C4—2444no—
519C2×C4—2442no—
520C2×C4C2×D4×D6112yes—
521C2×C4C2×D4×D6112yes—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4#1451982514yes—
524C2×C4C24×D6111yescharacteristic
525C8—24no—
526C8—1224no—
527C22—1222no—
528C22—1222no—
529C22—1222no—
530C22—4884no—
531C22—2442no—
532C22—2442no—
533C22—2442no—
534C22—2444no—
535C22#1684033712yes—
536C22#1684055812yes—
537C22#1684056112yes—
538C22C22×D4×D6111yescharacteristic
539C4—22no—
540C4—22no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—1222no—
545C4—1222no—
546C4—1222no—
547C4—2444no—
548C4—2442no—
549C4#1684033712yes—
550C4C2×#1451982512yes—
551C2—4882no—
552C2—2442no—
553C2#2145706014yesdirect product factor
554C2C2×#1684033711yescharacteristic
555C2C2×#1684055811yescharacteristic
556C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#501C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenterC2×#501D61
hypocenterC61C2×#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21457060C2direct (N × H)
4. C2×#16840172C2semidirect
5. C2×#16840124C2semidirect
6. C2×#16840122C2semidirect
7. C2×#16840105C2semidirect
9. C2×#16840072C2semidirect
10. C2×#16840065C2semidirect
11. C2×#16839817C2semidirect
12. C2×C61×#501C2semidirect
14. #16840317C22semidirect
34. #16840172C22semidirect
35. #16840124C22semidirect
36. #16840122C22semidirect
37. #16840105C22semidirect
39. #16840072C22semidirect
40. #16840065C22semidirect
41. #16839817C22semidirect
53. C61×#501C22semidirect
277. C2×#501D61semidirect
285. C2×C61#3240semidirect
315. #501C2×D61semidirect
335. C61C2×#3240semidirect
553. C2#21457060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403172
C2×#168402972
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