Finite Group Databasebeta

← C2×#21455985 #30548156

Subgroups — C2×#21455985 #30548156

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2C22×Q8×Dic61C211yesmaximal, characteristic, complemented
3#21455985C2116yesmaximal, direct product factor
4C2×#16840098C211yesmaximal, characteristic, complemented
5C2×#16840078C211yesmaximal, characteristic
6C2×#16840071C212yesmaximal, complemented
7C2×#16839982C212yesmaximal, complemented
8C2×#16839918C211yesmaximal, characteristic, complemented
9C2×#16839866C212yesmaximal, complemented
10C2×#16839863C212yesmaximal, complemented
11C2×#16839816C211yesmaximal, characteristic, complemented
12C2×C61×#448C211yesmaximal, characteristic
13C22×#11758202C2212yes—
14#16840293—24no—
15#16840293C2218yes—
16C2×#14519770—21no—
17C2×#14519768C2211yescharacteristic
18C2×#14519764C2211yescharacteristic
19C2×#14519758—21no—
20C2×#14519756C2211yescharacteristic
21C2×Q8×Dic61—21no—
22C2×Q8×Dic61—21no—
23C2×Q8×Dic61—24no—
24C2×Q8×Dic61C2212yes—
25C2×Q8×Dic61C2212yes—
26C2×Q8×Dic61C2218yescomplemented
27C2×#14519742C2211yescharacteristic
28C2×D4×Dic61—21no—
29C2×D4×Dic61C2211yescharacteristic
30C2×#14519733—21no—
31C22×C4⋊Dic61—21no—
32C22×C4⋊Dic61C2211yescharacteristic
33C22×C4×Dic61—21no—
34C22×C4×Dic61C2211yescharacteristic
35#16840098C2218yescomplemented
36#16840078C2218yes—
37#16840071C22116yescomplemented
38#16839982C22116yescomplemented
39#16839918C2218yescomplemented
40#16839866C22116yescomplemented
41#16839863C22116yescomplemented
42#16839816C2218yescomplemented
43C2×#14519711C2212yes—
44C2×#14519708C2212yes—
45C2×#14519706C2212yes—
46C2×#14519702C2212yes—
47C2×#14519701C2212yes—
48C2×#14519698C2212yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519687C2212yes—
51C23×Q8×C61C2211yescharacteristic
52C22×SD16×C61C2212yes—
53C2×#121×C61C2211yescharacteristic
54C61×#448C2218yes—
55C2×#103×C61C2212yes—
56C2×C22⋊C8×C61C2211yescharacteristic
57C22×Dic122C2311yescharacteristic
58C23×Dic61—21no—
59C23×Dic61—21no—
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C2×#11758202—28no—
63C2×#11758202C2318yes—
64C22×#92418C2312yes—
65#14519770—28no—
66#14519768—22no—
67#14519768C2314yes—
68#14519764—22no—
69#14519764C2314yes—
70#14519758—28no—
71#14519756—22no—
72#14519756C2314yes—
73Q8×Dic61—24no—
74Q8×Dic61—24no—
75Q8×Dic61—28no—
76Q8×Dic61—28no—
77Q8×Dic61C2318yes—
78Q8×Dic61C2318yes—
79#14519742—22no—
80#14519742C2314yes—
81D4×Dic61—28no—
82D4×Dic61—22no—
83D4×Dic61C2314yes—
84#14519733—28no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—28no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2312yes—
92C2×C4⋊Dic61C2314yes—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—28no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D414yes—
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2314yes—
111#14519711C2318yes—
112#14519708C2318yes—
113#14519706C2318yes—
114#14519702C2318yes—
115#14519701C2318yes—
116#14519698C2318yes—
117C22⋊#92418C2314yes—
118#14519687C2318yes—
119C22×Q8×C61—28no—
120C22×Q8×C61—21no—
121C22×Q8×C61—22no—
122C22×Q8×C61C2314yes—
123C22×Q8×C61C2312yes—
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—28no—
129C2×SD16×C61C2318yes—
130C22×C8×C61C2312yes—
131#121×C61—22no—
132#121×C61C2314yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#103×C61C2318yes—
136C22⋊C8×C61C2314yes—
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139C2×Q8×C61—216no—
140C2×Q8×C61—28no—
141C2×Q8×C61—216no—
142C2×Q8×C61—24no—
143C2×Q8×C61—22no—
144C2×Q8×C61—24no—
145C2×Q8×C61#4118yes—
146C2×Q8×C61C2414yes—
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—24no—
150C2×D4×C61—44no—
151C2×D4×C61C2412yes—
152C22×C4×C61—28no—
153C22×C4×C61—24no—
154C22×C4×C61—22no—
155C22×C4×C61—24no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2412yes—
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—24no—
162C22×Dic61—24no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—24no—
167C22×Dic61—42no—
168C22×Dic61—44no—
169C22×Dic61—44no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D414yes—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D414yes—
176C2×Dic122—24no—
177C2×Dic122—21no—
178C2×Dic122C2412yes—
179SD16×C61—216no—
180C2×C8×C61—24no—
181C2×C8×C61C2414yes—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C2412yes—
184C22⋊C4×C61—24no—
185C22⋊Dic61—24no—
186C22⋊Dic61—24no—
187C22⋊Dic61—24no—
188C22⋊Dic61—24no—
189#11758202—216no—
190C4⋊Dic61—24no—
191C4⋊Dic61—22no—
192C4⋊Dic61—21no—
193C4⋊Dic61—28no—
194C4⋊Dic61—28no—
195C4⋊Dic61—24no—
196C4⋊Dic61C2414yes—
197C4⋊Dic61C2412yes—
198#11758196—24no—
199#11758196—24no—
200#11758196—24no—
201C4×Dic61—28no—
202C4×Dic61—28no—
203C4×Dic61—24no—
204C4×Dic61C2×D414yes—
205C4×Dic61C2×D412yes—
206C4×Dic61C2×D412yes—
207C4×Dic61C2×D414yes—
208C4×Dic61C2412yes—
209C4×Dic61C2412yes—
210C2×#92418—24no—
211C2×#92418C2414yes—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61#13714yes—
219C23×C61C22×D412yes—
220C23×C61C22×D411yescharacteristic
221Q8×C61—216no—
222Q8×C61—28no—
223Q8×C61—24no—
224Q8×C61C2×#4118yes—
225D4×C61—24no—
226D4×C61—48no—
227D4×C61—42no—
228C2×C4×C61—216no—
229C2×C4×C61—28no—
230C2×C4×C61—22no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—42no—
236C2×C4×C61C22×D412yes—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4114yes—
239C2×C4×C61C2511yescharacteristic
240C2×Dic61—28no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—44no—
249C2×Dic61—48no—
250C2×Dic61—48no—
251C2×Dic61—42no—
252C2×Dic61—44no—
253C2×Dic61—42no—
254C2×Dic61C22×D412yes—
255C2×Dic61C22×D412yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258Dic122—24no—
259Dic122—42no—
260C8×C61—24no—
261#92418—24no—
262C2×#3117—611nomaximal, Sylow
263C22×C61—28no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—84no—
270C22×C61#52512yes—
271C22×C61C2×#13714yes—
272C22×C61C2×#13712yes—
273C22×C61#57512yes—
274C22×C61C23×D411yescharacteristic
275C4×C61—28no—
276C4×C61—22no—
277C4×C61—42no—
278C4×C61#52512yes—
279C4×C61C22×#4112yes—
280Dic61—22no—
281Dic61—22no—
282Dic61—22no—
283Dic61—22no—
284Dic61—42no—
285Dic61—44no—
286Dic61—42no—
287C2×#529—611no—
288C22×C4×Q8—611no—
289#3117—6116no—
290C2×#484—611no—
291C2×#481—611no—
292C2×#479—612no—
293C2×#464—612no—
294C2×#451—611no—
295C2×#448D6111yescharacteristic
296C2×#441—612no—
297C2×#440—612no—
298C2×#432—611no—
299C2×C61—24no—
300C2×C61—82no—
301C2×C61#311714yescomplemented
302C2×C61C2×#52511yescharacteristic
303C2×C61C22×#13711yescharacteristic
304C2×C61C2×#57511yescharacteristic
305C23×Q8C2×D6111yescharacteristic
306C22×Q16—612no—
307C22×SD16C2×D6112yes—
308#529—618no—
309#529—1224no—
310C2×#126—1221no—
311C2×#125—611no—
312C2×#124—611no—
313C2×#123—1221no—
314C2×C22⋊Q8—611no—
315C2×#121C2×D6111yescharacteristic
316C2×C4×Q8—612no—
317C2×C4×Q8—612no—
318C2×C4×Q8—618no—
319C2×C4×Q8—611no—
320C2×C4×Q8—1221no—
321C2×C4×Q8—1221no—
322C2×C4×Q8—1224no—
323C2×C4×D4—611no—
324C2×C4×D4—1221no—
325C2×#117—1221no—
326C22×C4⋊C4—611no—
327C22×C4⋊C4—1221no—
328C22×C42—611no—
329C22×C42—1221no—
330#484—618no—
331#481—618no—
332#479—6116no—
333#464—6116no—
334#451—618no—
335#448C2×D6118yes—
336#441—6116no—
337#440—6116no—
338#432—618no—
339C2×#107—612no—
340C2×#106—612no—
341C2×C4⋊C8—612no—
342C2×#103—612no—
343C2×#103—612no—
344C2×#103C2×D6112yes—
345C2×#102—612no—
346C2×C22⋊C8—611no—
347C2×C22⋊C8C2×D6111yescharacteristic
348C2×#97—612no—
349C61C2×#311711yescharacteristic, complemented, Sylow
350C22×Q8—28no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—611no—
354C22×Q8C22×D6114yes—
355C22×Q8C22×D6112yes—
356C22×D4—21no—
357C22×D4C22×D6111yescharacteristic
358C23×C4—21no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—1221no—
362C23×C4—1221no—
363C23×C4C22×D6111yescharacteristic
364C2×Q16—618no—
365C2×Q16—1228no—
366C2×SD16—28no—
367C2×SD16C22×D6118yes—
368C22×C8—612no—
369C22×C8C22×D6112yes—
370#126—1228no—
371#125—614no—
372#125—1222no—
373#124—614no—
374#124—1222no—
375#123—1228no—
376C22⋊Q8—614no—
377C22⋊Q8—1222no—
378#121—22no—
379#121C22×D6114yes—
380C4×Q8—618no—
381C4×Q8—618no—
382C4×Q8—614no—
383C4×Q8—1222no—
384C4×Q8—1228no—
385C4×Q8—1224no—
386C4×Q8—1224no—
387C4×Q8—1228no—
388C4×D4—614no—
389C4×D4—1222no—
390C4×D4—1228no—
391#117—1228no—
392C2×C4⋊C4—612no—
393C2×C4⋊C4—614no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—1228no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—614no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—614no—
416C2×C42—1221no—
417C2×C42—1228no—
418C2×C42—1222no—
419C2×C42—1222no—
420#107—618no—
421#106—618no—
422C4⋊C8—618no—
423#103—618no—
424#103—618no—
425#103C22×D6118yes—
426#102—618no—
427C22⋊C8—614no—
428C22⋊C8C22×D6114yes—
429#97—618no—
430C24—21no—
431C24D4×D6111yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—24no—
438C2×Q8—612no—
439C2×Q8—1221no—
440C2×Q8—1224no—
441C2×Q8#1175822418yes—
442C2×Q8C23×D6114yes—
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—24no—
446C2×D4—44no—
447C2×D4C23×D6112yes—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—614no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—614no—
459C22×C4—1224no—
460C22×C4—1224no—
461C22×C4—1224no—
462C22×C4—1222no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—2442no—
466C22×C4—2444no—
467C22×C4—2444no—
468C22×C4D4×D6112yes—
469C22×C4D4×D6111yescharacteristic
470C22×C4C23×D6112yes—
471C22×C4C23×D6111yescharacteristic
472Q16—12216no—
473SD16—216no—
474C2×C8—24no—
475C2×C8—614no—
476C2×C8—1224no—
477C2×C8C23×D6114yes—
478C4⋊C4—21no—
479C4⋊C4—614no—
480C4⋊C4—612no—
481C4⋊C4—1228no—
482C4⋊C4—1228no—
483C4⋊C4—1224no—
484C4⋊C4—1224no—
485C4⋊C4—1224no—
486C4⋊C4—1224no—
487C4⋊C4—1222no—
488C4⋊C4—1221no—
489C4⋊C4—1224no—
490C4⋊C4C23×D6112yes—
491C22⋊C4—24no—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—1224no—
495C22⋊C4—1224no—
496C42—614no—
497C42—612no—
498C42—612no—
499C42—614no—
500C42—612no—
501C42—612no—
502C42—1228no—
503C42—1228no—
504C42—1224no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#1451980614yes—
512C23C2×D4×D6112yes—
513C23C2×D4×D6111yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—1224no—
518Q8—2442no—
519Q8C2×#1175822418yes—
520D4—24no—
521D4—48no—
522D4—42no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—1228no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1224no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—2444no—
544C2×C4—2448no—
545C2×C4—2448no—
546C2×C4—2442no—
547C2×C4—2444no—
548C2×C4—2442no—
549C2×C4C2×D4×D6112yes—
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4C2×#1175822414yes—
552C2×C4C24×D6111yescharacteristic
553C8—24no—
554C8—1224no—
555C22—22no—
556C22—22no—
557C22—28no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—84no—
562C22#1684026812yes—
563C22C2×#1451980614yes—
564C22C2×#1451980612yes—
565C22#1684056112yes—
566C22C22×D4×D6111yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—1222no—
571C4—1222no—
572C4—1222no—
573C4—1222no—
574C4—2444no—
575C4—2442no—
576C4—2442no—
577C4#1684026812yes—
578C4C22×#1175822412yes—
579C2—24no—
580C2—82no—
581C2#2145598514yesdirect product factor
582C2C2×#1684026811yescharacteristic
583C2C22×#1451980611yescharacteristic
584C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#448D61
hypocenterC61C2×#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic61C2semidirect
3. #21455985C2direct (N × H)
4. C2×#16840098C2semidirect
6. C2×#16840071C2semidirect
7. C2×#16839982C2semidirect
8. C2×#16839918C2semidirect
9. C2×#16839866C2semidirect
10. C2×#16839863C2semidirect
11. C2×#16839816C2semidirect
26. C2×Q8×Dic61C22semidirect
35. #16840098C22semidirect
37. #16840071C22semidirect
38. #16839982C22semidirect
39. #16839918C22semidirect
40. #16839866C22semidirect
41. #16839863C22semidirect
42. #16839816C22semidirect
301. C2×C61#3117semidirect
349. C61C2×#3117semidirect
581. C2#21455985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402932
C22×Q8×Dic612
#214559852
C2×#168400982
C2×#168400782
C2×#168400712
C2×#168399822
C2×#168399182
C2×#168398662
C2×#168398632
C2×#168398162
C2×C61×#4482
C2×#311761