Finite Group Databasebeta

← C2×#21455991 #30548162

Subgroups — C2×#21455991 #30548162

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×#16840298C211yesmaximal, characteristic
2C22×Q8×Dic61C211yesmaximal, characteristic, complemented
3#21455991C2116yesmaximal, direct product factor
4C2×#16840095C211yesmaximal, characteristic, complemented
5C2×#16840081C211yesmaximal, characteristic
6C2×#16840067C212yesmaximal, complemented
7C2×#16839986C212yesmaximal, complemented
8C2×#16839901C211yesmaximal, characteristic
9C2×#16839869C212yesmaximal, complemented
10C2×#16839865C212yesmaximal, complemented
11C2×#16839816C211yesmaximal, characteristic, complemented
12C2×C61×#451C211yesmaximal, characteristic, complemented
13C22×#11758201C2212yes—
14#16840298—24no—
15#16840298C2218yes—
16C2×#14519772—21no—
17C2×#14519768C2211yescharacteristic
18C2×#14519766C2211yescharacteristic
19C2×#14519761—21no—
20C2×#14519751C2211yescharacteristic
21C2×Q8×Dic61—21no—
22C2×Q8×Dic61—21no—
23C2×Q8×Dic61—24no—
24C2×Q8×Dic61C2212yes—
25C2×Q8×Dic61C2211yescharacteristic
26C2×Q8×Dic61C2212yes—
27C2×Q8×Dic61C2218yescomplemented
28C2×#14519739C2211yescharacteristic
29C2×#14519737—21no—
30C2×#14519735—21no—
31C22×C4⋊Dic61—21no—
32C22×C4⋊Dic61C2211yescharacteristic
33C22×C4×Dic61—21no—
34C22×C4×Dic61C2211yescharacteristic
35#16840095C2218yescomplemented
36#16840081C2218yes—
37#16840067C22116yescomplemented
38#16839986C22116yescomplemented
39#16839901C2218yes—
40#16839869C22116yescomplemented
41#16839865C22116yescomplemented
42#16839816C2218yescomplemented
43C2×#14519710C2212yes—
44C2×#14519709C2212yes—
45C2×#14519706C2212yes—
46C2×#14519701C2212yes—
47C2×#14519701C2212yes—
48C2×#14519699C2212yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519687C2212yes—
51C23×Q8×C61C2211yescharacteristic
52C22×Q16×C61C2212yes—
53C2×C22⋊Q8×C61C2211yescharacteristic
54C61×#451C2218yescomplemented
55C2×#103×C61C2212yes—
56C2×C22⋊C8×C61C2211yescharacteristic
57C22×D244C2311yescharacteristic
58C22×C22⋊D61—21no—
59C23×Dic61—21no—
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—21no—
63C2×#11758201—28no—
64C2×#11758201C2318yes—
65C22×#92418C2312yes—
66#14519772—28no—
67#14519768—22no—
68#14519768C2314yes—
69#14519766—22no—
70#14519766C2314yes—
71#14519761—28no—
72#14519751—22no—
73#14519751C2314yes—
74Q8×Dic61—24no—
75Q8×Dic61—24no—
76Q8×Dic61—28no—
77Q8×Dic61—28no—
78Q8×Dic61—22no—
79Q8×Dic61C2318yes—
80Q8×Dic61C2318yes—
81Q8×Dic61C2314yes—
82#14519739—22no—
83#14519739C2314yes—
84#14519737—28no—
85#14519735—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—28no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2312yes—
94C2×C4⋊Dic61C2314yes—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—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#14519710C2318yes—
112#14519709C2318yes—
113#14519706C2318yes—
114#14519701C2318yes—
115#14519701C2318yes—
116#14519699C2318yes—
117C22⋊#92418C2314yes—
118#14519687C2318yes—
119C22×Q8×C61—28no—
120C22×Q8×C61—21no—
121C22×Q8×C61—22no—
122C22×Q8×C61C2311yescharacteristic
123C22×Q8×C61C2314yes—
124C22×Q8×C61C2312yes—
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C2×Q16×C61—28no—
128C2×Q16×C61C2318yes—
129C22×C8×C61C2312yes—
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61C2314yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#103×C61C2318yes—
136C22⋊C8×C61C2314yes—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C2×Q8×C61—216no—
140C2×Q8×C61—28no—
141C2×Q8×C61—216no—
142C2×Q8×C61—24no—
143C2×Q8×C61—22no—
144C2×Q8×C61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61—24no—
147C2×Q8×C61#4118yes—
148C2×Q8×C61C2412yes—
149C2×Q8×C61C2414yes—
150C22×C4×C61—28no—
151C22×C4×C61—24no—
152C22×C4×C61—22no—
153C22×C4×C61—24no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2412yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—24no—
161C2×C22⋊D61—44no—
162C22×Dic61—24no—
163C22×Dic61—24no—
164C22×Dic61—22no—
165C22×Dic61—21no—
166C22×Dic61—42no—
167C22×Dic61—44no—
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D414yes—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D414yes—
174C2×D244—24no—
175C2×D244—21no—
176C2×D244C2412yes—
177C2×C4×D61—24no—
178C2×C4×D61—44no—
179Q16×C61—216no—
180C2×C8×C61—24no—
181C2×C8×C61C2414yes—
182C4⋊C4×C61—24no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61C2412yes—
185C22⋊C4×C61—24no—
186#11758201—216no—
187#11758198—24no—
188#11758198—24no—
189#11758198—24no—
190#11758198—24no—
191C4⋊Dic61—24no—
192C4⋊Dic61—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—28no—
195C4⋊Dic61—28no—
196C4⋊Dic61—24no—
197C4⋊Dic61—24no—
198C4⋊Dic61C2414yes—
199C4⋊Dic61C2412yes—
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#13714yes—
215C23×C61C22×D412yes—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221Q8×C61—216no—
222Q8×C61—28no—
223Q8×C61—24no—
224Q8×C61—24no—
225Q8×C61—42no—
226Q8×C61C2×#4118yes—
227C2×C4×C61—216no—
228C2×C4×C61—28no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C22×D412yes—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4114yes—
240C2×C4×C61C2511yescharacteristic
241C22⋊D61—48no—
242C2×Dic61—28no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—22no—
249C2×Dic61—44no—
250C2×Dic61—48no—
251C2×Dic61—42no—
252C2×Dic61—44no—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255C2×Dic61C22×D412yes—
256C2×Dic61C22×D412yes—
257D244—24no—
258D244—42no—
259C4×D61—48no—
260C8×C61—24no—
261#92418—24no—
262C2×#3117—611nomaximal, Sylow
263C22×C61—28no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61#52512yes—
267C22×C61C2×#13714yes—
268C22×C61C2×#13712yes—
269C22×C61#57512yes—
270C22×C61C23×D411yescharacteristic
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—84no—
275C4×C61—28no—
276C4×C61—22no—
277C4×C61—42no—
278C4×C61—42no—
279C4×C61#52512yes—
280C4×C61C22×#4112yes—
281Dic61—22no—
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—42no—
286Dic61—44no—
287C2×#529—611no—
288C22×C4×Q8—611no—
289#3117—6116no—
290C2×#484—611no—
291C2×#481—611no—
292C2×#479—612no—
293C2×#464—612no—
294C2×#451D6111yescharacteristic, complemented
295C2×#448—611no—
296C2×#441—612no—
297C2×#440—612no—
298C2×#432—611no—
299C2×C61—24no—
300C2×C61#311714yescomplemented
301C2×C61C2×#52511yescharacteristic
302C2×C61C22×#13711yescharacteristic
303C2×C61C2×#57511yescharacteristic
304D61—82no—
305C23×Q8C2×D6111yescharacteristic
306C22×Q16C2×D6112yes—
307C22×SD16—612no—
308#529—618no—
309#529—1224no—
310C2×#126—1221no—
311C2×#125—611no—
312C2×#124—611no—
313C2×#123—1221no—
314C2×C22⋊Q8C2×D6111yescharacteristic
315C2×#121—611no—
316C2×C4×Q8—612no—
317C2×C4×Q8—612no—
318C2×C4×Q8—611no—
319C2×C4×Q8—618no—
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#451C2×D6118yescomplemented
335#448—618no—
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×Q8C22×D6114yes—
354C22×Q8C22×D6111yescharacteristic
355C22×Q8C22×D6112yes—
356C22×D4—611no—
357C22×D4—1221no—
358C23×C4—21no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—1221no—
362C23×C4—1221no—
363C23×C4C22×D6111yescharacteristic
364C2×Q16—28no—
365C2×Q16C22×D6118yes—
366C2×SD16—618no—
367C2×SD16—1228no—
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—22no—
377C22⋊Q8C22×D6114yes—
378#121—614no—
379#121—1222no—
380C4×Q8—618no—
381C4×Q8—618no—
382C4×Q8—614no—
383C4×Q8—1228no—
384C4×Q8—1224no—
385C4×Q8—1224no—
386C4×Q8—1228no—
387C4×Q8—1222no—
388C4×D4—614no—
389C4×D4—1222no—
390C4×D4—1228no—
391#117—1228no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—612no—
394C2×C4⋊C4—614no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1228no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1222no—
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—1221no—
431C24D4×D6111yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8#1175822418yes—
441C2×Q8C23×D6112yes—
442C2×Q8C23×D6114yes—
443C2×D4—612no—
444C2×D4—1224no—
445C2×D4—1221no—
446C2×D4—1224no—
447C2×D4—2444no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—614no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—614no—
460C22×C4—1224no—
461C22×C4—1224no—
462C22×C4—1224no—
463C22×C4—1222no—
464C22×C4—1221no—
465C22×C4—2444no—
466C22×C4—2442no—
467C22×C4—2444no—
468C22×C4D4×D6112yes—
469C22×C4D4×D6111yescharacteristic
470C22×C4C23×D6112yes—
471C22×C4C23×D6111yescharacteristic
472Q16—216no—
473SD16—12216no—
474C2×C8—24no—
475C2×C8—614no—
476C2×C8—1224no—
477C2×C8C23×D6114yes—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—614no—
481C4⋊C4—612no—
482C4⋊C4—1228no—
483C4⋊C4—1228no—
484C4⋊C4—1224no—
485C4⋊C4—1224no—
486C4⋊C4—1224no—
487C4⋊C4—1224no—
488C4⋊C4—1222no—
489C4⋊C4—1221no—
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—1222no—
508C23—2442no—
509C23—2442no—
510C23—2442no—
511C23#1451980914yes—
512C23C2×D4×D6112yes—
513C23C2×D4×D6111yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8C2×#1175822418yes—
520D4—1224no—
521D4—2448no—
522D4—2442no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—1228no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1224no—
543C2×C4—1222no—
544C2×C4—2448no—
545C2×C4—2444no—
546C2×C4—2448no—
547C2×C4—2442no—
548C2×C4—2444no—
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—4884no—
559C22—2442no—
560C22—2442no—
561C22—2442no—
562C22#1684026812yes—
563C22C2×#1451980914yes—
564C22C2×#1451980912yes—
565C22#1684056112yes—
566C22C22×D4×D6111yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—1222no—
572C4—1222no—
573C4—1222no—
574C4—1222no—
575C4—2442no—
576C4—2444no—
577C4#1684026812yes—
578C4C22×#1175822412yes—
579C2—24no—
580C2—4882no—
581C2#2145599114yesdirect product factor
582C2C2×#1684026811yescharacteristic
583C2C22×#1451980911yescharacteristic
584C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#451D61
hypocenterC61C2×#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic61C2semidirect
3. #21455991C2direct (N × H)
4. C2×#16840095C2semidirect
6. C2×#16840067C2semidirect
7. C2×#16839986C2semidirect
9. C2×#16839869C2semidirect
10. C2×#16839865C2semidirect
11. C2×#16839816C2semidirect
12. C2×C61×#451C2semidirect
27. C2×Q8×Dic61C22semidirect
35. #16840095C22semidirect
37. #16840067C22semidirect
38. #16839986C22semidirect
40. #16839869C22semidirect
41. #16839865C22semidirect
42. #16839816C22semidirect
54. C61×#451C22semidirect
294. C2×#451D61semidirect
300. C2×C61#3117semidirect
334. #451C2×D61semidirect
349. C61C2×#3117semidirect
581. C2#21455991direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402982
C22×Q8×Dic612
#214559912
C2×#168400952
C2×#168400812
C2×#168400672
C2×#168399862
C2×#168399012
C2×#168398692
C2×#168398652
C2×#168398162
C2×C61×#4512
C2×#311761