Finite Group Databasebeta

← #29680083

Subgroups — #29680083

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3#21448215C211yesmaximal, characteristic, complemented
4#21445913C212yesmaximal, complemented
5#21445833C212yesmaximal, complemented
6#21445827C212yesmaximal, complemented
7#21445756C212yesmaximal
8#21445652C211yesmaximal, characteristic, complemented
9#21445650C211yesmaximal, characteristic, complemented
10#21445644C211yesmaximal, characteristic, complemented
11C61×#1762C211yesmaximal, characteristic, complemented
12C22×#11758224C2211yescharacteristic
13C4×#11758224—24no—
14C4×#11758224C418yescomplemented
15C2×C4×Dic122C2211yescharacteristic
16C2×#14519742C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×#14519737—21no—
20C2×#14519735C2211yescharacteristic
21C2×#14519733—21no—
22C22×C4×Dic61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839817—24no—
25C2×#14519706C2212yes—
26C2×#14519702C2212yes—
27C2×#14519700C2212yes—
28C2×#14519698C2212yes—
29C2×#14519689C2212yes—
30C2×#14519688C2211yescharacteristic
31#16839629—21no—
32#16839627C2212yes—
33#16839624—21no—
34#16839619C2212yes—
35C4×C4⋊Dic61C2211yescharacteristic
36C4×#11758198—21no—
37#16839608—21no—
38#16839525C2212yes—
39#16839524C2212yes—
40#16839524C2212yes—
41C2×C4×D4×C61C2211yescharacteristic
42C2×#102×C61C2212yes—
43C2×#97×C61C2211yescharacteristic
44C4×C4⋊C4×C61C2211yescharacteristic
45C61×#340C2212yes—
46C2×#11758224—24no—
47C2×#11758224—22no—
48C2×#11758224—24no—
49C2×#11758224C2×C414yes—
50C22×Dic122C2311yescharacteristic
51C22×C22⋊D61—21no—
52C23×Dic61—21no—
53C23×Dic61—21no—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C22×#92418C2312yes—
58C4×Dic122—22no—
59C4×Dic122C2×C414yes—
60#14519742—22no—
61#14519742C2×C414yes—
62D4×Dic61—22no—
63D4×Dic61C2×C414yes—
64C4×C22⋊D61—28no—
65#14519737—28no—
66#14519735—22no—
67#14519735C2×C414yes—
68#14519733—28no—
69C2×C4⋊Dic61C2312yes—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×C22⋊Dic61—21no—
74C2×#11758198—21no—
75C2×#11758198—22no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—28no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C42×D61C2×C414yes—
85C42×D61D414yes—
86#14519706—24no—
87#14519702—24no—
88#14519700—24no—
89#14519698—24no—
90#14519689—24no—
91#14519688—22no—
92#14519684—21no—
93#14519684—22no—
94#14519684—22no—
95#14519684—22no—
96C22×D4×C61C2311yescharacteristic
97C23×C4×C61—21no—
98C22×C8×C61C2312yes—
99C4×D4×C61—22no—
100C4×D4×C61C2×C414yes—
101C2×C4⋊C4×C61C2312yes—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#102×C61—24no—
107#97×C61—22no—
108#95×C61—21no—
109C24×C61—21no—
110C23×D61C2×D411yescharacteristic
111C2×D4×C61—21no—
112C2×D4×C61—22no—
113C2×D4×C61C22×C412yes—
114C2×D4×C61#4114yes—
115C22×C4×C61—21no—
116C22×C4×C61—24no—
117C22×C4×C61—22no—
118C22×C4×C61—44no—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2411yescharacteristic
122C2×C22⋊D61—28no—
123C2×C22⋊D61—24no—
124C22×Dic61—28no—
125C22×Dic61—21no—
126C22×Dic61—24no—
127C22×Dic61—21no—
128C22×Dic61—24no—
129C22×Dic61—22no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135#11758224—216no—
136#11758224—28no—
137#11758224—28no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×C4×D61—42no—
143C2×C4×D61C22⋊C414yes—
144C2×C4×D61C22⋊C414yes—
145C2×C4×D61C22×C412yes—
146C2×C4×D61C2×D412yes—
147C2×Dic122—21no—
148C2×Dic122—22no—
149C2×Dic122C22×C412yes—
150C2×Dic122#4114yes—
151C2×C8×C61—22no—
152C2×C8×C61—22no—
153C2×C8×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61C22×C412yes—
158C22⋊C4×C61—24no—
159C42×C61—42no—
160C42×C61C22×C412yes—
161C42×C61C2×D412yes—
162C22⋊Dic61—24no—
163#11758198—24no—
164#11758198—44no—
165C4⋊Dic61—21no—
166C4⋊Dic61—22no—
167C4⋊Dic61—22no—
168C4⋊Dic61C22×C412yes—
169#11758196—24no—
170#11758196—24no—
171C4×Dic61—24no—
172C4×Dic61—24no—
173C4×Dic61—24no—
174C4×Dic61—42no—
175C4×Dic61C22⋊C414yes—
176C4×Dic61C22⋊C414yes—
177C4×Dic61C22×C412yes—
178C4×Dic61C2×D412yes—
179C2×#92418—22no—
180C2×#92418—22no—
181C2×#92418—22no—
182C23×C61—22no—
183C23×C61—24no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—42no—
187C23×C61C22×D411yescharacteristic
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—21no—
191C22×D61—21no—
192C22×D61C2×C22⋊C412yes—
193D4×C61—22no—
194D4×C61—24no—
195D4×C61#11714yes—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—48no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61C2×C22⋊C412yes—
206C2×C4×C61C2×C22⋊C412yes—
207C2×C4×C61C23×C411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C2×#4112yes—
210C2×C4×C61C2×#4112yes—
211C22⋊D61—216no—
212C2×Dic61—216no—
213C2×Dic61—22no—
214C2×Dic61—24no—
215C2×Dic61—22no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—48no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61C2×C22⋊C412yes—
227C2×Dic61C2×C22⋊C412yes—
228C2×Dic61C2×C22⋊C412yes—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—24no—
232C4×D61—44no—
233C4×D61—44no—
234Dic122—22no—
235Dic122—24no—
236Dic122#11714yes—
237C8×C61—42no—
238#92418—42no—
239#20742—611nomaximal, Sylow
240C22×C61—24no—
241C22×C61—44no—
242C22×C61—44no—
243C22×C61—42no—
244C22×C61—42no—
245C22×C61C22×C22⋊C411yescharacteristic
246C22×C61#52512yes—
247C22×C61#57511yescharacteristic
248C22×C61#57512yes—
249C22×C61#57511yescharacteristic
250C2×D61—22no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—42no—
254C2×D61—42no—
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—42no—
258C4×C61—82no—
259C4×C61C2×#11711yescharacteristic
260C4×C61C2×#11711yescharacteristic
261C4×C61#52512yes—
262Dic61—22no—
263Dic61—22no—
264Dic61—24no—
265Dic61—22no—
266Dic61—42no—
267Dic61—82no—
268C2×C4×#41—611no—
269C2×#432—611no—
270#2283—611no—
271#1825—612no—
272#1805—612no—
273#1804—612no—
274#1788—612no—
275#1763—611no—
276#1763—611no—
277#1762—611no—
278#1762D6111yescharacteristic, complemented
279C2×C61—44no—
280C2×C61#228011yescharacteristic
281C2×C61#289611yescharacteristic
282C2×C61#289611yescharacteristic
283C2×C61#311112yes—
284C2×C61#311112yes—
285D61—42no—
286C22×#41—611no—
287C4×#41—618no—
288C4×#41—1224no—
289C2×C4×Q8—611no—
290C2×C4×Q8—611no—
291C2×C4×D4—611no—
292C2×C4×D4—1221no—
293C2×C4×D4—1221no—
294C2×C4×D4C2×D6111yescharacteristic
295C2×#117—611no—
296C2×#117—1221no—
297C22×C42—611no—
298C22×C42—1221no—
299#432—1224no—
300C2×C4⋊C8—612no—
301C2×#103—612no—
302C2×#103—612no—
303C2×#102—612no—
304C2×#102C2×D6112yes—
305C2×C22⋊C8—612no—
306C2×#97—611no—
307C2×#97C2×D6111yescharacteristic
308#383—1221no—
309#382—612no—
310#381—1221no—
311#380—612no—
312C4×C4⋊C4—611no—
313C4×C4⋊C4C2×D6111yescharacteristic
314C4×C22⋊C4—1221no—
315#376—1221no—
316#340—612no—
317#340—612no—
318#340—612no—
319#340C2×D6112yes—
320C61#2074211yescharacteristic, complemented, Sylow
321C2×#41—614no—
322C2×#41—1222no—
323C2×#41—1224no—
324C2×#41—1224no—
325C22×Q8—611no—
326C22×D4—1221no—
327C22×D4C22×D6111yescharacteristic
328C23×C4—21no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—1221no—
333C23×C4—1221no—
334C22×C8—612no—
335C22×C8C22×D6112yes—
336C4×Q8—614no—
337C4×Q8—614no—
338C4×Q8—1222no—
339C4×Q8—1222no—
340C4×D4—22no—
341C4×D4—614no—
342C4×D4—1222no—
343C4×D4—1228no—
344C4×D4—1228no—
345C4×D4C4×D6114yes—
346#117—614no—
347#117—1228no—
348#117—1222no—
349C2×C4⋊C4—611no—
350C2×C4⋊C4—612no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4C22×D6112yes—
354C2×C4⋊C4C22×D6111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—1221no—
357C2×C22⋊C4—1221no—
358C2×C22⋊C4—1222no—
359C2×C42—21no—
360C2×C42—611no—
361C2×C42—611no—
362C2×C42—611no—
363C2×C42—614no—
364C2×C42—614no—
365C2×C42—1228no—
366C2×C42—1221no—
367C2×C42—1221no—
368C2×C42—1221no—
369C2×C42—1221no—
370C2×C42C22×D6111yescharacteristic
371C4⋊C8—1224no—
372#103—1224no—
373#103—1224no—
374#102—24no—
375#102—1224no—
376C22⋊C8—1224no—
377#97—22no—
378#97—1222no—
379#95—21no—
380#95—1222no—
381#95—1222no—
382#95—1222no—
383#95—1221no—
384C24—21no—
385C24—611no—
386#41—1228no—
387#41—12216no—
388#41—1228no—
389C2×Q8—612no—
390C2×Q8—614no—
391C2×Q8—1221no—
392C2×Q8—1222no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—1224no—
396C2×D4—1228no—
397C2×D4C2×C4×D6112yes—
398C2×D4#1175822214yes—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—44no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—612no—
407C22×C4—612no—
408C22×C4—614no—
409C22×C4—614no—
410C22×C4—1224no—
411C22×C4—1224no—
412C22×C4—1228no—
413C22×C4—1221no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1221no—
417C22×C4—1222no—
418C22×C4—2441no—
419C22×C4—2442no—
420C22×C4—2441no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4D4×D6111yescharacteristic
424C22×C4D4×D6111yescharacteristic
425C22×C4C23×D6111yescharacteristic
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—1222no—
430C2×C8—1222no—
431C2×C8—1222no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—612no—
436C4⋊C4—1224no—
437C4⋊C4—1221no—
438C4⋊C4—1224no—
439C4⋊C4—1222no—
440C4⋊C4—1222no—
441C4⋊C4C2×C4×D6112yes—
442C22⋊C4—24no—
443C22⋊C4—1224no—
444C22⋊C4—1224no—
445C22⋊C4—2444no—
446C42—42no—
447C42—612no—
448C42—612no—
449C42—614no—
450C42—614no—
451C42—1224no—
452C42—1224no—
453C42—1224no—
454C42—2442no—
455C42C2×C4×D6112yes—
456C42D4×D6112yes—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—612no—
463C23—1222no—
464C23—1222no—
465C23—1221no—
466C23—1221no—
467C23C2×D4×D6111yescharacteristic
468Q8—614no—
469Q8—1222no—
470Q8—1224no—
471D4—22no—
472D4—24no—
473D4—12216no—
474D4#1451973414yes—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—48no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—612no—
485C2×C4—612no—
486C2×C4—612no—
487C2×C4—12216no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1224no—
491C2×C4—1222no—
492C2×C4—1221no—
493C2×C4—1221no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1224no—
497C2×C4—1222no—
498C2×C4—2444no—
499C2×C4—2444no—
500C2×C4—2448no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4C22⋊C4×D6112yes—
507C2×C4C22⋊C4×D6112yes—
508C2×C4C22×C4×D6111yescharacteristic
509C2×C4C2×D4×D6111yescharacteristic
510C2×C4#41×D6112yes—
511C2×C4C2×#1175822212yes—
512C8—42no—
513C8—2442no—
514C22—24no—
515C22—44no—
516C22—44no—
517C22—42no—
518C22—42no—
519C22—1222no—
520C22—1222no—
521C22—1222no—
522C22—2442no—
523C22—2442no—
524C22C2×C22⋊C4×D6111yescharacteristic
525C22#1684027112yes—
526C22#1684055811yescharacteristic
527C22#1684055812yes—
528C22#1684056111yescharacteristic
529C4—22no—
530C4—22no—
531C4—42no—
532C4—82no—
533C4—1222no—
534C4—1224no—
535C4—1222no—
536C4—1222no—
537C4—4882no—
538C4—2442no—
539C4#117×D6111yescharacteristic
540C4C2×#1451973411yescharacteristic
541C4#1684027112yes—
542C2—44no—
543C2—2442no—
544C2#2144820011yescharacteristic
545C2#2145433311yescharacteristic
546C2#2145433511yescharacteristic
547C2#2145592412yes—
548C2#2145593212yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#20742
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. #21448215C2semidirect
4. #21445913C2semidirect
5. #21445833C2semidirect
6. #21445827C2semidirect
8. #21445652C2semidirect
9. #21445650C2semidirect
10. #21445644C2semidirect
11. C61×#1762C2semidirect
14. C4×#11758224C4semidirect
278. #1762D61semidirect
320. C61#20742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
C2×#168398172
#214482152
#214459132
#214458332
#214458272
#214457562
#214456522
#214456502
#214456442
C61×#17622
#2074261