Finite Group Databasebeta

← #29680084

Subgroups — #29680084

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2C2×#16839818C211yesmaximal, characteristic, complemented
3#21448212C211yesmaximal, characteristic, complemented
4#21445912C212yesmaximal, complemented
5#21445835C211yesmaximal, characteristic, complemented
6#21445831C211yesmaximal, characteristic, complemented
7#21445829C211yesmaximal, characteristic, complemented
8#21445756C212yesmaximal
9#21445648C212yesmaximal, complemented
10#21445646C212yesmaximal, complemented
11C61×#1804C211yesmaximal, 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#16839818—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519702C2212yes—
27C2×#14519700C2212yes—
28C2×#14519698C2212yes—
29C2×#14519689C2212yes—
30C2×#14519687C2212yes—
31#16839629—21no—
32#16839628C2211yescharacteristic
33#16839624—21no—
34#16839619C2212yes—
35C4⋊C4×Dic61C2212yes—
36#16839609—21no—
37#16839607—21no—
38#16839525C2212yes—
39#16839524C2212yes—
40#16839524C2212yes—
41C2×C4×D4×C61C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C2×#102×C61C2212yes—
44C61×#382C2211yescharacteristic
45C61×#340C2212yes—
46C2×#11758224—22no—
47C2×#11758224—22no—
48C2×#11758224—22no—
49C2×#11758224—22no—
50C2×#11758224—22no—
51C2×#11758224C2×C414yes—
52C22×Dic122C2311yescharacteristic
53C22×C22⋊D61—21no—
54C23×Dic61—21no—
55C23×Dic61—21no—
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×#92418C2312yes—
60C4×Dic122—22no—
61C4×Dic122C2×C414yes—
62#14519742—22no—
63#14519742C2×C414yes—
64D4×Dic61—22no—
65D4×Dic61C2×C414yes—
66C4×C22⋊D61—28no—
67#14519737—28no—
68#14519735—22no—
69#14519735C2×C414yes—
70#14519733—28no—
71C2×C4⋊Dic61C2312yes—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—21no—
77C2×#11758198—22no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—28no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C42×D61C2×C414yes—
87C42×D61D414yes—
88C4⋊#92418—22no—
89#14519702—24no—
90#14519700—24no—
91#14519698—24no—
92#14519689—24no—
93#14519687—24no—
94#14519684—21no—
95#14519684—21no—
96#14519684—22no—
97#14519684—22no—
98C22×D4×C61C2311yescharacteristic
99C23×C4×C61—21no—
100C22×C8×C61C2312yes—
101C4×D4×C61—22no—
102C4×D4×C61C2×C414yes—
103C2×C4⋊C4×C61C2312yes—
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61—21no—
106C2×C42×C61C2311yescharacteristic
107C4⋊C8×C61—22no—
108#102×C61—24no—
109#95×C61—21no—
110#95×C61—21no—
111C24×C61—21no—
112C23×D61C2×D411yescharacteristic
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—21no—
116C2×D4×C61C22×C412yes—
117C2×D4×C61#4112yes—
118C2×D4×C61#4112yes—
119C22×C4×C61—21no—
120C22×C4×C61—24no—
121C22×C4×C61—22no—
122C22×C4×C61—44no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C2×C22⋊D61—24no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—24no—
129C22×Dic61—24no—
130C22×Dic61—24no—
131C22×Dic61—21no—
132C22×Dic61—24no—
133C22×Dic61—21no—
134C22×Dic61—24no—
135C22×Dic61—22no—
136C22×Dic61—44no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140#11758224—28no—
141#11758224—28no—
142#11758224—28no—
143#11758224—28no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61C22⋊C414yes—
151C2×C4×D61C22⋊C414yes—
152C2×C4×D61C22×C412yes—
153C2×C4×D61C2×D412yes—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C22×C412yes—
158C2×Dic122#4112yes—
159C2×Dic122#4112yes—
160C2×C8×C61—22no—
161C2×C8×C61—22no—
162C2×C8×C61—22no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—24no—
168C42×C61C22×C412yes—
169C42×C61C2×D412yes—
170C22⋊Dic61—24no—
171#11758198—24no—
172#11758198—44no—
173C4⋊Dic61—21no—
174C4⋊Dic61—22no—
175C4⋊Dic61—22no—
176C4⋊Dic61C22×C412yes—
177#11758196—24no—
178#11758196—24no—
179C4×Dic61—24no—
180C4×Dic61—24no—
181C4×Dic61—24no—
182C4×Dic61—44no—
183C4×Dic61C22⋊C414yes—
184C4×Dic61C22⋊C414yes—
185C4×Dic61C22×C412yes—
186C4×Dic61C2×D412yes—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—22no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61—22no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61C22×D411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61C2×C22⋊C412yes—
201D4×C61—22no—
202D4×C61—22no—
203D4×C61—22no—
204D4×C61#11714yes—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—48no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61C2×C22⋊C412yes—
214C2×C4×C61C2×C22⋊C412yes—
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—216no—
222C2×Dic61—216no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—48no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61C2×C22⋊C412yes—
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C2×C22⋊C412yes—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—44no—
244C4×D61—44no—
245Dic122—22no—
246Dic122—22no—
247Dic122—22no—
248Dic122#11714yes—
249C8×C61—42no—
250#92418—42no—
251#20742—611nomaximal, Sylow
252C22×C61—24no—
253C22×C61—44no—
254C22×C61—44no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61C22×C22⋊C411yescharacteristic
258C22×C61#52511yescharacteristic
259C22×C61#52511yescharacteristic
260C22×C61#57512yes—
261C22×C61#57512yes—
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—42no—
266C2×D61—42no—
267C4×C61—22no—
268C4×C61—22no—
269C4×C61—42no—
270C4×C61—82no—
271C4×C61C2×#11711yescharacteristic
272C4×C61C2×#11711yescharacteristic
273C4×C61#52511yescharacteristic
274C4×C61#52511yescharacteristic
275Dic61—22no—
276Dic61—22no—
277Dic61—24no—
278Dic61—22no—
279Dic61—42no—
280Dic61—82no—
281C2×C4×#41—611no—
282C2×#432—611no—
283#2283—611no—
284#1825—612no—
285#1805—611no—
286#1805—611no—
287#1804—611no—
288#1804D6111yescharacteristic, complemented
289#1788—612no—
290#1763—612no—
291#1762—612no—
292C2×C61—44no—
293C2×C61#228011yescharacteristic
294C2×C61#289611yescharacteristic
295C2×C61#289611yescharacteristic
296C2×C61#311112yes—
297C2×C61#311112yes—
298D61—42no—
299C22×#41—611no—
300C4×#41—618no—
301C4×#41—1224no—
302C2×C4×Q8—611no—
303C2×C4×Q8—611no—
304C2×C4×D4—611no—
305C2×C4×D4—1221no—
306C2×C4×D4—1221no—
307C2×C4×D4C2×D6111yescharacteristic
308C2×#117—611no—
309C2×#117—1221no—
310C22×C42—611no—
311C22×C42—1221no—
312#432—1224no—
313C2×C4⋊C8—611no—
314C2×C4⋊C8C2×D6111yescharacteristic
315C2×#103—612no—
316C2×#103—612no—
317C2×#102—612no—
318C2×#102C2×D6112yes—
319C2×C22⋊C8—612no—
320C2×#97—612no—
321#383—1221no—
322#382—611no—
323#382C2×D6111yescharacteristic
324#381—1221no—
325#380—612no—
326C4×C4⋊C4—612no—
327C4×C22⋊C4—1221no—
328#376—1221no—
329#340—612no—
330#340—612no—
331#340—612no—
332#340C2×D6112yes—
333C61#2074211yescharacteristic, complemented, Sylow
334C2×#41—614no—
335C2×#41—1222no—
336C2×#41—1222no—
337C2×#41—1222no—
338C2×#41—1222no—
339C2×#41—1222no—
340C22×Q8—611no—
341C22×D4—1221no—
342C22×D4C22×D6111yescharacteristic
343C23×C4—21no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—1221no—
348C23×C4—1221no—
349C22×C8—612no—
350C22×C8C22×D6112yes—
351C4×Q8—614no—
352C4×Q8—614no—
353C4×Q8—1222no—
354C4×Q8—1222no—
355C4×D4—22no—
356C4×D4—614no—
357C4×D4—1222no—
358C4×D4—1228no—
359C4×D4—1228no—
360C4×D4C4×D6114yes—
361#117—614no—
362#117—1228no—
363#117—1222no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—612no—
366C2×C4⋊C4—1221no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4C22×D6112yes—
369C2×C4⋊C4C22×D6111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—1221no—
372C2×C22⋊C4—1221no—
373C2×C22⋊C4—1222no—
374C2×C42—611no—
375C2×C42—611no—
376C2×C42—611no—
377C2×C42—614no—
378C2×C42—614no—
379C2×C42—1228no—
380C2×C42—1221no—
381C2×C42—1221no—
382C2×C42—1221no—
383C2×C42—1222no—
384C2×C42C22×D6111yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—1222no—
387#103—1224no—
388#103—1224no—
389#102—24no—
390#102—1224no—
391C22⋊C8—1224no—
392#97—1224no—
393#95—21no—
394#95—21no—
395#95—1222no—
396#95—1222no—
397#95—1221no—
398#95—1221no—
399C24—21no—
400C24—611no—
401#41—1228no—
402#41—1228no—
403#41—1228no—
404#41—1228no—
405C2×Q8—612no—
406C2×Q8—612no—
407C2×Q8—612no—
408C2×Q8—1221no—
409C2×Q8—1221no—
410C2×Q8—1221no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—1224no—
415C2×D4—1224no—
416C2×D4—1224no—
417C2×D4C2×C4×D6112yes—
418C2×D4#1175822412yes—
419C2×D4#1175822612yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—614no—
430C22×C4—614no—
431C22×C4—1224no—
432C22×C4—1224no—
433C22×C4—1224no—
434C22×C4—1224no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1222no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4—2444no—
445C22×C4D4×D6111yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4C23×D6111yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—1222no—
452C2×C8—1222no—
453C2×C8—1222no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—612no—
458C4⋊C4—1224no—
459C4⋊C4—1221no—
460C4⋊C4—1224no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4C2×C4×D6112yes—
464C22⋊C4—24no—
465C22⋊C4—1224no—
466C22⋊C4—1224no—
467C22⋊C4—2444no—
468C42—612no—
469C42—612no—
470C42—614no—
471C42—614no—
472C42—1224no—
473C42—1224no—
474C42—1224no—
475C42—2444no—
476C42C2×C4×D6112yes—
477C42D4×D6112yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—612no—
484C23—1221no—
485C23—1221no—
486C23—1222no—
487C23—1222no—
488C23C2×D4×D6111yescharacteristic
489Q8—614no—
490Q8—1222no—
491Q8—1222no—
492Q8—1222no—
493D4—22no—
494D4—22no—
495D4—22no—
496D4—12216no—
497D4#1451973514yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—612no—
507C2×C4—612no—
508C2×C4—612no—
509C2×C4—12216no—
510C2×C4—1222no—
511C2×C4—1221no—
512C2×C4—1222no—
513C2×C4—1221no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1222no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—2444no—
523C2×C4—2444no—
524C2×C4—2448no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4C22⋊C4×D6112yes—
530C2×C4C22⋊C4×D6112yes—
531C2×C4C22×C4×D6111yescharacteristic
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4#41×D6111yescharacteristic
534C2×C4#41×D6111yescharacteristic
535C2×C4C2×#1175822411yescharacteristic
536C2×C4C2×#1175822611yescharacteristic
537C8—42no—
538C8—2442no—
539C22—24no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—1222no—
545C22—1222no—
546C22—1222no—
547C22—2442no—
548C22—2442no—
549C22C2×C22⋊C4×D6111yescharacteristic
550C22#1684027211yescharacteristic
551C22#1684027511yescharacteristic
552C22#1684055812yes—
553C22#1684055912yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—1222no—
559C4—1224no—
560C4—1222no—
561C4—1222no—
562C4—4882no—
563C4—2442no—
564C4#117×D6111yescharacteristic
565C4C2×#1451973511yescharacteristic
566C4#1684027211yescharacteristic
567C4#1684027511yescharacteristic
568C2—44no—
569C2—2442no—
570C2#2144820111yescharacteristic
571C2#2145433311yescharacteristic
572C2#2145433411yescharacteristic
573C2#2145592512yes—
574C2#2145593312yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenter#1804D61
hypocenterC61#20742
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#16839818C2semidirect
3. #21448212C2semidirect
4. #21445912C2semidirect
5. #21445835C2semidirect
6. #21445831C2semidirect
7. #21445829C2semidirect
9. #21445648C2semidirect
10. #21445646C2semidirect
11. C61×#1804C2semidirect
14. C4×#11758224C4semidirect
288. #1804D61semidirect
333. 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×#168398182
#214482122
#214459122
#214458352
#214458312
#214458292
#214457562
#214456482
#214456462
C61×#18042
#2074261