Finite Group Databasebeta

← #29645950

Subgroups — #29645950

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic
2#21454903C212yesmaximal, complemented
3#21444160C211yesmaximal, characteristic, complemented
4#21444158C212yesmaximal, complemented
5#21444151C212yesmaximal, complemented
6#21444150C212yesmaximal, complemented
7#21444138C212yesmaximal, complemented
8#21444130C212yesmaximal, complemented
9C61×#1466C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic
11#16840241—24no—
12#16840241—24no—
13C2×C4×Dic122C2211yescharacteristic
14C2×#14519742C411yescharacteristic
15C2×D4×Dic61C411yescharacteristic
16C2×C4×C22⋊D61C411yescharacteristic
17C2×C4×C22⋊D61C411yescharacteristic
18C2×#14519737C2211yescharacteristic
19C2×#14519737C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×#14519733C2211yescharacteristic
22C2×#14519733C2211yescharacteristic
23C22×#11758196C411yescharacteristic
24C22×#11758196C411yescharacteristic
25C2×C4⋊C4×D61C411yescharacteristic
26#16839891—24no—
27#16839890—24no—
28#16839819C2212yes—
29#16839816C2214yes—
30#16839812C2214yes—
31#16839487C2214yes—
32#16839486C2212yes—
33#16839486C2212yes—
34#16839485C2214yes—
35C2×C4×D4×C61C2211yescharacteristic
36C61×#432C2212yes—
37C61×#323C2212yes—
38C61×#323C2212yes—
39C2×#11758224—24no—
40C2×#11758224—24no—
41C2×#11758224—24no—
42C22×Dic122C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C22×C22⋊D61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C4×Dic122D414yes—
53C4×Dic122D414yes—
54#14519742—24no—
55D4×Dic61—24no—
56C4×C22⋊D61—22no—
57C4×C22⋊D61—22no—
58C4×C22⋊D61—22no—
59C4×C22⋊D61—22no—
60#14519737—24no—
61#14519737—24no—
62#14519734—22no—
63#14519734—22no—
64#14519733—24no—
65#14519733—24no—
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2311yescharacteristic
79C4⋊C4×D61—24no—
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2311yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C4⋊#92418—22no—
90#14519706—24no—
91#14519706—24no—
92C22⋊#92418C2314yes—
93#14519688—22no—
94#14519687—24no—
95C8×Dic61—24no—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2×C411yescharacteristic
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61C2311yescharacteristic
104C2×C42×C61C2311yescharacteristic
105C4⋊C8×C61—22no—
106C22⋊C8×C61C2314yes—
107#97×C61—22no—
108C24×C61C22×C411yescharacteristic
109C24×C61C22×C411yescharacteristic
110C23×D61C22×C411yescharacteristic
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—81no—
119C22×C4×C61—81no—
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C2411yescharacteristic
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61M1614yes—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—81no—
139C22×Dic61—81no—
140C22×Dic61M1614yes—
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148#11758224—232no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—81no—
155C2×C4×D61—81no—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122C22⋊C414yes—
159C2×C8×C61—24no—
160C4⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C42×C61C2×D412yes—
164C42×C61C2×D412yes—
165C22⋊Dic61—22no—
166C22⋊Dic61—22no—
167#11758198—21no—
168#11758198—21no—
169#11758198—22no—
170C4⋊Dic61C22⋊C414yes—
171#11758196—21no—
172#11758196—21no—
173#11758196—22no—
174#11758196—22no—
175#11758196—22no—
176#11758196—22no—
177#11758196—22no—
178#11758196C22⋊C412yes—
179#11758196C22⋊C412yes—
180#11758196C22⋊C412yes—
181#11758196C22⋊C412yes—
182C4×Dic61—22no—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61C2×D414yes—
186C4×Dic61C2×D414yes—
187C2×#92418—24no—
188C23×C61—21no—
189C23×C61—21no—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61C2×M1612yes—
197C23×C61C2×M1612yes—
198C23×C61C23×C411yescharacteristic
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61C2×M1612yes—
204D4×C61—28no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—81no—
214C2×C4×C61—81no—
215C2×C4×C61—81no—
216C2×C4×C61—81no—
217C2×C4×C61C2×C22⋊C412yes—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C22×D412yes—
221C22⋊D61—28no—
222C22⋊D61—28no—
223C2×Dic61—28no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—28no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—82no—
236C2×Dic61—82no—
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C2×C22⋊C412yes—
239C2×Dic61C2×C22⋊C412yes—
240C2×Dic61C2×C22⋊C412yes—
241C2×Dic61C2×M1612yes—
242C2×Dic61C2×M1612yes—
243C2×Dic61C2×M1612yes—
244C4×D61—28no—
245C4×D61—82no—
246C4×D61—82no—
247Dic122—28no—
248C8×C61—44no—
249#92418—44no—
250#17372—611nomaximal, Sylow
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61C22×C22⋊C411yescharacteristic
264C22×C61C22×M1611yescharacteristic
265C22×C61C22×M1611yescharacteristic
266C2×D61—22no—
267C2×D61—42no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—42no—
271C4×C61—22no—
272C4×C61—22no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277Dic61—22no—
278Dic61—22no—
279Dic61—22no—
280Dic61—22no—
281Dic61—41no—
282Dic61—41no—
283Dic61#40714yes—
284C2×#520—611no—
285#2983—612no—
286#1466—612no—
287#1466—611no—
288#1466D6111yescharacteristic, complemented
289#1464—612no—
290#1464—612no—
291#1460—612no—
292#1458—612no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—42no—
296C2×C61—42no—
297C2×C61C2×#40711yescharacteristic
298C2×C61#288411yescharacteristic
299C2×C61#288811yescharacteristic
300D61—42no—
301C22×#41—611no—
302#520—1224no—
303#520—1224no—
304C2×C4×Q8—611no—
305C2×C4×Q8—611no—
306C2×C4×D4—611no—
307C2×C4×D4—611no—
308C2×C4×D4—611no—
309C2×C4×D4—611no—
310C2×C4×D4—611no—
311C2×C4×D4C2×D6111yescharacteristic
312C2×#117—611no—
313C2×#117—611no—
314C2×#117—611no—
315C22×C4⋊C4—611no—
316C22×C4⋊C4—611no—
317C22×C4⋊C4—611no—
318#446—1224no—
319#446—1224no—
320#432—612no—
321#432—614no—
322#432C2×D6112yes—
323#431—614no—
324#324—614no—
325#323—612no—
326#323—612no—
327#323—614no—
328#323C2×D6112yes—
329#323C2×D6112yes—
330C61#1737211yescharacteristic, complemented, Sylow
331C2×#41—1224no—
332C2×#41—1224no—
333C2×#41—1224no—
334C22×Q8—611no—
335C22×D4—611no—
336C22×D4—611no—
337C22×D4C4×D6111yescharacteristic
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4C4×D6111yescharacteristic
346C23×C4C4×D6111yescharacteristic
347C4×Q8—614no—
348C4×Q8—614no—
349C4×Q8—1224no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—1224no—
353C4×D4—1224no—
354C4×D4—1222no—
355C4×D4—1222no—
356C4×D4—1222no—
357C4×D4—1222no—
358C4×D4—1224no—
359#117—1224no—
360#117—1224no—
361#117—1222no—
362#117—1222no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—1224no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1222no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4C4×D6111yescharacteristic
378C2×C22⋊C4—611no—
379C2×C22⋊C4—611no—
380C2×C22⋊C4—611no—
381C2×C22⋊C4—611no—
382C2×C22⋊C4C22×D6111yescharacteristic
383C2×C22⋊C4C22×D6111yescharacteristic
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42C22×D6111yescharacteristic
390C4⋊C8—22no—
391C4⋊C8—1224no—
392C4⋊C8—1224no—
393C4⋊C8—1222no—
394C22⋊C8—614no—
395C22⋊C8C22×D6114yes—
396#97—22no—
397#97—1224no—
398#97—1222no—
399C4×C8—1224no—
400C24—611no—
401C24C2×C4×D6111yescharacteristic
402C24C2×C4×D6111yescharacteristic
403#41—12232no—
404C2×Q8—614no—
405C2×Q8—1222no—
406C2×Q8—1222no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—614no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—614no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—4881no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4—4881no—
446C22×C4C2×C4×D6111yescharacteristic
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×C4×D6111yescharacteristic
449C22×C4C2×C4×D6111yescharacteristic
450C22×C4C23×D6111yescharacteristic
451C2×C8—24no—
452C2×C8—1224no—
453C4⋊C4—22no—
454C4⋊C4—612no—
455C4⋊C4—612no—
456C4⋊C4—612no—
457C4⋊C4—612no—
458C4⋊C4—614no—
459C4⋊C4—1222no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—1222no—
469C22⋊C4—1222no—
470C22⋊C4—1222no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C42—614no—
474C42—614no—
475C42—1222no—
476C42—1222no—
477C42—1222no—
478C42D4×D6112yes—
479C42D4×D6112yes—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—612no—
489C23—1221no—
490C23—1221no—
491C23—2441no—
492C23—2441no—
493C23M16×D6112yes—
494C23M16×D6112yes—
495C23C22×C4×D6111yescharacteristic
496Q8—1228no—
497D4—28no—
498D4—1228no—
499D4—1228no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—612no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—1228no—
520C2×C4—1228no—
521C2×C4—1228no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—4882no—
529C2×C4—4882no—
530C2×C4—4882no—
531C2×C4—4882no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C22⋊C4×D6112yes—
537C2×C4C22⋊C4×D6111yescharacteristic
538C2×C4C22⋊C4×D6111yescharacteristic
539C2×C4C2×D4×D6112yes—
540C8—44no—
541C8—2444no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—1222no—
555C22—2442no—
556C22—2442no—
557C22—2441no—
558C22—2441no—
559C22C2×C22⋊C4×D6111yescharacteristic
560C22C2×M16×D6111yescharacteristic
561C22C2×M16×D6111yescharacteristic
562C4—22no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—614no—
569C4—1222no—
570C4—1222no—
571C4—1222no—
572C4—1222no—
573C4—2441no—
574C4—2441no—
575C2—21no—
576C2—21no—
577C2—42no—
578C2—42no—
579C2—2442no—
580C2#407×D6111yescharacteristic
581C2#2145428111yescharacteristic
582C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1466C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C4
cosocleC22×C4×C61C24
hypercenter#1466D61
hypocenterC61#17372
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #21454903C2semidirect
3. #21444160C2semidirect
4. #21444158C2semidirect
5. #21444151C2semidirect
6. #21444150C2semidirect
7. #21444138C2semidirect
8. #21444130C2semidirect
9. C61×#1466C2semidirect
288. #1466D61semidirect
330. C61#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
#214549032
#214441602
#214441582
#214441512
#214441502
#214441382
#214441302
C61×#14662
#1737261