Finite Group Databasebeta

← #29646071

Subgroups — #29646071

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840371C211yesmaximal, characteristic
2#21454903C211yesmaximal, characteristic, complemented
3#21454899C211yesmaximal, characteristic, complemented
4#21444189C211yesmaximal, characteristic
5#21444187C212yesmaximal
6#21444186C211yesmaximal, characteristic
7#21444175C211yesmaximal, characteristic, complemented
8#21444173C212yesmaximal, complemented
9#21444141C212yesmaximal, complemented
10#21444132C212yesmaximal
11C61×#1470C211yesmaximal, characteristic, complemented
12#16840371—22no—
13#16840371—22no—
14#16840371—22no—
15#16840371—22no—
16C2×#14519776C411yescharacteristic
17C2×#14519772C411yescharacteristic
18C2×#14519772C411yescharacteristic
19C2×#14519772C2211yescharacteristic
20C2×#14519771C2211yescharacteristic
21C2×#14519768C411yescharacteristic
22C2×#14519767C411yescharacteristic
23C2×#14519767C411yescharacteristic
24C2×#14519767C2211yescharacteristic
25C2×#14519755C411yescharacteristic
26C2×#14519755C411yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×#14519742C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839891—22no—
31#16839890—22no—
32C8×Dic122—22no—
33#16839886—22no—
34#16839819C2211yescharacteristic
35#16839816C2212yes—
36#16839815C2211yescharacteristic
37#16839812C2212yes—
38#16839812C2212yes—
39#16839812C2212yes—
40#16839488C2212yes—
41#16839488C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×#125×C61C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#431C2211yescharacteristic
49C61×#324C2212yes—
50C61×#324C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54#14519776—22no—
55#14519776—22no—
56#14519772—22no—
57#14519772—22no—
58#14519772—22no—
59#14519772—22no—
60#14519772—22no—
61#14519772—22no—
62#14519771—21no—
63#14519771—21no—
64#14519771—21no—
65#14519771—21no—
66#14519768—22no—
67#14519768—22no—
68#14519767—22no—
69#14519767—22no—
70#14519767—22no—
71#14519767—22no—
72#14519767—22no—
73#14519767—22no—
74#14519755—22no—
75#14519755—22no—
76#14519755—22no—
77#14519755—22no—
78C4×Dic122D412yes—
79C4×Dic122D412yes—
80C4×Dic122D412yes—
81C4×Dic122D412yes—
82#14519742—22no—
83#14519742—22no—
84#14519735—22no—
85#14519735—22no—
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2311yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2311yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113#14519706—22no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519688—21no—
120#14519687—22no—
121C4×#92418—21no—
122C8×Dic61—22no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125#125×C61—21no—
126#125×C61—21no—
127#125×C61—21no—
128#125×C61—21no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2312yes—
140#97×C61—21no—
141C4×C8×C61—21no—
142C23×D61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C2×C4×D61—22no—
158C2×C4×D61—24no—
159C2×Dic122—24no—
160C2×Dic122—22no—
161C2×Dic122—24no—
162C2×Dic122C22⋊C412yes—
163C2×Dic122C22⋊C412yes—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61C2×D411yescharacteristic
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61C22⋊C412yes—
195C4⋊Dic61C22⋊C412yes—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196C22⋊C412yes—
208#11758196C22⋊C412yes—
209#11758196C22⋊C412yes—
210#11758196C22⋊C412yes—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61C2×D412yes—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C2×#92418—22no—
219C2×#92418—22no—
220C23×C61C23×C411yescharacteristic
221C22×D61—21no—
222C22×D61—22no—
223C22×D61—41no—
224C22×D61—41no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61C2×C22⋊C412yes—
253C2×Dic61C2×C22⋊C412yes—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61#13114yes—
256C4×D61—44no—
257Dic122—24no—
258Dic122—24no—
259Dic122—44no—
260C8×C61—42no—
261C8×C61—42no—
262#92418—42no—
263#92418—42no—
264#17391—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61C22×C22⋊C411yescharacteristic
268C22×C61C2×#13112yes—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—82no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283Dic61—22no—
284Dic61—22no—
285Dic61—22no—
286Dic61—41no—
287Dic61—41no—
288Dic61—41no—
289Dic61#40814yes—
290C2×#541—611no—
291#2983—611no—
292#2982—611no—
293#1473—611no—
294#1473—611no—
295#1473—612no—
296#1470—612no—
297#1470—611no—
298#1470D6111yescharacteristic, complemented
299#1461—612no—
300#1458—612no—
301C2×C61—22no—
302C2×C61C2×#40811yescharacteristic
303C2×C61#288411yescharacteristic
304C2×C61#288911yescharacteristic
305D61—81no—
306#541—1222no—
307#541—1222no—
308#541—1222no—
309#541—1222no—
310C2×C4⋊Q8—611no—
311C2×#126—611no—
312C2×#126—611no—
313C2×#126—611no—
314C2×#126—611no—
315C2×#125—611no—
316C2×#125—611no—
317C2×#125—611no—
318C2×#125—611no—
319C2×#125C2×D6111yescharacteristic
320C2×C22⋊Q8—611no—
321C2×C22⋊Q8—611no—
322C2×C4×Q8—611no—
323C2×C4×Q8—611no—
324C2×#117—611no—
325#446—1222no—
326#446—1222no—
327C8×Q8—1222no—
328C8×Q8—1222no—
329#432—611no—
330#432—612no—
331#432C2×D6111yescharacteristic
332#431—611no—
333#431—612no—
334#431—612no—
335#431—612no—
336#431C2×D6111yescharacteristic
337#324—612no—
338#324—612no—
339#324—612no—
340#324—612no—
341#324C2×D6112yes—
342#324C2×D6112yes—
343#323—612no—
344#323—612no—
345C61#1739111yescharacteristic, complemented, Sylow
346C22×Q8—611no—
347C22×Q8—611no—
348C23×C4—611no—
349C4⋊Q8—1222no—
350C4⋊Q8—1222no—
351#126—1222no—
352#126—1222no—
353#126—1222no—
354#126—1222no—
355#126—1222no—
356#126—1222no—
357#126—1221no—
358#126—1221no—
359#126—1221no—
360#126—1221no—
361#125—21no—
362#125—21no—
363#125—21no—
364#125—21no—
365#125—1222no—
366#125—1222no—
367#125—1222no—
368#125—1222no—
369#125—1222no—
370#125—1222no—
371#125—1222no—
372#125—1222no—
373C22⋊Q8—1222no—
374C22⋊Q8—1222no—
375C22⋊Q8—1222no—
376C22⋊Q8—1222no—
377C4×Q8—612no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—612no—
381C4×Q8—1222no—
382C4×Q8—1222no—
383#117—1222no—
384#117—1222no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4C4×D6111yescharacteristic
400C2×C4⋊C4C4×D6111yescharacteristic
401C2×C4⋊C4C4×D6111yescharacteristic
402C2×C4⋊C4C4×D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C22⋊C4—611no—
406C2×C22⋊C4—611no—
407C2×C22⋊C4—611no—
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42C22×D6111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—1222no—
420C4⋊C8—1222no—
421C4⋊C8—1222no—
422C4⋊C8—1222no—
423C4⋊C8—1221no—
424C4⋊C8—1221no—
425C22⋊C8—612no—
426C22⋊C8—612no—
427C22⋊C8C22×D6112yes—
428C22⋊C8C22×D6112yes—
429#97—21no—
430#97—1222no—
431#97—1221no—
432C4×C8—21no—
433C4×C8—1222no—
434C4×C8—1222no—
435C4×C8—1222no—
436C4×C8—1221no—
437C24—611no—
438C2×Q8—612no—
439C2×Q8—612no—
440C2×Q8—1224no—
441C2×Q8—1222no—
442C2×Q8—1224no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1222no—
451C22×C4—1224no—
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4C2×C4×D6111yescharacteristic
454C22×C4C2×C4×D6111yescharacteristic
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C23×D6111yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—1222no—
462C2×C8—1222no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—612no—
476C4⋊C4—612no—
477C4⋊C4—612no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C42—612no—
505C42—612no—
506C42—612no—
507C42—612no—
508C42—1222no—
509C42—1222no—
510C42—1222no—
511C42D4×D6111yescharacteristic
512C42D4×D6111yescharacteristic
513C42D4×D6111yescharacteristic
514C42D4×D6111yescharacteristic
515C23—1222no—
516C23—1221no—
517C23—2441no—
518C23—2441no—
519C23C22×C4×D6111yescharacteristic
520Q8—1224no—
521Q8—1224no—
522Q8—2444no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—612no—
535C2×C4—614no—
536C2×C4—612no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—1222no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1222no—
544C2×C4—2444no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4C22⋊C4×D6111yescharacteristic
550C2×C4C22⋊C4×D6111yescharacteristic
551C2×C4C22⋊C4×D6111yescharacteristic
552C2×C4C22⋊C4×D6111yescharacteristic
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4C2×D4×D6111yescharacteristic
555C8—42no—
556C8—42no—
557C8—2442no—
558C8—2442no—
559C22—21no—
560C22—21no—
561C22—4882no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22C2×C22⋊C4×D6111yescharacteristic
566C22#131×D6112yes—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—614no—
578C4—1222no—
579C4—1222no—
580C4—1222no—
581C4—2441no—
582C4—2441no—
583C4—2441no—
584C2—22no—
585C2—4881no—
586C2#408×D6111yescharacteristic
587C2#2145428111yescharacteristic
588C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1470C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1470D61
hypocenterC61#17391
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
2. #21454903C2semidirect
3. #21454899C2semidirect
7. #21444175C2semidirect
8. #21444173C2semidirect
9. #21444141C2semidirect
11. C61×#1470C2semidirect
298. #1470D61semidirect
345. C61#17391semidirect

Maximal subgroups

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

subgroupindex
C2×#168403712
#214549032
#214548992
#214441892
#214441872
#214441862
#214441752
#214441732
#214441412
#214441322
C61×#14702
#1739161