Finite Group Databasebeta

← #30616813

Subgroups — #30616813

Order 15616.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461895C211yesmaximal, characteristic
2#21461894C211yesmaximal, characteristic
3#21461891C211yesmaximal, characteristic
4#21461890C211yesmaximal, characteristic
5#21461879C211yesmaximal, characteristic, complemented
6#21461877C211yesmaximal, characteristic, complemented
7#21461875C211yesmaximal, characteristic, complemented
8#21461873C211yesmaximal, characteristic, complemented
9#21461605C211yesmaximal, characteristic, complemented
10C4×#14519844C211yesmaximal, characteristic, complemented
11#21461548C211yesmaximal, characteristic
12#21461548C211yesmaximal, characteristic
13#21461538C211yesmaximal, characteristic, complemented
14#21461476C211yesmaximal, characteristic, complemented
15#21448311C211yesmaximal, characteristic
16C2×#14519844C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×C4⋊#92420C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×#14519834C2211yescharacteristic
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519832C2211yescharacteristic
25C2×#14519832C2211yescharacteristic
26C2×#14519832C2211yescharacteristic
27C2×#14519832C2211yescharacteristic
28C2×C4×#92420C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30C2×C4×#92420C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519735C2211yescharacteristic
45#16839654C411yescharacteristic
46#16839653C411yescharacteristic
47#16839652C411yescharacteristic
48#16839651C411yescharacteristic
49#16839648C411yescharacteristic
50#16839647C411yescharacteristic
51#16839645C411yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839613C2211yescharacteristic
54#16839609C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839607C2211yescharacteristic
57C42×Dic61C2211yescharacteristic
58C61×#387C411yescharacteristic
59C22×#92420C2311yescharacteristic
60C22×#92420C2311yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67#14519844—22no—
68#14519844—22no—
69C4⋊#92420—22no—
70C4⋊#92420—22no—
71#14519834—22no—
72#14519834—22no—
73#14519834—22no—
74#14519834—22no—
75#14519832—22no—
76#14519832—22no—
77#14519832—22no—
78#14519832—22no—
79C4×#92420—22no—
80C4×#92420—22no—
81C4×#92420—22no—
82C4×#92420—22no—
83C22×C4×D61C2311yescharacteristic
84#14519735—22no—
85#14519735—22no—
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C42×C61C2×C411yescharacteristic
116#95×C61C2×C411yescharacteristic
117#95×C61C2×C411yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120C23×D61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C2411yescharacteristic
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×#92420—21no—
142C2×#92420—21no—
143C2×#92420—21no—
144C2×#92420—21no—
145C2×#92420—21no—
146C2×#92420—21no—
147C2×#92420—21no—
148C2×#92420—21no—
149C2×#92420—21no—
150C2×#92420—21no—
151C2×#92420—21no—
152C2×#92420—21no—
153C2×#92420—21no—
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420#4112yes—
162C2×#92420#4112yes—
163C2×#92420#4112yes—
164C2×#92420#4112yes—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—41no—
167C42×C61—41no—
168#11758198—22no—
169#11758198—22no—
170#11758198—22no—
171#11758198—22no—
172#11758198—41no—
173#11758198—41no—
174C4⋊Dic61—22no—
175C4⋊Dic61—22no—
176#11758196—22no—
177#11758196—41no—
178C4×Dic61—22no—
179C4×Dic61—22no—
180C4×Dic61—21no—
181C4×Dic61—21no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—41no—
191C4×Dic61#4112yes—
192C4×Dic61#4112yes—
193C23×C61C23×C411yescharacteristic
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61#11712yes—
221C2×C4×C61#13112yes—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61#11712yes—
239C2×Dic61#13112yes—
240C2×Dic61C2×#4111yescharacteristic
241C2×Dic61C2×#4111yescharacteristic
242C2×Dic61C2×#4111yescharacteristic
243C2×Dic61C2×#4111yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245C2×Dic61C2×#4111yescharacteristic
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250#92420—22no—
251#92420—22no—
252#92420—22no—
253#92420—22no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258#21436—611nomaximal, Sylow
259C22×C61C2×#11711yescharacteristic
260C22×C61C4×#4111yescharacteristic
261C22×C61C4×#4111yescharacteristic
262C22×C61C2×#13111yescharacteristic
263C22×C61C2×#13111yescharacteristic
264C22×C61#56811yescharacteristic
265C22×C61#56811yescharacteristic
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280Dic61—22no—
281Dic61—22no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61#52911yescharacteristic
287Dic61#52911yescharacteristic
288Dic61#52911yescharacteristic
289Dic61#52911yescharacteristic
290#2298—611no—
291#1924—611no—
292#1924—611no—
293#1923—611no—
294#1923—611no—
295#1917—611no—
296#1917—611no—
297#1916—611no—
298#1916—611no—
299#1767—611no—
300C4×C4⋊C8—611no—
301#1750—611no—
302#1750—611no—
303#1746—611no—
304#1726—611no—
305C2×C61#229811yescharacteristic
306C2×C61#292511yescharacteristic
307C2×C61#292511yescharacteristic
308C2×C61#296611yescharacteristic
309C2×C61#296711yescharacteristic
310C2×C61#296811yescharacteristic
311C2×C61#296911yescharacteristic
312D61—81no—
313C2×#117—611no—
314C2×C4⋊C8—611no—
315C2×C4⋊C8—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C22⋊C8—611no—
319C2×C22⋊C8—611no—
320C2×C22⋊C8—611no—
321C2×C22⋊C8—611no—
322C2×#97—611no—
323C2×#97—611no—
324C2×#97—611no—
325C2×#97—611no—
326C2×C4×C8—611no—
327C2×C4×C8—611no—
328C2×C4×C8—611no—
329C2×C4×C8—611no—
330#388—611no—
331#388—611no—
332#388—611no—
333#388—611no—
334#387—611no—
335#387—611no—
336#387—611no—
337#387#692311yescharacteristic
338C4×C4⋊C4—611no—
339C4×C4⋊C4—611no—
340C4×C22⋊C4—611no—
341C4×C22⋊C4—611no—
342#376—611no—
343C43—611no—
344#336—611no—
345#336—611no—
346#336—611no—
347#336—611no—
348#336—611no—
349#336—611no—
350#336—611no—
351#336—611no—
352#336—611no—
353#336—611no—
354#336—611no—
355#336—611no—
356C61#2143611yescharacteristic, complemented, Sylow
357C23×C4—611no—
358C22×C8—611no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366#117—1222no—
367#117—1222no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4C2×#692311yescharacteristic
373C2×C4⋊C4C2×#692311yescharacteristic
374C2×C22⋊C4—611no—
375C2×C22⋊C4—611no—
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C22⋊C4—611no—
379C2×C22⋊C4—611no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42C2×#692311yescharacteristic
390C4⋊C8—1222no—
391C4⋊C8—1222no—
392C4⋊C8—1222no—
393C4⋊C8—1222no—
394C22⋊C8—1222no—
395C22⋊C8—1222no—
396C22⋊C8—1222no—
397C22⋊C8—1222no—
398#97—1222no—
399#97—1222no—
400#97—1222no—
401#97—1222no—
402C4×C8—1222no—
403C4×C8—1222no—
404C4×C8—1222no—
405C4×C8—1222no—
406#95—611no—
407#95—611no—
408#95—611no—
409#95—611no—
410#95—611no—
411#95—611no—
412#95—611no—
413#95—611no—
414#95C2×#692311yescharacteristic
415#95C2×#692311yescharacteristic
416#95C2×#692311yescharacteristic
417#95C2×#692311yescharacteristic
418C24—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4C22×#692311yescharacteristic
433C22×C4C22×#692311yescharacteristic
434C22×C4C22×#692311yescharacteristic
435C22×C4C22×#692311yescharacteristic
436C22×C4C22×#692311yescharacteristic
437C22×C4C22×#692311yescharacteristic
438C22×C4C22×#692311yescharacteristic
439C2×C8—612no—
440C2×C8—612no—
441C2×C8—612no—
442C2×C8—612no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—2441no—
469C22⋊C4—1222no—
470C22⋊C4—1222no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—2441no—
474C22⋊C4—2441no—
475C42—41no—
476C42—612no—
477C42—612no—
478C42—1221no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1222no—
487C42—1221no—
488C42—1221no—
489C42—1222no—
490C42—2441no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1221no—
496C23—1221no—
497C23—1221no—
498C23C23×#692311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4#1451985612yes—
547C2×C4#1451986512yes—
548C8—1222no—
549C8—1222no—
550C8—1222no—
551C8—1222no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22C2×#1451985611yescharacteristic
564C22#41×#692311yescharacteristic
565C22#41×#692311yescharacteristic
566C22D61⋊#13111yescharacteristic
567C22C2×#1451986511yescharacteristic
568C22#1684084011yescharacteristic
569C22#1684084111yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—611no—
578C4—611no—
579C4—611no—
580C4—611no—
581C4—1222no—
582C4—1222no—
583C4—2441no—
584C4—2441no—
585C4—2441no—
586C4—2441no—
587C2—4881no—
588C2#2146228111yescharacteristic
589C2#2146251711yescharacteristic
590C2#2146251911yescharacteristic
591C2#2146263611yescharacteristic
592C2#2146264111yescharacteristic
593C2#2146264711yescharacteristic
594C2#2146265411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#387#6923
hypocenterC61#21436
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
5. #21461879C2semidirect
6. #21461877C2semidirect
7. #21461875C2semidirect
8. #21461873C2semidirect
9. #21461605C2semidirect
10. C4×#14519844C2semidirect
13. #21461538C2semidirect
14. #21461476C2semidirect
356. C61#21436semidirect

Maximal subgroups

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

subgroupindex
#214618952
#214618942
#214618912
#214618902
#214618792
#214618772
#214618752
#214618732
#214616052
C4×#145198442
#214615482
#214615382
#214614762
#214483112
#2143661