Finite Group Databasebeta

← #30623800

Subgroups — #30623800

Order 15616.

606 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
1#21461921C211yesmaximal, characteristic, complemented
2#21461921C211yesmaximal, characteristic, complemented
3#21461918C211yesmaximal, characteristic, complemented
4#21461894C211yesmaximal, characteristic
5#21461894C211yesmaximal, characteristic
6#21461891C211yesmaximal, characteristic
7#21461879C211yesmaximal, characteristic, complemented
8#21461878C211yesmaximal, characteristic, complemented
9#21461875C211yesmaximal, characteristic, complemented
10#21461767C211yesmaximal, characteristic
11#21461767C211yesmaximal, characteristic
12#21461767C211yesmaximal, characteristic
13#21461753C211yesmaximal, characteristic, complemented
14#21461748C211yesmaximal, characteristic, complemented
15#21449118C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25C2×C4⋊#92420C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
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
44C61⋊#401C411yescharacteristic
45#16839704C411yescharacteristic
46#16839702C411yescharacteristic
47#16839691C411yescharacteristic
48#16839689C411yescharacteristic
49#16839688C411yescharacteristic
50#16839684C411yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839613C2211yescharacteristic
54#16839609C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839609C2211yescharacteristic
57#16839607C2211yescharacteristic
58C61×#400C411yescharacteristic
59C2×#11758213—41no—
60C2×#11758213—41no—
61C2×#11758213—41no—
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70#14519844—41no—
71#14519844—41no—
72#14519844—41no—
73#14519844—41no—
74#14519844—41no—
75#14519844—41no—
76C4⋊#92420—41no—
77C4⋊#92420—41no—
78C4⋊#92420—41no—
79#14519834—41no—
80#14519834—41no—
81#14519834—41no—
82#14519832—41no—
83#14519832—41no—
84C4×#92420—41no—
85C22×C4×D61C2311yescharacteristic
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×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519684C2×C411yescharacteristic
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
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
115#95×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—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165#11758213—44no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168#11758198—22no—
169#11758198—41no—
170#11758198—41no—
171#11758198—41no—
172#11758198—41no—
173#11758198—41no—
174C4⋊Dic61—22no—
175C4⋊Dic61—41no—
176#11758196—22no—
177#11758196—41no—
178C4×Dic61—21no—
179C4×Dic61—21no—
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—
190C23×C61C23×C411yescharacteristic
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—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×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
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#13112yes—
237C2×Dic61H(5,𝔽2)11yescharacteristic
238C2×Dic61H(5,𝔽2)11yescharacteristic
239C2×Dic61H(5,𝔽2)11yescharacteristic
240C2×Dic612−1+411yescharacteristic
241C2×Dic612−1+411yescharacteristic
242C2×Dic612−1+411yescharacteristic
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255#23382—611nomaximal, Sylow
256C22×C61#52011yescharacteristic
257C22×C61#52011yescharacteristic
258C22×C61#52011yescharacteristic
259C22×C61C2×#13111yescharacteristic
260C22×C61#56811yescharacteristic
261C22×C61#56811yescharacteristic
262C22×C61#56811yescharacteristic
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277Dic61—22no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61#56011yescharacteristic
284Dic61#56311yescharacteristic
285Dic61#56311yescharacteristic
286Dic61#56311yescharacteristic
287#2401—611no—
288#1940—611no—
289#1940—611no—
290#1939—611no—
291#1924—611no—
292#1924—611no—
293#1923—611no—
294#1917—611no—
295#1917—611no—
296#1916—611no—
297#1851—611no—
298#1851—611no—
299#1851—611no—
300#1843—611no—
301#1840—611no—
302C2×C61#238311yescharacteristic
303C2×C61#299211yescharacteristic
304C2×C61#299311yescharacteristic
305C2×C61#299311yescharacteristic
306C2×C61#299511yescharacteristic
307C2×C61#299511yescharacteristic
308C2×C61#299511yescharacteristic
309D61—81no—
310C22×M16—611no—
311C2×C4⋊C8—611no—
312C2×C4⋊C8—611no—
313C2×C4⋊C8—611no—
314C2×C4⋊C8—611no—
315C2×C4⋊C8—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C22⋊C8—611no—
321C2×C22⋊C8—611no—
322C2×C22⋊C8—611no—
323C2×#97—611no—
324C2×#97—611no—
325C2×C4×C8—611no—
326#401—611no—
327#400—611no—
328#400—611no—
329#400#692311yescharacteristic
330#397—611no—
331#397—611no—
332#397—611no—
333#396—611no—
334C4×C4⋊C4—611no—
335C4×C4⋊C4—611no—
336C4×C4⋊C4—611no—
337C4×C22⋊C4—611no—
338C4×C22⋊C4—611no—
339C4×C22⋊C4—611no—
340#376—611no—
341#336—611no—
342#336—611no—
343#336—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—
353C61#2338211yescharacteristic, complemented, Sylow
354C23×C4—611no—
355C2×M16—2441no—
356C2×M16—2441no—
357C2×M16—2441no—
358C22×C8—611no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4C2×#692311yescharacteristic
371C2×C4⋊C4C2×#692311yescharacteristic
372C2×C22⋊C4—611no—
373C2×C22⋊C4—611no—
374C2×C22⋊C4—611no—
375C2×C22⋊C4—611no—
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C4⋊C8—2441no—
385C4⋊C8—2441no—
386C4⋊C8—2441no—
387C4⋊C8—2441no—
388C4⋊C8—2441no—
389C4⋊C8—2441no—
390C4⋊C8—2441no—
391C4⋊C8—2441no—
392C4⋊C8—2441no—
393C22⋊C8—2441no—
394C22⋊C8—2441no—
395C22⋊C8—2441no—
396#97—2441no—
397#97—2441no—
398C4×C8—2441no—
399#95—611no—
400#95—611no—
401#95—611no—
402#95—611no—
403#95—611no—
404#95—611no—
405#95—611no—
406#95—611no—
407#95—611no—
408#95—611no—
409#95—611no—
410#95C2×#692311yescharacteristic
411#95C2×#692311yescharacteristic
412#95C2×#692311yescharacteristic
413#95C2×#692311yescharacteristic
414#95C2×#692311yescharacteristic
415C24—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4C22×#692311yescharacteristic
430C22×C4C22×#692311yescharacteristic
431C22×C4C22×#692311yescharacteristic
432C22×C4C22×#692311yescharacteristic
433C22×C4C22×#692311yescharacteristic
434C22×C4C22×#692311yescharacteristic
435C22×C4C22×#692311yescharacteristic
436M16—2444no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
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—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—1222no—
464C4⋊C4—1222no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C22⋊C4—1222no—
468C22⋊C4—2441no—
469C22⋊C4—2441no—
470C22⋊C4—2441no—
471C22⋊C4—2441no—
472C22⋊C4—2441no—
473C42—1221no—
474C42—1221no—
475C42—1221no—
476C42—1221no—
477C42—1221no—
478C42—1221no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C23—1221no—
486C23—1221no—
487C23—1221no—
488C23—1221no—
489C23—1221no—
490C23—1221no—
491C23—1221no—
492C23C23×#692311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
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—611no—
515C2×C4—611no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—612no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
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—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C22—2441no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22#1684083111yescharacteristic
558C22#1684083111yescharacteristic
559C22#1684083111yescharacteristic
560C22D61⋊#13111yescharacteristic
561C22#1684084011yescharacteristic
562C22#1684084111yescharacteristic
563C22#1684084211yescharacteristic
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—611no—
572C4—611no—
573C4—611no—
574C4—611no—
575C4—1222no—
576C4—2441no—
577C4—2441no—
578C4—2441no—
579C4—2441no—
580C4—2441no—
581C2—4881no—
582C2#2146236611yescharacteristic
583C2#2146275911yescharacteristic
584C2#2146276011yescharacteristic
585C2#2146276311yescharacteristic
586C2#2146277511yescharacteristic
587C2#2146277611yescharacteristic
588C2#2146277711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#400C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#400#6923
hypocenterC61#23382
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #21461921C2semidirect
2. #21461921C2semidirect
3. #21461918C2semidirect
7. #21461879C2semidirect
8. #21461878C2semidirect
9. #21461875C2semidirect
13. #21461753C2semidirect
14. #21461748C2semidirect
353. C61#23382semidirect

Maximal subgroups

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

subgroupindex
#214619212
#214619182
#214618942
#214618912
#214618792
#214618782
#214618752
#214617672
#214617532
#214617482
#214491182
#2338261