Finite Group Databasebeta

← #30620722

Subgroups — #30620722

Order 15616.

688 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461879C211yesmaximal, characteristic, complemented
2#21461878C211yesmaximal, characteristic, complemented
3#21461877C211yesmaximal, characteristic, complemented
4#21461875C211yesmaximal, characteristic, complemented
5#21461767C211yesmaximal, characteristic
6#21461764C211yesmaximal, characteristic
7#21461747C211yesmaximal, characteristic, complemented
8#21461737C211yesmaximal, characteristic, complemented
9#21461713C211yesmaximal, characteristic
10#21461604C211yesmaximal, characteristic, complemented
11#21461560C211yesmaximal, characteristic
12#21461557C211yesmaximal, characteristic
13#21461538C211yesmaximal, characteristic, complemented
14#21461486C211yesmaximal, characteristic
15#21448311C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519832C2211yescharacteristic
25C2×#14519832C2211yescharacteristic
26C2×#14519832C2211yescharacteristic
27C2×C4×#92420C2211yescharacteristic
28#16840628C2211yescharacteristic
29#16840628C2211yescharacteristic
30#16840628C2211yescharacteristic
31#16840628C2211yescharacteristic
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
59C2×#11758213—22no—
60C2×#11758213—22no—
61C2×#11758213—41no—
62C2×D61⋊C8—22no—
63C2×D61⋊C8—22no—
64C2×D61⋊C8—41no—
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73#14519844—22no—
74#14519844—22no—
75#14519844—41no—
76C4⋊#92420—41no—
77#14519834—22no—
78#14519834—22no—
79#14519832—22no—
80#14519832—41no—
81#14519832—41no—
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#4112yes—
140C2×C4×D61#4112yes—
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#4112yes—
164C2×#92420#4112yes—
165#11758213—44no—
166D61⋊C8—44no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—41no—
169C42×C61—41no—
170#11758198—22no—
171#11758198—22no—
172#11758198—22no—
173#11758198—41no—
174#11758198—41no—
175#11758198—41no—
176C4⋊Dic61—22no—
177C4⋊Dic61—22no—
178#11758196—41no—
179#11758196—41no—
180C4×Dic61—22no—
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—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—41no—
194C4×Dic61—41no—
195C23×C61C23×C411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61#11712yes—
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—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61#11712yes—
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—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61#13112yes—
242C2×Dic61C2×#4111yescharacteristic
243C2×Dic61C2×#4111yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245C2×Dic61C2×#4111yescharacteristic
246C2×Dic61H(5,𝔽2)11yescharacteristic
247C2×Dic612−1+411yescharacteristic
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252#92420—22no—
253#92420—22no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258#92420—41no—
259#92420—41no—
260#22598—611nomaximal, Sylow
261C22×C61C2×#11711yescharacteristic
262C22×C61C4×#4111yescharacteristic
263C22×C61#52011yescharacteristic
264C22×C61C2×#13111yescharacteristic
265C22×C61#56811yescharacteristic
266C22×C61#56811yescharacteristic
267C22×C61#56811yescharacteristic
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—22no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282Dic61—22no—
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—41no—
288Dic61#55111yescharacteristic
289Dic61#55111yescharacteristic
290Dic61#55211yescharacteristic
291Dic61#55211yescharacteristic
292#2298—611no—
293#1917—611no—
294#1917—611no—
295#1917—611no—
296#1916—611no—
297#1851—611no—
298#1850—611no—
299#1839—611no—
300#1832—611no—
301#1818—611no—
302#1767—611no—
303#1753—611no—
304#1752—611no—
305#1746—611no—
306#1729—611no—
307C2×C61#234311yescharacteristic
308C2×C61#292311yescharacteristic
309C2×C61#292511yescharacteristic
310C2×C61#296711yescharacteristic
311C2×C61#296811yescharacteristic
312C2×C61#299311yescharacteristic
313C2×C61#299511yescharacteristic
314D61—42no—
315C22×M16—611no—
316C23×C8—611no—
317C2×#117—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8—611no—
321C2×C4⋊C8—611no—
322C2×C22⋊C8—611no—
323C2×C22⋊C8—611no—
324C2×#97—611no—
325C2×#97—611no—
326C2×#97—611no—
327C2×C4×C8—611no—
328#388—611no—
329#388—611no—
330#388—611no—
331#388—611no—
332#387—611no—
333#387—611no—
334#387—611no—
335#387#692311yescharacteristic
336C4×C4⋊C4—611no—
337C4×C4⋊C4—611no—
338C4×C22⋊C4—611no—
339C4×C22⋊C4—611no—
340#376—611no—
341C43—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—
353#336—611no—
354#336—611no—
355#336—611no—
356#336—611no—
357#336—611no—
358C61#2259811yescharacteristic, complemented, Sylow
359C23×C4—611no—
360C2×M16—1222no—
361C2×M16—1222no—
362C2×M16—2441no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—1222no—
372C22×C8—1222no—
373C22×C8—2441no—
374#117—1222no—
375#117—1222no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4C2×#692311yescharacteristic
381C2×C4⋊C4C2×#692311yescharacteristic
382C2×C22⋊C4—611no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42C2×#692311yescharacteristic
398C4⋊C8—1222no—
399C4⋊C8—1222no—
400C4⋊C8—2441no—
401C4⋊C8—2441no—
402C22⋊C8—1222no—
403C22⋊C8—1222no—
404#97—1222no—
405#97—2441no—
406#97—2441no—
407C4×C8—1222no—
408#95—611no—
409#95—611no—
410#95—611no—
411#95—611no—
412#95—611no—
413#95—611no—
414#95—611no—
415#95—611no—
416#95C2×#692311yescharacteristic
417#95C2×#692311yescharacteristic
418#95C2×#692311yescharacteristic
419#95C2×#692311yescharacteristic
420C24—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4C22×#692311yescharacteristic
435C22×C4C22×#692311yescharacteristic
436C22×C4C22×#692311yescharacteristic
437C22×C4C22×#692311yescharacteristic
438C22×C4C22×#692311yescharacteristic
439C22×C4C22×#692311yescharacteristic
440C22×C4C22×#692311yescharacteristic
441M16—2444no—
442C2×C8—612no—
443C2×C8—612no—
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—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—2444no—
467C4⋊C4—22no—
468C4⋊C4—41no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—2441no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C42—41no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1222no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42—2441no—
494C42—2441no—
495C23—612no—
496C23—1221no—
497C23—1221no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23C23×#692311yescharacteristic
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—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—612no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
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—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4#1451985612yes—
552C8—1222no—
553C8—1222no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C8—2441no—
560C22—1222no—
561C22—1222no—
562C22—1222no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22—2441no—
567C22C2×#1451985611yescharacteristic
568C22#41×#692311yescharacteristic
569C22#1684083111yescharacteristic
570C22D61⋊#13111yescharacteristic
571C22#1684084011yescharacteristic
572C22#1684084111yescharacteristic
573C22#1684084211yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—611no—
582C4—611no—
583C4—611no—
584C4—611no—
585C4—1222no—
586C4—2441no—
587C4—2441no—
588C4—2441no—
589C4—2441no—
590C4—2441no—
591C2—2442no—
592C2#2146232611yescharacteristic
593C2#2146250711yescharacteristic
594C2#2146251611yescharacteristic
595C2#2146264111yescharacteristic
596C2#2146264811yescharacteristic
597C2#2146276311yescharacteristic
598C2#2146277611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#387#6923
hypocenterC61#22598
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #21461879C2semidirect
2. #21461878C2semidirect
3. #21461877C2semidirect
4. #21461875C2semidirect
7. #21461747C2semidirect
8. #21461737C2semidirect
10. #21461604C2semidirect
13. #21461538C2semidirect
358. C61#22598semidirect

Maximal subgroups

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

subgroupindex
#214618792
#214618782
#214618772
#214618752
#214617672
#214617642
#214617472
#214617372
#214617132
#214616042
#214615602
#214615572
#214615382
#214614862
#214483112
#2259861