Finite Group Databasebeta

← #30616000

Subgroups — #30616000

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840786C211yesmaximal, characteristic, complemented
2C2×C4×#11758217C211yesmaximal, characteristic, complemented
3#21461893C211yesmaximal, characteristic, complemented
4#21461892C211yesmaximal, characteristic, complemented
5#21461878C211yesmaximal, characteristic, complemented
6#21461877C211yesmaximal, characteristic, complemented
7#21461796C211yesmaximal, characteristic
8#21461796C211yesmaximal, characteristic
9#21461766C211yesmaximal, characteristic, complemented
10#21461766C211yesmaximal, characteristic, complemented
11#21461607C211yesmaximal, characteristic, complemented
12#21461549C211yesmaximal, characteristic, complemented
13#21461545C211yesmaximal, characteristic, complemented
14#21461538C211yesmaximal, characteristic, complemented
15#21448259C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18#16840786—24no—
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C22⋊#92420C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C4×#11758217—24no—
30C2×#14519832C2211yescharacteristic
31C2×#14519832C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C2×#14519733C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49#16839656C411yescharacteristic
50#16839650C411yescharacteristic
51#16839647C411yescharacteristic
52#16839645C411yescharacteristic
53#16839642C411yescharacteristic
54#16839635C411yescharacteristic
55#16839634C411yescharacteristic
56#16839613C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59#16839607C2211yescharacteristic
60C61×#386C411yescharacteristic
61C2×#11758217—22no—
62C2×#11758217—22no—
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—22no—
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75#14519844—22no—
76#14519844—22no—
77C4⋊#92420—22no—
78C4⋊#92420—22no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85#14519832—22no—
86#14519832—22no—
87#14519832—22no—
88#14519832—22no—
89C4×#92420—22no—
90C4×#92420D414yescomplemented
91C23×Dic61C2×C411yescharacteristic
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94D4×Dic61—22no—
95D4×Dic61—22no—
96#14519733—22no—
97#14519733—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C24×C61C22×C411yescharacteristic
134C2×D4×C61—22no—
135C2×D4×C61—41no—
136C2×D4×C61—41no—
137C22×C4×C61—22no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—41no—
157C22×Dic61—41no—
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61#4112yes—
166C22×Dic61#4112yes—
167C22×Dic61C2411yescharacteristic
168#11758217—28no—
169#11758217—28no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—21no—
187C2×#92420—21no—
188C2×#92420—21no—
189C2×#92420—21no—
190C2×#92420C2×D412yes—
191C2×#92420C2×D412yes—
192C2×#92420#4112yes—
193C2×#92420#4112yes—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200C22⋊Dic61—41no—
201C22⋊Dic61—41no—
202C4⋊Dic61—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—41no—
206#11758196—41no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61C2×D412yes—
218C4×Dic61#4112yes—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61#11712yes—
233C23×C61C23×C411yescharacteristic
234D4×C61—44no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—44no—
250C2×C4×C61C4×D412yes—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—44no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61#11712yes—
280C2×Dic61C4×D412yes—
281C2×Dic61C22×D411yescharacteristic
282C2×Dic61C2×#4111yescharacteristic
283C2×Dic61C2×#4111yescharacteristic
284C2×Dic61C2×#4111yescharacteristic
285C2×Dic61C2×#4111yescharacteristic
286C2×Dic61C2×#4111yescharacteristic
287#92420—22no—
288#92420—22no—
289#92420—22no—
290#92420—22no—
291#92420—41no—
292#92420—41no—
293#92420—41no—
294#92420—41no—
295#21104—611nomaximal, Sylow
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61C2×#11711yescharacteristic
311C22×C61C2×C4×D411yescharacteristic
312C22×C61C4×#4111yescharacteristic
313C22×C61#56811yescharacteristic
314C22×C61#56811yescharacteristic
315C22×C61#56811yescharacteristic
316C22×C61#56811yescharacteristic
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322Dic61—22no—
323Dic61—22no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61—41no—
328Dic61—41no—
329Dic61#52511yescharacteristic
330Dic61#52511yescharacteristic
331Dic61#52911yescharacteristic
332Dic61#52911yescharacteristic
333C2×#433—611no—
334C2×C4×M16—611no—
335#2290—611no—
336#1924—611no—
337#1924—611no—
338#1917—611no—
339#1917—611no—
340#1870—611no—
341#1870—611no—
342#1851—611no—
343#1851—611no—
344#1768—611no—
345#1750—611no—
346#1749—611no—
347#1746—611no—
348C2×C61—42no—
349C2×C61—81no—
350C2×C61#229011yescharacteristic
351C2×C61#292111yescharacteristic
352C2×C61#292311yescharacteristic
353C2×C61#293011yescharacteristic
354C2×C61#293011yescharacteristic
355C2×C61#296711yescharacteristic
356C2×C61#296711yescharacteristic
357C22×M16—611no—
358C22×M16—611no—
359C2×C4×D4—611no—
360C2×#117—611no—
361C22×C42—611no—
362#433—1224no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×C22⋊C8—611no—
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C4×M16—1224no—
374C2×#97—611no—
375C2×#97—611no—
376C2×#97—611no—
377C2×#97—611no—
378C2×C4×C8—611no—
379C2×C4×C8—611no—
380#388—611no—
381#388—611no—
382#387—611no—
383#387—611no—
384#386—611no—
385#386#692311yescharacteristic
386#385—611no—
387#385—611no—
388C4×C4⋊C4—611no—
389C4×C22⋊C4—611no—
390C4×C22⋊C4—611no—
391#376—611no—
392#336—611no—
393#336—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336—611no—
399#336—611no—
400#336—611no—
401#336—611no—
402C61#2110411yescharacteristic, complemented, Sylow
403C22×D4C2×#692311yescharacteristic
404C23×C4—611no—
405C23×C4—611no—
406C23×C4—611no—
407C23×C4C2×#692311yescharacteristic
408C2×M16—1222no—
409C2×M16—1222no—
410C2×M16—1222no—
411C2×M16—1222no—
412C2×M16—1222no—
413C2×M16—1222no—
414C22×C8—611no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—611no—
422C4×D4—1222no—
423C4×D4—1222no—
424#117—1222no—
425#117—1222no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4—611no—
435C2×C22⋊C4—611no—
436C2×C22⋊C4C2×#692311yescharacteristic
437C2×C22⋊C4C2×#692311yescharacteristic
438C2×C22⋊C4C2×#692311yescharacteristic
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—1222no—
447C2×C42—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457C22⋊C8—1222no—
458#97—1222no—
459#97—1222no—
460#97—1222no—
461#97—1222no—
462C4×C8—614no—
463C4×C8—1222no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95—611no—
471#95—611no—
472#95C2×#692311yescharacteristic
473#95C2×#692311yescharacteristic
474C24C22×#692311yescharacteristic
475C24C22×#692311yescharacteristic
476C2×D4—22no—
477C2×D4—41no—
478C2×D4—41no—
479C22×C4—22no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—611no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—2441no—
504C22×C4—2441no—
505C22×C4C22×#692311yescharacteristic
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510M16—1228no—
511M16—1228no—
512C2×C8—612no—
513C2×C8—612no—
514C2×C8—612no—
515C2×C8—612no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—2441no—
540C4⋊C4—2441no—
541C22⋊C4—22no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—2441no—
548C22⋊C4—2441no—
549C42—612no—
550C42—612no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C42—1221no—
555C42—1221no—
556C42—1222no—
557C42—1221no—
558C42—1221no—
559C42—1221no—
560C42—1222no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23#1451985612yes—
575C23C23×#692311yescharacteristic
576D4—44no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—44no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—612no—
599C2×C4—612no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2444no—
628C2×C4D4×#692312yes—
629C8—1222no—
630C8—1222no—
631C8—1222no—
632C8—1222no—
633C8—2441no—
634C8—2441no—
635C8—2441no—
636C8—2441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#1451985611yescharacteristic
652C22C2×D4×#692311yescharacteristic
653C22#41×#692311yescharacteristic
654C22#1684084011yescharacteristic
655C22#1684084011yescharacteristic
656C22#1684084011yescharacteristic
657C22#1684084111yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—611no—
664C4—611no—
665C4—611no—
666C4—611no—
667C4—1222no—
668C4—1222no—
669C4—2441no—
670C4—2441no—
671C4—2441no—
672C4—2441no—
673C4—2441no—
674C2—42no—
675C2—81no—
676C2#2146227311yescharacteristic
677C2#2146249911yescharacteristic
678C2#2146250511yescharacteristic
679C2#2146253711yescharacteristic
680C2#2146253811yescharacteristic
681C2#2146263811yescharacteristic
682C2#2146264111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×D4×C61C2×C4
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#21104
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840786C2semidirect
2. C2×C4×#11758217C2semidirect
3. #21461893C2semidirect
4. #21461892C2semidirect
5. #21461878C2semidirect
6. #21461877C2semidirect
9. #21461766C2semidirect
10. #21461766C2semidirect
11. #21461607C2semidirect
12. #21461549C2semidirect
13. #21461545C2semidirect
14. #21461538C2semidirect
90. C4×#92420D4semidirect
402. C61#21104semidirect

Maximal subgroups

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

subgroupindex
C2×#168407862
C2×C4×#117582172
#214618932
#214618922
#214618782
#214618772
#214617962
#214617662
#214616072
#214615492
#214615452
#214615382
#214482592
#2110461