Finite Group Databasebeta

← #29699887

Subgroups — #29699887

Order 15616.

838 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839859C211yesmaximal, characteristic
2#21448780C211yesmaximal, characteristic, complemented
3#21448767C211yesmaximal, characteristic
4#21446699C211yesmaximal, characteristic
5#21446674C211yesmaximal, characteristic
6#21446461C211yesmaximal, characteristic, complemented
7#21446452C211yesmaximal, characteristic, complemented
8#21446441C211yesmaximal, characteristic
9#21445984C211yesmaximal, characteristic, complemented
10#21445827C211yesmaximal, characteristic
11#21445823C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13#21445711C211yesmaximal, characteristic, complemented
14#21445692C211yesmaximal, characteristic, complemented
15C61×#1926C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519742C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519733—21no—
20#16839859C418yescomplemented
21C2×#14519711C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839667C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839656—21no—
37#16839650—21no—
38#16839646—21no—
39#16839644—21no—
40#16839631C2211yescharacteristic
41#16839629—21no—
42#16839627C2211yescharacteristic
43#16839620—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×#11758196C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48#16839608—21no—
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C23×Dic61—21no—
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758200C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519742—22no—
68#14519742C2×C414yes—
69D4×Dic61—22no—
70D4×Dic61C2×C414yes—
71#14519733—44no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196D411yescharacteristic
79C2×#11758196D411yescharacteristic
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519711—41no—
90#14519710—22no—
91#14519710C2×C414yes—
92#14519708—22no—
93#14519706—22no—
94#14519702—41no—
95#14519702C2×C414yes—
96#14519700—41no—
97#14519698—41no—
98#14519688—22no—
99#14519687C2×C414yes—
100C8×Dic61—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112C22×D4×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#106×C61—41no—
123#102×C61—41no—
124#102×C61C2×C414yes—
125#95×C61—21no—
126C24×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—24no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C412yes—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C412yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C412yes—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—81no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—42no—
173C22⋊Dic61—24no—
174C22⋊Dic61—42no—
175C22⋊Dic61—81no—
176#11758200—28no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22×C412yes—
183#11758196—24no—
184#11758196—22no—
185#11758196—41no—
186#11758196—42no—
187#11758196—81no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—24no—
191C4×Dic61—42no—
192C4×Dic61—42no—
193C4×Dic61—42no—
194C4×Dic61C22×C412yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C22×C412yes—
200C2×#92418#4112yes—
201C2×#92418#4112yes—
202C23×C61—22no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61C22×D411yescharacteristic
210D4×C61—22no—
211D4×C61—22no—
212D4×C61—41no—
213D4×C61—41no—
214C2×C4×C61—22no—
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—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C23×C411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—48no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61C4×D412yes—
258C2×Dic61C4×D412yes—
259C2×Dic61AGL(1,ℤ/8)12yes—
260Dic122—22no—
261Dic122—22no—
262Dic122—41no—
263Dic122—41no—
264C8×C61—22no—
265C8×C61—41no—
266#92418—41no—
267#92418#11714yescomplemented
268#22820—611nomaximal, Sylow
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61C2×C4×D411yescharacteristic
277C22×C61#54711yescharacteristic
278C22×C61#55011yescharacteristic
279C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C61#57511yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57811yescharacteristic
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—42no—
286C4×C61—81no—
287C4×C61—81no—
288C4×C61C2×#11711yescharacteristic
289C4×C61#52011yescharacteristic
290C4×C61#55511yescharacteristic
291C4×C61#55611yescharacteristic
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—41no—
296Dic61—42no—
297Dic61—42no—
298Dic61—81no—
299Dic61—81no—
300C2×#440—611no—
301#2356—611no—
302#2354—611no—
303#1973—611no—
304#1968—611no—
305#1928—611no—
306#1927—611no—
307#1926D6111yescharacteristic
308#1925—611no—
309#1847—611no—
310#1804—611no—
311#1803—611no—
312#1776—611no—
313C4×#107—611no—
314#1771—611no—
315C2×C61—82no—
316C2×C61#235411yescharacteristic
317C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C61#294711yescharacteristic
319C2×C61#334311yescharacteristic
320C2×C61#334811yescharacteristic
321C2×C61#339711yescharacteristic
322C2×C61#340211yescharacteristic
323C22×SD16—611no—
324C2×C4×Q8—611no—
325C2×C4×D4—611no—
326C2×#117—1221no—
327#440—618no—
328C2×#107—611no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#106—611no—
332C2×#106C2×D6111yescharacteristic
333C2×C4⋊C8—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#102—611no—
338C2×#102C2×D6111yescharacteristic
339C2×#102C2×D6111yescharacteristic
340C2×#97—611no—
341C2×#97—611no—
342C2×C4×C8—611no—
343#391—611no—
344#391—611no—
345#390—611no—
346#390C2×D6111yescharacteristic
347#388—1221no—
348#388—1221no—
349#387—1221no—
350#387—1221no—
351#384—611no—
352#383—1221no—
353#382—611no—
354#380—1221no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—611no—
358C4×C4⋊C4—611no—
359C4×C4⋊C4C2×D6111yescharacteristic
360#376—1221no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340C2×D6111yescharacteristic
365#336—611no—
366#336C2×D6111yescharacteristic
367C61#2282011yescharacteristic, complemented, Sylow
368C22×Q8—611no—
369C22×D4C22×D6111yescharacteristic
370C23×C4—1221no—
371C2×SD16—614no—
372C2×SD16—1222no—
373C2×SD16—1222no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8C22×D6111yescharacteristic
377C22×C8C22×D6111yescharacteristic
378C4×Q8—614no—
379C4×Q8—1222no—
380C4×D4—614no—
381C4×D4—1222no—
382#117—2444no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C42—21no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—1221no—
403C2×C42—1221no—
404C2×C42—1221no—
405C2×C42—1221no—
406C2×C42C22×D6111yescharacteristic
407#107—614no—
408#107—1222no—
409#107—2441no—
410#106—41no—
411#106—1222no—
412C4⋊C8—1222no—
413#103—614no—
414#103—2441no—
415#103—2441no—
416#102—41no—
417#102—2441no—
418#102C4×D6114yes—
419#97—614no—
420#97—1222no—
421C4×C8—1222no—
422#95—21no—
423#95—611no—
424#95—611no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434C24—21no—
435C2×Q8—612no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D6112yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—1224no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—2442no—
460C22×C4—2442no—
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464SD16—1228no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—612no—
471C2×C8—612no—
472C2×C8—612no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8C2×C4×D6112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—612no—
483C4⋊C4—1222no—
484C4⋊C4—1224no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—4881no—
491C4⋊C4—2441no—
492C4⋊C4—2442no—
493C4⋊C4C2×C4×D6112yes—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—1224no—
497C22⋊C4—4881no—
498C22⋊C4—2442no—
499C42—21no—
500C42—21no—
501C42—42no—
502C42—612no—
503C42—612no—
504C42—1224no—
505C42—1221no—
506C42—1221no—
507C42—2442no—
508C42—2442no—
509C42—2442no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C2×D4×D6111yescharacteristic
518Q8—1222no—
519Q8—1222no—
520Q8—2441no—
521Q8—2441no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—2448no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4C22×C4×D6111yescharacteristic
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#1451982211yescharacteristic
571C2×C4#1451982411yescharacteristic
572C8—22no—
573C8—41no—
574C8—614no—
575C8—2441no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C4×D4×D6111yescharacteristic
584C22#1684041011yescharacteristic
585C22#1684043011yescharacteristic
586C22AGL(1,ℤ/8)×D6111yescharacteristic
587C22#1684055811yescharacteristic
588C22#1684056811yescharacteristic
589C22#1684057611yescharacteristic
590C4—42no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—1222no—
596C4—1222no—
597C4—1222no—
598C4—4881no—
599C4—4881no—
600C4—2442no—
601C4—2442no—
602C4—2441no—
603C4#117×D6111yescharacteristic
604C4#1684024111yescharacteristic
605C4#1684047411yescharacteristic
606C4#1684047911yescharacteristic
607C2—82no—
608C2#2144876511yescharacteristic
609C2#2145463011yescharacteristic
610C2#2145465511yescharacteristic
611C2#2145825211yescharacteristic
612C2#2145833711yescharacteristic
613C2#2145883411yescharacteristic
614C2#2145889711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1926C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#1926D61
hypocenterC61#22820
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #21448780C2semidirect
6. #21446461C2semidirect
7. #21446452C2semidirect
9. #21445984C2semidirect
11. #21445823C2semidirect
12. #21445717C2semidirect
13. #21445711C2semidirect
14. #21445692C2semidirect
20. #16839859C4semidirect
267. #92418#117semidirect
367. C61#22820semidirect

Maximal subgroups

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

subgroupindex
C2×#168398592
#214487802
#214487672
#214466992
#214466742
#214464612
#214464522
#214464412
#214459842
#214458272
#214458232
#214457172
#214457112
#214456922
C61×#19262
#2282061