Finite Group Databasebeta

← #29683128

Subgroups — #29683128

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839862C211yesmaximal, characteristic
2#21448182C211yesmaximal, characteristic, complemented
3#21446443C211yesmaximal, characteristic
4#21446436C211yesmaximal, characteristic
5#21446408C211yesmaximal, characteristic, complemented
6#21446387C211yesmaximal, characteristic, complemented
7#21446177C211yesmaximal, characteristic
8#21446177C211yesmaximal, characteristic
9#21446086C211yesmaximal, characteristic, complemented
10#21446072C211yesmaximal, characteristic, complemented
11#21445717C211yesmaximal, characteristic, complemented
12C4×#14519700C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic
14#21445571C211yesmaximal, characteristic, complemented
15C61×#2319C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16839862C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33C4×C4⋊Dic61C2211yescharacteristic
34C4×C4⋊Dic61C2211yescharacteristic
35#16839613—21no—
36#16839613—21no—
37#16839613—21no—
38#16839607—21no—
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#388—21no—
55C61×#388—21no—
56C61×#381—21no—
57C61×#380—21no—
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#376C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C2×#11758200—22no—
62C2×#11758200—22no—
63C2×#11758200C2×C414yes—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×Dic122—22no—
69C4×Dic122—22no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C4×Dic122C2×C414yes—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519710—22no—
87#14519710C2×C414yes—
88#14519708—22no—
89#14519700—22no—
90#14519700—22no—
91#14519700C2×C414yes—
92#14519698—22no—
93#14519698—22no—
94#14519698C2×C414yes—
95#14519688C2×C414yes—
96C4×#92418—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×D4×C61C2311yescharacteristic
101C23×C4×C61—21no—
102C4×D4×C61—22no—
103C4×D4×C61C2×C414yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
125C24×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61C22×C412yes—
132C22×C4×C61—21no—
133C22×C4×C61—24no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—81no—
137C22×C4×C61—81no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122C22×C412yes—
153C2×Dic122#4112yes—
154C2×Dic122#4112yes—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—81no—
161C4⋊C4×C61—81no—
162C4⋊C4×C61C22×C412yes—
163C22⋊C4×C61—24no—
164C22⋊C4×C61—81no—
165C22⋊C4×C61—81no—
166C22⋊C4×C61—81no—
167C22⋊C4×C61—81no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—81no—
173C42×C61C22×C412yes—
174C42×C61#4112yes—
175#11758200—28no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61C22×C412yes—
180C4⋊Dic61#4112yes—
181C4⋊Dic61#4112yes—
182#11758196—24no—
183#11758196—24no—
184#11758196—24no—
185C4×Dic61—24no—
186C4×Dic61—24no—
187C4×Dic61—24no—
188C4×Dic61—81no—
189C4×Dic61—81no—
190C4×Dic61—81no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202C2×#92418C22×C412yes—
203C23×C61—22no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61C22×D411yescharacteristic
211D4×C61—22no—
212D4×C61—22no—
213D4×C61—41no—
214D4×C61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—22no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—84no—
241C2×C4×C61C4×D412yes—
242C2×C4×C61C4×D412yes—
243C2×C4×C61C23×C411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261Dic122—22no—
262Dic122—22no—
263Dic122—22no—
264Dic122#11714yes—
265#92418—22no—
266#92418—22no—
267#92418—41no—
268#92418—41no—
269#21128—611nomaximal, Sylow
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61C2×C4×D411yescharacteristic
278C22×C61#52511yescharacteristic
279C22×C61#52511yescharacteristic
280C22×C61#57611yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57711yescharacteristic
283C22×C61#57811yescharacteristic
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61C2×#11711yescharacteristic
294C4×C61C4×#4111yescharacteristic
295C4×C61#52911yescharacteristic
296C4×C61#52911yescharacteristic
297Dic61—24no—
298Dic61—42no—
299Dic61—42no—
300Dic61—42no—
301C2×#440—611no—
302#2319D6111yescharacteristic
303#2276—611no—
304#1926—611no—
305#1925—611no—
306#1921—611no—
307#1918—611no—
308#1880—611no—
309#1880—611no—
310#1865—611no—
311#1863—611no—
312#1776—611no—
313C4×#103—611no—
314C4×#102—611no—
315#1746—611no—
316C2×C61—82no—
317C2×C61#229011yescharacteristic
318C2×C61#294611yescharacteristic
319C2×C61#294711yescharacteristic
320C2×C61#311911yescharacteristic
321C2×C61#312111yescharacteristic
322C2×C61#312411yescharacteristic
323C2×C61#312611yescharacteristic
324C22×SD16—611no—
325C2×C4×Q8—611no—
326C2×C4×Q8—611no—
327C2×C4×Q8—611no—
328C2×C4×D4C2×D6111yescharacteristic
329#440—618no—
330C2×#107—611no—
331C2×#107—611no—
332C2×#106—611no—
333C2×#103—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#102—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#97—611no—
340C2×C4×C8—611no—
341#390C2×D6111yescharacteristic
342#390C2×D6111yescharacteristic
343#389C2×D6111yescharacteristic
344#389C2×D6111yescharacteristic
345#388—21no—
346#388—21no—
347#381—21no—
348#380—21no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4—611no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—1221no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4—1221no—
355C4×C4⋊C4C2×D6111yescharacteristic
356#376—1221no—
357#376C2×D6111yescharacteristic
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368C61#2112811yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×D4C22×D6111yescharacteristic
371C23×C4—21no—
372C2×SD16—614no—
373C2×SD16—1222no—
374C2×SD16—1222no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C4×Q8—614no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×D4—22no—
386C4×D4C4×D6114yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—1221no—
405C2×C42—1221no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411C2×C42C22×D6111yescharacteristic
412C2×C42C22×D6111yescharacteristic
413#107—614no—
414#107—1222no—
415#106—1222no—
416#103—614no—
417#103—1222no—
418#103—1222no—
419#102—614no—
420#102—1222no—
421#102—1222no—
422#97—614no—
423C4×C8—1222no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95C22⋊D6111yescharacteristic
431#95C22⋊D6111yescharacteristic
432#95C22⋊D6111yescharacteristic
433#95C22⋊D6111yescharacteristic
434C24—21no—
435C2×Q8—612no—
436C2×Q8—612no—
437C2×Q8—612no—
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—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460C22×C4C2×C22⋊D6111yescharacteristic
461C22×C4C2×C22⋊D6111yescharacteristic
462C22×C4C2×C22⋊D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464SD16—1228no—
465C2×C8—612no—
466C2×C8—612no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—612no—
485C4⋊C4—612no—
486C4⋊C4—612no—
487C4⋊C4—1224no—
488C4⋊C4—1224no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1224no—
493C4⋊C4C2×C4×D6112yes—
494C22⋊C4—24no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—81no—
504C42—1224no—
505C42—1224no—
506C42—1224no—
507C42—4881no—
508C42—4881no—
509C42—4881no—
510C42C2×C4×D6112yes—
511C42#1175822212yes—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C22×C22⋊D6111yescharacteristic
520Q8—614no—
521Q8—1222no—
522Q8—1222no—
523Q8—1222no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4C4×C22⋊D6112yes—
567C2×C4C4×C22⋊D6112yes—
568C2×C4C22×C4×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#41×D6111yescharacteristic
571C2×C4#41×D6111yescharacteristic
572C2×C4#41×D6111yescharacteristic
573C2×C4C2×#1175822211yescharacteristic
574C8—1222no—
575C8—1222no—
576C8—2441no—
577C8—2441no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C4×C22⋊D6111yescharacteristic
586C22#1684026911yescharacteristic
587C22#1684026911yescharacteristic
588C22#1684056511yescharacteristic
589C22#1684057311yescharacteristic
590C22#1684057311yescharacteristic
591C22#1684057711yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—1224no—
602C4—2442no—
603C4—2442no—
604C4—2442no—
605C4#117×D6111yescharacteristic
606C4#1684023011yescharacteristic
607C4#1684029011yescharacteristic
608C4#1684029011yescharacteristic
609C2—82no—
610C2#2144825611yescharacteristic
611C2#2145465111yescharacteristic
612C2#2145465811yescharacteristic
613C2#2145601211yescharacteristic
614C2#2145604211yescharacteristic
615C2#2145607511yescharacteristic
616C2#2145610511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2319C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#2319D61
hypocenterC61#21128
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #21448182C2semidirect
5. #21446408C2semidirect
6. #21446387C2semidirect
9. #21446086C2semidirect
10. #21446072C2semidirect
11. #21445717C2semidirect
12. C4×#14519700C2semidirect
14. #21445571C2semidirect
20. #16839862C4semidirect
368. C61#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#168398622
#214481822
#214464432
#214464362
#214464082
#214463872
#214461772
#214460862
#214460722
#214457172
C4×#145197002
C4×#145196982
#214455712
C61×#23192
#2112861