Finite Group Databasebeta

← #29683082

Subgroups — #29683082

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839859C211yesmaximal, characteristic
2#21448466C211yesmaximal, characteristic, complemented
3#21448180C211yesmaximal, characteristic
4#21446459C211yesmaximal, characteristic, complemented
5#21446454C211yesmaximal, characteristic, complemented
6#21446408C211yesmaximal, characteristic, complemented
7#21446393C211yesmaximal, characteristic, complemented
8#21446153C211yesmaximal, characteristic
9#21446151C211yesmaximal, characteristic
10#21446082C211yesmaximal, characteristic
11#21445718C211yesmaximal, characteristic, complemented
12#21445638C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic
14#21445569C211yesmaximal, characteristic, complemented
15C61×#1862C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519742C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20#16839859C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839668C2211yescharacteristic
30#16839667C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839649—21no—
33#16839643—21no—
34#16839629—21no—
35#16839627—21no—
36C4⋊C4×Dic61C2211yescharacteristic
37C4⋊C4×Dic61C2211yescharacteristic
38C4⋊C4×Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40C22⋊C4×Dic61—21no—
41C22⋊C4×Dic61—21no—
42C4×C22⋊Dic61—21no—
43#16839608C2211yescharacteristic
44C2×#14519684—21no—
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C23×Dic61—21no—
62C23×Dic61—21no—
63C2×#11758200—22no—
64C2×#11758200—22no—
65C2×#11758200C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519742—22no—
69#14519742C2×C414yescomplemented
70D4×Dic61—22no—
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61C2×C414yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519710C2×C414yescomplemented
89#14519709—22no—
90#14519702—22no—
91#14519702C2×C414yescomplemented
92#14519700—22no—
93#14519698—22no—
94#14519687C2×C414yescomplemented
95C8×Dic61—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4×D4×C61—22no—
114C4×D4×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61—22no—
122#102×C61—22no—
123#102×C61C2×C414yes—
124#95×C61—21no—
125C24×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61C22×C412yes—
130C2×D4×C61#4112yes—
131C2×D4×C61#4112yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—24no—
135C22×C4×C61—21no—
136C22×C4×C61—81no—
137C22×C4×C61—81no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—24no—
145C22×Dic61—24no—
146C22×Dic61—21no—
147C22×Dic61—81no—
148C22×Dic61—81no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22×C412yes—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C22×C412yes—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—81no—
172C4⋊C4×C61C22×C412yes—
173C4⋊C4×C61#4112yes—
174C22⋊C4×C61—24no—
175C42×C61—21no—
176C42×C61—21no—
177C22⋊Dic61—24no—
178C22⋊Dic61—24no—
179#11758200—28no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—81no—
185C4⋊Dic61C22×C412yes—
186C4⋊Dic61#4112yes—
187#11758196—24no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—24no—
191C4×Dic61—81no—
192C4×Dic61—81no—
193C4×Dic61—81no—
194C4×Dic61—81no—
195C4×Dic61C22×C412yes—
196C4×Dic61#4112yes—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C22×C412yes—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61C22×D411yescharacteristic
211D4×C61—22no—
212D4×C61—22no—
213D4×C61—22no—
214D4×C61#11714yes—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
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×C61—41no—
230C2×C4×C61—84no—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
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—22no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—84no—
260C2×Dic61—84no—
261C2×Dic61C4×D412yes—
262C2×Dic61C4×D412yes—
263Dic122—22no—
264Dic122—22no—
265Dic122—41no—
266Dic122—41no—
267C8×C61—22no—
268C8×C61—41no—
269#92418—22no—
270#92418—41no—
271#21125—611nomaximal, Sylow
272C22×C61—24no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61C2×C4×D411yescharacteristic
280C22×C61#52511yescharacteristic
281C22×C61#52511yescharacteristic
282C22×C61#57611yescharacteristic
283C22×C61#57711yescharacteristic
284C22×C61#57711yescharacteristic
285C22×C61#57811yescharacteristic
286C4×C61—41no—
287C4×C61—42no—
288C4×C61—41no—
289C4×C61—42no—
290C4×C61—81no—
291C4×C61C2×#11711yescharacteristic
292C4×C61C4×#4111yescharacteristic
293C4×C61#52911yescharacteristic
294C4×C61#52911yescharacteristic
295Dic61—22no—
296Dic61—22no—
297Dic61—41no—
298Dic61—42no—
299Dic61—41no—
300Dic61—42no—
301Dic61—42no—
302Dic61—81no—
303C2×#440—611no—
304#2320—611no—
305#2275—611no—
306#1928—611no—
307#1927—611no—
308#1921—611no—
309#1918—611no—
310#1877—611no—
311#1877—611no—
312#1864—611no—
313#1862D6111yescharacteristic
314#1776—611no—
315C4×#103—611no—
316C4×#102—611no—
317#1746—611no—
318C2×C61—44no—
319C2×C61#229011yescharacteristic
320C2×C61#294611yescharacteristic
321C2×C61#294711yescharacteristic
322C2×C61#311811yescharacteristic
323C2×C61#312011yescharacteristic
324C2×C61#312311yescharacteristic
325C2×C61#312411yescharacteristic
326C22×SD16—611no—
327C2×C4×Q8—611no—
328C2×C4×D4—611no—
329C2×C4×D4—611no—
330C2×C4×D4C2×D6111yescharacteristic
331#440—618no—
332C2×#107—611no—
333C2×#107C2×D6111yescharacteristic
334C2×#106—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#102—611no—
339C2×#102C2×D6111yescharacteristic
340C2×#102C2×D6111yescharacteristic
341C2×#97—611no—
342C2×C4×C8—611no—
343#391—611no—
344#391—611no—
345#389—611no—
346#389C2×D6111yescharacteristic
347#387—1221no—
348#387—1221no—
349#383—1221no—
350#382—1221no—
351C4×C4⋊C4—611no—
352C4×C4⋊C4—611no—
353C4×C4⋊C4—611no—
354C4×C4⋊C4—611no—
355C4×C22⋊C4—1221no—
356C4×C22⋊C4—1221no—
357C4×C22⋊C4—1221no—
358#376—611no—
359C2×#95—1221no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340C2×D6111yescharacteristic
366#336—611no—
367#336—611no—
368#336—611no—
369#336C2×D6111yescharacteristic
370C61#2112511yescharacteristic, complemented, Sylow
371C22×Q8—611no—
372C22×D4C22×D6111yescharacteristic
373C23×C4—21no—
374C23×C4—1221no—
375C23×C4—1221no—
376C2×SD16—614no—
377C2×SD16—1222no—
378C2×SD16—1222no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8C22×D6111yescharacteristic
382C22×C8C22×D6111yescharacteristic
383C4×Q8—614no—
384C4×Q8—1222no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—614no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—1221no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411#107—22no—
412#107—614no—
413#106—1222no—
414#103—614no—
415#103—1222no—
416#103—1222no—
417#102—22no—
418#102—1222no—
419#102C4×D6114yes—
420#97—614no—
421C4×C8—1222no—
422#95—21no—
423#95—611no—
424#95—611no—
425#95—611no—
426#95—611no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436C24—21no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×C4×D6112yes—
447C2×D4#1175822412yes—
448C2×D4#1175822612yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1224no—
460C22×C4—1224no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—4881no—
466C22×C4—4881no—
467C22×C4—4881no—
468C22×C4—4881no—
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472SD16—1228no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—612no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8C2×C4×D6112yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—612no—
491C4⋊C4—612no—
492C4⋊C4—1224no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—4881no—
498C4⋊C4C2×C4×D6112yes—
499C4⋊C4#1175822412yes—
500C22⋊C4—24no—
501C22⋊C4—1224no—
502C22⋊C4—1224no—
503C42—21no—
504C42—21no—
505C42—612no—
506C42—612no—
507C42—1224no—
508C42—1221no—
509C42—1221no—
510C42—4881no—
511C42—4881no—
512C42—4881no—
513C42—4881no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D6111yescharacteristic
522Q8—1222no—
523Q8—1222no—
524Q8—2441no—
525Q8—2441no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#1451973514yes—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1222no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4884no—
562C2×C4—4884no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C22×C4×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4C2×#1175822411yescharacteristic
576C2×C4C2×#1175822411yescharacteristic
577C2×C4C2×#1175822611yescharacteristic
578C8—22no—
579C8—41no—
580C8—1222no—
581C8—2441no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C4×D4×D6111yescharacteristic
590C22#1684026811yescharacteristic
591C22#1684027511yescharacteristic
592C22#1684056311yescharacteristic
593C22#1684056911yescharacteristic
594C22#1684057211yescharacteristic
595C22#1684057811yescharacteristic
596C4—42no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—1222no—
602C4—1222no—
603C4—4881no—
604C4—2442no—
605C4—2442no—
606C4—2441no—
607C4—2442no—
608C4—2441no—
609C4C2×#1451973511yescharacteristic
610C4C4×#1175822411yescharacteristic
611C4#1684028911yescharacteristic
612C4#1684029811yescharacteristic
613C2—44no—
614C2#2144825511yescharacteristic
615C2#2145464411yescharacteristic
616C2#2145465911yescharacteristic
617C2#2145599611yescharacteristic
618C2#2145602611yescharacteristic
619C2#2145607311yescharacteristic
620C2#2145608611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1862C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#1862D61
hypocenterC61#21125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #21448466C2semidirect
4. #21446459C2semidirect
5. #21446454C2semidirect
6. #21446408C2semidirect
7. #21446393C2semidirect
11. #21445718C2semidirect
12. #21445638C2semidirect
14. #21445569C2semidirect
20. #16839859C4semidirect
69. #14519742C2×C4semidirect
88. #14519710C2×C4semidirect
91. #14519702C2×C4semidirect
94. #14519687C2×C4semidirect
370. C61#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#168398592
#214484662
#214481802
#214464592
#214464542
#214464082
#214463932
#214461532
#214461512
#214460822
#214457182
#214456382
#102×Dic612
#214455692
C61×#18622
#2112561