Finite Group Databasebeta

← #29699878

Subgroups — #29699878

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839862C211yesmaximal, characteristic
2#21448774C211yesmaximal, characteristic, complemented
3#21446699C211yesmaximal, characteristic
4#21446672C211yesmaximal, characteristic
5#21446460C211yesmaximal, characteristic, complemented
6#21446453C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic
8#21446436C211yesmaximal, characteristic
9#21445988C211yesmaximal, characteristic, complemented
10#21445831C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519710C211yesmaximal, characteristic, complemented
14#21445694C211yesmaximal, characteristic, complemented
15C61×#2357C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18#16839862C418yescomplemented
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839668C2211yescharacteristic
36#16839649—21no—
37#16839649—21no—
38#16839632C2211yescharacteristic
39#16839627—21no—
40C4⋊C4×Dic61—21no—
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#382C2211yescharacteristic
55C61×#381—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C22⋊C4×C61—21no—
60C22×Dic122C2311yescharacteristic
61C2×#11758200—22no—
62C2×#11758200—22no—
63C2×#11758200C2×C414yes—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×Dic122—22no—
69C4×Dic122C2×C414yes—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79#14519710—22no—
80#14519710—41no—
81#14519710C2×C414yes—
82#14519708—22no—
83#14519708—41no—
84C4⋊#92418—22no—
85#14519700—41no—
86#14519700—41no—
87#14519700C2×C414yes—
88#14519698—41no—
89#14519698—41no—
90#14519698C2×C414yes—
91#14519688—22no—
92#14519688C2×C414yes—
93C4×#92418—22no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
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×C61D411yescharacteristic
105C2×C4⋊C4×C61D411yescharacteristic
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×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
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×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122C22×C412yes—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61C22×C412yes—
163C22⋊C4×C61—24no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61—42no—
166C22⋊C4×C61—81no—
167C22⋊C4×C61—81no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—81no—
173C42×C61—81no—
174C42×C61C22×C412yes—
175C42×C61#4112yes—
176#11758200—28no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—42no—
183C4⋊Dic61—81no—
184C4⋊Dic61C22×C412yes—
185#11758196—24no—
186C4×Dic61—24no—
187C4×Dic61—81no—
188C4×Dic61—81no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C22×C412yes—
198C2×#92418C22×C412yes—
199C2×#92418#4112yes—
200C2×#92418#4112yes—
201C23×C61—22no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61C22×D411yescharacteristic
209D4×C61—22no—
210D4×C61—22no—
211D4×C61—41no—
212D4×C61—41no—
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—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—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—84no—
238C2×C4×C61C4×D412yes—
239C2×C4×C61C4×D412yes—
240C2×C4×C61#13712yes—
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—22no—
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×Dic61—41no—
258C2×Dic61—41no—
259Dic122—22no—
260Dic122—22no—
261Dic122—41no—
262Dic122—41no—
263#92418—22no—
264#92418—41no—
265#92418—41no—
266#92418#11714yes—
267#22819—611nomaximal, Sylow
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—81no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61C2×C4×D411yescharacteristic
276C22×C61#54711yescharacteristic
277C22×C61#55011yescharacteristic
278C22×C61C2×#13711yescharacteristic
279C22×C61#57511yescharacteristic
280C22×C61#57611yescharacteristic
281C22×C61#57711yescharacteristic
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—42no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61C2×#11711yescharacteristic
292C4×C61#52011yescharacteristic
293C4×C61#55511yescharacteristic
294C4×C61#55611yescharacteristic
295Dic61—42no—
296Dic61—42no—
297Dic61—81no—
298Dic61—81no—
299C2×#440—611no—
300#2357D6111yescharacteristic
301#2355—611no—
302#1973—611no—
303#1968—611no—
304#1928—611no—
305#1927—611no—
306#1926—611no—
307#1925—611no—
308#1847—611no—
309#1805—611no—
310#1802—611no—
311#1776—611no—
312C4×#107—611no—
313#1771—611no—
314C2×C61—82no—
315C2×C61#235411yescharacteristic
316C2×C61C4×#13711yescharacteristic
317C2×C61#294611yescharacteristic
318C2×C61#334611yescharacteristic
319C2×C61#335011yescharacteristic
320C2×C61#340011yescharacteristic
321C2×C61#340311yescharacteristic
322C22×SD16—611no—
323C2×C4×Q8—611no—
324C2×C4×D4C2×D6111yescharacteristic
325#440—618no—
326C2×#107—611no—
327C2×#107—611no—
328C2×#107—611no—
329C2×#106—611no—
330C2×#106—611no—
331C2×C4⋊C8—611no—
332C2×#103—611no—
333C2×#103—611no—
334C2×#103—611no—
335C2×#102—611no—
336C2×#102—611no—
337C2×#102—611no—
338C2×#97—611no—
339C2×#97—611no—
340C2×C4×C8—611no—
341#391—611no—
342#391—611no—
343#390C2×D6111yescharacteristic
344#390C2×D6111yescharacteristic
345#388—21no—
346#388—21no—
347#387—1221no—
348#387—1221no—
349#384—611no—
350#382—1221no—
351#382C2×D6111yescharacteristic
352#381—21no—
353C4×C4⋊C4—611no—
354C4×C4⋊C4—611no—
355C4×C4⋊C4—1221no—
356C4×C4⋊C4C2×D6111yescharacteristic
357C4×C4⋊C4C2×D6111yescharacteristic
358C4×C4⋊C4C2×D6111yescharacteristic
359C4×C22⋊C4—21no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#336—611no—
365#336—611no—
366C61#2281911yescharacteristic, complemented, Sylow
367C22×Q8—611no—
368C22×D4C22×D6111yescharacteristic
369C23×C4—21no—
370C2×SD16—614no—
371C2×SD16—1222no—
372C2×SD16—1222no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C4×Q8—614no—
378C4×Q8—1222no—
379C4×D4—22no—
380C4×D4C4×D6114yes—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4C22⋊D6111yescharacteristic
388C2×C4⋊C4C22⋊D6111yescharacteristic
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—1221no—
400C2×C42—1221no—
401C2×C42—1221no—
402C2×C42C22×D6111yescharacteristic
403C2×C42C22×D6111yescharacteristic
404C2×C42C22×D6111yescharacteristic
405#107—614no—
406#107—1222no—
407#107—2441no—
408#106—1222no—
409#106—2441no—
410C4⋊C8—1222no—
411#103—614no—
412#103—2441no—
413#103—2441no—
414#102—614no—
415#102—2441no—
416#102—2441no—
417#97—614no—
418#97—1222no—
419C4×C8—1222no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95C22⋊D6111yescharacteristic
431#95C22⋊D6111yescharacteristic
432C24—21no—
433C2×Q8—612no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×C4×D6112yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460C22×C4C2×C22⋊D6111yescharacteristic
461C22×C4C23×D6111yescharacteristic
462SD16—1228no—
463C2×C8—612no—
464C2×C8—612no—
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—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—612no—
483C4⋊C4—1221no—
484C4⋊C4—1224no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—4881no—
490C4⋊C4—2442no—
491C4⋊C4C2×C4×D6112yes—
492C22⋊C4—24no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—81no—
502C42—81no—
503C42—1224no—
504C42—4881no—
505C42—4881no—
506C42C2×C4×D6112yes—
507C42#1175822212yes—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D6111yescharacteristic
516Q8—1222no—
517Q8—1222no—
518Q8—2441no—
519Q8—2441no—
520D4—22no—
521D4—22no—
522D4—41no—
523D4—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4C4×C22⋊D6112yes—
562C2×C4C4×C22⋊D6112yes—
563C2×C4#1451980712yes—
564C2×C4C22×C4×D6111yescharacteristic
565C2×C4#41×D6111yescharacteristic
566C2×C4#41×D6111yescharacteristic
567C2×C4C2×#1175822211yescharacteristic
568C2×C4#1451982311yescharacteristic
569C2×C4#1451982411yescharacteristic
570C8—614no—
571C8—1222no—
572C8—2441no—
573C8—2441no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×C4×C22⋊D6111yescharacteristic
582C22#1684041111yescharacteristic
583C22#1684043111yescharacteristic
584C22C2×#1451980711yescharacteristic
585C22#1684056011yescharacteristic
586C22#1684056511yescharacteristic
587C22#1684057311yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—4881no—
598C4—4881no—
599C4—2442no—
600C4—2442no—
601C4#117×D6111yescharacteristic
602C4#1684024211yescharacteristic
603C4#1684047511yescharacteristic
604C4#1684048011yescharacteristic
605C2—82no—
606C2#2144876911yescharacteristic
607C2C4×#1451980711yescharacteristic
608C2#2145465111yescharacteristic
609C2#2145830411yescharacteristic
610C2#2145835811yescharacteristic
611C2#2145887211yescharacteristic
612C2#2145890311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2357C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#2357D61
hypocenterC61#22819
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #21448774C2semidirect
5. #21446460C2semidirect
6. #21446453C2semidirect
9. #21445988C2semidirect
10. #21445831C2semidirect
12. #21445717C2semidirect
13. C4×#14519710C2semidirect
14. #21445694C2semidirect
18. #16839862C4semidirect
366. C61#22819semidirect

Maximal subgroups

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

subgroupindex
C2×#168398622
#214487742
#214466992
#214466722
#214464602
#214464532
#214464432
#214464362
#214459882
#214458312
#214458192
#214457172
C4×#145197102
#214456942
C61×#23572
#2281961