Finite Group Databasebeta

← #29699897

Subgroups — #29699897

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×#16839862C211yesmaximal, characteristic
2#21448782C211yesmaximal, characteristic, complemented
3#21446699C211yesmaximal, characteristic
4#21446672C211yesmaximal, characteristic
5#21446460C211yesmaximal, characteristic, complemented
6#21446453C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic
8#21446436C211yesmaximal, characteristic
9#21445985C211yesmaximal, characteristic, complemented
10#21445829C211yesmaximal, characteristic
11#21445821C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519710C211yesmaximal, characteristic, complemented
14#21445694C211yesmaximal, characteristic, complemented
15C61×#2354C211yesmaximal, 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#16839643—21no—
37#16839643—21no—
38#16839629—21no—
39#16839628C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839607—21no—
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C2×#117×C61—21no—
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#388—21no—
54C61×#388—21no—
55C61×#384C2211yescharacteristic
56C61×#380—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
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⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61—21no—
77#14519710—22no—
78#14519710—41no—
79#14519710C2×C414yes—
80#14519708—22no—
81#14519708—41no—
82C4⋊#92418—22no—
83#14519700—41no—
84#14519700—41no—
85#14519700C2×C414yes—
86#14519698—41no—
87#14519698—41no—
88#14519698C2×C414yes—
89#14519688—22no—
90#14519688C2×C414yes—
91C4×#92418—22no—
92#14519684—21no—
93#14519684—21no—
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—
104#117×C61—44no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D411yescharacteristic
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
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—24no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—42no—
138C22×C4×C61—42no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C412yes—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—42no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61C22×C412yes—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—42no—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—81no—
170C22⋊C4×C61—81no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—42no—
176C42×C61—42no—
177C42×C61C22×C412yes—
178C42×C61#4112yes—
179#11758200—28no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C412yes—
186#11758196—24no—
187C4×Dic61—24no—
188C4×Dic61—42no—
189C4×Dic61—42no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C412yes—
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—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
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—48no—
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—41no—
238C2×C4×C61—41no—
239C2×C4×C61C4×D412yes—
240C2×C4×C61C4×D412yes—
241C2×C4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61C23×C411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C2×Dic61—22no—
249C2×Dic61—22no—
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—41no—
260Dic122—22no—
261Dic122—22no—
262Dic122—41no—
263Dic122—41no—
264#92418—22no—
265#92418—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—22no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—42no—
290C4×C61—81no—
291C4×C61—81no—
292C4×C61C2×#11711yescharacteristic
293C4×C61#52011yescharacteristic
294C4×C61#55511yescharacteristic
295C4×C61#55611yescharacteristic
296Dic61—42no—
297Dic61—42no—
298Dic61—81no—
299Dic61—81no—
300C2×#440—611no—
301#2356—611no—
302#2354D6111yescharacteristic
303#1973—611no—
304#1968—611no—
305#1928—611no—
306#1927—611no—
307#1926—611no—
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×D4C2×D6111yescharacteristic
326C2×#117—21no—
327#440—618no—
328C2×#107—611no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#106—611no—
332C2×#106—611no—
333C2×C4⋊C8—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#97—611no—
341C2×#97—611no—
342C2×C4×C8—611no—
343#391—611no—
344#391—611no—
345#390C2×D6111yescharacteristic
346#390C2×D6111yescharacteristic
347#388—21no—
348#388—21no—
349#387—1221no—
350#387—1221no—
351#384C2×D6111yescharacteristic
352#383—1221no—
353#382—611no—
354#380—21no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4C2×D6111yescharacteristic
358C4×C4⋊C4C2×D6111yescharacteristic
359C4×C4⋊C4C2×D6111yescharacteristic
360#376—1221no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#336—611no—
366#336—611no—
367C61#2282011yescharacteristic, complemented, Sylow
368C22×Q8—611no—
369C22×D4C22×D6111yescharacteristic
370C23×C4—21no—
371C2×SD16—614no—
372C2×SD16—1222no—
373C2×SD16—1222no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C4×Q8—614no—
379C4×Q8—1222no—
380C4×D4—22no—
381C4×D4C4×D6114yes—
382#117—44no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4C22⋊D6111yescharacteristic
390C2×C4⋊C4C22⋊D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42—1221no—
404C2×C42C22×D6111yescharacteristic
405C2×C42C22×D6111yescharacteristic
406C2×C42C22×D6111yescharacteristic
407#107—614no—
408#107—1222no—
409#107—2441no—
410#106—1222no—
411#106—2441no—
412C4⋊C8—1222no—
413#103—614no—
414#103—2441no—
415#103—2441no—
416#102—614no—
417#102—2441no—
418#102—2441no—
419#97—614no—
420#97—1222no—
421C4×C8—1222no—
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#95—1221no—
431#95—1221no—
432#95C22⋊D6111yescharacteristic
433#95C22⋊D6111yescharacteristic
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—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
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—612no—
468C2×C8—612no—
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—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—612no—
487C4⋊C4—1221no—
488C4⋊C4—1224no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4C2×C4×D6112yes—
494C22⋊C4—24no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C42—42no—
505C42—1224no—
506C42—2442no—
507C42—2442no—
508C42C2×C4×D6112yes—
509C42#1175822212yes—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×C22⋊D6111yescharacteristic
518Q8—1222no—
519Q8—1222no—
520Q8—2441no—
521Q8—2441no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
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—48no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—1222no—
552C2×C4—1222no—
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×C4—2441no—
562C2×C4—2441no—
563C2×C4C4×C22⋊D6112yes—
564C2×C4C4×C22⋊D6112yes—
565C2×C4#1451980312yes—
566C2×C4C22×C4×D6111yescharacteristic
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6111yescharacteristic
569C2×C4C2×#1175822211yescharacteristic
570C2×C4#1451982311yescharacteristic
571C2×C4#1451982411yescharacteristic
572C8—614no—
573C8—1222no—
574C8—2441no—
575C8—2441no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C4×C22⋊D6111yescharacteristic
584C22#1684041111yescharacteristic
585C22#1684043111yescharacteristic
586C22C2×#1451980311yescharacteristic
587C22#1684056011yescharacteristic
588C22#1684057311yescharacteristic
589C22#1684057711yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—4881no—
600C4—4881no—
601C4—2442no—
602C4—2442no—
603C4#117×D6111yescharacteristic
604C4#1684024211yescharacteristic
605C4#1684047511yescharacteristic
606C4#1684048011yescharacteristic
607C2—82no—
608C2#2144876911yescharacteristic
609C2C4×#1451980311yescharacteristic
610C2#2145465811yescharacteristic
611C2#2145825311yescharacteristic
612C2#2145833411yescharacteristic
613C2#2145883511yescharacteristic
614C2#2145889411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#2354D61
hypocenterC61#22820
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #21448782C2semidirect
5. #21446460C2semidirect
6. #21446453C2semidirect
9. #21445985C2semidirect
11. #21445821C2semidirect
12. #21445717C2semidirect
13. C4×#14519710C2semidirect
14. #21445694C2semidirect
18. #16839862C4semidirect
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×#168398622
#214487822
#214466992
#214466722
#214464602
#214464532
#214464432
#214464362
#214459852
#214458292
#214458212
#214457172
C4×#145197102
#214456942
C61×#23542
#2282061