Finite Group Databasebeta

← #29684347

Subgroups — #29684347

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839865C211yesmaximal, characteristic
2#21448294C211yesmaximal, characteristic, complemented
3#21448277C211yesmaximal, characteristic
4#21446697C211yesmaximal, characteristic
5#21446676C211yesmaximal, characteristic
6#21446556C211yesmaximal, characteristic, complemented
7#21446549C211yesmaximal, characteristic, complemented
8#21446514C211yesmaximal, characteristic
9#21446511C211yesmaximal, characteristic, complemented
10#21446502C211yesmaximal, characteristic
11#21445715C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic
14C4×#14519687C211yesmaximal, characteristic, complemented
15C61×#1933C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519735—21no—
20#16839865C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839654—21no—
40#16839652—21no—
41#16839647—21no—
42#16839645—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45#16839613—21no—
46#16839609—21no—
47#16839607—21no—
48C42×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758201—22no—
63C2×#11758201—22no—
64C2×#11758201C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67Q8×Dic61—22no—
68Q8×Dic61C2×C414yes—
69#14519739—22no—
70#14519739C2×C414yes—
71#14519735—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519710—22no—
94#14519710C2×C414yes—
95#14519708—22no—
96#14519701—22no—
97#14519699—22no—
98#14519699C2×C414yes—
99#14519697—22no—
100#14519687—22no—
101#14519687—22no—
102#14519687—22no—
103#14519687C2×C414yes—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×Q8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#103×C61—22no—
121#103×C61C2×C414yes—
122C4×C8×C61—22no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244C22×C412yes—
153C2×C4×D61—24no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C412yes—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61C22×C412yes—
169C42×C61—21no—
170C42×C61—21no—
171#11758201—28no—
172#11758198—24no—
173#11758198—42no—
174#11758198—42no—
175#11758198—42no—
176#11758198—42no—
177C4⋊Dic61—21no—
178C4⋊Dic61—24no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—42no—
184C4⋊Dic61C22×C412yes—
185#11758196—42no—
186#11758196—42no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—24no—
192C4×Dic61—41no—
193C4×Dic61—41no—
194C4×Dic61—42no—
195C4×Dic61—42no—
196C4×Dic61C22×C412yes—
197C4×Dic61#4112yes—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C22×C412yes—
201C2×#92418#4112yes—
202C2×#92418#4112yes—
203C2×#92418#4112yes—
204C23×C61C22×D411yescharacteristic
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212Q8×C61—22no—
213Q8×C61—22no—
214Q8×C61—41no—
215Q8×C61—41no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
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×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61AGL(1,ℤ/8)12yes—
233C2×C4×C61#13712yes—
234C2×C4×C61C23×C411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
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×Dic61C4×D412yes—
260C2×Dic61C4×D412yes—
261D244—22no—
262D244—22no—
263D244—41no—
264D244—41no—
265C4×D61—48no—
266C8×C61—22no—
267C8×C61—22no—
268#92418—22no—
269#92418#11714yescomplemented
270#21288—611nomaximal, Sylow
271C22×C61C2×C4×D411yescharacteristic
272C22×C61#53211yescharacteristic
273C22×C61#53211yescharacteristic
274C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C61C2×#13711yescharacteristic
276C22×C61#57511yescharacteristic
277C22×C61#57511yescharacteristic
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C2×D61—81no—
285C4×C61—22no—
286C4×C61—22no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61C2×#11711yescharacteristic
292C4×C61C4×#4111yescharacteristic
293C4×C61#52911yescharacteristic
294C4×C61#52911yescharacteristic
295Dic61—22no—
296Dic61—22no—
297Dic61—41no—
298Dic61—41no—
299Dic61—42no—
300Dic61—81no—
301Dic61—81no—
302C2×#440—611no—
303#2295—611no—
304#2293—611no—
305#1973—611no—
306#1968—611no—
307#1943—611no—
308#1942—611no—
309#1936—611no—
310#1935—611no—
311#1934—611no—
312#1933D6111yescharacteristic, complemented
313#1776—611no—
314#1763—611no—
315#1762—611no—
316C4×#97—611no—
317C2×C61#229311yescharacteristic
318C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C61C4×#13711yescharacteristic
320C2×C61#318011yescharacteristic
321C2×C61#318111yescharacteristic
322C2×C61#318211yescharacteristic
323C2×C61#318311yescharacteristic
324D61—82no—
325C22×SD16—611no—
326C2×C4×Q8—611no—
327C2×C4×D4—611no—
328C2×#117—1221no—
329#440—618no—
330C2×#107—611no—
331C2×#107—611no—
332C2×#106—611no—
333C2×#103—611no—
334C2×#103C2×D6111yescharacteristic
335C2×#103C2×D6111yescharacteristic
336C2×#102—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#97—611no—
340C2×#97—611no—
341C2×#97—611no—
342C2×#97—611no—
343C2×C4×C8—611no—
344C2×C4×C8C2×D6111yescharacteristic
345#391—611no—
346#391C2×D6111yescharacteristic
347#390—611no—
348#390—611no—
349#389—611no—
350#389—611no—
351#389—611no—
352#389C2×D6111yescharacteristic
353#388—1221no—
354#388—1221no—
355#387—1221no—
356#387—1221no—
357C4×C4⋊C4—611no—
358C4×C4⋊C4—611no—
359C4×C4⋊C4—1221no—
360C4×C22⋊C4—1221no—
361#376—1221no—
362C43—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340C2×D6111yescharacteristic
368#340C2×D6111yescharacteristic
369C61#2128811yescharacteristic, complemented, Sylow
370C22×Q8C22×D6111yescharacteristic
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—614no—
374C2×SD16—1222no—
375C2×SD16—1222no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C4×Q8—614no—
381C4×Q8—1222no—
382C4×D4—614no—
383C4×D4—1222no—
384#117—2444no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—1221no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42C22×D6111yescharacteristic
411#107—614no—
412#107—1222no—
413#106—1222no—
414#103—22no—
415#103—1222no—
416#103C4×D6114yes—
417#102—614no—
418#102—1222no—
419#102—1222no—
420#97—614no—
421#97—1222no—
422#97—1222no—
423#97—1222no—
424C4×C8—22no—
425C4×C8—1222no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436C24—1221no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D6112yes—
443C2×D4—612no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1224no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4C23×D6111yescharacteristic
466SD16—1228no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—612no—
472C2×C8—612no—
473C2×C8—612no—
474C2×C8—612no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8C2×C4×D6112yes—
478C2×C8#1175822412yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—612no—
486C4⋊C4—1224no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2442no—
493C4⋊C4—2442no—
494C4⋊C4—2442no—
495C4⋊C4C2×C4×D6112yes—
496C22⋊C4—1224no—
497C22⋊C4—2442no—
498C22⋊C4—2442no—
499C22⋊C4—2442no—
500C22⋊C4—2442no—
501C42—21no—
502C42—21no—
503C42—612no—
504C42—612no—
505C42—1224no—
506C42—1222no—
507C42—1221no—
508C42—1221no—
509C42—1222no—
510C42—2441no—
511C42—2441no—
512C42—2442no—
513C42—2442no—
514C23—1222no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23C2×D4×D6111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—1222no—
527D4—1222no—
528D4—2441no—
529D4—2441no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—2448no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4#1451980412yes—
569C2×C4#1451980912yes—
570C2×C4C22×C4×D6111yescharacteristic
571C2×C4#41×D6111yescharacteristic
572C2×C4#41×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4C2×#1175822411yescharacteristic
576C8—22no—
577C8—22no—
578C8—614no—
579C8—1222no—
580C22—4881no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22C4×D4×D6111yescharacteristic
588C22#1684030711yescharacteristic
589C22#1684031111yescharacteristic
590C22C2×#1451980411yescharacteristic
591C22C2×#1451980911yescharacteristic
592C22#1684055911yescharacteristic
593C22#1684055911yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—1222no—
601C4—1222no—
602C4—4881no—
603C4—4881no—
604C4—2442no—
605C4—2441no—
606C4—2441no—
607C4#117×D6111yescharacteristic
608C4C4×#1175822411yescharacteristic
609C4#1684028911yescharacteristic
610C4#1684029511yescharacteristic
611C2—4882no—
612C2#2144827911yescharacteristic
613C2C4×#1451980411yescharacteristic
614C2C4×#1451980911yescharacteristic
615C2#2145651011yescharacteristic
616C2#2145652311yescharacteristic
617C2#2145654011yescharacteristic
618C2#2145654711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1933C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1933D61
hypocenterC61#21288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. #21448294C2semidirect
6. #21446556C2semidirect
7. #21446549C2semidirect
9. #21446511C2semidirect
11. #21445715C2semidirect
12. #21445651C2semidirect
14. C4×#14519687C2semidirect
15. C61×#1933C2semidirect
20. #16839865C4semidirect
269. #92418#117semidirect
312. #1933D61semidirect
369. C61#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#168398652
#214482942
#214482772
#214466972
#214466762
#214465562
#214465492
#214465142
#214465112
#214465022
#214457152
#214456512
#214456432
C4×#145196872
C61×#19332
#2128861