Finite Group Databasebeta

← #29836868

Subgroups — #29836868

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458216C211yesmaximal, characteristic, complemented
2#21457507C211yesmaximal, characteristic, complemented
3#21448049C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21448007C211yesmaximal, characteristic, complemented
6#21447979C211yesmaximal, characteristic, complemented
7#21447914C211yesmaximal, characteristic, complemented
8#21447872C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447729C211yesmaximal, characteristic, complemented
11#21447663C211yesmaximal, characteristic, complemented
12C16×C22⋊D61C211yesmaximal, characteristic, complemented
13#21447527C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2215C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840459—21no—
19#16840409—21no—
20C2×#14519721C2211yescharacteristic, complemented
21C2×#14519718C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840163C2211yescharacteristic, complemented
24#16840145C2211yescharacteristic
25#16840083—21no—
26#16840079—21no—
27#16840064—21no—
28#16840004C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839976—21no—
31#16839914—21no—
32#16839905—21no—
33D8×Dic61C2211yescharacteristic, complemented
34#16839844C2211yescharacteristic
35C8×C22⋊D61C2211yescharacteristic
36#16839800C2211yescharacteristic, complemented
37#107×D61C2211yescharacteristic
38#16839589C2211yescharacteristic, complemented
39#16839587C2211yescharacteristic, complemented
40#16839580C2211yescharacteristic, complemented
41#16839567C2211yescharacteristic, complemented
42#16839567C2211yescharacteristic, complemented
43#16839565C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic, complemented
52C2×D16×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic, complemented
54C61×#466C2211yescharacteristic
55C61×#466C2211yescharacteristic, complemented
56C61×#366C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic, complemented
59C2×#11758222—21no—
60C2×D4×D61—21no—
61#14519799—22no—
62#14519799—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×#11758200—21no—
66C2×D488C2311yescharacteristic
67C2×#11758199—21no—
68D8×D61—22no—
69D8×D61—41no—
70C2×C8×D61C2311yescharacteristic
71#14519770—41no—
72#14519768—21no—
73#14519764—21no—
74#14519759—41no—
75#14519758—41no—
76#14519757—21no—
77#14519748—21no—
78#14519748—41no—
79#14519748—41no—
80#14519745—41no—
81D4×Dic61—21no—
82#14519739—21no—
83C4×C22⋊D61D411yescharacteristic
84#14519737—41no—
85#14519736—21no—
86C4⋊C4×D61—21no—
87C22⋊C4×D61—41no—
88#14519721—41no—
89#14519718—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92C16×D61—41no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519710—21no—
96#14519709—21no—
97#14519708—21no—
98#14519706D411yescharacteristic
99#14519700—21no—
100#14519698—21no—
101#14519698—21no—
102#14519697—21no—
103C22⋊#92418D411yescharacteristic
104#14519689D411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C2×D8×C61C2311yescharacteristic
107C2×D8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109#121×C61—21no—
110#121×C61—21no—
111D16×C61—41no—
112C2×C16×C61—41no—
113C2×C16×C61C2311yescharacteristic
114C2×C16×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#102×C61—21no—
118#102×C61—21no—
119C23×D61—41no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—41no—
123C2×D4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61D811yescharacteristic
129C22×Dic61—41no—
130D4×D61—42no—
131D4×D61—81no—
132#11758222—42no—
133#11758222—81no—
134C2×D244—21no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61C2×D411yescharacteristic
139C2×Dic122—21no—
140D8×C61—21no—
141D8×C61—21no—
142D8×C61—21no—
143D8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊Dic61—41no—
153C22⋊Dic61—41no—
154C22⋊Dic61—41no—
155C22⋊Dic61—41no—
156C22⋊Dic61—41no—
157C22⋊Dic61D811yescharacteristic
158#11758200—81no—
159#11758199—42no—
160#11758198—41no—
161#11758198—41no—
162#11758198D811yescharacteristic
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167#11758196—41no—
168#11758196—41no—
169#11758196D811yescharacteristic
170C4×Dic61—41no—
171C4×Dic61C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174Dic244—21no—
175Dic244—21no—
176D488—21no—
177D488#4112yes—
178#11758190—42no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61—82no—
190C22×D61—82no—
191C22×D61—161no—
192C22×D61C2×D811yescharacteristic
193D4×C61—41no—
194D4×C61—41no—
195D4×C61—41no—
196D4×C61—41no—
197D4×C61—161no—
198D4×C61—161no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C22⋊D61—22no—
206C22⋊D61—82no—
207C22⋊D61—82no—
208C22⋊D61—82no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—161no—
213C2×Dic61C2×D811yescharacteristic
214C2×Dic61C2×D811yescharacteristic
215C2×Dic61C2×D811yescharacteristic
216D244—22no—
217D244—41no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—82no—
221C4×D61—161no—
222C4×D61—161no—
223Dic122—41no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33864—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C22×D811yescharacteristic
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—42no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—164no—
247C2×D61#50812yes—
248C4×C61—21no—
249C4×C61—81no—
250C4×C61—81no—
251C4×C61#54611yescharacteristic
252C4×C61#57711yescharacteristic
253Dic61—21no—
254Dic61—21no—
255Dic61—21no—
256Dic61—81no—
257Dic61—81no—
258Dic61—81no—
259#3339—611no—
260#3280—611no—
261#2242—611no—
262#2236—611no—
263#2234—611no—
264#2228—611no—
265#2217—611no—
266#2215D6111yescharacteristic, complemented
267#2210—611no—
268#2186—611no—
269#2184—611no—
270C4×D16—611no—
271D4×C16—611no—
272#2138—611no—
273C2×#357—611no—
274C2×C61—41no—
275C2×C61—161no—
276C2×C61—161no—
277C2×C61#329411yescharacteristic
278C2×C61C2×#50811yescharacteristic
279C2×C61#341511yescharacteristic
280D61—22no—
281D61—82no—
282C2×#135—611no—
283C22×D8—611no—
284#553—1221no—
285#546—1221no—
286C2×SD32—611no—
287C2×D16—611no—
288C2×D16C2×D6111yescharacteristic
289C22×C16—611no—
290C22×C16C2×D6111yescharacteristic, complemented
291#499—611no—
292#495—611no—
293#482—1221no—
294#481—1221no—
295#478—1221no—
296#467—611no—
297#466—611no—
298#466C2×D6111yescharacteristic
299#466C2×D6111yescharacteristic, complemented
300#463—1221no—
301#450—1221no—
302#449—1221no—
303C4×D8—611no—
304C4×D8—611no—
305C8×D4—611no—
306#427—611no—
307C2×#107—611no—
308#367—611no—
309#366—611no—
310#366C2×D6111yescharacteristic, complemented
311C4⋊C16—611no—
312#358—611no—
313#358—611no—
314#358—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357C2×D6111yescharacteristic
321#357C2×D6111yescharacteristic, complemented
322C22⋊C16—611no—
323C22⋊C16—611no—
324C4×C16—611no—
325C61#3386411yescharacteristic, complemented, Sylow
326C2×#41—1221no—
327C22×D4—1221no—
328#135—1222no—
329#135—2441no—
330C2×Q16—611no—
331C2×SD16—1221no—
332C2×SD16—1221no—
333C2×D8—611no—
334C2×D8—1221no—
335C2×D8—1222no—
336C2×D8—2441no—
337C2×D8C22×D6111yescharacteristic
338C2×D8C22×D6111yescharacteristic
339C22×C8—611no—
340C22×C8C22×D6111yescharacteristic
341#126—2441no—
342#125—1221no—
343#124—1221no—
344#123—2441no—
345#123—2441no—
346C22⋊Q8—1221no—
347#121—21no—
348#121—21no—
349#121—1221no—
350#121—2441no—
351#121—2441no—
352#120—2441no—
353C4×D4—611no—
354C4×D4—1221no—
355C4×D4—1221no—
356C4×D4—2441no—
357#117—1221no—
358C2×C4⋊C4—1221no—
359C2×C22⋊C4—2441no—
360SD32—2441no—
361D16—41no—
362D16—1222no—
363C2×C16—41no—
364C2×C16—611no—
365C2×C16—611no—
366C2×C16—2441no—
367C2×C16C22×D6111yescharacteristic
368C2×C16C22×D6111yescharacteristic
369#107—611no—
370#107—611no—
371#107—1221no—
372#107C22×D6111yescharacteristic
373#107C22×D6111yescharacteristic
374#106—1221no—
375#106—1221no—
376C4⋊C8—611no—
377#103—1221no—
378#102—21no—
379#102—21no—
380#102—1221no—
381#102—1221no—
382#102—1221no—
383C22⋊C8—611no—
384C22⋊C8—611no—
385C4×C8—611no—
386C24—2441no—
387#41—4881no—
388#41—2442no—
389C2×Q8—1221no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—611no—
395C2×D4—1221no—
396C2×D4—4881no—
397C2×D4—2441no—
398C2×D4—2442no—
399C2×D4—2441no—
400C2×D4—2441no—
401C22×C4—611no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4D4×D6111yescharacteristic
407Q16—1221no—
408Q16—1221no—
409SD16—4881no—
410SD16—2442no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—612no—
416D8—1221no—
417D8—2442no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—611no—
421C2×C8—611no—
422C2×C8—1221no—
423C2×C8—1221no—
424C2×C8D4×D6111yescharacteristic
425C2×C8C23×D6111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—611no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—611no—
438C22⋊C4—611no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C22⋊C4—2441no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C42—611no—
447C42—2441no—
448C16—21no—
449C16—21no—
450C16—1221no—
451C16—1221no—
452C23—41no—
453C23—41no—
454C23—611no—
455C23—9761no—
456C23—4882no—
457C23—4882no—
458C23—2441no—
459C23D8×D6111yescharacteristic
460Q8—2441no—
461Q8—2441no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—161no—
467D4—161no—
468D4—1222no—
469D4—1222no—
470D4—4882no—
471D4—4882no—
472D4—4882no—
473D4—2441no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—9761no—
484C2×C4—9761no—
485C2×C4—9761no—
486C2×C4—4882no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4D8×D6111yescharacteristic
491C2×C4C2×D4×D6111yescharacteristic
492C8—21no—
493C8—1221no—
494C8—1221no—
495C8#41×D6111yescharacteristic
496C8#1451982211yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—612no—
507C22—1221no—
508C22—1221no—
509C22—9764no—
510C22—4881no—
511C22—4881no—
512C22—2442no—
513C22C2×D8×D6111yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—1221no—
518C4—1221no—
519C4—1221no—
520C4—4881no—
521C4—4881no—
522C4—4881no—
523C4#1684040111yescharacteristic
524C4#1684056911yescharacteristic
525C2—41no—
526C2—161no—
527C2—161no—
528C2—1222no—
529C2—4882no—
530C2#2145762711yescharacteristic
531C2#508×D6111yescharacteristic
532C2#2145895611yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2215C2
socleC22×C61C22×D8
hypercenter#2215D61
hypocenterC61#33864
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #21458216C2semidirect
2. #21457507C2semidirect
3. #21448049C2semidirect
4. #21448023C2semidirect
5. #21448007C2semidirect
6. #21447979C2semidirect
7. #21447914C2semidirect
8. #21447872C2semidirect
9. #21447740C2semidirect
10. #21447729C2semidirect
11. #21447663C2semidirect
12. C16×C22⋊D61C2semidirect
13. #21447527C2semidirect
14. #357×D61C2semidirect
15. C61×#2215C2semidirect
20. C2×#14519721C22semidirect
23. #16840163C22semidirect
33. D8×Dic61C22semidirect
36. #16839800C22semidirect
38. #16839589C22semidirect
39. #16839587C22semidirect
40. #16839580C22semidirect
41. #16839567C22semidirect
42. #16839567C22semidirect
43. #16839565C22semidirect
49. C22⋊#11758185C22semidirect
51. C16×Dic61C22semidirect
53. C22×C16×C61C22semidirect
55. C61×#466C22semidirect
56. C61×#366C22semidirect
58. C61×#357C22semidirect
266. #2215D61semidirect
290. C22×C16C2×D61semidirect
299. #466C2×D61semidirect
310. #366C2×D61semidirect
321. #357C2×D61semidirect
325. C61#33864semidirect

Maximal subgroups

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

subgroupindex
#214582162
#214575072
#214480492
#214480232
#214480072
#214479792
#214479142
#214478722
#214477402
#214477292
#214476632
C16×C22⋊D612
#214475272
#357×D612
C61×#22152
#3386461