Finite Group Databasebeta

← #29836880

Subgroups — #29836880

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#21458223C211yesmaximal, characteristic, complemented
2#21457503C211yesmaximal, characteristic, complemented
3#21448050C211yesmaximal, characteristic, complemented
4#21448020C211yesmaximal, characteristic, complemented
5#21448009C211yesmaximal, characteristic, complemented
6#21447977C211yesmaximal, characteristic, complemented
7#21447912C211yesmaximal, characteristic, complemented
8#21447902C211yesmaximal, characteristic, complemented
9#21447741C211yesmaximal, characteristic, complemented
10#21447729C211yesmaximal, characteristic, complemented
11C4×#14519718C211yesmaximal, characteristic, complemented
12#21447638C211yesmaximal, characteristic, complemented
13#21447525C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2210C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840462—21no—
19#16840405—21no—
20C2×#14519718C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic, complemented
23#16840164C2211yescharacteristic, complemented
24#16840085—21no—
25#16840079—21no—
26#16840062—21no—
27#16840000C2211yescharacteristic
28#16839995C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839995C2211yescharacteristic, complemented
31#16839974—21no—
32#16839911—21no—
33#16839906—21no—
34C4×D488C2211yescharacteristic
35C8×D244C2211yescharacteristic
36#16839799C2211yescharacteristic, complemented
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic, complemented
39#16839588C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839566C2211yescharacteristic, complemented
42#16839566C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic, complemented
48#16839562C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic, complemented
51C4×#11758185C2211yescharacteristic, complemented
52C2×SD32×C61C2211yescharacteristic, complemented
53C2×D16×C61C2211yescharacteristic
54C61×#495C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic, complemented
56C61×C4⋊C16C2211yescharacteristic, complemented
57C61×#358C2211yescharacteristic, complemented
58C61×#357C2211yescharacteristic
59C2×#11758226—21no—
60C2×D4×D61—21no—
61#14519800—22no—
62#14519800—41no—
63C2×#11758201—21no—
64C2×D488C2311yescharacteristic
65C2×#11758199—21no—
66D8×D61—22no—
67D8×D61—41no—
68C2×C8×D61C2311yescharacteristic
69C2×C8×D61C2311yescharacteristic
70#14519770—41no—
71#14519769—21no—
72#14519760—41no—
73#14519759—41no—
74#14519753—21no—
75#14519750—41no—
76#14519750—41no—
77#14519748—21no—
78#14519748—21no—
79#14519748—21no—
80#14519747—41no—
81C4×D244—21no—
82C4×D244D411yescharacteristic
83C4×C22⋊D61—41no—
84#14519735—21no—
85C4⋊C4×D61—21no—
86C22⋊C4×D61—41no—
87#14519718—22no—
88C2×#11758185C2311yescharacteristic
89C2×#11758185C2311yescharacteristic
90C16×D61—41no—
91C16×D61—41no—
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519710—21no—
96#14519709—21no—
97#14519708—21no—
98C4⋊#92418D411yescharacteristic
99#14519701—21no—
100#14519699—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519689D411yescharacteristic
105#14519689D411yescharacteristic
106C2×Q16×C61C2311yescharacteristic
107C2×SD16×C61—21no—
108C2×D8×C61C2311yescharacteristic
109C2×D8×C61C2311yescharacteristic
110#124×C61—21no—
111C4×D4×C61—21no—
112SD32×C61—41no—
113D16×C61—41no—
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C2×Q8×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C22×C4×C61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128#11758226—42no—
129#11758226—81no—
130D4×D61—42no—
131D4×D61—81no—
132C2×D244—21no—
133C2×D244—41no—
134C2×D244D811yescharacteristic
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140Q16×C61—21no—
141Q16×C61—21no—
142SD16×C61—81no—
143D8×C61—21no—
144D8×C61—21no—
145D8×C61—21no—
146D8×C61—21no—
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2411yescharacteristic
149C4⋊C4×C61—21no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C42×C61C2×D411yescharacteristic
154C22⋊Dic61—41no—
155C22⋊Dic61—41no—
156C22⋊Dic61—41no—
157#11758201—42no—
158#11758199—42no—
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198D811yescharacteristic
163#11758198D811yescharacteristic
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61D811yescharacteristic
168#11758196—41no—
169#11758196—41no—
170#11758196—41no—
171#11758196—41no—
172C4×Dic61—41no—
173C2×#92418C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175D488—21no—
176D488#4112yes—
177C8×D61—21no—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61—41no—
187C22×D61—41no—
188C22×D61—82no—
189C22×D61—82no—
190C22×D61—161no—
191C22×D61C2×D811yescharacteristic
192C22×D61C2×D811yescharacteristic
193Q8×C61—41no—
194Q8×C61—41no—
195D4×C61—41no—
196D4×C61—41no—
197D4×C61—41no—
198D4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—161no—
202C2×C4×C61C2×D811yescharacteristic
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C22⋊D61—82no—
206C22⋊D61—82no—
207C22⋊D61—161no—
208C22⋊D61—161no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61C2×D811yescharacteristic
213C2×Dic61C2×D811yescharacteristic
214D244—22no—
215D244—22no—
216D244—41no—
217D244—82no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—21no—
222C4×D61—82no—
223C4×D61—161no—
224C4×D61—161no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33864—611nomaximal, Sylow
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61C22×D811yescharacteristic
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
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—21no—
250C4×C61—81no—
251C4×C61—81no—
252C4×C61#54611yescharacteristic
253C4×C61#57711yescharacteristic
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#2215—611no—
267#2210D6111yescharacteristic, complemented
268#2186—611no—
269#2184—611no—
270C4×D16—611no—
271D4×C16—611no—
272#2138—611no—
273C2×#357—611no—
274C2×C61—161no—
275C2×C61—161no—
276C2×C61#329411yescharacteristic
277C2×C61C2×#50811yescharacteristic
278C2×C61#341511yescharacteristic
279D61—22no—
280D61—41no—
281D61—82no—
282C2×#135—611no—
283C22×D8—611no—
284#553—1221no—
285#546—1221no—
286C2×SD32C2×D6111yescharacteristic, complemented
287C2×D16—611no—
288C2×D16C2×D6111yescharacteristic
289C22×C16—611no—
290C22×C16—611no—
291#499—611no—
292#495C2×D6111yescharacteristic
293#482—1221no—
294#481—1221no—
295#478—1221no—
296#467—611no—
297#466—611no—
298#466—611no—
299#466—611no—
300#463—1221no—
301#450—1221no—
302#449—1221no—
303C4×D8—611no—
304C4×D8C2×D6111yescharacteristic, complemented
305C8×D4—611no—
306#427—611no—
307C2×#107—611no—
308#367—611no—
309#366—611no—
310#366—611no—
311C4⋊C16C2×D6111yescharacteristic, complemented
312#358—611no—
313#358—611no—
314#358C2×D6111yescharacteristic, complemented
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357C2×D6111yescharacteristic
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×Q16C22×D6111yescharacteristic
331C2×SD16—21no—
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×C8—611no—
341#126—2441no—
342#125—1221no—
343#124—21no—
344#123—2441no—
345#123—2441no—
346C22⋊Q8—1221no—
347#121—1221no—
348#121—1221no—
349#121—1221no—
350#121—2441no—
351#121—2441no—
352#120—2441no—
353C4×D4—21no—
354C4×D4—611no—
355C4×D4—1221no—
356C4×D4—2441no—
357#117—1221no—
358C2×C4⋊C4—1221no—
359C2×C22⋊C4—2441no—
360SD32—41no—
361D16—41no—
362D16—1222no—
363C2×C16—611no—
364C2×C16—611no—
365C2×C16—2441no—
366C2×C16—2441no—
367C2×C16C22×D6111yescharacteristic
368C2×C16C22×D6111yescharacteristic
369#107—611no—
370#107—611no—
371#107—611no—
372#107—1221no—
373#107C22×D6111yescharacteristic
374#106—1221no—
375#106—1221no—
376C4⋊C8—611no—
377#103—1221no—
378#102—21no—
379#102—1221no—
380#102—1221no—
381#102—1221no—
382#102—1221no—
383C22⋊C8—611no—
384C22⋊C8—611no—
385C4×C8C22×D6111yescharacteristic
386C24—2441no—
387#41—4881no—
388#41—2442no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4—4881no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2442no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C22×C4—41no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407Q16—21no—
408Q16—21no—
409SD16—81no—
410SD16—2442no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—612no—
416D8—1221no—
417D8—2442no—
418C2×C8—611no—
419C2×C8—611no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8—1221no—
423C2×C8—1221no—
424C2×C8D4×D6111yescharacteristic
425C2×C8C23×D6111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—611no—
428C4⋊C4—1221no—
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—41no—
438C22⋊C4—611no—
439C22⋊C4—611no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C22⋊C4—2441no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C42—2441no—
447C42D4×D6111yescharacteristic
448C16—21no—
449C16—21no—
450C16—1221no—
451C16—1221no—
452C23—41no—
453C23—41no—
454C23—611no—
455C23—611no—
456C23—9761no—
457C23—4882no—
458C23—4882no—
459C23—2441no—
460Q8—41no—
461Q8—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—1222no—
467D4—1222no—
468D4—9761no—
469D4—9761no—
470D4—4882no—
471D4—4882no—
472D4—4882no—
473D4—2441no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—161no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—9761no—
484C2×C4—9761no—
485C2×C4—4882no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4D8×D6111yescharacteristic
490C2×C4D8×D6111yescharacteristic
491C2×C4C2×D4×D6111yescharacteristic
492C8—21no—
493C8—1221no—
494C8—1221no—
495C8#41×D6111yescharacteristic
496C8#1451982211yescharacteristic
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—612no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—9764no—
510C22—4881no—
511C22—4881no—
512C22—2442no—
513C22C2×D8×D6111yescharacteristic
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—1221no—
519C4—1221no—
520C4—4881no—
521C4—4881no—
522C4—4881no—
523C4#1684040911yescharacteristic
524C4#1684057211yescharacteristic
525C2—161no—
526C2—161no—
527C2—1222no—
528C2—4882no—
529C2—2441no—
530C2#2145763511yescharacteristic
531C2#508×D6111yescharacteristic
532C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2210C2
socleC22×C61C22×D8
hypercenter#2210D61
hypocenterC61#33864
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. #21458223C2semidirect
2. #21457503C2semidirect
3. #21448050C2semidirect
4. #21448020C2semidirect
5. #21448009C2semidirect
6. #21447977C2semidirect
7. #21447912C2semidirect
8. #21447902C2semidirect
9. #21447741C2semidirect
10. #21447729C2semidirect
11. C4×#14519718C2semidirect
12. #21447638C2semidirect
13. #21447525C2semidirect
14. #357×D61C2semidirect
15. C61×#2210C2semidirect
22. C2×C16×D61C22semidirect
23. #16840164C22semidirect
30. #16839995C22semidirect
36. #16839799C22semidirect
38. #16839590C22semidirect
39. #16839588C22semidirect
40. #16839587C22semidirect
41. #16839566C22semidirect
42. #16839566C22semidirect
47. #16839563C22semidirect
50. #16839541C22semidirect
51. C4×#11758185C22semidirect
52. C2×SD32×C61C22semidirect
55. C4×D8×C61C22semidirect
56. C61×C4⋊C16C22semidirect
57. C61×#358C22semidirect
267. #2210D61semidirect
286. C2×SD32C2×D61semidirect
304. C4×D8C2×D61semidirect
311. C4⋊C16C2×D61semidirect
314. #358C2×D61semidirect
325. C61#33864semidirect

Maximal subgroups

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

subgroupindex
#214582232
#214575032
#214480502
#214480202
#214480092
#214479772
#214479122
#214479022
#214477412
#214477292
C4×#145197182
#214476382
#214475252
#357×D612
C61×#22102
#3386461