Finite Group Databasebeta

← #29834586

Subgroups — #29834586

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840191C211yesmaximal, characteristic, complemented
2#504×D61C211yesmaximal, characteristic, complemented
3#21455537C212yesmaximal, complemented
4#21447948C212yesmaximal, complemented
5#21447947C212yesmaximal, complemented
6#21447945C211yesmaximal, characteristic, complemented
7#21447944C211yesmaximal, characteristic, complemented
8#21447936C211yesmaximal, characteristic, complemented
9#368×D61C211yesmaximal, characteristic, complemented
10#21447565C212yesmaximal, complemented
11C61×#2221C211yesmaximal, characteristic, complemented
12#16840558—22no—
13C2×#14519796C2212yes—
14#131×D61C2211yescharacteristic
15#16840191—21no—
16#16840191—21no—
17#16840191—21no—
18#16840191—21no—
19C2×Dic488C2211yescharacteristic, complemented
20C2×#14519721C2212yescomplemented
21#16840180—21no—
22#16840180C2211yescharacteristic
23#16840179C2211yescharacteristic
24#16840178—21no—
25#16840178C2211yescharacteristic
26M32×D61—21no—
27M32×D61C2211yescharacteristic
28C2×C16×D61—21no—
29C2×C16×D61C2211yescharacteristic
30#16840038C2212yes—
31#16840037C2212yes—
32#16840029C2212yes—
33#16840024—22no—
34#16840023—22no—
35#108×D61C2212yes—
36#16839743—22no—
37#16839592C2211yescharacteristic, complemented
38#16839591C2212yescomplemented
39#16839579C2212yescomplemented
40#16839577C2212yescomplemented
41#16839575C2212yescomplemented
42C2×D16×C61C2211yescharacteristic, complemented
43C61×#504C2211yescharacteristic
44C61×#472C2212yes—
45C61×#368C2211yescharacteristic, complemented
46C61×#361C2212yescomplemented
47C2×#11758224—22no—
48#41×D61D411yescharacteristic
49#14519810—22no—
50#14519807—22no—
51#14519806—42no—
52#14519803—22no—
53#14519801—42no—
54#14519798—42no—
55#14519796—22no—
56#14519796—22no—
57#14519796—22no—
58#14519796—22no—
59#14519796—42no—
60C2×Dic244C2312yes—
61C2×#11758200—22no—
62#14519785—21no—
63#14519785D411yescharacteristic
64#14519784D411yescharacteristic
65#14519783—21no—
66#14519783C2311yescharacteristic
67M16×D61—21no—
68M16×D61—22no—
69M16×D61D411yescharacteristic
70C2×C8×D61—21no—
71C2×C8×D61C2311yescharacteristic
72Dic488—21no—
73Dic488—21no—
74#14519721—22no—
75#14519721—22no—
76#14519717—21no—
77#14519717C2311yescharacteristic
78#14519716—21no—
79#14519716—21no—
80#14519716—21no—
81C2×#11758185—21no—
82C2×#11758185C2311yescharacteristic
83C16×D61—21no—
84C16×D61—21no—
85C16×D61—21no—
86C16×D61D411yescharacteristic
87C16×D61D411yescharacteristic
88C16×D61D411yescharacteristic
89C16×D61D411yescharacteristic
90#14519713C2312yes—
91#14519712—22no—
92#14519695—22no—
93#14519695—22no—
94#14519694—22no—
95AGL(1,ℤ/8)×C61—22no—
96C2×D8×C61C2312yes—
97#131×C61C2311yescharacteristic
98D16×C61—21no—
99D16×C61—21no—
100M32×C61—21no—
101M32×C61C2311yescharacteristic
102C2×C16×C61—21no—
103C2×C16×C61C2311yescharacteristic
104#108×C61C2312yes—
105#100×C61—22no—
106#41×C61C2×D411yescharacteristic
107C2×D4×C61—22no—
108C2×C22⋊D61—42no—
109C22×Dic61—42no—
110#11758226D811yescharacteristic
111Q8×D61D811yescharacteristic
112#11758224—21no—
113#11758224—42no—
114#11758224—42no—
115#11758224—42no—
116#11758224—42no—
117#11758224D811yescharacteristic
118D4×D61—21no—
119D4×D61D811yescharacteristic
120#11758222—21no—
121#11758222C2×D411yescharacteristic
122C2×C4×D61—21no—
123C2×C4×D61C2×D411yescharacteristic
124C2×Dic122—22no—
125SD16×C61—42no—
126D8×C61—22no—
127D8×C61—22no—
128D8×C61—42no—
129M16×C61—21no—
130M16×C61—22no—
131M16×C61C2×D411yescharacteristic
132C2×C8×C61—21no—
133C2×C8×C61C2411yescharacteristic
134#11758202—42no—
135#11758200—42no—
136#11758200—42no—
137#11758200—42no—
138#11758200—42no—
139#11758199—42no—
140#11758194—21no—
141#11758194—22no—
142#11758194C2×D411yescharacteristic
143C2×#92418—21no—
144C2×#92418C2×D411yescharacteristic
145Dic244—22no—
146Dic244—22no—
147Dic244—42no—
148#11758190—42no—
149#11758189—21no—
150#11758189—21no—
151#11758189—21no—
152#11758189—42no—
153C8×D61—21no—
154C8×D61—21no—
155C8×D61—21no—
156C8×D61—42no—
157C8×D61C2×D411yescharacteristic
158C8×D61C2×D411yescharacteristic
159C8×D61#4111yescharacteristic
160C8×D61#4111yescharacteristic
161C16×C61—21no—
162C16×C61C2×D411yescharacteristic
163C16×C61C2×D411yescharacteristic
164#11758185—21no—
165#11758185C2×D411yescharacteristic
166#11758185C2×D411yescharacteristic
167C23×C61—42no—
168C22×D61—21no—
169C22×D61#13511yescharacteristic
170Q8×C61C2×D811yescharacteristic
171D4×C61—21no—
172D4×C61—42no—
173D4×C61—42no—
174D4×C61C2×D811yescharacteristic
175C2×C4×C61—21no—
176C2×C4×C61C22×D411yescharacteristic
177C22⋊D61—21no—
178C22⋊D61—21no—
179C22⋊D61—21no—
180C22⋊D61—82no—
181C22⋊D61—82no—
182C2×Dic61—21no—
183C2×Dic61—42no—
184C2×Dic61—82no—
185C2×Dic61—82no—
186C2×Dic61#13511yescharacteristic
187D244—21no—
188D244C2×D811yescharacteristic
189C4×D61—21no—
190C4×D61—21no—
191C4×D61—21no—
192C4×D61#12111yescharacteristic
193C4×D61#12111yescharacteristic
194C4×D61C2×D811yescharacteristic
195C4×D61C2×D811yescharacteristic
196Dic122—21no—
197Dic122—42no—
198Dic122—42no—
199Dic122C2×D811yescharacteristic
200C8×C61—21no—
201C8×C61—42no—
202C8×C61C22×D411yescharacteristic
203C8×C61C2×#4111yescharacteristic
204#92418—21no—
205#92418—42no—
206#92418#12111yescharacteristic
207#92418#12111yescharacteristic
208#33617—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—82no—
211C22×C61—162no—
212C22×C61C2×#13511yescharacteristic
213C2×D61—21no—
214C2×D61—41no—
215C2×D61—42no—
216C2×D61#46611yescharacteristic
217C2×D61#46611yescharacteristic
218C4×C61—21no—
219C4×C61C2×#12111yescharacteristic
220C4×C61C22×D811yescharacteristic
221Dic61—21no—
222Dic61—82no—
223Dic61#46611yescharacteristic
224Dic61#46611yescharacteristic
225C2×#508—611no—
226C2×#504—611no—
227#3067—612no—
228#2223—612no—
229#2223—612no—
230#2222—611no—
231#2222—611no—
232#2221—611no—
233#2221D6111yescharacteristic, complemented
234C2×#368—611no—
235#2148—612no—
236C2×C61—21no—
237C2×C61—41no—
238C2×C61—162no—
239C2×C61C2×#46611yescharacteristic
240D61—21no—
241D61—21no—
242D61—41no—
243#575—1222no—
244C2×#135—612no—
245C2×#131—611no—
246#508—1221no—
247#508—1221no—
248#508—1221no—
249#508—1221no—
250C2×Q32—611no—
251C2×SD32—612no—
252C2×D16C2×D6111yescharacteristic, complemented
253#504—611no—
254#504—611no—
255#504—611no—
256#504—1221no—
257#504—1221no—
258#504C2×D6111yescharacteristic
259C2×M32—611no—
260C2×M32—1221no—
261C22×C16—611no—
262C22×C16—1221no—
263#473—612no—
264#473—612no—
265#472—612no—
266#472C2×D6112yes—
267#471—1222no—
268#471—1222no—
269C2×#108—612no—
270#413—1222no—
271#368—611no—
272#368—612no—
273#368C2×D6111yescharacteristic, complemented
274#362—612no—
275#362—612no—
276#361—612no—
277#361C2×D6112yescomplemented
278C61#3361711yescharacteristic, complemented, Sylow
279C2×#41—611no—
280C2×#41—1222no—
281#137—1222no—
282#137—1222no—
283#137—2442no—
284AGL(1,ℤ/8)—22no—
285AGL(1,ℤ/8)—1222no—
286AGL(1,ℤ/8)—2442no—
287#135—1222no—
288#135—1222no—
289#135—1222no—
290#135—1222no—
291#135—2442no—
292#135—2442no—
293C2×Q16—612no—
294C2×SD16—1222no—
295C2×D8C22×D6112yes—
296#131—611no—
297#131—611no—
298#131—611no—
299#131—1221no—
300#131—1221no—
301#131C22×D6111yescharacteristic
302C2×M16—611no—
303C2×M16—1221no—
304C2×M16—1222no—
305C22×C8—611no—
306C22×C8—1221no—
307Q32—1221no—
308Q32—1221no—
309SD32—1222no—
310SD32—1222no—
311D16—21no—
312D16—21no—
313M32—21no—
314M32—611no—
315M32—1221no—
316M32—1221no—
317M32—1221no—
318M32—1221no—
319M32C22×D6111yescharacteristic
320C2×C16—21no—
321C2×C16—611no—
322C2×C16—611no—
323C2×C16—611no—
324C2×C16—611no—
325C2×C16—611no—
326C2×C16—1221no—
327C2×C16—1221no—
328C2×C16—1221no—
329C2×C16—1221no—
330C2×C16C22×D6111yescharacteristic
331#108—612no—
332#108—1222no—
333#108C22×D6112yes—
334#101—1222no—
335#101—1222no—
336#100—22no—
337#100—1222no—
338#41—611no—
339#41—611no—
340#41—611no—
341#41—1221no—
342#41—1221no—
343#41—2442no—
344#41—2442no—
345#41—2442no—
346#41—2442no—
347#41D4×D6111yescharacteristic
348C2×Q8—611no—
349C2×Q8—1222no—
350C2×D4—22no—
351C2×D4—611no—
352C2×D4—1221no—
353C2×D4—2442no—
354C22×C4—611no—
355C22×C4—1221no—
356C22×C4—2442no—
357Q16—1222no—
358Q16—1222no—
359Q16—2442no—
360Q16—2442no—
361SD16—42no—
362SD16—2442no—
363SD16—2442no—
364SD16—2442no—
365SD16—2442no—
366SD16—2442no—
367D8—22no—
368D8—22no—
369D8—42no—
370D8—2442no—
371M16—21no—
372M16—22no—
373M16—611no—
374M16—1221no—
375M16—1221no—
376M16—1221no—
377M16—1221no—
378M16—1222no—
379M16—2442no—
380M16D4×D6111yescharacteristic
381C2×C8—21no—
382C2×C8—611no—
383C2×C8—611no—
384C2×C8—611no—
385C2×C8—611no—
386C2×C8—611no—
387C2×C8—1221no—
388C2×C8—1221no—
389C2×C8—1221no—
390C2×C8—1221no—
391C2×C8—2442no—
392C2×C8C23×D6111yescharacteristic
393C16—21no—
394C16—611no—
395C16—611no—
396C16—1221no—
397C16D4×D6111yescharacteristic
398C16D4×D6111yescharacteristic
399C23—42no—
400C23—611no—
401C23—1221no—
402Q8—611no—
403Q8—1221no—
404Q8—2442no—
405Q8—2442no—
406Q8D8×D6111yescharacteristic
407D4—21no—
408D4—42no—
409D4—42no—
410D4—611no—
411D4—1221no—
412D4—1221no—
413D4—1221no—
414D4—1221no—
415D4—4882no—
416D4—4882no—
417D4D8×D6111yescharacteristic
418C2×C4—21no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—611no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—4882no—
429C2×C4—4882no—
430C2×C4—2442no—
431C2×C4C2×D4×D6111yescharacteristic
432C8—21no—
433C8—42no—
434C8—611no—
435C8—611no—
436C8—1221no—
437C8—2442no—
438C8C2×D4×D6111yescharacteristic
439C8#41×D6111yescharacteristic
440C22—21no—
441C22—82no—
442C22—162no—
443C22—611no—
444C22—611no—
445C22—1221no—
446C22—2441no—
447C22—2442no—
448C22#135×D6111yescharacteristic
449C4—21no—
450C4—611no—
451C4—611no—
452C4—1221no—
453C4—4882no—
454C4#121×D6111yescharacteristic
455C4C2×D8×D6111yescharacteristic
456C2—21no—
457C2—41no—
458C2—162no—
459C2—1221no—
460C2—1221no—
461C2—2441no—
462C2#466×D6111yescharacteristic
subgroupG/H
centerC2#466×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2221C2
socleC2×C61C2×#466
hypercenter#2221D61
hypocenterC61#33617
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #2221

Complements

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

NH ≅ G/Ntype
1. C2×#16840191C2semidirect
2. #504×D61C2semidirect
3. #21455537C2semidirect
4. #21447948C2semidirect
5. #21447947C2semidirect
6. #21447945C2semidirect
7. #21447944C2semidirect
8. #21447936C2semidirect
9. #368×D61C2semidirect
10. #21447565C2semidirect
11. C61×#2221C2semidirect
19. C2×Dic488C22semidirect
20. C2×#14519721C22semidirect
37. #16839592C22semidirect
38. #16839591C22semidirect
39. #16839579C22semidirect
40. #16839577C22semidirect
41. #16839575C22semidirect
42. C2×D16×C61C22semidirect
45. C61×#368C22semidirect
46. C61×#361C22semidirect
233. #2221D61semidirect
252. C2×D16C2×D61semidirect
273. #368C2×D61semidirect
277. #361C2×D61semidirect
278. C61#33617semidirect

Maximal subgroups

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

subgroupindex
C2×#168401912
#504×D612
#214555372
#214479482
#214479472
#214479452
#214479442
#214479362
#368×D612
#214475652
C61×#22212
#3361761