Finite Group Databasebeta

← #30622483

Subgroups — #30622483

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462565C211yesmaximal, characteristic, complemented
2#21462515C211yesmaximal, characteristic, complemented
3#21461971C212yesmaximal, complemented
4#21461952C211yesmaximal, characteristic, complemented
5#21461934C211yesmaximal, characteristic, complemented
6#21461902C212yesmaximal, complemented
7#21461811C212yesmaximal, complemented
8C4⋊C8×#6923C211yesmaximal, characteristic, complemented
9#21461596C212yesmaximal, complemented
10C4×#14519841C211yesmaximal, characteristic, complemented
11#21455275C211yesmaximal, characteristic
12C2×#14519865C2212yes—
13#16840796—21no—
14#16840792—22no—
15#16840790—21no—
16#16840786—22no—
17#16840783—21no—
18#16840778—21no—
19C2×#14519847C2212yes—
20#16840766C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22C2×#14519842C2212yes—
23C2×#14519842C2212yes—
24C2×#14519841C2211yescharacteristic
25C2×#14519841C2211yescharacteristic
26#16840737C2212yes—
27#16840736C2212yes—
28#16840727C2212yes—
29C4×#11758213C2211yescharacteristic
30C2×C8×#6923C2212yes—
31C42×#6923C2211yescharacteristic
32#16840638C2212yes—
33#16840632C2211yescharacteristic
34#16840632C2211yescharacteristic
35(C2×#6923)⋊C8C2212yes—
36C2×#14519798C2212yes—
37#16840313C2211yescharacteristic
38C4×#11758224C2211yescharacteristic
39#16839987C412yescomplemented
40#16839979C412yescomplemented
41#16839969C411yescharacteristic, complemented
42#16839963C411yescharacteristic, complemented
43#16839957C411yescharacteristic, complemented
44C4⋊C8×D61C2211yescharacteristic
45#16839757C2212yes—
46C61×#461C411yescharacteristic, complemented
47#14519865—24no—
48#14519865—42no—
49C2×#11758213—22no—
50C2×#11758213C2311yescharacteristic
51C2×#11758213C2312yes—
52C2×#11758213C2311yescharacteristic
53C2×D61⋊C8—22no—
54C2×D61⋊C8C2312yes—
55C2×C4×#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923C2311yescharacteristic
58C2×C4×#6923C2311yescharacteristic
59#14519847—42no—
60#14519844D412yes—
61C4⋊#92420—21no—
62C4⋊#92420—21no—
63C4⋊#92420D411yescharacteristic
64C4⋊#92420D411yescharacteristic
65#14519842—24no—
66#14519842—42no—
67#14519841—22no—
68#14519841—22no—
69#14519834—22no—
70#14519834—22no—
71C22⋊#92420—22no—
72C22⋊#92420—22no—
73#14519832—22no—
74#14519832—21no—
75C4×#92420—22no—
76C4×#92420—21no—
77C8×#6923—42no—
78C2×#11758226C2312yes—
79C2×#11758224C2311yescharacteristic
80#14519798—42no—
81#14519798—42no—
82C2×#11758202C2×C412yes—
83C2×#11758190C2×C412yes—
84C2×#11758199C2×C412yes—
85C2×C8×D61C2312yes—
86#14519774C2×C411yescharacteristic
87#14519766C2×C412yes—
88#14519752—21no—
89#14519752—21no—
90C4×Dic122C2×C411yescharacteristic
91#14519742C2×C411yescharacteristic
92D4×Dic61C2×C411yescharacteristic
93#14519739—21no—
94#14519739—21no—
95C4×C22⋊D61—21no—
96#14519737—21no—
97#14519735C2311yescharacteristic
98#14519733—21no—
99C2×C4×Dic61—21no—
100C42×D61C2311yescharacteristic
101C4⋊#92418C2×C411yescharacteristic
102#14519706C2×C412yes—
103#14519701C2×C412yes—
104#14519699C2×C412yes—
105#14519697C2×C412yes—
106C2×SD16×C61C2×C412yes—
107C4⋊Q8×C61C2×C411yescharacteristic
108C4×D4×C61C2×C411yescharacteristic
109C4⋊C8×C61C2×C411yescharacteristic
110#103×C61C2×C412yes—
111C22×#6923—21no—
112C22×#6923—21no—
113C2×Q8×C61C22×C412yes—
114C2×D4×C61C22×C411yescharacteristic
115C22×C4×C61—21no—
116C2×C22⋊D61—21no—
117C22×Dic61—21no—
118C22×Dic61—21no—
119#11758226—22no—
120#11758226—22no—
121#11758226—22no—
122#11758226—22no—
123#11758224—21no—
124#11758224—21no—
125#11758224—21no—
126#11758224—21no—
127C2×D244—22no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244C22×C412yes—
131C2×C4×D61—22no—
132C2×C4×D61#4111yescharacteristic
133C2×C4×D61#4111yescharacteristic
134C2×C4×D61C2411yescharacteristic
135C2×Dic122C22×C411yescharacteristic
136C2×#92420—21no—
137C2×#92420—22no—
138C2×#92420—21no—
139C2×#92420C2×D412yes—
140C2×#92420C2×D412yes—
141C4×#6923—24no—
142C4×#6923—21no—
143C4×#6923—21no—
144C4×#6923—21no—
145C4×#6923—42no—
146C4×#6923#4112yes—
147#11758213—21no—
148#11758213—21no—
149#11758213—22no—
150#11758213—22no—
151#11758213—21no—
152#11758213—44no—
153#11758213#4112yes—
154D61⋊C8—22no—
155D61⋊C8—22no—
156D61⋊C8—44no—
157SD16×C61—42no—
158C2×C8×C61C22×C412yes—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61C22×C411yescharacteristic
162C22⋊C4×C61—21no—
163C42×C61C22×C411yescharacteristic
164C22⋊Dic61—21no—
165#11758202—42no—
166#11758199—42no—
167#11758198—21no—
168#11758198—22no—
169#11758198—22no—
170C4⋊Dic61C22×C411yescharacteristic
171#11758196—21no—
172#11758196—21no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61C22×C411yescharacteristic
177C4×Dic61C2×D411yescharacteristic
178C4×Dic61C2×D411yescharacteristic
179C2×#92418C22×C412yes—
180#11758190—42no—
181C8×D61—22no—
182C8×D61—22no—
183C23×C61—21no—
184C22×D61—22no—
185C22×D61C2×#4111yescharacteristic
186C2×#6923—22no—
187C2×#6923—22no—
188C2×#6923—22no—
189C2×#6923—22no—
190C2×#6923—41no—
191C2×#6923—41no—
192Q8×C61—22no—
193Q8×C61—22no—
194D4×C61—21no—
195D4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—22no—
198C2×C4×C61—42no—
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C23×C411yescharacteristic
202C22⋊D61—41no—
203C22⋊D61—41no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—81no—
209C2×Dic61C4×D411yescharacteristic
210C2×Dic61C4×D411yescharacteristic
211C2×Dic61C22×D411yescharacteristic
212D244—22no—
213D244—22no—
214D244—42no—
215D244—42no—
216D244—42no—
217D244—81no—
218C4×D61—22no—
219C4×D61—41no—
220C4×D61—42no—
221C4×D61—42no—
222C4×D61C2×#4111yescharacteristic
223C4×D61C2×#4111yescharacteristic
224C4×D61H(5,𝔽2)11yescharacteristic
225C4×D61H(5,𝔽2)11yescharacteristic
226Dic122—21no—
227Dic122—21no—
228#92420—22no—
229#92420—22no—
230#92420—22no—
231#92420—41no—
232#92420—42no—
233C8×C61—22no—
234#92418—22no—
235#23113—611nomaximal, Sylow
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61C2×C4×D411yescharacteristic
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—42no—
245C2×D61#55311yescharacteristic
246C2×D61#55511yescharacteristic
247#6923—24no—
248#6923—42no—
249C4×C61—21no—
250C4×C61—42no—
251C4×C61—41no—
252C4×C61#44312yes—
253C4×C61C4×#4111yescharacteristic
254C4×C61#51811yescharacteristic
255Dic61—21no—
256Dic61—21no—
257Dic61—41no—
258Dic61—41no—
259Dic61#54611yescharacteristic
260Dic61#55011yescharacteristic
261#3035—611no—
262#2935—611no—
263#2925—611no—
264#1974—612no—
265#1962—611no—
266#1950—611no—
267#1929—612no—
268#1876—612no—
269C4×C4⋊C8—611no—
270#1764—612no—
271C4×#104—611no—
272C2×C61—81no—
273C2×C61#236311yescharacteristic
274C2×C61C2×#44311yescharacteristic
275C2×C61#295611yescharacteristic
276D61—21no—
277D61—21no—
278D61—82no—
279C2×#135—612no—
280C2×#131—612no—
281#532—611no—
282C4×#41—611no—
283#464—612no—
284#463—612no—
285#462—611no—
286#461#692311yescharacteristic, complemented
287#460—611no—
288#459—611no—
289#436—1221no—
290#435—1222no—
291C8×D4—1221no—
292#433—1222no—
293#432—1221no—
294#431—1221no—
295C2×#108—612no—
296#423—611no—
297C2×C4⋊C8—611no—
298C2×C4⋊C8—611no—
299C2×#104—611no—
300C2×#104—611no—
301C2×#104—612no—
302C2×#104—612no—
303#416—612no—
304#408—612no—
305#408—612no—
306#405—612no—
307C4×M16—611no—
308C2×C4×C8—612no—
309C43—611no—
310#341—612no—
311#339—611no—
312#339—611no—
313#336—612no—
314C61#2311311yescharacteristic, complemented, Sylow
315C2×#41—612no—
316C2×#41—611no—
317#135—2442no—
318#135—2442no—
319C2×Q16—612no—
320C2×SD16—612no—
321C2×SD16C2×#692312yes—
322C2×D8—612no—
323#131—1224no—
324#131—2442no—
325C2×M16—611no—
326C2×M16—611no—
327C2×M16—612no—
328C2×M16—1222no—
329C22×C8—612no—
330C22×C8—612no—
331C22×C8—1222no—
332C4⋊Q8C2×#692311yescharacteristic
333#127—611no—
334#124—612no—
335#121—1221no—
336#121—1221no—
337C4×Q8—611no—
338C4×Q8—611no—
339C4×D4—611no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
343C4×D4—1221no—
344C4×D4C2×#692311yescharacteristic
345#117—611no—
346#117—1221no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42—611no—
350C2×C42—1221no—
351C2×C42—1221no—
352C2×C42—1221no—
353#108—2442no—
354C4⋊C8—611no—
355C4⋊C8—611no—
356C4⋊C8—612no—
357C4⋊C8—612no—
358C4⋊C8—611no—
359C4⋊C8—1221no—
360C4⋊C8—1221no—
361C4⋊C8C2×#692311yescharacteristic
362#104—1222no—
363#104—1224no—
364#104—1222no—
365#104—2442no—
366#103—612no—
367#103C2×#692312yes—
368#102—612no—
369#102—612no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372C22⋊C8—1222no—
373C22⋊C8—1222no—
374#97—1221no—
375#97—1222no—
376C4×C8—1221no—
377C4×C8—1222no—
378C4×C8—2442no—
379#41—1221no—
380#41—1221no—
381#41—1221no—
382#41—1221no—
383#41—1222no—
384#41—1222no—
385#41—1222no—
386#41—1222no—
387C2×Q8—611no—
388C2×Q8C22×#692312yes—
389C2×D4—612no—
390C2×D4—1222no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4—1221no—
394C2×D4C22×#692311yescharacteristic
395C22×C4—21no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—1222no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404Q16—2442no—
405SD16—42no—
406SD16—2442no—
407D8—2442no—
408M16—612no—
409M16—1221no—
410M16—1221no—
411M16—1222no—
412M16—1222no—
413M16—1221no—
414M16—2444no—
415C2×C8—612no—
416C2×C8—612no—
417C2×C8—612no—
418C2×C8—1222no—
419C2×C8—1222no—
420C2×C8—1221no—
421C2×C8—1222no—
422C2×C8—1222no—
423C2×C8—1221no—
424C2×C8—1222no—
425C2×C8—2444no—
426C2×C8C22×#692312yes—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—611no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4C22×#692311yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—1222no—
435C22⋊C4—1222no—
436C22⋊C4—1221no—
437C22⋊C4—1221no—
438C42—611no—
439C42—611no—
440C42—611no—
441C42—612no—
442C42—1221no—
443C42—1221no—
444C42—1221no—
445C42—1221no—
446C42—1221no—
447C42—1224no—
448C42—1221no—
449C42—2442no—
450C42C22×#692311yescharacteristic
451C23—21no—
452C23—611no—
453C23—1222no—
454Q8—22no—
455Q8—22no—
456Q8—1221no—
457Q8—1221no—
458D4—21no—
459D4—21no—
460D4—1222no—
461D4—1222no—
462D4—4881no—
463D4—2442no—
464D4—2442no—
465D4—2441no—
466D4—2441no—
467D4—2442no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—611no—
475C2×C4—611no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—4881no—
486C2×C4—2441no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4D4×#692311yescharacteristic
494C2×C4D4×#692311yescharacteristic
495C2×C4C23×#692311yescharacteristic
496C8—22no—
497C8—1222no—
498C8—1222no—
499C8—1222no—
500C8—1222no—
501C8—2441no—
502C8—2442no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—611no—
507C22—611no—
508C22—1221no—
509C22—1221no—
510C22—2442no—
511C22—2442no—
512C22—2442no—
513C22C2×D4×#692311yescharacteristic
514C4—21no—
515C4—41no—
516C4—42no—
517C4—611no—
518C4—611no—
519C4—1224no—
520C4—1221no—
521C4—1221no—
522C4—2442no—
523C4—2441no—
524C4—2441no—
525C4#1684080512yes—
526C4#41×#692311yescharacteristic
527C4#1684082911yescharacteristic
528C2—81no—
529C2—1221no—
530C2—1221no—
531C2—4882no—
532C2#2146234611yescharacteristic
533C2C2×#1684080511yescharacteristic
534C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#461C4
socleC22×C61C2×C4×D4
prime radical#21455275C2
cosocleC2×C4×D61C24
hypercenter#461#6923
hypocenterC61#23113
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #21462565C2semidirect
2. #21462515C2semidirect
3. #21461971C2semidirect
4. #21461952C2semidirect
5. #21461934C2semidirect
6. #21461902C2semidirect
7. #21461811C2semidirect
8. C4⋊C8×#6923C2semidirect
9. #21461596C2semidirect
10. C4×#14519841C2semidirect
39. #16839987C4semidirect
40. #16839979C4semidirect
41. #16839969C4semidirect
42. #16839963C4semidirect
43. #16839957C4semidirect
46. C61×#461C4semidirect
286. #461#6923semidirect
314. C61#23113semidirect

Maximal subgroups

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

subgroupindex
#214625652
#214625152
#214619712
#214619522
#214619342
#214619022
#214618112
C4⋊C8×#69232
#214615962
C4×#145198412
#214552752
#2311361