Finite Group Databasebeta

← #29663799

Subgroups — #29663799

Order 15616.

798 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456394C211yesmaximal, characteristic, complemented
2#21455283C211yesmaximal, characteristic, complemented
3C2×D4×#92418C211yesmaximal, characteristic, complemented
4#21445258C212yesmaximal, complemented
5#21445254C212yesmaximal, complemented
6#21445206C212yesmaximal, complemented
7#21445172C212yesmaximal, complemented
8#21444577C211yesmaximal, characteristic, complemented
9#21444497C211yesmaximal, characteristic, complemented
10#21444496C211yesmaximal, characteristic, complemented
11C61×#3036C211yesmaximal, characteristic, complemented
12C2×#14519803—21no—
13C23×#92418—21no—
14#16840312C2211yescharacteristic
15#16840165C2211yescharacteristic, complemented
16#16840138C2211yescharacteristic, complemented
17#16840110C2211yescharacteristic, complemented
18#16840108C2211yescharacteristic, complemented
19#16839996—21no—
20#16839996—21no—
21#16839977—22no—
22#16839967C2212yes—
23#16839957C2212yes—
24C4×#11758199—21no—
25C4×#11758199—21no—
26D4×#92418—21no—
27D4×#92418—21no—
28D4×#92418C2212yes—
29D4×#92418C2212yes—
30#16839786C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32#16839761—21no—
33C2×C22⋊#92418—21no—
34C2×C4×#92418C2211yescharacteristic
35#16839514C2212yescomplemented
36#16839514C2212yescomplemented
37#16839509C2212yescomplemented
38#16839508C2212yescomplemented
39#16839506C2212yescomplemented
40#16839505C2212yescomplemented
41C2×AGL(1,ℤ/8)×C61—21no—
42C61×#532C2211yescharacteristic
43C2×C4×D4×C61C2211yescharacteristic
44C61×#463—22no—
45C61×#461C2212yes—
46C61×#459C2212yes—
47C61×#423C2211yescharacteristic
48C61×#417—21no—
49C2×#11758222—21no—
50#14519803—44no—
51C2×#11758200—22no—
52C2×#11758199—22no—
53C2×#11758199—21no—
54C2×#11758199—21no—
55C2×#11758194—21no—
56C22×#92418—21no—
57C22×#92418—22no—
58C22×#92418—22no—
59C22×#92418—44no—
60C22×#92418D411yescharacteristic
61C22×#92418D411yescharacteristic
62#14519777C2311yescharacteristic
63#14519774C2311yescharacteristic
64#14519765—21no—
65#14519751—21no—
66#14519751—21no—
67C4×D244—21no—
68C4×D244—21no—
69#14519710—21no—
70#14519710—21no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74C4⋊#92418C2312yes—
75#14519700—22no—
76#14519698—21no—
77#14519698—21no—
78#14519697—22no—
79#14519697—21no—
80#14519697—21no—
81C22⋊#92418—22no—
82C22⋊#92418—22no—
83C4×#92418D411yescharacteristic
84C4×#92418D411yescharacteristic
85C4×#92418C2311yescharacteristic
86C4×#92418C2311yescharacteristic
87C2×#41×C61—21no—
88C22×D4×C61D411yescharacteristic
89C23×C4×C61—21no—
90AGL(1,ℤ/8)×C61—44no—
91C2×SD16×C61—22no—
92C2×D8×C61—22no—
93C2×M16×C61—21no—
94C4⋊Q8×C61C2311yescharacteristic
95#127×C61C2311yescharacteristic
96#124×C61—21no—
97#121×C61—21no—
98#121×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101C4×D4×C61—21no—
102C4×D4×C61—21no—
103C4×D4×C61D412yes—
104C4×D4×C61C2312yes—
105C2×C4⋊C4×C61D411yescharacteristic
106C2×C22⋊C4×C61—21no—
107C2×C42×C61C2311yescharacteristic
108C4⋊C8×C61—21no—
109C4⋊C8×C61C2312yes—
110#103×C61—22no—
111#102×C61—22no—
112C24×C61—21no—
113#41×C61—42no—
114#41×C61—42no—
115C2×Q8×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—22no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—41no—
122C2×D4×C61D814yescomplemented
123C2×D4×C61C2×D412yes—
124C22×C4×C61—21no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—41no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61#4111yescharacteristic
133C2×C22⋊D61—41no—
134#11758222—42no—
135#11758222—42no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×C4×D61—41no—
140C2×Dic122—21no—
141SD16×C61—44no—
142D8×C61—44no—
143M16×C61—42no—
144C2×C8×C61—22no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61C2×D412yes—
149C22⋊C4×C61—22no—
150C22⋊C4×C61—22no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61#4111yescharacteristic
156C42×C61C2411yescharacteristic
157#11758200—44no—
158#11758199—42no—
159#11758199—44no—
160#11758199—42no—
161#11758198—41no—
162#11758198—41no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165#11758194—42no—
166C2×#92418—22no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—41no—
170C2×#92418—44no—
171C2×#92418—42no—
172C2×#92418—44no—
173C2×#92418C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176C2×#92418C2×D411yescharacteristic
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—41no—
182C23×C61#12111yescharacteristic
183C22×D61—41no—
184Q8×C61—41no—
185Q8×C61—41no—
186D4×C61—22no—
187D4×C61—24no—
188D4×C61—41no—
189D4×C61—41no—
190D4×C61—41no—
191D4×C61—41no—
192D4×C61—81no—
193D4×C61—82no—
194D4×C61C2×D814yes—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—22no—
198C2×C4×C61—41no—
199C2×C4×C61—44no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—41no—
204C2×C4×C61—82no—
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61#12111yescharacteristic
207C2×C4×C61#12111yescharacteristic
208C2×C4×C61C2×D812yes—
209C2×C4×C61#13512yes—
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C2×#4111yescharacteristic
213C22⋊D61—82no—
214C2×Dic61—41no—
215D244—41no—
216D244—41no—
217D244—41no—
218D244—41no—
219D244—81no—
220C4×D61—82no—
221Dic122—41no—
222Dic122—41no—
223C8×C61—42no—
224#92418—21no—
225#92418—21no—
226#92418—21no—
227#92418—42no—
228#92418—42no—
229#92418AGL(1,ℤ/8)12yescomplemented
230#19255—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—24no—
234C22×C61—48no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61#46612yes—
241C22×C61C2×#12111yescharacteristic
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—42no—
249C4×C61—81no—
250C4×C61#46612yes—
251C4×C61C22×D811yescharacteristic
252C4×C61C2×#13511yescharacteristic
253C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C61#57511yescharacteristic
255Dic61—81no—
256#3169—611no—
257#3036—611no—
258#3036D6111yescharacteristic, complemented
259C2×C8×D4—611no—
260#1681—612no—
261#1681—612no—
262#1673—612no—
263#1667—612no—
264#1567—611no—
265#1547—611no—
266#1547—611no—
267C2×C61—22no—
268C2×C61—44no—
269C2×C61—161no—
270C2×C61#303611yescharacteristic
271C2×C61C2×#46611yescharacteristic
272C2×C61#306711yescharacteristic
273D61—161no—
274C2×AGL(1,ℤ/8)—21no—
275C2×AGL(1,ℤ/8)—1221no—
276C23×C8—1221no—
277#532—611no—
278#532C2×D6111yescharacteristic
279C2×C4×D4C2×D6111yescharacteristic
280#500—611no—
281#493—611no—
282#486—611no—
283#486—611no—
284#466—1221no—
285#466—1221no—
286#463—22no—
287#463—1222no—
288#461—612no—
289#461C2×D6112yes—
290#459—612no—
291#459C2×D6112yes—
292C4×D8—1221no—
293C4×D8—1221no—
294C8×D4—612no—
295C8×D4—612no—
296C8×D4—1221no—
297C8×D4—1221no—
298#423—611no—
299#423C2×D6111yescharacteristic
300C2×C4⋊C8—611no—
301#417—21no—
302#417—1221no—
303C2×C22⋊C8—1221no—
304C2×C4×C8—611no—
305#335—612no—
306#335—612no—
307#332—612no—
308#332—612no—
309#331—612no—
310#331—612no—
311C61#1925511yescharacteristic, complemented, Sylow
312C2×#41—21no—
313C2×#41—1221no—
314C22×D4C22⋊D6111yescharacteristic
315C23×C4—21no—
316AGL(1,ℤ/8)—44no—
317AGL(1,ℤ/8)—2444no—
318C2×SD16—22no—
319C2×SD16—1222no—
320C2×D8—22no—
321C2×D8—1221no—
322C2×D8—1221no—
323C2×D8—1222no—
324C2×M16—21no—
325C2×M16—1221no—
326C22×C8—611no—
327C22×C8—611no—
328C22×C8—1222no—
329C22×C8—1222no—
330C22×C8—1221no—
331C22×C8—2444no—
332C4⋊Q8—611no—
333C4⋊Q8C22×D6111yescharacteristic
334#127—611no—
335#127C22×D6111yescharacteristic
336#124—21no—
337#124—1221no—
338#121—21no—
339#121—21no—
340#121—1221no—
341#121—1221no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—1221no—
347C4×D4—1221no—
348C4×D4C22⋊D6112yes—
349C4×D4C22×D6112yes—
350C2×C4⋊C4C22⋊D6111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C42C22×D6111yescharacteristic
353#107—1221no—
354#107—1221no—
355C4⋊C8—21no—
356C4⋊C8—612no—
357C4⋊C8—612no—
358C4⋊C8—1221no—
359C4⋊C8—1221no—
360C4⋊C8C22×D6112yes—
361#103—22no—
362#103—1222no—
363#102—22no—
364#102—1221no—
365#102—1221no—
366#102—1221no—
367#102—1221no—
368#102—1222no—
369C22⋊C8—1222no—
370C22⋊C8—1222no—
371C4×C8—611no—
372C4×C8—611no—
373C4×C8—611no—
374C4×C8—611no—
375C24—21no—
376#41—42no—
377#41—42no—
378#41—2442no—
379#41—2442no—
380C2×Q8—21no—
381C2×Q8—1221no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—41no—
388C2×D4—1221no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—2441no—
392C2×D4#1175819914yescomplemented
393C2×D4C2×C22⋊D6112yes—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—41no—
400C22×C4—2441no—
401C22×C4D4×D6111yescharacteristic
402C22×C4#1175822411yescharacteristic
403C22×C4C2×C22⋊D6111yescharacteristic
404SD16—44no—
405SD16—2444no—
406D8—44no—
407D8—2442no—
408D8—2442no—
409D8—2444no—
410M16—42no—
411M16—2442no—
412C2×C8—22no—
413C2×C8—611no—
414C2×C8—611no—
415C2×C8—611no—
416C2×C8—611no—
417C2×C8—1222no—
418C2×C8—1222no—
419C2×C8—1222no—
420C2×C8—2444no—
421C2×C8—2441no—
422C2×C8—2444no—
423C2×C8—2442no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4C2×C22⋊D6112yes—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C42D4×D6111yescharacteristic
437C42#1175822411yescharacteristic
438C42C2×C22⋊D6111yescharacteristic
439C42C23×D6111yescharacteristic
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—2441no—
446C23#1451974911yescharacteristic
447Q8—41no—
448Q8—41no—
449Q8—2441no—
450Q8—2441no—
451D4—24no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4—4881no—
460D4—4882no—
461D4—2441no—
462D4—2441no—
463D4—2441no—
464D4—2441no—
465D4C2×#1175819914yes—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—4882no—
477C2×C4—2441no—
478C2×C4#1451974911yescharacteristic
479C2×C4#1451974911yescharacteristic
480C2×C4#1451974911yescharacteristic
481C2×C4C2×#1175819912yes—
482C2×C4#1451979712yes—
483C2×C4C2×D4×D6111yescharacteristic
484C2×C4C22×C22⋊D6111yescharacteristic
485C2×C4C2×#1175822411yescharacteristic
486C8—42no—
487C8—612no—
488C8—1221no—
489C8—1221no—
490C8—1221no—
491C8—2442no—
492C8—2442no—
493C22—21no—
494C22—21no—
495C22—24no—
496C22—48no—
497C22—42no—
498C22—42no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—4881no—
503C22—4881no—
504C22—4881no—
505C22#1683999612yes—
506C22C2×#1451974911yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—4881no—
513C4#1683999612yes—
514C4C22×#1175819911yescharacteristic
515C4C2×#1451979711yescharacteristic
516C4AGL(1,ℤ/8)×D6111yescharacteristic
517C4#1684055811yescharacteristic
518C2—22no—
519C2—44no—
520C2—161no—
521C2—9761no—
522C2#2145528011yescharacteristic
523C2C2×#1683999611yescharacteristic
524C2#2145553611yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3036C2
socleC22×C61C2×#121
hypercenter#3036D61
hypocenterC61#19255
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #21456394C2semidirect
2. #21455283C2semidirect
3. C2×D4×#92418C2semidirect
4. #21445258C2semidirect
5. #21445254C2semidirect
6. #21445206C2semidirect
7. #21445172C2semidirect
8. #21444577C2semidirect
9. #21444497C2semidirect
10. #21444496C2semidirect
11. C61×#3036C2semidirect
15. #16840165C22semidirect
16. #16840138C22semidirect
17. #16840110C22semidirect
18. #16840108C22semidirect
35. #16839514C22semidirect
36. #16839514C22semidirect
37. #16839509C22semidirect
38. #16839508C22semidirect
39. #16839506C22semidirect
40. #16839505C22semidirect
122. C2×D4×C61D8semidirect
229. #92418AGL(1,ℤ/8)semidirect
258. #3036D61semidirect
311. C61#19255semidirect
392. C2×D4#11758199semidirect

Maximal subgroups

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

subgroupindex
#214563942
#214552832
C2×D4×#924182
#214452582
#214452542
#214452062
#214451722
#214445772
#214444972
#214444962
C61×#30362
#1925561